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LAMMPS-Cohesive Energy Density
LAMMPS-Cohesive Energy Density
LAMMPS-CED automates calculation of the cohesive energy density of molecular
systems, together with the closely related solubility parameter and heat of vaporization.
The term cohesive energy density (cohesive energy per unit volume, or CED)
was coined by physical chemist George Scatchard in his 1931 theoretical treatment of the thermodynamics of mixing of non-electrolyte solutions , which was an evolution of studies initiated more than a decade earlier by solution theory pioneer Joel Hildebrand.
Here, the term cohesive energy represents the increase in energy of a compound
if all the intermolecular forces are removed - e.g. as would occur if all
molecules were separated by an infinite distance. Scatchard's theory predicted
that the enthalpy of mixing in a binary nonelectrolyte mixture would be given by
the product of the volume fractions of the components multiplied by a term
involving the differences in the square roots of the cohesive energy densities
of the components. Hildebrand subsequently designated the latter as
the solubility parameters (δi) of the individual pure components .
Identification of the cohesive energy with the energy required to separate
molecules in a liquid by an infinite distance provides a convenient method for
experimental determination of cohesive energy densities and solubility
parameters from measured enthalpies of vaporization, namely using the relation:
where, ρ and M denote the density and molar mass, R is the gas constant and T
In classical forcefield-based molecular simulations, the cohesive energy
essentially corresponds to the intermolecular nonbonded energy averaged over
an equilibrium statistical mechanical ensemble of liquid configurations.
although this is conceptually simple, in practice the computation can require
examination of many thousands of individual configurations. The LAMMPS-CED
module of the MedeA®-LAMMPS software is designed to perform this operation
automatically without the need for post-processing of snapshots taken from
potentially unwieldy trajectory files. Moreover, since the nonbonded energy
typically contains contributions from both coulmbic and van der Waals repulsive
and dispersive interactions, LAMMPS-CED automatically reports this
decomposition, which can be helpful when the solubility parameter approach is
used to predict or understand thermodynamic compatibility of different
materials . As with other property calculations within the MedeA® environment,
monitoring of convergence and analysis of uncertainties is performed automatically
for the CED and associated quantities and reported at the end of the simulation.
In addition to use of the CED in correlating and predicting cohesive and adhesive
properties of materials, calculation of heats of vaporization (ΔHv) can be
particularly useful in assessing the quality of intermolecular potentials, or
forcefields. This is shown in the following table, which lists CED and
ΔHv values for a homologous series of hydrocarbons calculated using the
Materials Design® PCFF+ forcefield, clearly illustrating the high accuracy
achievable using the MedeA® software.
1. Scatchard, G., Equilibria in Non-Electrolyte Solutions in Relation to the
Vapor Pressures and Densities of the Components, Chem. Rev, 8, pp 321-333
2. Hildebrand, J.H., A Critique of the Theory of Solubility of
Non-Electrolytes, Chem. Rev. 44, pp 37-45 (1949).
3. Barton, A.F.M. CRC Handbook of Solubility Parameters and Other Cohesion
Parameters, 2nd Edition, CRC Press, Boca Raton, Florida, USA (1991).