# A review on laser-induced crystallization from solution

Vikram Korede  Process & Energy Department, Delft University of Technology,
Leeghwaterstraat 39, 2628 CB Delft, The Netherlands  Nagaraj Nagalingam
Process & Energy Department, Delft University of Technology, Leeghwaterstraat
39, 2628 CB Delft, The Netherlands  Frederico Marques  Department of Chemical
Engineering, KTH Royal Institute of Technology, Teknikringen 42, 114-28
Stockholm, Sweden  Process & Energy Department, Delft University of
Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands  Noah van der
Linden  Process & Energy Department, Delft University of Technology,
Leeghwaterstraat 39, 2628 CB Delft, The Netherlands  Johan T. Padding  Process
& Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628
CB Delft, The Netherlands  Remco Hartkamp<EMAIL_ADDRESS>Process &
Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628
CB Delft, The Netherlands  Huseyin Burak Eral<EMAIL_ADDRESS>Process &
Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628
CB Delft, The Netherlands

###### Abstract

Crystallization is abound in nature and industrial practice. A plethora of
indispensable products ranging from agrochemicals and pharmaceuticals to
battery materials, are produced in crystalline form in industrial practice.
Yet, our control over the crystallization process across scales, from
molecular to macroscopic, is far from complete. This bottleneck not only
hinders our ability to engineer the properties of crystalline products
essential for maintaining our quality of life but also hampers progress toward
a sustainable circular economy in resource recovery. In recent years,
approaches leveraging light fields have emerged as promising alternatives to
manipulate crystallization. In this review article, we classify laser-induced
crystallization approaches where light-material interactions are utilized to
influence crystallization phenomena according to proposed underlying
mechanisms and experimental setups. We discuss non-photochemical laser-induced
nucleation, high-intensity laser-induced nucleation, laser trapping-induced
crystallization, and indirect methods in detail. Throughout the review, we
highlight connections amongst these separately evolving sub-fields to
encourage interdisciplinary exchange of ideas.

denotes equal contribution denotes equal contribution

##  1 Introduction

Crystallization - how loosely correlated atoms in a solvent arrange themselves
to flawless symmetric structures - has long captivated scientists and
engineers alike. It is ubiquitous in nature and industrial practice, from the
production of nanostructured materials, explosives, catalysts, organic
electronics, pharmaceuticals to the formation of teeth and bones1, 2, 3, 4.
Despite its widespread use in industry as a separation and purification
process, fundamental understanding of crystallization from solution and our
ability to rationally dictate properties of emerging crystals is far from
complete5, 6, 7, 8, 9.

Crystallization consists of two fundamental phenomena: nucleation and growth.
Nucleation, also referred to as primary nucleation, is the emergence of an
ordered structure of solute molecules in solution. Classical nucleation theory
(CNT) and two-step nucleation theory (TSN) are two models proposed to
rationalize the nucleation process3, 10. CNT, widely used due to its
analytical simplicity, explains nucleation as a tug of war between the
tendency to form a new phase and the energy cost associated with forming a new
surface. In more formal terms, it describes nucleation as a one-step
stochastic process dictated by the Gibbs free energy change for the phase
transformation and the free energy change for the formation of a surface.
Despite its simplicity, it remarkably, yet qualitatively, predicts
experimentally observed trends11. CNT is not free of shortcomings12.
Shortcomings of CNT in explaining observations, particularly in protein
crystallization experiments, led to the proposal of the two-step nucleation
(TSN) model. In the TSN model, the formation of a sufficiently-sized amorphous
pre-nucleation cluster is followed by its reorganization into an ordered
structure13, 14. In industrial practice, nucleation and growth often occur in
the presence of turbulent flows in well-stirred vessels. These two fundamental
phenomena are always followed by secondary crystallization phenomena
intimately related to coupled mass, momentum, and heat transfer - such as
attrition, coalescence, and secondary nucleation unless the process is
specially designed to suppress these secondary phenomena15. Nucleation,
growth, and these secondary physical phenomena collectively dictate the
crystal quality parameters: crystal size distribution, polymorphism,
morphology, and purity, also referred to as the four pillars of industrial
crystallization 1, 2, 16, 15, 17.

In solution crystallization, nucleation plays a decisive role in determining
crystal properties3. Light-material interaction experiments usually but not
exclusively focus on nucleation. Approaches by-design targeting growth and
secondary nucleation phenomena exist in the literature, yet are less commonly
encountered18. Due to the interconnected nature of nucleation and growth, it
is hard to guarantee that a laser-induced method designed to steer nucleation
does not influence growth. These light-material interaction experiments which
we collectively refer to as laser-induced crystallization (LIC) have often,
but not always, been conducted by exposing a solution carrying a solute
dissolved in a solvent to a light source of a given wavelength, intensity,
exposure time, and pulse width. The exact experimental details including
experimental geometry (e.g., container geometry, how the beam interacts with
confining surfaces and solution), laser characteristics (intensity,
wavelength, polarization, continuous or pulsed laser, pulse width), exposure
time (ranging between femtoseconds to hours) and solution characteristics vary
considerably across the literature. Moreover, distinct mechanisms based on
molecular effects as well as continuum approaches have been proposed depending
on these experimental details. Efforts to classify these constantly evolving
LIC sub-fields in the literature may provide means to draw parallels among the
proposed underlying mechanisms.

In this review article, we summarize the existing experimental and
computational literature, classify the reported experimental techniques, while
discussing the proposed mechanisms. We will limit our classification to
methods that are non-photochemical in nature, at least not by intention. In
photochemical approaches, the frequency of irradiation is intentionally tuned
to trigger chemical reactions, whereas, in non-photochemical approaches, the
frequency is chosen so that neither the solute nor the solvent “significantly”
absorbs the irradiation. Figure 1 illustrates our early efforts to classify
existing LIC literature based on the energy of the light irradiation and pulse
width or exposure time when continuous lasers are concerned. In this
rudimentary effort, we classify three different methods leveraging light-
material interactions for LIC that have evolved as semi-independent research
fields, namely non-photochemical laser-induced nucleation (NPLIN), high-
intensity laser-induced nucleation (HILIN) and laser-trapping-induced
crystallization with optical tweezers (LTIC-OT) varying in energy density and
pulse width.

Figure 1: Laser induced crystallization phenomena. Classification of non-
photochemical laser-induced nucleation (NPLIN), high-intensity laser-induced
nucleation (HILIN), and laser-trapping-induced crystallization with optical
tweezers (LTIC) based on energy density and laser pulse width or exposure time
in case of continuous lasers used in LTIC. The NPLIN time-lapse image,
cavitation bubble produced by a high-intensity laser pulse, and LITC image are
reproduced from Kacker et al. 19, Hayasaka et al. 20 and Masuhara et al. 21
respectively.

We will first discuss NPLIN in Section 2 and summarize the underlying
mechanisms proposed in the literature. Gareth, Myerson, and coworkers22
serendipitously observed orders of magnitude faster nucleation kinetics upon
light irradiation compared to unperturbed supersaturated urea solutions at
identical supersaturation. Since this report, the NPLIN effect has been
reported in a considerable number of solute/solvent systems, yet the
discussion on the underlying mechanism is not yet settled. A recent review by
Alexander and Camp 23 provides a valuable source offering a summary of the
proposed mechanism while Clair et al. 22 provides a detailed account of
experimental setups utilized. We extend both on the discussion of the proposed
mechanism and the classification of experimental setups. Following a detailed
discussion on NPLIN, in Section 3, we will focus on high-intensity laser-
induced nucleation (HILIN) where the laser intensity of the pulse is orders of
magnitude higher than for NPLIN. HILIN is characterized by energy densities
above the optical breakdown threshold. At these high intensities, a plasma is
formed and non-linear optical effects come into play. We have deliberately
chosen the abbreviation HILIN as LIN will be used to refer to all laser-
induced nucleation methods. This field of research has a history dating back
to 1960s and early experiments with lasers connected to laser-induced boiling
and energy research of pure substances24. Triggered by efforts to pinpoint the
exact mechanism behind NPLIN, studies of HILIN on supersaturated solutions
opened new alleys of investigation. In Section 4, we collect and summarize the
efforts focused on laser-trapping-induced crystallization (LTIC), almost
exclusively studied using optical tweezers operating with low-intensity
continuous lasers21, 25, 26 as well as combinations of pulsed and continuous
lasers27, 28, 29 (as illustrated in Figure 1). In Section 5, we will bring
together indirect methods where auxiliary material-laser interactions are
utilized to influence nucleation and growth mechanism. Next, we discuss
molecular simulation efforts and opportunities to provide direct insight into
molecular length and time scales that are often hard to access experimentally.
In the summary section of each discussed LIC method, we attempt to highlight
open scientific questions. Finally, Section 7 offers a few concluding remarks.

##  2 Non-photochemical laser-induced nucleation (NPLIN)

###  2.1 Phenomenology

In 1996, while attempting to observe second-harmonic generation in
supersaturated aqueous urea solutions, Garetz et al.30 noticed unexpected
instantaneous crystallization upon light irradiation in solutions that would
otherwise take several weeks to crystallize spontaneously. In this study,
Garetz and co-workers exposed milliliter size vials as shown in Figure 2,
using a series of linearly polarized, unfocused
(50-$250\text{\,}\mathrm{M}\mathrm{W}\,\mathrm{c}\mathrm{m}^{-2}$), nanosecond
light pulses with $1064\text{\,}\mathrm{n}\mathrm{m}$ wavelength.

Garetz et al.30 referred to this observed light-induced phenomenon as non-
photochemical laser-induced nucleation, NPLIN. This phenomenon was considered
non-photochemical as: (i) neither the solute nor the solvent has strong
absorption bands at irradiated wavelengths and (ii) the applied laser
intensity ($\sim$\text{\,}\mathrm{M}\mathrm{W}\,\mathrm{c}\mathrm{m}^{-2}$$)
is considered too low to trigger photochemical reactions through non-linear
optical effects. They reported the formation of needle-like urea crystals
aligned with the polarization plane of the laser, suggesting an electric-
field-induced origin of the underlying mechanism. Over the following decades,
various groups have reported enhanced nucleation probabilities upon laser
irradiation, quantified by counting the fraction of vials nucleated after a
given time, compared to spontaneous nucleation in a broad range of
solute/solvent systems with comparable experimental parameters reported by
Garetz et al.30 (one or more unfocused laser pulses of
$\sim$$\text{\,}\mathrm{n}\mathrm{s}$ duration and
$532\text{/}1064\text{\,}\mathrm{n}\mathrm{m}$ wavelength, see Table 2 for a
detailed overview). Moreover, NPLIN has also been reported to offer control
over the polymorphic form nucleating from solution31, 32. Thus, the
observations of locally enhanced nucleation probability at the laser
irradiation position, and the potential to control the polymorphic form, point
out that NPLIN may be a promising primary nucleation control method (Figure
2). A solid understanding of the underlying NPLIN mechanism–a discussion yet
to be settled in the literature, holds the key to fulfilling its potential as
a broadly applied nucleation control method. In this section, we will
summarize the common observations in NPLIN experiments reported in the
literature, the proposed mechanisms, and classify the experimental setups and
solutions studied. Particularly, we critically discuss to what extent the
proposed mechanisms hold to explain the observations. Finally, we will
highlight future directions in the summary section.

The experimental observations and observed trends in NPLIN experiments may
shed light on the underlying mechanism. To this end, we present an extensive
list of observations compiled from the literature.

  1. 1.

A broad range of compounds under NPLIN: NPLIN has been reported for a range of
systems (predominantly in aqueous media), discussed in detail in section
section 2.4, including small organics 33, 34, 32, metal halides35, single
component systems 36, 37, dissolved gases38, 39 and a macromolecule -
lysozyme40.

  2. 2.

Not all solutions undergo NPLIN: Ward et al.41 reported that acetamide
($\textup{CH}_{3}\textup{CONH}_{2}$), an organic molecule with relatively high
solubility and molecular structure similar to urea (CH4N2O), does not exhibit
NPLIN. In the unpublished work of Barber42, aqueous sodium chlorate was also
reported to not undergo NPLIN.

  3. 3.

The NPLIN probability depends on laser peak intensity and supersaturation: the
fraction of samples nucleated under NPLIN was reported to increase with both
laser peak intensity and solution supersaturation. Along with others30, Kacker
et al.19 reported that NPLIN nucleation probability is both supersaturation
and laser peak intensity dependent for aqueous KCl solutions.

  4. 4.

Laser pulse duration matters: for similar peak intensities
($j_{\textup{peak}}$ $\approx$
$30\text{\,}\mathrm{M}\mathrm{W}\mathrm{c}\mathrm{m}^{-2}$ per pulse), aqueous
solutions of $\textup{CO}_{2}$, KCl, $\textup{NH}_{4}\textup{Cl}$ and CH4N2O
exposed to unfocused femtosecond-laser pulses ( $\approx$
$110\text{\,}\mathrm{f}\mathrm{s}$) did not nucleate while exposure to
nanosecond ($\approx$ $5\text{\,}\mathrm{n}\mathrm{s}$) pulses triggered
nucleation41. Although both femtosecond and nanosecond pulses had the same
peak intensity, the total energy per pulse
($\text{\,}\mathrm{J}\mathrm{c}\mathrm{m}^{-2}$) is 5 orders of magnitude
higher with the nanosecond pulse due to its longer pulse duration.

  5. 5.

Laser wavelength dependence: Kacker et al.19 reported that nucleation
probability of supersaturated aqueous KCl exposed to a single pulse of 355,
532 and $1064\text{\,}\mathrm{n}\mathrm{m}$ is not strongly dependent on the
laser wavelengths. Yet, shorter wavelengths, namely 355/532 nm, led to
slightly higher nucleation probability for KCl19, 35, KBr35 and urea33. Table
2 shows that almost exclusively the frequency multiples of the primary
wavelength ($1064\text{\,}\mathrm{n}\mathrm{m}$) of Q-switched Nd:YAG lasers
are used in the NPLIN literature.

  6. 6.

Dependence of the number of crystals/bubbles on laser peak intensity: with an
increase in the laser peak intensity, a linear increase in the number of
crystals for KCl43, 44 and glycine45, and a quadratic increase in the number
of $\textup{CO}_{2}$ bubbles39 was observed.

  7. 7.

Polarization switching: laser polarization is reported to influence the
polymorphic form of several simple organic molecules such as glycine34,
L-histidine32, carbamazepine46 and sulfathiazole54. However, this observation
could not be reproduced for glycine by Liu et al.47, nor later by Irimia et
al.48, indicating a subtle effect in the experimental conditions is at play.

  8. 8.

Laser intensity threshold: several authors report a threshold laser intensity
below which laser irradiation does not trigger nucleation30, 33, 47. Moreover,
this laser intensity threshold is observed to be dependent on the solute, the
wavelength of the laser light, and the temperature33, 35. Between solutes,
small organics33, 34 such as urea and glycine are observed to have a higher
laser peak-intensity threshold
($>$$50\text{\,}\mathrm{M}\mathrm{W}\,\mathrm{c}\mathrm{m}^{-2}$) compared to
metal halides35
($>$$3\text{\,}\mathrm{M}\mathrm{W}\,\mathrm{c}\mathrm{m}^{-2}$) such as KCl
and KBr.

  9. 9.

Dependence on solution aging: several authors45, 31 report that aging of
glycine aqueous solutions improved the nucleation probability under NPLIN.
However, the nucleation probability of metal halides was found to be invariant
to aging49.

  10. 10.

Effect of filtration and nanoparticle doping: Ward et al.41 studied how the
filtration and intentional addition of impurities, namely
$\textup{Fe}_{3}\textup{O}_{4}$ nanoparticles, alter NPLIN probability.
Filtration decreased the NPLIN probability while the addition of nanoparticles
increased the NPLIN probability reported at a fixed observation time.

  11. 11.

Product crystal alignment: in the experiments performed in aqueous urea by
Garetz et al.30, the direction of the needled-shaped crystals of urea were
reported to be aligned with the polarization plane of the laser. However, Liu
et al.50, in their experiments using aqueous urea, observed the angle between
crystal alignment and laser polarization to be random.

  12. 12.

Irradiation pathway matters: when compared to laser intensity threshold values
reported in the literature, Clair et al.22 observed a lower value in
experiments when passing the laser light via an air-liquid interface (from the
vial top) through a supersaturated aqueous glycine solution. Unfortunately, in
the same experiments, no trials were performed to pass the laser through the
glass-liquid interface for comparison.

  13. 13.

Direct solution-laser interaction matters: Kacker et al.19, in their
experiments with aqueous KCl, measured the pressure signal after a laser pulse
at a fixed distance from the laser path within the vial. Even though the
samples where laser light was masked with a black tape recorded higher
radiation pressure compared to the samples which allowed the laser to pass
through the solution, the former was not observed to undergo NPLIN.

Figure 2: NPLIN in action (a,b) Solution of NH4Cl before and approximately
$1.6\text{\,}\mathrm{s}$ after irradiating by a single laser pulse41. The path
of the laser beam through the solution is indicated by the dashed white lines,
with the start of nucleation visible as white dots between the lines. (c)
Nucleation of carbon dioxide bubbles within carbonated solution caused by the
passage of the laser pulse from left to right39.

###  2.2 Proposed mechanisms

In this section, we critically discuss the proposed NPLIN mechanisms and to
what extent these mechanisms explain the experimental observation listed
above. Sections 2.2.1 and 2.2.2 discuss molecular scale mechanisms based on
how the field induces polarizability of metastable pre-nucleating clusters are
considered to drastically reduce the induction time for nucleation51, 48. On
the other hand, the proposed mechanism in Section 2.2.3 explains NPLIN as a
result of laser heating of impurities present in the solution, a mechanism
bridging the molecular and macroscopic scale.

Figure 3: Plausible mechanisms for NPLIN. (a) Field-induced alignment of
molecules - optical Kerr effect. (b) Stabilization of otherwise subcritical
clusters under electric field39 \- dielectric polarization (where $r_{c}(0)$
and $r_{c}(E)$ are the critical cluster radius in the absence and presence of
laser light, respectively). (c) Evaporation of solvent surrounding a
nanoparticle due to local heating.

####  2.2.1 Optical Kerr effect (OKE)

The first hypothesized mechanism was based on the optical Kerr effect. This
hypothesis states that the laser produces a weak torque that aligns all
anisotropically polarizable molecules (or clusters of molecules) with their
most polarizable axis parallel to the direction of polarization of the
incident light (Figure 3a). For instance, the observed alignment of urea
crystals to the laser direction by Garetz et al.30 was argued based on the
urea molecule’s ability to align their $\textup{C}_{2}$ axes parallel to an
applied laser’s electric field. Consequently, it was proposed that the
electric-field-induced alignment reduces the free energy barrier for
nucleation. However, the permanent dipole moment of a molecule does not
contribute to the Kerr effect since the rotational timescales of solute
molecules52 are much larger than the duration of the change in the electric
field of the laser ($\sim 10^{-14}\,$ s).

The interaction energy induced by the optical Kerr effect on a molecule is
given by $-\Delta\alpha\ E^{2}/2$, where $\Delta\alpha$ is the polarizability
anisotropy and $E$ the local electric field53. The degree of alignment of the
molecular axes along the $x-$, $y-$, and $z-$ direction can be quantified by
the order parameters $K_{x}$, $K_{y}$ and $K_{z}$ respectively, which for
relatively weak light-solute interaction is defined by34

$\begin{gathered}K_{x}=\frac{1}{3}+\frac{\Delta\alpha
E^{2}}{90k_{B}T}\left(\frac{2-e^{2}}{1+e^{2}}\right),\hskip
2.84544ptK_{y}=\frac{1}{3}+\frac{\Delta\alpha
E^{2}}{90k_{B}T}\left(\frac{2e^{2}-1}{1+e^{2}}\right),\\\ \hskip
2.84544ptK_{z}=\frac{1}{3}-\frac{\Delta\alpha E^{2}}{90kT},\end{gathered}$ (1)

where $k_{B}$ is Boltzmann’s constant and $e$ is the elliptical polarization
of light, with the order parameters satisfying $K_{x}+K_{y}+K_{z}=1$. The
order parameters are $1/3$ each for an isotropic distribution in the absence
of an electric field. For linearly polarized light ($e=0$) along $x$, in the
limit of zero temperature or infinite interaction energy, we obtain perfect
alignment of rod-like building blocks in the $x$-direction, with $K_{x}=1$ and
$K_{y}=K_{z}=0$. Similarly, we have another uniaxial case for circularly
polarized light ($e=1$) with the electric field rotating in the $xy$-plane and
the symmetry axis along the $z$-direction favoring disk-like arrangement with
$K_{x}=K_{y}=1/2$.

For supersaturated solutions of urea, Matic et al.33 reported a lower laser
peak-intensity threshold and a higher nucleation probability for linearly
polarized light over circularly polarized light. This recorded difference
between laser light polarization is consistent with the optical Kerr mechanism
since urea was observed to exhibit rod-like arrangement in the experiments
conducted by Garetz et al.30. The effect of the laser’s polarization on the
polymorph of the product crystal has also been observed for several other
simple organic molecules such as glycine, L-histidine, carbamazepine, and
sulfathiazole 34, 32, 46, 54 (Section 2.4.1). This observed product polymorph
dependence on laser polarization further suggests that the mechanism of NPLIN
is not photochemical.

To have a quantitative estimate of the reported glycine dependence on laser
polarization34, using the known values for glycine’s polarizability,
$\Delta\alpha=$2\text{\times}{10}^{-40}\text{\,}\mathrm{F}\,\mathrm{m}$$, the
interaction energy per molecule is calculated to be $\Delta\alpha
E^{2}/kT=4\times 10^{-5}$. This value for interaction energy is much less than
unity. Therefore, it cannot account for the large order parameters (from eq.
1) necessary for the observed nucleation rates. When compared to a single
molecule, the cooperative effects among groups of glycine molecules within a
pre-nucleating cluster could have enhanced polarizabilities in the stacking
direction. However, Monte Carlo simulations using Potts lattice gas model by
Knott et al.55 suggest that this mechanism, even if bound together by
intermolecular forces in a very large cluster, seem too weak to explain the
observed nucleation rate enhancements23 (see Section 6).

Although the Kerr effect hypothesis supports the observed correlation between
the urea crystal and laser polarization by Garetz et al., Liu et al.50
reported the crystal orientation angle to be quite random under similar
experimental conditions (observation 11). Sun et al.34 in their experiments
with glycine, observed a narrow window of temperature and supersaturation
within which the circularly polarized light favored $\alpha$-glycine while
linearly polarized light favored $\gamma$-glycine (observation 7). This
reported influence of laser polarization on glycine polymorphism by Sun et
al.contradicts the results from Irimia et al.48. When using a single laser
pulse in aqueous glycine solutions, Irimia et al.did not observe any effect of
laser polarization on polymorphism. On comparing the results of Irimia et
al.with others who employed hundreds of laser pulses, one might suggest that
the interaction of laser light with microscopic crystals after nucleation can
trigger polymorphic transitions through polarization-dependent ablation and
secondary nucleation. Interestingly, the experiments of Irimia et al., when
employing multiple pulses of $1064\text{\,}\mathrm{n}\mathrm{m}$, showed an
increase in the solution temperature. However, the effect of temperature rise
on polymorph control is yet to be quantified. In addition, the Kerr effect
hypothesis fails to explain the reported laser peak-intensity threshold and
the weak wavelength dependence on the nucleation probability. The whole basis
of the Kerr effect lies in the ability of laser light to polarize a solute
molecule, yet the NPLIN of solutes without anisotropic polarizability, such as
metal halides, lacks explanation. Thus below we present the dielectric
polarization hypothesis that attempts to explain the observed NPLIN of
potassium halides such as KCl49 and KBr35.

####  2.2.2 Dielectric polarization (DP)

The dielectric polarization mechanism suggests that isotropic polarization of
pre-nucleating clusters by an electric field modifies the cluster’s free
energy by which it becomes stable. This means that a dielectrically
homogeneous cluster larger than a critical size, $r_{\mathrm{c}}$, is
stabilized by an electric field when its dielectric constant exceeds that of
the surrounding medium (Figure 3b). Unlike OKE which works on induced
polarization of solutes under laser light, DP stems from differences in the
dielectric permittivity of solutes compared to solvents. Including this effect
in classical nucleation theory (CNT), the free energy of a cluster of radius
$r$ in the presence of an electric field $E$ is given by49

$\displaystyle\Delta G(r,E)=4\pi r^{2}\gamma-\frac{4}{3}\pi
r^{3}(A\ln{S}+aE^{2}),$ (2)

where $\gamma$ is the solution-crystal interfacial tension, $A=\rho RT/M$, in
which $\rho$ is the mass density, $R$ is the gas constant, $M$ is the molar
mass of the solid and $S$ is the supersaturation ratio. The coefficient $a$
defines an effective dielectric constant

$\displaystyle
a=\frac{3\epsilon_{0}\epsilon_{s}}{2}\left(\frac{\epsilon_{p}-\epsilon_{s}}{\epsilon_{p}+2\epsilon_{s}}\right).$
(3)

For a particle with dielectric constant $\epsilon_{p}$ immersed in a medium of
dielectric constant $\epsilon_{s}$, the free energy is lowered in the presence
of an electric field provided that $\epsilon_{p}$ is greater than
$\epsilon_{s}$ \- a critical criterion for DP to work. Assuming a Poisson
distribution, the probability of obtaining at least one nucleus is calculated
using

$\displaystyle p(n\geq 1)=1-e^{-m\,j_{peak}}$ (4)

where $m\,j_{peak}$ is equal to the mean number of nuclei produced by a given
laser peak-intensity $j_{peak}$ and $m$ is the lability. For lower peak
intensities, using a truncated Taylor series for the exponential term in the
above equation, a linear relation between probability and $j_{peak}$ can be
achieved49. From CNT, the probability of a cluster of size $r$ within the
solution is expressed using the Boltzmann distribution, $e^{{-\Delta
G(r,E)}/{(k_{B}T)}}$. In the presence of laser light, under the conditions
where the change in a cluster’s bulk energy due to the light’s electric field
is significantly small ($aE^{2}\ll A\ln{S}$), we can analytically calculate
the lability as35

$\displaystyle m=\frac{3N_{\textup{molecules}}\gamma a}{2\pi\rho^{3}(k_{B}T\ln
S)^{2}}\times\frac{e^{-\Delta
G(r_{c},0)/(k_{B}T)}}{\int_{0}^{r_{c}(0)}r^{3}e^{-\Delta G(r,0)/(k_{B}T)}dr}$
(5)

where $r_{c}(0)$ is the critical radius in the absence of an electric field.
$N_{\textup{molecules}}$ is the number of ion pairs within the volume
illuminated by the laser, indicating an increase in the nucleation probability
with an increase in the irradiated volume.

The dielectric polarization model successfully predicts the linear relation of
the nucleation probability to low laser peak intensity for KCl35 (Equation 4).
By doing so, it also hypothesizes a mechanism under which ionic solutes such
as KCl and KBr35, that have no preferred orientation under laser, can nucleate
under NPLIN. Yet, it cannot explain the experimentally observed intensity
threshold, $j_{0}$ (observation 8). Therefore, phenomenological models use a
corrected value for the number of nuclei produced, $m(j_{peak}-j_{0})$, to
replicate the observed zero probabilities below $j_{0}$. Together with the
laser peak-intensity threshold, the dielectric polarization model fails to
answer the observed probability dependence on laser pulse duration,
wavelength, and the polymorph selectivity under different laser
polarizations53, 34, 32 (observations 4, 5, and 7). Moreover, NPLIN of
dissolved gases shown in Figure 2c in which the dissolved gas phase has a
lower dielectric constant than water cannot be explained by the dielectric
polarization hypothesis (observation 6). To explain the observed NPLIN of
dissolved gases and the effect of impurities on NPLIN probabilities of
NH4Cl41, we present below the impurity heating hypothesis, which attempts to
explain NPLIN as a function of inherent impurities rather than the solute-
laser interaction.

####  2.2.3 Impurity heating (IH)

The impurity heating hypothesis suggests that the interaction of the laser
irradiation with impurities plays a significant role in NPLIN. This hypothesis
emerged from the inability of the OKE and DP mechanisms to explain certain
observations common in NPLIN experiments, particularly the existence of a
threshold below which no nucleation is observed and the pronounced effect of
filtration on NPLIN (observation 10). In a nutshell, this hypothesis assumes a
scenario where insoluble impurities such as nanoparticles absorb laser energy
at the wavelength of irradiation and rapidly heat and evaporate the
surrounding solution. This phenomenon is expected to trigger nucleation by
locally enhancing the supersaturation. In order to test this, Ward et al.41
studied how the intentional addition of impurities, namely
$\textup{Fe}_{3}\textup{O}_{4}$ nanoparticles and a surfactant (polyethylene
glycol, $M_{\mathrm{r}}=8000$), alter the NPLIN probability and number of
crystals nucleating in supersaturated aqueous $\textup{NH}_{4}\textup{Cl}$
solutions. First, they compared filtered and non-filtered aqueous
$\textup{NH}_{4}\textup{Cl}$ solutions. The filtration was carried out using a
$0.2\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pore-size membrane with freshly
prepared samples at high temperatures to justify that only the impurities were
filtered out as opposed to the solute clusters. A stark difference in
nucleation probability and the number of crystals was observed between
filtered and unfiltered samples. The filtered samples showed a lower
nucleation probability and a lower number of crystals. In the same work, a
similar effect due to filtration was observed in other systems, such as in
aqueous urea and glycine. Furthermore, supporting the role of impurities, the
addition of both nanoparticles and surfactant showed an increase in the NPLIN
probability. While the impurities due to nanoparticles and surfactant would
serve as active sites for the local increase in supersaturation, the
surfactant was also expected to stabilize the dispersion of impurities -
promoting more viable nucleation sites.

Javid et al.51 performed NPLIN experiments with glycine for both filtered and
unfiltered samples. Irrespective of whether the solutions were irradiated or
not, filtration of glycine solutions across all supersaturations resulted only
in an $\alpha$-polymorph under the influence of the laser. The unfiltered
samples at higher supersaturations (1.5 and 1.6) showed a significant presence
of a $\gamma$-polymorph (40%) when irradiated, while non-irradiated solutions
nucleated almost exclusively the $\alpha$-polymorph at all supersaturations.

Ward et al.41 reported that for systems with $\textup{CO}_{2}$, KCl,
$\textup{NH}_{4}\textup{Cl}$ and CH4N2O, NPLIN was not observed using
unfocused femtosecond laser pulses ($\sim 110\text{\,}\mathrm{f}\mathrm{s}$,
$j_{peak}$ = $30\text{\,}\mathrm{M}\mathrm{W}\,\mathrm{c}\mathrm{m}^{-2}$),
while nanosecond pulses ($\sim 5\text{\,}\mathrm{n}\mathrm{s}$, $j_{peak}$ =
$12\text{\,}\mathrm{M}\mathrm{W}\,\mathrm{c}\mathrm{m}^{-2}$) induced
nucleation. The total energy per pulse, $\sim j_{peak}\times\textup{pulse
duration}$, limits the energy available for a nanoparticle to absorb. This
absorbed energy is hypothesized to evaporate the solvent surrounding the
nanoparticle and form a local vapor-filled cavity (Figure 3c). Consequently, a
region of high solute concentration at the vapor-liquid interface is expected
to emerge, due to the solvent that evaporated. This increased solute
concentration at the vapor-liquid interface is expected to contribute to a
higher local supersaturation and therefore trigger nucleation. The observed
differences in nucleation probabilities between the aforementioned pulse
durations were argued based on the energy available for the local cavity
formation surrounding the nanoparticle (observation 4). This supports the
hypothesis that heating solid nanoparticle impurities, which are intrinsically
present within a solution, act as a precursor to nucleation.

The nanoparticle heating hypothesis explains the observed laser intensity
threshold because enough energy must be supplied to induce cavitation around a
nanoparticle. The nanoparticle heating hypothesis however fails to explain two
sets of reported experimental results, namely the alignment of urea crystals30
and the influence of laser polarization on polymorphic form34 (observation 7).
Interestingly, Liu et al.50 failed to reproduce this alignment effect in
aqueous urea upon exposure to linearly polarized nanosecond pulses. One
possible explanation for this observed alignment of crystals might be due to
hydrodynamic interactions between the crystal and the surrounding fluid. The
Marangoni flow induced by local heating of the solution could apply torque and
align the crystals. At the current time, this explanation is merely
speculation without quantification of the flow fields and the local sample
heating under studied experimental conditions. Irimia et al.48 quantified the
temperature increase of aqueous glycine solutions when subjected to one or
more pulses of 532 and 1064 $\text{\,}\mathrm{n}\mathrm{m}$. Both Alexander et
al.and Irimia et al.observed that laser polarization does not influence the
polymorph formed. A possible explanation for the difference in the
observations made could rely on the nature of the impurity rather than the
solute. Moreover, the ability of nanoparticles to have a difference in
absorption, based on the ellipticity of laser polarization (circular or
linear), is left unexplored. This difference in laser absorption could dictate
the magnitude of the local supersaturation and thus the polymorph formed.

Alternatively, a new mechanism inspired by dielectric polarization can be
formulated by considering that the crystal grows on the surface of an inherent
nanoparticle - which acts as a favorable site over which solute clustering is
favorable. If we consider CNT (Equation 2), the nanoparticle could essentially
increase the magnitude of the electrostatic term ($a$) and modify the free
energy profile via the interfacial term ($\gamma$). However, the composition
of these nanoimpurities and their effect on NPLIN probability are yet to be
determined.

###  2.3 Experimental setups

Figure 4: Experimental setups for NPLIN. (a) Gel medium: dendritic growth of
glycine using supersaturated aqueous solutions in agarose gel56. (b) Micro-
batch/hanging droplet: crystallization of hen egg-white lysozyme and Bovine
pancreatic trypsin using microbatch and hanging droplet methods,
respectively40. (c) Carousel glass vials: high-throughput controlled
crystallization using a carousel22. (d) Levitated microdroplet:
crystallization in a levitating microdroplet supersaturated with KCl57. (e)
Continuous microfluidic setup: continuous production of KCl crystals using
microfluidic setup44. (f) Using evanescent wave: crystallization of KCl in a
microdroplet using evanescent wave58.

Classical NPLIN experiments were performed using milliliter-sized cylindrical
glass vials by manually replacing them in the path of the laser beam (Table
2). The laser light always passes through the side walls of the container.
These vials are then transferred to a temperature-controlled bath (if
required) after exposure. Below are some innovative ways adopted by different
authors to answer specific questions relating to proposed NPLIN mechanisms and
to address the shortcomings of previously proposed experimental techniques.

Gel medium: In an experimental setup leveraging a gel medium, a canonical
NPLIN setup with cylindrical glass vials filled with a mixture of agarose gel
and supersaturated aqueous solutions was used (Figure 4a). Gels are known to
prevent the convection-enhanced rehomogenization of solutions. As a result,
the formed crystals stay anchored to their point of origin. For KCl, Duffus et
al.43 used two low-intensity beams with a total energy equivalent to the
threshold laser intensity. Within the gel medium, nucleation was only induced
where the two beams crossed, thus opening the route to three-dimensional
control of nucleation. Tasni et al.56 reported that a laser, when passed
through the air-gel interface, resulted in a much higher nucleation
probability than through the glass-gel interface for glycine solutions. Also,
the air-to-gel laser path always gave rise to tree-branch dendrites composed
of pure $\alpha$-glycine. In contrast, when the laser was passed through the
glass-gel interface, a stellar dendrite was formed in the solution bulk with
$\gamma$-glycine concentrated in the core of the dendrite and $\alpha$-glycine
dominating the exterior.

Micro-batch/Hanging droplet: For nucleation studies with difficult-to-
synthesize or costly solutions, the use of smaller amounts is crucial. For
such solutions, a conventional microbatch or hanging drop system is adapted
for NPLIN studies (Figure 4b). The droplet containing the supersaturated
solution is irradiated using the laser to monitor crystallization40. The ease
of preparing and handling larger sample numbers also allows one to have better
statistics on nucleation probability and crystal quality.

Carousel glass vials: A carousel setup is an automated setup using the
canonical NPLIN vials with additional control over container temperature and
laser intensity (Figure 4c). Developed by Clair and Biré et al.22, it has a
high throughput with in-situ monitoring of the vials. The continuous
monitoring of the laser intensity and vials, together with the thermostated
water bath for vials, reduce the uncertainty regarding the induction of
nucleation. Just like the levitated microdroplet setup, the laser beam passes
through the air-solution interface. Using this setup, Clair and Biré et al.22
reported that glycine nucleated at the meniscus interface before falling down
to the bottom of the container.

Levitated microdroplet: To study the volume dependence in the absence of
container walls in NPLIN, Fang et al.57 performed experiments using levitated
micrometer-sized droplets containing supersaturated aqueous KCl (Figure 4d).
For the same peak-laser intensities as employed by Alexander et al.49 in bulk
solutions, NPLIN within droplets was reported only at dramatically higher
supersaturation. This observation was attributed to the possible low number of
nucleation events owing to the relatively low exposed volume.

Continuous microfluidic setup: Hua et al.44 developed a microfluidic device
operating under laminar flow conditions to have more statistics on crystal
size, shape, growth, and polydispersity (Figure 4e). For KCl, the mean crystal
size and polydispersity were observed to be independent of laser intensity,
while higher supersaturation resulted in a higher mean crystal size. Crystals
formed were cubic or cuboid in shape, with a unimodal distribution in crystal
size - evidencing the absence of secondary nucleation. For glycine45, the
morphology of the crystals was found to switch from prism-like to plate-like
with increasing supersaturation. NPLIN was observed only for glycine solutions
which were aged for 24 hours, supporting the existence of pre-nucleating
clusters.

Using evanescent waves: A supersaturated liquid droplet placed over a glass
enclosing a laser beam was used in this setup (Figure 4f). For a laser beam
undergoing total internal reflection within the glass, a medium present near
the interface can absorb the electromagnetic field and direct it perpendicular
to the interface. This directed wave is evanescent, meaning that within the
medium its amplitude decays exponentially with distance from the interface.
Using the short penetration depth characteristic of an evanescent wave, Ward
et al.58 performed NPLIN only in regions close to the glass-solution
interface. Hydrophobization of the interface was found to suppress nucleation
at the glass surface. This technique thus allows for localization of the
nuclei production in two dimensions parallel to the surface. The threshold
laser intensity determined for NPLIN was three factors higher than that of
samples in glass vials. However, the increase in the nucleation probability
with laser intensity by an evanescent wave was similar to previous works in
bulk solution above a laser intensity threshold.

###  2.4 Reported solutions

In an attempt to understand the mechanism(s) behind NPLIN, several aqueous
solutions involving different solute types:  i) organic/inorganic, and  ii)
solid/gas  , have been reported in the literature. Studies of NPLIN thus far
have been carried out almost exclusively in aqueous solutions, limiting the
understanding of the role of the solvent in NPLIN.

####  2.4.1 Small organic molecules

So far, NPLIN has been observed for several small organic molecular solutes
such as urea, glycine, L-histidine, carbamazepine, and sulfathiazole.

In the experiments performed using glycine by Zaccaro et al.31, it was
observed that linearly polarized (LP) and circularly polarized (CP) laser
light induces nucleation of different polymorphs. The effect was termed
polarization switching and was explained using the non-linear anisotropic
polarizability of the pre-nucleating clusters - i.e. the Kerr effect. Sun et
al.34 reported a supersaturation window for polarization switching under NPLIN
of aqueous glycine. In their experiment, for light intensities of
$0.46\text{\,}\mathrm{G}\mathrm{W}\,\mathrm{c}\mathrm{m}^{-2}$ and a
supersaturation window of 1.45-1.55, a small change in elliptical polarization
of the incident laser light was found to induce an abrupt change in the
polymorph formed. Consequently, LP and CP light was found to favor the
formation of rod-like ($\gamma$-glycine) and disk-like ($\alpha$-glycine)
glycine polymorphs, respectively53. The reported supersaturation window range
was observed to be considerably smaller at lower laser intensities
($0.24\text{\,}\mathrm{G}\mathrm{W}\,\mathrm{c}\mathrm{m}^{-2}$). In addition
to favoring polymorphism, Clair et al.22 found the laser to have an impact on
the glycine morphology - where three distinct morphologies were obtained as
opposed to the rod-like morphology obtained by spontaneous nucleation (Figure
5). Results showed the influence of the CP light, with an increase in $\gamma$
nucleation above a supersaturation of $1.56$. However, this observation is
counterintuitive with respect to the Kerr effect, where one might expect the
opposite. In addition, a lower laser intensity threshold was recorded when
compared to previously reported values from the literature. The observed
differences in both the polymorph formation and laser intensity threshold
could be because these experiments were performed with light passing through
the air-liquid interface as depicted in the carousel setup in Section 2.3.
This differs from the other conventional setups which have a laser beam enter
and exit through the glass walls.

For L-histidine32, polarization switching was observed in the supersaturation
range of $1.40-1.60$, where CP laser light and low supersaturation were found
to favor the formation of a pure orthorhombic polymorph. On the other hand, LP
laser light and high supersaturation were observed to result in a mixture of
orthorhombic and monoclinic polymorphs. This emphasizes the field-induced re-
arrangement of a pre-nucleating cluster as a likely mechanism for NPLIN.

Ikni et al.46 demonstrated the tendency of carbamazepine in acetonitrile to
form polymorph (needle-like and prism-like) mixtures and only prism-like
crystals under LP and CP light, respectively (Figure 5). However, in the same
experiments for carbamazepine in methanol, nucleation was reported to be
polarization independent, which resulted in the formation of only the prism-
like polymorph. In the experiments performed by Li et al.54 on sulfathiazole
in water/ethanol mixtures, LP light was observed to favor FIV polymorph
formation, while CP light favored the FIII polymorph. Moreover, the number of
sulfathiazole crystals was found to increase with increasing laser exposure
time or supersaturation, while the mean crystal size decreased.

Figure 5: Morphology and polymorph control using NPLIN. Morphologies of
$\alpha$-glycine under22: (a) spontaneous and (b) NPLIN crystallization.
Micrographs of carbamazepine crystals produced by NPLIN in acetonitrile46: (c)
phase III and (d) phase I.

For experiments performed with aqueous urea31, 33, supporting the role of pre-
nucleating clusters, the exposure of unaged solutions (solutions readily
exposed to the laser after preparation) to amplified laser pulses
($0.7\text{\,}\mathrm{G}\mathrm{W}\,\mathrm{c}\mathrm{m}^{-2}$) did not induce
any nucleation. For aged solutions, a higher nucleation probability and lower
laser intensity threshold were observed for LP light when compared to CP light
at both wavelengths ($532\text{/}1064\text{\,}\mathrm{n}\mathrm{m}$). This
observation is also consistent with the optical Kerr mechanism since the rod-
like arrangement of urea molecules is expected to be favored by LP light over
CP light.

Based on the observations made so far34, 47, it is evident that, for glycine,
NPLIN can still operate even with a mismatch between the symmetry of glycine’s
polarizability and the polarization of the laser light (always resulting in
$\alpha$ and $\gamma$ at low and high supersaturations, respectively). Irimia
et al.48, in their recent experiments with glycine, also demonstrated the
independence of the crystal polymorph formed to the polarization of the laser
used when subjected to both single and multiple laser pulses (600 pulses).
Interestingly, a higher percentage of $\gamma$ polymorph was observed within
laser-irradiated samples when compared to crashed-cooled samples.

Although the NPLIN of small organic molecules could be attempted to be
explained by the Kerr effect, simulations by Knott et al.55 suggest that
although the Kerr effect mechanism can lower the barrier to nucleation, the
solute–solute interactions are simply too strong to allow significant
alignment at the electric field strengths employed in NPLIN experiments. In
addition, when experiments were repeated for urea50, the correlation between
the direction of the laser and crystal formed appeared to be quite random at
both laser wavelengths ($532\text{/}1064\text{\,}\mathrm{n}\mathrm{m}$). In an
attempt to study the directional influence of laser light together with
mechanical shock and sonocrystallization on crystal formation, Liu et al.47
also observed an increasing propensity to form $\gamma$-glycine at higher
supersaturations. However, the results did not reproduce the binary
polarization switching of glycine under NPLIN as reported by Sun et al.34. At
the very least, the switch in preference from $\alpha$-glycine to
$\gamma$-glycine was observed to happen over a smaller range of
supersaturation for NPLIN compared to the mechanical shock and
sonocrystallization techniques.

####  2.4.2 Metal halides

In contrast to small organic molecules, in NPLIN of halide salts, there is no
preferred polarization axis, as needed for the Kerr effect. To further support
the claim on polarization independence, in experiments performed using KCl, no
effect of laser polarization over the nucleation probability was observed49.
In experiments using KCl, Alexander et al.49 reported a significantly lower
laser intensity threshold than was observed by Garetz et al.30, 33 for urea.
In the same experiment, the solution aging was found irrelevant and it was
possible to nucleate a single crystal of KCl with a single laser pulse.
Therefore, for metal halides, the crystallization pathway was hypothesized to
be based on the dielectric polarization mechanism. Complying with the proposed
mechanism, the observed intensity dependence for KCl was linear at low laser
intensities49 ($<$
$40\text{\,}\mathrm{M}\mathrm{W}\mathrm{c}\mathrm{m}^{-2}$).

The measure of how susceptible a solution is to NPLIN is called lability. Ward
et al.35 reported that a single pulse of $532\text{\,}\mathrm{n}\mathrm{m}$
laser light had a higher nucleation probability than
$1064\text{\,}\mathrm{n}\mathrm{m}$ light. In addition, KBr samples yielded
more crystals than KCl samples, with $532\text{\,}\mathrm{n}\mathrm{m}$
exhibiting relatively lower intensity thresholds for both salts. The observed
reduction in the efficiency for $1064\text{\,}\mathrm{n}\mathrm{m}$ light was
attributed to the higher absorption of near-infrared light by water. The heat
generated within the sample due to light absorption is expected to increase
the solubility, thus reducing the local supersaturation. In addition, for
experiments performed using the same supersaturation, samples maintained at
$33\text{\,}\mathrm{\SIUnitSymbolCelsius}$ were significantly more labile than
those at $23\text{\,}\mathrm{\SIUnitSymbolCelsius}$ owing to a higher
concentration. Experiments by Hua et al.44 with KCl using
$1064\text{\,}\mathrm{n}\mathrm{m}$ laser light, showed the nucleation
probability to be independent of the number of laser pulses.

Liu et al.59 recently studied NPLIN of aqueous CsCl in presence of an acidic
polymer (polyepoxysuccinic acid - PESA). It was observed that the added acidic
polymer highly decreased the number of nucleation sites, leading to a fewer
number of crystals compared to just aqueous CsCl under laser irradiation.
Moreover, with PESA, the morphology of the CsCl crystals was found to be
flower-like under NPLIN, while spontaneous nucleation resulted in cuboidal-
shaped crystals. The observed effect of PESA on the number of nucleation sites
and morphology was argued to be based on its potential to control
crystallization from nucleation to crystal growth. While PESA is expected to
increase the energy barrier to nucleation due to increased interfacial tension
(from CNT, eq. 2), thus reducing the number of nucleation sites, the presence
of PESA molecules surrounding a nucleus could also lower the crystal growth
rate, affecting the morphology.

####  2.4.3 Macromolecules

Organic molecules, due to their larger meta-stable zone width, exhibit
spontaneous nucleation only at relatively high supersaturated conditions. The
potential of laser irradiation to avoid poly-crystals and produce high
crystalline order at low supersaturation is therefore intriguing. Yennawar et
al.60 observed improvement in crystal size, growth speed, quality, and
resolution of diffraction for various proteins due to NPLIN, with no
indication of a change in crystal packing compared to non-irradiated
controlled samples.

Lee et al.40 performed NPLIN on small droplets of supersaturated hen egg-white
lysozyme (HEWL) solutions using picosecond
($532\text{\,}\mathrm{n}\mathrm{m}$) and nanosecond
($532\text{/}1064\text{\,}\mathrm{n}\mathrm{m}$) lasers. The nucleation
efficiency was reported to be higher with $532\text{\,}\mathrm{n}\mathrm{m}$
and at higher peak intensities
(0.223-$0.257\text{\,}\mathrm{G}\mathrm{W}\,\mathrm{c}\mathrm{m}^{-2}$) and
shorter pulse duration ($100\text{\,}\mathrm{p}\mathrm{s}$). While higher
laser peak intensity would maximize the electric field strength, a
$532\text{\,}\mathrm{n}\mathrm{m}$ laser with a shorter pulse duration is
expected to minimize the energy absorbed by a droplet. Owing to the long
molecular rotational timescales - larger than picoseconds61, at first, the
nucleation is unlikely to be attributed to electric-field-induced
reorganization. However, a slight change in the degree of anisotropic
interaction between protein molecules is reported to have a tremendous effect
on the nucleation rates62. In conjunction, laser light might restrict any
other alternative conformations of side chains, thus accelerating the
arrangement of protein molecules into a crystalline structure. However, in the
same experiments by Lee et al.40, the crystal number and size were observed to
reduce upon aging, probably because the system became more homogeneous through
diffusion. Thus, the clustering of globular proteins was expected to result in
increased nucleation probability.

####  2.4.4 Other systems

NPLIN of single-component systems has been tested by a few authors. The
absence of solvent reduces the complexity in the phase transition, making it
more attractive for experimental and theoretical study. Sun et al.36 studied
the non-photochemical laser-induced phase transition in supercooled
4’-$n$-pentyl-4-cyanobiphenyl (5CB) liquid crystal using linearly polarized
picosecond laser pulses. Slightly below the nematic-isotropic temperature
($308.4\text{\,}\mathrm{K}$), only those liquid domains whose directors were
along the polarization of the laser light and whose size were greater than a
critical value were observed to nucleate. In glacial acetic acid, for low
laser intensities
($<100\text{\,}\mathrm{M}\mathrm{W}\,\mathrm{c}\mathrm{m}^{-2}$), Ward et
al.37 reported a linear relation between the fraction of samples nucleated and
the employed laser intensity.

Knott et al.38 performed nucleation of $\textup{CO}_{2}$ bubbles in carbonated
water, where the threshold laser intensity was observed to decrease with
increasing supersaturation and was not a strong function of solution purity or
laser wavelength. Nucleation theory of solids from solutions is not
appropriate for gases since the pre-nucleating cluster is surely less dense
and cooperative effects between solute molecules are ruled out. In addition,
Knott et al.observed that for water co-supersaturated with argon and glycine,
the bubbles escaping the water induced crystal nucleation even without a
laser. It should be noted that NPLIN experiments are distinct from experiments
where cavitation is induced deliberately to cause crystallization, e.g., by
focusing a beam of light. Ward et al.39 reported that the number of bubbles
nucleated increases quadratically with laser intensity, with a generally lower
laser intensity threshold for unfiltered samples and a clear trend of
decreasing lability with better filtering and cleaning. In addition,
femtosecond pulses ($\sim 110\text{\,}\mathrm{f}\mathrm{s}$) at
$28\text{\,}\mathrm{M}\mathrm{W}\,\mathrm{c}\mathrm{m}^{-2}$ or
$11\text{\,}\mathrm{G}\mathrm{W}\,\mathrm{c}\mathrm{m}^{-2}$ did not produce
any bubbles. These results support the claim that the mechanism for NPLIN of
$\textup{CO}_{2}$ is non-photochemical since the high intensity of the
femtosecond pulses would be expected to favor non-linear or multiphoton
ionization processes.

In an effort to understand the nucleation pathway, Liu et al.63 studied the
formation of hematite nanocrystals from electrolyte - a photo-thermal process
where crystallization was thermally activated only for a short period of time
by a single laser pulse (Figure 6). A mechanism based on the strength of the
inter-molecular forces was used in a comprehensive nucleation theory built on
two-step nucleation (TSN): first, the formation of liquid-like clusters of
solute molecules, followed by the rate-limiting organization of this cluster
into a protocrystal. Based on the difference between the diffusion energy
barrier and the nucleation energy barrier, this pathway was reported to offer
an effective route to synthesize ultrafine and coarse nanocrystals by using
multiple low-intensity pulses and a single high-intensity pulse, respectively.

Figure 6: Nucleation of hematite nanocrystals using a single nanosecond laser
pulse63. (a) Hematite crystals under $220\text{\,}\mathrm{m}\mathrm{J}$ laser
pulse. (b) Amorphous particle under $160\text{\,}\mathrm{m}\mathrm{J}$ laser
pulse

Ward et al.64 observed that under laser-induced nucleation of molten sodium
chlorate, the sample crystallized into the enantiomorph of the original sample
prior to melting. Under similar experimental conditions, spontaneous
nucleation did not exhibit such retention of enantiomorphism. Moreover, the
molten samples made from fresh solid crystals, rather than being powdered
first, were reported to be more resistant to NPLIN. During the melting
process, the possibility of the formation of small particles of NaCl was
attributed to helping the original sodium chlorate in evading melting, thus
providing an active site to seed nucleation under NPLIN. It was also reported
that no polarization effect was observed and not all samples could be
nucleated by the laser at higher intensities
($0.24\text{\,}\mathrm{G}\mathrm{W}\,\mathrm{c}\mathrm{m}^{-2}$).

###  2.5 Summary

Owing to the work of a large number of research groups, a considerable amount
of observations has been accumulated in the literature. Table 1 provides a
visual summary of observation and the extent to which each proposed mechanism
can explain a given observation. Despite the ever-growing list of systems
exhibiting NPLIN, some basic questions remain unanswered. Can we a priori
predict whether a solution is NPLIN active or not, based on the
physicochemical properties of the solute and solvent? For a given solution,
what are the critical laser parameters for triggering NPLIN? As one can
immediately see in Table 1, none of the proposed mechanisms explain all
observations. In other words, more effort is required to extend our current
understanding of NPLIN from both the theoretical and the experimental side.

Various solutes, including small organics (urea, glycine, L-histidine,
carbamazepine, and sulfathiazole), metal halides (KCl, KBr), and gases
($\textup{CO}_{2}$) have been reported to undergo NPLIN (observation 1). There
is so far limited information on the list of solutions that do _not_ undergo
NPLIN. To the best of our knowledge, only acetamide and sodium chlorate are
reported to not undergo NPLIN (observation 2). Any contribution going beyond
the proposed mechanism has to both explain observations on NPLIN active
systems as well as rationalize why some systems do _not_ undergo NPLIN. Our
ability to exploit potential advantages of NPLIN in industrial settings
requires figuring out how laser-matter interaction(s), such as laser-solute
interaction, laser-impurity interaction, or both, dictate the NPLIN phenomena.
The answer to this question holds the key to explaining the observations
mentioned in Section 2.1. Below, we have made an effort to rationalize the
observations so far, by classifying them into laser and solution parameters
from a pragmatic application point of view.

Table 1: Observation and mechanism summary for NPLIN (inspired by Barber42). OKE = optical Kerr effect, DP = dielectric polarization, IH = impurity heating. Meaning of symbols: ✓- can be explained; x - cannot be explained; ? - needs more insight/analysis. | Observation | OKE | DP | IH
---|---|---|---|---
1 |  NPLIN is reported for a broad range of systems | Small organics | ✓ | x | ✓
| Metal halides | x | ✓ | ✓
| Gases | x | x | ✓
2 |  Not all solutions undergo NPLIN | x | x | ?
3 |  Dependence of NPLIN probability on laser peak intensity and supersaturation | ✓ | ✓ | ✓
4 |  Laser pulse duration matters | ✓ | x | ✓
5 |  Laser wavelength dependence | ? | x | ?
6 |  Product count vs laser peak intensity | Crystals | ✓ | ✓ | ✓
| Bubbles | x | x | ✓
7 |  Polarization switching | ✓ | x | ?
8 |  Laser intensity threshold | x | x | ✓
9 |  Dependence on solution aging | ✓ | ✓ | ✓
10 |  Effect of filtration and nanoparticle doping | x | ? | ✓
11 |  Crystal alignment | ✓ | x | x
12 |  Irradiation pathway matters | ✓ | ✓ | ✓
13 |  Direct solution-laser interaction matters | ✓ | ✓ | ✓

####  2.5.1 Laser parameters

For the reported aqueous solutions, irrespective of the solute type,
increasing the laser peak intensity and pulse duration have been observed to
enhance NPLIN probability (observations 3 and 4, respectively). For both
conditions, it is evident that the amount of laser-matter interaction
increases. The reported low influence of the laser wavelength on the
nucleation probability (observation 5), and its role in laser-matter
interaction is less conclusive. The absorption of near-infrared laser light by
water does explain the reported lower NPLIN probabilities for
$1064\text{\,}\mathrm{n}\mathrm{m}$ wavelength in aqueous solutions. But the
relatively high probability for $355\text{\,}\mathrm{n}\mathrm{m}$ wavelengths
compared to $532\text{\,}\mathrm{n}\mathrm{m}$ still lacks explanation.

The observed increase in the number of crystals with increasing laser peak
intensity (observation 6) can be rationalized by all mechanisms as seen in
Table 1. However, for the DP mechanism, when applied to glycine, the values of
the experimental parameters such as laser peak intensity and supersaturation
were not comparable to the theoretically calculated ones45. Similarly, the OKE
mechanism fails to explain the observations for KCl since dissolved KCl lacks
directional polarization under laser light. Moreover, for small organic
solutes, the effect of laser polarization on the polymorph formed (observation
7) is still under debate.

The lack of understanding of laser-matter interactions in NPLIN leaves us with
an unanswered question: why is there a laser intensity threshold to NPLIN
below which no nucleation occurs (observation 8)? As the existence of this
threshold cannot be explained by the OKE and DP mechanisms, this observation
may hold the key to solving the puzzle of laser-matter interaction in NPLIN.
As the nucleation probability increases with laser peak intensity above this
threshold, one may pragmatically ask if rather any supersaturated solution,
regardless of its chemical identity, may be forced to nucleate at high enough
laser intensities.

####  2.5.2 Solution parameters

For a fixed laser peak intensity above a threshold, the observed increase in
NPLIN probability with solution supersaturation (observation 3) can be
explained using classical nucleation theory (CNT), because the average size of
the pre-nucleating clusters will increase with supersaturation - favoring
stable nucleus formation. The observed increase in nucleation probability with
aging for small organics (observation 9) is also in line with the proposed CNT
model. The more time available for the solution to progress towards
equilibrium before the laser irradiation, the higher the likelihood of the
formation of large pre-nucleating clusters. Since the equilibrium timescale
for a solution would depend on the solute’s diffusivity, the reported higher
diffusion coefficient for metal halides65 compared to small organics66 could
be a possible reason why aging of metal halides is less significant for NPLIN
probability.

Within a solution, in addition to the intended solute and solvent, there are
often impurities that a laser can interact with. The majority of authors have
overlooked the composition of the impurities present in their solution. The
role of impurities in NPLIN has been demonstrated by Ward et al.41 who
observed a decrease in NPLIN probability with filtration (observation 10).
Thus, impurity composition and quantity may have led to the contradicting
results on polarization switching (observation 7). The reported increase in
the nucleation probability with laser peak intensity and pulse duration
(observations 3 and 4, respectively) can be rationalized using the increase in
the energy available to heat up a nano-impurity for triggering nucleation.
From theory, the current hypotheses based on both the OKE and DP mechanism
depend only on the laser peak power (Equations 1 and 2) and not on the
wavelength. However, the absorption spectra of impurities based on their
composition could be a deciding factor. The composition of the solution
impurities could vary depending on the solute manufacturer and solvent purity.

The reported laser peak-intensity threshold (observation 8) in NPLIN could be
reasoned as the minimum energy required to form a significant vapor bubble
surrounding a nano-impurity. Although the majority of observations can be
explained using the nano-impurity heating hypothesis, there exist only a few
theoretical works that explore the mechanism67, 68. These theoretical works
are largely phenomenological and lack the ability to quantify and predict the
experimentally observed correlation between laser peak intensity,
crystallization probability, and laser peak-intensity threshold. Nonetheless,
predicted qualitative trends from simulations offer a means to compare
experiments and theory. Hopefully, further efforts from both the theoretical
and the experimental side can answer questions on the exact nature of these
nano-impurities. This extended understanding can answer questions such as what
are the physical properties of a given nano-impurity (physicochemical state-
soluble or colloidal-, chemical structure, and more) that make it NPLIN
active?

While employing multiple nanosecond laser pulses of 532 and 1064 nm, the
reported alignment of urea crystals with a laser by Garetz et al.30 could not
be reproduced by Liu et al.50 (observation 11). The observation by Garetz et
al.could be attributed to the possible polarization-dependent ablation of the
crystals formed and secondary nucleation. The observed influence of
irradiation pathway on nucleation probability (observation 12) by Clair et
al.22 could be a result of increased irradiated volume while directing the
laser from the top of the vial. With an increased irradiated volume, the
likelihood of the laser encountering a nano-impurity or a pre-critical cluster
(possibly containing impurities) is larger. However, one cannot deny the
possibility of the air-liquid interface playing an important role. Moreover,
the reported zero nucleation probability by Kacker et al.19 for samples that
masked the laser entry within the solution further strengthens the argument on
the role of direct light-solution interaction in NPLIN (observation 13). Thus,
clear evidence on the type of light-solution interaction occurring in NPLIN
would help in establishing a concrete theory for predicting the NPLIN activity
of a solution.

##  3 High-Intensity Laser-induced nucleation (HILIN)

###  3.1 Phenomenology

The interaction of laser light with condensed matter at higher laser
intensities has generated substantial attention since the invention of the
laser in the 1960s 69. The interaction of a high-intensity laser pulse with
condensed matter leads to optical breakdown and cavitation70. Particularly for
liquids, the literature contains many definitions of optical breakdown, but
the most common definition considers it as the event connected to the minimum
threshold energy needed to generate a plasma within the liquid71. To generate
such a breakdown event, the experiment needs to be operated at very high laser
intensities ($\geq$GW/cm2) using pulsed laser beams typically ranging from
femtosecond to nanosecond pulse width 71. Earlier literature work72, 73
reports optical breakdown in pure substances, e.g. water, resulting from a
multiphoton absorption avalanche mechanism 74, as illustrated in Figure 7. In
this avalanche mechanism, the quasi-free electrons that are initially released
from atoms and molecules gain additional kinetic energy as they are
accelerated by the electric field of the laser. These electrons cause impact
ionization of other atoms and molecules, thereby producing more free
electrons. This event causes an electron avalanche, upon which a critical free
electron density is achieved, leading to the formation of plasma within the
liquid medium. The plasma generally heats up to several thousand Kelvins, upon
which its volume expands leading to the emission of shockwaves69.

Figure 7: Avalanche ionization leading to optical breakdown and plasma
formation74.

A considerable number of HILIN experiments have been reported in the
literature with a diverse set of experimental setups and solute/solvent
systems. The overarching goal of these experiments characterized with high
laser intensities (GW/cm2) and short laser pulses (ns to ps) range from
scientific exploration to improving the current understanding of laser-induced
nucleation30. The results of these experiments have opened the door to new
discussions concerning the control of nucleation mechanism as well as
properties of resulting crystal in high-intensity laser-induced nucleation
(HILIN)23, 75.

###  3.2 Proposed mechanism

Understanding how HILIN works in various solutions is intimately related to
how plasma, shock waves, and emerging cavitation bubble upon focused laser
irradiation interacts with solute and solvent. Vogel et al.76 suggested that a
near-infrared short femtosecond laser pulse, when tightly focused into a
solution, causes multiphoton absorption and subsequent ionization of solute
and solvent molecules. This fast conversion of energy results in thermoelastic
pressure along with the accumulation of heat, thereby increasing the vapor
pressure of the solution. Cavitation bubbles are finally produced when the
vapor pressure of the solution surpasses the atmospheric pressure76. As an
example, the process of cavitation has been visualized in the experiments
conducted by Yoshikawa et al.77 on a supersaturated solution of HEWL protein
using a near-infrared femtosecond laser. Microscopy images reveal that the
cavitation bubble expands and collapses in microseconds after laser
irradiation, as shown in Figure 8. The proposed nucleation mechanism among
various solutions proposed in the literature is discussed below. The
experimental conditions and sample compositions are summarized in Table 3.

Figure 8: HEWL protein supersaturated solutions observed by a high-speed
camera operating at $10^{6}$ frames/s after irradiation by a 200 fs pulse. The
arrow shown at 0 $\mu$s corresponds to the focal point of the laser. The black
sphere is the cavitation bubble expanding and collapsing after laser
irradiation. 77.  Figure 9: Urea crystallization observed by a high-speed
camera, obtained after femtosecond laser irradiation at an energy of 340
$\mu$J/pulse for 12 M concentration. The arrow mark at 20 s indicates the
focal point of the laser78.

Yoshikawa et al.78 performed experiments with different supersaturated
solutions of urea in water (10.5 M - 12 M) using a Ti:sapphire femtosecond
laser system (800 nm, 120 fs, 1 kHz) in 16 mm diameter pyrex glass tubes. The
laser was focused into the supersaturated solution through an objective lens
(10X, N.A. = 0.4) at approximately 5 mm from the bottom of the glass tube. The
generated crystals upon laser irradiation in the vicinity of the focal point
are shown in Figure 9. Microscopy images revealed the formation of many
cavitation bubbles of size ranging between 100 nm and 10 $\mu$m, subject to
each laser pulse, that later diffused and collapsed. It was also observed that
needle-shaped objects formed with a standard CCD camera twenty seconds after
irradiation, as shown in Figures 9d-9f. The crystallization threshold energies
for urea concentrations of 11 M, 11.5 M, and 12 M were found to be 50 $\mu$J,
50 $\mu$J, and 240$\mu$J respectively. The corresponding laser energy density
for these threshold energies was measured to be approximately 10 J/cm2, much
higher than the optical breakdown of the solution (0.2 J/cm2). At this laser
energy density, the authors predicted that the urea solution will undergo
multiphoton absorption at the focal point of the laser, leading to shockwaves
and cavitation bubble formation. The shockwaves resulting from the expansion
and collapse of cavitation bubbles79,80 generate transient pressures of the
order of MPa-GPa, and these variations in pressure could trigger nucleation81.
On the basis of these observations, the most plausible mechanism for crystal
formation was explained in two steps. The first step is the nucleation and
growth of urea crystals at the focal point of the laser due to the laser-
induced shock wave and cavitation bubbles and the second step is the laser
ablation of the already generated crystal leading to subsequent crystal growth
due to multiple laser pulses78.

Figure 10: Bubble formation process before anthracene crystallization observed
by a high-speed camera, obtained after single-shot femtosecond laser
irradiation into its supersaturated solution at an energy of 12.7 $\mu$J/pulse
with solution temperature at 25∘C82.

Similarly, Nakamura et al.82 conducted laser-induced nucleation experiments
with supersaturated solutions of anthracene in cyclohexane (supersaturation
1.1-1.9) using a femtosecond Ti:sapphire laser pulse (800 nm, 120 fs, 1 KHz)
in a 10 mm rectangular optical cell. The laser was focused into the
supersaturated solution through an objective (10X, N.A. = 0.25) a few
millimeters from the bottom of the cell, as shown in Figure 16d, and generated
polyhedral-shaped crystals. The cavitation bubble formation and subsequent
crystal growth follows from the optical breakdown in pure water70. According
to Nakamura et al.82, the temperature of the supersaturated solution of
anthracene increases rapidly at the laser focal point as the energy of the
femtosecond laser pulse is consumed effectively through multiphoton
absorption. This rapid temperature rise subsequently leads to shockwave
emission along with the formation of a cavitation bubble76. However, as time
progresses, the cavitation bubble further splits into small bubbles due to
asymmetrical convection caused by jet flow during the asymmetric collapse of
the cavitation bubble, as shown in Figure 10. Finally, after some seconds, it
was observed that polyhedral-shaped crystals of anthracene were formed at the
laser focal point, as shown in Figure 11. From these observations, the authors
hypothesized that the crystallization of anthracene might have taken place at
the interface between the cavitation bubble and solution. This hypothesis was
further verified based on the observation that the threshold energy (3.1
$\mu$J) reported for laser-induced bubble formation corresponds exactly with
the minimum laser pulse energy needed to observe crystallization of
anthracene82.

Figure 11: Anthracene crystallization observed by a high-speed camera,
obtained after single-shot femtosecond laser irradiation into its
supersaturated solution at an energy of 12.7 $\mu$J/pulse with solution
temperature at 25∘C 82.  Figure 12: (a) Fluorescence images of F-lysozyme in
agarose gel irradiated with a femtosecond laser pulse at 0 $\mu s$. The arrow
mark at -10 $\mu$s indicates the focal point of the laser, (b) Fluorescence
intensity profile of F-lysozyme in agarose gel at 20 $\mu$s83.

Cavitation bubbles were also observed in proteins subjected to laser pulse
irradiation. To judge whether the cavitation bubbles trigger the nucleation
mechanism, high-speed imaging experiments at an interval of 10 $\mu s$ have
been performed with the help of fluorescent dye-labeled protein F-lysozyme in
2% agarose gel using a femtosecond laser (780 nm, 100 fs, 1 KHz) in a
capillary (0.7 mm ID, 50 mm length) by Yoshikawa et al.83. The laser was
focused into the center of the capillary, containing supersaturated solution,
through an objective (10X, N.A. = 0.4), as shown in Figure 16f. The
fluorescence images and fluorescence intensity profile of supersaturated HEWL
protein solution in 2% agarose gel are shown in Figure 12. The bright spot at
the center of the fluorescence image directly after laser irradiation
corresponds to plasma emission. The plasma emission was subsequently followed
by a cavitation bubble that expanded and collapsed within 30 $\mu$s. However,
the peak fluorescence intensity at 20 $\mu$s was found to be three times
larger than the average peak intensity of the corresponding agarose gel
medium, visible as an intense bright spot. This bright spot was attributed to
a local high concentration of F-lysozyme at the focal point of the laser
beam83. On the other hand, there were no bright spots observed during the
expansion and collapse of the cavitation bubble after laser irradiation in the
absence of agarose gel within the solution. Previously Nakamura et al.82
hypothesized that the surface of the cavitation bubble acts as a preferential
location for the accumulation of protein molecules generated after laser
irradiation82. Therefore, the protein molecules that initially adsorbed onto
the bubble surface probably are gathered together at the focal point during
the rapid collapse of the cavitation bubble. The local increase in this
protein concentration not only leads to an increase in fluorescence intensity
but also to a nucleation event.

Figure 13: Cavitation bubbles observed by a high-speed camera operating at
$10^{6}$ frames/s after irradiation with a 200 fs pulse into supersaturated
cytochrome c solution84.

Later, Iefuji et al.84 performed laser-induced nucleation experiments with a
supersaturated solution of protein cytochrome c using a femtosecond laser
setup (780 nm, 200 fs, 1 KHz) and high-speed imaging in microbatch plates
containing wells. The laser was focused at the center of the microbatch well,
containing a supersaturated solution, through an objective (10X, N.A. = 0.25),
as shown in Figure 16c. Upon laser irradiation to the supersaturated solution,
the cavitation bubble expanded and collapsed in 40 $\mu$s, leaving behind
bright and dark areas, as shown in Figure 13. The bright area was observed at
the focal point of the laser beam and the dark area surrounding the
cavitation. These bright and dark regions were attributed to low and high
protein concentration regions, respectively. The high concentration area could
probably give rise to protein nuclei84. Despite the fact that the findings of
these studies suggest that bright and dark spots indicate low and high protein
concentration regions respectively, it is difficult to quantify this claim
simply by looking at Figure 13. Further quantification in terms of the protein
concentration as well as local temperature surrounding the cavitation bubble
after laser irradiation in a future study will be most informative in that
regard.

The experimental techniques proposed by Yoshikawa et al.83 and Iefuji et al.84
collectively contributed to the development of a mechanistic view of laser-
induced nucleation. On the application side, obtaining high-quality protein
crystal using a femtosecond laser can be helpful for X-ray crystallographic
structural studies85.

Also for a single component system, focused Nd:YAG nanosecond laser
irradiation (1064 nm, 8 ns, 20 Hz) into a rectangular cell containing
supercooled water resulted in the nucleation of ice at the location of
noncondensable gas bubbles, as shown in Figure 14. The laser was focused into
the center of the rectangular cell containing supercooled water through a
focusing lens, as shown in Figure 16k. Lindinger et al.86 claims that
homogeneous nucleation in the compressed liquid phase could be the possible
mechanism for crystal formation. This was supported by experiments showing
optical breakdown of supercooled water following laser irradiation along with
cavitation bubble formation and its subsequent collapse into numerous small
bubbles. It was also observed that when multiple laser shots were fired, the
preexisting microbubbles from previous laser pulses acted as a heteronucleant
for ice nucleation, if they were very close to the cavitation events happening
from new laser pulses86.

Figure 14: Ice crystallization observed by a high-speed CCD camera, induced by
optical breakdown using 8 ns laser irradiation at an energy of 2 mJ.86

Laser-induced nucleation experiments were performed with supersaturated
solutions involving simple salts like (NH4)2SO4 (0.2$\%$ and 0.4$\%$ relative
supersaturations) and KMnO4 (7$\%$, 14$\%$ and 21$\%$ relative
supersaturations) by Soare et al.87 using Nd:YAG nanosecond laser pulses (6
ns, 532 nm, 0.05-0.5 mJ). The laser was focused at the center of the two glass
plates (placed 50-100 $\mu$m apart) containing supersaturated solution through
a 20x objective, as shown in Figure 16f. In the case of the (NH4)2SO4
solution, it was observed that crystals were formed in the vicinity of the
optical disturbance a few seconds after the cavitation bubble collapse, as
shown in Figure 15. Although a mechanistic route by which the cavitation
bubble leads to crystal nucleation was not explicitly given, it was argued
that crystal nucleation took place at the bubble interface, based on changes
in the refractive index induced by the formation of nuclei at the maximum
evaporation rate. This hypothesis was supported by recently performed direct
numerical simulations of a laser-induced thermocavitation bubble by Hidman et
al.67. To estimate the degree of supersaturation of the solution surrounding
the vapor bubble, the initial growth stage of the bubble was modeled using
numerical simulations. Hidman et al.67 proposed that the evaporation of
solvent around the bubble interface causes an increase in the local
supersaturation and triggers nucleation in laser-induced nucleation
experiments. This would be the case provided the predicted supersaturation of
the solution in the vicinity of the bubble exceeds the solubility limit for a
given threshold laser energy in the experiments. Also, it was found that 10 to
30 crystals of (NH4)2SO4 (0.4$\%$ relative supersaturation) were formed per
laser pulse, whereas with KMnO4 higher supersaturations were needed for
nucleation to occur, and a smaller number of crystals were observed. In some
cases, more laser pulses were needed to induce crystal formation. Soare et
al.87 interpreted this observation to be based on an insufficient evaporation
rate emerging from a single laser pulse to induce nucleation, without actually
quantifying it.

Figure 15: Cavity evolution and formation of (NH4)2SO4 crystals observed by a
high speed camera87.

Barber et al.88 performed laser-induced nucleation experiments on
supersaturated solutions of NaClO3 at high energy densities (420 kJ cm-2)
using Nd3+:YAG laser at two different wavelengths (532 nm and 1064 nm) in 3 ml
vials. Laser irradiation in the form of circularly polarized light was focused
at the center of the vial with the help of a planoconvex lens, as shown in
Figure 16j, to understand the effect of helicity of light on the nucleation of
NaClO3 enantiomorphs. NaClO3 as a compound exists in two enantiomorphic forms
i.e. left-handed (l) and right-handed (r) enantiomorphs. Upon single laser
pulse irradiation to the supersaturated solution, only one or two crystals
were generated per vial at this high energy density. In addition, no
significant correlation between helicity of light and NaClO3 enantiomorphs was
observed. Also, the number of d and l NaClO3 crystals formed from the total
number of samples irradiated with a laser at both wavelengths was found to be
about identical for both right circular polarized light (RCP) and left
circular polarized light (LCP). Barber et al.88 proposed that crystallization
takes place by initially favoring nucleation of monoclinic phase III NaClO3
molecular clusters that later convert to cubic phase I NaClO3, following
Ostwald’s rule of stages8990. The selectivity of monoclinic NaClO3 phase III
crystal nucleation over NaClO3 phase I crystal was further attributed to its
higher solubility values at room temperature and higher Gibbs free energy
values below its melting point. Based on these observations, the plausible
mechanism was discussed on the basis of local high supersaturation surrounding
cavitation bubbles leading to monoclinic NaClO3 phase III crystal nucleation
upon laser irradiation. This was supported by a general idea that due to
evaporation, there is an increased solute concentration at the bubble
interface leading to nucleation after laser irradiation, as shown by the
direct numerical simulations by Hidman et al.67.

###  3.3 Reported solutions

High-intensity Laser-induced nucleation (HILIN) experiments have been
performed on different types of solutes, including small organic molecules and
proteins. A classification of the sample holders, based on their geometry,
volume, and position of the laser for HILIN experiments is schematically shown
in Figure 16.

####  3.3.1 Small organic molecules

Concerning small organic molecules, HILIN experiments have been performed with
supersaturated solutions consisting of
4-(Dimethylamino)-N-methyl-4-stilbazolium Tosylate (DAST) in methanol 85, urea
in water 78, anthracene in cyclohexane 82 and glycine in water 91.

Tsunesada et al.92, studied the nucleation of DAST crystals using Nd:YAG
nanosecond laser (1064 nm, 23 ns) and later Hosokawa et al.85 studied the
nucleation of the same crystals using focused short pulse femtosecond
Ti:sapphire laser (800 nm, 120 fs). It was found that the nucleation
probability of DAST crystals obtained by a femtosecond laser setup at a fixed
time interval is larger (10%) than by a nanosecond laser setup (3%), owing to
its large peak intensity values and multiphoton absorption in a very short
time. It was also observed that the nucleation probability of DAST crystals
increased with a decrease in the repetition rate of the laser pulses. This was
explained in terms of molecular cluster nuclei destruction by the train of
laser pulses when the time interval between them is larger85.

Liu et al.91 performed laser-induced crystallization experiments on
supersaturated solutions of glycine in water using femtosecond laser (800 nm,
160 fs) at both air/solution interface and glass/solution interface and found
that the crystallization probability at a fixed time interval is higher at the
air/solution interface than at the glass/solution interface. It was found that
the nucleation probability increased with an increase in the repetition rate
of laser pulses, laser pulse energy, and exposure time of the laser. Two of
the three above-mentioned parameters were kept constant while evaluating the
nucleation probability with respect to the changing parameter91.

####  3.3.2 Proteins

The first HILIN experiments focusing on supersaturated solutions of proteins
were performed in the early 2000’s with the purpose of obtaining high-quality
protein crystals. In these experiments, Adachi et al.93 studied the
crystallization of proteins including HEWL, glucose isomerase, and
ribonuclease H using a Ti:sapphire femtosecond laser. The important
observation of these experiments was that the number of HEWL crystals
generated upon laser irradiation increased with the number of irradiation
pulses93. The glucose isomerase protein crystals were also found to nucleate
from a low supersaturated solution upon focused laser pulse irradiation 93.
The induction time of Trypanosoma brucei prostaglandin F2$\alpha$ synthase
(TbPGFS) was decreased from many months to a few days by focused femtosecond
laser pulse93. Apart from these water-soluble proteins, focused femtosecond
laser pulse experiments were also carried out with membrane proteins. Adachi
et al.94 studied HILIN of membrane proteins like Aerobic respiration control
sensor protein (AcrB) by irradiating focused femtosecond laser pulses to three
different supersaturated solutions with various precipitant concentrations of
12%, 13% and 15% polyethylene glycol (PEG) 2000. It was observed that upon
laser irradiation, a supersaturated solution containing 13% PEG (meta-stable
region) generated large crystals (200 $\mu$m) of AcrB. However, for 15% PEG
spontaneous nucleation resulted in small crystals ($\leq$100 $\mu$m)94.

Figure 16: Schematic setups used in HILIN experiments.

###  3.4 Potential for controlling polymorphic form

Recently, focused femtosecond lasers have been reported to control the
polymorphic form of compounds. Ikeda et al.95 reported the first study on
polymorph control of indomethacin in acetonitrile supersaturated solution
($\sigma$ = 3.5) by focusing a femtosecond laser through a 10x objective at
800 nm wavelength in 1 ml glass vials. In these experiments, the laser was
focused in the center of the solution, close to the glass vial’s side wall and
at the air-liquid interface, as shown in Figure 16h.

At the location close to the glass vial side wall or at the air-liquid
interface, nucleation occurred within a day after laser irradiation, giving
rise to needle-shaped crystals with an approximate size of 1 mm. These
crystals were found to be of metastable $\alpha$-form, having at least 8
months of temporal stability at room temperature in air and at 0oC in
solution. However, laser irradiation focused at the center of the solution
resulted in plate-shaped crystals with an approximate size of 500-600 $\mu$m
in 48 hours, corresponding to stable $\gamma$-forms.

These observations were explained by the fact that the laser irradiation at
the glass vial’s side wall and at the air-liquid interface resulted in an
asymmetric bubble expansion and collapse with many long-lasting bubbles
reaching the region of the solution meniscus along the glass wall. It was also
observed that the nucleation of meta-stable $\alpha$-form crystals occurred at
the location of long-lasting bubbles. Ikeda et al.95 attributed this
observation to the higher evaporation efficiency of the lasting bubbles along
the solution meniscus, leading to higher local supersaturation and thus
preferentially enabling the nucleation of the meta-stable $\alpha$ phase due
to its lower interface energy, as described by the Ostwald rule of stages.
Further experiments quantifying this observation will be most useful.
Conversely, laser irradiation at the center of the solution resulted in a
symmetrical bubble expansion and collapse, with long-lasting bubbles present
along the region of the air/solution interface95. Ikeda et al.95 proposed that
the evaporation efficiency of long-lasting bubbles at the air/solution
interface would be lower than at the solution meniscus, resulting in mild
local supersaturation, without quantifying evaporation efficiency. Future
efforts on quantification of this hypothesis point will be essential to
predicatively control polymorphic form, a topic of primary interest for the
industry. The mild local supersaturation values were argued to be responsible
for the nucleation of the stable $\gamma$ phase. In summary, Ikeda et al.95
suggests that controlling crystal polymorphs requires precise control of the
laser focal point.

Shubo et al.96 performed laser-induced crystallization experiments on
supersaturated solutions of acetaminophen in water ($\sigma$ = 1.5) by
focusing femtosecond laser light (800 nm) through a 10x objective at the air-
solution interface of the solution, as shown in Figure 16i. The experiments
were performed to enhance the proportion of metastable crystals, i.e. Form II
and Form III polymorphs, by changing the laser pulse power and double-pulse
delay.

During irradiation and immediately after cavitation, bubbles expanded and
collapsed, and laser-induced crystallization of the acetaminophen solution
resulted in needle-shaped crystals. In contrast, spontaneous nucleation of the
same solution resulted in rhombic crystals. It was reported that laser
irradiation to the solution for 2 minutes resulted in statistically reliable
results and prevented the transition of metastable Form II and III crystals to
stable Form I crystals for several minutes. Furthermore, it was found that the
percentage of needle-shaped crystals decreased with increasing laser pulse
energy. Also, as laser pulse energies increased from 25 $\mu$J to 65 $\mu$J
per pulse, the percentage of Form II and Form III needle crystals with an
aspect ratio of 3 or higher increased from 5$\%$ to 20$\%$, then dropped to
5$\%$ as the laser pulse energies further increased to 95 $\mu$J per pulse. It
was also noticed that the percentage of acetaminophen needle-shaped crystals
increased in double-pulse experiments as compared to single-pulse experiments
for the same laser energy. Also, it was observed that the length of the
crystals decreased with an increase in the double pulse delay time. Finally,
it was reported that the aspect ratio distribution of crystals was much wider
for laser irradiation experiments, along with a 40$\%$ increase in Form II and
Form III crystals as compared to spontaneous nucleation experiments.

Yu et al.97 demonstrated polymorph control of sulfathiazole in a mixture of
water and ethanol supersaturated solution by focusing femtosecond laser light
(800 nm) through a 5x objective for a period of 1 minute, 500 $\mu$m from the
air-liquid interface, as shown in Figure 16i. In other experiments, the laser
source was combined with ultrasound, using a 40 kHz, 50 W ultrasonic cleaning
machine to check the influence of ultrasound exposure along with laser-induced
nucleation. The three main sulfathiazole polymorphs, II, III, and IV, were all
observed to crystallize due to laser-induced nucleation. Of the three
polymorphs, III is the most stable, making it the dominant polymorph for
spontaneous nucleation. At 130$\%$ supersaturation and at low laser power, the
III-polymorph was also observed to be the dominant nucleation product, but as
the laser power increased from 10 to 80 $\mu$J per pulse, the proportion of
metastable form II- and IV-polymorphs was seen to increase.

Figure 17: Schematic of sulfathiazole nucleation, comparing low intensity
(left) with high intensity (right) femtosecond laser exposure97.

The plausible mechanism for sulfathiazole crystal formation is shown in Figure
17. When an intense laser pulse is focused at the supersaturated solution, it
causes solution cavitation leading to bubble formation. Low laser powers lead
to lower number of crystals along with lower number of less-stable polymorphs.
This is primarily attributed to the lower quantity of cavitation bubbles
formation at low laser powers. However, a high laser power will create a large
number of bubbles, which then merge into stable and long-lasting bigger
bubbles. At this stage, it has been speculated that the interface of the
cavitation bubble decreases the nucleation barrier, increasing the nucleation
rate and thereby facilitating the crystallization of the less stable II- and
IV-polymorphs in higher quantity as compared to low laser powers. It has also
been reported that additional ultrasound will boost the merging process of
cavitation bubbles into further larger and more stable long-lasting bubbles,
thereby aiding in a faster nucleation process of less stable II- and IV-
polymorphs67.

###  3.5 Summary

We first summarize common observations in HILIN experiments. We then discuss
the consequences of these observations in terms of the proposed mechanism and
finally, the open questions are highlighted.

  1. 1.

A broad range of solute-solvent systems, as well as pure compounds, undergo
HILIN: Various small organic molecules (DAST in methanol85, urea in water78,
anthracene in cyclohexane82), inorganics ((NaClO388, NH4)2SO4 and KMnO4 in
water87) and proteins (HEWL77, glucose isomerase, and ribonuclease H in water)
have been crystallized upon exposure to high-intensity laser pulses with a
pulse duration ranging from nano- to femtoseconds. Even undercooled pure water
(single component) has been reported to crystallize86.

  2. 2.

HILIN probability depends on supersaturation and laser pulse energy: Nakamura
et al.82 reported that the nucleation probability measured at a fixed time
after laser exposure increases with increasing the supersaturation of
anthracene in cyclohexane. Increasing laser pulse energy also increases the
measured HILIN probability at a fixed time, while increasing solution
temperature is reported to decrease it.

  3. 3.

HILIN probability dependence of pulse duration and wavelength: Reported HILIN
experiments often focus on the cavitation phenomenon and characterizing the
resulting crystal properties. Despite a broad range of solute-solvent systems
and lasers utilized, reported HILIN experiments rarely report the dependence
of nucleation probability on pulse duration and wavelength, unlike NPLIN
experiments.

  4. 4.

Minimum HILIN threshold depends on supersaturation: A minimum laser threshold
energy is required to generate a cavitation bubble prior to crystal formation
in supersaturated solutions. Yoshikawa et al.observed that this threshold
depends on supersaturation78.

  5. 5.

Physical changes observed around the cavitation bubble following laser
irradiation: Soare et al.87 reported ring-shaped optical disturbances in the
vicinity of a cavitation bubble that was visible at least up to 30 seconds
after laser exposure (Figure 15). These optical disturbances have been
interpreted as high-density regions forming around cavitation bubbles due to
the local evaporation of the solvent. Moreover, long-lasting gas bubbles with
lifetimes (at least tens of seconds) much longer than the lifetime of
cavitation bubbles have been reported by various groups82, 87, 97.

  6. 6.

Polymorphic control: Control of polymorphic form crystallizing from solution
has been reported for indomethacin in acetonitrile 95, acetaminophen in
water96 and sulfathiazole in a mixture of water and ethanol supersaturated
solution97. Experiments of Ikeda et al.95 showed that controlling indomethacin
polymorphs necessitates fine control of the laser focal point. Ikeda et al.95
proposed that the focal point of the laser (at air-solution or at the center
of solution) alters the local evaporation rate. Shubo et al.96 observed
crystallization of distinct acetaminophen polymorphs depending on the laser
power.

HILIN experiments are characterized by high-intensity (GW/cm2) femtosecond or
nanosecond laser pulses interacting with supersaturated solutions. This
material-light interaction results in an optical breakdown, plasma formation,
emission of shockwaves, and thermocavitation along with nucleation of solute
from solution. The exact mechanism of how plasma formation, shockwaves, and
thermocavitation trigger nucleation and how these phenomena collectively
influence the physical properties of emerging crystals is still an open
question. The large collection of solute/solvent systems undergoing HILIN
(observation 1) provides a good basis for formulating a working mechanism. Yet
no information is available on the solute/solvent systems that do not undergo
HILIN. Hence practical questions such as “Can any supersaturated solution
undergo HILIN regardless of the chemical identity of the solute?” and “What
are the optimum laser parameters (pulse energy, wavelength) required?” remains
unanswered. Answering these questions requires a complete mechanistic
understanding explaining the role of plasma formation, shockwaves, and
cavitation in crystallization from solution. The mechanism proposed by Vogel
et al.76 emphasizes cavitation bubble formation due to multiphoton absorption
and subsequent ionization followed by fast conversion of energy into
thermoelastic pressure and formation of heat. As laser intensity increases,
one may expect the formation of plasma, shockwaves, and thermocavitation
bubbles to intensify and to have a more pronounced effect on crystallization.
In experiments with simple salts, Soare et al.87 observed fluctuations in the
refractive index of material surrounding the laser focus. The authors
hypothesized that these optical effects were caused by increased solute
concentration around the cavitation bubble. This observation was reproduced by
direct numerical simulations of a laser-induced thermocavitation bubble by
Hidman et al.67. Moreover, such enhanced concentration regions are also
measured with fluorescent labeled lysozyme with high-speed imaging82. These
studies are certainly a step in the right direction. However, the simulations
by Hidman et al.67 did not take into account the formation of plasma and
shockwaves. Furthermore, the experiments87, 82 did not quantify the
concentration and temperature increase during thermocavitation simultaneously
making it difficult to calculate exact supersaturation, the driving force
behind nucleation and growth. Following only the enhanced solute concentration
due to the evaporation hypothesis proposed by Soare et al.87 indicates that
any solution can be crystallized by simply increasing the laser intensity. The
limits of this postulate is another open question central to the adaptation of
HILIN in scientific and industrial settings.

Nakamura et al.82 and Yu et al.97 proposed that the surface of the cavitation
bubble could act as a preferential location for nucleation of solute molecules
upon laser irradiation. This is a logical reasoning to explain the
observations. However, at the early stages of plasma and bubble formation,
high temperatures at the focal point are expected as most reported solutions
have increasing solubility with increasing temperature. It is not sure that
high supersaturations values required for observed nucleation rates will be
created at the vicinity of the bubble interface during bubble expansion.

At this stage, combining experiments and simulations rationally is essential
to answer such questions. For instance, experimentally measurable quantities
such as bubble expansion dynamics or local temperature and concentration
measurements can guide simulations to pinpoint a working mechanism. A working
mechanism should explain all the observations listed above, particularly ones
related to physical disturbances around the thermocaviation bubble
(observation 5). Also, observations 2, 4 are shared between NPLIN and HILIN.
Moreover, it should shed light on questions such as “Is it possible to compare
NPLIN and HILIN directly and provide a common theory to explain these
phenomena?” An overarching physical reasoning supported by experiments is
required to answer this question. Furthermore, wider implementation of the
HILIN hinges on a complete mechanistic understanding.

##  4 Laser trapping-induced crystallization (LTIC)

###  4.1 Phenomenology

Laser trapping, also known as optical trapping, is a technique that allows the
controlled manipulation of particles and molecules using a tightly focused
continuous-wave laser beam, which exerts light-induced momentum on matter. The
fine manipulation ability can be used, for instance, in the assembly of
composite nanostructures98 and cell sorting99. It is a versatile laser-induced
phenomenon that can be applied to chemistry, physics, and bioscience research
as it is contactless, non-photochemical and non-destructive 100, 101, 102. The
technique was first demonstrated by Ashkin et al.103 using particles ranging
from 25 nm to 10 $\mu m$. Later on, it was seen that besides enabling the
manipulation of molecules and molecular clusters, the electric field induced
by the laser trapping also promoted the local increase of supersaturation in
solution, consequently inducing nucleation events. Thus, the technique shows
potential for spatiotemporal control of crystallization104, 105, crystal
growth 106 and polymorph control107, 108, 109.

According to Masuhara et al.21, laser trapping effects can be divided into
three categories: ‘just trapping’, ‘extended trapping’, and ‘nucleation and
growth’, see Figure 18. The first takes place when the optical force or
optical potential induces the gathering of nano-objects or the formation of
clusters around the focal volume - these clusters disassemble when the laser
is turned off. If the gathering of molecules and molecular assemblage grows
outside the focal volume, possibly due to the combined effects of laser
trapping with heat and mass convection or intermolecular interactions, then
‘extended trapping’ is taking place. Finally, one or both of the previous
effects can induce nucleation and, consequently, crystal growth.

Figure 18: Categorization of the phenomena induced by laser trapping in an
optical potential, according to Masuhara et al.21

While both NPLIN and HILIN are performed with pulsed laser beams of short
duration (femto- to nanoseconds), for the application of optical trapping,
continuous lasers with varying exposure times (from tens of seconds to hours)
are used. Long exposures can promote the assembly of solutes, inducing both
phase separation and nucleation. Long exposure times using 1064 nm laser have
been reported to elevate solution temperature by around 23 K/W in H2O and 2
K/W in D2O 110. Yuyama et al. reported that temperature elevation also varies
with the concentration of the solute108. Upon trapping, the authors estimated
temperature increases of 6.8, 6.0, and 5.4 K/W for supersaturated, saturated,
and unsaturated solutions, respectively. Thus, most reported studies have used
D2O as a solvent to suppress local temperature elevation caused by light
absorption (Table 4).

###  4.2 Proposed mechanisms

Despite being widely studied, the development of an accurate theoretical model
for optical trapping is still based on approximations102. A plausible
mechanism was proposed by Ashkin et al.103, based on photon forces using two
different cases, depending on the size of the object/molecule ($d$) and the
wavelength of the incident light ($\lambda$). When $d\gg\lambda$, the photon
force is explained using Mie scattering theory (ray optics approximation) -
i.e. the refraction of light by the object changes the light’s momentum which
generates a force. If $d\ll\lambda$, for molecules or clusters foregoing
nucleation, the optical trapping of an object can be explained using
Rayleigh’s theory (dipole approximation), in which the potential energy $U$
for laser trapping is given by

$\displaystyle U=\frac{(-\alpha|E|^{2})}{2}$ (6)

$\displaystyle\alpha=4\pi\epsilon_{2}r^{3}\frac{(\frac{n_{1}}{n_{2}})^{2}-1}{(\frac{n_{1}}{n_{2}})^{2}+2}$
(7)

where $E$ is the electric field vector of the incident light. $\alpha$ is the
“polarizability” of the particle to be trapped, $r$ is the radius of the
particle, and $\epsilon_{2}$ is the dielectric constant of the surrounding
medium. $n_{1}$ and $n_{2}$ are the refractive indices of the particle and the
surrounding medium, respectively. Note that, for the dipole approximation, the
electromagnetic fields inside the particle under trapping are assumed to be
homogeneous.

The optical forces are proportional to particle polarizability, which in turn
depends on the particle volume and laser power. Since polarizability decreases
with lower particle volume, trapping single molecules is particularly
difficult as the optical forces cannot compete with Brownian motion.
Therefore, the condition for stable trapping of a particle is $U\gg k_{B}T$,
where $k_{B}$ and $T$ are Boltzmann’s constant and the absolute temperature of
the system, respectively111, 112, 113. The dipole gradient force can optically
trap a wide range of small molecules as long as its refractive index ($n_{1}$)
is larger than the refractive index of the solution ($n_{2}$). This includes
small metallic nanoparticles ($d<$50 nm) and biological molecules, as
previously reported by several authors114, 115, 112, 25, 116.

Once the target molecule or cluster is trapped, more molecules start to
aggregate, resulting in an increase in volume and stronger radiation pressure.
Thus, a nonlinear increase in concentration with time can be seen, which may
induce liquid-liquid phase separation (LLPS) or crystal nucleation117. Since
the energy condition necessary for stable laser trapping to occur is ($U\gg
k_{B}T$), the radius of the trapped particle should be much larger than the
radius of a single molecule. Considering the solutes reported so far -
inorganic salts, small organic molecules, and proteins - this implies that
only a cluster of molecules or molecular aggregates can be trapped.

In addition to laser trapping forces, aggregation of amino acid molecules
(which undertake zwitterionic structure with a large dipole moment in aqueous
solutions) is accompanied by Coulombic interactions and hydrogen bonding118.

Thermodynamically, an explanation using the classical nucleation theory (CNT)
relies on the fact that growing nuclei have an energetically unfavorable
surface-to-volume ratio that hinders the formation of the crystalline state.
As a result, the nucleation depends uniquely on random fluctuations of the
cluster, until a critical radius is reached. However, the two-step nucleation
theory challenges CNT by claiming the existence of pre-nucleating clusters
since nucleation can be enhanced by choosing a concentration near its ‘oiling
out’ point. In this condition, the critical concentration fluctuations would
give rise to liquid-like crystal droplets with very high concentrations and a
high probability of nucleus formation. Under such circumstances, it would be
easier for an external force to manipulate concentration.26, 119

Walton and Wynne26, 119 presented a theoretical model based on the solution
model of mixing. The authors showed that the concentration-dependent free
energy can be manipulated near a critical point, and that optical tweezers can
pull the high-refractive index liquid out of the mixture. The basic idea
behind the model by Walton and Wynne is that the nucleation process can be
compared to a chemical reaction where the nucleus is the product and the
solute in the supersaturated solution is the reactant. When the focused laser
is turned on, the product state has its free energy lowered, even if the
nuclei are not yet formed. For this reason, the equilibrium would be displaced
towards the products, thus increasing the driving force for nucleation to
happen by reducing the energy necessary. Hence, the nucleation (“reaction”)
rate is increased. They called this process laser-induced phase separation
(LIPS), which later can be followed by nucleation (LIPSAN - laser-induced
phase separation and nucleation). The solution model of mixing was used to
demonstrate how easily the free energy can get around the critical molar
concentration. To account for the effect of the optical tweezing, the total
electromagnetic energy stored in the laser volume was incorporated into the
total free energy. Experiments performed to validate the model used a 785 nm
continuous-wave diode laser (maximum incident power 200 mW in elliptical mode
with a beam radius of 2.4 $\mu$m) focused by a 10x objective. Their model
showed that the optical trapping creates a zone of enhanced concentration with
a high refractive index within the exposed volume and, consequently, a
depletion zone around it, thus indicating phase separation. They also showed
that increases in the laser power provided deeper laser traps which enhanced
phase separation.

Figure 19: Depiction of a generic liquid-liquid phase diagram displaying the
effects of both heating and laser-induced phase separation26

Considering the schematic phase diagram provided by Walton and Wynne26 (Figure
19), which displays the combined effects of LIPS and heating, three possible
scenarios are possible, namely (e), (f), and (g). In the figure, panel (a)
represents the laser heating effect; (b) represents the enriched volume
surrounded by a depleted region, using the dot and the circle, respectively;
(c) the cooling after the laser is switched off and (d) the exposed volume
going back to equilibrium. In both situations (f) and (g) depleted and
enriched droplets will, due to fast cooling, fall into the unstable region
after the laser is off. For the enriched droplet, according to the lever rule,
phase separation will increase its concentration while reducing its size,
until it eventually fades. Thus, it is the depleted region that triggers phase
separation, which explains why the reported nucleation happens outside the
laser-exposed volume. For LIPSAN, LIPS will first generate the region enriched
with the compound with a high refractive index, and a depletion zone will form
around it. Upon switching off the laser, both regions, rich and poor, will
rapidly cool. The nuclei will then be formed in the depleted region. The
authors have correlated their model with the results described for previous
bulk NPLIN studies because the product, in general, shows a higher refractive
index than the initial state (some exceptions were also reported, e.g. laser-
induced gas bubble nucleation55 and pure glacial acetic acid nucleation37 in
which the refractive index of the products was lower). Most importantly, in
this model, nucleation (phase separation, if liquid-liquid) does not rely on
pre-existing clusters to be trapped and aggregated but on the laser creating a
potential that lowers the free energy of the solid (phase-separated) state.

###  4.3 Experimental setups

Figure 20: Example of a generic basic laser trapping setup. Adapted from
Shilpa et al.120

Laser trapping can be achieved by focusing a laser beam through an objective
lens with a high magnification, i.e. concentrating the laser power in a very
small area (typical diameter of a few microns). To achieve this, a simple
experimental setup can be built by coupling the laser source with an optical
microscope. This way, the objective can be used to both focus the laser beam
and image the sample using a camera. An example of a generic laser trapping
setup is shown in Figure 20. The figure shows a collimated laser beam that
passes by a dichroic mirror, which reflects the laser light toward the
objective. This allows the light coming from the source in a different
direction to reach the camera 120. Typical sample holders are similar to those
in Figure 16a and b, where (b) has been reported to be used both in the
absence and presence of preexisting crystals. The type of sample holder used
in each study is compiled in Table 4, along with other experimental
conditions.

###  4.4 Reported solutions

####  4.4.1 Small organic molecules

The first works on laser trapping used an intense continuous wave Nd3+-YVO4
laser beam (Neodymium-doped yttrium orthovanadate - 1064 nm) and a 40x
objective at the air solution interface of a supersaturated D2O glycine
solution121. For these experiments, supersaturated glycine solutions were
placed over a glass slide covered with a glass dish. Glycine crystals were
seen after $16\text{\,}\mathrm{s}$ of laser irradiation which kept growing
with further irradiation. The authors observed second harmonic generation
(SHG) during the trapping of a growing crystal. This was related to the
formation of $\gamma$-glycine polymorph that presents the chiral space group
(P31 or P32) required for SHG. The formation of large glycine clusters within
the solution was related to the large dipole moments of glycine. After being
trapped by the intense focused laser beam due to increased interactions
between clusters at the focal spot, these clusters would grow into critical
nuclei.

Sugiyama et al.106 showed the effect of laser trapping on glycine crystal
growth rate. For the experiments, a droplet of glycine solution was placed in
a covered glass slide (Figure 16b) until crystals were spontaneously formed.
Then, the laser beam was focused near the seed crystal. The crystal growth
rate was observed to be enhanced from the seed crystal toward the focal point
and completely stopped when the crystal reached the focal spot. When more than
one crystal was present, only one crystal showed growth while others dissolved
until they eventually vanished. This was explained in terms of Ostwald
ripening, using the differences in the surface free energy of the crystals.
The results also showed that a local higher concentration of glycine is
created by the laser beam not only at the focal point, but also in its
surroundings. This is attributed to the suppression of glycine diffusion by
the photon pressure at the focus of the beam as the laser traps large liquid-
like clusters.106.

Laser trapping-induced crystallization was also reported for undersaturated
solutions of glycine in D2O104. In this work, solutions were prepared with
concentrations of 50 and 68 % of the solubility limit. The authors considered
that glycine forms liquid-like clusters in solution (as reported by
Chattopadhyay et al.122). Since the solutions are undersaturated, the liquid-
like clusters were considered to be locally formed and transient. Exposure
times in these experiments were around 400 s. The photon pressure traps some
of the clusters at the focal point, promoting increased interaction within
these clusters which then leads to nucleation. However, when crystals grow
bigger than the focal spot, dissolution takes place as there is no photon
pressure to bring together more clusters. Dissolution continues until the
crystal reaches a size smaller than the focal spot, where it then grows again
and repeats the cycle.

In a different study, also using glycine in heavy water, Yuyama et al.123
describe the formation of a phase-separated glycine droplet of millimeter
dimensions (5 mm), much larger than the laser focal point. This was achieved
by focusing a 1064 nm CW laser through a 60x objective to the glass-solution
interface over $200\text{\,}\mathrm{s}$. They also reported a reduction in the
sample thickness along the laser light (from glass to air-solution interface),
from 130 to approximately 5 $\mu$m, along with the formation of a liquid-
liquid phase-separated droplet. The lowering of the sample thickness was
attributed to the heterogeneous distribution of the surface tension due to
temperature gradients. Further laser irradiation led to an increase in surface
thickness to approximately 145 $\mu$m and a droplet size increase. These
phenomena were attributed to an increase in glycine concentration around the
focal point due to the trapping of clusters, which presents a higher
refractive index. These droplets, consisting of high concentrations of
glycine, were seen to last a few tens of seconds even after the laser was
turned off. By focusing the laser at the air-solution interface, glycine
crystallization took place. Similar changes in the height of the solution -
from 130 to 5 $\mu$m, then increasing to 30 $\mu$m - were also observed when
nucleation occurred for approximately $20\text{\,}\mathrm{s}$ of laser
irradiation. Since both nucleation and the highly concentrated droplet were
seen after the changes in surface height (depression followed by elevation),
it was argued that a phase-separated droplet is formed right before
crystallization takes place.

While the above studies were made using glycine solutions in D2O, Masuhara and
others124 have investigated laser trapping-induced nucleation of saturated
glycine solutions in H2O, using a 1064 nm laser beam focused through a 60x
objective. After 30 s of laser irradiation at the air-solution interface, a
liquid-like domain was observed. The domain was not stable at the focal point
but it was seen to grow continuously and float away, probably due to
convection induced by a local increase in temperature. When this growing and
floating process stopped, the domain immediately turned into a well-defined
crystal. The experiments were repeated 10 times, showing the exact same
behavior. It was hypothesized that in water, the high-concentration domain
immediately turns into a crystal when the laser is stopped because the
temperature increase is suppressed, leading to a supersaturation spike. Time-
wise, the temperature elevation affects the rate of formation of the
concentrated domain for glycine in H2O so that it is comparable to the
nucleation time in the D2O solutions. Therefore, the domain is only visible
because the crystallization is hindered by the temperature increase,
otherwise, nucleation would take place faster due to the concentration
increase.

Yuyama et al.125 studied laser trapping of urea in heavy water for different
saturations (0.28 and 1.36) at room temperature, with a 1064 nm continuous-
wave linearly polarized laser beam at 1.1 W power. By focusing the laser at
the glass-solution interface, for the undersaturated solution, the formation
of concentrated droplets was observed, as previously reported for glycine106,
104. However, no crystallization was observed, regardless of the focal point
position. This was explained by the increase in temperature that sharply
reduces the supersaturation in urea-heavy water solutions. For urea, only
crystal growth and dissolution were observed when the laser focal point was
close to the surface of an existing crystal.

In their work, Tsuboi et al.118 used a CW Nd3+:YAG laser ($\lambda$ = 1064 nm)
to show that the photon forces of a near-infrared (NIR) focused laser beam are
able to manipulate molecular clusters of several amino acids via optical
trapping. They described the trapping of glycine, D,L-proline, D,L-serine, and
L-arginine in D2O with different laser power thresholds, based on the
compound. The laser power was varied from 0.6 W to 2.0 W with irradiation
times up to 30 min.

Yuyama et al.126 showed laser trapping-induced nucleation of L-phenylalanine
using a continuous wave Nd3+:YVO4 laser focused through a 60x objective even
for an undersaturated aqueous solution at
$25\text{\,}\mathrm{\SIUnitSymbolCelsius}$. Crystals were seen after 170 s of
laser exposure (1.1 W). This phenomenon was explained by the increase of local
supersaturation due to laser trapping of liquid-like clusters. Plate-like
crystals were formed, which corresponds to the anhydrous polymorph of
L-phenylalanine. This polymorph is only expected to form at temperatures
higher than $37\text{\,}\mathrm{\SIUnitSymbolCelsius}$, thus its formation
confirmed the temperature increase due to the laser trapping - which the
authors estimated to be around $25\text{\,}\mathrm{\SIUnitSymbolCelsius}$.
Further continuation of the laser trapping led to crystal growth. However,
contrary to what was observed by Rungsimanon et al.104, L-phenylalanine always
showed continuous growth and no dissolution. This was hypothesized to be due
to either heating, optical or electrostatic effects. The heating effect would
create convection and constantly supply molecules/clusters to the growing
surface. The optical effect would be promoted by the propagation of incident
light through the crystal, generating optical potential at the growing
surface. Lastly, the electrostatic effect would indicate that the laser
locally charged the crystal surface, attracting loose clusters from the
solution to the surface of the crystal. To investigate which of the
hypothesized effects was responsible for the phenomenon, an experiment was
performed where polystyrene particles (1$\mu$m) were added to the solution
right after crystal nucleation. With the laser off, these particles were
observed to exhibit Brownian motion around the crystal. When the laser was
turned on, these particles immediately aligned themselves toward the crystal
edges. The immediacy of the response and the observation of some optical
trails within the crystals pointed to the optical effect. Thus, trapping was
considered to be achieved by light propagation inside the crystal, confirmed
by crystal growth, and even tunable by changing laser power. Optical trails
were attributed to the optical anisotropy of the crystal.

In the same context, Yuyama et al.127 have also measured the 2D growth rate of
the single plate-like anhydrous crystal of L-phenylalanine, which was seen to
directly depend on the laser power. In a later paper from the same group128,
L-phenylalanine three-dimensional crystal growth was studied, aiming at the
changes in the thickness of the nucleated crystals, by applying reflection
imaging - introduction of white light along with the optical trap so that
constructive interference of the white light at the upper and lower faces of
the crystal can be observed. The growth rate in the direction related to
thickness was seen to be constant during laser trapping, while it decreased in
the direction parallel to the solution surface. This behavior was explained by
the thickness growth being directly promoted by the optical force from the
laser, while in the other directions it is promoted by the optical force
generated by the light propagation within the crystal.

In an attempt to couple the effects of enhanced laser trapping and laser
ablation, Wu et al.129 reported the nucleation and polymorph conversion of
L-phenylalanine by using femtosecond laser trapping (800 nm, 100 fs, 80 MHz).
Both undersaturated and supersaturated solutions were tested by focusing the
laser at the air-solution interface. In unsaturated solutions, no immediate
change was seen at the start of irradiation. After 3 minutes, a bright light
emission, indicating optical breakdown and the formation of several bubbles at
the focal point, was seen. After 12 minutes, plate-like crystals were
observed, compatible with the anhydrous polymorph of L-phenylalanine, which
continuously grew upon further irradiation. Interestingly, after some time,
whisker-like crystals (monohydrate) started to form at the surface of the
plate-like growing crystal. Both crystals dissolved when the laser was turned
off. The threshold for crystallization under these conditions was identified
to be 150 – 300 mW, which is estimated to be 3-4 times lower than with
continuous lasers (1064 nm) with a 2 times shorter crystallization time. The
crystallization was attributed to a combined effect of optical pressure and
cavitation bubbles. The supersaturated solutions were used to prepare
spontaneous whisker-like crystals which were then irradiated with the
femtosecond laser. After crystal formation, the remaining solution was
considered to be saturated and the laser was now focused near the glass-