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Abstract: A rigorous theory of liquid-crystal transitions is developed starting fromthe Liouville equation. The starting point is an all-atom description and a setof order parameter field variables that are shown to evolve slowly via Newton-sequations. The separation of timescales between that of atomic collisions andthe order parameter fields enables the derivation of rigorous equations forstochastic order parameter field dynamics. When the fields provide a measure ofthe spatial profile of the probability of molecular position, orientation, andinternal structure, a theory of liquid-crystal transitions emerges. The theoryuses the all-atom-continuum approach developed earlier to obtain a functionalgeneralization of the Smoluchowski equation wherein key atomic details areembedded. The equivalent non-local Langevin equations are derived andcomputational aspects are discussed. The theory enables simulations that aremuch less computationally intensive than molecular dynamics and thus does notrequire oversimplification of the system-s constituent components. Theequations obtained do not include factors that require calibration and can thusbe applicable to various phase transitions which overcomes the limitations ofphenomenological field models. The relation of the theory to phenomenologicaldescriptions of Nematic and Smectic phase transitions, and the possibleexistence of other types of transitions involving intermolecular structuralparameters are discussed.



Autor: Zeina Shreif, Stephen Pankavich, Peter Ortoleva

Fuente: https://arxiv.org/



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