By G.H. A. Cole
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Extra info for An Introduction to the Statistical Theory of Classical Simple Dense Fluids
The expression TABLE 2. 4) for the rare gas atoms. 4) is plotted schematically in Fig. 5. 4) and the details of Fig. 5, it is found that the distance OA is to be identified with the distance o while ε is to be identified with the depth BC. 4): a is still the particle size and A is still associated with the depth of the potential at its minimum value. 6) 0 FIG. 5. General form of the interparticle force potential for simple spherical particles. Many alternative values of m have been suggested for special problems :4 these usually lie in the range 10-15, although m = 28 has been used in connection with polar molecules.
Two special results for fluids are when ß ( p " , r") = NQ&19 and when Ô(PW, τ") = β ΐ ΐ λ Γι), ß 2 (p 1 ; ρ 2 , n , r 2 ). 31a) . . 24) has been used with h set successively equal to 1 and 2. These expressions can, in fact, be resolved further since the momentum and configuration contributions can be separated. 31a) applies to gases at sufficient dilution; the configuration contribution is weak and the singlet distribution describes the particle momentum. For more dense gases and liquids a separation is still possible but now, although the singlet distribution is sufficient for the treatment of the momentum components (as for a dilute gas), the configuration components can be discussed only within the doublet distribution.
3. THE LIOUVILLE THEOREM The system of particles is represented by a single point in y-space, and all possible phase developments for the physical system resulting from all possible initial phases can be represented as a cloud of points in y-space. Because the number of particles in the system is to be very large then so also is the set of initial phases and the y-space cloud is virtually a continuum. The time evolution is represented by the motion of the cloud and each particle moves according to the laws of mechanics.
An Introduction to the Statistical Theory of Classical Simple Dense Fluids by G.H. A. Cole