PART 2 Condensed Phases

This work was supported in part at both Pacific Northwest National Laboratory (PNNL) and the University of Minnesota (UM) by the Division of Chemical Sciences, Office of Basic Energy Sciences, U. S. Department of Energy (DOE), and it was supported in part (condensed-phase dynamics) at the University of Minnesota by the National Science foundation. Battelle operates PNNL for DOE. 

Many of the condensed phase effects mentioned above have been studied computationally using the PI-QTST approach outlined in die first part of the last section. One such study 48 has focused on the model synnnetric... 

Molybdenum trioxide is a condensed-phase flame retardant (26). Its decomposition products ate nonvolatile and tend to increase chat yields. Two parts of molybdic oxide added to flexible poly(vinyl chloride) that contains 30 parts of plasticizer have been shown to increase the chat yield from 9.9 to 23.5%. Ninety percent of the molybdenum was recovered from the chat after the sample was burned. A reaction between the flame retardant and the chlorine to form M0O2 012 H20, a nonvolatile compound, was assumed. This compound was assumed to promote chat formation (26,27). 

The question as to whether a flame retardant operates mainly by a condensed-phase mechanism or mainly by a vapor-phase mechanism is especially comphcated in the case of the haloalkyl phosphoms esters. A number of these compounds can volatilize undecomposed or undergo some thermal degradation to release volatile halogenated hydrocarbons (37). The intact compounds or these halogenated hydrocarbons are plausible flame inhibitors. At the same time, thek phosphoms content may remain at least in part as relatively nonvolatile phosphoms acids which are plausible condensed-phase flame retardants (38). There is no evidence for the occasionally postulated formation of phosphoms haUdes. Some evidence has been presented that the endothermic vaporization and heat capacity of the intact chloroalkyl phosphates may be a main part of thek action (39,40). 

Proper condensed phase simulations require that the non-bond interactions between different portions of the system under study be properly balanced. In biomolecular simulations this balance must occur between the solvent-solvent (e.g., water-water), solvent-solute (e.g., water-protein), and solute-solute (e.g., protein intramolecular) interactions [18,21]. Having such a balance is essential for proper partitioning of molecules or parts of molecules in different environments. For example, if the solvent-solute interaction of a glutamine side chain were overestimated, there would be a tendency for the side chain to move into and interact with the solvent. The first step in obtaining this balance is the treatment of the solvent-solvent interactions. The majority of biomolecular simulations are performed using the TIP3P [81] and SPC/E [82] water models. 

A detailed description of methods for studying dynamic (i.e. time-dependent) phenomena and condensed phases is outside the scope of this book. The common feature for all these methods, however, is the need for an energy surface upon which the dynamics can take place. The generation of such a surface normally relies at least partly on results from calculations of the types discussed in Chapters 2-6, and it may therefore be of interest to briefly discuss the fundamentals. 

Since does not take part in the reaction, the boundary line between M and MO is independent of logPsoj d so given by a straight vertical line at logPo2 = 16, parallel to the -axis (line 1 in Fig. 7.67). It should be noticed that stability areas across the boundary follow the sequence of condensed phases shown in the equation, i.e. on the left-hand side of the boundary pure metal is the stable phase and on the right-hand side the pure metal oxide. 

It may reasonably be assumed that the terms in the expression for the entropy which depend on the temperature diminish, like the entropy of a chemically homogeneous condensed phase, to zero when T approaches zero, and the entropy of a condensed solution phase at absolute zero is equal to that part of the expression for the entropy which is independent of temperature, and depends on the composition (Planck, Thennodynamik, 3 Aufi., 279). 

Use the Third Law to calculate the standard entropy, S°nV of quinoline (g) p — 0.101325 MPa) at T= 298,15 K. (You may assume that the effects of pressure on all of the condensed phases are negligible, and that the vapor may be treated as an ideal gas at a pressure of 0.0112 kPa, the vapor pressure of quinoline at 298.15 K.) (c) Statistical mechanical calculations have been performed on this molecule and yield a value for 5 of quinoline gas at 298.15 K of 344 J K l mol 1. Assuming an uncertainty of about 1 j K 1-mol 1 for both your calculation in part (b) and the statistical calculation, discuss the agreement of the calorimetric value with the statistical... 

Vapor pressures and vapor compositions in equilibrium with a hypostoichiometric plutonium dioxide condensed phase have been calculated for the temperature range 1500 I H 4000 K. Thermodynamic functions for the condensed phase and for each of the gaseous species were combined with an oxygen-potential model, which we extended from the solid into the liquid region to obtain the partial pressures of O2, 0, Pu, PuO and Pu02 as functions of temperature and of condensed phase composition. The calculated oxygen pressures increase rapidly as stoichiometry is approached. At least part of this increase is a consequence of the exclusion of Pu +... 

Most informative in this context is vibrational spectroscopy since the number of signals observed depends on the molecular size as well as on the symmetry of the molecule and, if it is part of a condensed phase, of its environment. In particular, Raman spectroscopy has contributed much to the elucidation of the various allotropes of elemental sulfur and to the analysis of complex mixtures such as hquid and gaseous sulfur. 

It is known that the interaction of the reactants with the medium plays an important role in the processes occurring in the condensed phase. This interaction may be separated into two parts (1) the interaction with the degrees of freedom of the medium which, together with the intramolecular degrees of freedom, represent the reactive modes of the system, and (2) the interaction between the reactive and nonreactive modes. The latter play the role of the thermal bath. The interaction with the thermal bath leads to the relaxation of the energy in the reaction system. Furthermore, as a result of this interaction, the motion along the reactive modes is a complicated function of time and, on average, has stochastic character. 

As mentioned previously, this can be attributed in part to the lack of structure-sensitive techniques that can operate in the presence of a condensed phase. Ultrahigh-vacuum (UHV) surface spectroscopic techniques such as low-energy electron diffraction (LEED), Auger electron spectroscopy (AES), and others have been applied to the study of electrochemical interfaces, and a wealth of information has emerged from these ex situ studies on well-defined electrode surfaces.15"17 However, the fact that these techniques require the use of UHV precludes their use for in situ studies of the electrode/solution interface. In addition, transfer of the electrode from the electrolytic medium into UHV introduces the very serious question of whether the nature of the surface examined ex situ has the same structure as the surface in contact with the electrolyte and under potential control. Furthermore, any information on the solution side of the interface is, of necessity, lost. 

The objective of this first part of the book is to explain in a chemically intelligible fashion the physical origin of microwave-matter interactions. After consideration of the history of microwaves, and their position in the electromagnetic spectrum, we will examine the notions of polarization and dielectric loss. The orienting effects of the electric field, and the physical origin of dielectric loss will be analyzed, as will transfers between rotational states and vibrational states within condensed phases. A brief overview of thermodynamic and athermal effects will also be given. 

To make QM studies of chemical reactions in the condensed phase computationally more feasible combined quantum me-chanical/molecular mechanical (QM/MM) methods have been developed. The idea of combined QM/MM methods, introduced first by Levitt and Warshell [17] in 1976, is to divide the system into a part which is treated accurately by means of quantum mechanics and a part whose properties are approximated by use of QM methods (Fig. 5.1). Typically, QM methods are used to describe chemical processes in which bonds are broken and formed, or electron-transfer and excitation processes, which cannot be treated with MM methods. Combined QM and MM methods have been extensively used to study chemical reactions in solution and the mechanisms of enzyme-catalyzed reactions. When the system is partitioned into the QM and MM parts it is assumed that the process requiring QM treatment is localized in that region. The MM methods are then used to approximate the effects of the environment on the QM part of the system, which, via steric and electrostatic interactions, can be substantial. The... 

This chapter introduces additional central concepts of thermodynamics and gives an overview of the formal methods that are used to describe single-component systems. The thermodynamic relationships between different phases of a single-component system are described and the basics of phase transitions and phase diagrams are discussed. Formal mathematical descriptions of the properties of ideal and real gases are given in the second part of the chapter, while the last part is devoted to the thermodynamic description of condensed phases. 

It is essential that all PSs are multiphase. The easiest case to handle is the biphase system consisting of a condensed phase (solid) and a void inside porous particles or between consolidated ensembles of nonporous or porous particles. The void occupies a part of the volume, s, which is referred to as porosity. The other part of a PS volume is equal to ri=(l -e), and is termed density of packing. It is filled with the condensed phase (see Section 9.4). Generally, PSs can include various condensed phases of different structure, including combinations of solid(s) and liquid(s). 

This part includes a discussion of the main experimental methods that have been used to study the energetics of chemical reactions and the thermodynamic stability of compounds in the condensed phase (solid, liquid, and solution). The only exception is the reference to flame combustion calorimetry in section 7.3. Although this method was designed to measure the enthalpies of combustion of substances in the gaseous phase, it has very strong affinities with the other combustion calorimetric methods presented in the same chapter. 

Most published enthalpies of formation and reaction in the condensed phase were determined by calorimetry (see databases indicated in appendix B). It is therefore not surprising that the discussion of calorimetric methods occupies a large fraction of part II. 

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