Renormalization of the one-loop theory of fluctuations in polymer blends and diblock copolymer melts

Abstract

Attempts to use coarse-grained molecular theories to calculate corrections to the random-phase approximation (RPA) for correlations in polymer mixtures have been plagued by an unwanted sensitivity to the value of an arbitrary cutoff length, {\it i.e.}, by an ultraviolet (UV) divergence. We analyze the UV divergence of the inverse structure factor $S^{-1}(k)$ predicted by a `one-loop' approximation similar to that used in several previous studies. We consider both miscible homopolymer blends and disordered diblock copolymer melts. We show, in both cases, that all UV divergent contributions can be absorbed into a renormalization of the values of the phenomenological parameters of a generalized self-consistent field theory (SCFT). This observation allows the construction of a UV convergent theory of corrections to SCFT phenomenology. The UV-divergent one-loop contribution to $S^{-1}(k)$ are shown to be the sum of: (i) a $k$-independent contribution that arises from a renormalization of the effective $\chi$ parameter, (ii) a $k$-dependent contribution that arises from a renormalization of monomer statistical segment lengths, (iii) a contribution proportional to $k^2$ that arises from a square-gradient contribution to the one-loop fluctuation free energy, and (iv) a $k$-dependent contribution that is inversely proportional to the degree of polymerization, which arises from local perturbations in fluid structure near chain ends and near junctions between blocks in block copolymers.

arXiv comment35 pages, 2 figures

References in corpus (1)

• Diagrammatic analysis of correlations in polymer fluids: Cluster diagrams via Edwards' field theory

Cited by in corpus (8)

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• Theory of Polymer Chains in Poor Solvent: Single-Chain Structure, Solution Thermodynamics and Theta Point
• Renormalized one-loop theory of correlations in polymer blends
• On the chain length dependence of local correlations in polymer melts and a perturbation theory of symmetric polymer blends
• Renormalized One-loop Theory of Correlations in Disordered Diblock Copolymers
• Stimuli-responsive brushes with active minority components: Monte Carlo study and analytical theory
• A hybrid particle-continuum resolution method and its application to a homopolymer solution
• Simple Calibration of Block Copolymer Melt Models