Translation entropy associated with

In order to calculate the free energy of micellization accurately, one needs to take into account the enthalpic terms describing the interactions between the block copolymer and solvent, the free energy of the micelle (Fniiceiie), the mixing free energy (Fniix), as well as the translational entropy associated with micelles and free chains (5ni). 

The translational entropy associated with the micelles and the unaggregated block copolymer chains can be written using the Hory-Huggins theory as ... 

The translational entropy associated with each chain is reduced by a factor of N to reflect that monomers in the same chain are connected and cannot be positioned independently. 

Entropy of unadsorbed ions. The free energy due to the translational entropy associated with (N - M + n+) unadsorbed counterions and n coions in volume V is the familiar entropy of mixing term... 

In some cases the adsorption is so weak that the entropy associated with the vibration replacing the translational motion perpendicular to the surface may not be negligible. The entropy associated with a vibration of frequency v is given by... 

There is a net release of 1 mole of ions into solution by this reaction, because 2 moles of protons are released for each mole of metal ions complexed. The greater degrees of rotational and translational freedom associated with this release contributes a positive entropy term and hence a more negative free energy for reaction 4.43. Consequently, the reaction is likely to be spontaneous in the direction written. 

Osmond et al. (1975) have also asserted their preference for a phase separation approach to incipient instability in a critique of theories of steric stabilization. They argued that phase separation occurred at a temperature close to the 0-temperature. This was claimed to result from the attachment of the stabilizing moieties to the surface of the colloidal particles. Attachment removes the configurational entropy associated with the translational motion of the stabilizing moieties. Osmond et al. did not, however, spell out whether the phase separation envisaged by them involved the formation of liquid/liquid interfaces, although it is difficult to conceive how phase separation can proceed without their formation. Many of the objections to the hypothesis of Cairns and Neustadter raised above are equally applicable in this instance. 

The percolation models discussed so far undergo piuely geometrical transitions because the objects treated have no center of mass translational motion. They are only randomly placed either on the lattices or in the continuum space. Therefore, they don t reveal any thermodynamic singularities. If particles are moving in a space, however, the entropy associated with the translational motion may partly vanish at the percolation point since the mass center of the infinite cluster (gel) ceases to move. If its derivative with respect to the concentration across the percolation point has a discontinuity, the transition becomes a real thermodynamic one. 

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