Thermodynamic and NMR study of aggregation of dodecyltrimethylammonium chloride in aqueous sodium salicylate solution

The complex aggregation processes of dodecyltrimethylammonium chloride (DTAC) have been studied in dilute solutions of sodium salicylate (NaSal) by isothermal titration calorimetry and electrical conductivity at temperatures between 278.15 K and 318.15 K. A structural transformation that was dependent on the concentrations of DTAC and NaSal was observed. The micellization process in dilute solutions of DTAC has been subjected to a detailed thermodynamic analysis and shown to occur at considerably lower critical micelle concentrations than reported for DTAC in water and NaCl solutions. Gibbs free energy, Δ _mic G ^o, and entropy, Δ _mic S ^o, were deduced by taking into account the degree of micelle ionization, β, estimated from conductivity measurements. From the temperature dependence of the enthalpy of micellization, Δ _mic H ^o, the heat capacities of micellization, D_mic c_p^o {\Delta_{{{\rm mic} }}}c_p^o were determined and discussed in terms of the removal of large areas of non-polar surface from contact with water upon micellization. The process is exothermic at all temperatures, indicating, in addition to the hydrophobic effect, the presence of strong interactions between surfactant and salicylate ions. These were confirmed by ¹H NMR spectroscopy and diffusion NMR experiments. Salicylate ions not only interact with the headgroups but also insert further into the micelle core. At c _NaSal/c _DTAC > 2.5, the structural rearrangements occur even at relatively low concentrations of NaSal.     

A temperature study on critical micellization concentration (CMC), solubility, and degree of counterion binding of α-sulfonatomyristic acid methyl ester in water by electroconductivity measurements

 For a sodium salt of α-sulfonatomyristic acid methyl ester (14SFNa), one of the α-SFMe series surfactants, critical micellization concentration (CMC), solubility and degree of counterion binding (β) were determined by means of electrocon-ductivity measurements at different temperatures (at every 5 °C) ranging from 15 to 50 °C. The phase diagram of 14SFNa in pure water was constructed from the CMC- and solubility-temperature data, in which the Krafft temperature (critical solution temperature) was found around 0 °C. The changes in the Gibbs energy, ΔG ⁰ _m, enthalpy, ΔH ⁰ _m, and entropy, ΔS ⁰ _m, upon micelle formation as a function of temperature were evaluated taking βvalues into calculation. Received: 28 August 1996 Accepted: 5 November 1996     

Conductometric studies of hexadecyltrimethylammonium bromide in aqueous solutions of ethanol and ethylene glycol

The effect of cosolvent on micellization of hexadecyltrimethyl ammonium bromide (CTAB) in aqueous solutions was studied. The conductivity of a mixture (cosolvent + water) as function of CTAB concentration was measured at different temperatures. Ethylene glycol and ethanol were used as a cosolvent. The conductivity data were used to determine the critical micelle concentration (CMC) and the effective degree of counterion dissociation of micelle in the temperature range 303.2 to 313.2 K. In all the cases studied, a linear relationship between log([CMC]_mix/mol dm⁻³) and the mass fraction of cosolvent in solvent mixture has been observed. The free energy (ΔG _mic ⁰ ), enthalpy (ΔH _mic ⁰ ), and entropy (ΔS _mic ⁰ ) of micellization were determined using the temperature dependence of CMC. The dependence of these thermodynamic parameters on solvent composition was determined. The standard free energy of micellization was found to be negative in all cases and becomes less negative as the cosolvent content increases. The enthalpy and entropy of micellization are independent of temperature in pure water, while ΔH _mic ⁰ and ΔS _mic ⁰ decrease dramatically with temperature in mixed cosolvents. Furthermore, the entropic contribution is larger than the enthalpic one in pure water, while in the mixed solvents, the enthalpic contribution predominates. The text was submitted by the authors in English.     

Micellization of dodecylpyridinium chloride in water-ethanol solutions

Micellar properties of dodecylpyridinium chloride (DPC) were investigated by means of electrical conductometry with emphasis on the influences of cosolvent-water content and temperature. Ethanol was used as a cosolvent. Conductivity measurements gave information about critical micelle concentration and micellar ionization degree of the water-ethanol micellar solutions at different temperatures. In all solvent mixtures, it was observed that the critical micelle concentration of DPC and the degree of the counterion dissociation increase with an increasing concentration of ethanol and increasing temperature. Micellar and thermodynamics data were obtained from the temperature dependence of critical micelle concentrations in various aqueous mixtures of ethanol. In order to explain the effect of the cosolvent, the differences in the Gibbs energies of micellization of DPC between water and binary cosolvent were determined. The standard free energy (ΔG°_mic) of micellization was found to be negative as the concentration of the solvent increases, but it is roughly independent of temperature. Although the enthalpic contribution was found to be larger than the entropic one, in particular at lower temperatures, an entropy-enthalpy compensation effect was observed for all systems. Also, enthalpy (ΔH°_mic) and entropy (ΔS°_mic) of micellization are strongly temperature dependent and decrease with increasing temperature and cosolvent content. The text was submitted by the authors in English.     

Studies on Hydrophobic Effect and Micelle Formation of Some Surfactant-Cr(III)-Cetylamine Complexes in Non-aqueous Solvents

Surface active micelle formable surfactant-Cr(III) complexes of the type cis-α-[Cr(trien)(C₁₆H₃₃NH₂)X]²⁺ (where trien = triethylenetetramine; X = F⁻, Cl⁻, Br⁻) have been studied in n-alcohol and in formamide at different temperatures by conductance measurements. Standard Gibbs energy changes (ΔG ^o _mic), enthalpies (ΔH ^o _mic) and entropies (ΔS ^o _mic) of micelle formation have been determined by studying the variation of the Critical Micelle Concentration (CMC) with temperature. Critical micelle concentrations have also been measured as a function of percentage concentration of alcohol added. It is suggested that alcohol addition leads to an increase in formamide penetration into the micellar interface that depends on the alcohol chain length. The results are discussed in terms of an increased hydrophobic effect, dielectric constant of the medium, the chain length of the alcohols and the surfactant in the solvent mixture.     

Studies on temperature dependent kinetics of <Emphasis Type="Italic">Aspergillus awamori</Emphasis> feruloyl esterase in water solutions

The initial reaction rate (V ₀) for the esterification reaction of feruloyl esterase (FAE-II) at different temperatures (288, 298, 308, 318, 328, 338, 348, and 358 K) and various ethyl ferulate concentrations [(2, 4, 6, 8, 10, 12, 14, and 16) × 10⁻⁴ mol l⁻¹ of ethyl ferulate in water] were determined. The Lineweaver-Burk double reciprocal plot yielded the kinetic parameters (maximal velocity V _max, Michaelis constant K _m, and second order rate constant V/K). The effects of temperature on those 3 kinetic parameters were presented and discussed. The thermodynamic parameters ΔH* (enthalpy of activation), ΔG* (free energy of activation), ΔS* (entropy of activation), ΔG _E-S (free energy change of substrate binding), ΔG _E-T (free energy change of transition state formation), related to that biochemical process were determined and discussed from van’t Hoff plot, Arrhenius plot, and Eyring plot.     

Studies on Thermodynamics of Micellization and Solvophobic Interactions of Novel Surfactant–Cr(III) Complexes in Non-aqueous Solvents

The critical micelle concentration (CMC) of surfactant–Cr(III)–dodecylamine complexes of the type cis-α-[Cr(trien)(C₁₂H₂₅NH₂)X]²⁺ (where trien = triethylenetetramine; X = F⁻, Cl⁻, Br⁻) has been studied in n-alcohol and in formamide at different temperatures, by electrical conductivity measurements. From the CMC values as a function of temperature, various thermodynamic properties have been evaluated: standard Gibbs energy changes (Δ_mic G ⁰), standard enthalpy changes (Δ_mic H ⁰) and standard entropy changes (Δ_mic S ⁰) for micellization. Critical micelle concentrations have also been measured as a function of the percentage composition of alcohol added. The solvent composition dependences of these thermodynamic parameters were determined. It is suggested that alcohol addition leads to an increase in formamide penetration into the micellar interface that depends on the alcohol’s chain length. The results are discussed in terms of an increased hydrophobic effect, dielectric constant of the medium, the chain length of the alcohols, and the surfactant in the solvent mixture.     

Effect of pressure on the adsorption and micelle formation of aqueous dodecyltrimethylammonium chloride solution-hexane system

The interfacial tension of aqueous dodecyltrimethylammonium chloride (DTAC) solution/hexane interface has been measured as a function of pressure at concentrations around the critical micelle concentration (CMC). The derivative of the interfacial tension with respect to pressure has been observed to change abruptly at the CMC as in the case of aqueous dodecylammonium chloride (DAC) solution-hexane system studied already. The volume changes associated with the adsorption of DTAC from its monomeric and micellar states have been calculated. The results have indicated that the micelle formation of surfactant is treated like the appearance of a new macroscopic phase in the system. It has also been concluded that the micelle solubilizing hexane bears resemblance to the adsorbed film in terms of the volume. The difference in the pressure dependence of the volume of micelle formation ^MW between DTAC and DAC has been attributed to a larger polar group of DTAC. The fact that the value of ^MW is larger than that estimated from the conductivity data has been explained by the solubilization of hexane into the micelle.     

Volumetric behavior and micelle formation of aqueous surfactant mixtures

A thermodynamic treatment of the volumetric behavior of surfactant mixtures in water have been developed on the basis of the thermodynamic treatment of mixed micelle by Motomura et al. Densities of aqueous solutions of mixtures of decyltrimethylammonium bromide (DeTAB) and dodecyltrimethylammonium bromide (DTAB) have been measured as a function of total molality at constant compositions. The apparent molar volumes of the mixtures have been derived from the density data and the mean partial molar volume of monomeric surfactant mixture V _t ^w , the molar volume of mixed micelle V^M/N _t ^M , the voluem of formation of mixed micelle _W ^M V, and the composition of surfactant in the mixed micelle have been evaluated. The V _t ^W , V^M/N _t ^M , and _W ^M V have been observed to depend on the composition. The linear dependence of V _t ^W and V^M/N _t ^M on the composition indicates that the mixing of DeTAB and DTAB is ideal both in the monomeric and micellar states. This has been confirmed further by the shape of the critical micelle concentration vs. composition curves.     

Thermochemistry of europium and dithiocarbamate complex Eu(C5H8NS2)3(C12H8N2)

A solid complex Eu(C₅H₈NS₂)₃(C₁₂H₈N₂) has been obtained from reaction of hydrous europium chloride with ammonium pyrrolidinedithiocarbamate (APDC) and 1,10-phenanthroline (o-phen⋅H₂O) in absolute ethanol. IR spectrum of the complex indicated that Eu³⁺ in the complex coordinated with sulfur atoms from the APDC and nitrogen atoms from the o-phen. TG-DTG investigation provided the evidence that the title complex was decomposed into EuS. The enthalpy change of the reaction of formation of the complex in ethanol, Δ_r H _m ^θ(l), as –22.214±0.081 kJ mol^–1, and the molar heat capacity of the complex, c _m, as 61.676±0.651 J mol^–1 K^–1, at 298.15 K were determined by an RD-496 III type microcalorimeter. The enthalpy change of the reaction of formation of the complex in solid, Δ_r H _m ^θ(s), was calculated as 54.527±0.314 kJ mol^–1 through a thermochemistry cycle. Based on the thermodynamics and kinetics on the reaction of formation of the complex in ethanol at different temperatures, fundamental parameters, including the activation enthalpy (ΔH _≠ ^θ), the activation entropy (ΔS _≠ ^θ), the activation free energy (ΔG _≠ ^θ), the apparent reaction rate constant (k), the apparent activation energy (E), the pre-exponential constant (A) and the reaction order (n), were obtained. The constant-volume combustion energy of the complex, Δ_c U, was determined as –16937.88±9.79 kJ mol^–1 by an RBC-II type rotating-bomb calorimeter at 298.15 K. Its standard enthalpy of combustion, Δ_c H _m ^θ, and standard enthalpy of formation, Δ_f H _m ^θ, were calculated to be –16953.37±9.79 and –1708.23±10.69 kJ mol^–1, respectively.     

Thermodynamic properties of molybdenum-transition metal-hydrogen (nitrogen) solid solutions

Using the experimental values ΔH _H^exc and ΔS _H^exc (ΔH _N^exc and ΔS _N^exc) for solid solutions of hydrogen and nitrogen in molybdenum, we calculate the parameters ɛ_H^Mand ɛ_N^M of interaction between hydrogen (nitrogen) and molybdenum lattice doped with small additives of transition metals M; the values of the activity coefficients on hydrogen and nitrogen γ_H^M and γ_N^M, ΔH _H, ΔH _N, ΔS _H, ΔS _N; enthalpy (η_H^M and η_N^M) and entropy (σ_H^M and σ_N^M) parameters of interaction over the 1100–1300 K range for alloys of Mo_{1 − y} M _y H _x and Mo_{1 − y} M _y N _x types (y = 0.01 and 0.02; x = 0.01 and 0.02).     

The kinetics study of the reduction of Fast Green dye with cetylpyridinum chloride as cationic surfactant

The kinetics of the reaction of Fast Green dye (FG) with cetylpyridinum chloride was studied in alkaline medium by UV-Visible spectrophotometer. Reduction of Fast Green dye was carried out by varying the fast green dye concentration, cetylpyridinum chloride concentration and concentration of sodium hydroxide. In the present study the reduction of dye was carried out in order to reduce the color content. The interaction of dye was carried out with reducing analyte (cetylpyridinum chloride). The rate of the reaction was determined by varying the above parameters at different temperatures. It was observed that the reduction followed pseudo first-order kinetics with respect to dye, surfactant, OH⁻ ion concentration according to the following reaction pathway. The mechanism for the photo bleaching of the dye has been proposed and well confirmed by the data simulation procedure. The activation parameters of the reaction like entropy of activation (ΔS) and free energy of activation (ΔG) showed the extremely solvated states of transient complex which was less disorderly arranged than the oxidized form of dye, whereas E _a values reflects a high amount of energy required for the reduction of dye with cetylpyridinum chloride.     

Charge-transfer interactions between nucleophilic compounds and chromatographic packings containing chemically bonded Cu(II) complexes

Summary Results are presented of studies of packings containing copper (II) acetylacetonate (acac), hexafluoroacetylacetonate (hfac), and chloride, chemically bonded via β-dik-etonate groups. The retention parameters retention factor (k) specific retention volume (V _g), and molecular retention index (M _e) were measured and used to calculate the thermodynamic parameters free energy of adsorption (ΔG _a) heat of adsorption (−ΔH _a), and entropy of adsorption (ΔS _a). These parameters enable, characterization of specific interactions between aromatic and cyclic hydrocarbons, ethers and thioethers and metal complexes chemically bonded, to a silica surface.     

Study of catalase immobilized on a silicate matrix for non-aqueous biocatalysis

Catalytic activity of catalase (CAT) immobilized on a modified silicate matrix to mediate decomposition of meta-chloroperoxibenzoic acid (3-CPBA) in acetonitrile has been investigated by means of quantitative UV-spectrophotometry. Under the selected experimental conditions, the kinetic parameters: the apparent Michaelis constat (K _M ), the apparent maximum rate of enzymatic reaction (V _max ^app ), the first order specific rate constants (k _sp ), the energy of activation (E _a ) and the pre-exponential factor of the Arrhenius equation (Z₀) were calculated. Conclusions regarding the rate-limiting step of the overall catalytic process were drawn from the calculated values of the Gibbs energy of activation ΔG^*, the enthalpy of activation ΔH^*, and the entropy of activation ΔS^*.     

Thermochemistry of the ternary solid complex Gd(C5H8NS2)3(C12H8N2)

The novel ternary solid complex Gd(C₅H₈NS₂)₃(C₁₂H₈N₂) has been obtained from the reaction of hydrous gadolinium chloride, ammonium pyrrolidinedithiocarbamate (APDC), and 1,10-phenanthroline (o-phen · H₂O) in absolute ethanol. The complex was described by an elemental analysis, TG-DTG, and an IR spectrum. The enthalpy change of the complex formation reaction from a solution of the reagents, Δ_r H _m ^ϑ (sol), and the molar heat capacity of the complex, c _m , were determined as being − 15.174 ± 0.053 kJ/mol and 72.377 ± 0.636 J/(mol K) at 298.15 K by using an RD496-III heat conduction microcalorimeter. The enthalpy change of a complex formation from the reaction of the reagents in a solid phase, Δ_r H _m ^ϑ (s), was calculated as being 52.703 ± 0.304 kJ/mol on the basis of an appropriate thermochemical cycle and other auxiliary thermodynamic data. The thermodynamics of the formation reaction of the complex was investigated by the reaction in solution. Fundamental parameters, the activation enthalpy (ΔH _≠ ^ϑ ), the activation entropy (ΔS _≠ ^ϑ ), the activation free energy (ΔG _≠ ^ϑ ), the apparent reaction rate constant (k), the apparent activation energy (E), the preexponential constant (A), and the reaction order (n), were obtained by the combination of the thermochemical data of the reaction and kinetic equations, with the data of thermokinetic experiments. The constant-volume combustion energy of the complex, Δ_c U, was determined as being −17588.79 ± 8.62 kJ/mol by an RBC-II type rotatingbomb calorimeter at 298.15 K. Its standard enthalpy of combustion, Δ_c H _m ^ϑ , and standard enthalpy of formation, Δ_f H _m ^ϑ , were calculated to be −17604.28 ± 8.62 and −282.43 ± 9.58 kJ/mol, respectively. The text was submitted by the authors in English.     

Interfacial and aggregation properties of some anionic/cationic surfactant binary systems II. Mixed micelle formation and surface tension reduction effectiveness

Mixed micelle formation and surface tension reduction effectiveness (γ_cmc) were investigated for the following systems: triethanolammonium dodecylpoly(oxyethylene)sulfate (TADPS, containing about two ethylene oxide units)/dodecyltrimethylammonium bromide, TADPS/hexadecyltrimethylammonium bromide and TADPS/hexadecylpyridinium chloride. For all these anionic/cationic systems, the mixed critical micelle concentration (cmc) values reflect a strong synergism in mixed micelle formation, with β^M values ranging from −13.8 to −18.3. The mixed micelle composition is mixing-ratio dependent and, for equimolar mixtures, the mixed micelle is richer in the surfactant with the lower cmc. Precipitation is inhibited to a certain extent, thanks to the presence of ethylene oxide groups in the anionic species. The conditions for synergism in γ_cmc, differently expressed in the literature, can be derived from the surface tension equations established in our previous article. They can be conveniently described by a few characteristic constants: Γ _i ^∞ (saturated Gibbs excess), K _i (constant in the Szyszkowski equation), the cmc of the individual surfactants and the interaction parameters, β^S and β^M, of their mixtures. Excellent agreement between theoretically predicted and experimental results is obtained. With the increase in surfactant chain length, the β^M values decrease faster than the β^S ones and this can result in the loss of synergism in γ_cmc. Received: 11 June 2000 Accepted: 4 September 2000     

The Potential Energies of Cohesion of a Crystalline Organic Enantiomer and the Racemate; on the Energy for the Liquid Racemate [1]

Summary. The cohesion potential energy of the crystal of one enantiomer of ethyl 3-cyano-3-(3,4-dimethyloxyphenyl)-2,2,4-trimethylpentanoate, −47.7 ± 0.1 kJ mol⁻¹ (0–90°C), was found out from the heat of sublimation (123.2 ± 5.1 kJ mol⁻¹, 78.6°C) and the kinetic energies for the gas phase and the crystal. It was found that the entropy function of Debye’s theory of solids mathematically agreed with the vibrational entropy of the gas (variationally obtained), allowing to disclose the vibrational energy using the Debye energy function (E _vib 835.0 kJ mol⁻¹ (78.6°C), E ⁰ included). E _kin for the crystal (771.1 kJ mol⁻¹ (78.6°C)) was obtained by Debye’s theory with the experimental heat capacity. The cohesion energy represented a moderate part of the sublimation energy. The cohesion energy of the racemic crystal, −44.2 kJ mol⁻¹, was obtained by the heat of formation of the crystal in the solid state (3.0 kJ mol⁻¹, 83.3°C) and E _kin for the crystal (by Debye’s theory). The decrease in cohesion on formation of the crystal accounted for the energy of formation. The change in potential energy on liquefaction of the racemate from the gas state was disclosed obtaining added-up E _{vib + rot} for the liquid in the way as to E _vib for the gas, the Debye entropy function being increasedly suited for the liquid (E _{vib + rot} 763.4 kJ mol⁻¹ (115.4°C)). Positive ΔE _pot, 13.0 kJ mol⁻¹, arised from the increase in electronic energy (Δ _l ν_mean − 154.3 cm⁻¹, by the dielectric nature of the liquid), added to the cohesion energy.     

Study of an Alcohol’s Influence on the CMC and Thermodynamic Functions of Anionic Surfactants in DMA/Long-chain Alcohol Solutions Using a Microcalorimetric Method

The power-time curves for the micelle formation process were determined for two anionic surfactants, sodium laurate (SLA) and sodium dodecyl sulfate (SDS), in mixed alcohol + N,N-dimethylacetamide (DMA) solvent using titration microcalorimetry. From the data of the lowest point and the area of the power-time curves, their critical micelle concentration (CMC) and ΔH _m^o were obtained. The other thermodynamic functions of the micellization process (ΔG _m^o and ΔS _m^o) were also calculated with thermodynamic equations. For both surfactants, the effects of the carbon number (chain length) of the alcohol, the concentration of alcohol, and the temperature on the CMC and thermodynamic functions are discussed. For systems containing identical concentrations of a different alcohol, values of the CMC, ΔH _m^o and ΔS _m^o increased whereas ΔG _m^o decreased with increasing temperature. For systems containing an identical alcohol concentration at the same temperature, values of the CMC, ΔH _m^o,ΔG _m^o and ΔS _m^o decrease with increasing carbon number of alcohol. For systems containing the same alcohol at the same temperature, the CMC and ΔG _m^o values increase whereas ΔH _m^o and ΔS _m^o decrease with increasing alcohol concentration.     

The Potential Energies of Cohesion of a Crystalline Organic Enantiomer and the Racemate; on the Energy for the Liquid Racemate [1]

The cohesion potential energy of the crystal of one enantiomer of ethyl 3-cyano-3-(3,4-dimethyloxyphenyl)-2,2,4-trimethylpentanoate, −47.7 ± 0.1 kJ mol⁻¹ (0–90°C), was found out from the heat of sublimation (123.2 ± 5.1 kJ mol⁻¹, 78.6°C) and the kinetic energies for the gas phase and the crystal. It was found that the entropy function of Debye’s theory of solids mathematically agreed with the vibrational entropy of the gas (variationally obtained), allowing to disclose the vibrational energy using the Debye energy function (E _vib 835.0 kJ mol⁻¹ (78.6°C), E ⁰ included). E _kin for the crystal (771.1 kJ mol⁻¹ (78.6°C)) was obtained by Debye’s theory with the experimental heat capacity. The cohesion energy represented a moderate part of the sublimation energy. The cohesion energy of the racemic crystal, −44.2 kJ mol⁻¹, was obtained by the heat of formation of the crystal in the solid state (3.0 kJ mol⁻¹, 83.3°C) and E _kin for the crystal (by Debye’s theory). The decrease in cohesion on formation of the crystal accounted for the energy of formation. The change in potential energy on liquefaction of the racemate from the gas state was disclosed obtaining added-up E _{vib + rot} for the liquid in the way as to E _vib for the gas, the Debye entropy function being increasedly suited for the liquid (E _{vib + rot} 763.4 kJ mol⁻¹ (115.4°C)). Positive ΔE _pot, 13.0 kJ mol⁻¹, arised from the increase in electronic energy (Δ _l ν_mean − 154.3 cm⁻¹, by the dielectric nature of the liquid), added to the cohesion energy.     

Film formation stages for poly(vinyl acetate) latex particles: a photon transmission study

Photon transmission technique was used to monitor the evolution of transparency during film formation from poly(vinyl acetate) (PVAc) latex particles. The latex films were prepared below the glass transition temperature (T _g) of PVAc. These films were annealed at elevated temperatures in various time intervals above the T _g of PVAc. It is observed that transmitted photon intensity (I _tr) from these films increased as the annealing temperature is increased. It is seen from I _tr curves that there are two film formation stages. These successive stages are named void closure (viscous flow) and interdiffusion. The activation energies for viscous flow (ΔH) and backbone motion (ΔE _b) were obtained by using well-defined models. The averaged values of the backbone (ΔE _b) and the viscous flow activation energies (ΔH) were found to be 188.6 and 5.6 kcal/mol, respectively. The minimum film formation (τ _M,T _M) and healing points (τ _H,T _H) were determined. Minimum film formation (ΔE _M) and healing activation energies (ΔE _H) were measured using these time–temperature pairs. ΔE _M and ΔE _H were found to be 32.5 and 28.3 kcal/mol, respectively.