Thermodynamic equilibrium permeable

At the initial stage of bulk copolymerization the reaction system represents the diluted solution of macromolecules in monomers. Every radical here is an individual microreactor with boundaries permeable to monomer molecules, whose concentrations in this microreactor are governed by the thermodynamic equilibrium whereas the polymer chain propagation is kinetically controlled. The evolution of the composition of a macroradical X under the increase of its length Z is described by the set of equations ... 

In Fig. 21.1, the condition for thermodynamic equilibrium is that the chemical potential of each membrane-permeable ion is identical between the left and right side solutions. The chemical potential /< can be defined either for the 1 1 salt or for the individual ions... 

Figure 1.2 Schematic representation of the pathway of elementary reaction ij in the traditional energetic coordinates with the activation barrier (a) and in the coordinates of thermodynamic rushes h of reactants (b). in the latter case, the reaction can be represented as a flow of a fluid between two basins separated by a membrane with permeability e-,j the examples are given for the left-to-right and right-to-left reactions (cases 1 and 3, respectively) case 2 illustrates the thermodynamically equilibrium system.

EQBATCH is based on the framework established by Bhuyan (1989), which has been presented elsewhere (e.g., Bhuyan et al., 1990). In EQBATCH, local thermodynamic equilibrium is assumed. It is also assumed that precipita-tion/dissolution, and cation exchange have a negligible effect on porosity and permeability. Ideal solutions are assumed so that the activity coefficients of the species are equal to unity. As a result, it is possible for activities to be replaced by their respective molar concentrations. For pure solids, activities are considered equal to unity. There are many species and reactions in alkaline flooding. 

Sousa et al [5.76, 5.77] modeled a CMR utilizing a dense catalytic polymeric membrane for an equilibrium limited elementary gas phase reaction of the type ttaA +abB acC +adD. The model considers well-stirred retentate and permeate sides, isothermal operation, Fickian transport across the membrane with constant diffusivities, and a linear sorption equilibrium between the bulk and membrane phases. The conversion enhancement over the thermodynamic equilibrium value corresponding to equimolar feed conditions is studied for three different cases An > 0, An = 0, and An < 0, where An = (ac + ad) -(aa + ab). Souza et al [5.76, 5.77] conclude that the conversion can be significantly enhanced, when the diffusion coefficients of the products are higher than those of the reactants and/or the sorption coefficients are lower, the degree of enhancement affected strongly by An and the Thiele modulus. They report that performance of a dense polymeric membrane CMR depends on both the sorption and diffusion coefficients but in a different way, so the study of such a reactor should not be based on overall component permeabilities. 

Two-Phase Region. The two-phase flow and heat transfer are given by the continuity equations for the i and g phases, the momentum equations (Eqs. 9.76 and 9.77), and the energy equation (Eq. 9.80). The two-phase region is assumed to be isothermal by neglecting the effect of the curvature (i.e., saturation) on the thermodynamic equilibrium state. This is justifiable, except for the very small pores (large pc). For the steady-state flow considered here, we have (for the assumed isotropic phase permeabilities)... 

If the cell and the surroundings have the same osmotic pressure then turgor pressure is zero and the system is in thermodynamic equilibrium. Osmotic pressure of the surroundings lower than that of the cell causes transfer of water into the cell. The cell swells, but the rigid cell wall limits the extent of swelling. A cell placed in a hypertonic solution (osmotic pressure higher than that of the cell) will lose water. The dehydration of a protoplast causes decrease of its volume and, in consequence, detachment of plasma lemma from the cell wall. This process is called plasmolysis (Figure 32.3). As the cell wall is permeable the volume between the cell wall and plasma lemma fills with the hypertonic solution. 

Osmosis results from the diffusion of a solvent through a semi-permeable membrane separating a solvent and solution. This occurs when the pressure Pq (corresponding to the chemical potential of the pure solvent fi°) is higher than the chemical potential of the solvent in the solution (/ij). The diffusion of the solvent into the solution takes place to establish a thermodynamic equilibrium. At equilibrium, the chemical potential of the solvent in the solution is equal to Thus ... 

An important application relates to oxygen diffusion through soft contact lenses (75). Soft contact lenses are made of poly(2-hydroxyethyl methacrylate) and its copolymers, in the form of cross-linked networks. These are swollen to thermodynamic equilibrium in water or saline solution. The hydroxyl group provides the hydrophilic characteristic and is also important for oxygen permeability. Oxygen permeability is important because of the physiological requirements of the eye. Thus the polymer is highly swollen with water and also serves as a semipermeable material. 

When air was used as the oxidant, the concentrations of hydrogen and carbon monoxide at the outlet of this converter reached 20% and 11%, respectively, which is dose to the thermodynamically equilibrium values. The possibility of an effective conversion of natural gas into syngas with a nearly optimal ratio of H2/CO = 2 was demonstrated. Permeable 3D matrices offer a way of designing relatively simple, compact, and efficient noncatalytic auto-thermal reformers for the partial oxidation of hydrocarbon gases of different origin and composition to syngas [331—332]. 

The pKa of a molecule, a charge-state-related parameter, is a descriptor of an acid-base equilibrium reaction [34,35]. Lipophilicity, often represented by the octanol-water partition coefficient Kp is a descriptor of a two-phase distribution equilibrium reaction [36]. So is solubility [37-39]. These three parameters are thermodynamic constants. On the other hand, permeability Pe is a rate coefficient, a kinetics parameter, most often posed in a first-order distribution reaction [40-42]. 

Our present topic is the relationship between permeability and lipophilicity (kinetics), whereas we just considered a concentration and lipophilicity model (thermodynamics). Kubinyi demonstrated, using numerous examples taken from the literature, that the kinetics model, where the thermodynamic partition coefficient is treated as a ratio of two reaction rates (forward and reverse), is equivalent to the equilibrium model [23], The liposome curve shape in Fig. 7.20 (dashed-dotted line) can also be the shape of a permeability-lipophilicity relation, as in Fig. 7.19d. 

Permeability (P) is usually defined as the product of a thermodynamic property and a transport property which are, respectively, the partition or solubility coefficient, K, and the diffusion coefficient, D. This partition coefficient is defined as the ratio at equilibrium of the solute concentration inside the gel to that in solution. A value of K less than 1 indicates that the solute favors the solution... 

In membrane osmometry the two compartments of an osmometer are separated by a semi-permeable membrane only solvent molecule can penetrate through the semi-permeable membrane which is closed except for capillary tubes. The polymer solute remains confined to one side of the osmometer and the activity of the solvent is different in the two compartments. Because of the thermodynamic drive towards equilibrium a difference in liquid level in the two capillaries results. 

Gibbs considered the statistical mechanics of a system containing one type of molecule in contact with a large reservoir of the same type of molecules through a permeable membrane. If the system has a specified volume and temperature and is in equilibrium with the resevoir, the chemical potential of the species in the system is determined by the chemical potential of the species in the reservoir. The natural variables of this system are T, V, and //. We saw in equation 2.6-12 that the thermodynamic potential with these natural variables is U[T, //] using Callen s nomenclature. The integration of the fundamental equation for yields... 

The osmotic pressure of a solute is the hydrostatic pressure that must be applied to a solution in order to increase the activity, a. (or fugacity, designated f, introduced by G. N. Lewis as a measure of thermodynamic escaping tendency . It is an effective gas pressure corrected for deviations from the perfect gas laws) of the solvent sufficiently to balance its decrease caused by the presence of the solute. Equilibrium is established through a membrane permeable only to the solvent. This pressure is, by integrating... 

The electrolytic permeability is a property of any solid electrolyte, since a local equilibrium involving ions and electrons is required by - thermodynamics for any conditions close to steady-state or global equilibrium. However, it is possible to optimize the level of permeability, depending on particular applications. In many cases, the permeability is a parasitic phenomenon leading to power losses in - fuel cells and - batteries, lower efficiency of solid-state electrolyzers and -> electrochemi-... 

Isothermal chemistry in fuel cells. Barclay (2002) wrote a paper which is seminal to this book, and may be downloaded from the author s listed web site. The text and calculations of this paper are reiterated, and paraphrased, extensively in this introduction. Its equations are used in Appendix A. The paper, via an equilibrium diagram, draws attention to isothermal oxidation. The single equilibrium diagram brings out the fact that a fuel cell and an electrolyser which are the thermodynamic inverse of each other need, relative to existing devices, additional components (concentration cells and semi-permeable membranes), so as to operate at reversible equilibrium, and avoid irreversible diffusion as a gas transport mechanism. The equilibrium fuel cell then turns out to be much more efficient than a normal fuel cell. It has a greatly increased Nernst potential difference. In addition the basis of calculation of efficiency obviously cannot be the calorific value of the... 

As discussed above for simple adsorption, polymer sorption can be treated in both thermodynamic and kinetic contexts. The quantity of an analyte that is sorbed by a polymer at equilibrium is referred to as the solubility of the analyte, while the rate at which the analyte is transported through the polymer is referred to as permeability. Although high solubility is generally a prerequisite for high permeability (on any reasonable time scale), there are some notable exceptions. Poly-siloxanes and polytetrafluoroethylene (Teflon ), for example, are quite permeable to water, but the solubility of water is not particularly large in either material. 

---