Enthalpic Components Research Articles

Solvation thermodynamics: An approach from analytic temperature derivatives

A method is presented that uses integral equation theory to determine analytic temperature derivatives of the radial distribution functions. It is illustrated by studying the solvation thermodynamics of monatomic solutes in aqueous solution. The results agree well with the density derivative method developed previously [Yu and Karplus, J. Chem. Phys. 89, 2366 (1988)]. An expression for the solvation enthalpy is derived which allows direct comparison with experimental and isobaric–isothermal (NPT) ensemble simulation data. Satisfactory agreement with experiment is found for pure water and for the aqueous solvation of monovalent ions. Simple equations that exploit the site–site HNC closures are given for the decomposition of the potential of mean force into its enthalpic (or energetic) and entropic components. Since the extended RISM (HNC-RISM) theory yields an incorrect (trivial) value of the dielectric constant, two different ways to correct for the asymptotic behavior of the solute–solute potential of mean force are compared. They lead to similar results but the method in which the solvent dielectric constant is modified from the outset can be applied more generally. The interactions between nonpolar and between polar solutes in water are decomposed into enthalpic and entropic contributions. This is difficult to do by computer simulations because of the lack of precision in such calculations. The association of nonpolar solutes in water is found to have comparable enthalpic and entropic contributions; this result disagrees with the usual description of an entropy-dominated hydrophobic interaction. For ions, the somewhat surprising result is that the association of like-charged species is enthalpy driven while for oppositely charged ions entropic effects are dominant. The process of bringing two like-charged ions together leads to higher local charge density; the more favorable solvation enthalpy arising from this increase in charge density (q2 dependence) more than compensates for the Coulombic repulsion. For oppositely charged ions, association leads to a partial charge neutralization in which the favorable Coulombic attraction is overwhelmed by the loss of stabilizing solvation enthalpy. The entropic increase is due to the greater freedom of the surrounding water molecules resulting from the partial charge neutralization.

Temperature dependence of electrocatalytic behaviour of some glassy transition metal alloys for cathodic hydrogen evolution in water electrolysis

A series of glassy transition metal alloys of various compositions, involving the elements Ni, Mo, V, Fe, Cr, Ti, together with B, have been investigated as electrocatalysts for the cathodic evolution of hydrogen. The polarization behaviour over a range of temperatures has been evaluated and exchange current-densities, Tafel slopes and apparent heats of activation have been determined. The Tafel slope behaviour as a function of temperature has been analysed to give the formal enthalpic ( α H) and entropic ( α S) components of the transfer coefficient or, for certain conditions, the barrier symmetry factor for charge transfer. Potential-relaxation experiments, following interruption of cathodic polarization currents, enable the pseudocapacitance, C φ , for H adsorption to be evaluated as a function of overpotential, η. Integration of the C φ vs η relation for one of the NiMo based alloys suggests that cathodic H 2 evolution takes place through proton discharge on to a surface substantially covered by H, a factor that is related to the tendency for some of these glassy metals to form hydride phases during H 2 generation.

Role of coupling entropy in establishing the nature and magnitude of allosteric response.

The coupling free energy between an allosteric ligand and a substrate, delta Gax, is an explicit measure of the nature as well as the magnitude of impact that an allosteric ligand has on the binding of the substrate ligand to the enzyme, with positive values indicating inhibition and negative values indicating activation. By measuring the variation with temperature of the coupling free energy between the allosteric ligand and the substrate, it is possible to determine the enthalpic and entropic components that give rise to the coupling free energy. We have performed this analysis on two different K-type allosteric systems: the allosteric inhibition of rat liver phosphofructokinase by MgATP, and the allosteric activation of beef heart NAD+-dependent isocitrate dehydrogenase by ADP. In both cases the coupling free energy arises as the net result of opposing enthalpic and entropic components, with the coupling enthalpy (delta Hax) favoring activation and the coupling entropy (delta Sax) favoring inhibition. For phosphofructokinase at 25 degrees C, the absolute value of T delta Sax is greater than the absolute value of delta Hax, and net inhibition of rat liver phosphofructokinase by MgATP is realized. For isocitrate dehydrogenase, delta Hax dominates; however, the net activation is substantially mitigated by the magnitude of T delta Sax. Hence, the coupling entropy plays an important role in establishing both the nature and magnitude of the allosteric response. We hypothesize that the negative coupling entropy arises from the particular constraint placed upon the internal dynamical properties of the enzyme by the simultaneous binding of both allosteric and substrate ligands.

Energetics of an Electrochemical Reaction Derived from the Intersection of Tafel Lines Determined at Different Temperatures

AbstractUnder most conditions in electrode kinetics, the slopes of Tafel relationships for a given electrode process are dependent on temperature. Tafel lines determined at different temperatures therefore intersect at some singular potential, Ecr, for which the Gibbs energy of activation must be zero. The absolute value of the Gibbs energy of activation can then be evaluated by reference to this critical potential. For the oxygen reduction reaction at Pt electrodes in acid solutions, Ecr = 0.36 E vs. RHE. This critical potential yields a value of the Gibbs energy of activation at 0.8 V vs. RHE of 21 kJ mol‐1. A comparison of this energy with the apparent enthalpies of activation Δ≠Hap (= 21 and 24 kJ mol‐1), obtained previously from the Arrhenius plots at the same potential and in the same solution, shows that TΔS≠ is small. The values for the enthalpic component, βH (= 0.44), and entropic component, Tβs (= 0.07 at room temperature), of the overall symmetry factor, β, are determined. They show that, in this case, the kinetics are controlled mainly by the effect of electrode potential on the enthalpic component of the Gibbs energy of activation. It is shown that the electron energy level, ϵ0, of the reacting complex in the ground‐state can be obtained from Ecr. For oxygen reduction at Pt, it is ‐4.72 eV with respect to the electron energy in vacuum.

Comparison of entropic and enthalpic components of the barrier symmetry factor, β, for proton discharge at liquid and solid Hg in relation to the variation of Tafel slopes and β with temperature

In order to provide information from a new direction on the temperature variation of the barrier symmetry factor, β, and the corresponding Tafel slope, b=RT/βF, for the step of proton discharge at the Hg electrode, the kinetics of the cathodic H2 evolution reaction have been studied over a wide temperature range through the melting point of Hg from several proton donors, in a series of suitable non-aqueous solvents that enable low-temperature experiments to be performed. The potential dependence of both the heat and entropy of activation has been determined through the melting point of Hg, enabling the corresponding enthalpic (βH) and entropic (βS) components of β in the relation β=βH+TβS to be evaluated. Substantial differences in βH and βs for solid and liquid Hg surfaces are found including, in some cases, a difference of sign of the βs factor. The temperature-dependence of β, which is associated with the non-conventional variation of b with temperature, now demonstrated for many systems, arises in a complex way which is depnendent on the state and structure of the electrode metal's surface, in relation probably to solvent adsorption and orientation at the interface. The usually assumed value of 0.5 for the barrier symmetry factor is entirely coincidental when this quantity is identified with βH, derived for 298 K. Only when βs= 0, is βH near 0.5, otherwise there is a compensatory variation of βH with Tβs at a given T.

Kinetic and thermodynamic analysis of hydrogen evolution at nickel electrodes

iR-corrected steady-state polarization curves for hydrogen evolution in alkaline solution at crystalline and amorphous nickel electrodes were measured at different temperatures, showing at higher c.d. the establishment of a limiting c.d. due to increasing H ad coverage. The experimental behaviour is in perfect agreement with a complete kinetic model based on the Volmer—Tafel mechanisms. Symmetry factors and rate constants for forward and backward direction of both reactions were determined by a non-linear fitting procedure. Activation energies, enthalpic and entropic components of the symmetry factor, and thermodynamic quantities as equilibrium constant of the Tafel reaction, equilibrium potential of the Volmer reaction, enthalpy and entropy of adsorbed hydrogen atoms could be derived from these data providing new quantitative knowledge of elementary steps of hydrogen evolution at crystalline and amorphous nickel electrodes.

A thermodynamic analysis of monovalent cation permeation through a K +-selective ion channel

Ionic selectivity characteristics of the K + channel from the sarcoplasmic reticulum were studied as a function of temperature in order to decompose the profile of Gibbs free energy along the conduction pore into its enthalpic and entropic components. For Li +, Na +, K +, and Rb +, the enthalpy of binding to the channel is close to zero. Activation enthalpies for transferring ions from bulk aqueous solution to the channel's selectivity region are 20–25 kl/mol for Na +, K +, and Rb + and substantially higher for Li + and Cs +. Transfer of Li + and Na + to the selectivity region involved large favorable entropies. The results argue that the group IA cations shed about half their waters of hydration in permeating the selectivity region of this channel.

Catastrophe situation for potential‐assisted electron transfer in relation to temperature‐dependence of tafel slopes

AbstractThe conventional representation of Tafel slopes, b, for activation‐controlled electrode processes as b = RT/βF with β a constant having the significance of a barrier symmetry factor or Brønsted type coefficient, is rarely followed with respect to the observed dependence of b on T. Rather, b is represented more generally in the form b = RT/(βH + TβS) F where βH and Tβs are formally enthalpic and entropic components of the overall β that determines the effect of changing electrode potentials (V) on the electrochemical Gibbs energy of activation and hence on the rate. — Special attention is directed to a “catastrophe” situation that arises in some experimentally observed behaviour where b is virtually independent of T, i.e. when TβS ≫ βH, so that apparently the normal effect of V on the electron exit energy that determines the potential‐dependence of the activation energy, is obscured. — Discussion of this situation, and presentation of recent new results for proton transfer at Hg, indicates that there are important effects of V “external” to the metal on both the entropy and enthalpy of activation, in addition to the effect of V on the electron Fermi level, relative to vacuum. Compensation effects between variations of the enthalpy and entropy of activation are related to this “external” effect of V.

Entropic and enthalpic components of the symmetry factor for electrochemical proton transfer from various proton donors over a wide temperature range

In order to provide new information on the potential-modulated activation process in the elementary proton- and electron-transfer step of proton discharge in the hydrogen evolution reaction (h.e.r.), the enthalpic (β H ) and entropic ( Tβ S ) components of the overall charge-transfer symmetry factor, β, have been evaluated. These data are obtained from polarization curves for the h.e.r. at Hg from a series of oxonium, ammonium and molecular acid type proton donors in various solvents over a wide range of temperature through the m.p. of Hg. β S and β H define the form of the Tafel slope b as a function of temperature: b = RT/( β H + Tβ S ) F. β S and β H are not related to dielectric polarizability of the solvent but may depend on its proton affinity. However, clear linear relations are demonstrated between β S and the log of the electrochemical Arrhenius factor containing the entropy of activation, and between β H NH + and Δ H ≠. These relations have different slopes for proton discharge from OH + proton donors. Also Δ H ≠ and δ S ≠ are linearly related for the series of proton donors in the way familiar in “compensation effect” plots between Δ H and Δ S quantities in condensed media. β S and β H usually change discontinuously, for a given system, through the m.p. of Hg.

Environmental stress cracking of glassy polymers and solubility parameters

The use of solubility parameters to predict critical stress (σ c * ) or strains (ɛc) for environmental cracking/crazing in several glassy polymers (e.g. PMMA, PPO, PS, PVC, PSF and PC) is re-examined. It is shown that the enthalpic component (χ H ) of the Flory-Huggins semi-interaction parameter (χ) does not always give a good correlation between ɛc and χ H even though solvent molar volume and polymer-solvent molecular interactions have already been considered. Re-analysis of available experimental data using Gent's theory shows that there is a general trend for σ c * (or ɛc) to increase with χ. These results, therefore, support Gent's proposed mechanism of environmental stress crazing/cracking. It is finally concluded that unless a definite relationship can be established between ɛc or σ c * with χ H it is not possible to predicta priori ɛc or σ c * , given the empirical solubility parameters of a solvent. Unfortunately, there are not many such relationships as discovered in this paper.

Experimental evidence for the potential-dependence of entropy of activation in electrochemical reactions in relations to the temperature-dependence of tafel slopes

By means of steady-state polarization and of non-isothermal potential measurements, the kinetics of the H2 evolution reaction at Hg in aqueous HCl, CF3SO3H and the CF3SO−3H3O+ melt, and of the Br2 evolution reaction at vitreous carbon in CH3CN were investigated; it is shown that the true entropy of activation or the corresponding frequency factor for the proton discharge step in cathodic H2 evolution is appreciably potential-dependent, and not constant as has often been assumed. Similar results are found for the Br2 evolution reaction. This situation corresponds to a temperature-dependence of Tafel slopes, b, which is not that conventionally assumed viz, b=±2.3RT/βF. The actual behaviour is rather of the form b=±2.3RT/(βH+βST) where βH and βST are enthalpic and entropic components, respectively, of the overall symmetry factor, β, or transfer coefficient, α. Kinetic experiments on the H2 and Br2 evolution reactions at Hg and C, respectively, enable the βH and βST components of the transfer coefficient to be evaluated. The behaviour observed shows that the effects of potential on electrode reaction rates are to be represented not only by a simple variation of the Fermi level of electrons by “±ΔVF” with a corresponding relative change of transition state energy by (1−β)ΔVF, but in addition by an appreciable variation of the molecular state of the transition complex with change of field across the double-layer. The origin of such effects could be the changing solvational and solvent-structure environment of the reacting particle in the double-layer due to potential-dependent solvent dipole orientation and changing volume fraction of solvated reactant ions in the interphase. Current quantal theories of proton and electron transfer have not taken this important aspect of electrode-kinetic behaviour into account. Analogies to the Bronsted relation for homogeneous proton transfer processes are drawn.

Enthalpies of ligand binding to bovine neurophysins.

Flow microcalorimetry and batch microcalorimetry have been used to survey the energetics of ligand binding by bovine neurophysins I and II. Calorimetry studies were supplemented by van't Hoff analyses of binding constants determined by circular dichroism. Free energies of binding of a series of di- and tripeptides that bind to the strong hormone binding site of neurophysin were partitioned into their enthalpic and entropic components. The results indicate that, at 25 degrees C, the binding of most peptides is an enthalpy-driven reaction associated with negative entropy and heat capacity changes. Studies elsewhere, supported by evidence here, indicate that the principal component of the negative enthalpy change does not arise from the increase in neurophysin dimerization associated with peptide binding. Accordingly, the negative enthalpy change is attributed to direct bonding interactions with peptide and possibly also to peptide-induced changes in tertiary or quaternary organization. Comparison of the binding enthalpies of different peptides indicated two types of bonding interactions that contribute to the negative enthalpy change of peptide ligation. Substitution of an aromatic- or sulfur-containing side chain for an aliphatic side chain in position 1 of bound peptides led to increases in negative enthalpy of from 1 to 6 kcal/mol, demonstrating that interactions typically classified as hydrophobic can have a significant exothermic component at 25 degrees C. Similarly, loss of hydrogen bonding potential in the peptide decreased the enthalpy change upon binding, in keeping with the expected enthalpic contribution of hydrogen bonds. In particular, the data suggested that the peptide backbone between residues 2 and 3 and the phenolic hydroxyl group in position 2 participate in hydrogen bonding.(ABSTRACT TRUNCATED AT 250 WORDS)

Study of the thermodynamics of dilute solutions of polyarylates

The authors have studied the hydrodynamic and thermddynamic characteristics of dilute solutions of the polyarylate P-2 based on terephthalic acid and phenolphthalein and also the polyarylate DP based on diphenyl phthalide dicarboxylic acid and dihydroxydiphenyl in different solvents. It is shown that the results of evaluation of the thermodynamic quality of the solvents from the viscometric data within the confines of the theory of Gaussian semipermeable coils are close to those given by the light scatter method. The contributions of the entropic and enthalpic components to the excess free energy of dilution are defined and their dependence on the temperature and molecular weight of the polymer close to the θ temperatures obtained. The influence of the ratio of fragments of the chain on the thermodynamic function of the polymer-solvent system is investigated.

Comparative thermodynamics of benzodiazepine receptor ligand interactions in rat neuronal membranes.

The effects of temperature on the interaction of various ligands with the benzodiazepine receptor were studied in rat brain membrane preparations. The affinities of all ligands studied were reduced on raising the temperature from 4 to 37 degrees C. The variation of affinity constant with temperature deviated from the classical relationship for both the anticonvulsant ligand [3H]flunitrazepam and the proconvulsant ligand [3H]ethyl beta-carboline-3-carboxylate. This implies a variation of observed enthalpy change of binding with temperature. Possible reasons for this are discussed. Gamma-Aminobutyric acid and sodium chloride both enhance the binding of [3H]flunitrazepam--the former by an increase in the entropic component of the binding energy, and the latter by an increase in the enthalpic component. In a series of ligands of different biological activities, no simple correlation was observed between biological activity and temperature dependence of binding.

Entropic and enthalpic contributions to the solvent dependence of the thermodynamics of transition-metal redox couples: Part II. Couples containing ammine and ethylenediamine ligands

The formal potentials E f for Ru(NH 3) 6 3+/2+, Ru(en) 3 3+/2+, Co(en) 3 3+/2+ and Co(sep) 3+/2+ (where en=ethylenediamine, sep=sepulchrate) were evaluated using cyclic voltammetry as a function of temperature in eight solvents (water, dimethylsulfoxide, N,N-dimethylformamide, N-methylformamide, formamide, propylene carbonate, acetonitrile and nitromethane). Estimates of the transfer free energy of each redox couple from water to the non-aqueous solvents Δ(Δ G rc 0) s−w were made from the solvent dependence of E f at 25°C, and values of the reaction entropy Δ S rc 0 of the redox couples in each solvent were obtained from the temperature dependence of E f using a non-isothermal cell arrangement. The values of Δ(Δ G rc 0) s−w vary over a wide range, from about −4 to 8 kcal mol −1. These variations arise predominantly from the enthalpic component Δ(Δ H rc 0) s−w and correlate broadly with the electron-donating ability of the solvent as given by the donor number, suggesting that solvent-solute donor-acceptor interactions involving amine hydrogens in the oxidized form of the couple provide a major influence upon the redox thermodynamics. However, substantial positive values of Δ(Δ S rc 0) s−w were also observed ( ca. 5–30 cal K −1 mol −1) which failed to correlate with the solvent donor number, instead increasing as the “internal order” of the bulk solvent decreases. These behavioral differences between the enthalpic and entropic contributions to Δ(Δ G rc 0) s−w appear to result from the tendency of the entropic term to reflect the extent of additional solvent orientation induced by the oxidized form of the redox couple, rather than the strength of the solvent-solute interactions involved.

Entropic and enthalpic contributions to the solvent dependence of the thermodynamics of transition-metal redox couples: Part I. Couples containing aromatic ligands

Measurements of the formal potentials E f for Cr(bpy) 3 3+/2+, Fe(bpy) 3 3+/2+, Co(bpy) 3 3+/2+ and Co(phen) 3 3+/2+ (where bpy=2,2′-bipyridine, phen=1,10-phenanthroline) were evaluated as a function of temperature using cyclic voltammetry in eight solvents (water, dimethylsulfoxide, N-N-dimethylformamide, N-methylformamide, formamide, propylene carbonate, acetonitrile and nitromethane) in order to unravel the various structural influences of the solvent upon the redox thermodynamics of such simple redox couples where the oxidized and reduced forms have identical structures and the composition of the coordination shell remains unchanged when the solvent is varied. The reaction entropies Δ S rc 0 for each redox couple in each solvent were evaluated from the temperature dependence of E f using a nonisothermal cell arrangement. Estimates of the free energy of transfer for each redox couple Δ(Δ G rc 0) s−w from water to each non-aqueous solvent were obtained from the difference in E f relative to the corresponding differences for the ferricinium-ferrocene couple. The corresponding enthalpies of transfer Δ(Δ H rc 0) s−w were obtained by combining these values of Δ S rc 0 and Δ(Δ G rc 0) s−w. Substantially larger values of Δ S rc 0 were found for all four redox couples in non-aqueous solvents compared to water, particularly in aprotic media where for a given couple Δ(Δ S rc 0) s−w ∼20–40 cal K −1 mol −1. Markedly larger values of Δ S rc 0 in each solvent were found for the Co(III)/(II) couples compared with the low spin Cr(III)/(II) and Fe(III)/(II) couples. These entropic variations appear to reflect the ease by which solvent molecules are able to be oriented by the additional field around the oxidized compared to the reduced form of the redox couple. Small negative values of Δ(Δ G rc 0) s−w were typically obtained as a result of partial compensation of the entropic terms by the corresponding enthalpic components. The utility of reaction entropy measurements for interpreting the dependence of electron-transfer kinetics upon the nature of the solvent is pointed out.

Thermodynamic Properties of Liquids Including Solutions. XV. Intramolecular Contacts and Their Effects on Excess Enthalpies of Solutions of Chain Molecules, Especially Benzene Solutions of Normal Alkanes and Polymethylenes

The theory of excess enthalpy (HE) and enthalpic component of the interaction parameter (χh), dealt with in previous papers of this series, is extended to allow for the effects of intramolecular contacts in chain molecule solutes. The number of these contacts, as a function of the number of mers in the chain molecules and their concentration in the solution, is estimated from enumerations over a class of self-avoiding walks (paths) in a lattice-graph. Applied to solutions of polymethylenes in benzene, for which the equilibrium constant parameter (K) has been previously estimated to be unity, we find intramolecular contacts to have little effect on the excess enthalpy at 25°C even for long chains. The enthalpic part of the interaction function is predicted to depend strongly on the extent of intramolecular contacting. Extensions of the theory to solutions for which K≠1 are briefly considered.

Coboglobins

Abstract It has been previously found possible to reconstitute apomyoglobin with cobalt protoporphyrin IX to form oxygen-carrying cobaltoproteins which are presumably isomorphous with the natural hemoproteins. We have here observed the influence of an apoprotein upon the reactivity of a prosthetic group by comparing oxygen binding to the dimethyl ester of cobalt protoporphyrin IX with that to the metalloporphyrin incorporated in apomyoglobin. The protein environment causes no major alteration on the electronic structure of cobalt porphyrin or its oxygen adduct, yet produces a large effect on the stabilities of the cobaltoxygen linkage: at 25°, both whale and horse skeletal muscle cobaltomyoglobin have the same free energy changes upon oxygenation (+2.4 Cal per mole), and a binding constant ∼300 times greater than that for the N-methyl imidazole complex of porphyrin in solution. Furthermore, the two cobaltomyoglobins have substantially different enthalpies and entropies of oxygen binding: for horse the values are ΔH = -11.3 Cal per mole, ΔS = -46 e.u.; for whale ΔH = -13.3, ΔS = -53 e.u. A formal thermochemical cycle is used to obtain the contributions from apoprotein-prosthetic group interactions to the enthalpy and entropy of oxygen binding. These in turn are used to partition the binding enhancement (300-fold) for the two proteins into enthalpic and entropic contributions. The enhancement of oxygen binding in horse cobaltomyoglobin is entirely entropic, whereas that in whale cobaltomyoglobin is roughly balanced between enthalpic (20-fold) and entropic (15-fold) components. We have thus, for the first time, directly observed how two proteins of similar structure and function achieve similar modifications in prosthetic group reactivity through a different balance of enthalpic and entropic factors.