Semiflexible Copolymer Materials¶
The physical behavior of semiflexible copolymers is frequently analyzed using a field-theoretic formulation that is capable of predicting the impact of spatially varying concentration profiles on the system thermodynamics. This approach for semiflexible copolymers necessitates evaluation of the vertex functions for a quartic-order perturbation of the free energy in terms of component density fields. This evaluation requires the 2-, 3-, and 4-point density correlation functions, which is an extension of the multi-point structure factor for a homopolymer (see Structure Factor). In this section, we develop the theory and analysis of the multi-point structure factors for diblock and random copolymers as the basis for evaluating the vertex functions.
Diblock Copolymer Multi-point Structure Factor¶
For our polymer-chain representation, we define the monomer-segment identity metric \(\sigma_{\alpha}(s)\) (for \(\alpha = A, B\)), which equals 1 if the monomer segment at \(s\) is the \(\alpha\) species. For a diblock copolymer with an \(A\)-block of length \(f_{A} N\), we have \(\sigma_{A}(s < f_{A} N)=1\) and \(\sigma_{A}(s \ge f_{A} N)=0\).