Van Der Waals Lab Report

Van der Waals (EW) interactions are described using a Lennard-Jones potential (L-J 12-6 potential) Eq.4. The Lennard-Jones is a mathematically simple model widely used in molecular simulation that estimates the interaction between a pair of neutral atoms or molecules. Where i and j represent the force centres, Ɛ is the depth of the potential well, r is the distance between the particle i and j, and ϭ is the distance at which the potential reaches its minimum i.e. the separation between the particle i and j when energy is Zero. As it explained in chapter one that the physical description of adsorption is the balancing of intermolecular forces (attractive and repulsive) [10]; when the adsorbate species is a minimum distance from a solid surface

The Lennard-Jones parameters are normally estimated based on properties of single atoms (e.g., size of carbon atom for ϭCC). But these parameters will need to be different when two atoms of different type come together (e.g., C and H in methane will require ϭCH). In this case, we often apply combination rules. The most common are the Lorentz-Berthelot combining rules: Combining rules are somewhat empirical, but they help reduce the number of free parameters in a molecular model. Electrostatics normally modelled by point charges on each atom. Electrostatic (EE) interactions are expressed in terms of partial charges using classical Coulomb’s law which is describing the electronegativity differences between atoms in free space. In the presence of a dielectric material (such as water), the Electrostatic (EE) interactions between points charges is reduced by a factor d called the relative permittivity.

ε0 is the dielectric constant in vacuo and rij is the distance between the point charges considered.

The charge equilibration method was used to calculate the charges for MOFs in this dissertation, which is implemented in Material Studio. Charge equilibration is a scheme that finds the set of partial atomic charges that minimize the energy of the system. Wilmer et al. in 2012 modified Rappe and Goddard work by estimating partial atomic charges that uses all of the measured ionization energies for every atom in the periodic table [12].

The standard force fields such as UFF [13] (Universal Force Field), OPLS [14] [15] (Optimized Potentials for Liquid Simulations) or Dreiding [16] seem to be able to appropriately simulate the gas behaviour on MOF families. However, despite some studies in the literature, it's more difficult to reproduce experimental crystal-structure and adsorption data for some MOFs families [17][18][19][20][21]. The focus of this dissertation is the use of standard generic force fields for the analysis of the adsorption behaviour of gases on