Potential

POTENTIAL. The quantity of any kind of energy can be expressed as the product of two different quantities, one of which characterizes the "level of energy" and determines the direction in which its transition must occur; for example, a heavy body can release energy only if it falls, i.e., transitions to a lower level. This quantity, expressing the level of energy (height of elevation of a heavy body, pressure of compressed gas, temperature), is designated as the intensity factor, in distinction from the second quantity necessary for characterizing the total amount of energy—the capacity factor. In the field of electricity, the intensity factor is the electric P., which expresses the work that must be performed to transfer an electric charge equal to one unit from a given point of an electric field to an infinitely large distance. The magnitude of the electric charge equals the product of the capacity of the charged body and its P., but the transition of electricity from one body to another is entirely determined by the existing difference of P. between them. In a state of equilibrium, electricity at all points of a conductor has the same P. Difference of potential at the boundary of phases. Carriers of electric charge are ions or, in a metallic conductor, free electrons, and any difference of P. must necessarily be accompanied by their uneven distribution. In a homogeneous medium, any unevenness in the distribution of ions is quickly smoothed out and equalized by diffusion. Only at the boundary of two different contacting phases does a stable difference of P. arise. The difference of P. at boundary surfaces can have very different origins. Its principal types are as follows. Electrode P. If a metal is immersed in a solution, a difference of P. arises at the boundary between them; the theory of this phenomenon was developed by Nernst. Metals have the peculiarity that their atoms dissolve only in the form of positively charged ions. Passing into the solution, they therefore leave on the electrode a negative charge equal in magnitude to the sum of the positive charges they carry. Of course, this electric charge, attracting the metallic ions going into the solution, prevents their further dissolution in analytically detectable quantities. Only the magnitude of the negative electric P. acquired by the electrode is therefore an indicator of the degree of solubility of the given metal: the higher it is, the greater this solubility. Nernst gave it the name "elasticity of dissolution" of the metal. It has the smallest magnitude in noble metals and rapidly increases in the Volta series: platinum, silver, mercury, copper, lead, nickel, zinc, manganese. When two different metallic electrodes are immersed in a solution, for example copper and zinc in an acid solution, the more soluble metal (standing further in the given series) acquires a higher negative P. If copper and zinc are connected by a metallic conductor, an electric current will flow in the latter from copper to zinc, smoothing out the difference of P. The latter, however, will immediately be restored, since from the zinc electrode a new quantity of ions, no longer held back by electrostatic attraction, will pass into the solution. The displaced hydrogen ions of the acid are released on the copper electrode, giving it their charge and giving rise to a galvanic current. In such a simplest galvanic cell, due to the change in the chemical composition of the solution at the electrodes (polarization), the current has a non-constant strength, and the quantitative relationships are extremely complicated. Of particular interest are the differences of P. obtained when the same metal is immersed in two different solutions. If the solution already contains, in the form of some electrolyte, free ions of the given metal, then its tendency to pass into the solution (and consequently the negative P. it acquires) will be weakened to the greater extent the higher the concentration of these ions. At a certain, sufficiently high concentration of metal ions, their osmotic pressure completely balances the elasticity of dissolution of the metal; at an even higher concentration, the ions are deposited on the metallic electrode, giving it a positive P. If S-elasticity of dissolution of the given metal, s-concentration of its ions in the solution, then the electrode P. equals: π = RT ln - , s' where R-gas constant, T-absolute temperature and In--sign of natural logarithm. The described relationship makes it possible to construct a special form of galvanic circuit—a concentration circuit. It consists of two identical metallic electrodes immersed in two contacting solutions containing the salt of the same metal in different concentrations. If both metallic electrodes are connected, a current will flow in the external circuit from the electrode with a higher concentration of metal ions to the electrode immersed in the more dilute solution (which is more electronegative). Due to such equalization of the difference of P. existing at each electrode, the ionic equilibrium on them will be disturbed. In the more dilute solution, metal ions, no longer held by the attraction of the electrode, will pass into the solution, while in the more concentrated solution the increase in negative P. causes the deposition of an equal quantity of ions on the electrode. A galvanic current in such a circuit will flow until complete equalization of concentrations at both electrodes. Therefore, the difference of P. between the electrodes of a concentration circuit is expressed by the same formula as the osmotic work (see Osmotic pressure) necessary to create such a difference of concentrations. If s₁ and s₂-concentration in both solutions, then the difference of P., as established by Nernst, equals π=RT\n°±

(1) Using this formula, it is possible by measuring the electrode difference of P. to determine the concentration of metal ions in one of the solutions, if it is known in the other. This is the basis of electrometric measurement of ion concentrations, which has found particularly wide application for determining the concentration of hydrogen ions (see Gas circuit). Me phase boundary potentials. Significant differences of P. can also arise on non-metallic surfaces. An example of such a surface can be the boundary of water and any liquid not miscible with it, conventionally called "oil." The distribution of dissolved substances between two liquids is determined by the distribution coefficient characteristic of each substance. In the case of a strongly dissociated electrolyte, which actually represents a mixture of two different ions, each ion must have its own distribution coefficient, and as a rule these distribution coefficients do not coincide: in one phase cations prove to be more soluble, in the other-anions. As a result, the boundary surface of the first acquires a positive, the second-a negative charge. Of course, this negative P. quickly prevents any noticeable separation of oppositely charged ions. Indeed, if for example the non-aqueous phase, due to excess content of cations, acquires a positive charge, the latter will hinder further dissolution of cations and, on the contrary, will promote additional absorption of anions. Thanks to this, in the bulk of each phase the total quantity of cations proves equal to the sum of anions, and the actual content of the electrolyte represents the average between the true solubility of its cation and anion. Only near the phase boundary does a difference in concentration of oppositely charged ions arise, creating a difference of P.—the more significant, the greater the difference in ionic solubilities. The magnitude of this boundary P. can be calculated as follows. Let in a two-phase system water-oil some electrolyte, for example AgN0₃, be dissolved, distributing between both liquids. Obviously equilibrium will not be disturbed if identical silver electrodes are inserted into both solutions and connected between them. In this case a system is obtained: water s_a AgN0₃ oil s_b AgN0₃ ^g It is in equilibrium and therefore cannot give any current. Meanwhile, at the boundary of the metallic electrodes with the solution of the corresponding ions, the electrode P. described above arise. If s_a and s_b-concentrations of silver ions in the aqueous and non-aqueous phases, S_a and S_b-elasticities of dissolution of silver in these two liquids, then the electrode P. equal: π₁=-RT ln^ and π₂=RT ln^. If the difference of P. between both metallic electrodes nevertheless proves equal to zero, this can depend only on the fact that the third, boundary difference of P. (at the phase boundary surface) is equal in absolute value but opposite in sign to the difference of electrode potentials π₁ - π₂: S_b s_a s_b π = RT ln^- RT ln^= RT In ^ + RT \n% ^Sbs_aS_bs_a 1.since - is a constant quantity, then π " the second member of this equation represents for a given ion some constant K. Thus

^v Thus, the boundary potential depends on the ratio of the ion concentrations common to both contacting phases. With a suitable combination of two different boundary interfacial potentials, a system can be obtained which, in contrast to the one just described, will not be in complete equilibrium and will give an electric current when closed. Let, for example, the same non-aqueous phase on the other side border a second aqueous solution of a different electrolytic composition. The difference in potential between them will be expressed by a similar formula: π' = RT ln-" + K'. Ч The constants K and K' cannot be determined directly. However, if they refer to the same ion, they have the same value in both cases and are eliminated upon subtraction. Thus, in the presence of at least one ion common to the entire system, measuring its concentration in different parts of the system allows one to calculate the prevailing potential difference π~π'. Such "oil chains", in which the non-aqueous phase forms a layer between two aqueous solutions of electrolytes, have been studied in detail by Beutner. In the "glass electrode" of Haber and Klemensiewicz, serving to measure the concentration of hydrogen ions, the role of the "oil" is played by the thinnest glass plate. Diffusion potential. The potentials arising at the boundary of two phases due to the unequal dissolution of various ions in them have been considered above. The unequal diffusion rate of ions can also serve as a source of potential difference. It arises at the boundary of a concentrated electrolyte solution with a more dilute solution of the same electrolyte or with pure water. The dilute solution takes on the sign of the charge characteristic of the more mobile ion, while in the concentrated solution there is some excess of the slower ion. If the electrolytic mobility (conductivity) of the cation is denoted by u and that of the anion by v, and the concentration of the electrolyte in both aqueous solutions by c₁ and c₂, then for the diffusion potential difference at their boundary the following formula can be derived: ~~RT ln^C2- U + VC1 (3) Obviously, it becomes zero only in the case where both ions have the same mobility. In the concentration cell, in addition to the electrode potentials considered above, a diffusion potential difference must also arise at the boundary of both contacting solutions, which significantly complicates theoretical calculations. To eliminate it, the following method is usually used in practice: between both electrolyte solutions, a concentrated KCl solution is introduced, which does not give a measurable diffusion potential, since both its ions have approximately the same mobility. Membrane potential. Under certain conditions, however, the diffusion potential cannot be eliminated, but on the contrary, can be significantly strengthened. This is achieved when a membrane with unequal permeability for both ions of the electrolyte is introduced between both electrolyte solutions. Such semi-permeable membranes, while freely passing some ions, can more or less significantly retard others, whose mobility is thus reduced, and the difference u-v (in formula 3) correspondingly increased. In the limiting case, one of the ions is completely retarded, its rate of movement in the membrane becomes zero, and consequently u + v equals ± 1. The formula for the diffusion potential then transforms into the following formula for the membrane potential, in which c₁ and c₂ are the concentrations of the ion passing through the membrane in both solutions: π = RT ln^c1/c2.

(4) As will be described below, depending on the electrokinetic potential of the membrane, the latter can retain ions of one sign, more or less easily passing ions of the opposite sign. Another reason causing unequal permeability of the membrane for different ions may be the size of the ion. In particular, many membranes that freely pass any crystalloids retain colloidal particles. Therefore, in the case of a colloidal electrolyte, an excess of colloidal ions is obtained on one side of the membrane, and of oppositely charged crystalloids on the other. In all these cases, the result is the emergence of a difference in potential on both sides of the membrane. If, in addition to the electrolyte, one of the ions of which is retained by the membrane, the solution contains an electrolyte that passes freely through it, it has a significant effect on both the membrane equilibrium of diffusing ions and the membrane potential caused by it. The resulting ratios, which have cardinal importance for the behavior of colloids, were studied by Donnan (see Donnan equilibrium). Oxidation-reduction potentials. A completely special group is formed by electrical potentials arising as a result of chemical reactions. In particular, sources of potential differences are oxidation-reduction reactions associated with the transfer of electric charges from one atom to another. According to the modern theory of valence, during oxidation, electrons are removed from the atom being oxidized, during reduction, electrons are added (see Oxidation). This is most clearly manifested in those cases where oxidation-reduction reactions are directly expressed in a change in the valence and charge of the oxidized or reduced ion, for example, in the oxidation of iodide ion to elementary iodine (during oxidation of KJ) or of divalent iron to trivalent (transition of FeCl₂ to FeCl₃). As is known, metals have the ability to accept and donate free electrons. Therefore, a metal electrode immersed in an oxidation-reduction system acquires a positive charge in the case of the oxidative direction of the reaction (due to the removal of electrons by the substance being oxidized), and a negative charge in the case of the reductive. The stronger the oxidizing agent of a given system, the higher the positive potential acquired by the electrode in the equilibrium state. The same is true with respect to the negative potential and the reducing ability of the system. Therefore, the magnitude of the potential can serve as an exact measure of the oxidation-reduction properties of a reversible system. Potentials of biological systems. In living organisms, significant potential differences are often observed, showing a close dependence on the physiological state and vital activity of the biological surface: the potential difference between normal and damaged cell surfaces, between active and resting parts of the cell (see Bioelectric currents, Animal electricity). Their explanation was impossible until non-metallic galvanic circuits were discovered, giving sufficiently significant potential differences. In a living cell, the possibility arises of both interfacial boundary and membrane potentials. According to the first conception, developed by Betner, living cells represent "oil circuits," with the role of "oil" played by non-aqueous phases of the cell, in particular lipoids. In this case, according to the lipoid theory of cell permeability, the lipoid phase should form a thin layer covering the protoplasm and separating it from the external solution. Differences in the composition and concentration of electrolytes in the protoplasm and in the external fluid bathing the cell should create a significant potential difference on both sides of the lipoid shell. This potential difference is measured directly when the cell is damaged and its shell is partially destroyed. Thus, for example, if non-polarizing electrodes are connected (with identical NaCl solutions) on one side with an undamaged cell surface, and on the other with exposed (as a result of damage to the shell) protoplasm, the following circuit is obtained: NaCl solution—Lipoid shell—Protoplasm—NaCl solution. The galvanic current it produces represents, according to Betner, the so-called injury current. As a model that clearly illustrates the electrical properties of the cell, Betner used an apple: its pulp corresponds to the protoplasm, and the skin to the lipoid shell. The injury current is obtained in the case when the solution surrounding one electrode directly contacts the skin, while the other is immersed in the pulp of the fruit. A similar scheme is also applicable to action currents. To explain them, it must be assumed that at the moment of excitation, the integrity of the lipoid shell is also violated, albeit reversibly. Another conception, developed mainly by Bernstein (Bernstein), does not resort to the assumption of the existence of a lipoid shell as a separate phase on the cell surface, but proceeds from the experimentally established fact of selective ion permeability of the protoplasm surface. With a difference in the electrolyte composition of the cell contents and surrounding fluids, the unequal permeability of the cell shell for different ions should inevitably lead to the emergence of membrane potentials. Numerous studies show that during excitation, ion permeability increases and to a greater or lesser degree loses its selective character. Hence—the biological potential difference between a normally polarized cell surface and a surface depolarized reversibly (due to excitation) or irreversibly (as a result of damage). Both theories considered lead to similar formulas and quantitative relationships, which extremely complicates the resolution of the dispute between them on the basis of experimental data. According to both theories, the source of biological potential is the cell shell, which polarizes due to the unequal solubility of different ions in it or their unequal permeability. At present, it is still difficult to say whether oxidation-reduction potentials, which should arise as a result of continuously occurring oxidation-reduction reactions in a living cell, play any role in bioelectric phenomena. Thermodynamic and electrokinetic potentials. To measure all the electrical potentials considered here, essentially the same methods are used. By asymmetric combination of different electrodes, aqueous solutions or non-aqueous phases, unequal potentials are created at the ends of the circuit, which are led to a galvanometer or other electrical measuring instrument. However, the presence of a potential difference on boundary surfaces can also be detected by a completely different method—by means of electrokinetic phenomena: cataphoresis and electroosmosis. The first phenomenon consists in the movement of particles suspended in a liquid, which in an electric field move to one of the poles. The reverse phenomenon occurs in electroosmosis. If a solid phase is fixed immovably in the form of a porous plug or diaphragm dividing the vessel between electrodes, then when current is passed, the liquid moves—instead of cataphoresis, electroosmosis is obtained. Cataphoresis and electroosmosis occur in opposite directions: both contacting phases—the solid body and the liquid—carry opposite charges on their boundary surfaces. Just as the passage of current causes the movement of liquid or particles suspended in it, so conversely, an electric current can be obtained as a result of the mechanical movement of contacting phases, for example, during the mechanical pressing of liquid through a porous filter or through capillary tubes. Measurement of the speed of electrokinetic phenomena makes it possible to determine the magnitude of the potential differences at the boundary surfaces underlying them. However, the values found in this way differ sharply from those corresponding to the theoretical calculations given above or to the corresponding electrometric measurements. The theory of electrokinetic phenomena provides the key to understanding this fundamental discrepancy. According to the theory of Helmholtz (Helmholz), the boundary potential difference, which plays a role in electrokinetic phenomena, depends on the uneven distribution of ions at the phase boundary. Ions of one sign predominate near the surface of the solid body, creating an electric charge here. The forces of electrostatic attraction cause in the immediately adjacent layer of liquid the accumulation of a completely identical excess of ions of the opposite sign. A certain resemblance to a capacitor is obtained, the plates of which correspond to both ionic layers. Helmholtz called this arrangement of ions the electric double layer (see). However, as Gouy later pointed out, the outer ionic layer cannot be as sharply delimited as the inner one. The excess of ions of the opposite sign, collecting around the charged surface, forms around it an "ionic atmosphere," gradually thinning out and diffusely passing into a uniform distribution of ions of both signs (the so-called "diffuse double layer").

If in electrokinetic phenomena both ionic layers were completely separated from each other (the inner layer being held by the suspended particle, the outer layer being carried along by the surrounding liquid), then the electrokinetic difference of P. would equal the full difference of P. between both phases. In reality, however, particles suspended in liquid always carry along with them in their movement the adjacent layer of liquid that is tightly attached to them. This is evidenced among other things by the well-known fact that for any bodies suspended in liquid, the resistance is determined by the coefficient of internal friction (viscosity) of the liquid: friction does not occur at the boundary between the solid body and the liquid, *but always between two layers of liquid—the freely movable layer and the layer that is tightly attached to the solid surface. Therefore, a certain part of the double layer (not only the inner ionic layer, but also part of the oppositely charged ions attracted by it) is firmly held by the suspended particle. In electrokinetic phenomena, only the difference of P. between this inner part of the double layer and the free mass of liquid plays a role. This 'electrokinetic potential' thus constitutes only a part of the entire difference of P. between both phases. Since the values of the latter were derived from basic thermodynamic equations, it is often called 'thermodynamic.' The electrokinetic P. is usually denoted by the Greek letter ζ (zeta-potential), the thermodynamic one by the letter e. It should be noted that the electrokinetic P. is much more variable compared to the thermodynamic one. Besides the conditions affecting the latter (see above), the ζ-potential depends on the structure of the double layer itself. With the same value of e-potential, the ζ-potential can have very different values depending on how closely the ionic layers are brought together and, consequently, what part of the ionic atmosphere 'sticks' to the suspended particle. Adsorption of ions present in the solution particularly strongly affects the ζ-P., which in the extreme case (e.g., in the adsorption of multivalent ions) can even cause a complete reversal of the potential, leading to the formation of a new double layer of opposite direction (see Recharging of colloids). When transitioning from one sign of charge to the opposite, the particle at a certain moment becomes electrically neutral, completely devoid of electric charge. The electrokinetic potential is one of the most important properties of suspended particles, determining their behavior not only in relation to electric current, but also to many other influences (in particular to the action of ions). Of particular interest is the value of the electrokinetic potential as the most important factor in the stability of colloids (see Coagulation). In the case of hydrophobic colloids, coagulation occurs only when the ζ-potential of the colloidal particles falls below a certain value called the critical coagulation potential. The stability of hydrophilic colloids is ensured not only by the ζ-potential but also by their affinity for the solvent. Electrokinetic potential of biological surfaces. The electrokinetic P. of cell surfaces has been studied many times by observing the cataphoresis of cell suspensions, in some cases also by means of experiments on electroosmosis through plate-like tissues. Red and white blood cells, spermatozoa, many bacteria, and protozoa have been studied. All sufficiently accurate and verified observations indicate a negative charge on the surface of living protoplasm: in an electric field it migrates to the anode. This sign of charge is sufficiently explained by the chemical nature of cellular colloids, which are amphoteric bodies whose gas-electric point (see) is in most cases shifted far to the acidic side. Therefore, at a reaction close to neutrality, in which life processes usually occur, most cellular colloids should have a negative charge. Most studies of cellular ζ-potentials are limited to determining their sign and only rarely approach determining their absolute magnitude. The latter is more often characterized indirectly—by the concentration of those electrolytes whose addition causes the removal of charge or recharging of the cell surface. Such recharging can be achieved by adding multivalent cations, e.g., salts of lanthanum, cerium, or thorium, which must be added in higher concentrations the higher the initial negative potential was. Another way of changing the charge is by adding acids, lowering the pH of the solution. In accordance with the general influence of the reaction on the nature of dissociation and on the charge of amphoteric colloids, the boundary potential should* fall to zero as the pH approaches the isoelectric point of cellular colloids and acquire the opposite sign upon further acidification of the solution.--Particularly many studies have been devoted to measuring the P. and determining the isoelectric point of erythrocytes. Most researchers find it at a pH of approximately 4.6-4.7. Its position, however, depends on the electrolytes present in the solution, which can cause more or less significant shifting of it. For example, in Eggerth's experiments, the addition of 1/109 K2SO4 caused the isoelectric point of rabbit erythrocytes to shift from pH 4.7 to 4.0. In other cases, a more acidic reaction is often required to eliminate the negative 'P.' of the cell surface. Recharging of bacteria in Winslow's and his colleagues' experiments occurred only at pH below 3.0. Similar results were obtained by Schroeder's experiments on euglena, before the reversal of the potential sign, cell death occurred. However, the numerical results obtained by various authors require strict critical verification and cannot always be used to characterize the electrokinetic potential of living, undamaged protoplasmic surface. This applies even to erythrocytes, on which a particularly large number of experiments have been performed. As recent studies by Eggerth and Abramson have shown, the above value of the isoelectric point of erythrocytes actually refers to damaged cells or to cells that, while not damaged themselves, have changed their surface by adsorbing breakdown products from other destroyed cells. The actual isoelectric point of erythrocytes apparently lies at significantly lower pH values. There can be little doubt of the great importance for the life activity of the cell of such a significant physical quantity as the electrokinetic P. of its surface. However, at present, very little is known about its biological significance. Here, one should first point to the importance of the ζ-potential for the stability of cell suspensions and for their agglutination. The latter, like coagulation of colloids, occurs after the P. on the surface of bacteria or erythrocytes falls below a certain critical value. Agglutinins, by binding to the cell surface, change its properties and sensitivity to electrolytes. But agglutination itself can only occur in the presence of electrolytes that reduce the boundary potential of the cells. In the reaction of erythrocyte sedimentation, their ζ-potential also apparently plays a significant role as one of the factors reducing the rate of sedimentation. Using the concentration of lanthanum salt required for recharging to characterize the magnitude of the potential, Mines showed that increased agglutinability and increased sedimentation rate of erythrocytes are accompanied by a decrease in their potential. The examples given illustrate the role of P. in the specific phenomena of agglutination and precipitation of cell suspensions. Of much wider interest is the role that modern theory of ion permeability assigns to the potential. As Michaelis established on dried collodion membranes, with a sufficiently small pore diameter, the membrane exhibits selective ion permeability. The sign of the latter is determined by the ζ-potential of the pore walls: the membrane passes ions of opposite charge (if they do not exceed the pore diameter) and offers strong resistance to the passage of similarly charged ions. Apparently the same principle applies to the ion permeability of living cells, which thus turns out to be directly related to the ζ-potential of the cell surface. However, one should not forget about the complex composition of the cell membrane, which may represent a mosaic combination of different areas that probably have different electrical properties. Consequently, the actual potential of individual areas of the plasmatic surface, determining the nature of their ion permeability, may differ from the total potential of the cell given by cataphoretic measurements. In particular, Mond's experiments show that despite the total sharply negative potential of erythrocytes, their ion permeability is determined by electropositive areas embedded in the surface. Clarification of our knowledge about the localization and distribution of ζ-potentials on biological surfaces should form the basis of the doctrine of ion permeability and of the cellular processes associated with it.