Exchange between phases, simple

Ganguly and Ruitz (1986) investigated the significance of closure temperature in terms of simple equilibrium thermodynamics. Assuming Rb-Sr exchanges between phases a and jS to be representable in terms of the equilibrium... 

The concept of mole fraction of a component used in Equation (4.1) is a convenient measure of concentration when dealing with trace quantities and dilute solutions, often experienced in environmental systems. This is especially the case with transport phenomena and equilibrium between phases, where it results in simple quantitative expressions. The phenomena of interest when dealing with the exchange of odorous compounds and oxygen between wastewater and a sewer atmosphere are, in this respect, relevant examples. 

Kinetic fractionations can occur when there is incomplete isotopic exchange between the different phases present in a system. A thorough introduction to kinetic stable isotope fractionation theory is unfortunately beyond the scope of the present review. Flowever, it is useful to include a brief discussion of some basic aspects, particularly in comparison to equilibrium fractionation theory. A simple example of kinetic fractionation is the evaporation of a liquid water droplet into a vacuum, in this example FljO molecules entering the gas phase are physically removed from the vicinity of the droplet, so there is no chance for isotopic equilibration between vapor-phase molecules and the residual liquid. Isotopic fractionation in this case is determined by a one-way reaction path, and will not, in general, be the same as the fractionation in a system where vapor-phase molecules are able to equilibrate and exchange with the liquid. In other reactions, isotopic exchange is limited by an energy barrier—an... 

The stationary phase may be a solid or liquid on a solid support. The mechanisms responsible for distribution between phases include surface absorption, ion exchange, relative solubilities and steric affects . High performance liquid chromatography is a useful method for quinolizidine alkaloid analysis, especially when pure standards are available". This method was recently used for alkaloid metabolite extraction and analysis . A simple reversed-phase liquid chromatographic method has been developed for the simultaneous quantitation of four anticancerous alkaloids vincristine, vinblastine, and their precursors catharanthine and vindoline using a specific HPLC column . 

Simple component exchange between solid phases is accomplished by diffusion. If only two components (such as Fe " and Mg) are exchanging, the diffusion is binary. The boundary condition is often such that the exchange coefficient between the surfaces of two phases is constant at constant temperature and pressure. The concentrations of the components on the adjacent surfaces may be constant assuming interface equilibrium. The solution to the diffusion equation... 

The simple theory also provides estimates of the gas exchange between the bubble and the emulsion phase. For a two-dimensional bed of unit thickness the flow of gas through the bubble is u = 4Me m/ 6, and for a three-dimensional bed the flow of gas through the bubble is u =. ... 

Processes of heat transfer accompanied by phase change are more complex than simple heat exchange between fluids. A phase change involves the addition or subtraction of considerable quantities of heat at constant or nearly constant temperature. The rate of phase change may be governed by the rate of heat transfer, but it is often influenced by the rate of nucleation of bubbles, drops, or crystals and by the behavior of the new phase after it is formed. This chapter covers condensation of vapors and boiling of liquids. Crystallization is discussed in Chap. 27. 

It is instructive to compare the spectra of a simple molecule obtained in the solution and solid state. Figure 4.11 shows three such spectra of paracetamol (structure as shown in Fig. 4.11). The high resolution proton decoupled spectmm of pure paracetamol dissolved in DMSO-dg shows one resonance for each chemically distinct carbon atom - in this case six signals (Fig. 4.11 A). The positions 2 and 2 are chemically equivalent due to the rapid rotation of the benzene nucleus and so have identical chemical shifts. This is not the case in the solid state (Fig. 4.1 IB), which shows that the carbon atoms labelled 2 and 2 are now inequivalent, suggesting that the exchange between these positions (rotation of the benzene nucleus) is slow on the NMR time scale in the solid phase. There are eight distinct carbon resonances in this spectrum, one for each carbon atom in the molecule. The spectmm in Fig. 4.11C shows the CP-MAS spectmm of a formulation blend of paracetamol. The resonances of the dmg molecule can easily be seen by comparison with Fig. 4.1 IB, the other resonances are from the various excipients used in the formulation, in this case mainly lactose and avicel. 

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