Donnan Potential Measurement

The Donnan potentials contain the individual ionic activities and cannot be measured by using a purely thermodynamic procedure. In the concentration range where the Debye-Hiickel limiting law is valid, the ionic activities can be replaced by the mean activities. 

When a constant ionic strength of the test solution is maintained and the reference electrode liquid bridge is filled with a solution of a salt whose cation and anion have similar mobilities (for example solutions of KCl, KNO3 and NH4NO3), the liquid-junction potential is reasonably constant (cf. p. 24-5). However, problems may be encountered in measurements on suspensions (for example in blood or in soil extracts). The potential difference measured in the suspension may be very different from that obtained in the supernatant or in the filtrate. This phenomenon is called the suspension (Pallmann) effect [110] The appearance of the Pallmann effect depends on the position of the reference electrode, but not on that of ISE [65] (i.e. there is a difference between the potentials obtained with the reference electrode in the suspension and in the supernatant). This effect has not been satisfactorily explained it may be caused by the formation of an anomalous liquid-junction or Donnan potential. It... 

The potential of each channel may be composed of two potentials. One is an oxidation-reduction potential generating at the boundary surface between the Ag electrode and the lipid membrane. The other is a Donnan potential at the boundary between the lipid membrane and the aqueous medium or more generally a Gouy-Chapman electrical double-layer potential formed in the aqueous medium [24]. Figure 7 shows a potential profile near the lipid membrane. The oxidation-reduction potential would not be affected by the outer solution in short time, because the lipid membrane had low permeability for water. Then the measured potential change by application of the taste solution is mainly due to the change in the surface electrical potential. 

The equivalent circuit corresponding to this interface is shown in Fig. 6.1b. The charge-transfer resistances for the exchange of sodium and chloride ions are very low, but the charge-transfer resistance for the polyanion is infinitely high. There is no direct sensing application for this type of interface. However, it is relevant for the entire electrochemical cell and to many practical potentiometric measurements. Thus if we want to measure the activity of an ion with the ion-selective electrode it must be placed in the same compartment as the reference electrode. Otherwise, the Donnan potential across the membrane will appear in the cell voltage and will distort the overall result. 

The membrane perm-selectivity (y.m) is defined as the ratio between the actual and theoretical transfer of counterions through any IEM. It can be simply determined as the percentage ratio between the experimental and theoretical Donnan potential differences as measured using a test system consisting of two cells provided with calomel electrodes and filled with well-mixed standardized aqueous solutions of KC1 (at 0.1 and 0.5 kmol/m3), kept at 25 °C, and separated by the IEM sample under testing. 

As a result of a stepwise increase in electrolyte concentration, the Donnan potentials of the protein layer will diminish, thereby also diminishing the potential of the membrane itself versus the bulk solution. Furthermore, protons will be released by negatively charged protein molecules or taken up hy positively charged protein molecules because the dissociation is changed with the ion concentration. The underlying ISFET measures the change in the potential of the membrane with respect to the bulk solution as well as the pH effect of the protons released or taken up. The pH effect of the protons is responsible for almost the entire response on an ion step. 

The double-layer model of the membrane consists of many particles (assume a diameter of 0.1 gm) that are impenetrable for solution and carry a surface charge. Electrical double layers exist around each particle, and because the dimensions of the membrane pores are of the same order as the double layers around the particles, double layers exist throughout the membrane pores. The potential measured by the underlying ISFET, with respect to the bulk potential, is on one hand determined by the mean pore potential, which is the net result of the contribution of all surface potentials of the charged particles, and on the other hand by the pH at the membrane-1 SFET interface. The measured ISFET response in equilibrium is therefore the same as that of an ISFET without a membrane, because the distribution of the protons between membrane and solution results in a pH difference, which compensates the mean membrane potential (this is the same mechanism as in the Donnan model). The relation between the surface charge on the particles a (C/cm2) and the surface potential jx of each particle is given by... 

First, assume that the surface charge on the membrane particles does not interact with the mobile protons (no proton release or uptake). An ion step will result in an increase in the double-layer capacitances of the particles and consequently in a decrease of the surface potentials fr, because the charge densities remain constant. The ISFET will measure a transient change in the mean pore potential. As a result of the potential changes, an ion redistribution will take place and the equilibrium situation is re-established. The theoretical maximum ion step response is the change in the mean pore potential. This is comparable with the Donnan model where the theoretical maximum is determined by the change in the Donnan potential at the membrane solution interface. 

In addition to the repulsive part of the potential given by Eq. (4), a short-range attraction between the macroions may also be present. This attraction is due to the van der Waals forces [17,18], and can be modelled in different ways. The OCF model can be solved for the macroion-macroion pair-distribution function and thermodynamic properties using various statistical-mechanical theories. One of the most popular is the mean spherical approximation (MSA) [40], The OCF model can be applied to the analysis of small-angle scattering data, where the results are obtained in terms of the macroion-macroion structure factor [35], The same approach can also be applied to thermodynamic properties Kalyuzhnyi and coworkers [41] analyzed Donnan pressure measurements for various globular proteins using a modification of this model which permits the protein molecules to form dimers (see Sec. 7). 

In the present chapter, the relationship between the electrode potential and the activity of the solution components in the cell is examined in detail. The connection between the Galvani potential difference at the electrode solution interface and the electrode potential on the standard redox scale is discussed. This leads to an examination of the extrathermodynamic assumption which allows one to define an absolute electrode potential. Ion transfer processes at the membrane solution interface are then examined. Diffusion potentials within the membrane and the Donnan potentials at the interface are illustrated for both liquid and solid state membranes. Specific ion electrodes are described, and their various modes of sensing ion activities in an analyte solution discussed. The structure and type of membrane used are considered with respect to its selectivity to a particular ion over other ions. At the end of the chapter, emphasis is placed on the definition of pH and its measurement using the glass electrode. 

Higa M, Tanioka A, Kira A. A novel measurement method of Donnan potential at an interface between a charged membrane and mixed salt solution. J Membr Sci 1998 140 213-221. 

Higa et al. (1998) measured the Donnan potential at a membrane interface. They found that the effective charge density was the same for all ions tested. The potential in the system was determined by the counter-ion with the highest valence. Takagi et al (1996) determined Donnan potential from zeta potential. Donnan potential was vety large compared to zeta potential, due to the low pore volume of RO membranes. The effective charge was due to chloride adsorption, as the CA membrane possessed no fixed charge. Adsorption on the surface and in pores was identical. 

Therefore, the measurable Volta potential difference A p°f includes information on the corrosion potential at the buried metal/electrolyte interface only if the Donnan potential is known or small. Usually the Donnan potential is significant only for polymers with a high density of fixed charges (e.g., in ion-exchange membranes), as polymers with fixed cationic functional groups will exchange exclusively anions, and vice versa [27]. Adhesives or lacquers used for corrosion protec-... 

Brooks and coworkers [136,141] measured drop electrophoretic mobilities in ATPSs. They were surprised to discover that the sign of the droplet mobilities was opposite to that predicted from the phosphate partition and the Donnan potential. They also found mobility to be directly proportional to drop radius, which is a contradiction of standard colloid electrokinetic theory [144]. Levine [140] and Brooks et al. [141] hypothesized that a dipole potential at the phase boundary oriented in a way that reverses the potential gradient locally is responsible for the paradox of the sign of electrophoretic mobilities of ATPS droplets. 

From electric potential measurements Loeb could derive the pu of the liquid. The results were in conformity with the Donnan equilibrium. From the experimental data the osmotic pressure difference could be calculated. Plotted against the pH of the outer liquid, the maximum value of A coincided with the pH corresponding to maximum swelling, as shown by the following selected figures. 

Donnan dialysis In Donnan dialysis, a cation-exchange membrane separates the donor and receptor solutions. Cationic metal species are transported across the membrane driven by the negative electrostatic potential (the Donnan potential) across the membrane, until equilibrium is achieved. Matching of the ionic strengths of donor and acceptor solutions is necessary. Since cationic species exchange readily compared to neutral and anionic species, it is claimed that the measurement more closely relates to the free metal ion. 

The ISE membrane thus behaves as a permselective membrane and the signal measured is given by the Donnan potential, which depends on the selectivity of the interfacial interaction, given by the equilibrium constants of the interactions of the membrane with the analyte(s) and interferents. Moreover, a diffusion potential develops across the membrane, as charge is passed on the passage of ions between the solution and the membrane. 

The osmotic pressure measurements of micellar solutions has shown that the Donnan potential at the micelle-water interface varies linearly with the added electrolyte concentration, as expected from theory [2,3,13,23]. 

Summarizing it is demonstrated that variation in the Donnan potential as a function of the electrolyte concentration is experimentally accessible as long as the electrolyte concentration remains below the ion exchanger s fixed-charge concentration. The Volta-potential measurements give in addition information on a surface dipole layer that forms on the membrane surface when it is removed from the electrolyte. 

The results of Volta-potential measurements on the emersed PMPy-coated electrodes are summarized in Fig. 3.22, which presents the results at various electrode potentials derived from the preceding measurements. The increasingly positive slope indicates that the polymer assumes the state of an anion exchanger as it is oxidized. In Fig. 3.23 the expected Donnan potentials were calculated with Eqn. 18 the polaron/bipolaron density, obtained by integrating the oxidation current in Fig. 3.21, was assumed to constitute the fixed-charge density c. At the electrolyte concentration = 0.1 M, the calculated and experimental values (see Fig. 3.22) were matched, and at lower concentrations, theoretical and experimental values were plotted. The agreement can be considered quite good. Based on this analysis. Fig. 

The membranes used in ion-selective electrodes separate two different electrolytes and are not equally permeable to all kinds of ions. At the interface between the two electrolytes, different events contribnte to the measured membrane potential. First, a diffusion potential arises from differences in mobility and concentration of ions in contact at the interface, as seen in liquid junctions. Second, a Donnan potential arises when the membrane completely prevents the diffnsion of at least one species from solution to the other. Third, the exchange equilibria between the electrolyte and the membrane interface must also be considered to adequately describe the membrane potential of ion-selective electrodes with solid or liquid electrolyte manbranes. 

---