PERMEABILITY OF IONS THROUGH INORGANIC GELS AND A STUDY OF THEIR ELECTRODES SYSTEM

Abstract

The importance of transport phenomenon in engineering, technology, biology and medicine is well recognised. Chemists and chemical engineers fabricate membranes for fundamental studies on permeability and diffusion of solutions, for exchange studies and for many unit operations when a membrane of any desired property or properties is to be employed for a particular chemical process. Basic research in the field of physiology and medicine involves the use of simple models to understand the behaviour of complex cell membranes. It is difficult to give a precise definition of the word "membrane" (l). Any complete definition given to cover all the facts of membrane behaviour will be inexact and precise statement will be incomplete. However, the characteristic feature of membrane in their selective permeability, in other words, their function as barriers irrespective of the name given to the membrane system. Thus membranes considered from the physico-chemical standpoint are given the name "physicochemical membranes" (2). Other terminologies associated with membranes are 'Semipermeable'; 'homogeneous phase membranes' (oil membranes); 'membranes of porous character's; 'ion-exchange membranes' etc. From the physico-chemical point of view; ' a membrane is a phase or structure interposed between two phases or compartments which obstracts or completely prevents gross mass movement between the latter, but -2- permits passage, with various degrees of restriction, of one or several species of particles from the one to the other or between the two adjacent phases or compartments, and which thereby acting as a physicochemical machine transforms with various degrees of efficiency according to its nature and the nature and composition of the two adjacent phases or compartments the free energy of the adjacent phases or compartment, or energy applied from the outside to the latter into other forms of energy (3). Similar views were held by Krogh (4). The thermodynamics of transport of ordinary solutions, though as such not simple, becomes all the more complex in the case of electrolytes where numerous additional effects may be observed, such as static or dynamic membrane potentials, anomalous osmosis, movement of ions against concentration gradient, electro-osmosis etc. It is necessary to distinguish two basic classes of membranes "homogenous phase membranes" (oil membranes) and 'membranes of porous character'. Homogenous phase membranes exert their typical membrane function by means of selective differential solubility (5). Membranes of porous character act as sieves that screen out the various species of solute particles according to their different size and to some extent according to their different adsorbabilities and in the case of ions, also according to the sign and magnitude of their charge. The question of membrane structure becomes of -3- great importance when a membrane is not completely inactive (in fact a complete inactive membrane is difficult to realise in practice). The ionogenic groups fixed to the membrane matrix, as seen in well character ised ion exchange membranes, or adsorbed as found in some colloidal systems (6) greatly influence the transport phenomenon. The presence of ionogenic groups and pores in the membrane confers certain functionality to the membrane which is described in the literature by the words permselectivity (7) and/or semipermeability. The phenomenological transport property which controls the former is the 'transport number't.whereas the latter is determined by the reflection coefficient o- (ratio of the actual hydrostatic pressure required to give zero net volume flow to that which is required if the membrane were truly semipermeable) introduced by Staverman (8-14). Grossly porous membranes (wide pores) are neither permselective nor semipermeable; whereas "ion sieve" membranes with narrow pores are semipermeable but may not be permselective if the number of fixed ionogenic groups are too few in number. As the presence of narrow pores and high fixed charge density of ionogenic groups gives high values for "t^ and <r- , membrane's characterised by these values i.e. ion-exchange membrane prove useful and industrially important. As a result, the bulk of the membrane literature abounds in papers describing the work on ion-exchange membranes. Ion-exchange membranes in contact with external -4- electrolyte solutions take up electrolytes in a way different from nonion-exchange membranes. Because of the presence of ionogenic groups fixed to the resin matrix-negative groups like -0O3, -COO" et seq., in case of cation exchangers, and positive groups like -NH3, ^NHp, ^N+- et seq. in case of anion exchangers- the membrane excludes the co-ions (ions of same sign - or + charge as the fixed groups) by electrostatic repulsion. The amount of exclusion is governed by the concentration of the external electrolyte. At very low concentration, the amount of co-ion in the membrane is almost zero, but as the external concentration is increased, the co-ion content of the membrane phase increases. There will be less number of co-ions than counterions (ions of opposite charge to fixed groups) by an amount equal to the number of fixed groups; whereas in the nonionexchange membrane, the distinction between co-ion and counterion being non existent because of the absence of fixed groups there will be equal numbers of positive and negative ions. In the case of non electrolytes, both types of membranes will behave alike. The theoretical aspect of membrane phenomenon was first of all considered by Donnan (15) some fifty years back. In a series of papers published, the distribution of ions across a copper ferroeyanide membrane (semi permeable in character) was discussed from different angles. He also for the first time pointed towards the importance of distribution of ions in biological studies and showed that if two solutions are separated by a " -5- ^membrane which is impermeable to atleast one of the ionic species (usually a colloidal component) present in one of the solutions, an unequal distribution for the other ionic species to which the membrane is permeable results. At equilibrium the two solutions show a difference in pressure and if the two calomel electrodes are connected to the solution by means of salt bridges, an E.M.F. is found to be present. Verifica tion of Donnan's theory was made by studying the dis tribution of sodium ferroeyanide and potassium ferroeyanide across copper ferroeyanide and amyl alcohal membranes. Analysis of the two solutions in the two compartments proved that the equation CHa)Ix(K)I = (Na)n x (K)n holds good. Donnan's theory has found many applications in biological processes. Le@b (16) and collaborators investigated the effects of acids, alkalis, and salt, on the osmotic pressure and membrane potential of amphoteric proteins. Loeb has shown that the simple theory of membrane equilibria was capable of accounting fairly quantitatively many of his experimental results. On the basis of his studies on protein ampholytes he was able to show that the diffusion phenomenon with proteins is due to simple chemical reaction and not to the adsorption of ions by colloid aggregates or micelles. Here the simple ionised molecules or the ionic micelles are subjected to the same constraint, namely, inability to diffuse freely through the membrane. This constraint - then imposes a restraint on equal distribution on both w -6m sides of the membrane of otherwise freely diffusible ions, thus giving rise to the concentration, osmotic and electrical effects with which the theory deals. Proctor (17) and collaborators had used the Donnan's theory to account for the effects of acids and salts on the swelling of gelatin. The hydrogen ions of the acid react chemically with the gelatin molecule thereby becoming ionised. Although no membrane exists, the necessary constraint is provided by the inability of the gelatin ions to leave the structural network owing to the forces of cohesion which hold it together. A restraint on the free diffusibility of ions thus sets in leading to an unequal distribution of hydrogen ions and anions of the acid between the jelly phase and the surrounding aqueous solution. On the basis of this theory Proctor and Wilson (laccfy were able to account quantitatively for the remarkable effects of acids in low concentration in first increasing and then diminishing the swelling of gelatin jelly. The difference of ionic concentration gives rise to excess of osmotic pressure of the jelly accompanied by entrance of water in it and consequently swelling. Loeb (loc.cit) adopted Proctor's theory of the effects of acid in support of his experimental results. The case of biological membrane, the fundamental unit of transport in human body is much more complicated one. It is the membrane which regulate the transport in the body, elg., the passage of food stuffs of Various kinds from the stomach and intestines to the blood, from C=£ J; Qv) AP \ >- l- \ STREAMING POTENTIAL STREAMING CURRENT ?0*{S *>' *'& o z < o o Oe. t- O Ul —I LU J ^1 FIG.I. SCHEME OF DIFFERENT TRANSPORT PHENOMENA ACROSS MEMBRANF -7- the blood to extra cellular fluids and the tissue cells. The cell membranes are responsible for the transport forces. Polarization micrdfeopejhave explained the well oriented structures of proteins and lipoids. The electrical activity in the nerve- the nerve signal is ,as well known an electrical event with frequency modulated signals. The secret of the electrical nerve communication signal is in fact a permeability process and thus a membrane phenomenon. It is a question of ionic transport process. The phenomenon have been most ingeniously characterized, analysed and partly synthesised by Hodgkin, Katz, Keynes and Hauxly. When a membrane separates two solutions, the number of forces that may normally operate to cause a flow or flux of molecular or ionic species through it are: (a) difference of chemical potential Ap-, (b) differ ence of electric potential Avf , (c) difference of pressure £>P, and (d) difference of temperature ^T. These forfies when they operate severally or in combination may generate a number of phenomena and these are indicated in Fig.l (18, 19). The current membrane theories may be divided roughly into three groups based on the nature of the flux equation used in the treatment ( Schlogl (20)). In the first group fall many of the theories based on the Nernst-Planck flux equations for their refinements. In the second group are included all the theories using the principle of irreversible thermodynamics. In the -3- third group is included the theory which utilizes the concepts of the theory of rate processes. In general, the theories of group one are based on the ideas of classical thermodynamics or quasi-thermodynamics which is restricted to isolated systems. The theories of group two, apart from being more rigorous and realistic, allow a better understanding of transport phenomena in membranes and is useful in dealing with non-isothermal systems. The theories of group three contain parameters which are still unknown for the membrane and hence have restricted applicability. The relationships based on the three different groups are mathematically represented in the following manner: (a) Nernst-Plenck Flu* equations: The diffusional flux caused by chemical potential is given by the equation: Ji(d) =- Di I!!. <i) dx where Ji(d) is diffusional flux, Di is the diffusion coefficient and Ci is concentration. The flux due to an electrical field is given by the equation: Ji(e) = - % _F Zi Ci d* (ii) RT dx where Ji(e) is flux due to electric field, Zi is the valence, Di is diffusional coefficient. and the total flux in an ideal system is given by: Ji = Ji(d) +Ji(e) =- Di ^1 +Z.CilL 4±. (iii) dx x xrt dx ) -9- and on introducing the activity coefficient term: Ji =-Di *2i- +ZiCi dt. + Ci dU^ (iv) dx dx dx The flux of the counter ions due to convection of pore liquid may be given as: Ji(c) q V* (v) where Ci is the concentration of counterions in the membrane phase (barred terms refer always to membrane phase) and V is the velocity of movement of the center of gravity of the pore liquid. V While the convection velocity is given by V* = 3£K£ d* = w u0 1^- (vi) Sov° dx dx where is the specific flow resistance of the membrane, v0 is the fractional pore volume, X is the concentration of fixed charge and w is the sign of the fixed charge (-for negatively charged membrane and + for positively charged membrane) and u0 = -J2L. is the 'mobility' of pore liquid. Equation (vi) when added to equation (iii) would give the total flux Ji. (b) Thermodynamics of Irreversible Processes: A membrane acting as a restrictive barrier to the flow of various chemical species between two subsystems ( ' ) and ( " ) contacting the two membrane faces is considered to maintain differences in concentration (^0* temperature ( AT), pressure ( AP) and electric potential (At*) across it. The subsystems are kept so well stirred as to obtain uniform values of these variables through out each subsystem and to have the whole difference ) -10- occurring only across the membrane. The fundamental theorem of the thermodynamics of irreversible process is (21, 22) that the forces and the fluxes are so chosen as to conform to the equations T =5Ji Xi (i) where Xi (£=1, 2, 3 ...n) incorporate , T, P, and Ji (i=l, 2, 3 ...n) the fluxes. The phenomenological cofficient Lik (i,k=l,2.. .n) in the equations: Ji = Ii Llk Xk (ii) k=l satisfy the Onsagar reciprocal relations Lik = L^ (iii) A recent review of the existing data by Miller (23) gives the experimental justification for regarding the Onsagar law as a law of nature (24). The description of transport processes in a system of n components therefore requires the measurement of only n (n+l)/2 coefficients and not all n2 coefficients. 0= dis is dt the rate of entropy production due to irreversible processes within the system. The evaluation of 0 requires the use of the law of conservation of mass and energy and Gibb's relationship for the second law of thermodynamics. Based on the above considerations the final general expression for the material fluxes is given by: Ji • f Hn (-VkdP - KT din afc-Zk Pdy - { f- > where Ji is total flux, Lik phenomenological coefficients Lik (i,k = 1,2..n), Vk valence of sign of species k, Qk is heat'transport, Zk is the valence sign including sign of species k. ) -11- Moreover the observable electrical parameters may be written in terms of the phenomenological co efficients (23, 24, 25, 26). (1) Current density I =F ^- Z^ Ji and substituting for Ji from equation (iii) . 1 = i" k~ ^ FLik **"** dP-RTd lnak-Q^ dlnT) " f f Zi \ Lik p2 d* (iv> (2) Electrical conductance k = - (I/dvp ) (dP=£, dT=0, d In ak=0) k- f f zi \ p2 Lik (v) where k is Electrical conductance, I is current density. (3) Transport number *k = (FZk Jk/D <<3P = 0, dT = 0, d In ak = o) F f Zj Zk FLlk d _ ?2f-W Lik (Vi) where tk is transport number, Jk is matter flux. Staverman (26) has defined a useful quantity the reduced electrical transport number Ek which has also been called mass transport number (27). Thus t/ =(tk/zk) =?2 f- %Lik/k (vii) The flow of uncharged molecules e.g. water, may be expressed in terms of their reduced transport number where ^ Z^. tfcr =1. Rearranging equation (iv) for d and substituting from equation (v) and (vii), the potential gradient at any point in the membrane may be obtained. Thus dy = -(I/K) - (3/F) ^ tkr (VkdP + RTd lnak + Q* d in Tk) (viii) ) - 12- The first term is given by the purely electrical part and the second term is due to the chemical part . Various special cases follow directly from equation (viii). (a) Isothermal diffusion potential is obtained at uniform temperature and pressure: dy= - M H tkr d In ak (ix) This has been derived many years ago by Nernst using Thomson's method and more recently by Staverman (26) and Kirkwood (27). (b) Streaming potential is obtained at uniform tempera ture and chemical potential: (c) Thermal diffusion potential is obtained at uniform pressure and activity, d^ =- F k~ **' £ dln T (xi) In the considerations given above nothing has been said explicitly about the reference frame work to which the fluxes are referred. It is implied that the reference frame was the membrane (28). Some choices about the frame of reference are possible. For example the solvent in the membrane phase may be considered stationary and therefore taken as one of the frames of reference. Hills, Jacobs and Lakshiminaryanaiah (24) have given a treatment choosing for reference frame work, the plane normal to the direction of fluxes and passing through the center of mass of the system.