CCL: translational entropy in solution

 Sent to CCL by: "VITORGE Pierre 094605" [Pierre.VITORGE,cea.fr]
 A dimmer with very long distance between the 2 monomers is meaningless.
 Deciding you have a dimmer (or any chemical species) means you make an
 approximation where you split atomic interactions between (strong)
 intramolecular and (weak or even zero for the ideal systems) intermolecular
 ones: when the dimmer is formed there is a strong enough bound between the
 monomers and they are at short distance.
 This difference between strong/zero interatomic interactions is at the basis of
 the thermodynamic demonstration of the law of mass action and the corresponding
 equilibrium "constant" (actually a function of P and T) K, where
 delta_G° = -RTlnK (G°, not G) and so on...
 Besides this thermodynamic feature, note that solvation often has a huge
 contribution to the total energy with eventually both enthalpic and entropic
 contributions.
 --
 Pierre Vitorge
 http://www.vitorge.name
 -----Message d'origine-----
 De : owner-chemistry+pierre.vitorge==cea.fr_+_ccl.net [mailto:owner-chemistry+pierre.vitorge==cea.fr_+_ccl.net] De la part de
 Andreas Klamt klamt/./cosmologic.de
 Envoyé : vendredi 12 décembre 2008 08:46
 À : VITORGE Pierre 094605
 Objet : CCL: translational entropy in solution
 Sent to CCL by: Andreas Klamt [klamt%a%cosmologic.de]
 >  > Let us for a moment assume that A = B i.e. consider
 >
 >> A +A --> AA
 >>
 >> and the interactions and surface of AA are just twice the interactions
 >> of A. We may consider the case of 2 cyclohexane molecules getting bound
 >> together by a virtual stiff bond which is long enough so that there are
 >> no relevant interactions between the 2 parts. In the gasphase this
 leads
 >> to a large loss of free energy due to the loss of the translational and
 >> rotational free energy (not just entropy) of one of the particles
 >>
 >
 > Actually if there is a loss in the entropy of the system its free energy
 increases:
 >
 > dG = dH - TdS
 > dS < 0 , dG increases.
 >
 Sorry for being a little unprecise here regardig the sign, but I think
 it is clear what I am talking about.
 > Also, there is an increase in the enthalpy of the system(considering that
 no kind of interaction is going on between A and A,what is quite contradictory
 anyway) after the reaction. The new vibrational modes in AA are going to have a
 zero point energy that is bigger than the rotational and translational energies
 of the reagents, increasing the enthalpy of the system, which is another reason
 for an increase in G and for this reaction to be non-spontaneous
 >
 >
 >> I believe that the physics is correct here. The solvent definitely
 >> reduces the motional (kinetic) phase space. The molecules cannot move
 >> and rotate as freely as they can in the gasphase, and hence the part of
 >> the free energy arising from the integration over momentum and
 >> rotational momentum must be reduced in solution. Obviously, and here I
 >> agree with the other people in the discussion, the solute can take all
 >> positions and orientations, as in the gasphase, and hence the free
 >> energy arsing from these integrals are the same as in the gasphase.
 >>
 >
 > Actually, although the solute can take all positions and orientations, in
 solution some of these are going to be very disfavored energetically, while
 others are going to be more favored, and that is introduced by the term U
 (potential energy) in the integral used to calculate the molecular partition
 function. So the molecular partition function is not going to be the same as in
 the gas phase.
 >
 Indeed, I mentioned this in the next partof  my last CCL entry (see
 below) . My argument is that these contributions are unlikely to cancel.
 Indeed, I have no estimate which contribution is stronger. We have no
 chance to sest that, because my virtual case of a dimerization with a
 virtual long connection between the two parts will never be realized in
 nature. Association here alway goes along with interactions and hence
 with large changes in the interaction integrals. Usually the overall
 external polarity of the dimer will be strongly reduced in association.
 Hence we will never be able to proof my arguments in reality.
 >
 >
 >> Obviously, in reality, if we generate real close contact associates or
 >> even product molecules, the loss of the external degrees of freedom
 will
 >> be partly compensated by additional internal vibrational modes. But it
 >> is unlikely that this exactly matches the loss of external degrees of
 >> freedom. Please note, that usually the change in the vibrational free
 >> energies upon solvation is parameterized int the surface proportinal
 >> part of solvation models, i.e. the non-electrostatic parts.
 >>
 >
 > Non-electrostactic contributions in most of the solvent models
 also(actually they should, but in most cases don't) account for the change in
 all of the other components of free energy. What about COSMO-RS? I don't have
 access to your book and I'm going to read a paper on COSMO-RS soon, but I'm very
 curious on the physical foundations of the 2 extra terms (the one proportional
 to lnV and the one that depends on the temperature) you've mentioned. Where does
 these terms come from? What is parametrized in the model?
 >
 There are typically 3 contributions to the non-electrostatic terms:
 1) the "cavitation energy" often expressed as a kind of solvent
 specific
 surface tension. This part is not required in COSMO-RS but it
 automatically aises from the statistical thermodynamics for the slute
 and solvent surface interactions. The free energy required to break the
 solvent-solvent contacts in order to enable solute-solvent contacts
 automatically and termodynamically consistently follows rom that. Hence
 COSMO-RS does not need such a thing as a solvent surface tension: This
 automatically follows from the sigma-profile (COSMO charges) of the solvent.
 2) the non-electrostatic interactions: The hydrogen bond interations in
 COSMO-RS are part of the surface interations taken into account in the
 statistical thermodynamics, quantified approximately based on the
 surface polarities (COSMO polarization charge densities) of donor and
 acceptor. The vdW-interactions are the weekest part of COSMO-RS: They
 are just taken into account as surface proportial with element specific
 vdW-surface tensions (one of the 2 element specific parameters of
 COSMO-RS, the other being the element specific radius). We assume that
 the the vdW-interactions have a generic temperature dependence (hence a
 split into enthalpic and entropic contributions).
   Other solvation models need to parameterize all this into empirical
 corrections or solvent specific radii scaling, ...
 >
 >> This
 >> allows for the treatment of phase diagrams, vapor pressures, .... the
 >> entire fluid phase equilibrium thermodynamics. And in difference to
 >> dielectric solavtion models COSMO-RS yields entropic and enthalpic
 >> contributions of the solvation energy (because it does a statistical
 >> thermodynamics!!!) For example, it correctly describes the solvation of
 >> alkanes n water as a mainly entropic effect, in best agreement with the
 >> experiment.
 >>
 >
 > Do you mean that COSMO-RS yields each
 component(translational/rotational/vibrational/electronic) of entropy and
 enthalpy or that it only separates the free energy of solvation  in enthalpy and
 entropy contributions?
 No, COSMO-RS does not yield all the contributions separately. What we
 can separate are the electrostatic, hydrogen bonding and vdWs
 contribution to the interaction enthalpy. The other components are
 essentially parameterized into the few adjusted pareters of COSMO-RS.
 Since there is no fundamental theory of the translations, rotations and
 vibrations in solution, there is no chance to do this rigorously. And
 fitting to exp. free energies of solvation does not allow us to split
 the contributions with respect to the physical origin. But we can quite
 clearly say that we find a significant (~3 kcal/mol at 298 K)
 contribution to the free energy of solvation which is directly connected
 to the molecule and not indirectly via its interactions and surface.
 Best regards
 Andreas
 --
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