Molecular Dynamics Simulations of Amorphous Systems

Department of Pharmaceutical Sciences, College of Pharmacy, University of Kentucky, Lexington, KY, USA 

Computational Pharmaceutical Solid State Chemistry, First Edition. Edited by Yuriy A. Abramov. 2016 John Wiley Sons, Inc. Published 2016 by John Wiley Sons, Inc. 

Full-atom simulations have been of particular interest because of their relevance to real pharmaceutical systems in that the molecular structures are constructed in full atomic detail. In this chapter, simulations of amorphous systems at temperatures below and in some cases above the glass transition temperature (T ) will be explored. While amorphous pharmaceutical systems are generally at temperatures below r, validation of simulations may be more readily done by comparisons at temperatures near or above the where molecular mobility may be sufficiently high that both the simulated and experimental systems may be closer to equilibrium. Above the F certain dynamic processes are sufficiently rapid that they can be studied both experimentally and in the time frames accessible by current MD simulations (typically 1 ps). 

Once the molecular assembly is constructed, energy minimization is necessary to reduce steric contacts and the system is heated to a desired temperature (corresponding to velocities in the Maxwell-Boltzmann distribution) to generate initial positions and velocities of the atoms. During dynamic runs, changes in position and velocity in response to the force field according to Newton s laws of motion are determined with the calculations repeated every 1 or 2fs. 

For the most part, the timescales for the aforementioned kinetic processes are well beyond the accessible timescale for fuUy atomistic MD simulations. Local dynamics such as rotation of a methyl group or a polymer side chain can certainly be explored. For example, in a polymer melt at a temperature of lOOK above the T, the timescale for methyl-group rotations is about Ips and approximately 1-lOns for segmental a-relaxation in a polymer [4b]. Diffusion for even a small molecule such as water in 

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When partially hydrated samples are cooled down to 77 K, no crystallization peak is detected by differential thermal analysis. The x-ray and neutrons show that an amorphous form is obtained and its structure is different from those of low-and high-density amorphous ices already known [5]. Samples with lower levels of hydration corresponding to one monolayer coverage of water molecules are under investigation. This phenomenon looks similar in both hydrophilic and hydrophobic model systems. However, in order to characterize more precisely the nature of the amorphous phase, the site-site partial correlation functions need to be experimentally obtained and compared with those deduced from molecular dynamic simulations. 

The review of models and applications in this section proceeds from few- to many-electron systems. This is not historically accurate, since the first first-principles molecular dynamics simulations were performed on larger systems. However, applications to solids, amorphous materials and liquids have been stressed in other reviews [44-47], so we will take the opportunity to place more emphasis on systems of chemical interest. 

Perhaps a sensible procedure is to consider an approach which incorporates both interatomic potentials (classical forces) and fully quantum mechanical methods. One can compute the properties of smaller systems with quantum mechanical approaches and establish the accuracy, or inaccuracy, of interatomic potentials. For example, some elastic anomalies have been reported for a-cristobalite. These elastic anomalies indicated the presence of a negative Poisson ratio in this crystalline form of silica. With the use of interatomic potentials, it is a trivial matter to compute these properties. If the anomalies are confirmed via such calculations, it is likely that the experimental measurements are accurate, and more computationally intense calculations with quantum forces are merited. Another useful role of interatomic potentials is to perform molecular dynamics simulations, e.g., to examine the amorphization of quartz under pressure. One can easily compute the free energy of large systems as a function of both temperature and pressure via interatomic potentials. Sueh calculations can be useful as guides if interpreted in a judicious fashion. 

Different simulation methods are appropriate for different penetrant polymer systems, depending on the dynamical state of the polymer chains. Within a rubbery polymer or an amorphous polymer above its glass temperature, penetrants diffuse quickly enough 10 cm s ) to use molecular dynamics simulations [22] (see also Chapter 6 of this book). 

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