Thermodynamic equilibria interface

Mass-Transfer Principles Dilute Systems When material is transferred from one phase to another across an interface that separates the two, the resistance to mass transfer in each phase causes a concentration gradient in each, as shown in Fig. 5-26 for a gas-hquid interface. The concentrations of the diffusing material in the two phases immediately adjacent to the interface generally are unequal, even if expressed in the same units, but usually are assumed to be related to each other by the laws of thermodynamic equihbrium. Thus, it is assumed that the thermodynamic equilibrium is reached at the gas-liquid interface almost immediately when a gas and a hquid are brought into contact. 

The anticipated content of impurities in the refined metal may be calculated a priori by assuming thermodynamic equilibrium at both metal/gas interfaces, and using the relevant stabilities of tire gaseous iodides. Adequate thermodynamic data could provide the activities of the impurities widr that of zirconium close to unity, but tire calculation of tire impurity transport obviously requires a knowledge of activity coefficients in the original impure material, which are not sufficiently well known. 

At each phase boundary there exists a thermodynamic equilibrium between the membrane surface and the respective adjacent solution. The resulting thermodynamic equilibrium potential can then be treated like a Donnan-potential if interfering ions are excluded from the membrane phase59 6,). This means that the ion distributions and the potential difference across each interface can be expressed in thermodynamic terms. 

The boundary conditions are given by specifying the panicle currents at the boundaries. Holes can be injected into the polymer by thermionic emission and tunneling [32]. Holes in the polymer at the contact interface can also fall bach into the metal, a process usually called interlace recombination. Interface recombination is the time-reversed process of thermionic emission. At thermodynamic equilibrium the rates for these two time-reversed processes are the same by detailed balance. Thus, there are three current components to the hole current at a contact thermionic emission, a backflowing interface recombination current that is the time-reversed process of thermionic emission, and tunneling. Specifically, lake the contact at Jt=0 as the hole injecting contact and consider the hole current density at this contact. 

The discovery development interface is important with respect to drug aqueous solubihty. In earlier discovery stages kinetic solubihty assays are perfectly acceptable even more desirable than the thermodynamic equilibrium solubihty assay. 

Monolayers of distearoylphosphatidylcholine spread on the water-1,2-dichloro-ethane interface were studied by Grandell et al. [52] in a novel type of Langmuir trough [53]. Isotherms of the lipid were measured at controlled potential difference across the interface. Electrocapillary curves derived from the isotherms agreed with those measured under the true thermodynamic equilibrium. Weak adsorption or a stable monolayer was found to be formed, when the potential of the aqueous phase was positive or negative respectively, with respect to the potential of the 1,2-dichloroethane phase [52]. This result... 

When an aqueous phase (noted w) is brought in contact with a second immiscible phase (noted o), the different species dissolved in one or the two phases spontaneously distribute depending on their hydrophilic-lipophilic balance until the thermodynamic equilibrium is reached. The distribution of the charged species generates an interfacial region, in which the electrical field strength differs from zero, so that an electrical Galvani potential difference, is established across the interface ... 

At constant pressure and temperature, after the building up of the interface, thermodynamic equilibrium is obtained when the electrochemical potentials for each component distributed between the two phases are equal ... 

For a nucleus to become useful as a seed for subsequent bubble growth, the size of the nucleus must exceed that of thermodynamic equilibrium corresponding to the state of the liquid. The condition for thermodynamic equilibrium at a vapor-liquid interface in a pure substance can be written as... 

First, we must consider a gas-liquid system separated by an interface. When the thermodynamic equilibrium concentration is not reached for a transferable solute A in the gas phase, a concentration gradient is established between the two phases, and this will create a mass transfer flow of A from the gas phase to the liquid phase. This is described by the two-film model proposed by W. G. Whitman, where interphase mass transfer is ensured by diffusion of the solute through two stagnant layers of thickness <5G and <5L on both sides of the interface (Fig. 45.1) [1—4]. 

To understand the role of the noble metal in modifying the photocatalysts we have to consider that the interaction between two different materials with different work functions can occur because of their different chemical potentials (see [200] and references therein). The electrons can transfer from a material with a high Fermi level to another with a lower Fermi level when they contact each other. The Fermi level of an n-type semiconductor is higher than that of the metal. Hence, the electrons can transfer from the semiconductor to the metal until thermodynamic equilibrium is established between the two when they contact each other, that is, the Fermi level of the semiconductor and metal at the interface is the same, which results in the formation of an electron-depletion region and surface upward-bent band in the semiconductor. On the contrary, the Fermi level of a p-type semiconductor is lower than that of the metal. Thus, the electrons can transfer from the metal to the semiconductor until thermodynamic equilibrium is established between the two when they contact each other, which results in the formation of a hole depletion region and surface downward-bent band in the semiconductor. Figure 12.6 shows the formation of semiconductor surface band bending when a semiconductor contacts a metal. 

The DICTRA programme is based on a numerical solution of multi-component diffusion equations assuming that thermodynamic equilibrium is locally maintained at phase interfaces. Essentially the programme is broken down into four modules which involve (1) the solution of the diffusion equations, (2) the calculation of... 

Behavior of trace element that can be treated as effective binary diffusion The above discussion is for the behavior of the principal equilibrium-determining component. For minor and trace elements, there are at least two complexities. One is the multicomponent effect, which often results in uphill diffusion. This is because the cross-terms may dominate the diffusion behavior of such components. The second complexity is that the interface-melt concentration is not fixed by thermodynamic equilibrium. For example, for zircon growth, Zr concentration in the interface-melt is roughly the equilibrium concentration (or zircon saturation concentration). However, for Pb, the concentration would not be fixed. 

Figure 19.3 schematically describes in more detail the transport phenomena occurring during pervaporation. First, solutes partition into the membrane material according to the thermodynamic equilibrium at the liquid-membrane interface (Fig. 19.3a), followed by diffusion across the membrane material owing to the concentration gradient (Fig. 19.3b). A vacuum or carrier gas stream promotes then continuous desorption of the molecules reaching the permeate side of the membrane (Fig. 19.3c), maintaining in this way a concentration gradient across the membrane and hence a continuous transmembrane flux of compounds.

Normally transport by convection is sufficiently fast that the concentrations are homogeneous, and the crossing of the gas-liquid interface is instantaneous there is no resistance to transfer. There is thus thermodynamic equilibrium at the interface. This assumption is questionable in culture media containing proteins, inorganic ions, etc. 

A Criterion of Thermodynamic Equilibrium between Two Phases Equality of Electrochemical Potentials. It has been stated that ihe total driving force responsible for Ihe flow or transport of a species j is the gradient d lj/dx of its electrochemical potential. However, when there is net flow or flux of any species, this means that the system is not at equilibrium. Conversely, for the system to be at equilibrium, it is essential that there be no drift of any species—hence, that there should be zero gradients for the electrochemical potentials of all the species. It follows, therefore, that, for an interface to be at equilibrium, the gradients of electrochemical potential of the various species must be zero across the phase boundary, i.e.,... 

Nonpolarizable Interfaces and Thermodynamic Equilibrium. It has just been shown that for an interface to be in thermodynamic equilibrium, the electrochemical potentials of all the species must he the same in both the phases constituting the interface. Since the difference in electrochemical potential of a species i between two phases is the work done to cany a mole of this species from one phase (e.g., the electrode) to the other (e.g., the solution), it must be the same as the work in the opposite direction. This implies a free flow of species across the interface. However, an interface that maintains an open border is none other than a nonpolarizable interface (see Section 63.3). 

A simple conclusion follows Thermodynamic equilibrium exists at a nonpolarizable interface. Hence, one can immediately apply the criterion of thermodynamic equilibrium to a nonpolarizable interface. That is, from Eq. (6.38),... 

The nonpolarizable characteristics of the second interface M2/S, which is a necessary part of the cell and measuring setup, are now introduced. It is recalled that there is thermodynamic equilibrium at this interface, and thus... 

In the case of an electrode-solution interface, the thermodynamic equilibrium between the media in contact is attained by means of electron-ion exchange processes. Since the process of attaining the equilibrium is governed by charged particles, the equilibrium state is characterized by a certain potential difference between the phases. If they are in direct contact, we deal with the potential difference between two points in different media, for example, inside a semiconductor electrode and inside a solution. This potential difference is called the Galvani potential. 

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