Condensed phases, definition

The total interaction between two slabs of infinite extent and depth can be obtained by a summation over all atom-atom interactions if pairwise additivity of forces can be assumed. While definitely not exact for a condensed phase, this conventional approach is quite useful for many purposes [1,3]. This summation, expressed as an integral, has been done by de Boer [8] using the simple dispersion formula, Eq. VI-15, and following the nomenclature in Eq. VI-19 ... 

Conceptual definition, 195 Condensed phases, 27, 68, 78 electrical properties, 78 Conductivity, electrical in metals, 8l in water solutions, 78 of solids, 80... 

Again, if we consider the initial substances in the state of liquids or solids, these will have a definite vapour pressure, and the free energy changes, i.e., the maximum work of an isothermal reaction between the condensed forms, may be calculated by supposing the requisite amounts drawn off in the form of saturated vapours, these expanded or compressed to the concentrations in the equilibrium box, passed into the latter, and the products then abstracted from the box, expanded to the concentrations of the saturated vapours, and finally condensed on the solids or liquids. Since the changes of volume of the condensed phases are negligibly small, the maximum work is again ... 

With this definition, T is the numerical value of the activity for the substance under some pressure p. It is also the ratio of the fugacity of the pure condensed phase under pressure p to that of the phase under 1 bar pressure. 

Matter can also be categorized into three distinct phases solid, liquid, and gas. An object that is solid has a definite shape and volume that cannot be changed easily. Trees, automobiles, ice, and coffee mugs are all in the solid phase. Matter that is liquid has a definite volume but changes shape quite easily. A liquid flows to take on the shape of its container. Gasoline, water, and cooking oil are examples of common liquids. Solids and liquids are termed condensed phases because of their well-defined volumes. A gas has neither specific shape nor constant volume. A gas expands or contracts as its container expands or contracts. Helium balloons are filled with helium gas, and the Earth s atmosphere is made up of gas that flows continually from place to place. Molecular pictures that illustrate the three phases of matter appear in Figure 1-12. 

While related to its carbon analogs, the existence of the RsSi species as a free ion in condensed phases had been doubted for a long time. However, NMR characterization using bulky aryl substituents has provided evidence for the triply coordinated silicon cation. " However, definitive evidence was recently reported by the groups of Reed and Lambert with a silyl cation species bound to three mesityl groups and a carborane [HCBnMesBrg] counterion (Eig. 7.5). It was suggested that... 

Ionization in the condensed phase presents a challenge due to the lack of a precise operational definition. Only in very few cases, such as the liquefied rare gases (LRG), where saturation ionization current can be obtained at relatively low fields, can a gas-phase definition be applied and a W value obtained (Takahashi et al., 1974 Thomas and Imel, 1987 Aprile et al., 1993). 

Quinone oximes and nitrosoarenols are related as tautomers, i.e. by the transfer of a proton from an oxygen at one end of the molecule to that at the other (equation 37). While both members of a given pair of so-related isomers can be discussed separately (see, e.g., our earlier reviews on nitroso compounds and phenols ) there are no calorimetric measurements on the two forms separately and so discussions have admittedly been inclusive—or very often sometimes, evasive—as to the proper description of these compounds. Indeed, while quantitative discussions of tautomer stabilities have been conducted for condensed phase and gaseous acetylacetone and ethyl acetoacetate, there are no definitive studies for any pair of quinone oximes and nitrosoarenols. In any case. Table 4 summarizes the enthalpy of formation data for these pairs of species. 

The term ionization may refer to different processes depending on the context. For radiation effects in the gas phase, it usually implies the removal of the least bound electron to infinity. Such a theoretical definition is not feasible in the condensed phase and it is necessary use a heuristic or operational procedure. Thus, in liquid hydrocarbons, one may use the electron scavenging reaction or a conductivity current to quantify the electrons liberated from molecules. It has only been possible to extrapolate the conductivity current at a low irradiation dose and at a relatively low external field to saturation in the cases of liquefied... 

We define the cohesive energy Ecoh (Johansson, Skriver ) as the difference between the energy of an assembly of free atoms in their ground state (see Table 1 of Chap. A) and the energy of the same assembly in the condensed phase (the solid at 0 °K), (this definition yields a positive number for Ecoii). It coincides with the enthalpy of sublimation AHj (see Chap. A) (which is usually extrapolated at room temperature). 

Abstract The theoretical basis for the quantum time evolution of path integral centroid variables is described, as weU as the motivation for using these variables to study condensed phase quantum dynamics. The equihbrium centroid distribution is shown to be a well-defined distribution function in the canonical ensemble. A quantum mechanical quasi-density operator (QDO) can then be associated with each value of the distribution so that, upon the application of rigorous quantum mechanics, it can be used to provide an exact definition of both static and dynamical centroid variables. Various properties of the dynamical centroid variables can thus be defined and explored. Importantly, this perspective shows that the centroid constraint on the imaginary time paths introduces a non-stationarity in the equihbrium ensemble. This, in turn, can be proven to yield information on the correlations of spontaneous dynamical fluctuations. This exact formalism also leads to a derivation of Centroid Molecular Dynamics, as well as the basis for systematic improvements of that theory. 

Definition of spike pressure and probability of its existence are briefly discussed in this Vol under Detonation (and Explosion) in Condensed-Phase Explosives". The so-called spike theory is discussed under "Detonation, Spike Theory in . A more detailed description is given by Cook (Ref 41, pp 69-87)... 

Not surprisingly, bifunctional species preceded the definition of the term distonic, both in the gas and condensed phases. For example, Hammond et al. studied the cage effect for radical pairs generated by decomposition of azo compounds. Among their targets was the doubly protonated amidine (27), whose decomposition yielded a pair of distonic radical cations (28 +).Attachment of the spin-bearing carbon in the 2-position of the diazaallyl function ensures minimal delocalization of unpaired spin into the latter. 

Although the number of valence electrons present on an atom places definite restrictions on the maximum formal oxidation state possible for a given transition element in chemical combination, in condensed phases, at least, there seem to be no a priori restrictions on minimum formal oxidation states. In future studies we hope to arrive at some definitive conclusions on how much negative charge can be added to a metal center before reduction and/or loss of coordinated ligands occur. Answers to these questions will ultimately define the boundaries of superreduced transition metal chemistry and also provide insight on the relative susceptibility of coordinated ligands to reduction, an area that has attracted substantial interest (98,117-119). 

Let us introduce a system of coordinates in which the flame is at rest. For the sake of definiteness we shall make the coordinate plane YOZ coincident with the interface between the condensed phase (briefly, c-phase) and the gas, with the c-phase located to the left at x < 0. In a system in which the flame is at rest, the material must move. The velocity of the material u... 

In the gaseous phase, an electron ejected from a molecule becomes free, and so for each filled electron level we have only one ionization potential. However, in the condensed phase an ejected electron can be in three different states free, quasi-free, and solvated. So the definition of the ionization potential becomes ambiguous. 

A liquid, like a gas, has no shape of its own, but it does have a definite volume. Both states of matter are referred to as fluids because of their mobility, or tendency to flow. A gas is actually a low density fluid because the molecules are much farther apart than in a liquid where molecules are in close contact with each other. For example, at room temperature and at atmospheric pressure the density of air is about 0.0012 grams (0.000042 ounces) per cubic centimeter (g/cm3), whereas the density of liquid air is approximately 0.810 g/cm3 (atits normal boiling point of—209°C, or —344°F). This corresponds to an average separation between molecules in the gas phase that is about nine times larger than that for the liquid. A liquid is thus called a condensed phase—or a high density fluid—and is roughly 1,000 times more dense than a gas. 

---