Rotational Isomeric States

2.4 Rotational Isomeric States

All bond lengths and angles are the same
Correlations among the bond angles are treated as before.
Each monomer can assume one of a limited number of discrete torsional states, t, g_- or g₊.
The probability of sequences of states is modified by relevant energetic penalties
Successfully applied in statistical mechanics calculations of polymer conformations

2.4.1 The Ising Chain

The rotational isomeric state model provides a direct map between calculation of polymer conformations and the familiar 1D Ising model. In this frame, we consider the energy of the chain as

∑n U = u(φi-1,φi) i=2

(11)

where u(φ_i-1,φ_i) is the pair interaction energy, and bonds are not energetically independent. We calculate the partition function by summing over all configurational states represented by the set of {φ_i}, after which the thermodynamic functions follow in the usual manner.

∑ Z = exp (- U (φi)∕kT) {φi} Fp = - kT ln Z S = - ∂F ∕∂T p p U = Fp + TSp (12)

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