Crystallization simulation

To date, a number of simulation studies have been performed on nucleic acids and proteins using both AMBER and CHARMM. A direct comparison of crystal simulations of bovine pancreatic trypsin inliibitor show that the two force fields behave similarly, although differences in solvent-protein interactions are evident [24]. Side-by-side tests have also been performed on a DNA duplex, showing both force fields to be in reasonable agreement with experiment although significant, and different, problems were evident in both cases [25]. It should be noted that as of the writing of this chapter revised versions of both the AMBER and CHARMM nucleic acid force fields had become available. Several simulations of membranes have been performed with the CHARMM force field for both saturated [26] and unsaturated [27] lipids. The availability of both protein and nucleic acid parameters in AMBER and CHARMM allows for protein-nucleic acid complexes to be studied with both force fields (see Chapter 20), whereas protein-lipid (see Chapter 21) and DNA-lipid simulations can also be performed with CHARMM. 

Concerning the VDW parameters, the ability to directly apply previously optimized values makes convergence criteria unnecessary. If VDW parameter optimization is performed based on pure solvent or crystal simulations, then the heats of vaporization or sublimation should be within 2% of experimental values, and the calculated molecular or unit cell volumes should be also. If rare gas-model compound data are used, the references cited above should be referred to for a discussion of the convergence criteria. 

A commonly used model system in liquid crystal simulation is the Gay-Beme fluid. It can be regarded as a Lennard-Jones fluid generalised to ellipsoidal molecular cores. 

C. Diffraction-Crystal simulates powder, fiber, and single-crystal diffraction from crystalline models, which helps interpret the experimental data from molecular, inorganic, and polymeric crystalline materials. 

To illustrate the solvent effect on the average structure of a protein, we describe results obtained from conventional molecular dynamics simulations with periodic boundary conditions.92,193 This method is well suited for a study of the global features of the structure for which other approaches, such as stochastic boundary simulation methods, would not be appropriate. We consider the bovine pancreatic trypsin inhibitor (BPTI) in solution and in a crystalline environment. A simulation was carried out for a period of 25 ps in the presence of a bath of about 2500 van der Waals particles with a radius and well depth corresponding to that of the oxygen atom in ST2 water.193 The crystal simulation made use of a static crystal environment arising from the surrounding protein molecules in the absence of solvent. These studies, which were the first application of simulation methods to determine the effect of the environment on a protein, used simplified representations of the surround-... 

With the availability of faster computers, BPTI was simulated in aqueous solution and in a solvated crystal with a more realistic (three-center) water model.92 The simulations were limited to 8 ps of equilibration and 12 ps of analysis, somewhat short for definitive conclusions to be drawn recently, a crystal simulation of BPTI that extended over 40 ps has been reported.322 The average structures obtained from the various simulations are compared in Table VII. In the three calculations made with the same empirical potential, the van der Waals solvent and static crystal field results yielded an average structure closer to the experimental crystal structure than did the vacuum calculation. The full crystal simulations, including crystal waters, gave an average structure still closer to the X-ray result, while the deviation from the crystal structure of the average structure obtained from the aqueous solution simulation was similar to the earlier vacuum result. 

Vac, Sol, and Crys refer to vacuum, solvent, and crystal simulations, respectively. Source Ref. 193. 

Under this condition, the size effect (load effect) as measured in single crystals simulates the grain size influence of the hardness in polycrystalline materials. 

Zumstein, R.C. and Rousseau, R.W. (1987) Utilization of industrial data in the development of a model for crystallizer simulation. AIChE Symposium Series, No. 253, 83, 130-139. 

Hu WB (2005) Molecular segregation in polymer melt crystallization simulation evidence and unified-scheme interpretation. Macromolecules 38 8712-8718 Hu WB, Cai T (2008) Regime transitions of polymer crystal growth rates molecular simulations and interpretation beyond Lauritzen-Hoffman model. Macromolecules 41 2049-2061 Jeziomy A (1971) Parameters characterizing the kinetics of the non-isothermal crystallization of poly(ethylene terephthalate) determined by DSC. Polymer 12 150-158 Johnson WA, Mehl RT (1939) Reaction kinetics in processes of nucleation and growth. Trans Am Inst Min Pet Eng 135 416-441... 

Overall, these molecular dynamics crystal simulations showed that random, uncorrelated conformational disorder was governed by three processes (1) the intramolecular dynamics leading to local isomeric transition (2) the number of intermolecular collisions and (3) the restrictiveness of the crystal environment [5b]. These initial conformational defects do not corr pond to a potential energy minimum and thus cannot easily be predicted by molecular mechanics calculations. They are the result of the dynamic interaction of skeletal vibrations... 

The Gay-Berne potential has successfully been used for many liquid crystal simulations, and (depending on the parameterisation used and the state points studied) can be used to simulate nematic, smectic-A and smectic-B phases. Variants of the GB potential have also been used to study the biaxial nematic phase (biaxial GB potential) [21] and the smectic C phase (GB with quadrupole) [22]. The GB model has been used also to provide predictions for key material properties, such as elastic constants [23] and rotational viscosities [24], which have an important role in determining how a nematic liquid crystal responds in a liquid crystal display (LCD). 

The size of crystal simulated in this fashion is determined by both the range of interactions included in the computation of the potential E/(q), and the resolution of wavevectors in the BZ. As mentioned earlier, for periodic systems like crystals, Ewald summation permits the efficient evaluation of interactions for a material of infinite extent. Evaluation of thermodynamic properties for an infinite crystal requires accurate evaluation of integrals... 

Jeon Young Jae, Bingzhu Yin, Rhee June Tak, et al. Application and new developments in polymer-dispersed liquid crystal simulation studies. Macromol. Theory. Simul. 16 no. 7 (2007) 643-659. 

Hu W (1998) Structural transformation in the collapse transition of the single flexible homopolymer model. J Chem Phys 109(9) 3686-3690 Hu W (20(X)) The melting point of chain polymers. J Chem Phys 113(9) 3901-3908 Hu W (2005) Molecular segregation in polymer melt crystallization simulation evidence and unified-scheme interpretation. Macromolecules 38(21) 8712-8718 Hu W (2007) Intramolecular crystal nucleation. In Reiter G, Strobl GR (eds) Lecture notes in physics progress in understanding of polymer crystallization. Springer, Berlin, pp 47-63 Hu W (2013) Polymer physics a molecular approach. Springer, Wien... 

Hu W. Molecular segregation in polymer melt crystallization Simulation evidence and unified-scheme interpretation. Macromolecules 2005 38 8712-8718. 

Stouch. Based on the Discover force field, Stouch et al. created a lipid force field. It was used in several diffusion studies of DPPC, and of small solutes in a DPPC bilayer, and tested with crystal simulations. A recent test on a crystal using NPT boundary conditions gave good agreement with experimental data. ... 

In this chapter, I d like to share my personal experience in the two areas of liquid crystal simulation continuum simulatiOTi and molecular simulation. I showed one example, research and development of the IPS-mode LCD, for which the continuum simulation of liquid crystals contributed a lot in the latest quarter of a century. In contrast, the molecular simulation did not aid much in the material development in the same period. In this sense, the contribution of these two simulation approaches have to be evaluated differently from the viewpoint described in the introduction of this paper. Existence of a greatly differing perspective on the contributions of simulations for liquid crystal science itself shows that this field is still developing. 

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