单分子层受限冰-水共存界线毛细波与固-液相变动力学

doi:10.6023/A20090423

摘要/Abstract

冰-水界面动力学性质在冰形核、生长、表界面熔化中扮演核心角色, 长期以来一直被广泛关注. 然而, 受限水体系中冰-水界面的动力学性质却鲜有报道. 本工作利用平衡态分子动力学模拟方法和受限固-液两相平衡模拟技术, 对两种水模型(恒定偶极矩、可极化)描述的单分子层受限冰-水两相平衡体系中的一维固-液界线开展研究. 通过对一维受限冰-水界线的追踪, 计算了其热涨落波动的振幅与时间自关联函数色散谱, 进而计算一系列固-液界线动力学性质. 冰-水界线波动在短波长区域复合了快、慢两种不同时间尺度的弛豫过程, 在长波长区域则由慢弛豫过程主导. 相比块体冰-水界面体系, 以Rayleigh波为主的高频微观物理过程更多地参与了一维冰-水界线的动力学弛豫. 我们发现冰-水界线波动弛豫特征衰减时间的波矢依赖关系符合现有固-液界面动力学理论, 但一维界线弛豫的特征衰减时间比二维界面体系低了一个数量级左右. 计算了两种水模型体系冰-水界线的动力学系数, 并与块体冰-水界面比较, 发现受限冰-水(固-液)界线动力学系数远高于块体冰-水界面体系. 我们推测水分子转动自由度在受限腔中被强烈压制可能是导致受限体系超快冰-水(固-液)相变速率的主要原因. 本工作将在受限水体系超快相变(储能、传感)器件的设计工作中提供一定的理论指导意义.

关键词: 受限水, 固-液界面, 毛细波动力学, 结晶动力学, 分子动力学

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

引用此文

梁尊, 张鑫, 吕松泰, 梁洪涛, 杨洋. 单分子层受限冰-水共存界线毛细波与固-液相变动力学[J]. 化学学报, 2021, 79(1): 108-118.

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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图/表 8

图1. 平衡态单分子层受限冰-水两相共存固-液界线的分子动力学模拟坐标快照. 受限温压条件: 熔点温度, 5×108 Pa. 水分子中氧原子颜色变化遵循代表结构序参量数值的色谱变化, 二维固相冰红色、液相水蓝色. (a)和(b)分别画出SWM4-NDP(Drude)极化模型体系和TIP4P/2005模型体系结果. 黑色粗线标出了快照时刻下的瞬时冰-水界线位置. (a)和(b)的插图画出时间平均的细粒氧原子密度分布函数(黑色线)和粗粒水分子偶极矩分布函数(红色线),x轴0 点对应固-液界线平均位置. 结构序参量和粗细粒度分布函数计算方法参见文献[ 30].

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	-	-	$8 (2) × 10 - 2$	-

表1. 受限单分子层冰-水(固-液)界线动力学系数和界线刚度, 以及冰-水两相平衡温度下液相扩散系数D. 第四列$\mu$的上标星号表示使用约化(扩散)时间单位, 其中f是研究体系的系统空间维度. Benet等[10]先前报道的块体冰-水(棱柱晶面方向)界面体系以及Lennard-Jones(LJ)固-液(100方向)界面体系相应结果在表格下方列出. 表中括号内数字代表95%置信度的统计误差.

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.

图2. 平衡态单分子层受限冰-水两相共存固-液界线的时间演化. Drude极化水模型的10个时刻结果, 间隔20个约化时间单位. 为了更清楚地展示, 平移了固-液界线位置.

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.

图3. 单分子层受限冰-水(固-液)界线波动振幅的时间自关联函数$f_{q}(t)$ (a)和(b)中分别画出SWM4-NDP(Drude)极化模型体系和TIP4P/2005模型体系结果. 在每个图中, 六组数据点对应六个不同波矢$q=2\pi k/L_{y}(k≤ 6)$. 实线对应着应用双指数函数对$f_{q}(t)$数据点进行的加权拟合. 每个数据点上误差棒表代表95%置信度的统计误差.

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.

图4. (a)两个水模型体系描述的一维受限冰-水界线体系, 双指数函数中拟合系数A(q)的结果(黑方块Drude极化水模型; 红圆圈TIP4P/2005水模型), 以及与Benet等[10]报道的TIP4P/2005块体冰-水(棱柱晶面方向)界面体系结果(蓝色星号)的比较. (b)和(d)特征衰减时间$\tau_{q}^{C}$和$\tau_{q}^{R}$的波矢依赖关系, 其中虚线作为参考线, 辅助检查$q^{-2}$幂律. (c)参与界面动力学相变的团簇尺寸概率分布$P(N_{c})$.

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.

图5. (a) 1 / τ q C 与 q 2 的线性关系. 图中数据与以及展示方式与图4(b)相同. 实线表示利用公式(5)对数据点的加权线性拟合, 实线的斜率反映了表1中的动力学系数数值大小. (b) 固-液界线毛细波涨落振动谱.

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.

图6. 三个不同热库参数(10 fs, 100 fs和1000 fs)的$f_{q}(t)$结果. 彩色数据点对应100 fs热库参数. 灰色与黑色数据点分别对应着10 fs和1000 fs的热库参数体系结果.

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.

图7. 二维单分子层受限Drude和TIP4P/2005模型水的扩散系数与模拟盒子尺寸1/L xy 的变化关系. 水分子数从66到6400. 方块代表分子动力学模拟结果, 实线为线性拟合.

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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