Perturbation Theories for the Thermodynamic Properties of Fluids and Solids

Perturbation Theories for Molecular Fluids 245

form a trimer with a change in the free energy F

bond

(3) =−k

B

T ln g(1, 2).Next,an

additional monomer is bonded at one of the ends of the trimer to form a tetramer with

F

bond

(4) =−k

B

T ln g(1, 3), and so on, so that the formation of an n-mer involves the

change in free energy

F

bond

(

n

)

=−k

B

T

n−1



i=1

ln

[

g

(

1, i

)

]

. (8.120)

Let us now assume g(1, i)  g(1, 2) for i ≥ 2, an approximation that is supported by

simulations of Kumar et al. (1996). Then, for the whole system with N

n

chains with

n-monomers each, we will have

F

bond

N

n

k

B

T

=−ln g

(

1, 1

)

−

(

n −2

)

ln g

(

1, 2

)

. (8.121)

Here, g(1, 1) is the contact RDF g

HS

(σ) of the reference ...