Dynamic Monte Carlo simulation, pore

Dynamic Monte Carlo Simulation and Dielectric Measurements of the Effect of Pore Size on Glass Transition Temperature and tiie State of the Glass... 

L. D. Gelb and K. E. Gubbins, Liquid-liquid Phase Separation in Cylindrical Pores Quench Molecular Dynamics and Monte Carlo Simulations, Phys. Rev. E 56 (1997) 3185-3196 Kinetics of Liquid-liquid Phase Separation of a Binary Mixture in Cylindrical Pores, Phys. Rev. E 55 (1997) R1290-R1293. 

A combination of characterization techniques for the pore structure of meso-and microporous membranes is presented. Equilibrium (sorption and Small Angle Neutron Scattering) and d)mamic (gas relative permeability through membranes partially blocked by a sorbed vapor) methods have been employed. Capillary network and EMA models combined with aspects from percolation theory can be employed to obtain structural information on the porous network topology as well as on the pore shape. Model membranes with well defined structure formed by compaction of non-porous spherical particles, have been employed for testing the different characterization techniques. Attention is drawn to the need for further development of more advanced sphere-pack models for the elucidation of dynamic relative permeability data and of Monte-Carlo Simulation for the analysis of equilibrium sorption data from microporous membranes. 

Apart from the introductory section, the article is subdivided into four major sections NMR Methods Modeling of Chain Dynamics and Predictions for NMR Measurands Experimental Studies of Bulk Melts, Networks, and Concentrated Solutions and Chain Dynamics in Pores. First, the NMR techniques of interest in this context will be described. Second, the three fundamental polymer dynamics theories, namely the Rouse model, the tube/reptation model, and the renormalized Rouse theories are considered. The immense experimental NMR data available in the literature will be classified and described in the next section, where reference will be made to the model theories wherever possible. Finally, recent experiments, analytical treatments, and Monte Carlo simulations of polymer chains confined in pores mimicking the basic premiss of the tube/reptation model are discussed. 

Below we will come back to the reptation model in context with the dynamics of polymers confined in tube-like pores formed by a solid matrix. For a system of this sort the predictions for limits (II)de and (III)de (see Table 1) could be verified with the aid of NMR experiments [11, 95] as well as with an analytical formalism for a harmonic radial potential and a Monte Carlo simulation for hard-pore walls [70]. The latter also revealed the crossover from Rouse to reptation dynamics when the pore diameter is decreased from infinity to values below the Flory radius. 

The theoretical background of the confinement effect in (artificial) tubes was recently examined in detail with the aid of an analytical theory as well as with Monte Carlo simulations [70]. The analytical treatment referred to a polymer chain confined to a harmonic radial tube potential. The computer simulation mimicked the dynamics of a modified Stockmayer chain in a tube with hard pore walls. In both treatments, the characteristic laws of the tube/reptation model were reproduced. Moreover, the crossover from reptation (tube diameter equal to a few Kuhn segment lengths) to Rouse dy-... 

Equilibrium Systems. Magda et al (12.) have carried out an equilibrium molecular dynamics (MD) simulation on a 6-12 Lennard-Jones fluid In a silt pore described by Equation 41 with 6 = 1 with fluid particle Interactions given by Equation 42. They used the Monte Carlo results of Snook and van Me gen to set the mean pore density so that the chemical potential was the same In all the simulations. The parameters and conditions set In this work were = 27T , = a, r = 3.5a, kT/e = 1.2, and... 

The principal tools have been density functional theory and computer simulation, especially grand canonical Monte Carlo and molecular dynamics [17-19]. Typical phase diagrams for a simple Lennard-Jones fluid and for a binary mixture of Lennard-Jones fluids confined within cylindrical pores of various diameters are shown in Figs. 9 and 10, respectively. Also shown in Fig. 10 is the vapor-liquid phase diagram for the bulk fluid (i.e., a pore of infinite radius). In these examples, the walls are inert and exert only weak forces on the molecules, which themselves interact weakly. Nevertheless,... 

Essential progress has been made recently in the area of molecular level modeling of capillary condensation. The methods of grand canonical Monte Carlo (GCMC) simulations [4], molecular dynamics (MD) [5], and density functional theory (DFT) [6] are capable of generating hysteresis loops for sorption of simple fluids in model pores. In our previous publications (see [7] and references therein), we have shown that the non-local density functional theory (NLDFT) with properly chosen parameters of fluid-fluid and fluid-solid intermolecular interactions quantitatively predicts desorption branches of hysteretic isotherms of nitrogen and argon on reference MCM-41 samples with pore channels narrower than 5 nm. 

FIGURE 9.5 Comparison of the equation of state (reduced axial pressure versus reduced numerical density) of Square-Well molecules of = 1.5 confined in cylindrical hard pore with diameter, D/a = 2.2, obtained by isobaric-isothermal Monte Carlo (NPT MC) and molecular dynamic (MD) simulations. Here, squares indicate NPT MC result and circles the MD result. The solid line indicates an analytical fit of the result at the fluid branch, and the dash line is the second order polynomial fit to the solid branch. Error bars are the standard deviation of five independent runs. (From Huang, H. C., J. Chem. Phys., 132, 224504, 2010. With permission. Copyright 2010, American Institute of Physics.)... 

Adsorption is modelled by Grand Canonical Monte Carlo (GCMC) fiill details of flie method and simulation protocols may be fi)und elsewhere [2]. By flying Grand Canonical molecular dynamics (GCMD) [8] to the model solid in an initially evacuated state, the pore throats in T passed through and pores in II accased by the fluids are also identified. 

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