Nonequilibrium Molecular Conformations in Polymer Self-Consistent Field Theory

Abstract

The morphology of a multicomponent polymer melt within selfconsistent field theory (SCFT) is completely characterized by the spatial density distribution of the components. SCFT therefore assumes that the molecular conformations are fast variables that adopt their equilibrium statistics with respect to a given density distribution. There are multiple situations, e.g., the early stages of structure formation, where this assumption breaks down because the densities evolve significantly on the time scale of the single-chain relaxation. Here, we develop a SCFT that uses as slow variables both densities and the variance of the first, most slowly relaxing Rouse mode and we design a numerical scheme for its solution based on singlechain propagators. Applications to diblock and multiblock copolymers are presented.

Dynamics of Nonequilibrium Single-Chain Conformations in Triblock Copolymers

“…We employ an additional Hubbard− Stratonovich transformation to decouple these nonlocal interactions via an auxiliary variable η. 28 For λ > 0, we employ i k j j j j j y { z z z z z i k j j j j j y…”

“…Here, we only provide a brief description of the salient features of SCFT with constrained variance of the first Rouse modes and refer the reader to ref for the general formalism. The free energy (per chain in units of k B T ) of the constrained system takes the form …”

“…The calculation of the single-chain partition function is a challenge because the term represents pairwise interactions between different segments along the molecular contour. We employ an additional Hubbard–Stratonovich transformation to decouple these nonlocal interactions via an auxiliary variable η . For λ > 0, we employ …”

“…Recently, we have developed a SCFT strategy 28 that can account for nonequilibrium molecular configurations by using both the locally varying A density, ϕ A (r), and the average variance of the first Rouse modes,  1 2 , as slow, collective order parameters (vide infra SCFT) and calculate the free-energy functional,…”

“…Recently, we have developed a SCFT strategy that can account for nonequilibrium molecular configurations by using both the locally varying A density, ϕ A ( r ), and the average variance of the first Rouse modes, , as slow, collective order parameters ( vide infra SCFT) and calculate the free-energy functional, , within mean-field approximation. The first Rouse mode of the i th macromolecule with configuration r ̂ i ( s ) is defined by the vector and characterizes the large-scale conformations of this macromolecule.…”