Numerical simulation of star polymers under shear flow using a coupling method of multi-particle collision dynamics and molecular dynamics

Abstract

The numerical simulation of flow-induced structures is important for the flow analysis of complex fluids. Several schemes have been proposed for coupling the macro-flow computation and the microsimulation of the inner structure of complex fluids. In the present study, the flow-induced structure of star polymers was numerically simulated using a coupling method of multi-particle collision dynamics (MPCD) and coarse-grained molecular dynamics (MD). The polymers were modeled as elastic dumbbells, which consist of finitely extensible nonlinear elastic springs and beads. The motion of the beads was computed by MD. The MPCD was applied to model the effect of Brownian motion and hydrodynamic interactions among the beads. In the present study, the MPC-AT+a algorithm was employed for the collision steps in MPCD computations. The behavior of linear polymers in a shear flow was numerically analyzed to confirm the validity of the present simulation scheme. The numerical results agree well with both experimental results and predictions by other numerical methods. Furthermore, the simulation of star polymers under shear flow was carried out. The present simulation captured characteristic behaviors such as the configuration of the star polymers, which was more compact for polymers with more arms due to extruded volume effects, polymers tumbling at high Weissenberg numbers, and the fluctuation in expansions in the direction of flow decreasing for polymers with more arms.

Deciphering the dynamics of star molecules in shear flow

“…The prefactor in eqn (15) for rings in solution results to be c y C 2.6 while for starts in solution we get c y C 3.1. The scaling relations for linear chains in shear flow are also in agreement with eqn (14) and its large-shear rate limit. Simulations 17 and experiments 18 reported m g = Wi a and tumbling frequency f tb B Wi a , typically with a C 2/3, although these exponents might change in semiflexible chains.…”

“…The frequency ratio o L /O can be a useful quantity for determining different dynamic regimes of the sheared molecules. We find that O (in eqn (14)) and o L (or more precisely o G in eqn (10)) are directly connected with the polymer shape.…”

“…where c f should be an O(1) constant. Before falsifying eqn (14) against simulation results, it is interesting to consider the force-balance in the molecular frame coordinates, given by the eigenvectors of the gyration tensor. In this frame, the molecular elongations can be taken as the square root of the eigenvalues of G, and we note them as X a 0 = G a 1/2 .…”

“…More recently, Xu and Chen 7 have presented a numerical study of star polymers with a range of functionality f A [3,60] and m = 20 in melts under shear, and Yamamoto et al have revisited the problem of sheared star polymers in solution. 14 At large enough shear rates, any measure of the polymer extension in the flow plane reveals the onset of alternating extensions and contractions of the molecule, typically analyzed from the cross correlation of the molecular elongations in the flow and gradient directions C XY (t). 15,16 This behavior is quite general and it has also been studied in linear chains (either free 17,18 or tethered 16 ) and in polymer rings under shear.…”

Rotation Dynamics of Star Block Copolymers under Shear Flow

“…To date there has been a considerable amount of work on the response of flexible polymers with different architectures (e.g., linear, ring, hyperbranched and star polymers) to shear stress, which has revealed generic and specific properties of such systems. On top of experimental techniques, the development of simulation methods allowing to efficiently couple the solvent particles and monomers, a wide spectrum of behaviors has been found regarding the average deformation and the orientation as a function of the shear rate, as well as, multiple dynamic responses [3][4][5][6][7][8]. The latter encompass stretching and recoil, tumbling, tank-treading, rupture, and collapse of polymers and ultimately determine the (complex) viscoelastic response of dilute bulk phases.…”