Crystal-Melt Interface Kinetics and the Capillary Wave Dynamics of the Monolayer Confined Ice-Water Coexistence Lines

doi:10.6023/A20090423

Abstract

The ice-water interface's kinetics has long been paid much attention because of its central role in ice nucleation, growth and surface/interface melting. However, there exist few studies focused on the kinetics of the confined ice-water interface. In this paper, we employ the equilibrium molecular dynamics simulation and the phase equilibrium technique for the confined water and ice to study the 1D crystal-melt coexistence line of an equilibrium mono-layer ice-water coexistence system, described by two well-known water molecule models, i.e., constant dipole moment TIP4P/2005 model and polarizable SWM4-NDP water model. The mono-layer ice-water phase equilibria are confined in the hydrophobic slab pore of 0.65 nm, under 0.5 GPa lateral pressure. By tracking the 1D ice-water coexistence line's position, we calculate the power spectrum of the equilibrium line fluctuation and the time-dependent autocorrelation function of the line fluctuation Fourier amplitudes and then calculate a series of kinetic properties of the 1D crystal-melt coexistence line. We demonstrate that the processes involved in the relaxation of the crystal-melt coexistence line fluctuation with long wavelengths are coupled with a fast and a slow decay process characterized by two distinct time scales, while just the slow decay processes dominate the crystal-melt coexistence line fluctuation with short wavelengths. By comparing with bulk ice-water interface systems, we find that the high-frequency processes such as Rayleigh waves participate more in the relaxation of the 1D crystal-melt coexistence line fluctuation. We see that the wave vector dependence of the characteristic relaxation time (of the crystal-melt line fluctuation) is consistent with the crystal-melt interface's existing kinetic theory. Nevertheless, the characteristic relaxation time of the 1D crystal-melt coexistence line relaxation is around one order of magnitude lower than that of the 2D bulk ice-water interface system. We calculate the kinetic coefficients of the 1D crystal-melt coexistence line for the two water model systems, compare with the bulk interface systems, and find the kinetic coefficient of the confined ice-water (crystal-melt) coexistence line is much higher than that of the bulk ice-water interface system. The significant increase in the magnitude of the kinetic coefficient of the confined 1D ice-water coexistence line system may be understood by the substantial suppression of the rotational degree of freedom of the confined water molecules. The current achievement of the fundamental insight and simulation results could potentially facilitate the theoretical advancements in designing new devices of ultrafast phase-change (energy storage, sensor) devices based on confined water systems.

Key words: confined water, solid-liquid interface, capillary wave dynamics, crystallization kinetics, molecular dynamics

Cite this article

Zun Liang, Xin Zhang, Songtai Lv, Hongtao Liang, Yang Yang. Crystal-Melt Interface Kinetics and the Capillary Wave Dynamics of the Monolayer Confined Ice-Water Coexistence Lines[J]. Acta Chimica Sinica, 2021, 79(1): 108-118.

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Fig. & Tab. 8

Figure 1. Snapshot of the crystal-melt boundary lines (black) from the equilibrium molecular-dynamic simulations of the confined monolayer ice-water coexistences, under a lateral pressure of 5×108 Pa and two-phase coexistence temperatures (Tm). Oxygen particles are colored according to the extent to which their local environment resembles that of the 2D ice crystal lattice, red for crystal and blue for melt. Panel (a) and (b) plot results of the SWM4-NDP (Drude) polarizable and the TIP4P/2005 model system. Thick black line in each panel depicts the instantaneous 1D ice-water crystal-melt boundary. Insets in (a) and (b) plots the in-plane fine-grained area-density of oxygen atoms profile (solid line) and coarse-scaled profiles for dipole moments distribution (dashed line). The zero point of x corresponds to the time averaged position of the crystal-melt coexistence interface. Readers are referred to Ref. [ 30] for more details of determining fine/coarse-scaled profiles

Confined 1D-line	$D / (nm 2 ns - 1)$	$γ ? / (k B T σ - 1)$	$μ * / 2 fD σ K$	$μ / cm (sK)$
SWM4-NDP	2.44(11) ^b	$0.45 (9)$	$3.2 (4) × 10 - 2$	$99 (13)$
TIP4P/2005	3.37(10) ^b	$0.46 (10)$	$3.5 (4) × 10 - 2$	$149 (20)$
Bulk 2D-interface	$D / (nm 2 ns - 1)$	$γ ? / (k B T σ - 2)$	$μ * / 2 fD σ K$	$μ / cm (sK)$
TIP4P/2005 (Prism) ^a	0.39	0.43	$0.3 (1) × 10 - 2$	2.2(3)
LJ $100$ ^a	-	-	$8 (2) × 10 - 2$	-

Confined 1D-line	$D / (nm 2 ns - 1)$	$γ ? / (k B T σ - 1)$	$μ * / 2 fD σ K$	$μ / cm (sK)$
SWM4-NDP	2.44(11) ^b	$0.45 (9)$	$3.2 (4) × 10 - 2$	$99 (13)$
TIP4P/2005	3.37(10) ^b	$0.46 (10)$	$3.5 (4) × 10 - 2$	$149 (20)$
Bulk 2D-interface	$D / (nm 2 ns - 1)$	$γ ? / (k B T σ - 2)$	$μ * / 2 fD σ K$	$μ / cm (sK)$
TIP4P/2005 (Prism) ^a	0.39	0.43	$0.3 (1) × 10 - 2$	2.2(3)
LJ $100$ ^a	-	-	$8 (2) × 10 - 2$	-

Table 1. Calculated liquid phase diffusion coefficient, line stiffness, and the kinetic coefficient for the (semi-)two dimensional confined monolayer ice-water coexistence system, of the SWM4-NDP polarizable model system as well as the TIP4P/2005 model system. The superscript * above represents the dimensionless unit (reduced by the diffusive time) employed in this work.f=2 or 3, refers to the number of system dimensions. The data are compared with Benetet al.in their previous work[10] for the bulk ice-water interfacial system and Lennard-Jones crystal-melt interfacial systems. The numbers in parentheses are 95% confidence errors for the last digits shown.

Figure 2. The time dependence of a fluctuating crystal-melt boundary line of the confined monolayer ice-water coexistence. 10 successive trajectories of the Drude model system are shown, with a 20 reduced time unit interval. For clarity, the average position of the boundary line has been offset at each time.

Figure 3. Autocorrelation functions $f_{q}(t)$ for the crystal-melt boundary line of the confined monolayer ice-water coexistence. Panel (a) and (b) plot results of the Drude polarizable and the TIP4P/2005 model system. In each plot, six group of data-points correspond to wavevectors $q=2\pi k/L_{y}$, with k≤ 6. Solid lines correspond to the weighted double exponential ﬁts to the data-points. The error bars represent 95% conﬁdence intervals estimated from statistical average.

Figure 4. (a) Prefactor A(q) for the double exponential ﬁts for two model systems investigated, compared to that reported by Benet et al.[10] for the bulk TIP4P/2005 ice-water prismatic interface. 1D ice-water boundary line described by Drude and TIP4P/2005 model, as well as 2D ice-water interface described by TIP4P/2005 model are shown in open black squares, filled red circles and blue stars, respectively. (b), (d) Log-log plot of dimensionless characteristic time $\tau_{q}^{C}(q)$ and $\tau_{q}^{R}$ for the $f_{q}(t)$ relaxation governed by the capillary waves and the high frequency processes, respectively. The dashed lines, included in (b) and (d) for visual reference, indicates a power law of $q^{-2}$. (c) Probablity distribution of the size of the clusters which participate the attachment/detachment kinetic processes of the ice-water interfaces.

Figure 5. (a) Plots of the inverse relaxation time 1 / τ q C versus q - 2 . The presentation is as in Fig. 4(b). The kinetic coefﬁcient can be extracted from weighted linear fitting to the data points via Eq. (5). (b) Log-log plot of the power spectra of equilibrium ?uctuations for 1D ice-water boundary line for the two water model systems.

Figure 6. Autocorrelation functions $f_{q}(t)$ for the crystal-melt boundary line of the confined monolayer ice-water coexistence, for the three selected thermostat relaxation times. The colored data-points correspond to systems with thermostat relaxation time set as 100 fs. While the gray and black data-points correspond to systems with thermostat relaxation times of 10 fs and 1000 fs.

Figure 7. Diffusion coefficients of Drude (a) and TIP4P/2005 (b) 2D confiled monolayer water as a function of the inverse box length 1/Lxy for 66~6400 water molecules. Square symbols show results from MD simulations, with error bars estimated from block averages. The solid line is a linear fit of the diffusion coefficients D to 1/Lxy.

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