# Viologen-based supramolecular crystal gels:
gelation kinetics and sensitivity to temperature

Julien Bauland  ENS de Lyon, CNRS, Laboratoire de physique, UMR 5672, F-69342
Lyon, France  Vivien Andrieux  ENS de Lyon, CNRS, LCH, UMR 5182, 69342, Lyon
cedex 07, France  Frédéric Pignon  Univ. Grenoble Alpes, CNRS, Grenoble INP,
LRP, F-38000 Grenoble, France  Denis Frath<EMAIL_ADDRESS>ENS de
Lyon, CNRS, LCH, UMR 5182, 69342, Lyon cedex 07, France  Christophe Bucher
<EMAIL_ADDRESS>ENS de Lyon, CNRS, LCH, UMR 5182, 69342, Lyon
cedex 07, France  Thomas Gibaud<EMAIL_ADDRESS>ENS de Lyon, CNRS,
Laboratoire de physique, UMR 5672, F-69342 Lyon, France

###### Abstract

Supramolecular crystal gels, a subset of molecular gels, form through self-
assembly of low molecular weight gelators into interconnecting crystalline
fibers, creating a three-dimensional soft solid network. This study focuses on
the formation and properties of viologen-based supramolecular crystalline
gels. It aims to answer key questions about the tunability of network
properties and the origin of these properties through in-depth analyses of the
gelation kinetics triggered by thermal quenching. Experimental investigations,
including UV-Vis absorption spectroscopy, rheology, microscopy and scattering
measurements, contribute to a comprehensive and self-consistent understanding
of the system kinetics. We confirm that the viologen-based gelators
crystallize into nanometer radius hollow tubes that assemble into micro to
millimetric spherulites. We then show that the crystallization follows the
Avrami theory and is based on pre-existing nuclei. We also establish that the
growth is interface controlled leading to the hollow tubes to branch into
spherulites with fractal structures. Finally, we demonstrate that the gel
properties can be tuned depending on the quenching temperature. Lowering the
temperature results in the formation of denser and smaller spherulites. In
contrast, the gels elasticity is not significantly affected by the quench
temperature, leading us to hypothesize that the spherulites densification
occurs at the expense of the connectivity between spherulite.

##  I Introduction

Supramolecular crystal gels represent a subset of molecular gels [1],
characterized by the self-assembly of low molecular weight gelator into
crystalline fibers that interconnect to create a three-dimensional soft solid
network [2, 3, 4, 5, 6]. These gels find applications in many fields such as
food [7], cosmetics, drug delivery [8], tissue engineering [9], organic
electronics [10] or chemical sensing [11]. They have also proved useful as
templates for materials synthesis [12], and for artwork conservation [13]. In
addition, the reversible nature of the interactions involved in the assemblies
gives these materials the ability to respond to different stimuli such as
heat, light and sound.[14]

We have recently demonstrated that supramolecular crystal gels exhibiting
remarkable ionic conductivities can be obtained from viologen-based low
molecular weight gelator [6]. As can be seen in Fig. 1, this gelator
$Chol_{2}V^{2+}$ consists of two cholesteryl arms covalently linked to a
4,4’-bispyridinium plateform (best known as viologen. This dicationic molecule
is not only redox- and photo-active, it is also capable of interacting with
its environment through a wide range of “weak” van der Wall, electrostatics or
Donor/Acceptor interactions. We have shown in previous works that a
temperature quench triggers a spontaneous self-assembly of those monomers in
hollow tubes. Those tubes then grow to form spherulite ultimately percolating
into a crystal gel network.

In general, viologen based gelators $V^{2+}$ present numerous advantages for
creating conductive gels and hybrid materials. Beyond supplying two mobile
counter anions, they have the potential to engage in electron transport
through two consecutive one-electron reductions yielding stable radical
cations $V^{+\bullet}$ and dianions $V^{0}$. These electron-responsive
properties have already been extensively utilized in the development of
molecular machines, electrochromic devices, and organic batteries [15, 16].
Viologens have also been widely used as mediators in catalysis and sensing[17,
18] or more recently to enhance charge transport in single molecule [19, 20]
and large-area molecular junctions [21, 22]. However, only a few examples of
supramolecular gels involving viologen-based gelators can be found in the
literature. Viologen-based gels have for instance been obtained upon
exploiting their ability to form charge transfer complexes [23, 24, 25, 26,
27]. Gels have also been obtained by functionalizing the bipyridinium core
with selected functions facilitating self-assembly, including van der Waals
interactions [28], H bonds [29], Coulomb forces [30], or metal-ligand bonds
[31, 32, 33].

In continuation of our previous works in the field [6], we now report detailed
analyses of the mechanical and structural properties of supramolecular crystal
gels obtained by self-assembly of the cholesteryl-appended viologen
$Chol_{2}V^{2+}$ (Fig. 1a). We have already demonstrated that the
$Chol_{2}V^{2+}$-based solution undergoes crystallization into fibers, which
grow into fractal spherulites, ultimately forming a gel. However, the
crystallization mechanism and how the gel properties are influenced by
temperature quench remain unknown. Can we tune the network properties, such as
its elasticity and its structure, based on the temperature quench depth $T$?
Can we rationalize the origin of these properties by studying the gelation
kinetics, including the evolution of elastic and viscous moduli, the growth of
crystalline spherulites, and the development of the network structure? This
work aims to provide answers to these key questions and to improve our
understanding of the complex phenomena involved in the formation of
supramolecular gels.

Figure 1:  Characterization of the fibrous network in gel samples (a) Chemical
structure of the viologen gelator $Chol_{2}V^{2+}$, composed of a
4,4’-bipyridinium unit bearing two cholesteryl substituants. (b)
Microstructure of the gel assessed by small-angle X-ray scattering
measurements. The scattering intensity $I(q)$ (circles) at high $q$ is best
modeled by the form factor of a hollow cylinders (green curve). The inset
figure represents the scattering length density profile of the hollow
cylinder, with $\Delta\rho=\rho_{1}-\rho_{2}=5.10^{-7}\leavevmode\nobreak\
\rm{\AA}^{-2}$ the difference of scattering length densities between the
solvent and the viologen gelator. $r_{i}=5.2\leavevmode\nobreak\ \rm nm$ and
$t_{s}=2.6\leavevmode\nobreak\ \rm nm$ are the core radius and shell thickness
of the cylinder, respectively. (c)-(d) Fibrous structure of the gel observed
by transmission electron cryomicroscopy and atomic force microscopy,
respectively.

As outlined in [34], the properties of supramolecular crystal gels depend
mainly on three factors: (i) the way and type of crystals formed; (ii) the
process by which the crystals grow and finally (iii) the way in which the
crystals percolate and interact to establish a space-spanning elastic network.

The first stage is specific to the nature of the gelator molecule. The early
stage of crystallization is driven by thermodynamics [3], specifically by the
difference in chemical potential between the solution and the crystal:
$\Delta\mu=\mu_{\text{sol}}-\mu_{\text{Xtal}}$. When $\Delta\mu>0$, the system
becomes supersaturated, a thermodynamic prerequisite for the onset and
progression of a crystalline phase. In this metastable state, the
concentration of the solute $C$ exceeds the maximum solubility $C_{eq}$, i.e.
the solution contains more dissolved solute than it would typically
accommodate under equilibrium conditions at a specified temperature and
pressure. The driving force for crystallization can then be expressed in terms
of supersaturation, defined as $\sigma\simeq(C-C_{\text{eq}})/C_{\text{eq}}$.
In the protocol we used, the solutions are prepared at $T=80$ °C to improve
the solubility of the gelator, followed by cooling which reduces the
solubility and causes crystallization and gelation.

A common approach for quantifying the early stage of crystallization kinetics
involves use of the Avrami equation [35]. Introduced by the Soviet scientist
M. Avrami, this equation has found widespread use in diverse fields, including
materials science, metallurgy, chemistry, and physics [36]. The equation
establishes a relationship between the evolution of the crystal fraction $X$
and time $t$ through a reaction rate $k$, taking the form:

$X=1-e^{-kt^{n}}$ (1)

The Avrami exponent $n$ [36, 37] is a dimensionless parameter that
encapsulates the nucleation growth mechanism through $n_{G}$, the
dimensionality of growth through $d$, and the nucleation rate index through
$n_{N}$:

$n=n_{N}+dn_{G}\\\ \text{with
}\begin{cases}n_{G}=&\begin{cases}0.5&\text{diffusion controlled-growth}\\\
1&\text{interface controlled-growth}\end{cases}\\\ d&\text{dimension of the
growth}\\\ n_{N}=&\begin{cases}0&\text{pre-existing nuclei}\\\
[0,1]&\text{decreasing nucleation rate}\\\ >1&\text{increasing nucleation
rate}\end{cases}\end{cases}$ (2)

In our case, the viologen-based gelators crystallize as fibers [6]. The
nucleation rate index $n_{N}$ and whether fiber growth is interface-controlled
($n_{G}=1$) as in [38, 39, 40], or diffusion-controlled ($n_{G}=0.5$) as in
[41, 42], remain unknown.

In the second stage, fibers may grow to form more complex structures. All our
studies conducted so far on gels formed with $Chol_{2}V^{2+}$ support the
conclusion that the crystal fibers undergo branching under the effect of
crystallographic mismatches, ultimately forming spherulites [43, 3, 44, 45].
This process, known as ”Fiber Tip Branching”, occurs at high supersaturation
values, at which point nucleation and growth with crystallographic mismatches
take place at the tips of the fibers, leading to branching. The resulting
spherulites exhibit radial arms growing from a primary nucleation center
branching into Cayley-like tree structures.

However, it remains unclear how these spherulites contribute to the formation
of a 3D network. Do the branches entangle between neighboring spherulites, or
do branches stick to one another due to attractive interactions? Predictions
[46, 47, 48, 49] were made at the macroscopic level to establish a direct link
between the crystal gel structure and its mechanical properties. In this
context, the spherulites are best described as Cayley trees of size $\xi$ and
fractal dimension $d_{f}$ composed of branching segment of length $l$ and
radius $a$. Based on simulations, Shi et al. [43] assimilated the gel
elasticity to that of the spherulites. In [46, 47, 48, 49], the authors
proposed a model derived from the Avrami model [35] that links the temporal
evolution of the elastic modulus to the fractal dimension $d_{f}$ of the
crystal gel network. The model establishes that $X$, the ratio of the volume
fraction of crystal material at time $t$ to the volume fraction at
$t\to\infty$, is linked to the evolution of the norm of the complex viscosity
$\eta^{*}$ through the equations
$X=\frac{|\eta^{*}|-|\eta^{*}(0)|}{|\eta^{*}_{\infty}|-|\eta^{*}(0)|}$ and
$\ln(1-X)=k(t-t_{g})^{d_{f}}$, assuming $n_{N}=0$ and $n_{G}=1$ et Eq. 2.

In the present study, we utilize Small Angle X-ray Scattering (SAXS) and
transmission electron cryomicroscopy (CryoTEM) to establish that the viologen-
based gelators [6] crystallize in the form of hollow tubes. Then, we establish
the dependence of crystal supramolecular gel properties on the quench
temperature: lowering the quench temperature prompts the growth of hollow
tubes into smaller spherulites, a phenomenon observed through microscopy, and
denser structures, as inferred from Ultra Small Angle Light Scattering
(USALS). Interestingly, rheological measurements reveal seemingly constant gel
elasticity across all tested temperature quenches. Next, our focus shifts to
gelation kinetics, aiming to precisely understand the origin of the influence
of temperature quench on the final gel properties. We first focus on
identifying the growth mechanism by tracking the spherulite growth under
microscope. We then measure using UV-Vis absorption spectrosopy the crystal
fraction $X$ and fit its time evolution with the Avrami equation. Those two
complementary analysis allow us to conclude that the crystallization is based
on pre-existing nuclei, the growth is interface controlled and undergo
branching due to crystallographic mismatch to afford in fine spherutlites
displaying fractal structures. Finally we explore the evolution of the viscous
$G^{\prime\prime}$ and elastic $G^{\prime}$ moduli. We demonstrate that the
model derived from the Avrami equation is inadequate [43, 3, 44, 45] for
describing the time evolution of $G^{\prime\prime}$ and $G^{\prime}$. Instead,
the rheological properties must depend on both the elasticity of the
spherulites and the nature of their connections.

##  II Material and methods

###  II.1 Viologen-based gelator

The viologen-based gelator used for all experiments is a cholesteryl-
substituted viologen noted $Chol_{2}V^{2+}$ (Fig. 1a). It was obtained as a
bromide salt $V(Br)_{2}$ using a protocol described previously [6]. The
gelation ability of $Chol_{2}V^{2+}$ was first reported by Xue et al., who
demonstrated that the gel fibrillar network could be efficiently used as a
template for obtaining monodisperse mesoporous silica [28]. Our previous work
showed that self-assembly of $Chol_{2}V^{2+}$ in 1-Pentanol relies on the
formation of charge transfer (CT) complexes between $Chol_{2}V^{2+}$ (acceptor
unit) and halide ions, $Br^{-}$ or $I^{-}$ (donor unit). The anions associated
with the dicationic species $Chol_{2}V^{2+}$ play a major role in the self-
assembly process and that the rheological, optical and electrical properties
of the gels can be tuned by the addition of salts. We also showed that the
addition of lithium bis(trifluoromethanesulfonyl) ($LiTFSI$) helps to increase
the solubility of $Chol_{2}V^{2+}$ in pentanol but that too much TFSI anions
can prevent gelation. Addition of $TBAI$ also increases the amount of donors
species available to form the $[Chol_{2}V^{2+}/I^{-}]$ CT complexes promoting
gelation but yields opaque gels displaying high gelation temperature. An
optimal composition of $TBAI$ and $LiTFSI$ has thus been determined to obtain
a translucent and robust gel featuring a moderate gelation temperature and a
high ionic conductivity [6]. This study specifically focuses on this optimal
composition consisting of $Chol_{2}V(Br)_{2}$ (1.3 mM, 0.2 wt%), $TBAI$ (50
mM), and $LiTFSI$ (100 mM) in 1-Pentanol. In all experiments, the sol-gel
transition was induced by thermally quenching homogeneous solutions at a rate
of $\sim 0.6^{\circ}$C/s from 80 ∘C to a final temperature $T$ using a Peltier
module. The shallower quench where carried out to a final temperature
$T=50^{\circ}$C while the deeper quenches where carried out down to
$T=20^{\circ}$C.

###  II.2 Transmission Electron Cryo-microscopy (CryoTEM)

The mixture (0.2 wt%, 100 mM $TFSI$, 50 mM $TBAI$ in pentanol) was heated
until full solubilization using a hair dryer. 4 $\mu$L of the liquid sample
were collected using an Eppendorf pippette cone. For the freezing process, the
liquid sample was then quickly injected on a TEM grid placed in the
thermalized chamber of the plunge freezing device (Thermo Fisher Vitrobot) at
40∘C. After around 10 s on the grid, the excess liquid was absorbed using
filter paper (1s blotting time) and the sample was vitrified in liquid ethane
at a temperature of -170 ∘C Finally, the frozen samples were transferred to
the TEM cryogenic sample holder (Fischione model 2550), and was maintained at
a temperature of -172 ∘C during the TEM observations. Experiments were
performed under an accelerating voltage of 120 kV with a JEOL 1400Flash TEM
equipped with a Gatan RIO 16 Mpx camera at Centre Technologique des
Microstructures (CT$\mu$, Université Claude Bernard Lyon 1, Villeurbanne,
France).

###  II.3 Rheology

Rheological characterizations were conducted using a stress-controlled
rheometer (Anton Paar MCR301) employing a smooth parallel-plate geometry
(diameter of 35 mm) with a 0.5 mm gap. Samples were preheated in the liquid
state and introduced into the rheometer, which was thermalized at
85${}^{\circ}C$. To prevent evaporation of the organic solvent, the outer edge
of the geometry was filled with a fluorinated oleophobic liquid (Fomblin ®Y
25/6) [50]. The sol-gel transition was induced by thermally quenching the
sample using a Peltier module embedded in the bottom plate. The loss
$G^{\prime\prime}$ and elastic $G^{\prime}$ moduli were recorded over time at
a frequency $f=0.1$ Hz and strain amplitude $\gamma=0.1$ %. The gel
viscoelastic spectrum was recorded from $f=10^{1}$ to $10^{-2}$ Hz at a strain
amplitude $\gamma=0.1$ %.

###  II.4 Bright field microscopy

Microscopy measurements were performed using a Nikon Ti-eclipse inverted light
microscope operating in bright-field mode. A Zyla camera from Andor, equipped
with a 10× objective, was employed to capture images of the samples. A 455 nm
led lamp (M455, Thorlabs) was used as a light source, which significantly
improved the contrast of the images due to the large absorption band of the
gel centered at 440 nm [6]. Samples, initially in the liquid state, were
loaded into custom optical cells consisting of a microscope borosilicate glass
slide and a cover slip separated by a 200 µm thick double-sided adhesive
spacer to ensure airtightness (Gene Frame, Thermo Scientific). The sol-gel
transition was induced by thermally quenching the sample using a dedicated
Peltier cell (MHCS120i, Microptik). Image analysis was conducted using MATLAB
(version: 9.13.0.2320565) and the Image Processing Toolbox (version 11.6).
Images were segmented by first removing large background structures using a
bottom-hat filter. Second, the branched structure of the growing spherulites
was ”filled” using successive morphological erosion and dilatation steps,
which afterwards improved their contour detection. Finally, thresholding was
performed using an hysteresis method. The edge detection of the spherulites in
the binary images was then performed using the matlab function regionprops,
allowing to calculate their area $A$ as function of time and an equivalent
sphere radius $r=\sqrt{A/\pi}$. The matlab code used for the image analysis
can be found in Supplementary materials.

###  II.5 Small Angle X-ray Scattering (SAXS)

Small Angle X-ray Scattering was conducted at the SWING beamline (Synchrotron
Soleil, Saint-Aubin, France) [51]. The samples were enclosed in 1 mm
borosilicate capillaries (WJM-Glass Muller GmbH) and positioned in a thermally
controlled holder (Linkam Scientific Instruments, Tadworth, UK). The beam
energy was set to 12 KeV. To derive the scattering intensity $I(q)$ as a
function of norm of the scattering wave vector $q$, the two-dimensional
scattering profiles of the viologen suspension and the background solvent were
subtracted. The resulting scattering intensity remained isotropic, and an
azimuthal average was performed to obtain a one-dimensional $I(q)$.

###  II.6 Ultra Small Angle Light Scattering (USALS)

Ultra small angle light scattering (USALS) was performed on a laboratory-made
setup as described in [52]. Briefly, the sample is illuminated with a 2 mW
laser beam (He-Ne, $\lambda=632.8$ nm) and the forward scattered light is
focused with a Fresnel lens on a monochrome digital camera (AV MAKO G-419B
POE, Allied Vision). 2D scattering images were processed using a specifically
developed software (Vimba Matlab), allowing to regroup and average scattering
data with SAXSutilities software [53]. The scattering intensity remained
isotropic for all samples and an azimuthal average was performed to obtain a
one-dimensional intensity $I(q)$, with $q$ the scattering vector given by
$q=(4\pi/\lambda)\sin(\theta/2)$, where $\lambda$ the wavelength of the light
and $\theta$ the scattering angle. Gel samples were prepared between slide and
a cover slip and heated to 85∘C before being quenched at a final temperature
$T$ for 3h. The gel samples were then mounted on the USALS setup and $I(q)$
was measured at room temperature. After a 3-hour quench at $T$, we verified,
using optical microscopy, that the gel structure remained unchanged when left
at room temperature.

###  II.7 UV-Vis absorption spectroscopy

Kinetic evolution of the absorption spectra was recorded during the sol-gel
transition using an MCS 601 UV-NIR spectrophotometer, operating in the
$\lambda=250$ to $1000$ nm range. As for microscopy imaging, samples were
prepared between a slide and a cover slip and the temperature was controlled
with a Peltier cell. Absoprtion spectra of samples prepared for the measurment
of supersaturation concentration (see Appendix V.1) were recorded using the
same spectrophotometer operating in the $\lambda=200$ to $800$ nm range.

##  III Results and discussion

###  III.1 Self assembly at the local scale

We have recently demonstrated that the gel forms macroscopic spherulites
composed of nano-fibers [6]. As illustrated in Fig. 1b, the fine-scale
structure of these fibers is well characterized by SAXS measurements. The
scattered intensity $I(q)$ plotted against the modulus of the scattering
vector $q$ is accurately described, for $q>0.1$ nm-1, by a hollow core–shell
cylinder model [54] with a well defined inner radius $r_{i}=5.2$ nm and shell
thickness $t_{s}=2.6$ nm, resulting in a total diameter of 15.6 nm. This fit
is corroborated by electron microscopy images where single or bundles of
fibers can be observed [Fig. 1(c)]. Besides, electron microscopy images
indicates that fiber branching occurs through an self-epitaxial nucleation
mechanisms rather than a fiber tip branching mechanism [5]. The fibers are
further structured into a percolated and fractal-like network, as revealed by
in situ imaging of the gel using fluid immersion atomic force microscopy [Fig.
1(d)].

###  III.2 Effect of the thermal quench on the gel structure and rheology

Figure 2: (a)-(c) Microstructure of the gel determined from light microscopy
after a thermal quench at T = 35 (yellow), 40 (orange) 45 (red) and 50∘C
(violet), respectively. (e) Scattering curves $I(q)$ vs. $q$ of the gels
obtained from light scattering. Black curve is the best power law fit
$I(q)\sim q^{-p}$ for $4.10^{-4}<q<1.10^{-3}$ nm-1. Inset displays the the
power exponent $p_{s}$ as function of the quench temperature. Errors bars are
the standard deviation obtained from 10 replicates. (f) Storage (G′) and loss
(G′′) moduli as function of the frequency ($f$). Inset displays the averaged
storage modulus $\overline{G}^{\prime}(f)$ as function of the quench
temperature.

We first investigate the effect of the quench temperature $T$ on the final
properties of the gels, i.e. after reaching a steady state as observed from
microscopy imaging or rheometric measurements. The micrographs displayed in
Fig. 2(a)-(d) reveal that the size of the spherulites decreases with $T$, down
to few tens of microns at 35∘C. Besides, the small spherulites formed at low
$T$ appear more contrasted and therefore denser. In Fig. 2(e), we characterize
the inner structure of the spherulites on length scales ranging from 2 to 500
µm using USALS. The USALS scattering intensity $I(q)$ displayed against the
scattering wave vector $q$ exhibits a power law behavior $I\propto q^{p_{s}}$
for $4.10^{-4}<q<1.10^{-3}$ nm-1. The inset graph in Fig. 2(e) shows that
$p_{s}$ ranges between 1.7 and 2.5, indicating that the spherulites display a
fractal organization with a fractal dimension $d_{f}=p_{s}$ [2]. The later
increases as $T$ decreases, indicating that the spherulites are more compact
when formed at low $T$, which is consistent with the visual inspection of the
spherulites in microscope images. The mechanical spectra displayed in Fig.
2(f) show that for all quench temperatures, the gels display typical
viscoelastic behavior of a soft solid, with the elastic modulus
$G^{\prime}(f)$ showing no clear dependence with the frequency and dominating
the viscous modulus $G^{\prime\prime}(f)$. Besides the elasticity of the gel
does not show any clear dependence on $T$ and is about $10^{3}$ Pa.

###  III.3 Supersaturation as function of temperature

Figure 3: Supersaturation measurements. (a) Corrected absorption spectra (see
Appendix V.1) recorded in a 1 mm optical cell (quartz) after applying the
syringe (lines, temperature is color-coded from black 80 ∘C to orange 20 ∘C)
and the centrifuge methods (dash blue at $T=20$ ∘C) to gel samples quenched at
different temperatures; The inset graph shows the maximum concentration
$C_{eq}$ of the gelator deduced from the intensity of the absorption band at
265 nm using the absorption coefficient of
$\epsilon_{\lambda=265nm}^{path=1cm}=27000$ mol/L/cm. The dotted line is the
initial concentration in gelators ($C=1.3$ mM) and the dashed line delimits
the gel state obtained at low temperatures. (b) Evolution of $\ln(C_{eq})$ as
a function of $1/T$. The red line is the best fit.

The changes observed in the structural and mechanical properties of the gel
stem from the variation of the supersaturation $\sigma=(C-C_{eq})/C_{eq}$ with
$T$, where the initial concentration of the gelator is $C=1.3$ mM. The maximum
solubility at equilibrium $C_{eq}$ was measured using two different techniques
(see Appendix V.1). In the first technique, we centrifuged the mature gel at
$10^{4}\leavevmode\nobreak\ g$ for 10 minutes at $T$, then recovered the
supernatant at $C_{eq}$. In the second technique, we embedded the gel in a 1
mL syringe and recover the supernatant at $C_{eq}$ by pressing the gel through
a filter (Appendix V.1). Following mass conservation, we also deduced the
concentration of $Chol_{2}V^{2+}$ integrated in the crystal network:
$C_{X}=C-C_{eq}$. In both cases, the concentration $C_{eq}$ was determined by
UV-vis absorption spectroscopy measurements based on the peak intensity at
$\lambda=265$ nm. Fig. 3(a) demonstrates that both techniques yield similar
results. In Fig. 3(a-Inset), we display the evolution of $C_{eq}$ as function
of $T$. We observe, as expected, that $C_{eq}$ decreases when the quenches
become deeper, i.e. as $T$ decreases. The Gel state is only observed below 50
∘C. In Fig. 3(b), we show that the solubility follows a Van’t Hoff law :
$\ln(1/C_{eq})=-\Delta_{r}H/RT+\Delta_{r}S/R$. According to the fit
parameters, we found $\Delta_{r}H=-37\pm 2$ kJ/mol and $\Delta_{r}S=-56\pm 8$
J mol-1K-1. This thermodynamic data are consistent with thermodynamic data
reported for the self-assembly of cholesterol derivatives [55, 56].

###  III.4 Gelation kinetics

In this section, we relate the gelation kinetics and the structure of the gels
using crystal growth and nucleation models. Accordingly, we monitor the
gelation at different quench temperature using microscopy, UV-Vis absorption
spectroscopy and rheology measurements. This synergetic approach aims to
identify the mechanisms at play during the gelation process.

Figure 4: Gelation kinetics assessed by SAXS upon cooling at 0.5∘C$/$s. The
azimuthally averaged intensity $I(q)$ is displayed vs. the wave vector $q$ at
different times during the cooling ramp. The first scattered signal was
measured at T = 27∘C (bottom curve) and acquisitions were performed every
$5\leavevmode\nobreak\ \rm s$. Indicated time corresponds to the time elapsed
since the beginning of the temperature quench from $T=90\leavevmode\nobreak\
\rm^{\circ}C$. Red curves represent the form factor of a core shell cylinder
with constant parameters: core radius $r_{i}=5.5\leavevmode\nobreak\ \rm$,
shell thickness $t_{s}=2.9\leavevmode\nobreak\ \rm nm$ and cylinder length
$L=700\leavevmode\nobreak\ \rm nm$.

Hallow fibers nucleation – Using time-resolved SAXS during the temperature
quench, we monitor the formation of the hallow fibers, Fig 4. The analysis of
the scattering intensity $I(q)$ indicates that the gelators assemble directly
into hollow tubes. Their geometrical properties, the core radius
$r_{i}=5.5\leavevmode\nobreak\ \rm$ and the shell thickness
$t_{s}=2.9\leavevmode\nobreak\ \rm nm$ remains unchanged during the kinetics.
This evidences that crystalline fibers self-assemble into hollow cylinders,
without intermediary structure allowing us to rule out mechanisms where the
gelators self-assembles into large 2D sheets that subsequently fold into tubes
[57, 58]. We also observe that the intensity of the scattering intensity
increases with time indicating that the fibers concentration increases to
rapidly form spherulite on larger length scales.

Growth of the spherulites – Moving to the macroscopic scale, we now focus on
the spherulite growth. Within the nucleation and growth framework, the process
can be either interface-controlled or diffusion-controlled [36, 37]. In the
next, the growth mechanism is determined by measuring the temporal evolution
of the spherulite size $r\propto t^{n_{G}}$ from microscopy data.

Individual spherulite radius $r$ were determined by automatic image processing
as described in the Material and Methods section. The very low contrast of the
spherulites formed at 50∘C did not allow for satisfying edge detection by our
tracking algorithm, and only the gels formed at $T$ = 35, 40 and 45 °C were
investigated (see Appendix V.2). Besides, spherulites could only be detected
when their size exceeded 20 $\mu$m. Consequently, we define the nucleation
time $t^{micro}_{N}$ as the time needed to obtain spherulites with diameters
of 50 µm, well above the detection limit of the algorithm.

Figure 5: Growth kinetics of spherulites assessed by bright field microscopy
measurements. (a) Example of edge detection during the growth of a spherulite
at $T=45^{\circ}$C. From top to bottom, $t_{1}<t_{2}<t_{3}$. (b) Equivalent
radius $r$ of the spherulite displayed in (a) as function of time. The times
corresponding to each image of (a) are indicated in magenta. Plain black curve
is the best linear fit of the data obtained from the tracking algorithms.
Dotted black curves is an extrapolation of the linear growth of the spherulite
up to its final size. (c) Nucleation time $t_{n}$ as function of the
temperature of quench. (d) Growth rate $\overline{v}$ of individual
spherulites as function of the temperature of quench. (e) Final radius
$\overline{r}_{\infty}$ of the spherulites as function of the temperature of
quench. Error bars are standard deviations.

A typical evolution of a spherulite radius $r$ with time $t$ is shown in Fig.
5(a)-(b) . We observe that $r$ increases linearly over time with a velocity
$v$ [Fig. 5(b)]. On larger timescales, the spherulite size saturates to reach
a maximum value $\overline{r}_{\infty}$. The linear evolution of the
spherulite size with time is indicative of an interface-controlled growth
mechanisms with $n_{G}=1$, where the limiting step of the growth process is
the assembly of viologen-gelators into crystalline fibers. In Fig. 5(d), the
average growth speed $\overline{v}$ is about 2 µm.s-1 and this value decreased
slightly when the quench temperature increases [Fig. 5(d)], highlighting that
the diffusion of gelators is not the limiting step of the spherulite growth
process. In contrast with $\overline{v}$, the nucleation time $t^{micro}_{N}$
and the average final spherulite radius $\overline{r}_{\infty}$ show a clear
dependence with $T$, and increase when the quench temperature increases [Fig.
5(c) and Fig. 5(e)].

Those variations were also observed in other systems [38, 39, 40] and can be
rationalized with variations of the driving force $\sigma$ upon changing the
quench temperature. When the growth process is controlled by surface kinetics,
it was concluded that variations in the driving force have much more effects
on the nucleation rate $J$ than on the growth speed [40]. This is consistent
with the small effect of $T$ on $\overline{v}$ and the increase of
$t^{micro}_{N}$ with $T$. Associated with the lower nucleation rate at high
$T$, the spherulites have less neighbors and are allowed to grow further,
explaining the dependence of $\overline{r_{\infty}}$ with $T$. Besides, SALS
experiments have shown that the fractal dimension of the spherulites decreases
with $T$. For an heterogeneous nucleation mechanisms, the average branching
length $l$ depends on the speed growth and on the nucleation rate according
$l=\overline{v}/J$. Consequently, as $\overline{v}$ is roughly constant and
$J$ decreases with $T$, the spherulite formed at high quench temperature are
less branched with a lower fractal dimension.

In the following sections, we relate the fractal dimension of the spherulites
with the macroscopic kinetics of gelation assessed by UV-Vis absorption
spectroscopy and rheology measurements.

Figure 6: Growth kinetics assessed by UV-vis absorption spectroscopy
measurements. (a) Absorbance spectra recorded over time after thermal quench
at 35∘C. (b) Crystallinity of the system $X_{abs}$ as a function of the time
elapsed since the nucleation time $t_{n}$. Colors code for the temperature of
quench: T = 35 (yellow), 40 (orange) 45 (red) and 50 ∘C (violet). $X_{abs}$ is
calculated from the time-evolution of the absorbance of the charge transfer
band at $\lambda=440$ nm, according to
$X_{abs}(t)=[A_{CT}(t)-A_{CT}(t=0)]/[A_{CT}(t=\infty)-A_{CT}(t=0)]$, with
$A_{CT}(t=0)$ and $A_{CT}(t=\infty)$ the absorbance at $t=t_{N}^{abs}$ and
$t=\infty$. Black curves represent the Avrami relation which parameters are
determined in (c)-(f). Inset displays a semi-log plot of the same data.
(c)-(f) Avrami plots of the data displayed in (b). Black line is the best
power law fit of the data. The power exponent $p_{abs}$ is displayed in (g) as
function of the quench temperature $T$. (h) Nucleation time $t_{N}^{abs}$ as
function of the temperature of quench.

Evolution of the crystal fraction – In a crystallization process, the kinetics
of the reaction can be related to the mechanisms of gelation, especially the
dimension of growth, using the Avrami equation [35]. The extent of the
reaction is typically assessed by the fraction of the crystalline phase with
respect to the gelator concentration in solution. In Fig. 6(a), we display the
evolution of the absorbance $A$ during the self-assembly of $Chol_{2}V^{2+}$
at 35∘C. We observe 3 main contributions to the absorption signal. In the low
wavelength range ($\lambda<350$ nm) we observe the tail of the viologen-
centered $\pi-\pi^{*}$ absorption band ($\lambda<270$ nm). At $\lambda=370$ nm
and on short time scales, the large absorption band is attributed to solvated
charge transfer species $[Chol_{2}V^{2+}/I^{-}]_{sol}$ [59]. Upon self-
assembly of the gelator, this CT band grows and is progressively shifted to
longer wavelength, resulting in a broad absorption peak centered at
$\lambda=440$ nm. The observed shift is attributed to the aggregation of
charge transfer complexes $[Chol_{2}V^{2+}/I^{-}]_{agg}$ which are structuring
elements of the supramolecular fibers. As previously described by Nishikiori
et. al. [60], this red shift of the CT band can be attributed to an increase
in the electronic delocalization upon aggregation of the
$[Chol_{2}V^{2+}/I^{-}]$ CT complexes. In the following, we focus on the broad
adsorption signal at $\lambda=440$ nm.next, we focus on the broad adsorption
peak at $\lambda=440$ nm. We established that the absorbance of the charge
transfer band at $\lambda=440$ nm, $A_{CT}$, is proportional to the
concentration of crystal fibers and follows the Beer-Lambert law, (see
Appendix V.3). The intensity of the UV absorption band at $\lambda=440$ nm
thus provides a direct estimation of the crystal fraction
$X_{abs}(t)=\frac{A_{CT}(t)-A_{CT}(t=0)}{A_{CT}(t=\infty)-A_{CT}(t=0)}$. We
note $t_{N}^{abs}$, the nucleation time measured by UV absorption
spectroscopy, define as $A_{CT}(t_{N}^{abs})=0.05$ [Fig. 6(h)]. The evolution
of $X_{abs}$ as a function of the reduced time $t-t_{N}^{abs}$ is displayed in
Fig. 6(b) for different quench temperatures.

Inspired by earlier reports [2, 47], we use the Avrami representation
$-\ln(1-X_{abs})$ vs. $t-t^{abs}_{N}$ [Fig. 6(c)-(f)]. In this representation,
we observe three regimes. At short time scales, $-\ln(1-X_{abs})$ evolves
slowly with time. At intermediate time scales $-\ln(1-X_{abs})$ follows a
power law evolution with an exponent $p_{abs}$:
$\ln(1-X)=k(t-t^{abs}_{N})^{p_{abs}}$. At long time scales $-\ln(1-X_{abs})$
tends to plateau as the gelation reaction is finished. The early time scales
regime pertains to the initial stage of the self-assembly of the gelator into
hollow tubes. We propose that a cooperative supramolecular polymerization
mechanism occurs during this process, where the formation of a tubular
structure strongly promotes the self-assembly of $Chol_{2}V^{2+}$[61],
resulting in an apparent ’instantaneous growth’ of the fibers. This hypotheses
is backed up by two observations. First, when we plot $A(t)-A(t=0)$ (see
Appendix V.4), thus removing the contribution of the peak at $\lambda=370$ nm,
we observe that both the shape and position along the $\lambda$-axis of the
broad adsorption peak at $\lambda=440$ nm remain unchanged. This suggests that
at the interaction scales, the viologen gelators consistently interact in the
same manner and likely do not assemble into structures other than hollow tubes
in agreement with the time resolved SAXS presented in Fig. 4. The intermediate
time scale regime allows us to determine the Avrami exponent $n$ in Eq. 2,
here denoted $p_{abs}$. In Fig. 6(g), $p_{asb}$ is consistent with the fractal
dimension $d=p_{SALS}$ determined from scattering measurements, and decreases
with $T$ [Fig. 2(e)]. Given that $n_{G}=1$ as determined from microscopy
measurements, and since we identified that $d=p_{abs}=p_{SALS}$, this suggests
that $n_{N}\approx 0$, indicating either pre-existing nuclei conditions or a
decrease in the nucleation rate.

At this stage, we have validated the Avrami model and demonstrated that the
viologen gelator crystallizes into hollow tubes, forming fractal spherulites.
The growth conditions are determined by three factors: interface-controlled
growth, the presence of pre-existing nuclei, and the relevant growth dimension
being the fractal dimension of the spherulite.

Figure 7: Growth kinetics assessed by small-angle oscillatory rheometry
measurements. (a) Evolution of the rescaled elasticity
$\tilde{G^{\prime}}=G^{\prime}/A_{CT}(t=\infty)$ with the rescaled time
$t/t_{n}$. $\tilde{G^{\prime}}$ accounts for the variation crystallized
gelator concentration with the temperature estimated by $A_{\infty}$, the
final absorbance at $\lambda=440$ nm. Colors code for the temperature of
quench: T = 35 (yellow), 40 (orange) 45 (red) and 50∘C (violet). Inset
displays the time-evolution of the storage (G′) and loss (G′′) moduli. (b)
Crystallinity of the system $X_{rheo}$ as function of the time elapsed since
the gel time $t_{g}$, estimated by the cross-over between G${}^{\prime}(t)$
and G${}^{\prime\prime}(t)$. $X_{rheo}$ is calculated from the time-evolution
of the complex viscosity $\eta^{*}$, according to
$X_{rheo}(t)=(\eta^{*}(t)-\eta_{0})/(\eta^{*}_{\infty}-\eta_{0})$, with
$eta_{0}$ the penthanol viscosity at the temperature of quench. Black curves
represent the Avrami relation which parameters are determined in (c)-(f).
(c)-(f) Avrami plots of the data displayed in (b). Black line is the best
power law fit of the data. The power exponent $p_{rheo}$ is displayed in (g)
as function of the temperature of quench. (h) Gel time $t_{g}$ as function of
the temperature of quench.

Evolution of the gel mechanical properties – Finally, we assess the
macroscopic kinetics of gelation using rheometric measurements. Fig. 7(a)
displays the temporal evolution of the elastic modulus $G^{\prime}$ and the
viscous modulus $G^{\prime\prime}$ for different quench temperatures. At short
time scales, $G^{\prime\prime}$ dominates over $G^{\prime}$, while at longer
time scales, $G^{\prime}$ surpasses $G^{\prime\prime}$. This behavior is
characteristic of a sol-gel transition, and we estimate the gel time $t_{g}$
as the time for which $G^{\prime}>G^{\prime\prime}$. The gelation times
displayed in Fig. 7(h) are of the same order of magnitude than the nucleation
times determined from microscopy and UV-Vis absorption spectroscopy
measurements, as expected from the large growth speed of the fibers ($\approx
2$ µm.s-1). At low quench temperatures, the viscoelastic moduli undergoes a
small decrease after reaching a maximum value [Fig. 7(a)]. This behavior is
attributed to negative normal forces, resulting from a contraction of the gel
as reported for bio-polymer gels [62]. In the inset graph of Fig. 7(a), we
rescale the elastic modulus by the absorbance value $A_{CT}$ to account for
variations in the concentration of crystallized gelator with $T$. When
displayed against the rescaled time $t/t_{g}$, $\tilde{G^{\prime}}$ reaches a
plateau value equals to about 1000 Pa for all quench temperatures. In previous
reports, the elasticity of multi-domain networks increased with a decrease of
$\overline{r}_{\infty}$ [5]. Given the strong variations of the final
spherulite radius $\overline{r}_{\infty}$ and fractal dimension with $T$ [Fig.
5(e) and Fig. 2(e)], the present results suggest that the mesoscopic structure
of the gel has little effect of its mechanical properties. However, potential
differences may be masked by the small value of the gap ($e=500$ µm). The
final spherulite radius ($200\leq\overline{r}_{\infty}\leq 800$ µm)
approximately matches the value of $e$, indicating that rheometric
measurements predominantly assess the elasticity of the fibers or more
localized interactions, such as fiber side branching, rather than the
elasticity of the spherulites themselves [34, 5, 43, 63]. In line with the
work of Liu and coworkers [2, 3, 64], the fraction of crystalline phase $X$ of
a fiber network could be deduced from the norm of the complex viscosity
$\eta^{*}=(G^{\prime}+iG^{\prime\prime})/\omega$, where $\omega$ is the
angular frequency of small amplitude oscillation used to measure the
viscoelastic moduli. By applying Einstein’s relation
($\eta/\eta_{0}=(1+2.5\phi)$), one may connect the normalized viscosity and
volume fraction of spherulite $\phi$. Accordingly, the fraction of crystalline
phase at a given time is calculated as
$X_{rheo}=\frac{|\eta^{*}(t)|-|\eta^{*}(t=0)|}{|\eta^{*}(t=\infty)|-|\eta^{*}(t=0)|}$.
In Fig. 7(b), $X_{rheo}$ is displayed as a function of the reduced time
$t-t_{g}$ for different quench temperatures. As with UV-vis absorption
spectroscopy measurements, we use Avrami plots $-\ln(1-X_{rheo})$ vs $t-t_{g}$
to determine the Avrami exponents [Fig 7(c)-(e)]. In Fig. 7(g), we found that
the exponents determined from rheological measurement $p_{rheo}$ are comprised
between 3.6 and 2.3, and are thus overestimated in comparison with exponents
determined from scattering and UV-Vis absorption spectroscopy measurements
(Fig. 2(d-inset) and Fig. 6(g)). We cannot identify $p_{rheo}$ to $d$ as we
identified $p_{abs}$ and $p_{SALS}$ to $d$ in the Avrami equation Eq. 2. We
believe that these discrepancies stem from the assumption of the linear
relation between the viscosity of the solution and the volume fraction $\phi$,
which is not valid in the present system. Indeed, the Einstein’s relation was
derived in the case of a hard sphere suspension in diluted regime. While the
spherulites may behave like a dilute suspension during the early stages of
crystallization (i.e., $t<<t_{g}$), the spherulites grow and interact to form
network for $t\geq t_{g}$, with numerous relaxation modes [65].

Finally, we surprisingly observe that the elasticity of the final gels (Fig.
2(f-Inset)) is not significantly affected by the quench temperature. One could
have indeed expected that gels formed at lower temperatures would exhibit
greater elasticity due to the formation of denser and smaller spherulites [43]
and to an increase in the concentration of the gelator incorporated in the gel
network. We therefore suspect that the elasticity of the gel stems from both
the spherulite elasticity and the way they connect to one another. While the
spherulite elasticity certainly increases with lower quench temperatures as
they become denser, we hypothesize that their connections become weaker. In
other words, the spherulites densification occurs at the expense of the
connectivity between spherulites leading to an elastisticity which does not
vary significantly with the quench temperature.

##  IV Conclusion

In conclusion, this study sheds light on the formation and characteristics of
viologen-based supramolecular crystal gels, a subset of molecular gels formed
by self-assembly of low molecular weight gelators into interconnected
crystalline fibers, resulting in a three-dimensional soft solid network. Our
in-depth analyzes of the gelation kinetics triggered by thermal quenching
reveal the tunability of the 3D network and provide clear insights into the
mechanism of gel formation.

Experimental analyses, encompassing UV-Vis spectroscopy, rheology, microscopy,
and scattering experiments, provide a comprehensive understanding of the
system’s kinetics. We first confirm that the viologen-based gelator
$Chol_{2}V^{2+}$ crystallizes into nanometer-radius hollow tubes, which
further assemble into micro to millimetric spherulites. Then, we demonstrate
the spherulite growth is consistent with the Avrami theory. Local
characterization of the growth kinetics using optical microscopy and USALS
techniques allowed us to determine independently the exponents in the Avrami
model (Eq. 2: $n=n_{N}+dn_{G}$). It reveals that the crystallization process
is driven by pre-existing nuclei ($n_{N}=0$), with growth controlled by
interfaces ($n_{G}=1$) and characterized by branching resulting in the
formation of fractal spherulites of fractal dimension $d$. Finally, our
results demonstrate the possibility of adjusting the gel properties by varying
the quenching temperature. Lowering the quenching temperature leads to the
formation of denser and smaller spherulites. We establish that the elastic
properties of the gel cannot be described by the model proposed in [2, 3, 64].
We speculate that the elasticity of the gel stems from both the spherulite
elasticity and the way they connect to one another: the spherulites
densification obtained at low quenching temperature occurs at the expense of
the connectivity between spherulite. This comprehensive analysis provides
valuable insights into the design and manipulation of supramolecular crystal
gels.

We are now considering studying the growth of fibers between electrodes using
this thermal control in combination with other stimulation: magnetic/electric
field, mechanical stress etc. This could lead to materials with controlled
organization and orientation of the fibers opening up very promising
perspective for the study and modulation of the electronic conductivity in
this type of supramolecular assemblies.

##  V Appendix

###  V.1 Experimental conditions used to determine $C_{eq}$

In order to measure the supersaturation concentration $C_{eq}$ in Fig. 3(a),
samples of same initial composition ([$VBr_{2}$] = 1.3 mM, [$LiTFSI$] = 100
mM, [$TBAI$] = 50 mM in pentanol) were quenched at different temperatures
(20°C, 30°C, 40°C, 45°C, 50°C and 60°C) then filtered (Rotilabo-syringe
filter, PTFE filter, 0.20 µm pore size) to recuperate the gelator that did not
participate to gel network. All samples were prepared in Eppendorf 2mL tube
and were homogenized at 80°C and 1500 rpm in the Eppendorf Thermomix C (this
device will be called Thermomix1), the obtained hot solutions were then
maintained at 80°C. A second Eppendorf Thermomix device was set at to the
quench temperature $T$ (this device will be called Themomix2), Teflon filters
were at all time stored in Themomix2. In order to perform the filtration at
thermal equilibrium at $T$ we used the following protocole. A plastic syringe
was left for 10 minutes at 80°C in Thermomix1, then the syringe was used to
take 0.9mL of hot solution. The full syringe was then quickly placed in
Thermomix2, set at a temperature $T$, the syringe was maintained at this
temperature for a time $t_{therm}$ allowing thermal equilibrium to be reached.
Once thermal equilibrium was reached the sample was filtered on the
thermalized Teflon filter, the filtrate was recovered and diluted (from a
factor between 1 and 10). An absorbance spectrum $A_{filtered}$ was measured
from the diluted filtrate, the measured absorbance spectra was then multiplied
by the applied dilution factor in order to obtain the corrected absorbance
data in Fig. 3(a). One of the samples prepared at 80°C was not filtered and
simply diluted by a factor 10 in order to be used as a reference, the obtained
corrected absorbance is noted $A_{ref}$. The value of $C_{eq}(T)$
corresponding to the solubility of $Chol_{2}V^{2+}$ was then calculated from
the corrected absorbance values at 265nm (corresponding to $\pi-\pi^{*}$
absorption band of the viologen) using the relation:
$C_{eq}=(A_{filtered}(T))/A_{ref}\times 1.3$ mM. The time needed to reach
equilibrium was estimated through the rheological measurements of growth
kinetics reported in Fig. 7(a) and is noted $t_{min}$. The time $t_{therm}$
were chosen accordingly to the $t_{min}$ values such that $t_{therm}>t_{min}$
for all temperatures. The sample corresponding to the 60°C data was left
overnight (22h) at 60°C before filtration. All the data from these experiments
are available in Table Tab. 1.

T | Sample | tmin | ttherm | Dilution | A265nm | A265nm | Ceq
---|---|---|---|---|---|---|---
(°C) | processing | (min) | (min) | factor | measured | corrected | (mM)
20 | centrifugation | 5 | 10 | 1 | 0.515 | 0.515 | 0.19
20 | filtration | 5 | 10 | 1 | 0.520 | 0.520 | 0.19
30 | filtration | 5 | 10 | 2 | 0.48 | 0.96 | 0.35
40 | filtration | 8 | 10 | 2 | 0.62 | 1.24 | 0.45
45 | filtration | 34 | 45 | 4 | 0.44 | 1.76 | 0.64
50 | filtration | 75 | 140 | 4 | 0.52 | 2.08 | 0.75
60 | filtration | / | 1320 | 10 | 0.340 | 3.40 | 1.22
80 | none | / | 60 | 10 | 0.36 | 3.60 | 1.3
Table 1: Data corresponding to $C_{eq}$ measurements

###  V.2 Radius of the spherulites over time

Average quantities in Fig.5 are calculated from the measurements shown in
Fig.8, where we illustrate the evolution of the radius of the spherulites as a
function of time. These measurements were obtained using bright field
microscopy and determined through automatic image processing.

Figure 8: Evolution of the radius of the spherulites obtained using bright
field microscopy for samples at (a) $T=35$, (b) $40$ and (c)
$45\leavevmode\nobreak\ ^{\circ}$C.

###  V.3 Absorption spectra of the viologen Iodine $VI_{2}$ used to determine
the Beer Lambert law.

In order to characterize the formation of ${Chol_{2}V^{2+}/I^{-}}$ CT
complexes in the absence of any other anionic species the viologen salt
$VI_{2}$ was prepared using the following protocol. Compound $VBr_{2}$ (0.410
g, 0.32 mmol), $LiTFSI$ (3.494 g, 6.4 mmol) and 400 mL technical $EtOH$ were
introduced in a 1L round bottom flask and refluxed overnight under stirring.
80% of the solvent was evaporated under reduced pressure, 200mL water were
added and the mix was left in the fridge overnight. The mix was filtered on
and washed with 3x40mL water. The white solid was then dried under vacuum,
420mg of colorless solid was recovered. This solid was dissolved in 20 mL
acetone, Tetrabuthylammonium iodide (820 mg, 2.2mmol) were added and the mix
was stirred at room temperature for 1h. The mix was filtered and washed with
acetone (3x20mL). $Chol_{2}VI_{2}$ was obtained as an orange solid in 73%
yield. The evolution of the UV-Vis absorption spectrum of $Chol_{2}VI_{2}$ is
displayed in Fig. 9(a). In Fig. 9(b), we observe that the absorption at
$\lambda=440$ nm increase linearly with $Chol_{2}VI_{2}$ concentration leading
to an adsorption coefficient is $\epsilon_{\lambda=450nm}^{path=1cm}=6.3\pm
0.3\times 10^{3}$ mol/L/cm.

Figure 9: a) Absorption spectra obtained at 20°C from $VI_{2}$ solutions and
gels in pentanol (2mm quartz cuvette). Samples were prepared after applying a
heating cooling cycle to $VI_{2}$ suspensions in 1-Pentanol. b) Evolution of
the Absorbance at 440 nm with the concentration in $VI_{2}$. The continuous
red line to the best linear fit.

###  V.4 Absorption peak at $\lambda=450$ nm

Fig. 10 represents the results of a slight modification of the data analysis
of the absorption spectrum plotted in Fig. 6(a). In Fig. 10, we have indeed
subtracted to the absorption $A(t)$ the absorption signal acquired at
$t=t_{N}$ to highlight that the evolution of the $[Chol_{2}V_{2}^{+}/I^{-}]$
CT band observed upon gelation corresponds to the growth of a unique
absorption signal centered at $\lambda=450$ nm.

Figure 10: Evolution of sample absorption during the first minute following
nucleation at 35°C. The absorption signal at $t=t_{N}$ was used as a baseline
and subtracted from the other spectra. The experiment corresponds to the data
displayed Fig. 6(a).

## Author contributions

JB, VA, FP and TG carried out the experiments. JB and VA analysed the data. JB
and TG wrote the article. DF, CB and TG designed and managed the project. All
authors participated to the discussion of the data and the editing of the
text.

## Conflicts of interest

There are no conflicts to declare.

## Acknowledgment

This work was supported by the Région Auvergne-Rhône-Alpes “Pack Ambition
Recherche”, the LABEX iMUST (ANR-10-LABX-0064) of Université de Lyon, within
the program ”Investissements d’Avenir” (ANR-11-IDEX-0007), the ANR grants
(ANR-18-CE06-0013 and ANR-21-CE06-0020-01) and by the ”Mission pour les
initiatives transverses et interdisciplinaires” MITI CNRS. This work benefited
from meetings within the French working group GDR CNRS 2019 “Solliciter LA
Matière Molle” (SLAMM) and Block Allocation Group (BAG) at the beamline SWING
with Javier Perez at Soleil obtained via the GDR SLAMM. We thank the Centre
Technologique des Microstructures (CT$\mu$), Université Claude Bernard Lyon 1,
Villeurbanne, France, for the CryoTEM measurements. We acknowledge the Ecole
Normale Supérieure de Lyon (ENSL) and the Centre National de la Recherche
Scientifique (CNRS) for financial, logistical, and administrative supports. V.
A. thanks ENSL for the CDSN PhD Grant.

## Data availability

Data and/or code will be made available on request by contacting the authors.

## References

  * Weiss and Terech [2006] R. G. Weiss and P. Terech, Molecular gels, Materials with Self-Assembled Fibrillar Networks (2006).
  * Liu and Sawant [2001] X. Y. Liu and P. D. Sawant, Formation kinetics of fractal nanofiber networks in organogels, Applied Physics Letters 79, 3518 (2001).
  * Liu and Sawant [2002] X. Y. Liu and P. D. Sawant, Determination of the fractal characteristic of nanofiber-network formation in supramolecular materials, ChemPhysChem 3, 374 (2002).
  * Lescanne  _et al._ [2003] M. Lescanne, A. Colin, O. Mondain-Monval, F. Fages, and J.-L. Pozzo, Structural aspects of the gelation process observed with low molecular mass organogelators, Langmuir 19, 2013 (2003).
  * Li and Liu [2010] J. L. Li and X. Y. Liu, Architecture of supramolecular soft functional materials: From understanding to micro-/nanoscale engineering, Advanced Functional Materials 20, 3196 (2010).
  * Andrieux  _et al._ [2023] V. Andrieux, T. Gibaud, J. Bauland, T. Divoux, S. Manneville, S. Guy, A. Bensalah-Ledoux, L. Guy, F. Chevallier, D. Frath, and C. Bucher, Chiral and conductive viologen-based supramolecular gels exhibiting tunable charge-transfer properties, J. Mater. Chem. C 11, 12764 (2023).
  * Pernetti  _et al._ [2007] M. Pernetti, K. van Malssen, D. Kalnin, and E. Flöter, Structuring edible oil with lecithin and sorbitan tri-stearate, Food Hydrocolloids 21, 855 (2007).
  * Webber and Langer [2017] M. J. Webber and R. Langer, Drug delivery by supramolecular design, Chemical Society Reviews 46, 6600 (2017).
  * Saunders and Ma [2019] L. Saunders and P. X. Ma, Self-healing supramolecular hydrogels for tissue engineering applications, Macromolecular bioscience 19, 1800313 (2019).
  * Ajayaghosh  _et al._ [2008] A. Ajayaghosh, V. K. Praveen, and C. Vijayakumar, Organogels as scaffolds for excitation energy transfer and light harvesting, Chemical Society Reviews 37, 109 (2008).
  * Kartha  _et al._ [2012] K. K. Kartha, S. S. Babu, S. Srinivasan, and A. Ajayaghosh, Attogram sensing of trinitrotoluene with a self-assembled molecular gelator, Journal of the american chemical society 134, 4834 (2012).
  * Van Bommel  _et al._ [2003] K. J. Van Bommel, A. Friggeri, and S. Shinkai, Organic templates for the generation of inorganic materials, Angewandte Chemie International Edition 42, 980 (2003).
  * Carretti  _et al._ [2010] E. Carretti, M. Bonini, L. Dei, B. H. Berrie, L. V. Angelova, P. Baglioni, and R. G. Weiss, New frontiers in materials science for art conservation: responsive gels and beyond, Accounts of chemical research 43, 751 (2010).
  * Jones and Steed [2016] C. D. Jones and J. W. Steed, Gels with sense: Supramolecular materials that respond to heat, light and sound (2016).
  * Striepe and Baumgartner [2017] L. Striepe and T. Baumgartner, Viologens and their application as functional materials, Chemistry–A European Journal 23, 16924 (2017).
  * Kathiresan  _et al._ [2021] M. Kathiresan, B. Ambrose, N. Angulakshmi, D. E. Mathew, D. Sujatha, and A. M. Stephan, Viologens: a versatile organic molecule for energy storage applications, Journal of Materials Chemistry A 9, 27215 (2021).
  * Fang  _et al._ [2018] W. Fang, Y. Zhang, J. Wu, C. Liu, H. Zhu, and T. Tu, Recent advances in supramolecular gels and catalysis, Chemistry – An Asian Journal 13, 712 (2018).
  * Dzhardimalieva  _et al._ [2020] G. I. Dzhardimalieva, B. C. Yadav, S. Singh, and I. E. Uflyand, Self-healing and shape memory metallopolymers: state-of-the-art and future perspectives, Dalton Trans. 49, 3042 (2020).
  * Chen  _et al._ [2021] H. Chen, V. Brasiliense, J. Mo, L. Zhang, Y. Jiao, Z. Chen, L. O. Jones, G. He, Q.-H. Guo, X.-Y. Chen, _et al._ , Single-molecule charge transport through positively charged electrostatic anchors, Journal of the American Chemical Society 143, 2886 (2021).
  * Li  _et al._ [2021] J. Li, S. Pudar, H. Yu, S. Li, J. S. Moore, J. Rodríguez-López, N. E. Jackson, and C. M. Schroeder, Reversible switching of molecular conductance in viologens is controlled by the electrochemical environment, The Journal of Physical Chemistry C 125, 21862 (2021).
  * Nguyen  _et al._ [2018] Q. V. Nguyen, P. Martin, D. Frath, M. L. Della Rocca, F. Lafolet, S. Bellinck, P. Lafarge, and J.-C. Lacroix, Highly efficient long-range electron transport in a viologen-based molecular junction, Journal of the American Chemical Society 140, 10131 (2018).
  * Han  _et al._ [2020] Y. Han, C. Nickle, Z. Zhang, H. P. Astier, T. J. Duffin, D. Qi, Z. Wang, E. Del Barco, D. Thompson, and C. A. Nijhuis, Electric-field-driven dual-functional molecular switches in tunnel junctions, Nature materials 19, 843 (2020).
  * [23] K. V. Rao, K. Jayaramulu, T. K. Maji, and S. J. George, Supramolecular hydrogels and high-aspect-ratio nanofibers through charge-transfer-induced alternate coassembly, Angewandte Chemie International Edition 49, 4218.
  * Datta  _et al._ [2017] S. Datta, N. Dey, and S. Bhattacharya, Electrochemical probing of hydrogelation induced by the self-assembly of a donor–acceptor complex comprising pyranine and viologen, Chem. Commun. 53, 2371 (2017).
  * Yuan  _et al._ [2017] T. Yuan, Y. Xu, C. Zhu, Z. Jiang, H.-J. Sue, L. Fang, and M. A. Olson, Tunable thermochromism of multifunctional charge-transfer-based supramolecular materials assembled in water, Chemistry of Materials 29, 9937 (2017).
  * [26] T. Yuan, M. Vazquez, A. N. Goldner, Y. Xu, R. Contrucci, M. A. Firestone, M. A. Olson, and L. Fang, Versatile thermochromic supramolecular materials based on competing charge transfer interactions, Advanced Functional Materials 26, 8604.
  * Dhiman  _et al._ [2020] S. Dhiman, K. Jalani, and S. J. George, Redox-mediated, transient supramolecular charge-transfer gel and ink, ACS Applied Materials & Interfaces 12, 5259 (2020).
  * Xue  _et al._ [2004] P. Xue, R. Lu, D. Li, M. Jin, C. Bao, Y. Zhao, and Z. Wang, Rearrangement of the aggregation of the gelator during sol-gel transcription of a dimeric cholesterol-based viologen derivative into fibrous silica, Chem. Mater. 16, 3702 (2004).
  * Suzuki  _et al._ [2001] M. Suzuki, C. C. Waraksa, H. Nakayama, K. Hanabusa, M. Kimura, and H. Shirai, Supramolecular assemblies formed by new l-lysine derivatives of viologens, Chem. Commun. , 2012 (2001).
  * Datta and Bhattacharya [2016] S. Datta and S. Bhattacharya, Carbon-nanotube-mediated electrochemical transition in a redox-active supramolecular hydrogel derived from viologen and an l-alanine-based amphiphile, Chemistry – A European Journal 22, 7524 (2016).
  * Kahlfuss  _et al._ [2018] C. Kahlfuss, T. Gibaud, S. Denis-Quanquin, S. Chowdhury, G. Royal, F. Chevallier, E. Saint-Aman, and C. Bucher, Redox-Induced Molecular Metamorphism Promoting a Sol/Gel Phase Transition in a Viologen-Based Coordination Polymer, Chemistry - A European Journal 24, 13009 (2018).
  * Chowdhury  _et al._ [2021] S. Chowdhury, Q. Reynard-Feytis, C. Roizard, D. Frath, F. Chevallier, C. Bucher, and T. Gibaud, Light-Controlled Aggregation and Gelation of Viologen-Based Coordination Polymers, Journal of Physical Chemistry B 125, 12063 (2021), arXiv:2106.15688 .
  * Roizard  _et al._ [2022] C. Roizard, V. Andrieux, S. A. Shehimy, S. Chowdhury, Q. Reynard-Feytis, C. Kahlfuss, E. Saint-Aman, F. Chevallier, C. Bucher, T. Gibaud, and D. Frath, Photoredox processes in the aggregation and gelation of electron-responsive supramolecular polymers based on viologen, ECS Advances 1, 020502 (2022).
  * Yu  _et al._ [2015] R. Yu, N. Lin, W. Yu, and X. Y. Liu, Crystal networks in supramolecular gels: Formation kinetics and mesoscopic engineering principles, CrystEngComm 17, 7986 (2015).
  * Avrami [1941] M. Avrami, Granulation, phase change, and microstructure kinetics of phase change. iii, The Journal of chemical physics 9, 177 (1941).
  * Shirzad and Viney [2023] K. Shirzad and C. Viney, A critical review on applications of the avrami equation beyond materials science, Journal of the Royal Society Interface 20, 20230242 (2023).
  * Gila-Vilchez  _et al._ [2021] C. Gila-Vilchez, M. C. Mañas-Torres, J. A. González-Vera, F. Franco-Montalban, J. A. Tamayo, F. Conejero-Lara, J. M. Cuerva, M. T. Lopez-Lopez, A. Orte, and L. Á. de Cienfuegos, Insights into the co-assemblies formed by different aromatic short-peptide amphiphiles, Polymer Chemistry 12, 6832 (2021).
  * Ma  _et al._ [2008] Z. Ma, G. Zhang, X. Zhai, L. Jin, X. Tang, M. Yang, P. Zheng, and W. Wang, Fractal crystal growth of poly (ethylene oxide) crystals from its amorphous monolayers, Polymer 49, 1629 (2008).
  * Taguchi  _et al._ [2001] K. Taguchi, H. Miyaji, K. Izumi, A. Hoshino, Y. Miyamoto, and R. Kokawa, Growth shape of isotactic polystyrene crystals in thin films, Polymer 42, 7443 (2001).
  * Heijna  _et al._ [2007] M. C. Heijna, M. J. Theelen, W. J. van Enckevort, and E. Vlieg, Spherulitic growth of hen egg-white lysozyme crystals, The Journal of Physical Chemistry B 111, 1567 (2007).
  * Mareau and Prud’Homme [2005] V. H. Mareau and R. E. Prud’Homme, In-situ hot stage atomic force microscopy study of poly ($\varepsilon$-caprolactone) crystal growth in ultrathin films, Macromolecules 38, 398 (2005).
  * Zhu  _et al._ [2007] D.-S. Zhu, Y.-X. Liu, E.-Q. Chen, M. Li, C. Chen, Y.-H. Sun, A.-C. Shi, R. M. Van Horn, and S. Z. Cheng, Crystal growth mechanism changes in pseudo-dewetted poly (ethylene oxide) thin layers, Macromolecules 40, 1570 (2007).
  * Shi  _et al._ [2009] J. H. Shi, X. Y. Liu, J. L. Li, C. S. Strom, and H. Y. Xu, Spherulitic networks: from structure to rheological property, The journal of physical chemistry b 113, 4549 (2009).
  * Wang  _et al._ [2006] R. Wang, X.-Y. Liu, J. Xiong, and J. Li, Real-time observation of fiber network formation in molecular organogel: supersaturation-dependent microstructure and its related rheological property, The journal of physical chemistry b 110, 7275 (2006).
  * Shtukenberg  _et al._ [2012] A. G. Shtukenberg, Y. O. Punin, E. Gunn, and B. Kahr, Spherulites, Chemical reviews 112, 1805 (2012).
  * Liu  _et al._ [2002] X. Y. Liu, P. D. Sawant, W. B. Tan, I. Noor, C. Pramesti, and B. Chen, Creating new supramolecular materials by architecture of three-dimensional nanocrystal fiber networks, Journal of the American Chemical Society 124, 15055 (2002).
  * Lakshminarayanan  _et al._ [2021] V. Lakshminarayanan, C. Chockalingam, E. Mendes, and J. H. van Esch, Gelation kinetics-structure analysis of ph-triggered low molecular weight hydrogelators, ChemPhysChem 22, 2256 (2021).
  * Lam  _et al._ [2010] R. Lam, L. Quaroni, T. Pedersen, and M. A. Rogers, A molecular insight into the nature of crystallographic mismatches in self-assembled fibrillar networks under non-isothermal crystallization conditions, Soft Matter 6, 404 (2010).
  * Nasr  _et al._ [2021] P. Nasr, H. Leung, F.-I. Auzanneau, and M. A. Rogers, Supramolecular fractal growth of self-assembled fibrillar networks, Gels 7, 46 (2021).
  * Newbloom  _et al._ [2012] G. M. Newbloom, K. M. Weigandt, and D. C. Pozzo, Electrical, mechanical, and structural characterization of self-assembly in poly(3-hexylthiophene) organogel networks, Macromolecules 45, 3452 (2012).
  * Thureau  _et al._ [2021] A. Thureau, P. Roblin, and J. Pérez, Biosaxs on the swing beamline at synchrotron soleil, Journal of Applied Crystallography 54, 1698 (2021).
  * Piau  _et al._ [1999] J.-M. Piau, M. Dorget, J.-F. Palierne, and A. Pouchelon, Shear elasticity and yield stress of silica–silicone physical gels: Fractal approach, Journal of Rheology 43, 305 (1999).
  * Sztucki and Narayanan [2007] M. Sztucki and T. Narayanan, Development of an ultra-small-angle X-ray scattering instrument for probing the microstructure and the dynamics of soft matter, Journal of Applied Crystallography 40, s459 (2007).
  * Livsey [1987] I. Livsey, Neutron scattering from concentric cylinders. intraparticle interference function and radius of gyration, Journal of the Chemical Society, Faraday Transactions 2: Molecular and Chemical Physics 83, 1445 (1987).
  * Murata  _et al._ [1994] K. Murata, M. Aoki, T. Suzuki, T. Harada, H. Kawabata, T. Komori, F. Ohseto, K. Ueda, and S. Shinkai, Thermal and light control of the sol-gel phase transition in cholesterol-based organic gels. novel helical aggregation modes as detected by circular dichroism and electron microscopic observation, Journal of the American Chemical Society 116, 6664 (1994).
  * Sarkar  _et al._ [2020] A. Sarkar, R. Sasmal, C. Empereur-Mot, D. Bochicchio, S. V. Kompella, K. Sharma, S. Dhiman, B. Sundaram, S. S. Agasti, G. M. Pavan, _et al._ , Self-sorted, random, and block supramolecular copolymers via sequence controlled, multicomponent self-assembly, Journal of the American Chemical Society 142, 7606 (2020).
  * Lai  _et al._ [2016] Z. Lai, Y. Chen, C. Tan, X. Zhang, and H. Zhang, Self-assembly of two-dimensional nanosheets into one-dimensional nanostructures, Chem 1, 59 (2016).
  * Landman  _et al._ [2018] J. Landman, S. Ouhajji, S. Prévost, T. Narayanan, J. Groenewold, A. P. Philipse, W. K. Kegel, and A. V. Petukhov, Inward growth by nucleation: Multiscale self-assembly of ordered membranes, Science advances 4, eaat1817 (2018).
  * Monk  _et al._ [1999] P. M. Monk, N. M. Hodgkinson, and R. D. Partridge, The colours of charge-transfer complexes of methyl viologen: effects of donor, ionic strength and solvent, Dyes and pigments 43, 241 (1999).
  * Yoshikawa and Nishikiori [2005] H. Yoshikawa and S.-i. Nishikiori, Crystal structures and spectroscopic properties of polycyano–polycadmate host clathrates including a ct complex guest of methylviologen dication and aromatic donor, Dalton Transactions , 3056 (2005).
  * De Greef  _et al._ [2009] T. F. De Greef, M. M. Smulders, M. Wolffs, A. P. Schenning, R. P. Sijbesma, and E. W. Meijer, Supramolecular polymerization, Chemical Reviews 109, 5687 (2009).
  * Mao  _et al._ [2016] B. Mao, T. Divoux, and P. Snabre, Normal force controlled rheology applied to agar gelation, Journal of Rheology 60, 473 (2016).
  * Yuan  _et al._ [2011] B. Yuan, X.-Y. Liu, J.-L. Li, and H.-Y. Xu, Volume confinement induced microstructural transitions and property enhancements of supramolecular soft materials, Soft Matter 7, 1708 (2011).
  * Liu  _et al._ [2014] Y. Liu, R. Y. Wang, J. L. Li, B. Yuan, M. Han, P. Wang, and X. Y. Liu, Identify kinetic features of fibers growing, branching, and bundling in microstructure engineering of crystalline fiber network, CrystEngComm 16, 5402 (2014).
  * Song  _et al._ [2023] J. Song, N. Holten-Andersen, and G. H. McKinley, Non-Maxwellian viscoelastic stress relaxations in soft matter, Soft Matter 19, 7885 (2023).