Dynamics of Polymers: a Mean-Field Theory

We derive a general mean-field theory of inhomogeneous polymer dynamics; a theory whose form has been speculated and widely applied, but not heretofore derived. Our approach involves a functional integral representation of a Martin-Siggia-Rose type description of the exact many-chain dynamics. A saddle point approximation to the generating functional, involving conditions where the MSR action is stationary with respect to a collective density field $\rho$ and a conjugate MSR response field $\phi$, produces the desired dynamical mean-field theory. Besides clarifying the proper structure of mean-field theory out of equilibrium, our results have implications for numerical studies of polymer dynamics involving hybrid particle-field simulation techniques such as the single-chain in mean-field method (SCMF)

Hydrodynamic Self-Consistent Field Theory for Inhomogeneous Polymer Melts

We introduce a mesoscale technique for simulating the structure and rheology of block copolymer melts and blends in hydrodynamic flows. The technique couples dynamic self consistent field theory (DSCFT) with continuum hydrodynamics and flow penalization to simulate polymeric fluid flows in channels of arbitrary geometry. We demonstrate the method by studying phase separation of an ABC triblock copolymer melt in a sub-micron channel with neutral wall wetting conditions. We find that surface wetting effects and shear effects compete, producing wall-perpendicular lamellae in the absence of flow, and wall-parallel lamellae in cases where the shear rate exceeds some critical Weissenberg number.Comment: Revised as per peer revie

Spin facilitated Ising model with long range interaction

We study the dynamics of a spin facilitated Ising model with long range kinetic constraints. To formulate those restrictions within an analytical approach we introduce the size of a kinetic active environment of a given spin. Based on a Master equation in second quantized form, the spin-autocorrelation function is calculated. It exhibits a pronounced slow dynamics, manifested by a logarithmic decay law of the spin-autocorrelation function. In case of an infinite kinetic interaction the mean field solution yields an asymptotic exact expression for the autocorrelation function which is in excellent agreement with Monte Carlo Simulations for finite interaction lengths. With increasing size of the active zone the cooperative processes, characterizing the facilitated model with short range kinetic interaction, become irrelevant. We demonstrate that the long range kinetic interaction dominates the actual spin configurations of the whole system and the mean field solution is the exact one.Comment: 18 pages, 5 figure

Orientations of the lamellar phase of block copolymer melts under oscillatory shear flow

We develop a theory to describe the reorientation phenomena in the lamellar phase of block copolymer melt under reciprocating shear flow. We show that similar to the steady-shear, the oscillating flow anisotropically suppresses fluctuations and gives rise to the parallel-perpendicular orientation transition. The experimentally observed high-frequency reverse transition is explained in terms of interaction between the melt and the shear-cell walls.Comment: RevTex, 3 pages, 1 figure, submitted to PR