Cation-exchange equilibrium for Ca-K-montmorillonite was studied at 35°, 50°, and 90°C and at three total normalities of the equilibrium solution (0.1, 0.05, and 0.01 N). Changes of the standard free energy for the exchange from K-montmorillonite to Ca-montmorillonite were determined to be −53, −270, and −393 cal/eq at 35°, 50°, and 90°C, respectively. Changes of the standard enthalpy and entropy were 1.7 kcal/eq and 5.6 cal/eq/degree at 35°C, respectively. The sign of the change of the standard free energy was found to be determined mainly by the entropy change, in particular, by the hydration entropy of the cations.

The calculation of the excess functions indicates that the mixing model of Ca-K-montmorillonite approximates that of a regular solution. Montmorillonite having potassium equivalent ion fraction of 0.1 to 0.7 consists of a random interstratification of Ca-montmorillonite (15.6 Å) and K-montmorillonite (12.6 Å).

Measurements of the differential heats of K-Ca exchange are used to show that 6 groups of sites (ranging from −13.8 to −5.1 kJ/eq and with as many as 4 in any one sample) exist in kaolins that range from 0 to 15% in their 2:1 phyllosillicate content. These heat values, coupled with entropies of exchange, suggest that 0.1−10% vermiculitic, micaceous, and smectitic layers are present, presumably interstratified with kaolinitic layers which are assumed to have no permanent charge. Changes in the activity coefficients of adsorbed K with K saturation confirm these conclusions qualitatively. Thus, fK values at x ↑ 0 correlate inversely (r2 = 0.655) with the content of vermiculite + partially expanding micas, and x values at maximum fK indicate the content of vermiculite + nonexpanding mica + partially expanding micas (r2 = 0.732).

Adsorption isotherms for water on homoionic (Ca2+, Li+, Na+, and K+) exchanged forms of Crook County, Wyoming, montmorillonite (CMS Source Clay SWy-1) were measured between 25° and 70°C using a vacuum microbalance having automated control of water vapor pressure. From these adsorption data, integral enthalpies and entropies of adsorption were calculated. Both quantities were negative, but decreased in magnitude with increasing amounts of adsorbed water. For all four cationic forms of the clay, the amount of initial water adsorption at 25°C and at low relative humidities was sensitive to the sample temperature during prior evacuation of water, less water being adsorbed by samples evacuated at 100°C compared with samples evacuated at 25°. For Ca- and Na-montmorillonite, these changes were reversible after several subsequent desorption/adsorption cycles, but recovery was not observed for the Li-SWy-1 clay, probably because of migration of Li+ into the aluminosilicate structure.

The heterogeneity of sites for Ca→K exchange was examined by microcalorimetry in the <0.2-μm fractions of some selected smectites. Six groups of sites, ranging in exothermic exchange enthalpy (-d(ΔHx)/dx) from 5.7 to 10.9 kJ/eq were identified. In Wyoming bentonites, only three groups with enthalpies of 5.7 to 7.5 kJ/eq were distinguished, although in the 0.2-1.0-μm fraction, a 10.7-kJ/eq group was also observed. Redhill and Camp Berteau smectites contained, in addition, groups with enthalpies of 8.7-10.9 kJ/eq, but a New Mexico sample only had groups with the higher values. Thus, the exchange enthalpies of four main groups of sites (reclassified from those observed) appear to be inversely related to the extents of interlayer expansion in the samples by the adsorption of polar molecules. Consequently, a 'true mont-morillonite,’ such as a <0.2-μm Wyoming bentonite, contains only fully expanding layers with -d(ΔHx)/ dx values between 5.7 and 7.5 kJ/eq. As such, it is less heterogeneous and should have a much greater swelling capability than Camp Berteau montmorillonite which has, in addition, groups with exchange enthalpies of 8.7 and 10.3 kJ/eq.

The dehydration temperature of K-montmorillonite, obtained by ion exchange of a Na-mont-morillonite, was determined at pressures to 2 kbar, using high-pressure differential thermal analysis. Dehydration reactions were found at about 50° and 100°C above the liquid-vapor curve of water. At pressures above the critical point of water the dehydration temperatures increased only slightly. The temperature of the first dehydration reaction is 10°C higher than for Na-montmorillonite, indicating a slightly greater stability of the hydration shell around the potassium interlayer cation. The second dehydration reaction occurs at a slightly lower temperature. The data were used to determine the enthalpy of the dehydration ΔH(dh) and the bonding enthalpy of the interlayer water ΔH(iw) at 1 atm. The first dehydration reaction of the K-exchanged montmorillonite has a ΔH(dh) = 46.16 ± 0.06 kJ/mole and a ΔH(iw) = 7.8 ± 0.5 kJ/mole, whereas for the second reaction, ΔH(dh) = 56.7 ± 2 kJ/mole and ΔH(iw) = 19.8 ± 2 kJ/mole. These values compare with a ΔH(dh) = 46.8 ± 0.3 kJ/mole and a ΔH(iw) = 7.8 ± 0.5 kJ/mole for the first dehydration reaction of the Na-montmorillonite and a ΔH(dh) = 62.9 ± 2 kJ/mole and ΔH(iw) = 27.1 ± 2 kJ/mole for the second dehydration.

The enthalpy of hydration of natural clinoptilolite was determined by isothermal immersion calorimetry on Ca-, Na- and K-exchanged clinoptilolite (Fish Creek Mountains, Nevada). Heats of immersion of clinoptilolite were determined at initial H2O contents ranging from θ = 0.02 to 0.85 (where θ is the ratio [H2O content]/[maximum H2O content]). The heat of immersion (liquid H2O reference state) of Ca-clinoptilolite ranged from -7.5 (θ = 0.87) to -25.7 kJ/mol-H2O (θ = 0.19); values for Na-clinoptilolite ranged from -6.3 (θ = 0.85) to -21.8 kJ/mol-H2O (θ = 0.11); and values for K-clinoptilolite ranged from -7.7 (θ = 0.80) to -24.6 kJ/mol-H2O (θ = 0.02). Linear regression of the calorimetric data provided the following values for the complete heat of immersion (from θ = 0): Ca-clinoptilolite, -30.3 ± 2.0; Na-clinoptilolite, -23.4 ± 0.6; and K-clinoptilolite, -22.4 ± 0.8 kJ/mol-H2O.

The heat of immersion measurements were compared with the enthalpy of hydration results of Carey and Bish (1996) determined in a thermogravimetric study of the same samples. The heat of immersion data are similar but of smaller magnitude than the values of enthalpy of hydration and are believed to be more accurate because they represent direct measurements of this thermodynamic property.

The effect of dehydration of clinoptilolite on the thermal evolution of the potential high-level radioactive waste repository at Yucca Mountain was considered by comparing the amount of energy consumed by clinoptilolite dehydration with the amount of energy necessary to heat rocks lacking hydrous minerals. The extra energy consumed on heating clinoptilolite from 25 to 200 °C ranges between 70 and 80% in excess of that required for nondehydrating materials (that is, clinoptilolite acts as a heat sink). These results indicate that accurate thermohydrologic modeling of rock units at Yucca Mountain should consider the thermal effect of dehydration/hydration processes in clinoptilolite and other hydrous minerals, in addition to the water produced/adsorbed during heating/cooling.

The selectivities of clay minerals for larger organic cations over smaller ones have been attributed to favorable clay-organic interactions in clay interlayers and to hydrophobic effects resulting from (partial) dehydration of organic cations in the clay interlayers, but the magnitudes of these energy components have not been estimated. The objective of this study was to differentiate and quantify the contributions of clay-phase and aqueous-phase energy changes to the overall thermodynamics of cation exchange, and thereby to determine which forces control the general selectivity of smectites for organic cations. We compiled literature measurements and estimates for the free energies of overall cation exchange reactions and also for the free energies of organic cation hydration. Our study suggests that organic cation-exchange thermodynamics can be broken into three classes: (1) For two organic cations with identical head-groups, the difference in their cation exchange selectivities is driven almost quantitatively by the difference in their free energies of hydration. Here, the mechanism for organic cation selectivity is almost pure hydrophobic expulsion of the larger cation from water. The clay interlayer simply behaves like a subaqueous phase into which the least hydrophilic organic cations partition and the essentials of such cation exchange selectivity can be explained without any favorable clay-organic interactions. (2) For two organic cations with rather different head-groups, the difference in their cation exchange selectivities is just a small percentage of the difference in their free energies of hydration. This indicates that the clay phase interacts much more strongly with the cation having the smaller head-group, as might be expected on the basis of simple electrostatics. Here, the clay has an intrinsic strong preference for the cation with smaller head-group yet ‘selects’ for the cation with larger head-group because the aqueous-phase preference for the cation with smaller head-group is even stronger than the clay preference. (3) When the clay is already substantially loaded with organic cations, then van der Waals forces apparently can play a significant role in determining organic cation exchange selectivity differences.

A calorimetric method for determining isothermal partial and integral heats of hydration reactions ($\text{Δ}{\overline{H}}_{\text{R,}T,P}$${\rm{\Delta }}{\bar H_{{\rm{R,}}T,\,P}}$ and $\text{Δ}{\stackrel{\sim }{H}}_{\text{R,}T,P}$${\rm{\Delta }}{\tilde H_{{\rm{R,}}T,\,P}}$, respectively) in zeolites and other mineral hydrates is presented. The method involves immersing a dehydrated sample in a humid gas stream under isothermal conditions within a thermal analysis device that records simultaneous differential scanning calorimetric (DSC) and thermogravimetric analysis (TGA) signals. Monitoring changes in sample mass (corresponding to extent of reaction progress) coincident with a quantitative measurement of heat flow allows for direct detection of $\text{Δ}{\overline{H}}_{\text{R,}T,P}$${\rm{\Delta }}{\bar H_{{\rm{R,}}T,\,P}}$ as a function of the extent of hydration, which can be integrated to determine $\text{Δ}{\stackrel{\sim }{H}}_{\text{R,}T,P}$${\rm{\Delta }}{\tilde H_{{\rm{R,}}T,\,P}}$. In addition, it eliminates uncertainties associated with imprecise knowledge of the starting and final states of a sample during hydration. Measurement under isothermal conditions removes uncertainties associated with heat capacity effects that complicate interpretations of DSC measurements of dehydration heats conducted under traditional scanning temperature conditions. Example experiments on the zeolites natrolite, analcime and chabazite are used to illustrate strategies for quantifying $\text{Δ}{\overline{H}}_{\text{R,}T,P}$${\rm{\Delta }}{\bar H_{{\rm{R,}}T,\,P}}$ and $\text{Δ}{\stackrel{\sim }{H}}_{\text{R,}T,P}$${\rm{\Delta }}{\tilde H_{{\rm{R,}}T,\,P}}$ and minimizing errors associated with baseline uncertainties. Results from this method agree well with previously published values determined by other calorimetric techniques and regression of phase equilibrium data. In the case of chabazite, the results allowed detailed measurements of the variation in $\text{Δ}{\overline{H}}_{\text{R,}T,P}$${\rm{\Delta }}{\bar H_{{\rm{R,}}T,\,P}}$ for energetically different water types encountered progressively as the sample absorbed water. This technique complements and in many cases improves the quality of thermodynamic data obtained through phase equilibrium observations and other calorimetric techniques.

Because adsorption is a major factor controlling herbicide persistence, activity, and mobility in soils, an extensive literature exists on the measurement of this process. The adsorption data are usually fitted to the Freundlich equation, but attempts to interpret this equation theoretically have had only limited success. A meaningful thermodynamic interpretation of the Freundlich equation can be developed using a proposed standard state for adsorbed herbicide, which assumes that soil organic matter forms a solid solution with the herbicide. When herbicide vapor pressures and aqueous solubilities are taken into account, the losses in free energy of different herbicides, on adsorption onto wetted soil surfaces, are shown to be similar to each other and are slightly less than the loss on absorption to the solid herbicides themselves. The Freundlich exponent is related in a simple way to the decreasing energy of available soil sites as the amount of herbicide adsorbed increases, but this change is relatively small over the range of concentrations used in adsorption experiments. Sample results are given for six triazine, three urea, and one uracil herbicides.

A Stefan problem is a free boundary problem where a phase boundary moves as a function of time. In this article, we consider one-dimensional and two-dimensional enthalpy-formulated Stefan problems. The enthalpy formulation has the advantage that the governing equations stay the same, regardless of the material state (liquid or solid). Numerical solutions are obtained by implementing the Godunov method. Our simulation of the temperature distribution and interface position for the one-dimensional Stefan problem is validated against the exact solution, and the method is then applied to the two-dimensional Stefan problem with reference to cryosurgery, where extremely cold temperatures are applied to destroy cancer cells. The temperature distribution and interface position obtained provide important information to control the cryosurgery procedure.

We have made a comparative structure based analysis of the thermodynamics of lectin-carbohydrate (L-C) binding and protein folding. Examination of the total change in accessible surface area in those processes revealed a much larger decrease in free energy per unit of area buried in the case of L-C associations. According to our analysis, this larger stabilization of L-C interactions arises from a more favorable enthalpy of burying a unit of polar surface area, and from higher proportions of polar areas. Hydrogen bonds present at 14 L-C interfaces were identified, and their overall characteristics were compared to those reported before for hydrogen bonds in protein structures. Three major factors might explain why polar–polar interactions are stronger in L-C binding than in protein folding: (1) higher surface density of hydrogen bonds; (2) better hydrogen-bonding geometry; (3) larger proportion of hydrogen bonds involving charged groups. Theoretically, the binding entropy can be partitioned into three main contributions: entropy changes due to surface desolvation, entropy losses arising from freezing rotatable bonds, and entropic effects that result from restricting translation and overall rotation motions. These contributions were estimated from structural information and added up to give calculated binding entropies. Good correlation between experimental and calculated values was observed when solvation effects were treated according to a parametrization developed by other authors from protein folding studies. Finally, our structural parametrization gave calculated free energies that deviate from experimental values by 1.1 kcal/mol on the average; this amounts to an uncertainty of one order of magnitude in the binding constant.

A database for thermodynamic properties of group-III nitrides and relevant species involved into growth of these materials is developed in this paper. Standard formation enthalpies of materials and coefficients of polynomial approximations of the reduced Gibbs free energies are collected in the tables. They allow one to determine the Gibbs free energy, enthalpy, entropy and specific heat of a species as a function of temperature. The database covers solid and gaseous group-III nitrides, elemental species, gaseous metal-organic compounds, chlorides and hydrides of group-III elements, nitrogen containing precursors and organic byproducts of various chemical reactions proceeding during growth processes. Thermodynamic properties of adducts which can be formed in the vapor phase while mixing ammonia and metal-organic compounds are presented in the database as well. Much of the data given in this paper is presented for the first time. All the data are checked for self-consistency and therefore can be used for thermodynamic calculations.