Thermodynamic results

Another well-known thermodynamic result, the Clapeyron equation, applies to first-order transitions (subscript 1) ... 

The molecular weight analysis presented above is a purely thermodynamic result and is independent of any model. The procedure requires dilute solutions, but is not based on the assumption of ideality, even though Eq. (8.88) is a variation of the van t Hoff equation. 

Protein-DNA complexes present demanding challenges to computational biophysics The delicate balance of forces within and between the protein, DNA, and solvent has to be faithfully reproduced by the force field, and the systems are generally very large owing to the use of explicit solvation, which so far seems to be necessary for detailed simulations. Simulations of such systems, however, are feasible on a nanosecond time scale and yield structural, dynamic, and thermodynamic results that agree well with available experimen-... 

JThis calculation is one of the most satisfying in science. The values of the thermodynamic properties of the ideal gas calculated from molecular parameters are usually more accurate than the same thermodynamic results obtained from experimental measurements. 

The reason is that classical thermodynamics tells us nothing about the atomic or molecular state of a system. We use thermodynamic results to infer molecular properties, but the evidence is circumstantial. For example, we can infer why a (hydrocarbon + alkanol) mixture shows large positive deviations from ideal solution behavior, in terms of the breaking of hydrogen bonds during mixing, but our description cannot be backed up by thermodynamic equations that involve molecular parameters. 

Both our new chemistry building and the science of thermodynamics are functional, but beautiful. The building is a very modern combination of glass, steel, concrete, and brick, set on the edge of a hill, where it projects an image of strength, stability, and beauty. The aesthetic beauty of thermodynamics results from the rigor of the discipline. Thermodynamics is one of the pre-eminent... 

Guillaume et al. [69] presented a high performance liquid chromatographic method for an association study of miconazole and other imidazole derivatives in surfactant micellar using a hydrophilic reagent, Montanox DF 80. The thermodynamic results obtained showed that imidazole association in the surfactant micelles was effective over a concentration of surfactant equal to 0.4 pM. In addition, an enthalpy-entropy compensation study revealed that the type of interaction between the solute and the RP-18 stationary phase was independent of the molecular structure. The thermodynamic variations observed were considered the result of equilibrium displacement between the solute and free ethanol (respectively free surfactant) and its clusters (respective to micelles) created in the mobile phase. 

In many cases, however, the silicas are formed under kinetic control,16 and not thermodynamic, resulting often in living materials that undergo structural modifications, and thus changes in reactivity, even months after preparation (Figure 5.5). 

In the case of the graphite-to-diamond transformation, thermodynamic results predict that graphite is the stable allotrope at a fixed temperature at all pressures below the transition pressure and that diamond is the stable aUotrope at all pressures above the transition pressure. But diamond is not converted to graphite at low pressures for kinetic reasons. Similarly, at conditions at which diamond is the thermodynamically stable phase, diamond can be obtained from graphite only in a narrow temperature range just below the transition temperature, and then only with a catalyst or at a pressure sufficiently high that the transition temperature is about 2000 K. 

An important thermodynamic result is that the free-energy change can be related to the reaction equilibrium constant. Begin by considering again the reaction of Eq. 9.3, which describes chemical conversion of A and B to X and Y in the molar ratios shown. If the reaction proceeds by some infinitesimal amount dS, then the number of moles of each chemical species changes by an amount... 

So many different catalytic mechanisms are possible that the kinetic interpretation of this simple thermodynamical result is rather complex, but the general principle is easily illustrated by simple instances. Suppose the reaction AB —>A + B is accelerated by a homogeneous catalyst, which forms a complex with the molecule AB. 

Issue is taken here, not with the mathematical treatment of the Debye-Hiickel model but rather with the underlying assumptions on which it is based. Friedman (58) has been concerned with extending the primitive model of electrolytes, and recently Wu and Friedman (159) have shown that not only are there theoretical objections to the Debye-Hiickel theory, but present experimental evidence also points to shortcomings in the theory. Thus, Wu and Friedman emphasize that since the dielectric constant and relative temperature coefficient of the dielectric constant differ by only 0.4 and 0.8% respectively for D O and H20, the thermodynamic results based on the Debye-Hiickel theory should be similar for salt solutions in these two solvents. Experimentally, the excess entropies in D >0 are far greater than in ordinary water and indeed are approximately linearly proportional to the aquamolality of the salts. In this connection, see also Ref. 129. 

The overview in this section is intended to only provide a brief background for discussion of MD and MC techniques as applied to thermodynamic results. For the reader interested in MD or MC details, Table 5.11 includes a list of standard references. The LD technique, which was originally applied for low temperature solids, will not be considered in this brief overview (see the standard reference in Table 5.11). Kinetic results for molecular simulations are in Chapter 3. 

Table 16.7 Thermodynamic results from the study of the effects of cisplatin binding on the melting of the GG20 duplex... 

Thermodynamic studies performed on a number of other guanosine adducts show some examples where binding represents an enthalpic destabilized, but entropy stabilized, process and others that are enthalpically stabilized, but entropically destabilized. The net thermodynamic result, however, appears to be a relatively modest localized free-energy destabilization that could form the basis for some recognition mechanism. 

Because of the approximations involved in this analysis, the thermodynamic results have to be considered with caution. This is not only due to a rather crude analysis of the electrostatic effects but also, and this is a general problem, to the neglect of solvation in the molecular mechanics refinement. However, the structures presented in Fig. 9.6 are valuable because they are based not only on the structure optimization by molecular mechanics but also on spectroscopic data. This example is therefore instructive for two reasons first, it demonstrates that, depending on the study, the often-neglected electrostatic effects may be of considerable importance. Second, not only may experimental observables help to refine solution structures, they can prevent a wrong conclusion. As in this example, the combination of experimental data with molecular mechanics calculations is often the only way to get reliable structural information. 

Not all published and widely accepted thermodynamic values are reliable. Nordstrom and Archer (2003) provide a detailed review of the controversies, uncertainties, and problems related to thermodynamic data for arsenic and its compounds and aqueous species. Many of the data are contradictory and the methods that produce the data are sometimes questionable or have not been thoroughly documented. Too often, data in the literature have been passed from reference to reference without critical evaluations. Some of the data have high measurement errors, were produced under undefined or poorly defined laboratory conditions, and involved unrepresentative sampling (Matschullat 2000, 298 Nordstrom and Archer, 2003). Furthermore, other questionable data originate from obscure documents or are written in languages that many individuals cannot read and properly interpret. Therefore, thermodynamic results must be accepted with a certain amount of caution. The table in this appendix includes thermodynamic data from various sources, which provide users with some idea of their variability. Although sometimes unavoidable, users... 

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