Characterization of microscopic deformation through two-point spatial correlation functions

The molecular rearrangements of most fluids under flow and deformation do not directly follow the macroscopic strain field. In this work, we describe a phenomenological method for characterizing such nonaffine deformation via the anisotropic pair distribution function (PDF). We demonstrate how the microscopic strain can be calculated in both simple shear and uniaxial extension, by perturbation expansion of anisotropic PDF in terms of real spherical harmonics. Our results, given in the real as well as the reciprocal space, can be applied in spectrum analysis of small-angle scattering experiments and nonequilibrium molecular dynamics simulations of soft matter under flow.

Figure 1

The variation between the analytical formula [Eq. (56)] and the formulas of perturbation expansion [Eqs. (33), (35)] as a function of $Q{R}_g$ for (a) $\mathrm{\Delta }{S}_2^{-2}\left(Q\right)$ and (b) $\mathrm{\Delta }{S}_0^0\left(Q\right)$ with different shear strains.

Figure 2

The (a) $g\left(r\right)$ and (b) $g_2^{-2}\left(r\right)$ from molecular dynamics simulation using the LAMMPS software and SLLOD algorithm, where $N=16000$, $\rho =0.07843{\AA }^{-3}$, shear rate $1.3143\times {10}^{11}\mathrm{se}{\mathrm{c}}^{-1}$, temperature $1500\mathrm{K}$, time step 1 fs, and modified Johnson potential were used.

Figure 3

The nonaffine strain distribution as a function of $r$ predicted by Eq. (22) and Eq. (37), where the data points were obtained from molecular dynamics simulation using LAMMPS software and SLLOD algorithm.