The statistical probability of state of a solution containing a reacting receptor M, a ligand A (and eventually proton H) is described by a molar partition function ZM = exp(-ΔG/RT) referred to M, or ZA or ZH, respectively. The partition function for one class of sites can be expressed as the function of site constants kj and cooperativity functions γj,i = exp{bj (i − 1)}. Binding in a single class can be represented by a vector Jp(t) whose elements correspond to single species. For more classes of sites, the joined probability is obtained as tensor product of single class vectors giving rise to complexation matrices Mpqr. There is one partition function for each component of the system. If the complexes are of type HPMQAR there are three partition functions ZH, rmZM and ZA. The relationships between partition functions and total analytical amounts TH, TM, TA, respectively are given. The experimental data obtained in a potentiometric titration with electrode reversible to [H] or other free component can be reproduced as the function of site constants kj and cooperativity functions exp{bj(i -1)} for each class j. The best values of kj and bj, can be calculated following a nonlinear least squares procedure by means of a computer program that is here presented.

In order to obtain experimental evidence for the complexation between β-cyclodextrin and piroxicam (4-hydroxy-2-methyl-N-2-pyridyl-2H-1,2-benzothiazine-3-carboxamide-1,1-dioxide) and to investigate the thermodynamics of this interaction, a flow microcalorimetric study of this system has been undertaken. In fact, the mixing of ,β-cyclodextrin and piroxicam in ratio 1:1 in given experimental conditions gives rise to a system showing better pharmacological properties than piroxicam alone. The results confirm the formation of a complex between β-cyclodextrin and piroxicam and allow the evaluation of the equilibrium constant for the process, assuming the formation of a 1: 1 complex. It results in log K′ = 3.54, where K′ is the apparent formation constant at pH 9.00, in good agreement with literature data for similar compounds. The values of ΔH and ΔS are also reported.

An algorithm is proposed for the estimation of binding parameters for the interaction of biologically important macromolecules with smaller ones from electrometric titration data. The mathematical model is based on the representation of equilibria in terms of probability concepts of statistical molecular thermodynamics. The refinement of equilibrium concentrations of the components and estimation of binding parameters (log site constant and cooperativity factor) is performed using singular value decomposition, a chemometric technique which overcomes the general obstacles due to near singularity. The present software is validated with a number of biochemical systems of varying number of sites and cooperativity factors. The effect of random errors of realistic magnitude in experimental data is studied using the simulated primary data for some typical systems. The safe area within which approximate binding parameters ensure convergence has been reported for the non-self starting optimization algorithms.

The protonation constants log k(app) of a series of disubstituted benzoic acids in aqueous solution at different temperatures between 5 degrees and 55 degrees C have been determined potentiometrically. The data of log k(app) have been analyzed under the light of a statistical thermodynamic model. The curvature of the function log k(app) = f (1/T) is related to the number n(w) of water molecules involved in the protonation and hydration reaction. The upward concavity of the curves of dinitro compounds are steeper that those for monosubstituted acids and imply higher number of water molecules. The curves of polyalkyl-substituted benzoic acids as determined by other authors show opposite (downward concavity) curvatures corresponding to negative numbers n(w) of water molecules. The values of log k(app) at 25 degrees C of disubstituted and polyalkyl-substituted benzoic acids plotted against the Hammett substituent constants sigma(Ham) deviate significantly from the line of the Hammett model. (C) 1998 Elsevier Science B.V. All rights reserved.

We report a thermodynamic study of the aqueous solutions of 1-(3,3,4,4,5,5,6,6,6-nonafluorohexyl) pyridinium chloride, bromide, and iodide andN-octyl pyridinium iodide. Dilution enthalpies and osmotic coefficients of the aqueous solutions of these cationic surfactants have been measured at 313 K as a function of the concentration. The experimental data are expressed in terms of apparent and partial molar quantities. The changes in thermodynamic properties upon micellization have been obtained from the experimental data by using a pseudo phase transition approach. The cmc at 313 K have been evaluated from the plot of the milliosmolality, the measured quantity, vs molality. From the comparison with the trends of the enthalpies at 298 K of the same set of compounds, the effect of temperature on the energetics of their solutions can be derived. The trends of thermodynamic properties vs molality and the micellization parameters confirm that the effect of the counterions, however strong and inversely proportional to the radius of the hydrated counterion, seems to be reduced with respect to the hydrogenated analogs. The curves of the apparent and partial molar enthalpies vsmfor the bromide and the iodide are lowered, with respect to the curve of the chloride, by an amount comparable to that at 298 K. This observation suggests that the changes in the absolute trends of the curves and in the micellization enthalpies are due to the modification of the more mobile hydrophobic hydration shell of the perfluoroalkyl chain, whereas the hydration sphere of the counterions is practically unaffected. The heat capacity data and the comparison with the behaviour of hydrogenated analogs is in agreement with the above observation. The trends of the free energies confirm that the degree of counterion binding, β, and the aggregation number,n, increase with the increasing of the radius of the hydrated counterion.

The isobaric heat capacity of liquid H2O, Cp, as a function of temperature, decreases between 0° and about 35°C and then increases up to 100°C. Analogous behaviour is shown by liquid D2O. A statistical thermodynamic model has been applied to the experimental heat capacity data. The behaviour is explained by assuming that an equilibrium A + B = AB is established between clusters A and AB of water of different composition. The total heat capacity is considered as the sum of three terms Cp = (1 − α)Cp,0,AB + αCp,0,A + ΔCp,app. The term ΔCp,app depends explicitly on the reaction enthalpy. In H2O, the enthalpy ΔH = − 18.4 kJ mol−1 for the dissociation reaction and the heat capacity Cp,B = 47.8 J K−1 mol−1 for free water molecules are calculated. Analogous calculations performed for D2O yield the enthalpy, ΔH = − 1.64 kJ mol−1 and the heat capacity, Cp,B = 49.18 J K−1 mol−1.

We report a thermodynamic study of the aqueous solutions of 1-(3,3,4,4,5,5,6,6,6-nonafluorohexyl) pyridinium chloride, bromide, and iodide andN-octyl pyridinium iodide. Dilution enthalpies and osmotic coefficients of the aqueous solutions of these cationic surfactants have been measured at 313 K as a function of the concentration. The experimental data are expressed in terms of apparent and partial molar quantities. The changes in thermodynamic properties upon micellization have been obtained from the experimental data by using a pseudo phase transition approach. The cmc at 313 K have been evaluated from the plot of the milliosmolality, the measured quantity, vs molality. From the comparison with the trends of the enthalpies at 298 K of the same set of compounds, the effect of temperature on the energetics of their solutions can be derived. The trends of thermodynamic properties vs molality and the micellization parameters confirm that the effect of the counterions, however strong and inversely proportional to the radius of the hydrated counterion, seems to be reduced with respect to the hydrogenated analogs. The curves of the apparent and partial molar enthalpies vsmfor the bromide and the iodide are lowered, with respect to the curve of the chloride, by an amount comparable to that at 298 K. This observation suggests that the changes in the absolute trends of the curves and in the micellization enthalpies are due to the modification of the more mobile hydrophobic hydration shell of the perfluoroalkyl chain, whereas the hydration sphere of the counterions is practically unaffected. The heat capacity data and the comparison with the behaviour of hydrogenated analogs is in agreement with the above observation. The trends of the free energies confirm that the degree of counterion binding, β, and the aggregation number,n, increase with the increasing of the radius of the hydrated counterion.

Thermodynamic properties of aqueous solution of bisquaternary ammonium salts, which are derivatives of N,N-bisdimethyl-1,2-ethanediamine (bis-Cn-BEC), of general formula/CnH2n+1OOCCH2(CH3)2N$^{\oplus}CH2CH2N$^{\oplus}(CH3)2CH2COOCn-H2n+1/2Cl-(bis-Cn-BEC, where the subscript n stands for the number of carbon atoms of the alkyl chain bound to the carboxyl group) are here reported and compared with those of the corresponding monomers. Dilution enthalpies have been measured by means of a flow type microcalorimeter at 313 K, and densities have been measured by means of a vibrating tube densimeter at 298 K. Apparent and partial molar quantities have been obtained from the experimental data and expressed as a function of molalities, assuming the infinite dilution as standard state. The changes in enthalpy and in volume upon micellization have been evaluated by assuming the pseudo-phase transition model. From the calculated enthalpy changes at 313 K and that previously reported at 298 K, the changes in heat capacity for micellization has been evaluated. The data suggest the hypothesis that the alkyl chain in the dimers are already partially associated in solution. Moreover, the trends of the cmc as a function of the chain length for monomers and dimers suggest that the association of the chains probably leaves out the first three methylene groups of the alkyl chains bound to the carboxylic groups. The packing parameter, P, gives 0.37 for bis-C10-BEC, and the formation of rod-like micelles is therefore suggested.

The thermodynamic statistical model based on the distribution of molecular populations among energy levels has been employed for the analysis of the solubility of hydrocarbons and other inert gases or liquids in water at different temperatures. The statistical distribution is described by a convoluted partition function ZG·ζs. The product of a grand canonical partition function ZG represents the distribution of the species in the reaction while the canonical partition function ZG represents the properties of the solvent. The first derivative of the logarithm of the partition function with respect to 1/T is the apparent enthalpy which is the result of the contributions of the separate partition functions, {ΔHaap}T=ΔHo+nwCp,wT, where {ΔHapp}T refers to ZG, nwCp,wT=−ΔHw to ζs, and ΔHo is the change in enthalpy of hydrocarbon-water reaction. The plot {ΔHapp}T vs/ T results in a straight line with slope nw at constant Cp,w. The apparent enthalpy is obtained from the coefficients of the polynomial fitting of the solubility data, as a function of 1/T. Alternatively, the apparent enthalpy can be determined calorimetrically. The enthalpy thus obtained is a linear function of the Kelvin temperature. The values of nw range from 1.6, 1.9, 5.6 to 5.8 for helium, hydorgen, butane and hexane, respectively. For fluorocompounds the range of nw is 10.1 to 11.1 indicating that nw is a function of the number of water molecules expelled from the cage of solvent to form a cavity to host the solute molecule. The analysis of several sets of calorimetric or solubility data with the present molecular thermodynamic model yields values of ΔHo and nw consistent with the size of the dissolved molecules.