Thermodynamics atomistic simulation approach

Exploiting the principles of statistical mechanics, atomistic simulations allow for the calculation of macroscopically measurable properties from microscopic interactions. Structural quantities (such as intra- and intermolecular distances) as well as thermodynamic quantities (such as heat capacities) can be obtained. If the statistical sampling is carried out using the technique of molecular dynamics, then dynamic quantities (such as transport coefficients) can be calculated. Since electronic properties are beyond the scope of the method, the atomistic simulation approach is primarily applicable to the thermodynamics half of the standard physical chemistry curriculum. 

Atomistic simulations can be used to estimate defect free energies which can then be used as input parameters in thermodynamic models for copolymer crystallization. Recent work by Wendling et al [167-170] has demonstrated the utility of this combined approach conclusively. It is anticipated that such investigations will become increasingly more common in the future. 

Jawalkar, S. S., Adoor, S. G., Sairam, M., Nadagouda, M. N., and Aminabhavi, T. M. 2005. Molecular modeling on the binary blend compatibility of poly(vinyl alcohol) and poly(methyl methacrylate) An atomistic simulation and thermodynamic approach. Journal of Physical Chemistry B 109 15611-15620. 

Diallo MS, Cagin T, Faulon JL, Goddard WA (1998) Thermodynamic properties of asphaltenes a predictive approach based on computer assisted structure elucidation and atomistic simulations. In Asphaltenes and Asphalts, II. Yen TF, Chilingarian GV (eds), Elsevier Science, p 103-127 Domine F (1987) Influence de la pression et de la temperature sur la cinetique de pyrolyse d hydrocatbures purs. Etude experimentale et simirlation nirmerique. Implications geochemiques. Thesis, 1987, Univ. P. and M. Curie, Paris. 

Before we can discuss in detail the simulation of adsorption and diffusion in zeolites using atomistic simulation we must ensure that the methods and potentials are appropriate for modelling zeolites. The work of Jackson and Catlow reviewed in the previous section shows the success of this approach. Perhaps the most critical test is to apply lattice dynamics and model the effect of temperature as any instability will cause the calculation to fail. Thus we performed free energy minimization calculations on a range of zeolites to test the methodology and applicability to zeolites. As noted in Section 2.2, the extension of the static lattice simulation technique to include the effects of pressure and temperature leading to the calculations of thermodynamic properties of crystals and the theoretical background to this technique have been outlined by Parker and Price [21], and this forms the basis of the computer code PARAPOCS [92] used for the calculations. 

An early version of a CG model with explicit solvent was developed by Smit et al., to study the dynamical interface between water and oil [26]. A similar strategy was also used by Goetz and Lipowsky [30] to simulate the self-assembly of a model surfactant into micelles and bilayers. Later, Klein and coworkers employed thermodynamic properties derived from atomistic simulations to develop a CG model for surfactants that includes the chemical structure [24, 31]. In this form, the procedure used to obtain the simplified potential functions of the CG model bears some level of similarity to the force-matching method used to fit simple potential functions for pairs of atoms against a fully electronic description [32]. Voth and coworkers later essentially followed this latter approach to also define an algorithm based on the force-matching procedure specific for CG-MD [33-35]. 

A number of direct ways for linking atomistic and meso-scale melt simulations have been proposed more recently. The idea behind these direct methods is to reproduce structure or thermodynamics of the atomistic simulation on the meso-scale self-consistently. As this approach is an optimization problem, mathematical optimization techniques are applicable. One of the most robust (but not very efficient) multidimensional optimizers is the simplex optimizer, which has the advantage of not needing derivatives, which are difficult to obtain in the simulation. The simplex method was first applied to optimizing atomistic simulation models to experimental data. We can formally write any observable, like, for example, the density p, as a function of the parameters of the simulation model Bj. In Eq. [2], the density is a function of the Lennard-Jones parameters. 

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