Ion homeostasis is a crucial process in plants that is closely linked to the efficiency of nutrient uptake, stress tolerance and overall plant growth and development. Nevertheless, our understanding of the fundamental processes of ion homeostasis is still incomplete and highly fragmented. Especially at the mechanistic level, we are still in the process of dissecting physiological systems to analyse the different parts in isolation. However, modelling approaches have shown that it is not individual transporters but rather transporter networks (homeostats) that control membrane transport and associated homeostatic processes in plant cells. To facilitate access to such theoretical approaches, the modelling of the potassium homeostat is explained here in detail to serve as a blueprint for other homeostats. The unbiased approach provided strong arguments for the abundant existence of electroneutral H+/K+ antiporters in plants.

The sequence of mineral reactions involving zeolites and other authigenic phases in tuffaceous sedimentary rocks can be explained by growth- and dissolution-reaction kinetics. Kinetic factors may determine the specific authigenic phases which form and the temporal and spatial constraints on the solution composition during irreversible dissolution and growth reactions in glass-bearing rocks. The glass phase generates a high level of supersaturation with respect to a variety of aluminosilicates in the pore fluid. The sequence of assemblages formed during a series of metastable reactions resembles an Ostwald step sequence. Metastable reactions occur because formation of less stable phases such as gels, clays, and disordered zeolites may lower the total free energy of the glass-bearing system faster than the growth of the stable assemblage including ordered feldspars, quartz, and micas. Eventually, after a series of steps, the most stable silicate assemblage for the bulk composition, temperature, and pressure may form. However, the formation of intermediate metastable phases can delay the attainment of equilibrium by as much as tens of millions of years.

The integral thermodynamic quantities of adsorbed water on Na- and Ca-montmorillonite have been calculated from water adsorption isotherms on Na- and Ca-montmorillonite at 298° and 313°K and from one adsorption isotherm and calorimetric measurements at 298°K. The integral entropy values decrease and then increase as the amount of adsorbed water approaches zero. In both systems, the curves approach the entropy value of free liquid water at the high content water. The thermodynamics of adsorbate on a non-inert adsorbent is discussed in some detail. The two-isotherm method gives the energy change of the water phase only, whereas the colorimetric method gives the energy change of the whole system (clay, exchangeable cations, and the adsorbed water). Only when the energy changes in the solid phase are negligible (=inert surface) should the two methods give similar results. An hypothesis was developed to explain the entropy-change data of water adsorbed on clay surfaces, in which the clay surface behaves as a non-inert adsorbent.

Electron probe analyses of diagenetic illites in Eocene sandstones from Kettleman North Dome, California, along with analyses of coexisting interstitial waters were used to calculate apparent molal free energies of formation of the illites at the in situ conditions of 100°C and 150 bars. Various triangular and rectangular compositional plots, once contoured for free energy, crudely indicate that the free energy decreases as the potassium content increases, decreases as the Al-for-Si substitution increases, and appears to be a minimum along a narrow composition valley having ~3% Fe2O3 of octahedral cations. Qualitatively, the shape of the free energy surface suggests only small departures from ideality.

The illites and water samples used in the calculations were chosen as close to each other as possible and are in equilibrium. The waters contain mainly Cl−, SO42−, Na+, and Ca2+ and have a total salinity of ~10,000 ppm. The illites, which coexist in the sandstones with diagenetic quartz, albite, and K-feldspar, are phen-gitic and contain 5–9% K2O, 1–3% total FeO, 1% MgO, and minor Na2O, MnO, and TiO2. The Fe2O3/FeO ratio has been set arbitrarily to 7 by comparison with published analyses.

Log K (100°C) was first calculated for the equilibrium illite ⇄ ions from the ionic activities obtained through speciation calculations for each water sample. The apparent free energies of formation of illites at 100°C were then calculated. The effect of instrumental uncertainty on the values of ΔGf was assessed by accepting a 2.5 or 3.5% error in the probe analyses and by using a Monte Carlo method of error propagation. The free energies of formation obtained (on the basis of O10(OH2)) range from -1280 to -1320 kcal/mole at 100°C and 150 bars, and their Monte-Carlo uncertainties are less than ±2 kcal/mole. Combining the compositions of natural, coexisting aqueous solutions and mineral solid solutions through thermodynamic equations constitutes a fast method to determine, at least crudely, the free energy-composition surface for the solid solution. This is in contrast to experimental methods such as calorimetry or hydrothermal equilibrium, which are very time-consuming and difficult.

The exchange of Na, K, and Ca ions in vermiculite has been studied between 50 and 150°C at a total normality of 0.1. The free energy changes were negative in the Na → K, Ca → K, and Na → Ca exchange reactions, and the cation preference in the vermiculite was Na < Ca < K in the temperature range examined. The enthalpy changes, calculated by application of the van't Hoff equation to the relation between equilibrium constant and temperature, were positive. The cation preference in the vermiculite seems to have been largely controlled by the increase in entropy which was due to the positive values of the entropy change term in the solid for the Na-K and Ca-K exchanges and the positive values of the entropy change in the solution for the Na-Ca exchange. From a thermodynamic analysis of the cation-mixing properties in vermiculite, the observed free energy change in the Na-K exchange was determined solely by the differences of the intrinsic electrostatic binding energy of the cations on the clay surface. That in the Na-Ca exchange was interpreted by taking into account an extra interaction energy of Ca-Ca pairs in addition to the intrinsic energy change. Furthermore, an additional interaction energy between K ions and the clay surface appears to have been added to the free energy change in the Ca-K exchange. In the Na → K and Ca → K exchange reactions a structural modification occurred in the K-equivalent fraction (X̄K) range 0.05–0.6, and a regularly interstratified phase of 15-Å and 10-Å members was formed at 0.05 < X̄K < 0.4.

Clay/electrolyte systems are best characterized using a new variable, notional interfacial content (NIC). The NIC approach emphasizes that any division of the total amount of a species present in a clay/electrolyte system into that part which ‘belongs’ to the clay and that part which ‘belongs’ to solution is necessarily arbitrary. It carries out this division by choosing one of the species as a reference species and defining it as being completely in a notional bulk solution which had the same composition, but not extent, as the real bulk solution. The NIC of each of the other species present, that is that part of their total amount not in the notional bulk solution, therefore represents the amounts of those species ‘belonging’ to the clay.

The NIC concept is universal and hence encompasses several other, older terms. For example, by choosing different reference species, the variables hitherto called ‘water adsorption’ and ‘negative adsorption’ (which have been used to describe the same phenomenon) may be obtained. Similarly, certain earlier definitions of exchangeable and adsorbed cations (some being pragmatic are not included) as well as that of ion surface excesses may be accounted for. The NIC approach thus provides a rationalization of several earlier terms which are, in fact, plagued by a multiplicity of definition which makes their use very complicated.

The activities of thermodynamic components of clay minerals corresponding in composition to pyrophyllite, muscovite, paragonite, and margarite were computed from chemical analyses reported in the literature assuming ideal mixing of atoms on homological sites in the minerals. These activities were then used to generate stability fields for smectites, illites, and mixed-layer clays on logarithmic activity diagrams representing equilibrium among minerals and aqueous solutions at 25°C and 1 bar. Comparative analysis indicates that the approach affords close approximation of both mineral and water compositions in geologic systems.

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.

Fe(II)–Fe(III) green rust identified in soil as a natural mineral is responsible for the blue-green color of gley horizons, and exerts the main control on Fe dynamics. A previous EXAFS study of the structure of the mineral confirmed that the mineral belongs to the group of green rusts (GR), but showed that there is a partial substitution of Fe(II) by Mg(II), which leads to the general formula of the mineral: ${[{\text{Fe}}_{1-x}^{2+}{\text{Fe}}_x^{3+}{\text{Mg}}_y{(\text{OH})}_{2+2y}]}^{x+}{[x{\text{OH}}^{-}\cdot m{\text{H}}_2\text{O}]}^{x-}$${[{\rm{Fe}}_{1 - x}^{2 + }{\rm{Fe}}_x^{3 + }{\rm{M}}{{\rm{g}}_y}{({\rm{OH}})_{2 + 2y}}]^{x + }}{[x{\rm{O}}{{\rm{H}}^ - } \cdot m{{\rm{H}}_2}{\rm{O}}]^{x - }}$. The regular binary solid-solution model proposed previously must be extended to ternary, with provision for incorporation of Mg in the mineral. Assuming ideal substitution between Mg(II) and Fe(II), the chemical potential of any Fe(II)-Fe(III)-Mg(II) hydroxy-hydroxide is obtained as: $\text{μ}=X_1{\text{μ}}_{\text{1}}^{\text{o}}+X_2{\text{μ}}_{\text{2}}^{\text{o}}+X_3{\text{μ}}_{\text{3}}^{\text{o}}+\text{R}T[X_1\text{ln}{X}_1+X_2\text{ln}{X}_2+X_3\text{ln}{X}_3]+A_{12}{X}_2(1-X_2)$${\rm{\mu }} = {X_1}{\rm{\mu }}_{\rm{1}}^{\rm{o}} + {X_2}{\rm{\mu }}_{\rm{2}}^{\rm{o}} + {X_3}{\rm{\mu }}_{\rm{3}}^{\rm{o}} + {\rm{R}}T[{X_1}{\rm{ln}}{X_1} + {X_2}{\rm{ln}}{X_2} + {X_3}{\rm{ln}}{X_3}] + {A_{12}}{X_2}(1 - {X_2})$. All experimental data show that the mole ratio X2 = Fe(III)/[Fetotal + Mg] is constrained (1) structurally and (2) geochemically. Structurally, Fe(III) ions cannot neighbor each other, which leads to the inequality $X_2\alpha \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right..$${X_2}\leqslant {\raise0.5ex\hbox{$\scriptstyle 1$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle 3$}}.$ Geochemically, Fe(III) cannot be too remote from each other for GR to form as Fe(OH)2 and Mg(OH)2 are very soluble, so $X_2\alpha \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$${X_2}\geqslant {\raise0.5ex\hbox{$\scriptstyle 1$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle 4$}}$. A linear relationship is obtained between the Gibbs free energy of formation of GR, normalized to one Fe atom, and the electronegativity ϰ of the interlayer anion, as: μo/n = −76.887ϰ — 491.5206 (r2 = 0.9985, N = 4), from which the chemical potential of the mineral fougerite μ is obtained in the limiting case X3 = 0, and knowing ${\text{μ}}_{\text{1}}^{\text{o}}=-489.8$${\rm{\mu }}_{\rm{1}}^{\rm{o}} = - 489.8$ kJmol−1 for Fe(OH)2, and ${\text{μ}}_{\text{3}}^{\text{o}}=-832.16$${\rm{\mu }}_{\rm{3}}^{\rm{o}} = - 832.16$ kJmol−1 for Mg(OH)2, the two unknown thermodynamic parameters of the solid-solution model are determined as

${\text{μ}}_{\text{2}}^{\text{o}}=+119.18{\text{kJmol}}^{-1}$${\rm{\mu }}_{\rm{2}}^{\rm{o}} = + 119.18\;{\rm{kJmo}}{{\rm{l}}^{ - 1}}$ for Fe(OH)3 (virtual), and A12 = −1456.28 kJmol−1 (non-ideality parameter). From Mössbauer in situ measurements and our model, the chemical composition of the GR mineral is constrained into a narrow range and the soil solutions-mineral equilibria computed. Soil solutions appear to be largely overstaurated with respect to the two forms observed.

Heavy metals in the environment are a problem due to their toxicity and bioaccumulation. Adsorptive removal of heavy metals by clay minerals has garnered increasing attention due to the abundance, low cost, and exceptional physicochemical properties of the clays. The purpose of the present study was to investigate the utilization of two Turkish sepiolite samples, nodular sepiolite (NS) and industrial sepiolite (IS), as adsorbents in removing Ni2+ ions from aqueous solutions. The specific surface areas of NS and IS are 182.19 m2 g–1 and 63.78 m2 g–1, respectively. The effects of adsorbent dosage, initial pH, contact time, initial concentration, and temperature on the adsorption of Ni2+ ions onto the sepiolite samples were investigated using a batch method. The optimum adsorbent dosage was determined as 0.6 g/50 mL of adsorbent and the optimum pH value was 6.0, for both sepiolite samples. The adsorption process obeyed the Freundlich isotherm model (KF: 4.89–9.73 mg1–1/n L1/n g–1 for NS and 4.27–6.42 mg1–1/n L1/n g–1 for IS) and the pseudo-second order kinetics model (k2: 0.0049–0.0397 g mg–1 min–1 for NS and 0.0688–0.1195 g mg–1 min–1 for IS). The adsorption process was spontaneous and endothermic, and the randomness increased. The samples exhibited large adsorption capacities through three cycles of adsorption-desorption tests. The results revealed that the sepiolite samples are promising as cost-effective adsorbents for the removal of Ni2+ ions from aqueous solutions.

Toxic metal contamination of waste waters can be mitigated by metal adsorption to clay and zeolitic minerals, but in developing countries such environmental remediation can be cost prohibitive if these minerals are not readily available. Because of its abundance, low cost, and excellent selectivity for several toxic metal ions, clinoptilolite from the Zlatokop deposit in Serbia was investigated for its ability to remove copper ions from aqueous solutions and serve as an effective local resource for this purpose. The sorption capacity of the clinoptilolite at 298 K varied from 8.3 mg Cu g−1 (for C0 = 100 mg Cu dm−3) to 16.8 mg Cu g−1 (for C0 = 400 mg Cu dm−3). The sorption data were best described by the Freundlich isotherm and the sorption kinetics followed the pseudo-second-order model. Intra-particle diffusion of Cu2+ was present but it is not the rate-limiting step. The sorption of Cu2+ on the clinoptilolite occurred spontaneously, the free energy change decreasing with temperature. The sorption was endothermic and was accompanied by an increase in entropy. Dehydration of the Cu-loaded clinoptilolite at 540°C led to the formation of nanocrystalline Cu(I) oxide particles with an average size of ~2 nm, suggesting possible novel applications for the Cu-loaded clinoptilolite.