The Interpretation of Calorimetric Data

While the measurement of thermodynamic parameters by ITC is straightforward, interpretation of the derived values is not. It is important to recall that thermodynamic properties represent the sum of all molecular processes that occur during a binding event. A range of intermolecular interactions must be considered carefully before interpreting thermodynamic properties in terms of solute-solute interaction. Below we consider some of the processes that contribute to net measured thermodynamic processes and, where possible, describe experimental techniques for the evaluation of the contribution of each set of microscopic events to overall ligand binding thermodynamics. 

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Thermochemical investigations of molybdate solutions have been carried out and reaction heats were measured (108,109). As the interpretation of calorimetric data depends heavily on the correct reaction model, progress in determining reliable enthalpy and entropy changes for condensation reactions have been hampered. However, since there is little doubt that [M07O24]6 is the first polyanion which forms on acidification, the enthalpy and entropy changes obtained for its formation should be meaningful. The values for Eq. (30) are AH° =... 

The standard free energy is therefore determined by measurement of the mixture CMC holding the micellar composition fixed. This analysis assumes that a is known as a function of temperature and micellar composition and is independent of the electrolyte composition. The heat of micellization cannot be determined from measurement of the temperature dependence of CMCj( without knowledge of the micellar composition and of a. Interpretation of calorimetric data is not possible without information regarding micellar composition. Ultrafiltration techniques designed to measure micellar compositions, take an added importance when considering heats of micellization. 

Although adsorption data and calorimetric data, for example, can be measured repro-ducibly to within about one percent, the interpretations of such data are somewhat semi-quantitative. Such parameters as surface area and PSDs, certainly, do not possess that level of accuracy. Why this should be is explained below. It may come as a shock to readers that it is more than sufficient to quote surface areas to values 25 m g . ... 

Of course, a decisive prerequisite in any meaningful evaluation of calorimetric data is the judicious choice of experimental conditions, the appropriate correction of the data with respect to ubiquitous nonspecific contributions like the heat of dilution or mixing and above all the adequate choice of a model representing the relevant processes in solution. Similar to many other data evaluations where several individual contributions convene to generate a singular output (as e.g. in kinetics) adherence of the experimental data to a certain model does not ultimately prove the model, but surely disproves all non-fitting alternatives. The various options are discussed further below. At this point we shall focus the attention on the production of good quality data that in the end will be all decisive on the success of interpretative attempts. 

Calorimetric data have shown that only half of the total water sorbed by elastin (about 0.6 g water / g dry protein) is really "bound", the remaining water being freezable ( 1). The volumetric data reported in the literature (15,16) refer therefore to an essentially heterophase system, so that the negative and very large coefficient of thermal expansion of the fully hydrated protein does not appear to be suitable for the Interpretation of the thermoelastic data and calculation of the... 

Energy of activation values calculated from rate data between 75 and 150°C ranged from 22.7 to 24.4 kcal/mole with the minimum at 90°C. This agrees well with the value of 22.8 kcal/mole for formic acid decomposition on nickel powder between 125 and 150°C. The interpretation of the infrared data was further supported by calorimetric measurements. Thus, the heat of adsorption of formic acid at monolayer coverage was 18 kcal/mole which compares favorably with the heat of formation for mole of Ni (OOCH)2, 13 kcal. 

On the basis of calorimetric measurements, an interpretation of the 4-methylpentan-2-ol conversion data can be formulated which takes into account the role of the concentration and strength of the sites in governing the competition among the various mechanisms for dehydration and dehydrogenation [127]. 

Liquid-flow microcalorimefry is a reliable method to measure simultaneously the enthalpy changes and amounts of adsorption under dynamic conditions. Calorimetry experiments may be carried out in two different ways by following a pulse or saturation operating mode [64, 78-83]. In the pulse mode, small aliquots of a stock solution at a known concentration are injected into the carrier liquid (pure solvent) flowing through the adsorbent bed placed inside the calorimetric cell. In this case, the calorimetric system contains an additional loop injection facility (a manual injection valve with appropriate injection loops). The interpretation of the enthalpy data obtained is straightforward only when the whole amount of the solute injected is irreversibly adsorbed on the solid surface. 

A few examples of adsorption processes accompanied by an endothermic step due to the deformation/reconstruction of the surface in interaction with molecules were illustrated. In the reported cases, the heat measured within the calorimetric cell was the combination of an exothermic (adsorption) and an endothermic (surface reconstruction) effect, which caused the calorimetrically measured heat to be lower than what expected on the basis of a plain adsorption. An extra-care in interpreting (at molecular level) the experimental calorimetric results should be addressed in several cases, and in this respect it is quite fhiitful to complement the molar volumetric-calorimetric data with results from other approaches, typically the various spectroscopic methods and/or the ab initio molecular modeling. 

The more complex the mechanism which is to be discussed for the interpretation of the recorded reaction courses, the larger the probability that the run of the reaction can be interpreted also by a somewhat different, complex mechanism, especially due to the restricted accuracy in measurement. The number of mechanisms which is compatible with the recorded data can be large. To be precise, after the calorimetric analysis, the measured data are not inconsistent with the assumed mechanism, rates and heats of the reaction. ... 

It was proven that microcalorimetry technique is quite well developed and very useful in providing information on the strength and distribution of acidic and basic sites of catalysts. When interpreting calorimetric data, caution needs to be exercised. In general, one must be careful to determine if the experiments are conducted under such conditions that equilibration between the probe molecules and the adsorption sites can be attained. By itself, calorimetry only provides heats of interaction. It does not provide any information about the molecular nature of the species involved. Therefore, other complementary techniques should be used to help interpreting the calorimetric data. For example, IR spectroscopy needs to be used to determine whether a basic probe molecule adsorbs on a Brpnsted or Lewis acid site. 

Raman-spectral studies of cerebrosides in the solid and gel phases have been reported.201 Assignments of frequencies, and comparison of peak heights for characteristic vibrations, allowed elucidation of the conformation of both the chain and head-group portions of these molecules. Interpretation of the spectral data was found in agreement with calorimetric and X-ray structural data. 

These distonic superelectrophiles (145-147) have been characterized by low-temperature H NMR (and 13C NMR in the case of 147) from FSO3H-SbFs solution. Dication 146 was also studied by calorimetric studies to determine the heat of diprotonation of 2,5-hexanedione.48 It was found that the heat of diprotonation for the y-diketones (like 2,5-hexanedione) is about 5 kcal/mol less than expected, when compared to twice the heat of protonation of acetone or other monoketones. The destabilization of dication 146 by 5 kcal/mol can be the result of electrostatic effects, and it can be considered evidence for the superelectrophilic character of such dications. When 2,6-admantanedione is reacted in FSO3H—SbFj solution, the dication 148 is formed as a persistent species, observable by and 13C NMR.12 The carboxonium carbons of 148 are observed at Z I3C 247.7, while the mono-cationic species (149) has a carboxonium carbon at 513C 267.1. These 13C NMR data were interpreted as evidence for the increasing importance of the carboxonium-type resonance structure (148a) due to electrostatic repulsive effects. Some examples of aromatic diketones (i.e., diacetylbenzenes) have also been reported to produce bis-carboxonium dications in their protonation reactions in superacids.47... 

The aim of this chapter is simply to introduce a selection of the most appropriate thermodynamic quantities for the processing and interpretation of adsorption isotherm and calorimetric data, which are obtained by the methods described in Chapter 3. We do not consider here the thermodynamic implications of capillary condensation, since these are dealt with in Chapter 7. Special attention is given to the terminology and the definition of certain key thermodynamic quantities, for example, the difference between corresponding molar integral quantities and differential quantities. 

Presuming that calorimetric data are available, the central problem is that of interpretation. This will be clear from the brief description of some systems which have been studied recently. 

AjG data for B-TiO are reviewed on the table for a-TiO (9). Values of A H derived from a G" depend on the value of S (see Entropy). There are additional references on the A G which deserve comment. Solid-state emf data of Hoch et al. ( ) are insufficient to yield AjG (B), especially in the direct way used by Drowart et al. (19). Their interpretation is inconsistent with phase diagrams (, 1 ) and extensive emf data (7) which show bivariant behavior in which A C(02) is a strong function of (0/Tl). It is not useful to reinterpret the emf data ( 8) they show a temperature dependence of the wrong sign and we do not know the necessary electrode compositions. The often quoted A G of Kubaschewski and Dench (2 1) is not an independent value since it assumes the correctness of the calorimetric data of the Bureau of Mines (, 1 ). Kubaschewski s reassessment (, 8) of... 

The problems associated with freeze drying of peptides and proteins for therapeutic use have also received calorimetric attention recently - particularly, attempts to understand and interpret the dynamics of amorphous solids. Structural relaxation time is a measure of molecular mobility involved in enthalpy relaxation and thus is a measure of the dynamics of amorphous (glassy) solids. These dynamics are important in interpretation of the physicochemical properties and reactivities of drugs in amorphous formulations. The authors conclude that microcalorimetry may provide data useful for rational development of stable peptide and protein formulations and for control of their processing . 

The calorimetric studies of the surface heterogeneity of oxides were initiated half a century ago, and experimental findings as well as their theoretical interpretation have been recently reviewed by Rudzinski and Everett [2]. The last two decades have brought a true Renaissance of adsorption calorimetry. A new generation of fully automatized and computerized microcalorimeters has been developed, far more accurate and easy to manipulate. This was stimulated by the still better recognized fact that calorimetric data are much more sensitive to the nature of an adsorption system than adsorption isotherm for instance. It is related to the fact that calorimetric effects are related to temperature derivatives of appropriate thermodynamic functions, and tempearture appears generally... 

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