Free Energy Of Exchange Research Articles

Potassium depletion under long-term fertilization in a semi-arid soil in India

SUMMARYIn 12-year (1975–87) fertilizer trial on a pearl millet-wheat rotation, there were no responses to applied K and exchangeable K decreased from 620 to 200 kg/ha. In spite of progressively diminishing exchangeable K, removal of K by crops was independent of soil K status, indicating that exchangeable K had no relation to K uptake in this soil. Thus, nonexchangeable K made a major contribution to plant K, up to 90% in untreated plots and > 70% in K-treated plots. A significant (r = -·708) relationship between nonexchangeable K and K fixation capacity was found. Nonexchangeable K was also significantly but negatively correlated (r = -0·583) with free energy exchange (ΔGr). Potassium supply values, expressed by pK-½p (Ca + Mg), were positively and significantly correlated with K removal by crops in 1987 and with the K saturation values of the exchange phase, so that both these measures can be successfully used to test soil K availability. The results of this study suggested that on this soil, under a pearl millet-wheat crop system, inclusion of K in the fertilizer programme may soon be needed.

Role of arginine 67 in the stabilization of chymotrypsin inhibitor 2: examination of amide proton exchange rates and denaturation thermodynamics of an engineered protein

We have examined the contribution to protein stability of an interaction involving a charged hydrogen bond from an arginyl side chain (Arg67) in the serine proteinase inhibitor chymotrypsin inhibitor 2 (CI-2), by replacing this side chain with an alanyl residue by protein engineering. Using nuclear magnetic resonance spectroscopy (NMR), we have examined the effect of this mutation on the hydrogen-deuterium exchange rates of several backbone amide protons in the native and engineered proteins at 50 degrees C. These exchange rates provide a localized probe at multiple discrete sites throughout the protein and from comparison of native and mutant exchange rates allow calculation of the difference in free energy of exchange (delta delta Gex) resulting from the mutation. The results show that for the majority of amides observed this mutation results in delta delta Gex of ca. 1.7 kcal mol-1 over the whole CI-2 molecule. However, for two relatively exposed amide protons the exchange rates are found to be far less perturbed, implying that local unfolding mechanisms predominate for these protons. Direct measurement of the stability of both proteins to denaturation by guanidinum hydrochloride shows that the interaction contributes 1.4 kcal mol-1 to the stability of the molecule. This value is comparable to those obtained from the NMR exchange measurements and indicates that the exchange processes reflect the differences in stability between the native and mutant proteins.(ABSTRACT TRUNCATED AT 250 WORDS)

Effects of oscillations and energy-driven fluctuations on the dynamics of enzyme catalysis and free-energy transduction.

It has been shown that many enzymes should be capable of utilizing free energy supplied by external time-dependent perturbations to drive the chemical or transport reactions they catalyze away from equilibrium. This property is analyzed in terms of thermodynamic and kinetic theory. An explicit demonstration using irreversible thermodynamics, through second order, is given for the case of a simple model enzyme in the presence of a periodic external perturbation. Three reasons for an enzyme to drive a reaction in a nonstationary environment may be identified: the average values of the forces, the root mean square of the external time-dependent perturbation, and the frequency-dependent correlation between the applied perturbation and the enzyme response. The extent to which the output reaction responds to any of these is governed by the kinetic constants of the enzyme. Even if the catalyzed reaction (e.g., the transport of an uncharged substance across a membrane) is in and of itself thermodynamically independent of the periodic perturbation (e.g., an ac electric field), the enzyme is competent to mediate free-energy exchange between the two. This originates from the fact that at high frequencies, the enzyme response lags behind the applied perturbation. It is sufficient that the enzyme interact with the applied field, and that the catalytic rate constants display the kinetic asymmetry typical of many, and particularly transport, enzymes. These results highlight the role of enzymes as free-energy converters in addition to that of biological catalysts.

Concentration scales and ion exchange thermodynamics

Three dimensionless concentration scales of interest in ion exchange use respectively mole fractions, which in zeolites and clay minerals include the zeolitic water and cation mole and cation equivalent fractions, which do not. Activity coefficients and assumptions as to what represents ideal behaviour differ among these scales. Standard states are the same for cation mole and cation equivalent fraction scales but differ from those for the mole fraction scale. Consequently, standard thermodynamic quantities, such as the free energy of exchange, differ for the mole fraction scale from those for the other two scales, for which they are the same. This difference arises because only the standard states for the mole fraction scale involve the free energies of reversible isothermal hydration (or dehydration) of each homoionic exchange form. For anhydrous exchangers such as felspars the Gibbs-Duhem relation gives for the ideal case on the cation equivalent fraction scale a relationship which can be universally satisfied only if a mole of homoionic exchanger is defined as the amount containing one equivalent of cations. This, and the absence of zeolitic water, makes all three concentration scales identical.

Water quality and soil properties of ponds as influenced by Makhana (Euryale ferox) cultivation

Analysis of regularly collected samples of soil and water from Makhana (Euryale ferox) growing ponds indicated that pH of soil and water were established near neutrality and C/N of soil near ten. Bicarbonate dominated soil extract while chloride dominated standing water. During grand growth period (March to June), Ca2++Mg2+, NH4+ K+ increased while Na+ increased during decay of the plant (July to September) both in soil and plants. The soil had high contents of micro-nutrients, K and P. S.A.R. of soil was 3 to 4 times that of water. Free energy of exchange indicated stability and spontaneity.

Thermodynamics of exchange in clays: Ion exchange equilibria of transition metals and sodium ions on illite

Ion exchange equilibria of bivalent transition metal ions have been studied at 20, 30 and 45°C on illite surface. The exchange isotherms and free energy changes indicate a higher preference of the illite surface for the metal ions. Cd2+ and Mn2+ ions were preferred throughout the entire range while reversal of behaviour occurred during Cu2+, Zn2+ and Co2+ ions exchange on the illite surface. Enthalpy changes suggested a stronger preference of transition metal ions for the illite surface. Entropy changes indicated an increase in the order of system. The surface phase coefficients of the cations showed that with increasing metal ion saturationf m continuously increases whilef Na decreases. The excess thermodynamic functions snowed that the exchange reactions were non-ideal.

Observations on the determination of the availability of potassium for rhodes grass grown in open-cut mine overburden

A potassium availability index, the value of the free energy of exchange of calcium and potassium, was determined when Rhodes grass growing in mine overburden and in topsoil exhibited visual potassium deficiency symptoms. The value was found to be -4060 � 100 cal equiv.-1. There was no significant difference in this value between the overburdens and topsoil studied. The potassium characteristics of the growth media changed form during the growth of the Rhodes grass.

Mechanism of active transport: free energy dissipation and free energy transduction.

The thermodynamic pathway for "chemiosmotic" free energy transduction in active transport is discussed with an ATP-driven Ca2+ pump as an illustrative example. Two innovations are made in the analysis. (i) Free energy dissipated as heat is rigorously excluded from overall free energy bookkeeping by focusing on the dynamic equilibrium state of the chemiosmotic process. (ii) Separate chemical potential terms for free energy donor and transported ions are used to keep track of the thermodynamic state of each substrate through the reaction cycle. These procedures clarify the mechanism of free energy transduction, even without step-by-step analysis. The results show that free energy exchange must occur in its entirety among protein-bound species. Imposition of conditions for an adequate rate of physiological function further indicates (i) that the standard free energy of hydrolysis of protein-bound ATP (to yield protein-bound products) needs to differ substantially from the standard free energy of hydrolysis in solution and (ii) that binding sites for the transported ions must have different affinities when facing opposite sides of the membrane. The results also demonstrate that step-by-step "basic" free energy changes (often used in the form of free energy level diagrams) are inherently unsuited for analysis of the mechanism of free energy transduction.

A tabulation and evaluation of ion exchange data on smectites

An extensive search of the literature was made for ion exchange data on smectites. The data, in the form of ion exchange equilibrium constants and free energies of exchange, have been tabulated and evaluated. Equilibrium constants describing monovalent-monovalent and monovalent-divalent types of exchange for the same reaction on the same type of smectite were found to differ by as much as an order of magnitude. While some of the difference can be attributed to variance in experimental procedures, much of the difference appears due to differences in charge densities and effective field strengths of the smectites, which are in turn related to the amount and type of substitution on intercrystalline octahedral and tetrahedral sites.

Effect of hyaluronic acid on neutrophil adhesion.

The effects of hyaluronate on rabbit neutrophil adhesion were studied using a variety of techniques. Exogenous hyaluronate inhibited neutrophil aggregation under conditions of both turbulent flow and constant shear rate. Hyaluronate also inhibited neutrophil adhesion to glass. Inhibition was dose-dependent above 100 micrograms ml-1 and a minimum molecular weight for hyaluronate of 1 x 10(4) was required. These effects were not simply the result of increased bulk viscosity of the hyaluronate-containing medium, nor did they appear to be mediated by putative cell-surface receptor mechanisms. Instead, physical factors such as hindrance and/or changes in the interfacial free-energy exchange at the cell surface due to the unusual hydrodynamic properties of the hyaluronate molecule were considered to be more important. Since neutrophil migration in vivo occurs through hyaluronate-rich connective tissue matrices, the relevance of these findings for processes such as inflammation and wound healing is clear.

Alkali Cation Selectivity and Fixation by Clay Minerals

AbstractTwo variables must be considered when calculating exchange free energies (ΔG°ex) for 2:1 clays: (1) anionic field strength, as expressed by equivalent anionic radius (ra), and (2) interlayer water content, as expressed by interlayer molality. For smectites that are in a state of high hydration, interlayer molality is determined by the cations undergoing exchange. Thus ΔG°ex for an exchanging cation pair can be calculated solely from measurements of ra. ra is related to layer charge per half unit cell (C) and ab unit cell area (A) by: ra = (-A/8πC)1/2. The layer charge necessary for cation fixation can be predicted by calculating the ra at which cation exchange with an illite structure expresses a AG°ex equal to that of exchange with a smectite structure. The theory can also be applied qualitatively to understand the high selectivity of illite for Cs+, the fixation of K+ rather than Na+ in shales during diagenesis, the stability of illite over muscovite in the weathering environment, and cation segregation in smectite.

Exchange quantum corrections in the one-component plasma

The leading term of the exchange quantum correction to the free energy of a dense one-component plasma is computed in the near-classical limit. Two-body exchange is dominant. The path-integral method is used in its semi-classical limit. The exchange free energy is found to be exponentially small.

Estimation of available potassium for cotton by soil analysis

Measurements of exchangeable K, percentage of exchangeable K of the total exchange capacity (EPP), K extracted in a CaCl2 solution, and the change in free-energy of exchange of K for Ca+Mg (ΔF), were compared as methods for estimation of available K in soil for growing irrigated cotton. A significant correlation was found between each of the methods and the response to K fertilizer. The different methods are discussed; the advantages of extraction with CaCl2 solution are that it reflects the change in free energy and is easy to operate. For sandy soils, it is suggested that determination of exchangeable K be added.

Exchange of alkylammonium ions in the zeolite-L

A study has been made of the ion-exchange equilibria of NH+4, CH3NH+3, C2H5NH+3, n-C3H7NH+3, n-C4H9NH+3, (CH3)2NH+2, (CH3)3NH+, (C2H5)2NH+2 and (C2H5)3NH+ by the zeolite L. None of the alkylammonium ions could effect a complete replacement of the cations initially present in the zeolite. The maximum extent of exchange and the standard free energy of exchange were related to the molecular weight of the entering alkylammonium ions.It is suggested that there was an equilibrium distribution of the exchangeable cations over the different sites (C and D), governed by the nature and affinity of the entering alkylammonium ion and the cation initially present in the zeolite.

Studies on the thermodynamics of exchange in clays—III Nickel exchange on Na-, Ca- and Mg-Montmorillonites

Exchange equilibria involving Ni ions on Na-, Ca- and Mg-montmorillonites were studied with the help of the thermodynamic models of earlier workers. The exchange isotherms and free energy changes were indicative of a lower preference of Ni for the base saturated montmorillonites. The exchange was in accordance with the Hofmeister series. Enthalpy changes indicated a stronger binding of Ni on Ca- and Mg-montmorillonites than on Na-clay. Entropy findings were indicative of a dehydrated and disordered arrangement of Ni ions during their adsorption on Na-montmorillonite. The effect of dehydration on the entropy was the reverse in the case of Ca- and Mg-montmorillonites. The diversity of the exchange equilibria involving Ni, Na, Ca and Mg ions on the montmorillonite surface was further confirmed from our observations on the activity coefficients and the values of Δ G m x , Δ H m x and Δ S m x .

On calculating activity coefficients and other excess functions from the intracrystalline exchange properties of a double-site phase

For a phase at equilibrium in which two cation species are partitioned ideally between two sub-lattice sites, the excess functions of mixing (free energy, enthalpy and entropy) are directly related to the bulk composition of the phase and ΔGE°(T, P), the standard-state intra- crystalline exchange free energy. If the phase is not at equilibrium internally, an additional ordering parameter is necessary to fix the excess free energy of mixing, GmixEX, unambiguously. Conversely, for any fixed GmixEX there exists an infinity of possible intracrystalline cation dis- tributions, only one of which is the equilibrium distribution for the specified temperature and pressure. As ideal intraphase cation ordering becomes more pronounced, GmixEX decreases. In response, the total free energy of mixing for the phase decreases progressively for non-end member compositions, approaching, at the limits of ordering, values appropriate for stabilizing compounds of intermediate composition.The model-dependent activity coefficient for component A in the phase, γAT, can be calculated for any bulk composition, XAT, either from GmixEX directly or from more basic equations involving the interrelation of chemical potentials at equilibrium. A general form for γAT is ln γAT= 1n[2(XAαXAβ)12/(XAα+XAβ)]+Y, where Xjκ denotes the mole fraction of species j in site κ. The first term on the right-hand side of this equation is the contribution to γAT from ideal intracrystalline partitioning, and is common to the several theories lately presented to model intraphase cation partitioning. It can be shown rigorously that this term contributes to a negative deviation from ideality for the bulk phase. The second term is the contribution to the macroscopic activity coefficient from non-ideal intraphase partitioning, and is related to an enthalpy of mixing, HmixN in excess of that resulting from ideal inter-site cation ordering. While the expression represented by Y can take several functional forms, the additional enthalpy can be evaluated explicitly for specific non-ideal partitioning models from the relation HmixN = 2RT(1− XAT) ∝ Y(1 − XAT)2dXAT.In those cases, GmixEX can also be determined exactly.

Two methods for evaluating parameters for the partitioning of cations between coexisting single- and double-site phases

The proposed methods for estimating two free energy partitioning parameters of a one site-two site model have been specifically developed for cases where data are few or inconveniently grouped and utilize pairs of values of the mole fractions of the partitioned species A in the multi-site phase (XAT) and the single site phase (XAm). Where (XAT) exceeds 0.7 the mod may become unstable such that small changes in the distribution curve gradient result in large changes in the evaluated intracrystalline exchange free energy. Such behaviour is exemplified by data from the system olivine-orthopyroxene.

Thermodynamics of Ion Exchange

AbstractThe local formulation of nonequilibrium thermodynamics is used to define the electrochemical potentials in the ion‐clay‐water system, thus enabling development of an improved nonempirical approach to cation‐exchange processes. The presence of the electrical field in the system is expressed by a proportional increase of the pressure in the double layer. The effect of the electrical field on the chemical potentials of the exchangeable cations is divided into the common electrostatic term and a term dependent on their polarizabilities. For systems containing a mixture of monovalent ions it can be assumed that the electrostatic effect of the electrical field is the same for each of the exchangeable cations. Using values of the polarizabilities and intrinsic volumes of the alkali metal cations, the free energies of exchange with sodium in montmorillonite were calculated. The calculated free energies were found to be in good agreement with experimental values.

The partitioning of cations between coexisting single- and multi-site phases with application to the assemblages: orthopyroxene-clinopyroxene and orthopyroxene-olivine

The partitioning of cations between coexisting phases is a function of the number of energetically distinct cation sites available within each phase and the exchange free energies between the intracrystalline sites, as well as an inter-phase exchange energy, temperature and composition. The form of the function describing partitioning between a single-site phase and a phase containing two or more energetically distinct sites can be deduced from the cation exchange free energies between pairs of sites. In some cases the cation exchange free energies between pairs of sites can be deduced explicitly from the form of the partitioning curve. If a phase, φ 2, containing equal numbers of two energetically distinct sites, α and β, with ideal solution of cations A and B on both sites, coexists in equilibrium with an ideal one-site phase, φ 1, the standard state free energy of intercrystalline exchange between φ 1 and φ 2, ΔG T 0, is ▪, where X A 1 is the mol fraction of species A in 1 measured at X A φ 2 = 1 2 . The standard state free energy of intracrystalline exchange between α and β in φ 2, ΔG E 0, is ▪ for ΔG T 0 ≠ 0, where ( ∂X A φ 1 ∂X A φ 2 )′ is the slope of the observed partition function at X A φ 2 = 1 2 . For ΔG T 0 = 0, Δ E 0 = 2 RT arc cosh [2( ∂X A φ 1 ∂X A φ 2 )′ − 1]. If φ 1 is non-ideal, the expressions for ΔG T 0 and Δ E 0 are somewhat more complex. In the double-site phase, an enthalpy of mixing term arises when intracrystalline partitioning is imposed upon ideal mixing on the individual sites. This enthalpy is directly related to the free energy of exchange between the sites by the expression, H mix = (x A β−X A α) 2 ΔG E 0 , where X A α and X A β are the sublattice mol fractions. A single site-double site model is proposed to explain the Fe-Mg partitioning observed at different temperatures in the natural and experimental assemblages orthopyroxene-clino-pyroxene and orthopyroxene-olivine.

Calculation of the Standard Free Energy of Cation Exchange in Clay Systems

AbstractThe paper deals with methods for calculation of the standard free energy of cation exchange on clays, by assuming certain models for the distribution of the cations between the adsorbed phase and the equilibrium solution. From a comparison of the results calculated with the help of a hypothetical discharging/charging process of the exchanger in the respective homoionic forms, with those found from graphical integration of In K(exchange) over the equivalent fraction adsorbed (method of Gaines and Thomas), the free energy change of the “associated‐solvent” appearing in the latter procedure is identified with that of the “salt‐free” solvent present in the system. The calculated values of ΔG0 (exchange) corresponding to the chosen models are given for the purpose of comparison with experimental values that are found in, or could be derived from, the relevant literature.