**PRISM Theory Study of Amphiphilic Block Copolymer Solutions with Varying
Copolymer Sequence and Composition**

I Lyubimov and DJ Beltran-Villegas and A Jayaraman, MACROMOLECULES, 50, 7419-7431 (2017).

DOI: 10.1021/acs.macromol.7b01419

We present a comparison of Polymer Reference Interaction Site Model (PRISM) theory and molecular dynamics (MD) simulations for studying amphiphilic block copolymers in solution. We use a generic coarse- grained model to represent amphiphilic A-B block copolymers in implicit solvent with the solvophobicity of the B segments captured using effective B-B pairwise attraction modeled using the Lennard-Jones potential. We study the assembly of the amphiphilic A B block copolymer as a function of solvophobicity for varying copolymer sequences (diblock and triblock) and composition (solvophobic-rich or solvophilic-rich). The PRISM theory equation along with the atomic Percus-Yevick closure is solved to obtain the intermolecular pair correlations in real space, g(r), and structure factors in Fourier space, S(k), for block copolymer solutions at increasing values of solvophobicity. The real-space intermolecular pair correlation functions and structure factors from PRISM theory and from MD simulations are compared directly. We find excellent quantitative agreement in g(r) between PRISM predictions and MD simulations at low solvophobicities where the block copolymer solution is in a disordered state. PRISM theory captures the concentration fluctuations at low solvophobicities well but fails to converge to a numerical solution at higher solvophobicities where we see evolution of ordered structures in MD simulations. Despite this drawback, PRISM theory is a valuable tool as the low solvophobicity results from PRISM predict many of the thermodynamic and structural signatures of the block copolymer solutions at higher solvophobicities. For example, we find that the inverse microphase peak 1/S(k*) at low solvophobicities obtained from PRISM theory, which when extrapolated to zero quantifies the spinodal transition solvophobicity value, is in good quantitative agreement with MD simulations. Additionally, in those systems where MD simulations predict aggregation of the micelles/clusters at high solvophobicity, the structure factors from PRISM theory at low solvophobicity also present an increasing value in the zero-wave vector structure, indicating a tendency toward macrophase separation at higher solvophobicity. These results show the capability of PRISM theory to predict assembly over a wide range of design parameters of copolymers and guide the use of computationally intensive molecular simulations.

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