Koksal Karakus, Valeriy V Ginzburg, Keith Promislow, Leela Rakesh
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Subsequently, by employing the molecular dynamics (MD) simulation data of Cheng <i>et al.</i>, we approximate the density profile of a supported liquid thin film as a stationary solution of a fourth-order partial differential equation (PDE). We then construct an appropriate density functional, from which the density profile emerges through the minimization of free energy. Our final assumption is that of a consistent, temperature-independent scaled density profile, ensuring that the free volume throughout the entire nanocomposite increases with temperature in a smooth, monotonic fashion. Considering the established relationship between glycerol relaxation time and temperature, we can employ Doolittle-type analysis (\"naïve\" free-volume model), to calculate the relaxation time based on temperature and film thickness. 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引用次数: 0
摘要
无定形薄膜和纳米复合材料接近玻璃化转变时的动力学与结构之间的关系是软物质物理学中的一个重要问题。在此,我们开发了一种简单的理论方法来描述甘油-二氧化硅纳米复合材料(S. Cheng et al., J. Chem. Phys., 2015, 143, 194704)的密度曲线和α-松弛时间。我们首先应用德雅金近似,用平面代替粒子的曲面;这样,纳米复合材料的建模就简化为约束薄膜的建模。随后,我们利用 Cheng 等人的分子动力学(MD)模拟数据,将支撑液体薄膜的密度曲线近似为四阶偏微分方程(PDE)的静态解。然后,我们构建了一个适当的密度函数,通过自由能的最小化得出密度曲线。我们的最后一个假设是,与温度无关的缩放密度曲线保持一致,确保整个纳米复合材料的自由体积随着温度的升高而平滑、单调地增加。考虑到甘油弛豫时间与温度之间的既定关系,我们可以采用杜利特尔分析法("天真 "自由体积模型),根据温度和薄膜厚度计算弛豫时间。然后,我们将薄膜厚度换算成颗粒间距离,进而换算出纳米复合材料的填料体积分数,并将模型预测结果与实验数据进行比较,结果显示两者吻合得很好。所提出的方法可以很容易地扩展到其他纳米复合材料和薄膜体系。
Modeling the structure and relaxation in glycerol-silica nanocomposites.
The relationship between the dynamics and structure of amorphous thin films and nanocomposites near their glass transition is an important problem in soft-matter physics. Here, we develop a simple theoretical approach to describe the density profile and the α-relaxation time of a glycerol-silica nanocomposite (S. Cheng et al., J. Chem. Phys., 2015, 143, 194704). We begin by applying the Derjaguin approximation, where we replace the curved surface of the particle with the planar one; thus, modeling the nanocomposite is reduced to that of a confined thin film. Subsequently, by employing the molecular dynamics (MD) simulation data of Cheng et al., we approximate the density profile of a supported liquid thin film as a stationary solution of a fourth-order partial differential equation (PDE). We then construct an appropriate density functional, from which the density profile emerges through the minimization of free energy. Our final assumption is that of a consistent, temperature-independent scaled density profile, ensuring that the free volume throughout the entire nanocomposite increases with temperature in a smooth, monotonic fashion. Considering the established relationship between glycerol relaxation time and temperature, we can employ Doolittle-type analysis ("naïve" free-volume model), to calculate the relaxation time based on temperature and film thickness. We then convert the film thickness into the interparticle distance and subsequently the filler volume fraction for the nanocomposites and compare our model predictions with experimental data, resulting in a good agreement. The proposed approach can be easily extended to other nanocomposite and film systems.