Reference hypernetted-chain

One should perhaps mention some other closures that are discussed in the literature. One possibility is to combine the PY approximation for the hard core part of the potential and then use the HNC approximation to compute the corrections due to the attractive forces. Such an approach is called the reference hypernetted chain or RHNC approximation [48,49]. Recently, some new closures for a mixture of hard spheres have been proposed. These include one by Rogers and Young [50] (RY) and the Martynov-Sarkisov [51] (MS) closure as modified by Ballone, Pastore, Galli and Gazzillo [52] (BPGG). The RY and MS/BPGG closure relations take the forms... 

The reference-hypernetted-chain approximation (RHNC) proposed by Lado (1973) approximates the bridge function Cj j( ) by the bridge function C j (r) for the corresponding short-range potential ... 

In the previous section we have described how to implement TPTl for a mixture of Lennard-Jones chains with a FENE bonding potential. Before considering binary mixtures, however, we shall restrict our attention to the particular case of a one component system of polymers. In order to describe the thermodynamic properties of such a system, we will consider two TPTl implementations, which we denote TPTl-MSA and TPTl-RHNC. In TPTl-MSA, we employ the fiilly analytic equation of state described in the previous section. In TPTl-RHNC, the Lennard-Jones reference system is described by means of the Reference Hypernetted Chain theory (RHNC). This is an integral equation theory which can only be solved numerically. 

A closure similar to the RHNC is the modified hypernetted chain (MHNC), introduced by Rosenfeld and Ashcroft [67]. This approximation is based on the empirical observation that the bridge functions for a wide variety of pair potentials belong to the same family of curves. This means that the bridge functions calculated for a suitable reference fluid can be used to a good approximation for another fluid. The reference fluid is usually... 

The relation is referred to as the hypernetted-chain (HNC) approximation. Further linearizing expt(r, r ) in 1.23, one has the Percus-Yevick (PY) approximation,... 

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