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Lattice Models in Molecular Thermodynamics: Merging the Configurational and Translational Entropies
Per-Olof Åstrand1, Rodrigo de Miguel2
1Department of Chemistry, NTNU─Norwegian University of Science and Technology, Trondheim NO-7491, Norway.
The Journal of Physical Chemistry. B
|December 13, 2024
Summary
Merging configurational and molecular translational entropy in lattice models reveals a new equation of state. This modified statistical thermodynamics approach introduces temperature-dependent heat capacity, enhancing classical models.
Area of Science:
- Statistical Thermodynamics
- Physical Chemistry
- Condensed Matter Physics
Background:
- Lattice models are fundamental in statistical thermodynamics for calculating configurational entropy.
- Existing models often treat configurational and molecular translational entropy separately.
- A unified approach is needed for a more consistent thermodynamic description.
Purpose of the Study:
- To demonstrate the necessity of merging configurational and molecular translational entropy within lattice models.
- To develop a modified lattice model for a consistent thermodynamic framework.
- To derive a new equation of state and explore its implications.
Main Methods:
- Utilizing a lattice model framework.
- Replacing the conventional lattice site volume with a quantum volume (thermal wavelength cubed).
- Deriving a modified equation of state.
Main Results:
- A new equation of state, the Bragg-Williams equation of state, was derived.
- A generalized van der Waals equation of state was obtained from the new model.
- The derived models exhibit temperature-dependent heat capacity, unlike standard van der Waals.
Conclusions:
- Merging configurational and molecular translational entropy is crucial for consistent lattice models.
- The Bragg-Williams equation of state offers a more comprehensive description of thermodynamic systems.
- The temperature-dependent heat capacity highlights the advancements over traditional models.
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