Hagita Katsumi, Murashima Takahiro
Department of Applied Physics, National Defense Academy, 1-10-20 Hashirimizu, Yokosuka 239-8686, Japan.
Department of Physics, Tohoku University, 6-3, Aramaki-aza-Aoba, Aoba-ku, Sendai, 980-8578, Japan.
Soft Matter. 2022 Jan 26;18(4):894-904. doi: 10.1039/d1sm01641e.
To study the linear region of entropic elasticity, we considered the simplest physical model possible and extracted the linear entropic regime by using the least squares fit and the minimum of the mean absolute error. With regard to the effect of the fluctuation of the strand length , the strand length with fluctuation was set to a form proportional to (1.0 + ( - 0.5)), where is a uniform random number between 0 and 1 and is the amplitude of fluctuation. This form enabled us to analytically calculate the fluctuation dependence of the elastic modulus . To reveal the linear regions of entropic elasticity as a function of the strand length between neighboring nodes in lattices, molecular dynamics (MD) simulations of condensed lattice networks with harmonic bonds without the excluded volume interactions were performed. Stress-strain curves were estimated by performing uniaxial stretching MD simulations under periodic boundary conditions with a bead number density of 0.85. First, we used a diamond lattice with functionality = 4. The linear region of the entropic elasticity was found to become larger with the increasing number of beads in a strand . For = 100, the linear region had a strain of up to 8 for a regular diamond lattice. We investigated the effect of strand length fluctuation on the diamond lattice, and we confirmed that the equilibrium shear modulus increases as the obtained analytical prediction and the linear entropic region in the stress-strain curves becomes narrower with increasing fluctuation of . To investigate the difference in network topology with the same functionality and uniform strand length , we performed MD simulations on regular networks of the BC-8 structure with = 4 prepared from the DFT calculations of carbon at high pressure. We found that the elastic behavior depends on the network connectivity (, topology). This indicates that the network topology plays an important role in the emergence of nonlinearity owing to the crossover from entropic to energetic elasticity.
为了研究熵弹性的线性区域，我们考虑了尽可能简单的物理模型，并通过最小二乘法拟合和平均绝对误差最小值来提取线性熵区域。关于链长波动的影响，有波动的链长被设定为与(1.0 + ( - 0.5))成比例的形式，其中 是0到1之间的均匀随机数， 是波动幅度。这种形式使我们能够解析计算弹性模量的波动依赖性。为了揭示作为晶格中相邻节点间链长函数的熵弹性线性区域，我们对具有谐和键且无排除体积相互作用的凝聚晶格网络进行了分子动力学(MD)模拟。通过在周期性边界条件下进行单轴拉伸MD模拟，珠子数密度为0.85，估计应力 - 应变曲线。首先，我们使用了功能度 = 4的金刚石晶格。发现熵弹性的线性区域随着链中珠子数量的增加而变大。对于 = 100，规则金刚石晶格的线性区域应变高达8。我们研究了链长波动对金刚石晶格的影响，并且我们证实平衡剪切模量 如所获得的解析预测那样增加，并且应力 - 应变曲线中的线性熵区域随着 的波动增加而变窄。为了研究具有相同功能度 和均匀链长的网络拓扑差异，我们对由高压下碳的 DFT计算制备的功能度 = 4的BC - 8结构的规则网络进行了MD模拟。我们发现弹性行为取决于网络连通性(即拓扑结构)。这表明网络拓扑在由于从熵弹性到能弹性的转变而导致的非线性出现中起重要作用。
