Transport across phase boundaries

Following the introduction of basic kinetic concepts, some common kinetic situations will be discussed. These will be referred to repeatedly in later chapters and include 1) diffusion, particularly chemical diffusion in different solids (metals, semiconductors, mixed conductors, ionic crystals), 2) electrical conduction in solids (giving special attention to inhomogeneous systems), 3) matter transport across phase boundaries, in particular in electrochemical systems (solid electrode/solicl electrolyte), and 4) relaxation of structure elements. 

P. Kuban, A. Slampova, P. Bocek, Electric field-enhanced transport across phase boundaries and membranes and its potential use in sample pretreatment for bioanalysis, Electrophoresis 31 (2010) 768. 

For a gas in laminar flow over a condensed phase sample of length L, the mass transport across the boundary layer, in terms of the flux of molecules from the sample to die gas phase, is therefore... 

The first is pollutant transport across the boundary layer or surface film to the exterior surface of the adsorbent solid phase particle (i.e.,soils/sediments and their components). 

As shown in Illustrative Examples 19.3 and 19.4, often it is not immediately known whether an exchange process is controlled by transport across a boundary layer or by transport in the bulk phase. In Illustrative Example 19.3 we look at the case of resuspension of particles from the polluted sediments of Boston Harbor. We are interested in the question of what fraction of the pollutants sorbed to the particles (such as polychlorinated biphenyls) can diffuse into the open water column while the particles are resuspended due to turbulence produced by tidal currents in the bay. To answer this question we need to assess the possible role of the boundary layer around the particles. 

If the ranges of homogeneity of the phases taking part in the transformation are wider than those of line compounds, the kinetic coefficients in Eqns. (12.22) and (12.23), that is v jf, yb, and A b, are certainly not composition independent. It may then be questionable if transport across the boundary (Eqn. (12.22)) and the simultaneous structure change (Eqn. (12.23)) are independent processes as was tacitly assumed by formulating the kinetic relations in Eqns. (12.22) and (12.23). Let us emphasize that the foregoing analysis is meant to clarify the physico-chemical conceptual frame in which first-order transitions which include matter transport should be discussed. Pertinent experiments are still rare. 

Recovery of metals such as copper, the operation of batteries (cells) in portable electronic equipment, the reprocessing of fission products in the nuclear power industry and a very wide range of gas-phase processes catalysed by condensed phase materials are applied chemical processes, other than PTC, in which chemical reactions are coupled to mass transport within phases, or across phase boundaries. Their mechanistic investigation requires special techniques, instrumentation and skills covered here in Chapter 5, but not usually encountered in undergraduate chemistry degrees. Electrochemistry generally involves reactions at phase boundaries, so there are connections here between Chapter 5 (Reaction kinetics in multiphase systems) and Chapter 6 (Electrochemical methods of investigating reaction mechanisms). 

A cell may be considered as a heterogenous system at equilibrium with restrictions. In most cells the pressure on each phase is the same and a change of pressure of the system would cause the same change of pressure on all phases. However, it is possible to construct a cell so that the various phases may have different pressures. Then the pressures of some phases may be held constant while the pressures of other phases are changed. In such cases some of the derivatives of the chemical potentials in Equation (12.86) would be zero unless matter would have to be transported across the boundary between phases in order to maintain the equilibrium conditions with a change of pressure. 

Diffusive transport of chemicals also occurs across phase boundaries. However, it is no longer a concentration gradient that serves to describe this process, but a difference in chemical potential. Diffusive exchange across the air-water interface may serve as an example to illustrate how rates of diffusive interfacial chemical transfer are being derived. A common conceptual approach... 

One arrow is drawn to connect the surface water to the solid phase box it represents chemical deposition, which also involves diffusion across phase boundaries. From the viewpoint of physical transport, however, it may correspond with either uranium going back to stream sediments or uranium remaining trapped in aquifer rocks. 

Recall that the mass balance equations of Eqs. (1.1a) and (1.1b) incorporate not only terms for internal chemical reactions but also terms for physical mass transport across the boundaries of the control volume. Often, useful control volume boundaries coincide with boundaries between phases, such as between air and water or between water and solid bottom sediment, as discussed for the lake control volume in Section 1.3.1. Note, however, that the terms "environmental media" and "phases" are not interchangeable. For example, chemicals in the gas phase can refer to chemicals present in gaseous form in the atmosphere or in air bubbles in surface waters or in air-filled spaces in the subsurface environment. Chemicals in the aqueous phase are chemicals dissolved in water. Chemicals in the solid phase include chemicals sorbed to solid particles suspended in air or water, chemicals sorbed to soil grains, and solid chemicals themselves. In addition, an immiscible liquid (i.e., a liquid such as oil or gasoline that does not mix freely with water) can occur as its own nonaqueous phase liquid (NAPL, pronounced "napple"). Some examples of mass transport between phases are the dissolution of oxygen from the air into a river (gas phase to aqueous phase), evaporation of solvent from an open can of paint (nonaqueous liquid phase to gas phase), and the release of gases from new synthetic carpet (solid phase to gas phase). Mass transport between phases is affected both by physics and by the properties of the chemical involved. Thus, it is important to imderstand both the types of chemical reactions that are common in the environment, and the relative affinities that various chemicals have for gas, liquid, and solid phases. 

Mass Flux across Phase Boundary Henry s Law When there is species transport across a phase boundary (e.g., gas into a liquid), there is a discontinuous change in the molar concentration of the species across the phase interface, as shown in Figure 5.16. The concentration discontinuity across the phase boundary between a liquid and gas on across a membrane to gas interface is typically modeled with Henry s law ... 

A consequence of this theoretical approach which includes kinetic parameters is the establishment and coupling of certain ion fluxes across the phase boundary (equality of the sum of cathodic and anodic partial currents leading to a mixed potential). If a similar approach can be applied to asymmetric biological membranes with different thermodynamic equilibrium situations at both surfaces, the active ion transport could also be understood. 

The mechanisms by which this interaction occurs may be divided into two distinct groups (S4) first, the hydrodynamic behavior of a multiphase system can be changed by the addition of surface-active agents, and, as a result, the rate of mass transfer is altered secondly, surface contaminants can interfere directly with the transport of matter across a phase boundary by some mechanism of molecular blocking. 

The characteristic feature of solid—solid reactions which controls, to some extent, the methods which can be applied to the investigation of their kinetics, is that the continuation of product formation requires the transportation of one or both reactants to a zone of interaction, perhaps through a coherent barrier layer of the product phase or as a monomolec-ular layer across surfaces. Since diffusion at phase boundaries may occur at temperatures appreciably below those required for bulk diffusion, the initial step in product formation may be rapidly completed on the attainment of reaction temperature. In such systems, there is no initial delay during nucleation and the initial processes, perhaps involving monomolec-ular films, are not readily identified. The subsequent growth of the product phase, the main reaction, is thereafter controlled by the diffusion of one or more species through the barrier layer. Microscopic observation is of little value where the phases present cannot be unambiguously identified and X-ray diffraction techniques are more fruitful. More recently, the considerable potential of electron microprobe analyses has been developed and exploited. 

The mode of action of the antifouling polymers thus conforms to the bulk abiotic bond cleavage model. All the controlling factors, viz., diffusion of water into the polymer matrix, hydrolysis of the tributyltin carboxylate, diffusion of tributyltin species from the matrix to the surface, phase transfer of the organotin species, and its migration across the boundary layer, are analyzed. It is found that the transport of the mobile tributyltin species in the matrix is the rate limiting factor. 

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