#  Dipole Alignment of Water Molecules Flowing Through Carbon Nanotube

Hemant Kumar<EMAIL_ADDRESS>Saheb Bera  School of Basic Sciences, Indian
Institute of Technology Bhubaneswar, Argul, Odisha 752050, India  Subhadeep
Dasgupta  A. K. Sood  Department of Physics, Indian Institute of Science,
Bangalore, 560012, India  Chandan Dasgupta  Department of Physics, Indian
Institute of Science, Bangalore, 560012, India  International Centre for
Theoretical Sciences, TIFR, Bangalore 560089, India  Prabal K. Maiti
<EMAIL_ADDRESS>Department of Physics, Indian Institute of Science,
Bangalore, 560012, India

###### Abstract

The fast flow rate of water through nanochannels has promising applications in
desalination, energy conversion, and nanomedicine. We have used molecular
dynamics simulations to show that the water molecules passing through a wide
single-walled carbon nanotube (CNT) cavity get aligned by flow to have a net
dipole moment along the flow direction. With increasing flow velocity, the net
dipole moment first increases and eventually saturates to a constant value.
This behavior is similar to the Langevin theory of paraelectricity with the
flow velocity acting as an effective aligning field. We show conclusively that
the microscopic origin of this behavior is the preferential entry of water
molecules with their dipole vectors pointing inward along the CNT axis.

Recent years have seen an upsurge of interest in exploring ultrafast transport
of water in various nanochannels with potential applications such as
desalination, separation process, and energy conversion Bocquet (2020); Xie
_et al._ (2018); Shen  _et al._ (2021); Rabinowitz  _et al._ (2020); Bao  _et
al._ (2021); Falk  _et al._ (2010); Siria  _et al._ (2013); Heiranian  _et
al._ (2020); Chen  _et al._ (2013); Davis  _et al._ (2020); Zhang  _et al._
(2013). However, a quantitative understanding of flow-induced effects in
nanochannels is still lacking Heiranian and Aluru (2020); Gong  _et al._
(2008). Recent progress in nanofabrication and the development of measurement
techniques have enabled direct investigation of fluids confined to
nanochannels Li  _et al._ (2017); Zhong  _et al._ (2020); Agrawal  _et al._
(2017); Faucher  _et al._ (2021); Verhagen  _et al._ (2020). Tunuguntla et al.
demonstrated a high permeability of water across narrow carbon nanotubes of
diameter $\sim 0.8$nm and significantly lower for wider CNTs (diameter $\sim
1.5$ nm)Tunuguntla  _et al._ (2017). Radha et al. observed relatively fast
flow rates when a slit pore is narrow to accommodate only a monolayer of water
molecules Radha  _et al._ (2016). The flow across the nanochannels can also be
modulated by applying static or oscillating electric fields, indicating a
strong correlation between the dipole ordering and the flow rate Mouterde  _et
al._ (2019); Rinne  _et al._ (2012); Zhu  _et al._ (2020); Wang  _et al._
(2020); Zhang  _et al._ (2020). However, such an association of structural
ordering and flow rate is not demonstrated yet Wei  _et al._ (2014). Yuan et
al. have shown, using ab-initio molecular simulation, that the net dipole
moment of water molecules inside a carbon nanotube can polarize the tube, thus
creating a potential difference across the nanotube endsYuan and Zhao (2009).
Ghosh et al. have shown experimentally the generation of voltage (and current)
across the CNT due to the pressure-induced flow of water molecules across
nanotube bundlesGhosh  _et al._ (2003). This observation motivated us to ask
if water dipoles order when water flows inside the CNTs. The answer indeed is
in the affirmative as shown in our present molecular dynamics (MD)
simulations.

Water molecules inside narrow carbon nanotubes (diameter $\sim 0.8$ nm) in
equilibrium are arranged in a single file manner, with all the dipoles
pointing in the same directions along the nanotube axis Mukherjee  _et al._
(2007); Chakraborty  _et al._ (2017). These dipoles flip collectively on a
time scale that depends on the length of the nanotubeMukherjee  _et al._
(2008). Lin et al. have shown that in equilibrium, the dielectric relaxation
of confined water molecules inside CNTs is much faster along the cross-section
but slower along the axisLin  _et al._ (2009). Inside narrow CNTs, the dipole
vector of the water molecules prefers to stay along the axis while it relaxes
faster perpendicular to the nanotube axis. However, as the diameter of the
nanotube increases, water molecules are no longer arranged in a single file
manner, and there is no apparent ordering at ambient conditions of pressure
and temperature.

In this paper, we demonstrate that the water dipoles confined inside a wider
(10, 10) nanotube (diameter 1.4 nm), which exhibit no net dipole polarization
in equilibrium, can show net dipole ordering under the effect of flow
generated by a pressure gradient. The net alignment of dipoles along the flow
direction increases with flow velocity, saturating to a finite value. This
behavior of confined water can be very well explained by treating them as
independent dipoles under some effective aligning field that depends on the
flow velocity. The electric field stems from the asymmetric dielectric
interface at the CNT ends where water molecules from the bulk enter the CNT
cavity. This observation not only demonstrate the existence of a novel
physical phenomenon but also suggests pathways for various nano-
electromechanical devices.

We have performed MD simulations of a 10 nm long armchair (10, 10) carbon
nanotube (diameter 1.4 nm) solvated in TIP3P Jorgensen  _et al._ (1983) water
as shown in Fig. 1a using LAMMPS Plimpton (1995). Carbon atoms were modeled as
uncharged Lennard-Jones (LJ) particles with parameters taken from AMBER force-
field Wang  _et al._ (2004); Majumdar  _et al._ (2021). Interaction between
water and carbon atoms was included through LJ interaction between carbon and
oxygen atoms. Long-range electrostatic interactions between charged entities
were computed using PPPM algorithm with the real space cut-off of 10 Å
Plimpton (1995). We initially run equilibrium MD simulation in NPT keeping
temperature at 280 K and pressure P = 1 atm. Nose-Hoover thermostat and
barostat as implemented in LAMMPS were used to maintain the constant
temperature and pressureShinoda  _et al._ (2004); Martyna  _et al._ (1994).
After equilibrating the system at T = 280 K and P = 1 atm, we switched to NVT
ensemble using Nose-Hover thermostat with a coupling constant of 1 ps. To
simulate pressure gradient induced flow, we pushed a 5 Ålayer of water on both
the ends of the water-box along the nanotube axis by adding extra force on the
oxygen atoms of each water molecule lying in these layers [Fig 1a]. This
protocol for simulating hydrostatic pressure gradients is known to mimic
pressure-induced flow Zhu  _et al._ (2002). We waited for 5 ns of simulation
time to achieve a steady state. Later, 50 ns of flow simulation was used to
analyze the behavior of water dipoles at different flow velocities.

Figure 1:  Figure 1: a)  Simulated system, highlighted water molecules at both
ends represent the layers on which additional force was applied to simulate
the flow. b)  Structure of water molecules confined inside the carbon
nanotube. A typical water molecule before entering CNT with dipole pointing
inward (panel c) and outward (panel d). Figure 2: a) Distribution of the angle
between the dipole moment of individual water molecules inside a (10, 10)
carbon nanotube and the flow direction. In the absence of flow, the
probability shows peaks of equal height at $\theta=40^{\circ}$ and
$\theta=140^{\circ}$ . Flow creates asymmetry, and more dipoles are orientated
along the flow direction, b) Probability distribution of the net dipole
projection of all confined water molecules for various flow velocities. Inset
shows the temporal variation of the net dipole projection of confined water
molecules along the CNT axis in equilibrium.

At equilibrium, when there is no flow, water dipoles spend an almost equal
amount of time aligned either parallel or antiparallel to the nanotube axis,
and the average dipole moment of the confined water molecules over a long
trajectory is zero. Fig. 2a shows the probability of finding a dipole in a
particular alignment for different flow velocities. Equal height peaks at
$\theta=40^{\circ}$ and $\theta=140^{\circ}$ in equilibrium demonstrate the
equal preference for both the alignments. At finite flow velocity, more
dipoles prefer to be aligned along the flow direction. Fig. 2a clearly brings
out that the probability of alignment along the flow direction (+z axis) at
$\theta=40^{\circ}$ increases while alignment opposite to the flow direction
(peak at $\theta=140^{\circ}$ ) (-z axis) decreases, leading to a net dipole
moment along the direction of flow.

Figure 3:  Variation of the average dipole moment per molecule of the confined
water molecules, projected in the flow direction, with the flow velocity for
temperatures T = 280 K and 300 K. The variation can be fitted well with the
Langevin function (Eq. 1, $D_{0}=0.39$ and $a=13.28K/m.s^{-1}$ for T = 280 K
and $D_{0}=0.27$ and $a=13.28K/m.s^{-1}$ for T = 300 K), which implies that
the flow effect can be well described by an effective field created due to the
flowing water molecules. As shown in Fig. S3, the Langevin description works
for CNTs of different length and the average dipole moment increases with the
CNT length. Variation of the net dipole moment of the confined water molecules
with flow velocity at three different lengths.

To investigate the nature of this alignment, we study the spatial ordering of
confined water molecules for different flow velocities by calculating the
pair-correlation function $g(z)$ of the confined water molecule using
$g(z)=\displaystyle\sum\limits_{i=1}^{N}\sum\limits_{j>i}^{N}\langle\frac{\delta(z-z_{ij})}{N}\rangle$,
where $N$ is the number of water molecules inside the nanotube in each
snapshot of the system and $z_{ij}$ is the separation along the nanotube axis
between $i^{th}$ and $j^{th}$ water molecules. The computed pair correlation
functions for the confined water molecules at different flow velocities
demonstrate that $g(z)$ is almost independent of flow velocities with a very
slight increase in the ordering at higher flow velocities (Fig. S1). This
implies that flow does not alter positional ordering, but its net effect is to
create an aligning field that tends to orient the dipoles of confined water
molecules in the direction of flow. At a given temperature, increasing the
flow velocity increases the net dipole moment along the flow direction, and
then it saturates to a constant value. Fig. 3 shows the variation of the
average projection of the dipole moment vector of the confined water molecules
for two different temperatures. The value of the saturated dipole moment
depends on the temperature for a given nanotube. For 10 nm long (10, 10) CNT
the saturated value is $\sim 0.39$. This value is less than 1 (perfect
alignment of all the dipoles along the nanotube axis) because perfect
alignment along the axis is energetically unfavorable due to the loss of
hydrogen bonds.
Such alignment of dipoles is very similar to the paraelectric behavior of
dipoles under the effect of an aligning field. This led us to propose an
analogy with the Langevin theory of paraelectrics. In this description, the
interaction between atomic dipoles is negligible and they are randomly
oriented at a finite temperature in the absence of aligning electric fields.
In the presence of an external electric field $(E_{a})$, the dipole moments
tend to orient along the field direction. The average polarization per unit
volume for a given field at temperature $T$ is given by:
$D=D_{0}\left(coth\beta-1/\beta\right)$, where $\beta$ = $\mu_{0}E_{a}/k_{B}T$
and $D_{0}=n\mu_{0}$ ; $n$ being the number of dipoles per unit volume and
$\mu_{0}$ is the individual dipole moment. To quantify the flow-induced
effective field which aligns the confined water dipoles, we propose a similar
Langevin function for the net dipole moment $(D)$ of the system of confined
water molecules with $\beta=av/T$ where $a$ is a scaling parameter that
describes the proportionality of the effective aligning field with the flow
speed $v$:

$D=D_{0}\left[\coth\left(\frac{av}{T}\right)-\frac{T}{av}\right]$ (1)

For a given temperature $T$, we have fitted the variation of the average
dipole moment per water molecule , projected in the flow direction, with
different $v$ to the above Langevin function where $D_{0}$, the saturation
dipole moment and $a$ are fitting parameters. A good fit shown in Fig.3
implies that a flow-induced field aligning the dipoles is a good description
of this effect. This fit also allows us to extract an effective field
generated by the flow. The temporal evolution of the net dipole projection of
confined water molecules shown in inset of Fig. 2(b) indicates that the
confined molecules prefer aligned states with the dipoles pointing along the
CNT axis. The collective flip between parallel (along the flow) and
antiparallel (opposite to the flow) aligned states occurs at regular time
intervals. (Data shown here is for 10 nm long CNT, as the length of the CNT
increases, this description becomes more accurate, as shown in Fig. S2). The
probability distribution of the net dipole projection shown in Fig.2b depicts
that the probability of finding a net dipole moment along +z and -z directions
is almost equal without flow. As the flow velocity increases, the probability
of finding a net dipole projection aligned with the flow direction increases,
as evident from the increasing height of the peak near the net dipole of $0.4$
and decreasing height of the peak around $-0.4$ that corresponds to the
antiparallel aligned state. Such a variation of probabilities with flow
suggests that, on average, confined water molecules spend a longer time in the
state with dipoles aligned with the flow direction. This time continues to
increase with flow velocities. To quantify this, we compute the average
duration for which the confined molecules continuously remain aligned before
initiating a successful orientational flip to the opposite alignment. We start
by simplifying the dipole trajectory by allowing only three possible values
for dipole projections such that a state corresponding to net dipole $\geq
0.2$ is assigned a dipole projection of 1 (parallel to the flow), $\leq-0.2$
is assigned as $-1$ (antiparallel to flow), and anything between $0.2$ to
$-0.2$ is assigned as 0 (transition state). The variation of the average dwell
time of parallel and antiparallel alignment with the flow velocity extracted
from this modified trajectory is shown in Fig.4a. It clearly demonstrates that
the average dwell time for the parallel aligned state increases and the dwell
time for the antiparallel aligned states decreases with increasing flow
velocity.

Figure 4:  a)The variation of the average dwell time for both alignment states
with the flow velocity. The dwell time increases with the flow velocity for
the parallel alignment and decreases for the state of antiparallel alignment.
The inset shows the construction of the simplified dipole trajectory described
in the text. b) The number of water molecules entering from the bulk into the
CNT cavity with their dipole moments pointing inward or outward. More water
molecules enter with dipole pointing inward to the nanotube from both ends at
equilibrium. As the flow velocity increases from zero, the flux from the flow-
entry end increases while the flux from the opposite end decreases.(Lines are
the guide to the eye only).

To understand how flow impacts the dwell time, we begin by analyzing the
reorientation mechanism in equilibrium conditions Laage and Thompson (2012);
Laage  _et al._ (2012). Dipole reorientation inside narrow CNTs, where the
dipoles are aligned in a single file manner, is initiated through defect
nucleation at one of the CNT ends Mukherjee  _et al._ (2008). When a water
molecule enters the CNT such that its dipole is pointing in the opposite
direction to those of the confined water dipoles, it is characterized as an
orientational defect. When such a defect moves through the confined water
chain, it leaves behind flipped individual dipoles. A successful collective
flip of the dipole moments occurs when a defect entering from one end exits
from the other end. A similar reorientation mechanism can be extended for the
wider CNT considered here. First, we characterize the dipole moments of water
molecules that enter the CNT. We separated the entry events based on dipole
moment of the entering water molecules. A strong preference was observed for
water molecules to enter with dipoles pointing inwards (dipole projection $>0$
for the left end, $<0$ for the right end) in equilibrium condition. Of all the
water molecules entering inside the CNT cavity from both ends, 55% of water
molecules have dipole pointing inward while only 45% have dipole pointing
outwards. Moreover, the average interaction energy of a water molecule just
before entry with its dipole vector pointing inward is $-9.798$ kcal/mol and
$-9.391$ kcal/mol for outward-pointing dipole vector of entering water
molecules. This preference arises due to distinct hydrogen bonding
environments near the entrance of the nanotube for the two dipole
orientations, as highlighted in Fig. 1(c, d). Due to different surrounding
environments, the average number of hydrogen bonds for an inward-pointing
dipole is $3.8$ as compared to $3.4$ for the outward-pointing dipoles, thus
showing energetics to be responsible for the preferred entry of molecules with
inward-pointing dipoles.

Favorable bias for the entry of inward-pointing water molecules and defect-
assisted orientational flip mechanism are the key ingredients to understand
the emergence of net alignment due to flow. In the absence of flow, the influx
from both ends of the CNT is equal; hence the probability of defect nucleation
to initiate the collective dipole flip is the same for both the net
alignments. This explains the similar dwell times for both the alignments.
However, during the flow, a larger number of water molecules enter from the
flow-entry edge of CNT as compared to the flow-exit edge. As there is a strong
preference for water molecules to enter with their dipoles pointing inward,
more water molecules will enter through the flow-entry end with dipole
pointing in the flow direction [Fig. 4b]. These water molecules do not destroy
the alignment of the dipoles inside the CNT if the alignment is in the flow
direction. However, a smaller number of water molecules also go inside the CNT
with their dipole moments pointing outward and serve as orientational defects
if the dipolar alignment inside the CNT is in the direction of the flow. The
situation is reversed if the alignment of the dipoles inside the CNT is
opposite to the flow direction: in that case, the larger number of water
molecules entering with dipole moments pointing inwards act as defects that
can lead to a collective flip of the dipolar alignment. Hence, the probability
of a reorientational flip is higher for antiparallel alignment. The net effect
of preferred orientation at the flow-entry edge is to increase the probability
of defect nucleation for antiparallel alignment. At the opposite end, water
molecules prefer to enter with their dipoles pointing opposite to the flow
(inward). Such entry events are likely to initiate flips for a parallel
aligned state. However, being the flow-exit edge, the influx from this end
decreases with the flow velocity resulting in a reduced probability of
flipping for the parallel aligned state [Fig. 4b].

To summarize, we have demonstrated that a net dipole alignment in the flow
direction emerges for the water molecules flowing through a (10, 10) CNT and
the dipole alignment increases with the flow velocity. The net alignment
arises due to the asymmetry in the dipole orientation with which water
molecules enter the nanotube. The preferential entry of water molecules with
dipole pointing inwards decreases (increases) the probability of orientational
flips when the confined water dipoles are aligned parallel (antiparallel) to
the flow direction. This makes the time-averaged net dipole projection in the
steady state to point in the flow direction. This observation presents a
unique example where confinement produces entirely different behavior from the
bulk counterparts.

The correlation between dipole alignment and flow rate can be exploited for
various nanofluidic devices as it gives us a way to control the net dipole
moment via external pressure. This observation also raises an important
question: is dipolar alignment necessary for the ultrafast transport which has
been observed in narrow nanopores? The answer to this question requires more
detailed investigation. The net dipole moment of water inside a carbon
nanotube can polarize it and this effect can be used to engineer a potential
difference across nanotube ends Yuan and Zhao (2009). As demonstrated here,
such polarization can be obtained inside wider nanotubes that confine more
significant dipole moments per unit length. It will potentially lead to more
significant potential differences across the nanotube ends. As the flow
modulates dipole relaxation, this also offers a possibility of making devices
where the flow velocity of the water controls the dielectric constant.

###### Acknowledgements.

HK would like to thank National PARAM Supercomputing Facility at C-DAC, India
for computational support. PKM, CD and AKS thank DST, India for financial
support.

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