Fluid-wall interactions

S. Sarman. The influence of the fluid-wall interaction potential on the structure of a simple fluid in a narrow slit. J Chem Phys 92 4447—4455, 1990. 

There is no fluid/wall interaction (except purely viscous). 

It was recognized many years ago (Foster, 1932) that the Kelvin equation is likely to break down as the meniscus curvature approaches a limiting value. Molecular simulation studies (Jessop et ai, 1991) have indicated that the Kelvin equation fails to account for the effects of the fluid-wall interactions and the associated inhomogeneity of the pore fluid. These and other studies (Lastoskie et ai., 1993) reveal that the Kelvin equation probably underestimates the pore size and that its reliability may not extend below a pore size of 7.5 nm. 

Figure 1.38. Molecular dynamics simulation of the density profiles for spherical molecules in a cylinder, mimicking SFg in controlled pore glass (CPG-10). Fluid-fluid and fluid-wall interaction modelled by Lennard-Jones interactions. Reference A. de Keizer. T. Michalski and G.H. Findenegg, Pure Appl. Chem. 63(1991) 1495.

Figure 2.4 has been taken from a Monte Carlo simulation and applies to simple spherical molecules near a solid wall. The consequences of a number of different types of intermolecular Interactions, fluid-wall interactions and bulk densities, were studied. Undulations over a few molecular diameters are obtained, which in this example become more pronounced if there is fluid-wall... 

R. Radhakrishnan, K.E. Gubbins and M. Sliwinska-Bartkowiak, Effect of the Fluid-Wall Interaction on Freezing of Confined Fluids Towards the Development of a Global Phase Diagram, J. Chem. Phys. 112 (2000) pp. 11048-11057... 

The intermolecular interactions between two molecules and fluid-wall interactions in SWNTs were given by a 12-6 Lennard-Jones (LJ) potential. Methane was modeled as a spherical LJ molecule and ethane as two LJ sites with the unified methyl group. The interactions were cut at 2.286nm which corresponding to 5 times the methane a parameter. 

The above results reinforces strong connection between fluid-wall interaction potential and the freezing point. Through a simple thermodynamic treatment the following equation was obtained to express the extent of freezing point elevation ST. 

Here, the cr s and e s are the size and energy parameters in the LJ potential, the subscripts / and w denote fluid and wall respectively, 2 is the coordinate perpendicular to the pore walls and kg is the Boltzmann s constant. The fluid-wall interaction energy parameters corresponding to a graphite pore were taken from Ref. [8]. For a given pore width H, the total potential energy from both walls is given by,... 

The strength of the fluid wall interaction is determined by the parameter a =... 

The Landau free energy surfaces provide clear evidence of the existence of a contact layer with different structural properties compared to the pore interior, thereby supporting the experimental observation. The nature of the contact layer phase depends on the strength of the fluid-wall potential. For purely repulsive or mildly attractive pore-walls, the contact layer phase exists only as a metastable phase. As the strength of the fluid-wall attraction is increased, the contact layer phase becomes thermodynamically stable. Like the direction of shift in the freezing temperature, the structure of the contact layer phase also depends on the strength of the fluid wall interaction (i.e., whether the contact layer freezes before or after the rest of the inner layers). 

A systematic study of the influence of the strength of the fluid-wall interaction parameter a revealed that, for a < 0.5, the intermediate phase B remains metastable for all temperatures. For the range 0.5 < a < 1.2. phase B becomes thermodynamically stable with the contact layer freezing at a temperature below that of the inner layers and for Q > 1.6, phase B becomes thermodynamically stable with the contact layer freezing at a temperature above that of the the inner layers [9]. 

Salamacha and coworkers304 306 have carried out a series of studies on Lennard-Jones fluids confined to nanoscopic slit pores made from parallel planes of face centred cubic crystals. Grand canonical and canonical ensemble MC simulations have been used to determine the structure and phase behaviour as the width of the pore and the strength of the fluid-wall interactions were varied. The pore widths were small accommodating 2 to 5 layers of fluid molecules.304,305 The strength of the fluid-wall interaction is linked to the degree of corrugation of the surface, and it is found that the structure of the... 

Many questions have been raised concerning the validity of the Kelvin equation, in particular, the lower limit of the pore size that one could use with this approach. Clearly, this method does not apply when the pore size approaches molecular dimensions, or a few molecular sizes. Molecular simulations by Jes-sop et al. (1991) showed that the Kelvin equation fails to account for the effects of fluid-wall interactions. The density functional theory study of Lastoskie et al. (1993), as well as other work, indicated that the Kelvin equation would underestimate the pore size and should not be extended below a pore size of 7.5 nm. 

Radhakrishnan, R., Gubbins, K.E., and Shwinska-Bartkowiak, M. Effect of the fluid-wall interaction on freezing of confined fluids Toward the development of a global phase diagram. 2000. 7. Ghem. Phys. 112 11048. 

The fluid/fluid interactions were modeled using Lennard-Jones potentials with parameters that reproduce properties of the bulk liquids. The cross-species A/B parameters were calculated using the Lorentz-Beithelot combining rules [15], The slit pore was described as an assembly of two structureless parallel walls. Periodic boundary conditions were applied in the directions parallel to the pore walls. The fluid/wall interaction was calculated usirg the Steele TO-4-3 potential [16]. The fluid/wall parameters, Cw/x, nw/x (X = A or B) were... 

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