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Simple microscopic models of complex systems

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The use of hard-core and square-well interaction potentials in the modelling of condensed phase systems has a long history dating back to the study of virial expansions of the equation of state of a liquid in 1885. Models based on these simple interactions continue to be useful since such interaction potentials frequently capture the relevant physical characteristics of a system yet are analytically tractable. In this talk some illustrations of the use of discontinuous potentials are presented.

First, the construction of discontinuous potential models of protein-like chains is discussed. It is shown that for a protein-like chain in which the constituents interact via hard-core and square-well interactions, the structure and folding dynamics of the system can be analyzed via a Markov state model in which the temperature dependence of the thermodynamic and kinetic parameters in the Markov state model are known. This knowledge enables a thorough analysis of the connection between the morphology of the free energy landscape and the folding dynamics of the protein-like chain.

Next, it is shown how models of systems in which constituents interact through continuous potentials can be used to develop discontinuous potential models through energy terracing. This approach is demonstrated for a fluid system composed of interacting rigid bodies using the exact rotational motion of the rigid components.

Finally, a simple microscopic model of chemically-powered Janus motors is presented in which motor interactions with solvent particles occurs through hard collisions. The spherical Janus particles, consisting of catalytic and non-catalytic hemispheres, produce a gradient in concentration of chemical species that leads to self-generated diffusiophoretic motion. The simple nature of the interactions enables analytic expressions for the propulsion velocity as well as the concentration and fluid velocity fields to be obtained. The analysis of the emergent collective properties of the model from first principles provides a foundation from which the validity and limitations of approximate theories of the dynamics may be assessed.

This talk is part of the Theoretical Chemistry Informal Seminars series.

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