randcopoly

This folder contains Matlab scripts to calculate and plot the structure factor and spinodal decomposition of an A-B semiflexible random copolymer based on a polymer field theoretic formulation [1].
For a given chemical correlation λ, number of monomers N, and monomer length (in Kuhn segments) N_M, this package calculates the melt structure factor (density-density correlations), the spinodal Flory-Huggins parameter χ_S, and critical wavemode of phase segregation q^*. The folder "functions" provides functions s2invwlc and kmaxwlc that calculate the structure factor of semiflexible (wormlike chain model) random copolymer (s2invwlc) and the critical wavemode (location of peak) in the structure factor (kmaxwlc). Similar codes can be found for flexible random copolymers based on the Gaussian chain model (s2invgc and kmaxgc) and for perfectly rigid random copolymers (s2invrr and kmaxrr).

This package was developed by Shifan Mao, Quinn MacPherson, and Andrew Spakowitz [1]

Installation

Open Matlab and change directory to randcopoly. Then add the folder functions to path with

addpath('functions')

Example Usage

Here is an example of using the package to calculate the structure factor (density-density correlations) of rigid, anti-correlated random copolymers.

% Example 1: plot density-density correlations vs wavevector at different CHI
N=100;  % total of 100 monomers
NM=0.1; % each monomer has 0.1 Kuhn steps
LAM=-0.75; % anti-correlated random copolymer
FA=0.5;    % equal chemical composition

% find spinodal CHIS
[kval,sval]=kmaxwlc(N,NM,FA,LAM);
CHIS=0.5*sval;
CHI=CHIS*[0 0.2 0.4 0.6 0.8];  % range of CHI values (scaled by spinodal)

RM=sqrt(r2wlc(NM));  % end-to-end distance of a monomers
K0=1e-2;  % minimum wavevector
KF=1e2;   % maximum wavevector
NK=201;  % number of wavevectors
K=transpose(logspace(log10(K0),log10(KF),NK))/RM;

% evaluate s2inv
[SINV]=s2invwlc(N,NM,FA,LAM,K);
figure;hold
for I=1:length(CHI)
    COL=(I-1)/(length(CHI)-1);
    loglog(RM*K,1./(-2*CHI(I)+SINV),'-','LineWidth',2,'Color',[COL 0 1-COL])
end
xlabel('R_Mq');ylabel('S(q)');box on;
set(gca,'xscale','log');set(gca,'yscale','log');axis([K0 KF 1e-2 1e1])

As another example, the spinodal (order-disorder transition) of flexible random copolymers can be calculated as follows

% Example 2: find spinodal vs. fraction of A monomers
N=100;  % total of 100 monomers
NM=10; % each monomer has 10 Kuhn steps
LAM=0; % ideal random copolymer

FAV = linspace(0.1,0.9,101);
CHIS = zeros(length(FAV),1);
for ii = 1:length(FAV)
    FA = FAV(ii);
    [kval,sval,d2gam2]=kmaxwlc(N,NM,FA,LAM);
    CHIS(ii)=0.5*sval;  % spinodal
end
figure;plot(FAV,CHIS*NM,'k-','linewidth',2)
xlabel('f_A');ylabel('\chi_S v N_M')

[1] Mao, Shifan, Quinn J. MacPherson, Steve S. He, Elyse Coletta, and Andrew J. Spakowitz. "Impact of Conformational and Chemical Correlations on Microphase Segregation in Random Copolymers." Macromolecules (2016).