Entropy mobility

We shall now discuss the depression of the static permittivity of water by the addition of eiectrolyte solutes, which is a phenomenon of some importance in the understanding of the hydration sheath of the ions. It is essentially a dielectric saturation phenomenon the strong electric fields in the neighbourhood of the ions produce a non-linear polarization, which renders the local water moleodes ineffective as regards orientation in the applied field. It is possible to make estimates of the extent of hydration, or hydration number , of water molecules considered to be bound irrotationally to the average ion these estimates are in reasonable agreement with hydration numbers estimated on the basis of activity coefficients, entropies, mobilities, and viscosities. The hydration number must be distinguished from the number of water molecules actually adjacent to the ion in the first or second layers of hydration (the hydration sheath) it does not follow that all of these molecules can be considered to be attached to the ion as it moves in the solution. 

The state of an adsorbate is often described as mobile or localized, usually in connection with adsorption models and analyses of adsorption entropies (see Section XVII-3C). A more direct criterion is, in analogy to that of the fluidity of a bulk phase, the degree of mobility as reflected by the surface diffusion coefficient. This may be estimated from the dielectric relaxation time Resing [115] gives values of the diffusion coefficient for adsorbed water ranging from near bulk liquids values (lO cm /sec) to as low as 10 cm /sec. 

Thus the entropy of localized adsorption can range widely, depending on whether the site is viewed as equivalent to a strong adsorption bond of negligible entropy or as a potential box plus a weak bond (see Ref. 12). In addition, estimates of AS ds should include possible surface vibrational contributions in the case of mobile adsorption, and all calculations are faced with possible contributions from a loss in rotational entropy on adsorption as well as from change in the adsorbent structure following adsorption (see Section XVI-4B). These uncertainties make it virtually impossible to affirm what the state of an adsorbed film is from entropy measurements alone for this, additional independent information about surface mobility and vibrational surface states is needed. (However, see Ref. 15 for a somewhat more optimistic conclusion.)... 

The standard entropy of adsorption AS2 of benzene on a certain surface was found to be -25.2 EU at 323.1 K the standard states being the vapor at 1 atm and the film at an area of 22.5 x T per molecule. Discuss, with appropriate calculations, what the state of the adsorbed film might be, particularly as to whether it is mobile or localized. Take the molecular area of benzene to be 22 A. ... 

In general, it seems more reasonable to suppose that in chemisorption specific sites are involved and that therefore definite potential barriers to lateral motion should be present. The adsorption should therefore obey the statistical thermodynamics of a localized state. On the other hand, the kinetics of adsorption and of catalytic processes will depend greatly on the frequency and nature of such surface jumps as do occur. A film can be fairly mobile in this kinetic sense and yet not be expected to show any significant deviation from the configurational entropy of a localized state. 

Neither the thermodynamic nor the rheological description of surface mobility has been very useful in the case of chemisorbed films. From the experimental point of view, the first is complicated by the many factors that can affect adsorption entropies and the latter by the lack of any methodology. 

We note that is positive and goes through a maximum as a increases. If the positive holes were localised on the cations, they would give an entropy contribution exactly equal to. The positive holes have, however, considerable mobility (see below), and are perhaps best treated as an ideal gas consisting of particles of effective mass m. In this case ... 

The configurational entropy of the mobile guest ions, assuming random mixing and a concentration x, residing in x° lattice sites of equal energy, is... 

One notes in Table 1.2 a uniform increase in the adsorption energies of the alkanes when the microspore size decreases (compare 12-ring-channel zeohte MOR with 10-ring-channel TON). However, at the temperature of hydroisomerization the equilibrium constant for adsorption is less in the narrow-pore zeohte than in the wide-pore system. This difference is due to the more limited mobility of the hydrocarbon in the narrow-pore material. This can be used to compute Eq. (1.22b) with the result that the overall hydroisomerization rate in the narrow-pore material is lower than that in the wide-pore material. This entropy-difference-dominated effect is reflected in a substantially decreased hydrocarbon concentration in the narrow-pore material. 

Hence, according to the transition state theory, adsorption becomes more likely if the molecule in the mobile physisorbed precursor state retains its freedom to rotate and vibrate as it did in the gas phase. Of course, this situation corresponds to minimal entropy loss in the adsorption process. In general, the transition from the gas phase into confinement in two dimensions will always be associated with a loss in entropy and the sticking coefficient is normally smaller than unity. 

Clearly, the sticking coefficient for the direct adsorption process is small since a considerable amount of entropy is lost when the molecule is frozen in on an adsorption site. In fact, adsorption of most molecules occurs via a mobile precursor state. Nevertheless, direct adsorption does occur, but it is usually coupled with the activated dissociation of a highly stable molecule. An example is the dissociative adsorption of CH4, with sticking coefScients of the order 10 -10 . In this case the sticking coefficient not only contains the partition functions but also an exponential... 

Transition metal colloids can also be prevented from agglomeration by polymers or oligomers [27,30,42,43]. The adsorption of these molecules at the surface of the particles provides a protective layer. In the interparticle space, the mobility of adsorbed molecules should be reduced decreasing the entropy and thus increasing the free energy (Fig. 2). 

Three types of methods are used to study solvation in molecular solvents. These are primarily the methods commonly used in studying the structures of molecules. However, optical spectroscopy (IR and Raman) yields results that are difficult to interpret from the point of view of solvation and are thus not often used to measure solvation numbers. NMR is more successful, as the chemical shifts are chiefly affected by solvation. Measurement of solvation-dependent kinetic quantities is often used (<electrolytic mobility, diffusion coefficients, etc). These methods supply data on the region in the immediate vicinity of the ion, i.e. the primary solvation sphere, closely connected to the ion and moving together with it. By means of the third type of methods some static quantities entropy and compressibility as well as some non-thermodynamic quantities such as the dielectric constant) are measured. These methods also pertain to the secondary solvation-sphere, in which the solvent structure is affected by the presence of ions, but the... 

The fact that the water molecules forming the hydration sheath have limited mobility, i.e. that the solution is to certain degree ordered, results in lower values of the ionic entropies. In special cases, the ionic entropy can be measured (e.g. from the dependence of the standard potential on the temperature for electrodes of the second kind). Otherwise, the heat of solution is the measurable quantity. Knowledge of the lattice energy then permits calculation of the heat of hydration. For a saturated solution, the heat of solution is equal to the product of the temperature and the entropy of solution, from which the entropy of the salt in the solution can be found. However, the absolute value of the entropy of the crystal must be obtained from the dependence of its thermal capacity on the temperature down to very low temperatures. The value of the entropy of the salt can then yield the overall hydration number. It is, however, difficult to separate the contributions of the cation and of the anion. 

In polymer electrolytes (even prevailingly crystalline), most of ions are transported via the mobile amorphous regions. The ion conduction should therefore be related to viscoelastic properties of the polymeric host and described by models analogous to that for ion transport in liquids. These include either the free volume model or the configurational entropy model . The former is based on the assumption that thermal fluctuations of the polymer skeleton open occasionally free volumes into which the ionic (or other) species can migrate. For classical liquid electrolytes, the free volume per molecule, vf, is defined as ... 

Estimated side chain entropies TSppn for each residue simulated that possesses a mobile side chain are given in Table II along with entropy estimates, TSoisorderecb f°r side chains in a tripeptide model for disordered states taken from Creamer (2000), and the difference in entropy, TAS. In all cases, Y .Sppn in the peptides restricted to the PPII conformation is higher than that in disordered states, leading to positive values... 

Guillaume et al. [69] presented a high performance liquid chromatographic method for an association study of miconazole and other imidazole derivatives in surfactant micellar using a hydrophilic reagent, Montanox DF 80. The thermodynamic results obtained showed that imidazole association in the surfactant micelles was effective over a concentration of surfactant equal to 0.4 pM. In addition, an enthalpy-entropy compensation study revealed that the type of interaction between the solute and the RP-18 stationary phase was independent of the molecular structure. The thermodynamic variations observed were considered the result of equilibrium displacement between the solute and free ethanol (respectively free surfactant) and its clusters (respective to micelles) created in the mobile phase. 

Holroyd (1977) finds that generally the attachment reactions are very fast (fej - 1012-1013 M 1s 1), are relatively insensitive to temperature, and increase with electron mobility. The detachment reactions are sensitive to temperature and the nature of the liquid. Fitted to the Arrhenius equation, these reactions show very large preexponential factors, which allow the endothermic detachment reactions to occur despite high activation energy. Interpreted in terms of the transition state theory and taking the collision frequency as 1013 s 1- these preexponential factors give activation entropies 100 to 200 J/(mole.K), depending on the solute and the solvent. 

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