Molecular dynamics studies of entropic elasticity of condensed lattice networks connected with uniform functionality f = 4

Abstract

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 N_s, the strand length with fluctuation was set to a form proportional to (1.0 + C (R − 0.5)), where R is a uniform random number between 0 and 1 and C is the amplitude of fluctuation. This form enabled us to analytically calculate the fluctuation dependence of the elastic modulus G. 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 f = 4. The linear region of the entropic elasticity was found to become larger with the increasing number of beads in a strand N_s. For N_s = 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 G increases as the obtained analytical prediction and the linear entropic region in the stress–strain curves becomes narrower with increasing fluctuation of N_s. To investigate the difference in network topology with the same functionality f and uniform strand length N_s, we performed MD simulations on regular networks of the BC-8 structure with f = 4 prepared from the ab initio DFT calculations of carbon at high pressure. We found that the elastic behavior depends on the network connectivity (i.e., 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.