Monte Carlo simulation cylindrical pores

Gelb, L. D. Gubbins, K. E., Studies of binary liquid mixtures in cylindrical pores phase separation, wetting and finite-size effects from Monte Carlo simulations, Physica A 1997, 244, 112-123... 

Recent Monte Carlo simulations of N2 in cylindrical pores fully support the results of the NLDFT calculations [28]. Thus, it appears that the failure of the NLDFT to predict the disappearance of the hysteresis loop at relative pressures below ca, 0.4 and pores smaller than ca, 4 nm is of a fundamental nature and cannot be explained by approximations made in the theory. 

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. 

Further, Imdakm and Matsuura [61] have developed a Monte Carlo simulation model to smdy vapor permeation through membrane pores in association with DCMD, where a three-dimensional network of interconnected cylindrical pores with a pore size distribution represents the porous membrane. The network has 12 nodes (sites) in every direction plus boundary condition sites (feed and permeate). The pore length / is assumed to be of constant length (1.0 p,m), however, it could have any value evaluated experimentally or theoretically [62]. 

Panagiotopoulos, A. (1987). Adsorption and capillary condensation of fluids in cylindrical pores by Monte Carlo simulation in the Gibbs ensemble. Mol. Phys., 62, 701-19. 

The friction coefficient f has been determined either from the hydrodynamic diffusion tensor using Monte Carlo simulation [67] or by using one of several simple analytical expressions for a sphere translating through a right cylindrical pore [31, 68-70]. The most commonly used is Eq. (11) [71], where X is the characteristic ratio of solute size to pore size... 

A polymer chain with repulsive interactions between the segments confined into a cylindrical pore has been studied by Monte Carlo simulations by Milchev et al. [115]. Besides the equilibrium conformation of the molecules in the confined geometry, the time-dependent mean-square displacements of the segments was also studied. It is shown fliat relaxation times scaling with hP- as well as hP play a role in the reptative motion of the chain in these tubes. 

Figure 3 Morphologies of bulk cylinder-forming diblock copolymers confined in cylindrical pores from Monte Carlo simulations. The model diblock copolymer is at the strong segregation region and so the cylinders are robust. The morphologies can be viewed as different arrangements of the basic cylindrical structure. Reproduced from Yu, B. Jin, Q. Ding, D. et a . Macromolecules 2008, 41,4042, with permission. Copyright 2008, American Chemical Society.

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,... 

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.)... 

GCMC simulations, in which the temperature, the volume of the simulation cell and the chemical potential of the adsorbate are kept constant, were carried out for the adsorption isotherms of methane and ethane in slit-sh ed pores (representing pores in BPL carbon) and of ethane in cylindrical pores (representing pores in MCM-41). The absolute configurational energy of the adsorbates was obtained by a Canonical Monte Carlo (CMC) simulation, in which the number of molecules in the pore, the temperature and the volume of the simulation cell are kept constant. Details of the GCMC and CMC simulations can be found in refe. [8,9]. 

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