Atomistic models phase behavior

Except for the fullerenes, carbon nanotubes, nanohoms, and schwarzites, porous carbons are usually disordered materials, and cannot at present be completely characterized experimentally. Methods such as X-ray and neutron scattering and high-resolution transmission electron microscopy (HRTEM) give partial structural information, but are not yet able to provide a complete description of the atomic structure. Nevertheless, atomistic models of carbons are needed in order to interpret experimental characterization data (adsorption isotherms, heats of adsorption, etc.). They are also a necessary ingredient of any theory or molecular simulation for the prediction of the behavior of adsorbed phases within carbons - including diffusion, adsorption, heat effects, phase transitions, and chemical reactivity. 

PT has also been used successfully to perform ergodic simulations with Lennard-Jones clusters in the canonical and microcanonical ensembles [53,54]. Using simulated tempering as well as PT, Irback and Sandelin studied the phase behavior of single homopolymers in a simple hydro-phobic/hydrophilic off-lattice model [55]. Yan and de Pablo [56] used multidimensional PT in the context of an expanded grand canonical ensemble to simulate polymer solutions and blends on a cubic lattice. They indicated that the new algorithm, which results from the combination of a biased, open ensemble and PT, performs more efficiently than previously available teehniques. In the context of atomistic simulations PT has been employed in a recent study by Bedrov and Smith [57] who report parallel... 

Molecular dynamics (MD) is an invaluable tool to study structural and dynamical details of polymer processes at the atomic or molecular level and to link these observations to experimentally accessible macroscopic properties of polymeric materials. For example, in their pioneering studies of MD simulations of polymers, Rigby and Roe in 1987 introduced detailed atomistic modeling of polymers and developed a fundamental understanding of the relationship between macroscopic mechanical properties and molecular dynamic events [183-186]. Over the past 15 years, molecular dynamics have been applied to a number of different polymers to study behavior and mechanical properties [187-193], polymer crystallization [194-196], diffusion of a small-molecule penetrant in an amorphous polymer [197-199], viscoelastic properties [200], blend [201,202] and polymer surface analysis[203-210]. In this article, we discuss MD studies on polyethylene (PE) with up to 120,000 atoms, polyethylproplyene (PEP), atactic polypropylene (aPP) and polyisobutylene (PIB) with up to 12,000 backbone atoms. The purpose of our work has been to interpret the structure and properties of a fine polymer particle stage distinguished from the bulk solid phase by the size and surface to volume ratio. 

Finally, Honeycutt" has applied blend PRISM theory at an atomistic RIS model level to study the effect of tacticity (stereochemical differences) on the phase behavior of a commercially important binary polymer mixture. Tacticity is found to result in significant changes of the computed spinodal boundaries, which serves to again emphasize the importance of monomer structure and local packing on the free energy of mixing. 

The outline of this article is as follows after a short discussion of some of the models (Sect. 2) we recall the basic aspects of MD and MC methods (Sect. 3). Results of simulations of chemically detailed atomistic models for short alkanes, polyethylene melts, and polybutadiene melts are mentioned. Section 4 is devoted to a discussion of coarse-grained models for the description of the phase behavior of alkanes in various solvents (Sects. 4.1 and 4.2). Also, qualitative models for semiflexible polymers that exhibit nematically ordered phases [121-123] and for block copolymer solutions that exhibit micelle formation [124, 125] will be discussed. Section 5 presents our conclusions. 

Consequently, we focus here on computer simulations exclusively. The outline of the remainder of this chapter is as follows Section 1.2 presents on overview of polymer models (from lattice models to atomistic descriptions) and will also describe the most important aspects of Monte Carlo simulations of these models. As an example, recent work on simple short alkanes and solutions of alkanes in supercritical carbon dioxide [47,48] will be presented, to clarify to what extent a comparison of Monte Carlo results on phase behavior and experimental data is sensible, and which experimental input into the models is indispensable to make them predictive. 

Oa = 0.5(oa-I-Ob)). Figure 1.3 shows a projection of the phase diagram and the critical line onto the pressure-temperature plane. Even though the model is very simple and lacks atomistic details it can describe adequately the phase behavior of the mixture without additional fitting parameters. If, however, the quadrupolar moment of CO2 is not taken into account, a modification of the Lorentz-Berthelot rule is required < 1). This emphasizes that atomistic detail is not always required to describe the phase behavior correctly. However, it is advisable to include physically relevant quantities like the quadrupolar moment of CO2. 

The new features of the current work relate to the approach adopted in the modeling of the polymer matrix and the investigation of the CNT polymer interfacial properties as appose to the effective mechanical properties of the RVE. The idea behind the ABC technique is to incorporate atomistic interatomic potentials into a continuum framework. In this way, the interatomic potentials introduced in the model capture the underlying atomistic behavior of the different phases considered. Thus, the influence of the nanophase is taken into account via appropriate atomistic constitutive formulations. Consequently, these measures are fundamentally different from those in the classical continuum theory. For the sake of completeness, Wemik and Meguid provided a brief outline of the method detailed in their earlier work [133-134]. 

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