Integral equation theory of block copolymer liquids. II. Numerical results for finite hard-core diameter chains

Abstract

The spatially local and long wavelength properties of diblock copolymer melts are studied using the polymer reference interaction site model theory. Two new molecular based closure approximations, the ‘‘reference-molecular mean spherical approximation’’ (R-MMSA) and the ‘‘reference-molecular Percus–Yevick’’ (R-MPY) approximation are investigated numerically for structurally symmetric, flexible, and semiflexible copolymers with finite hard-core diameters. For these models both closures lead to a destruction of all spinodal instabilities for finite degrees of polymerization. Results using the R-MMSA closure for the larger chain lengths studied approach the analytic predictions of the Gaussian thread model. On the other hand, numerical results for the R-MPY closure show a temperature regime in which there is an apparent chain length independent fluctuation stabilization for moderate degrees of polymerization in qualitative agreement with recent Monte Carlo simulations. However, we believe this apparent scaling arises from a very slow approach towards the asymptotic, finite size fluctuation behavior analytically derived in the previous paper for the Gaussian thread model. In accord with recent simulations, the peak scattering wave vector exhibits temperature dependence due to collective, many chain fluctuation effects. Predictions of the local structure and composition in the disordered phase are made which show that considerable length scale dependent deviations from homopolymer melt packing emerge at low temperatures.

Theoretical coarse-graining approach to bridge length scales in diblock copolymer liquids

“…Schweizer and coworkers developed an integral equation description of block copolymer melts that formally recovers the scaling behaviors obtained in field theories with only small differences [28,29,37,39,40]. In this case, however, the stabilization of the disordered state close to the MST is of enthalpic origin.…”

“…The calculation described so far is standard in PRISM theory and examples have been reported in several papers. [28,29,37,38] The cooling curves, obtained from the self-consistent solution of Eq. (56) for the system in this study, are presented in Fig.…”

“…Moreover, repulsive interactions between segments of different chemical nature are quantified by the interaction parameter, χ eff . Concentration-fluctuation stabilization enters through the polymer reference interaction site model (PRISM) theory for the monomer-level description, [27,28,29] and deviations from mean-field theory [30] are predicted by the coarse-grained approach as well. The two blocks follow Gaussian intramolecular statistics, which is a good approximation for copolymer melts, when each block has a degree of polymerization N α > 30, with α ∈ A, B, and for the region in the phase diagram from the high-temperature to the weak segregation regime (χ ef f N << 10.5 for symmetric composition f = 0.5), where the system is isotropic.…”

Influence of monomer sequence on microstructure of nonadditive hard chain copolymers: Simulation and equation of state

“…1 The developed theories predict the ODT as well as spacing between structural units and shape of microstructures as a function of copolymer structure, volume fraction and strength of interaction among components of the copolymer. [2][3][4][5][6][7][8][9][10] Mean field theories were developed to predict the periodic spacing in copolymers in the weak as well as strong segregation regimes ͑SSR͒. [2][3][4]9 Banaszak and White-more developed a self-consistent field theory ͑SCFT͒ to predict the properties of copolymers in the SSR and intermediate segregation regime ͑ISR͒.…”

Systematic and simulation-free coarse graining of homopolymer melts: a relative-entropy-based study

“…[12] (referred to as Paper I), we proposed a systematic and simulation-free strategy for coarse graining of polymer melts, where we used integral-equation theories, [13][14][15] instead of many-chain molecular simulations, to obtain the structural and thermodynamic properties of both original and coarse-grained (CG) systems, and quantitatively examined how the pair potentials between CG segments and the thermodynamic properties of CG systems vary with the number of CG segments per chain N . [12] (referred to as Paper I), we proposed a systematic and simulation-free strategy for coarse graining of polymer melts, where we used integral-equation theories, [13][14][15] instead of many-chain molecular simulations, to obtain the structural and thermodynamic properties of both original and coarse-grained (CG) systems, and quantitatively examined how the pair potentials between CG segments and the thermodynamic properties of CG systems vary with the number of CG segments per chain N .…”