Membrane potential diffusion

When paint films are immersed in water or solutions of electrolytes they acquire a charge. The existence of this charge is based on the following evidence. In a junction between two solutions of potassium chloride, 0 -1 N and 0 01 N, there will be no diffusion potential, because the transport numbers of both the and the Cl" ions are almost 0-5. If the solutions are separated by a membrane equally permeable to both ions, there will still be no diffusion potential, but if the membrane is more permeable to one ion than to the other a diffusion potential will arise it can be calculated from the Nernst equation that when the membrane is permeable to only one ion, the potential will have the value of 56 mV. 

It is easy to measure the potential of this system and it has been found that membranes of polystyrene, linseed oil and a tung oil varnish yielded diffusion potentials of 43-53 mV, the dilute solution being always positive to the concentrated. Similar results have been obtained with films of nitrocellulose, cellulose acetate , alkyd resin and polyvinyl chloride . 

Concentration of Electrolyte Myer and Sievers"" applied the Donnan equilibrium to charged membranes and developed a quantitative theory of membrane selectivity. They expressed this selectivity in terms of a selectivity constant, which they defined as the concentration of fixed ions attached to the polymer network. They determined the selectivity constant of a number of membranes by the measurement of diffusion potentials. Nasini etal and Kumins"" extended the measurements to paint and varnish films. 

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. 

If a diffusion potential occurs inside the membrane, the relation between mass transport and electrochemical potential gradient — as the driving force for the diffusion of ions — has to be examined in more detail. This can be done by three different approaches ... 

According to the nine assumptions and approach a) for the diffusion potential inside the membrane the selectivity coefficient Kg , can be expressed by other parameters. Table 3 shows the results for the different kinds of membranes 66). In some cases the expressions for K J i contain ion-mobilities inside the membrane... 

We shall write (p) and (q) for the membrane surface layers adjacent to solutions (a) and (p), respectively. Using the equations reported in Section 5.3, we can calculate the ionic concentrations in these layers as well as the potential differences and between the phases. According to Eq. (5.1), the expression for the total membrane potential additionally contains the diffusion potential within the membrane itself, where equilibrium is lacking. Its value can be found with the equations of Section 5.2 when the values of and have first been calculated. 

Since the membrane is permeable for cations but not for the anions A, it should intrinsically contain anions R . When these are fixed, their concentration, Cr, will remain the same everywhere. Hence in layers ( J,) and (ii) the overall cation concentration should also be the same, and the diffusion potential (which is caused by a possible difference in cation mobilities) is extremely small. In the left-hand part of the membrane system, the concentration of cations M + in each of the phases is equal to the given (invariant) concentration of anions A or, respectively the potential difference between the phases is determined, according to Eq. (5.10), by the cation concentration ratio. The right-hand part of the membrane system corresponds to the system (5.22), where phase (P) now takes the place of phase (a), and phase (rj) takes that of phase (y). As a result, we obtain for the membrane potential. 

A diffusion potential (p can develop in the membrane since in the case being considered, it contains two types of mobile ion. However, this potential is small. 

An ion-selective electrode contains a semipermeable membrane in contact with a reference solution on one side and a sample solution on the other side. The membrane will be permeable to either cations or anions and the transport of counter ions will be restricted by the membrane, and thus a separation of charge occurs at the interface. This is the Donnan potential (Fig. 5 a) and contains the analytically useful information. A concentration gradient will promote diffusion of ions within the membrane. If the ionic mobilities vary greatly, a charge separation occurs (Fig. 5 b) giving rise to what is called a diffusion potential. 

Apart from the necessity of excluding interferences from any diffusion potential, normal potentiometry requires accurate determination of the emf, i.e., without any perceptible drawing off of current from the cell therefore, usually one uses the so-called Poggendorff method for exact compensation measurement the later application of high-resistance glass and other membrane electrodes has led to the modern commercial high-impedance pH and PI meters with high amplification in order to detect the emf null point in the balanced system. 

A permeable membrane, which merely serves to prevent rapid mixing of components within solutions on both sides of the membrane in principle, no potential occurs unless a diffusion potential occurs. 

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. 

In coulometry these exchange membranes are often used to prevent the electrolyte around the counter electrode from entering the titration compartment (see coulometry, Section 3.5). However, with membrane electrodes the ion-exchange activity is confined to the membrane surfaces in direct contact with the solutions on both sides, whilst the internal region must remain impermeable to the solution and its ions, which excludes a diffusion potential nevertheless, the material must facilitate some ionic charge transport internally in order to permit measurement of the total potential across the membrane. The specific way in which all these requirements are fulfilled in practice depends on the type of membrane electrode under consideration. 

We assume that between the membrane phase (n) and the solutions (S and S0) no diffusion potentials occur, i.e., the potential differences (n/S) and 0(n/So) are merely caused by ion-exchange activity. Further, all phases are considered to be homogeneous so that is constant within the membrane and also pi = plQ within the solutions. Let us at first consider the simple system of selective indication of an univalent anion A in the presence of an interfering univalent anion B. Here we obtain the following exchange equilibrium ... 

PBP model considers the membrane potential as a sum of the potentials formed at the membrane-solution interfaces (phase boundary potentials), and generally neglects any diffusion potential within the membrane ... 

The acid-base chemistry of nicotine is now well known and investigations have shown that nicotine in tobacco smoke or in smokeless tobacco prodncts can exist in pH-dependent protonated or nnprotonated free-base forms. In tobacco smoke, only the free-base form can volatilize readily from the smoke particnlate matter to the gas phase, with rapid deposition in the respiratory tract. Using volatility-based analytical measurements, the fraction of nicotine present as the free-base form can be quantitatively determined. For smokeless tobacco products, the situation differs because the tobacco is placed directly in the oral cavity. Hence, the pH of smokeless tobacco prodncts can be measured directly to yield information on the fraction of nicotine available in the nnprotonated free-base form. It is important to characterize the fraction of total nicotine in its conjugate acid-base states as this dramatically affects nicotine bioavailability, because the protonated form is hydrophilic while the nnprotonated free-base form is lipophilic and thus readily diffuses across membranes (Armitage and Turner 1970 Schievelbein et al. 1973). As drug delivery rate and addiction potential are linked (Henningfield and Keenan 1993), increases in delivery rate due to increased free-base levels affect the addiction potential. 

Allcock et al. also have investigated the use of phosphonated polyphosphazenes as potential membrane materials for use in direct methanol fuel cells (Figure A2) Membranes were found to have lEC values between 1.17 and 1.43 mequiv/g and proton conductivities between 10 and 10 S/cm. Methanol diffusion coefficients for these membranes were found to be at least 12 times lower than that for Nafion 117 and 6 times lower than that for a cross-linked sulfonated polyphosphazene membrane. 

A further important step forward was the work of Nemst [73, 74] and Planck [81, 82] on transport in electrolyte solutions. Here the concept of the diffusion potential was defined diffusion potential arises when the mobihties of the electrically-charged components of the electrolyte are different and is important both for description of conditions within membranes as well as for quantitative determination of the liquid-junction potential. 

This chapter is based on the thermodynamic theory of membrane potentials and kinetic effects will be considered only in relation to diffusion potentials in the membrane. The ISE membrane in the presence of an interferent can be thought of as analogous to a corroding electrode [46a] at which chemically different charge transfer reactions proceed [15, 16]. Then the characteristics of the ISE potentials can be obtained using polarization curves for electrolysis at the boundary between two immiscible electrolyte solutions [44[Pg.35]

First consider the system in which no diffusion potential is formed in the membrane. The membrane potential is then determined by the conditions at the membrane/aqueous electrolyte solution boundary. In the simplest situation, a salt of a monovalent ion-exchanger ion, anion A", with monovalent determinand cation J is dissolved in the membrane. In order for this system to be the basis for a usable ISE with Nemstian response to the determinand ion in a sufficiently broad activity interval, it is necessary that the distribution coefficient kj be... 

Consider a test solution containing both determinand and interferent K, neither of which fonns an ion-pair with ion-exchanger ion A". The mobilities of and K are identical, so that no diffusion potential is fonned in the membrane. The effect of the interferent is based on the fact that it may replace the determinand in the membrane phase as a result of the exchange reaction... 

A further system is characterized by the determinand and interferent having different charge numbers, for example +1 and +2. Neither ion pairs nor diffusion potential are formed in the membrane. The exchange reaction is then... 

Consider a system in which the analyte contains both determinand J and interferent K, and where a diffusion potential is formed in the membrane as a result of their different mobilities. A simplification that provides the basic characteristics of the membrane potential employs the Henderson equation for calculation of the diffusion potential in the membrane. According to (2.1.9) the membrane potential is separated into three parts, two potential differences between the membrane and the solutions A 0 and Aq with which it is ip contact, and the diffusion potential inside the membrane... 

Finally, the result of a theoretical treatment of a similar system with almost complete association in the membrane will be given without calculations [66,67]. The diffusion potential in the membrane depends not only on electrodiffusion of J, and A but also on diffusion of associates JA and KA. The resultant formula for the membrane potential is... 

In conclusion, it should be mentioned that extraction parameters (the equilibrium constants of exchange reactions and ion-pair stabilities) were introduced into the theory of ion-selective electrodes in [2, 31,33, 34, 35,69]. The theory of ISEs with a liquid membrane and a diffusion potential in the membrane was extended by Buck etal. [11, 13, 14, 73, 74] and Morf [54]. 

Because a similar equation holds for the membrane/solution 2 phase boundary and no diffusion potential is formed within the membrane, (3.2.3) is valid for the membrane potential. 

As the complexes of various ions with a single ionophore usually have the same structure (they are isosteric [17, 23, 25]), their mobihties in the membrane are the same and consequently no diffusion potential is formed in the membrane. The selectivity coefficient is then (see p. 35) ... 

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