RESUMO
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.
RESUMO
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 and N-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 vs m for 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, beta, and the aggregation number, n, increase with the increasing of the radius of the hydrated counterion.
RESUMO
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.
