Confined fluid correlations

Since we shall also be interested in analyzing the confined fluid s microscopic structure it is worthwhile to introduce some useful structural correlation functions at this point. The simplest of these is related to the instantaneous number density operator... 

The translational microscopic structure of the confined fluid is partially revealed by correlations in the number density operator, given by... 

L. Bocquet and J. L. Barrat, Phys. Rev. Lett., 70, 2726 (1993). Hydrodynamic Boundary Conditions and Correlation Function of Confined Fluids. 

The choice of the weighting function w depends on the version of density functional theory used. For highly inhomogeneous confined fluids, a smoothed or nonlocal density approximation is introduced, in which the weighting function is chosen to give a good description of the hard sphere direct pair correlation function for the uniform fluid over a... 

We will see that, as expected, the presence of charges in the matrix strongly modifies the long range (i.e. screening) behavior of the fluid-fluid correlation functions. In order to illustrate the effects of confinement on the dipolar fluid properties, calculations for the corresponding fully equilibrated system - i.e. an electrolyte with explicit solvent - have also been carried out in the hyper-netted chain (HNC) approximation. This is known to be accurate enough for the thermodynamic states under consideration. 

The replica method can be also applied to express some of the thermodynamic properties of a confined fluid in terms of the correlation functions of the system. The details of the procedure can be found elsewhere [6, 26], In our system, we need to rearrange some expressions so as to avoid the difficulties in the numerical calculations due to the long range behavior of some correlation functions. 

One may, for example, regfnd the (planar) substrate(s) of a slit-pore as the surface of a spherical particle of infinite radius. The confiniKl fluid plus the substrates may then be perceived as a binary mixture in which macro-scopically large (i.e., colloidal) particles (i.e., the substrates) are immersed in a sea of small solvent molecules. The local density of the confined fluid may then be interpreted as the mixture (A-B) pair correlation function representing correlations of solvent molecules (A) caused by the presence of the solute (B). 

Because of Eq. (5.60), experimentally accessible portions of the pseudo-experimental data can bn related to the local stress at the point (0,0,. s = h) of minimum distance between the surfaces of the macroscopic sphere and the planar substrate (see Fig. 5.2). By correlating the local stress r (h) with the confined fluid s local structure at (0,0,/i) da p z), one can establish a direct correspondence between pseudo-experimental data [i.e., F (h) //Z] and the local microscopic structure of the confined fluid. 

The observed system-size dependence clearly indicates that the correlation length associated with density fluctuations in the confined fluid exceeds the dimensions of the simulation cell [178]. This is indicative of a near-critical thennodynamic state of the confined fluid. Because of the density of the participating phases in this near-critical region we conclude that the critical point is the one at which fluid bridge and liquid-like phases become in-... 

R. Biswas and B. Bagchi, A kinetic Ising model study of dynamical correlations in confined fluids emergence of bofli fast and slow time scales. J. Chem. Phys., 133 (2010), 084509-1-7. 

Phase transitions of confined fluids were extensively studied by various theoretical approaches and by computer simulations (see Refs. [28, 278] for review). The modification of the fluid phase diagrams in confinement was extensively studied theoretically for two main classes of porous media single pores (stit-Uke and cylindrical) and disordered porous systems. In a slit-like pore, there are true phase transitions that assume coexistence of infinite phases. Accordingly, the liquid-vapor critical point is a true critical point, which belongs to the universality class of 2D Ising model. Asymptotically close to the pore critical point, the coexistence curve in slit pore is characterized by the critical exponent of the order parameter = 0.125. The crossover from 3D critical behavior at low temperature to the 2D critical behavior near the critical point occurs when the 3D correlation length becomes comparable with the pore width i/p. 

The equilibrium properties of a fluid are related to the correlation fimctions which can also be detemrined experimentally from x-ray and neutron scattering experiments. Exact solutions or approximations to these correlation fiinctions would complete the theory. Exact solutions, however, are usually confined to simple systems in one dimension. We discuss a few of the approximations currently used for 3D fluids. 

To illustrate the relationship between the microscopic structure and experimentally accessible information, we compute pseudo-experimental solvation-force curves F h)/R [see Eq. (22)] as they would be determined in SEA experiments from computer-simulation data for T z [see Eqs. (93), (94), (97)]. Numerical values indicated by an asterisk are given in the customary dimensionless (i.e., reduced) units (see [33,75,78] for definitions in various model systems). Results are correlated with the microscopic structure of a thin film confined between plane parallel substrates separated by a distance = h. Here the focus is specifically on a simple fluid in which the interaction between a pair of film molecules is governed by the Lennard-Jones (12,6) potential [33,58,59,77,79-84]. A confined simple fluid serves as a suitable model for approximately spherical OMCTS molecules confined... 

In general terms, the phenomena described above belong to the class of phase transitions and critical phenomena in confined spaces. From the field of statistical physics, some far-reaching results applying to such problems are knovm. One fruitful concept used in statistical physics is the correlation length (see, e.g., [64]). The correlation length describes how a local field quantity evaluated at one point in space is correlated with the same quantity at another point. As an example, the correlation length crfor density fluctuations in a fluid is defined via... 

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