**At-a-Glance**

The *MedeA* ^{®}[1] *CED* module automates calculation of the cohesive energy density
of molecular systems, together with the closely related solubility parameter, and heat of vaporization.
Both quantities have been widely used in expressions predicting a variety of material properties,
including tensile and bulk moduli, surface tension, glass temperatures, stress to initiate crazing, and
thermodynamic compatibility of mixtures and blends, to cite a few examples [5].

**Key Benefits**

- Performs
*on-the-fly*computation of CED, avoiding the need to save large trajectory files - Reports van der Waals and elactrostatic components separately
- Reports related quantities such as the heat of vaporization of fluids conveniently
- Works with JobServer and TaskServer to run your calculations on the appropriate hardware, centralizing the results
- Integrates with MedeA Forcefields for advanced forcefield handling and assignment of a wide variety of organic liquids and amorphous materials

The term **cohesive energy density** (cohesive energy per unit volume, or CED), was introduced by
physical chemist George Scatchard in his 1931 theoretical treatment of the thermodynamics of mixing
of non-electrolyte solutions [2], which was the result 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 to be separated by an infinite distance. Scatchard’s
theory predicted that the enthalpy of mixing of a binary non-electrolyte mixture would be found
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 (\(\delta\)_{i})
of the individual pure components [3].

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 \(\rho\) and *M* denote the density and molar mass, *R* is the gas constant, and *T* the
temperature.

‘The MedeA LAMMPS-CED module makes it really straightforward to include this important property calculation in any simulation workflow. It automatically performs the essential averaging over configurations without having to save large unwieldy trajectory snapshots, and delivers the results in a format easily imported into database and spreadsheet applications.’

In classical forcefield-based molecular simulations, the cohesive energy essentially corresponds
to the intermolecular nonbond energy averaged over an equilibrium statistical mechanical ensemble
of liquid configurations. Although this is conceptually simple, in practice the computation may
require the examination of 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 extracted from large and potentially unwieldy trajectory files.
Moreover, since the nonbonded energy typically contains contributions from both coulombic 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 [4]. As with other
property calculations within the MedeA environment, monitoring convergence and analyzing
uncertainties are performed automatically for the CED, and associated quantities are reported at
the end of the simulation.

In addition to the use of the CED in correlating and predicting cohesive and adhesive properties
of materials, calculation of heats of vaporization (\(\Delta\) *H*_{v}) can be
particularly useful for assessing the quality of intermolecular potentials, or forcefields. This
is shown in the following table, which lists CED and \(\Delta\) *H*_{v} values for a
homologous series of hydrocarbons calculated using the Materials Design^{®} PCFF+ forcefield,
clearly illustrating the high accuracy achievable using MedeA software.

- Uses the LAMMPS forcefields engine for high performance on any computer from a scalar workstation to a massively parallel cluster

*MedeA Environment**MedeA LAMMPS**MedeA Forcefield**MedeA JobServer and TaskServer*

Learn more about how *MedeA LAMMPS-CED* can been used to compute one of the most commonly used predictors of the properties of polymers and organic materials by viewing the following webinar:

[1] | MedeA and Materials Design are registered trademarks of Materials Design, Inc. |

[2] | Scatchard, G., Equilibria in Non-Electrolyte Solutions in Relation to the Vapor Pressures and Densities of the Components, Chem. Rev., 8, 321-333 (1931). |

[3] | Hildebrand, J.H., A Critique of the Theory of Solubility of Non-Electrolytes, Chem. Rev., 44, 47-45 (1949). |

[4] | Barton, A.F.M., CRC Handbook of Solubility Parameters and Other Cohesion Parameters, 2nd Edition, CRC Press, Boca Raton, Florida, USA (1991). |

[5] | van Krevelen, D.W., Properties of Polymers, 3rd Ed., Elsevier, New York (1990) |

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