Abstract
Physical cluster formation in a fluid system causes a characteristic dependence of the pair correlation function on the distance r between a specific pair of particles at the liquid–vapor critical point. Its dependence deviates from that expressed by the product of a negative power r−1 and a specific function provided by a Taylor series with respect to positive powers of r. The effects of the physical cluster formation can be estimated by representing the pair correlation function as a sum of two correlation functions; these two correlation functions can be provided as exact solutions for two differential equations that result from a system of two integral equations equivalent to the Ornstein–Zernike equation.
Highlights
The dependence of g on the distance r between a specific pair of particles4 is expressed by a product of r−1 and a particular function given by a Taylor series with respect to positive powers of r
When a fluid system characterized by g(r) = P(r) + D(r) with P(r) ≠ 0 is maintained under a condition specified by T = Tc and 0
The behavior of g(r) deviates from that of a pair correlation function expressed as the product of r−1 and a particular function given by a Taylor series with respect to positive powers of r
Summary
A feature of a fluid near the liquid–vapor critical point causes the pair correlation function g to behave characteristically. Under several specific conditions, the dependence of g on the distance r between a specific pair of particles is expressed by a product of r−1 and a particular function given by a Taylor series with respect to positive powers of r.5,6 the dependence of g on r deviates near the liquid–vapor critical point from that expressed by the product of r−1 and the function given by the Taylor series. The dependence should be influenced by physical clusters that are formed by particles via attractive forces between them. When a fluid system characterized by g(r) = P(r) + D(r) with P(r) ≠ 0 is maintained under a condition specified by T = Tc and 0 < (ρc − ρ)/ρc ≪ 1 near the liquid–vapor critical point, mutually attractive forces between particles cause density fluctuations to reach the maximum strength as their density increases.. If P(r) is ignored because of a lack of physical clusters near the liquid–vapor critical point, the dependence of g(r) on r at a large r is expressed by the product of r−1 and a function provided by the Taylor series with respect to the positive powers of r. According to the mean spherical approximation (MSA), the direct correlation function satisfies c(r) ≠ 0 within the range wherein u(r) ≠ 0 is satisfied; it decays to zero as rapidly as −βu(r), which retains a microscopic feature This implies that the behavior of c(r) is expressed as.
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