Homogeneous membrane

Another way to cross-link polymers based on styrene is to use diamines that give a very high ratio of ammonium groups. Pandey et al. [102,103] developed cross-linked 

ANION EXCHANGE MEMBRANES FOR ALKALINE FUEL CELLS 

8 Schematic representation of the synthesis of an AEM based on norbomene and dicyclopentadiene [107]. 

9 Tetraalkylainmonium funclionali/ed cyclooclene-based membrane synthesis [lOSJ. 

The PVDF-based membrane [104,116-119] obtained after amination and the alkaline exchange process is a very brittle material due to a physical degradation of the backbone. Moreover, these materials exhibited low lECs (0.7 x 10 equiv./g) and would be unsuitable for use in any kind of fuel cell or electrochemical device. However, membranes based on FEP, ETFE-co-FEP, and ETFE obtained high enough conductivities to be tested for AFC application. FEP-based AEMs showed conductivities on the order of 10-20 X10 S/cm at room temperature [104,116,124]. Fuel cell test data obtained with FEP-based MEAs (with 0.5 x 10 g/cm Pt/C (20wt%) electrodes) show a peak power density of 55 x 10 W/cm at 0.5 V at 50 °C and 100% relative humidity [104,126]. AEM based on FEP exhibited a conductivity of 30 X 10 S/cm when fully hydrated [127]. This result represents a high level of conductivity for a solid alkaline polymer without incorporation of metal hydroxide species. Unfortunately, at lower humidity, the conductivity of these membranes drops considerably and even if they are operational with low-humidity gases, they exhibit low efficiency. 

---

Reverse osmosis models can be divided into three types irreversible thermodynamics models, such as Kedem-Katchalsky and Spiegler-Kedem models nonporous or homogeneous membrane models, such as the solution—diffusion (SD), solution—diffusion—imperfection, and extended solution—diffusion models and pore models, such as the finely porous, preferential sorption—capillary flow, and surface force—pore flow models. Charged RO membrane theories can be used to describe nanofiltration membranes, which are often negatively charged. Models such as Dorman exclusion and the... 

This linear regime is achieved to within 90% of ] by 2/. For an ideal homogeneous membrane... 

The way to obtain the membranes as well their composition has been optimized. The main operational criterion for the membranes is the solubility of applicable ionic pairs. The solubility should be quite low - else the substance will be outwashed from the membrane. At the same time, the ionic pairs which have very low solubility are not suitable too because of the complicated obtaining homogeneous membranes. 

A. E. Yaroshchuk, S. S. Durkhin. Phenomenological theory of reverse osmosis in macroscopically homogeneous membranes and its specification for the capillary charged model. J Memb Sci 79 133, 1993. 

The general theoretical treatment of ion-selective membranes assumes a homogeneous membrane phase and thermodynamic equilibrium at the phase boundaries. Obvious deviations from a Nemstian behavior are explained by an additional diffusion potential inside the membrane. However, allowing stationary state conditions in which the thermodynamic equilibrium is not established some hitherto difficult to explain facts (e.g., super-Nemstian slope, dependence of the selectivity of ion-transport upon the availability of co-ions, etc.) can be understood more easily. 

Membranes with a relatively uniform pore size distribution throughout the thickness of the membrane are referred to as symmetric or homogeneous membranes. Others may be formed with tight skin layers on the top or on both the top and bottom of the membrane surfaces. These are referred to as asymmetric or nonhomogeneous membranes. In addition, membranes can be cast on top of each other to form a composite membrane. 

The basic flux across the membranes may be related to that across a thin film [83]. Pick s First Law of Diffusion indicates that the total flux of diffusant across a homogeneous membrane, /, is proportional to the concentration gradient of the diffusant ... 

Fick s first law applied to homogeneous membranes at steady state is a transport equation... 

Depending on their structure, membranes can be separated into porous, where matter is transported through pores in the membrane, and compact, where the substance is transported either through the entire homogeneous membrane phase or its homogeneous parts. 

Yasuda s free volume theory [57] has been proposed to explain the mechanism of permeation of solutes through hydrated homogeneous polymer membranes. The free volume theory relates the permeability coefficients in water-swollen homogeneous membranes to the degree of hydration and molecular size of the permeant by the following mathematical expression ... 

Despite the success of the comparatively simple models presented so far, they implicitly assume that the skin barrier may be modeled by a homogeneous membrane—which implies that the properties of the barrier do not change with depth and that there exists only a single pathway through the barrier. Obviously, skin is not a homogeneous membrane and therefore in several studies the simple model was extended to include several subsequent skin layers. In addition, possible transport along hair follicles and sweat ducts, for example, was sometimes included. 

Most models of the permeation of drugs through skin consider only steady-state conditions the drug amount in the donor is infinite and the concentration of accumulated drug in the acceptor is comparatively small and therefore negligible. Under these conditions the concentration-depth profile for a homogeneous membrane at time t is given by... 

Figure 2.14. The structure of an anodized aluminum oxide membrane (Anopore) as shown in Anotec Separations (1986) (a) is a homogeneous membrane (b) an asymmetric membrane.

The glass electrode also belongs among homogeneous membranes. For the sake of completeness, its properties will be described in chapter 6, but for construction details the reader is referred to the literature ([48]). 

Other types of ISE with silver halides are based on homogeneous membranes [6, 383]. With silver chloride or bromide, a single crystal or membrane from a salt melt can be prepared, while silver iodide membranes are prepared from... 

This difference is largely accounted for by the difference in thickness of the homogeneous membranes involved, such that the product of water permeation constant and membrane thickness is about the same for both membranes. The constant arises from the diffusion model of permeation in which ... 

All measurements have been made on homogeneous membranes of Eastman Kodak 398-3 cellulose acetate (6). The membranes were cast on glass plates and evaporated slowly to dryness from 2% w/v solution in pure acetone in a controlled atmosphere. The membranes were carefully outgassed under vacuum at 40°C before annealing in water for 30 minutes at 80°C during which they became detached from their casting plates. 

On account of the relatively low water regain of cellulose acetate, the molal concentration of ionic groups in the swollen material exceeds Smmolal. This is comparable to the concentration of 300 ppm sodium chloride, a typical reverse osmosis product solution. Our homogeneous membranes are believed to be very similar to the active layer of an asymmetric membrane as developed by Loeb and Sourirajan. It is evident therefore that the concentration of fixed charges in the membrane is sufficient to exercise a significant Donnan exclusion of co-ions on the downstream side of the membranes in a reverse osmosis plant. 

In conclusion, it can be claimed that a combination of kinetic and equilibrium conductance and membrane potential measurements provides a powerful method for investigating the permselective properties of membranes of low fixed charge density. Such methods should be applicable also to other polymers useful in hyperfiltration if they can be prepared in the form of homogeneous membranes. 

Symbol in equation (lO) means for homogeneous membrane of acetyl content C, and (Ca) without for asymmetric membrane. Rj(Ca) for IJaOCl in membrane of any degree of acetyl content are obtained and shown on Table 5> assuming that relation of solute permeabilities in homogeneous membrane for IJaCl and NaOCl may be expressed as follows... 

R,(C.) on Table 5 are shown in Figure 12 where pure water and sodium chloride permeabilities in homogeneous membranes obtained by Lonsdale etal( ) are also shown. 

Figure 12. An increase of the solute and pure water permeabilities for homogeneous membranes due to a decrease of acetyl content and f,(CA) and fi(CA) vi. acetyl content...

In order to gain some understanding of the behavior of an asymmetric membrane, let s consider a composite membrane consisting of two homogeneous membranes laminated together as shown in Figure 3. The same model has been studied recently by Henkens et al. (10). The first layer solution is ... 

For a non-homogeneous membrane,both the diffusivity and salt distribution coefficient may vary as a function of position across the membrane. However, the steady-state conditions require that the molar salt flux and the total volume flux remain constant throughout the membrane. Therefore, the integrated expression,... 

Eq. (19) is still applicable to the non-homogeneous membrane system. Following the same scheme as for the case of the homogeneous membrane with the modified salt distribution coefficients ... 

The present study shows that the asymptotic salt rejection, r, is determined by the top skin layer of a membrane. This is a result of the steady-state mass balance and the boundary conditions. Although there are no experimental data to support this, it has been shown theoretically that the asymptotic salt rejection is identical to the reflection coefficient for the homogeneous membrane, r = 0. 

---