Testing universality in block copolymers

• Applicant: Dr. Jens Glaser
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2012 to 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 215350019

The standard theoretical description of microphase separation in diblock copolymers, self consistent field theory (SCFT), yields a phase diagram that depends on only a few parameters, but that can be applied to a wide variety of chemical systems and computational models. Recent work predicts the existence of a generalized equation of state that instead depends on the parameters of SCFT and on one additional parameter, the invariant degree of polymerization. This parameter is a measure of the degree of overlap between polymers in the melt, and is proportional to chain length. Two microscopically different systems with equal SCFT parameter values are equivalent if and only if they have the same invariant degree of polymerization. SCFT is recovered in the limit of infinitely strongly overlapping polymers of this more complete description. I propose to compare extensive computer simulations of both disordered and ordered phases of several different coarse-grained computational models of diblock copolymers to quantitatively test whether any generalized equation of state of the proposed form can accurately describe data from a variety of models. To the extent that the behavior is indeed universal, I will test how accurately it is described by specific approximations, including the "renormalized one-loop" approximation. These simulations will combine use of graphics processing units (GPUs) as a fast engine with extended ensemble and thermodynamic integration techniques to equilibrate melts of long chains and accurately identify phase transitions. Novel methods of analysis will focus on testing predictions of universal relationships among measurable quantities that follow directly from the existence of a universal equation of state. Successful demonstration of universality would provide a compelling justification for the study of coarse-grained models, and a more sophisticated theoretical framework for analyzing simulations and experimental studies of such systems.

• DFG Programme: Research Fellowships
• International Connection: USA
• Host: Professor Dr. David Morse