Donnan effect equilibrium

Note that the sodium ion concentrations in the two compartments are quite different in this last case, as are the hydroxyl ion concentrations. This is the Gibbs-Donnan equilibrium effect. The fact that each ion partitions unevenly between the two compartments results in a contribution to the osmotic pressure from the ions in addition to that which results... 

Thus, the breakthrough curves of 0.1 N HCl shift from ca 1.5 column volumes in 5N LiCl to more than 8 column volumes in the concentrated (16 N) LiCl solution. A similar strong retention of HCl (because of the reduced activity coefficient of HCl ) was also characteristic of the ION solution of MgCl2. Yet, retention of HCl in amphoteric resins and anion exchangers contradicts the concept of ion exclusion according to which all strong electrolytes should be effectively excluded from absorption into ion-exchange resins, because of the Donnan equilibrium effect [117, 118]. 

When the Donnan equilibrium is operative the entry of ions into the membrane is restricted. Consequently as the concentration of ions in the solution increases the resistance of the membrane remains constant until the concentration of ions in the solution reaches that of the fixed ions attached to the polymer network. At this point their effect will be swamped and the movement of ions will be controlled by the concentration gradient. 

A semi-permeable membrane, which is unequally permeable to different components and thus may show a potential difference across the membrane. In case (1), a diffusion potential occurs only if there is a difference in mobility between cation and anion. In case (2), we have to deal with the biologically important Donnan equilibrium e.g., a cell membrane may be permeable to small inorganic ions but impermeable to ions derived from high-molecular-weight proteins, so that across the membrane an osmotic pressure occurs in addition to a Donnan potential. The values concerned can be approximately calculated from the equations derived by Donnan35. In case (3), an intermediate situation, there is a combined effect of diffusion and the Donnan potential, so that its calculation becomes uncertain. 

For homopolyelectrolyte, we first studied the ellipsometric measurement of the adsorption of sodium poly(acrylate) onto a platinum plate as a function of added sodium bromide concentration (5). We measured the effect of electrolyte on the thickness of the adsorbed layer and the adsorbances of the polyelectrolyte. It was assumed that the Donnan equilibrium existed between the adsorbed layer and the bulk phase. The thickness was larger and the adsorbance of the polyelectrolyte was lower for the lower salt concentration. However, the data on the molecular weight dependence of both the adsorbance and the thickness of the adsorbed polyelectrolyte have been lacking compared with the studies of adsorption of nonionic polymers onto metal surfaces (6-9). 

For our purpose here, we are interested in the following question How do the membranes maintain the ionic environments in the cell over long periods of time while simultaneously allowing transmembrane passage of the needed ions The mechanism that makes this possible is the so-called Donnan equilibrium we discuss the details of this equilibrium in this chapter, but a qualitative picture of the Donnan effect can be obtained with the help of a simplified model of a cell shown in Figure 3.1 (See, also, Section 3.5a.). 

Elementary and advanced treatments of such cellular functions are available in specialized monographs and textbooks (Bergethon and Simons 1990 Levitan and Kaczmarek 1991 Nossal and Lecar 1991). One of our objectives in this chapter is to develop the concepts necessary for understanding the Donnan equilibrium and osmotic pressure effects. We define osmotic pressures of charged and uncharged solutes, develop the classical and statistical thermodynamic principles needed to quantify them, discuss some quantitative details of the Donnan equilibrium, and outline some applications. 

The combined effects of electroneutrality and the Donnan equilibrium permits us to evaluate the distribution of simple ions across a semipermeable membrane. If electrodes reversible to either the M+ or the X ions were introduced to both sides of the membrane, there would be no potential difference between them the system is at equilibrium and the ion activity is the same in both compartments. However, if calomel reference electrodes are also introduced into each compartment in addition to the reversible electrodes, then a potential difference will be observed between the two reference electrodes. This potential, called the membrane potential, reflects the fact that the membrane must be polarized because of the macroions on one side. It might be noted that polarized membranes abound in living systems, but the polarization there is thought to be primarily due to differences in ionic mobilities for different solutes rather than the sort of mechanism that we have been discussing. We return to a more detailed discussion of the electrochemistry of colloidal systems in Chapter 11. 

Note that this treatment inherently takes into account the effect of the Donnan equilibrium. The osmotic coefficient obtained therefore is that of the polyelectrolyte with no further Donnan correction term being necessary. 

Mapleson WW (1987) Computation of the effect of Donnan equilibrium on pH in equilibrium dialysis. J Pharmacol Methods 17(3) 231-242... 

Sep. 5,1870, Colombo, Ceylon (British Empire), now Sri Lanka - Dec. 16,1956, Canterbury, Kent, UK). Donnan was a British chemist who greatly contributed to the development of colloid chemistry, physical chemistry, and electrochemistry [i—iii]. In different periods of his life, he was working with van t - Hoff, -> Ostwald, F. W., and Ramsay. In electrochemistry, he studied (1911) the electrical potential set-up at a semipermeable membrane between two electrolytes [iv], an effect of great importance in living cells [v], Donnan is mostly remembered for his theory of membrane equilibrium, known as - Donnan equilibrium. This equilibrium results in the formation of - Donnan potential across a membrane. 

The values for g obtained from Equation 4.22 do not seem to be very different from those obtained from Equation 4.20, as shown in Table 4.1 and Figure 4.3a. It is easy to see that g must be equal to /2 as Os tends to zero by expanding the exponentials in the linear approximation (Debye limit). Naturally, Equation 4.15 gives us i = 1 in this limit, as an uncharged layer does not expel co-ions and salt is equally distributed between regions I and II. However, as shown in Table 4.2 and Figure 4.3b, the predicted salt-fractionation effect obtained by substituting Equation 4.22 into Equation 4.15 is markedly different from the Donnan equilibrium. 

Donnan dialysis is a membrane separation process that uses ion-selective membranes to prevent the flow of certain ions from one solution to another. A schematic of the process is presented in Figure 29.8. When a salt solution is separated from its corresponding acid by a cation-exchange membrane, the anions are excluded from the membrane, whUe the cations are redistributed across the membrane to attain Donnan equilibrium. By changing the salt solution periodically, it would be possible to shift the equilibrium favorably to effect simultaneous neutralization of acid on one side of the membrane (feed compartment) and acid recovery on the other side (receiver compartment). The driving force for ion migration is the chemical potential gradient for the cation across the membranes. 

In spite of the partial success in theoretical description, we believe that more realistic models are needed for the theory to have a predicting power. For example, measurements usually take place in the presence of a large excess of simple electrolyte. The electrolyte present is often a buffer, a rather complicated mixture (difficult to model perse) with several ionic species present in the system. Note that many effects in protein solutions are salt specific. Yet, most of the theories subsume all the effect of the electrolyte present into a single parameter, the Debye screening parameter n. In the case of the Donnan equilibrium we measure the subtle difference between the osmotic pressures across a membrane permeable to small ions and water but not to proteins. We believe that an accurate theoretical description of protein solutions can only be built based on the models which take into account hydration effects. 

If, however, a carrier-mediated transport membrane containing charged species — in the form of either mobile ions or fixed sites — were placed between two electrolytic mixtures, significant Donnan effects could be expected. For example, consider a membrane in which the carrier is a counterion to the permeant. The permeant would be expected to be preferentially included in the membrane phase. If significant inclusion were to occur, the use of simple first-kind boundary conditions would be inappropriate and could lead to underestimation of flux. On the other hand, if the permeant and carrier were coions, the permeant could be excluded and failure to account for exclusion could lead to overprediction of flux. Further complications would arise if the complex were charged or if other charged species were present, since the net charge density inside the membrane defines Donnan equilibrium conditions. 

The Donnan equilibrium theory implies that dilution of a clay/water system containing monovalent and divalent cations displaces the equilibrium in such a manner that the absorption of divalent ions increases, whereas the absorption of monovalent ions decreases. The ionic charge is not the only determining factor in the absorption effect. Factors such as temperature, pH, and specific ions also play important roles. Hydration energy, which appears to be one of the most important factors for the absorption and fixation of cations, displaces the ionic equilibria in a manner opposing the Donnan equilibrium theory. According to Sawhney (1972), "cations with low hydration energy such as Ca, Mg and Sr, produce expanded interlayers and are not fixed". 

Calcium Transport Systems. Because intracellular Ca " " has an enormous range of effects in both excitable and quiescent cells, transport systems that affect the level of cytoplasmic Ca + have been receiving increasing attention. Intracellular Ca + concentrations are on the order of 1 X 10 to 1 X 10 M if the Donnan equilibrium were solely responsible for the gradient of intra- to extracellular Ca concentrations, the level within the cell would be many orders of magnitude higher. Hence, the presence of transport systems is very important for the maintenance of the observed cytoplasmic Ca concentrations. 

Under certain circumstances, the establishment of the Donnan equilibrium can lead to other effects, such as changes in pH. Suppose, for example, that an electrolyte NaP (where P is a large anion) is on one side of a membrane, with pure water on the other. The Na" ions will tend to cross the membrane and, to restore the electrostatic balance, H ions will cross in the other direction, leaving an excess of OH " ions. Dissociation of water molecules will occur as required. There will thus be a lowering of pH on the NaP side of the membrane, and a raising on the other side. 

These are both instances of what is known as active transport. Care must be taken to distinguish true active transport from certain other effects. For example, the concentration of Mg ions is much greater in most cells than in the surrounding fluid, This does not imply active transport, since the Mg " ions are strongly bound in the cells, a process which reduces the effective concentration of the ions and so disturbs the equilibrium. Another effect which can give a false impression of active transport is the Donnan equilibrium discussed in Section 7.6. We saw there that there can be an abnormal distribution of ions across a membrane because of the presence of large cations or anions to which the membrane is impermeable. 

Effect of Electrolyte, Emulsions stabilized with hydrophobically modified poly(acrylic acid) are sensitive to electrolytes. Upon contact with a brine solution, emulsion stability is immediately lost, and rapid coalescence of the oil droplets ensues (Figure 23). This instability can be understood by consideration of the Donnan equilibrium of counterions in polyelectrolytes (discussed earlier in this chapter). Addition of salt causes collapses of the polyelectrolyte microgels that are adsorbed at the oil-water interface. Shrinkage of the microgels could conceivably lead to immediate loss of stability, as depicted schematically in Figure 24. 

Donnan Equilibrium and Electroneutrality Effects for charged membranes are based on the fact that charged functional groups attract counter-ions. This leads to a deficit of co-ions in the membrane and the development of Donnan potential. The membrane rejection increases with increased membrane charge and ion valence. This principle has been incorporated into the extended Nemst-Planck equation, as described in the NF section. This effect is responsible for the shift in pH, which is often observed in RO. Chloride passes through the membrane, while calcium is retained, which means that water has to shift its dissociation equilibrium to provide protons to balance the permeating anions (Mallevialle et al. (1996)). 

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