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UNIVERSITY OF WATERLOO
Waterloo Institute for Nanotechnology (WIN); Department of Chemical Engineering; Department of Physics & Astronomy
Prof. Mark W. Matsen

This is new novel type of simulation for high-molecular-weight block copolymers [1]. Conventional particle-based simulations become exceedingly slow as the length of the polymers is increased to values characteristic of typical experiments. However, this problem can be overcome by inserting some mathematical identities into the partition function, which effectively replace direct interactions between molecules by interactions with fields. This, in turn, allows one to explicitly integrate over the polymer coordinates, leaving just integrals over the fields. In effect, this transforms the particle-based model into a mathematically equivalent field-based model, which is relatively simple to simulate. In particular, it is easily applied to complicated block copolymer architectures [2] and blends [3], which is not the case for traditional particle-based simulations.

The challenge with FTS, however, is that they become computationally intensive and an ultraviolet (UV) divergence emerges as the molecular weight is reduced to experimentally relevant values. Our first application of FTS [4] removed the UV divergence by renormalizing the χ interaction parameter, but this starts to fail just as the molecular weight approaches realistic values. The problem was recently overcome by switching to an effective χ defined using the Morse calibration for particle-based simulations [5]. On the heels of that, we developed a highly efficient algorithm [6], which now allows FTS to be performed at realistic molecular weights. Given these new developments, the future for FTS is very bright. This has been recently demonstrated with simulations of bicontinuous microemulsions [7,8].

For anyone that is interested in trying out FTS, Ref. [9] provides a detailed tutorial on the subject along with open-source code.

[1] M. W. Matsen, Field theoretic approach for block polymer melts: SCFT and FTS. 152, 110901 (2020) J. Chem. Phys. 152, 110901 (2020). ref

[2] R. K. W. Spencer and M. W. Matsen, Field-theoretic simulations of bottlebrush copolymers. J. Chem. Phys. 149, 184901 (2018). ref

[3] R. K. W. Spencer and M. W. Matsen, Fluctuation effects in blends of A+B homopolymers with AB diblock copolymer. J. Chem. Phys. 148, 204907 (2018). ref

[4] P. Stasiak and M. W. Matsen, Monte Carlo field-theoretic simulations for melts of symmetric diblock copolymer. Macromolecules 46, 8037 (2013). ref

[5] T. M. Beardsley and M. W. Matsen, Calibration of the Flory-Huggins interaction parameter in field-theoretic simulations. J. Chem. Phys. 150, 174902 (2019). ref

[6] T. M. Beardsley, R. K. W. Spencer and M. W. Matsen, Computationally efficient field-theoretic simulations for block copolymer melts. Macromolecules 52, 8840 (2019). ref

[7] B. Vorselaars, R. K. W. Spencer and M. W. Matsen, Instability of the microemulsion channel in block copolymer-homopolymer blends. Phys. Rev. Lett. 125, 117801 (2020). ref

[8] R. K. W. Spencer and M. W. Matsen, Coexistence of polymeric microemulsion with homopolymer-rich phases. Macromolecules 54, 1329 (2021). ref

[9] M. W. Matsen and T. M. Beardsley, Field-theoretic simulations for block copolymer melts using the partial saddle-point approximation. Polymers 13, 2437 (2021). pdf