.. _wlc_copoly:
.. .. automodule:: wlc_copoly

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 :ref:`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
:math:`\sigma_{\alpha}(s)` (for :math:`\alpha = A, B`), which equals 1 if the monomer
segment at :math:`s` is the :math:`\alpha` species.
For a diblock copolymer with an :math:`A`-block of length :math:`f_{A} N`,
we have
:math:`\sigma_{A}(s < f_{A} N)=1` and
:math:`\sigma_{A}(s \ge f_{A} N)=0`.



Two-point Structure Factor for a Diblock Copolymer
--------------------------------------------------