Determination of thermodynamic parameters

In the standard ITC apparatus, the protein-ligand interaction proceeds in a sample cell of relatively small volume (usually 1-3 mL). One component (e.g., protein) of the reaction is placed in the reaction cell, and the other component (e.g., ligand) is added in stepwise fashion by an automated injection system in preset measured amounts for preset measured times. A built-in stirrer ensures that the reaction is continuously and well mixed. The reaction cell is composed of material 

If the protein-ligand interaction is endothermic, more power (peal s ) is required relative to the reference cell. The power that is required, over baseline, comprises the raw data output of the ITC equipment. If the reaction is exothermic, less power is required, which is recorded as a downward deflection in output (Fig. 3.2). The overall interaction between a protein (enzyme or receptor) and a ligand (substrate, inhibitor, neurotransmitter, hormone, or drug) is carried out in a sequence of automated titrations. At each injection step, the power is recorded as a function of time. Each subsequent injection in the series is made after the power function returns to baseline. The output, therefore, forms an S-shaped curve, mirroring the progression of binding of the interacting species from initial 

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SG Penn, ET Bergstrom, DM Goodall, JS Loran. Capillary electrophoresis with chiral selectors. Optimization of separation and determination of thermodynamic parameters for binding of ticonazole enantiomers to cyclodextrins. Anal Chem 66 2866-2873, 1994. 

A prerequisite for kinetic studies is a reliable knowledge of the thermodynamics of the system. The reaction always takes the system closer to equilibrium, the rate is zero at equilibrium and has opposite signs on each side of the equilibrium composition. The rate thus depends on the thermodynamics. However, kinetic measurements are not suitable for determination of thermodynamic parameters. Before we can begin studies of the kinetics, we must know the thermodynamics either from calculation or from measurements. 

In the early years of GC, more consideration was given to partition (GLC) than to adsorption (GSC) systems. For GLC, the mechanism of retention was well understood, all of the mathematics were derived, and the chromatographic peak shapes were symmetrical. At that time, GSC had been utilized only for the separation of permanent gases. In recent years much has been accomplished in the determination of thermodynamic parameters in GSC separations. Part of the reason for the upsurge of interest was due to the desire to predict sample separations at any temperature, since most GSC data was reported at only one temperature. 

Titration calorimetry has been successfully employed in the determination of thermodynamic parameters for complexation (Siimer et al., 1987 Tong et al., 1991a). The technique has the advantage of employing direct calorimetric measurements and has been proposed as the most reliable method (Szejtli, 1982). It should be noted that the information derived from multistep series reactions is macroscopic in nature. In contrast to spectrophotometric methods that provide information concerning only the equilibrium constant(s), titration calorimetry also provides information about the reaction enthalpy that is important in explaining the mechanism involved in the inclusion process. 

To check this behavior, in Fig. 5.5 are plotted the voltammograms corresponding to a planar electrode calculated from Eq. (5.50) (Fig. 5.5a), those calculated from Eq. (5.63) for different values of the electrode radius (Fig. 5.5b), and, finally, the current corresponding to a spherical electrode, calculated as the sum of these two contributions (Fig. 5.5c). Thus, the decrease of the electrode size leads to an increase of the dimensionless current of the spherical electrode and to a change of the voltammogram shape in the way indicated above. For small electrodes (see curves in Fig. 5.5c for a radius rs = 10 microns), the peak of the second scan has disappeared and that corresponding to the first scan is poorly defined. Therefore, in these conditions the determination of thermodynamic parameters of the experimental systems under study lies in the study of the half-wave potential of the voltammograms (see below). 

Determination of Thermodynamic Parameters from Ion Exchange Kinetics 123... 

DETERMINATION OF THERMODYNAMIC PARAMETERS FROM ION EXCHANGE KINETICS... 

Weixlbaumer, A., Wemer, A., Flamm, C., Westhof, E., and Schroeder, R. (2004). Determination of thermodynamic parameters for HIV DIS type loop-loop kissing complexes. Nucleic Adds Res. 32, 5126—5133. 

Millen DJ, Mines GW (1974) Hydrogen bonding in the gas phase. Part II. Determination of thermodynamic parameters for amine-methanol systems from pressure, volume, temperature measurements. J Chem Soc Farad Dans II 70 693 -699... 

Scholte, Th. G., "Determination of Thermodynamic Parameters of Polymer- Solvent Systems by Light Scattering," Eur. Polym. J., 6, 1063 (1970). 

Emmerik, P. T. van Smolders, C. A., "Phase Separation in Polymer Solutions. II. Determination of Thermodynamic Parameters of Poly(2,6-dimethyl-1,4-phenylene oxide)Toluene Mixtures," J. Polym. Sci., Part C., 21, 311 (1972). 

Calculational methods for the accurate determination of thermodynamic parameters (particularly for solution-phase calorimetry) have only recently become available through the BCHMP chemical test and reference reaction. It is likely therefore that values reported for enthalpy, for example, are likely to be significantly in error for some of the earlier work using flow calorimetry. These errors can be rectified, however, through the calculation of the thermal volume and relevant adjustment of the calorimetric data. 

IGC enables rapid determination of thermodynamic parameters as well as... 

Calorimetric measurements of the heat evolved from the reactions of sodium polyacene dianion salts with water afforded the determination of thermodynamic parameters 70). For all the polyacene dianion salts, the heats of formation were found to be negative. Crystal lattice energies between 400 and 440 kcal/mol were found. These studies add a very important insight into the properties of 4nrc conjugated polycyclic dianions (Sect. 6.4). The measurements were carried out on solvent free dianions in a colimeter... 

Hamdaoui, O. and Naffrehoux. E.. Modeling of adsorption isotherms of phenol and chlorophenols onto granulai- activated carbon. Part I. Two-parameter models and equations allowing determination of thermodynamic parameters, J. Hazardous Mater., 147, 381, 2007. 

The separation of these cumulative effects is not an easy task, but is necessary for the determination of thermodynamic parameters, such as chemical bond strengths. Measuring very dilute water solutions at 3.9 °C, where the thermal expansion coefficient of water vanishes (or at slightly lower temperatures in more concentrated aqueous solutions, such as buffer solutions) can be used to separate the so-called structural volume changes from the thermal effects due to radiationless deactivation.253,254 In this way, it is also possible to determine the entropy changes concomitant with the production or decay of relatively short-lived species (e.g. triplet states), a unique possibility offered by these techniques.254 255... 

As is evident from the previous discussion, a clear understanding of the process of micellization is necessary for rational explanation of the effects of structural and environmental factors on the value of the CMC and for predicting the effects on it of new structural and environmental variations. The determination of thermodynamic parameters of micellization AG c, A//mio and A,S mic has played an important role in developing such an understanding. 

First we describe the major symbols, then the methods for the determination of thermodynamic parameters relevant for cationic ring-opening polymerization, the factors affecting these parameters, and finally deviations of real systems from ideality. On this basis we discuss fundamental principles and peculiarities observed in the thermodynamics of cationic ring-opening polymerization, and, eventually we show how these principles are applied for preparation of some homo- and copolymers. 

Figure 25. Left Base stacking in double-stranded DNA (only one strand shown) Right Determination of thermodynamic parameters of duplex formation Oligonucleotides 3 -dA(U]-A(MEQ1-5 and T 12) were diluted starting from 9 pM to 4.5 pM in 0.15 M NaCl, 0.01 M Tris-HCl, pH 7.0,25 °C and hybridization data were collected. From [149],...

The relationship between E° and temperature for Cyt c in water and heavy water has been extensively investigated for the determination of thermodynamic parameters (e.g., AG, A5, A//). In general, the... 

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