Rounding of Phase Transitions in Cylindrical Pores

Abstract

Phase transitions of systems confined in long cylindrical pores (capillary condensation, wetting, crystallization, etc.) are intrinsically not sharply defined but rounded. The finite size of the cross section causes destruction of long range order along the pore axis by spontaneous nucleation of domain walls. This rounding is analyzed for two models (Ising/lattice gas and Asakura-Oosawa model for colloid-polymer mixtures) by Monte Carlo simulations and interpreted by a phenomenological theory. We show that characteristic differences between the behavior of pores of finite length and infinitely long pores occur. In pores of finite length a rounded transition occurs first, from phase coexistence between two states towards a multi-domain configuration. A second transition to the axially homogeneous phase follows near pore criticality. PACS numbers: 64.75Jk, 64.60.an, 05.70Fh, 02.70Tt Fluids and fluid mixtures in nano-and microporous materials (pore diameters from 1 nm to 150 nm) play important roles in various industries (extracting oil and gas from porous rocks; use as catalysts or for mixture separation in the chemical and pharmaceutical industry; nanofluidic devices, etc.) [1][2][3]. The interplay of finite size and surface effects strongly modifies the phase behavior of such confined fluids [1,[3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] in comparison with the bulk. The vapor to liquid transition is shifted ("capillary condensation"), as well as critical points [3,4,9,12]. Effects of wetting [20] on phase coexistence give rise to interesting patterns (plugs versus capsules versus tube structures etc. [7]). However, although various phase diagrams (different from the bulk) have been proposed (e.g. [1,3,7,9,12,13,17]), many aspects hitherto are not well understood. E.g., the "critical point" where adsorption/desorption hysteresis vanishes seems to be systematically lower than the critical temperature where the density difference between the vapor-like and liquid-like states vanishes [12], in contrast to what theories have predicted [14].However, a crucial aspect (stressed only in a few pioneering studies [3,8], and in the context of Ising/lattice gas models [21][22][23]) is the rounding of all transitions, caused by the quasi-one-dimensional character of a fluid in a long cylindrical pore with cross-sectional radius R. With the current progress of producing pores of wellcontrolled diameter varying from the nanoscale (carbon nanotubes [23][24][25]) to arrays of pores in silicon wafers [26], up to 150 nm wide and of well-controlled length, experiments become feasible which are not plagued by effects of random disorder, which occur in porous glasses [1,27]. Thus, it is important to understand the phase transitions in pores more precisely, considering both the radius R and the length L of the pore as variables (the important role of L has so far been largely disregarded). In the present Letter, we elucidate the rounding of vaporliquid type transitions in cylindrical pores, based on Monte Carlo sim...

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