Crossover behavior coexistence curves

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. 

Here, (J) and coexistence phases, respectively. The values of exponent P and the coefficients were determined by the least-squares fitting of eqs 1-3 with the fixed value of A = 0.5. The obtained values with critical temperature Tc and critical composition (t>c are summarized in Table 3. The exponents p suggest the presence of the crossover[13, 14] from the mean-field to the Ising behavior with increasing the content of diluent DBP. Coexistence curve of the blend A without DBP exhibited the mean-field type critical exponent, while the blend C with DBP of more than 20 wt% has the Ising type critical exponent. The blend B with an intermediate DBP content shows an intermediate value of p. 

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