Theory of polymers in poor solvents: Inter-chain interaction, second virial coefficient, and Θ point

Abstract

Quantifying inter-chain interaction and determining Θ point is of fundamental importance in polymer science and engineering. Here, we apply a constrained self-consistent field theory which can fully capture the coupling between the position-dependent interaction and chain conformation. By tracking the density profile and free energy as a function of center-of-mass separation distance, we analyze the kinetic process of fission/fusion and calculate the potential of mean force as well as the second virial coefficient B 2 thereby in poor solvents. We show that the fission of the two-chain associate exhibits a necking behavior and a discontinuous breaking point, which shares the similarity with the tensile process of typical macroscopic bulk materials. The Θ point is determined by extrapolating the χ -dependence of B 2 plot to the vanishing point for very long chains. Our theory predicts a linear relationship between χ Θ ( N ) and N −1/2 , with a positive slope. The intercept yields χ Θ (∞) = 0.5, which coincides with the prediction from Flory-Huggins theory and verifies the consistency of the Θ point defined by different criteria in the limit of infinitely long chain. Furthermore, the slope of χ Θ ( N ) versus N −1/2 becomes larger as chain stiffness increases. χ Θ ( N ) = 0.5 for infinitely flexible polymers. Our theoretical predictions are in good agreement with the results obtained by off-lattice Monte Carlo simulation. • A constrained SCFT is applied to capture the coupling between the position-dependent interaction and chain conformation. • Potential of mean force (PMF) is quantified and kinetic process during fission/fusion of two polymer chains is analyzed. • Θ point χ Θ is determined by extrapolating the χ -dependent second virial coefficient curve. • χ Θ ( N ) is found to linearly depend on N −1/2 with a positive slope and the intercept χ Θ (∞) = 0.5. • The slope of χ Θ ( N ) versus N −1/2 increases with chain stiffness. For infinitely flexible polymers, χ Θ ( N ) = 0.5.