The Partition Function and Thermodynamic Properties

In Chapter 4 we considered that the total energy of a system is given by relativity theory as E,. = rru - and that the internal energy of thermodynamics is some unspecified smaller quantity such that = U + constant. In statistical mechanics the energy 

Thus the internal energy and heat capacity are simply related to the change in the partition function with temperature. For certain simple systems such as gases at low temperatures, the partition function can be estimated theoretically. For most systems of geological interest such as minerals and concentrated salt solutions, additional experimental information is required. This might take the form of spectroscopic data on electronic or molecular vibrational frequencies, or direct measurement of some of the non-ideal thermodynamic properties themselves. 

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Structural characteristics of adsorbed chains, such as the mean distance of chain ends from the surface and the fraction of segments in each layer, derive from P(i,s). The partition function and thermodynamic properties depend on the eigenvalues of W (Flory, 1969). In the limit n - oo, calculation of thermodynamic functions simplifies because one eigenvalue, denoted by A, dominates the free energy per segment,... 

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