- Our Capabilities
- Software
- MedeA®
- InfoMaticA
- Specialty Builders
- Analysis and Properties
- Electronics
- Mechanical/Thermal Properties
- Phonon - Thermodynamic Properties
- Transition State Search
- P3C Polymer Property Prediction using Correlations
- LAMMPS-Diffusion
- LAMMPS-Thermal conductivity
- LAMMPS-Viscosity
- Embedded Atom Potentials
- Forcefields
- ForcefieldOptimizer
- LAMMPS-CED
- MedeA Surface Tension
- MedeA-HT
- MedeA-Morphology

- Compute Engines
- JobServer

TaskServer - Climbing Length Scales

- Services
- Library

# 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 [1], 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

**(δ**

*solubility parameters*_{i}) of the individual pure components [2].

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*

the temperature.

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 [3]. 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 (ΔH_{v}) can be

particularly useful in assessing the quality of intermolecular potentials, or

forcefields. This is shown in the following table, which lists CED and

ΔH_{v} values for a homologous series of hydrocarbons calculated using the

Materials Design® PCFF+ forcefield, clearly illustrating the high accuracy

achievable using the MedeA^{®} software.

### References

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

(1931).

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).