Simulation of entangled polymer solutions

Abstract

We present a computer simulation of entangled polymer solutions at equilibrium. The chains repel each other via a soft Gaussian potential, appropriate for semi-dilute solutions at the scale of a correlation blob. The key innovation to suppress chain crossings is to use a pseudo-continuous model of a backbone which effectively leaves no gaps between consecutive points on the chain, unlike the usual bead-and-spring model. Our algorithm is sufficiently fast to observe the entangled regime using a standard desktop computer. The simulated structural and mechanical correlations are in fair agreement with the expected predictions for a semi-dilute solution of entangled chains.

Entanglement Reduction Induced by Geometrical Confinement in Polymer Thin Films

“…Every chain has N degrees of freedom that correspond to the usual Rouse modes (or alternatively to N beads through the usual Rouse transformation, see Ref. 21), and follows the stochastic first order equation of motion:…”

Dynamical structure of entangled polymers simulated under shear flow

“…Entire studies have been devoted to relate the coarse interaction parameters with the atomistic details of a particular chemical species 58 . However, within the numerical prefactor, the physical properties on the large scale are found to be universal across vastly different polymer models, ranging from lattice-based 43 , to hard bead-and-spring 59 , to our soft blobs 54 . We do not attempt a one-to-one correspondence with any particular experiment, and for a generic model we pick the natural choice of the excluded volume v = λ 3 = b 3 .…”

“…6 ), with an added excluded volume field that we have implemented in Ref. 54 , as well as a shear field that is described in Appendix A of this article. Here ζ = 6πη s bN is the friction coefficient of the chain center of mass, defining the unit of time:…”

5D Entanglement in Star Polymer Dynamics

“…The compromise that we have chosen here is = 128τ at which point we could not detect any chain crossings using direct geometrical analysis on a small system, [21] as well as indirectly by observing chain dynamics on a big system. The frequency of chain crossings, hence the probability of overcoming this energy barrier, is expected to decrease as ∝ exp(−const.…”

“…[13][14][15] Its main outcome is the exponential growth of the relaxation time τ a ∝ e N/Na , where N a is the arm length at the onset of star dynamics. This model was presented in our earlier simulation on linear chains at equilibrium [21] and under shear flow. [16] At the microscopic scale of the monomer, star dynamics have been probed by NSE [17] and computer simulations.…”