Configurational distribution function

The average force f(r) in the chain when the ends are held a distance r apart could then be obtained from Eq. (10) providing the appropriate configuration distribution function p(r) is known. In the limit of a small extension ratio, p(r) is approximately proportional to peq(r) ... 

From the configuration distribution function, i/ o(R), the elasticity of flexible polymer molecules can be predicted. Suppose the ends of the polymer chain are held fixed so that the end-to-end vector of the chain is R. The number of internal configurations,, of the chain that satisfies this constraint is = ct fo(R), with c a constant. The entropy, S, is then (Wall 1942)... 

Since the orientations of all the segments in the chain are independent of each other, i.e. all the segmental vectors are independent stochastic variables, the configurational distribution function l/( b ) can be simply written as the product of the random distribution functions for the individual segments. That is... 

Then the configurational distribution function of the chain is given by... 

Interbead potential energies Singlet configurational distribution functions... 

Pair configurational distribution functions Singlet configurational distribution function Tensor in relative velocity vector Chain-space rotation matrices... 

Here, we have assumed that the temperature is a linear function of position (see Eq. (12.3)). When this expression for u = C[f3] is inserted into Eq. (10.6), an equation for the configurational distribution function T, is obtained. The resulting equation is often referred to as the d usion equation for T,. 

Thus, the N -particle configurational distribution function can be expressed as... 

Equations (4.52) and (4.53) illustrate the BBGKY hierarchy for the equilibrium configurational distribution functions some truncation (closure) is necessary to obtain solutions. For example, neglecting three-body effects by setting cb(ri, rs) = 0, gives from Eq. (4.52) the dilute gas... 

TV is a normalization constant. is the single chain configuration distribution function... 

In this section we will derive an expression for the configurational distribution function, correct to order A , for a system of interacting linear molecules. 

IV. THE CONFIGURATIONAL DISTRIBUTION FUNCTION OF A SYSTEM OF INTERACTING SYMMETRICAL TOPS IN THE APPROXIMATION OF SMALL QUANTUM CORRECTIONS... 

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