CCL: translational entropy and solvation

 Sent to CCL by: "Raphael  Ribeiro" [raphaelri a hotmail.com]
 Dear Michael,
 I think you forgot that the mathematical expression that you're talking about
 for translational entropy is based on the ideal gas model, the partition
 function in this case is calculated using the particle in a box model.In this
 case the problem of calculating the energy levels of the whole system is reduced
 to calculating the energy levels of a molecule (translational,rotational and
 vibrational energy levels of the molecule). Also,and more important, as you
 might know in this formulation no intermolecular forces or external fields are
 considered.
 If you look at Landau and Lifschitz, Vol.5 Statistical Physics, you are going to
 see that when he talks about the ideal Boltzman gas(pages 120-123) he derives
 the equation of state of an ideal gas using a partition function that was
 calculated using the translational energy levels we're talking about
 (particle-in-a-box energy levels) and also the energy levels of the internal
 motion of the ideal gas. This means that systems in which the translational
 partition function is calculated by the particle-in-a-box model have the
 equation of state of an ideal gas. That is why I can not agree that
 translational partition functions are the same in the ideal gas phase and in the
 solvated phase.
 Again, http://biophysics.med.jhmi.edu/amzel/people/siebert/strsl_2col_bw_letter.pdf
 in this article the authors talk about a statistical mechanics framework for the
 estimation of translational entropy loss in associations while taking
 explicitely into account the intermolecular interactions between the solute and
 the solvent, it is called CM formalism.
 The following quote from the paper corroborates what I said before about ideal
 gas translational partition function and non-ideal gas translational partition
 function, by talking about the entropy in different systems (entropy and
 partition functions are directly related).
 "Thus, the estimation of dStrans depend solely on the evaluation of the
 integral in Eq.2 which, after integration over the momenta dp, yields:
 Eq. 4
 where (De Broglie wavelenght)  = h/(2piMkT)^1/2 is the de Broglie wavelength of
 a solute molecule.
   If the N solutes were an ideal gas  (i.e. without solvent nor intermolecular
 interactions, (U=0), the integral in eq. 4 would be equal to V, leading to the
 so called "Sackur-Tetrode"(ST) formula for translational entropy[14]:
 Eq.5
 This formula is sometimes used as the basis for estimating entropies of
 molecular associations in solution[3,13,16]. However, the presence of a nonzero
 potential U complicates considerably the evaluation of the configurational
 integral in Eq.4, requiring approximate methods[1]. The goal of this paper is to
 provide a framework based on cell models [2,15,17,18], to approximate
 efficiently dStrans."
 As you might have noticed the presence of an external potential (create by
 intermolecular forces) changes the way(ideal gas phase model) we calculate
 translational entropies. And that is why people make models to calculate this
 component of entropy (as it was done in this paper) and understand the role of
 translational component of entropy in some situations. This other article http://www.biophysj.org/cgi/content/abstract/89/4/2701 uses
 a sophisticated statistical mechanic theory to analyse the role of translational
 entropy of solvent molecules in the proteing folding process.
 To conclude, the molecular partition function we've learned and are used to work
 with is very good for ideal gases system, but not for solvated systems, as it
 does not include molecular interactions and without interactions there would be
 no solvated phase.
 Raphael Ribeiro