Donnan Theory Research Articles

The shrinkage of cherries in jelly

AbstractIt is demonstrated that cherries gradually shrink if set in a gelatin jelly and that the main factor governing the extent of the shrinkage is the gel pH. The pH of minimum shrinkage depends on the isoelectric pH of the gel and the results are discussed in the light of Donnan's theory of membrane equilibrium.

95—A GENERALIZED THEORY FOR THE COMBINATION OF ACID OR ALKALI WITH WOOL KERATIN

A generalized Donnan theory (assuming ions to be adsorbed at sites) is developed to describe the titration curve of an insoluble protein which possesses unequal numbers of carboxyl and amino groups. The equations derived apply to combination with acid or alkali and include a treatment of the isoelectric point. From the constancy of the isoelectric pH of keratin it is concluded that K+ and Cl− do not combine with keratin.

Colligative properties of polyelectrolyte solutions. VI. Donnan membrane equilibrium

AbstractThe Donnan membrane equilibrium of a linear polyelectrolyte solution was studied, using sodium polyvinyl alcohol sulfate as the sample and sodium chloride as the diffusible salt. Simultaneous measurements of membrane potential, sodium and chloride ion activities, sodium chloride distribution, osmotic pressure, and viscosity were carried out. The measurements of membrane potential and ionic activities gave consistent results which could be accounted for by the Donnan theory. The second virial coefficient, which was found to be much lower than the ideal Donnan term, was examined according to Scatchard's theory. It was found that while the theory gave a good qualitative explanation to the experimental results, it could not be used for quantitative discussion. For quantitative examination of the experimental second virial coefficient, the value of second virial coefficient was calculated from the assumption that osmotic pressure is proportional to the difference of the sum of solute activities on both sides of membrane, and was found to be nearly equal to the observed value.

THE STUDY ON THE HALOGENIC ACIDS COMBINED WITH WOOL TO WHICH DONNAN THEORY WAS APPLIED

Absorption isotherm curve of pure halogenic acids on wool has been obtained by electro-conductivity method. The values of 0.85 and 0.88 equivalents of HCl and HI per kilogram of wool have respectively been determined by inspection of the curve and by appling the Donnan theory of menbrane equilibrium the value obtained for the pH at 0.85/2 and 0.88/2 equivalents absorbed by wool are 2.3 and 2.5 Donnan theory supports that none of the halogen ions are combined with wool, but it was found from the above that I- has an affinity of wool as compared with the Cl-. Therefore the complete treatment of Donnan theory, considering anion affinity, leads to the following expression:instead of where a is the total hydrogen ions taken up by the fiber, V, the volume of internel solution, and f, the corrective coefficient (0-1) of anion affinity.

35—THE MECHANISM OF THE OXIDATION OF CELLULOSE BY PERIODATE

The effects of temperature, electrolytes, and pH, on the rate of oxidation of cotton cellulose by periodate have been studied. It has been shown that the reaction proceeds by way of an intermediate complex, which breaks down into the oxidation products more slowly than it is formed. The extent of complex formation is increased by lowering the temperature and by the addition of salts to the periodate solution. If it is assumed that the complex is electrically charged, the effect of added salts may be explained by application of the Donnan theory of membrane equilibrium. When periodate solutions of pH>7 are used, the insoluble reaction products (oxycelluloses) differ considerably from those produced by solutions of pH<7. A detailed study of the reaction at pH 10 has been made, and the implications of the results are discussed.

The Neutralisation of Acid‐treated Wool by Solutions of Sodium Carbonate

Neutralisation of acid‐treated wool by solutions of sodium carbonate has been examined by measurgment of hydrogen‐ion concentrations. The effects of concentration, time, liquor ratio, and temperature on the equilibration process have been studied. A qualitative interpretation of results is given, and a quantitative treatment employing the Donnan theory of membrane equilibria has been examined.

The Measurement of Donnan Potentials with Dyed Cellulose and Aqueous Salt Solutions

Measurements have been made of the electrical potential difference (Donnan potential) between dyed Cellophane and aqueous solutions of alkali‐metal chlorides. The presence of adsorbed coloured ions of negative electric charge increases the negative potential of cellulose, whereas positively charged coloured ions may reverse the sign of the charge. The measured potentials, whilst smaller than those predicted by the application of the Donnan theory, after making the usual simplifying assumptions, are in good general agreement with modern views of the mechanism of direct dyeing.

Some Observations on the Absorption of Alkali by Wool Keratin from Aqueous Solutions of Sodium Carbonate and Bicarbonate

Sorption of alkali by wool from aqueous solutions of sodium carbonate and bicarbonate has been examined by measurement of hydrogen‐ion concentrations. The effects of concentration of alkaline salt, time of immersion, liquor ratio, and temperature of equilibration have been studied in relation to subsequent measurement of the pH of an aqueous extract of a treated sample. A qualitative interpretation of results is given, and a quantitative treatment employing the Donnan theory of membrane equilibria has been attempted.

The Combination of Wool with Acids

In reply to criticism by L. Peters, comparisons between different methods of calculating and predicting equilibrium constants (pK) for exchange of Cl‐ and SO ions on wool are considered. The Gilbert‐Rideal theory accounts for the experimental value of pK=0.50‐1.00, whereas the Donnan theory does not. The influence of swelling volume and ionic volumes, the meaning of pK &gt; 0, the relationship between thermodynamic potential and pH, and the influence of the ionic strength are also discussed, providing further justification for the use of the Gilbert‐Rideal theory. Thus the earlier conclusions of the author are in the main correct.

Theory of ionic absorption on wool keratin

AbstractAt low pH wool behaves as an anion exchanger. The equilibrium constant for absorption of Cl− and SO4−2 in mixtures has been determined and used for a statistical control of theoretical constants. It is demonstrated that the Donnan theory is not applicable. The reason for this is the existence of a nonvanishing difference in standard thermodynamic potential (Δμ) between liquid and fiber phase. If a theory considering adsorption on localized sites is used (Gilbert‐Rideal) and the Δμ‐value is associated with adsorption energy it is found that the energy of Cl− and SO4−2 adsorption is comparable to the energy of water absorption on fibers. The consequences for the general application of the Donnan theory are discussed.

The Application of the Gouy Theory to Soil‐Water Systems

AbstractThis paper shows how the Gouy theory may be used to describe the properties of soil and clay suspensions. The volume charge density and the potential distribution in a single layer may be calculated for widely different clay suspensions if the surface density of charge and the concentration of free electrolyte are known. The interaction between two diffuse double layers of adjacent particles leads to a differential equation describing the volume charge and potential distribution that can be solved only for suspensions containing symmetric electrolytes. Sufficiently accurate approximations of the charge and potential distribution may be made, however, for suspensions containing asymmetric electrolytes. Due consideration must be given to the specific adsorption potential of ions in the Stern layer. By means of the Gouy theory it is possible to calculate such measurable quantities as negative adsorption, osmotic pressure, and membrane potential. A comparison of the applicability of the Donnan and the Gouy theories shows that the Gouy theory is superior in describing and predicting the properties of deflocculated clay suspensions. Indeed, the application of the Donnan theory to such systems leads to serious errors.

Combination of Wool with Acids

1. Titrations of wool with mixtures of hydrochloric acid and sulphurio acid in different total and relative concentrations have been performed, and the absorption of hydrogen, chloride, and sulphate ions has been determined.2. The experimental results are compared with results calculated on the basis of the Gilbert‐Rideal, Donnan, and ion‐exchange theories.3. Statistical dnalysis proves the applicability of the Gilbert‐Rideal theory. The Donnan theory is not applicable, as there are speoiflo thermodynamio differences between fibre and solution phases. The ion‐exohange theory is more general, including the other two theories.4. A theoretical study of the attachment of the sulphate ion at one or two positive sites in the fibre has been made. Experimental values are not conclusive, but make it possible that there is either a one‐site attachment or a distribution between one and two sites.

The distribution of ions between cellulose and solutions of electrolyte

The cationic and anionic distribution ratios for some simple salts between cellulose and water have been measured by chemical analysis. In an attempt to throw light on the origin of the cation binding power of cellulose, oxycelluloses and dyed celluloses have also been employed. The ionic distribution is in general agreement with the Donnan theory if water is regarded as the solvent in both phases. In concentrated solutions it may however be necessary to take account of a specific affinity between the salt and cellulose, and when large numbers of anionic groups are present in the cellulose there is evidence of reduced activity of the counter ions.

The Combination of Wool with Acids–a Quantitative Interpretation in terms of the Donnan Theory of Membrane Equilibrium*

A quantitative interpretation of the combination of wool with hydrochloric aoid, sulphuric acid, and hydrochloric acid in presence of different concentrations of potassium chloride has been obtained in terms of the Donnan theory of membrane equilibrium. The course of combination is determined by the pH inside the fibre, which can be calculated although it is incapable of direct measurement. When the amount of combined acid is plotted as a function of the “internal” pH, the mid–point of the titration curve is found to lie between pH 4. 15 and 4. 35 in the case of hydrochloric acid, as would be expected if combination were due to back–titration of the carboxyl groups of salt linkages. Similarly, in the case of sulphuric acid the mid–point is at pH 4. 45, and the unification of the hydrochlorio acid and sulphuric acid titration curves, as well as the agreement between the observed and expected pK values, affords strong evidence in support of the Donnan theory. In addition, it has been shown that the curves obtained by titrating wool with hydrochloric acid in presence and absence of potassium chloride, the amounts of potassium chloride being sufficient to give a constant chloride ion concentration, are unified when the amounts of combined acid are plotted against the calculated “internal” pH values. The Donnan theory also provides a precise interpretation of the manner in which the pH corresponding to half–maximum combination with acid varies with changing salt concentration.

Uptake of Water by Collagen in Solutions of Alkalis and Strong and Weak Organic Bases

The swelling of collagen and other structured proteins in solutions of strong acids takes place in accordance with the Donnan theory of membrane equilibrium1,2,3. Lyotropic effects of anions4,5 and effects due to fixation of the anions by the protein6,7,8 can also be observed.

Average Valence of the Gelatin Ion Determined by a Modified Theory of Membrane Equilibrium

From Donnan's theory we can calculate the depression of the osmotic pressure of a gelatin solution, by the addition of a salt like NaCl. According to this theory this depression should never exceed 50% of the pressure of the colloid electrolyte in complete absence of a diffusible electrolyte. Experimental observations show that this is far from being true. As shown by Loeb and others, salt addition depresses the osmotic pressure of gelatin chloride frequently to less than one-tenth of its original size. Manifestly such a deviation must be due to an insufficiency of the premises of the theory, probably to the too simple assumption of Donnan that the colloidal micellae carry single electrical charges. Calculations based on the assumption of the presence of multiple charges of the colloidal ion—to be published in extenso later—show that the fraction of osmotic pressure which remains after the maximal lowering by a salt excess amounts to 1/n+1 of the pressure in absence of a diffusible electrolyte—where n signifies the valence of the colloidal ion; hence the pressure is depressed to one-half for monovalent, 1/3 for bivalent, 1/11 for 10 valent colloidal ions, etc. From Loeb's measurements we can figure the osmotic pressure of gelatin chloride by adding to the observed values of osmotic pressure the counterpressure which is due to unequal distribution of the H+ ions on either side of the membrane. This latter magnitude can also be figured from Loeb's data. By the addition of an excess of HCl practically the entire gelatin is transformed into gelatin chloride. For a 1 % solution of gelatin chloride the osmotic pressure is thus figured as about 1520 mm. water column. By the addition of an excess of NaCl this is depressed to as low a value as nearly 23 mm.—all these data being taken from Loeb.

An application of the Donnan theory to the adsorption of ions by colloidal silicic acid

An application of the Donnan theory to the adsorption of ions by colloidal silicic acid

THE EFFECT OF PURE PROTEIN SOLUTIONS AND OF BLOOD SERUM ON THE DIFFUSIBILITY OF CALCIUM

1. A comparative study has been made of the diffusibility of calcium in solutions of crystalline egg albumin, serum globulin, and human blood serum. 2. In all three of these solutions, at pH 7.4, molal Ca concentrations within the membrane are greater than the calcium concentrations in the outside solutions, quite in accordance with the Donnan theory. 3. At pH 7.4, the ratio of See PDF for Structure varies directly with the protein concentration whether the solution be one of egg albumin, serum globulin, or blood serum. This is also in accordance with the Donnan theory. 4. On the acid side of the isoelectric point of the proteins, the concentration of Ca outside becomes greater than the concentration in the solution of blood serum or pure protein, as is demanded by the Donnan theory. 5. The magnitude of the Ca ratios on the alkaline and acid sides of the isoelectric points is probably the resultant of the Donnan equilibrium and the formation of complex Ca-protein ions. Northrop and Kunitz have shown the probability of the existence of such ions in the case of Zn(++), K(+), and Li(+), where satisfactory electrodes have been developed for E.M.F. measurements.

SOME CONSEQUENCES OF THE THEORY OF MEMBRANE EQUILIBRIA

In applying Donnan's theory of membrane equilibria to systems where the non-diffusible ion is furnished by a weak acid, base, or ampholyte, certain new relations have been derived. Equations have been deduced which give the ion ratio and the apparent osmotic pressure as functions of the concentration and ionization constant of the weak electrolyte, and of the hydrogen ion concentration in its solution. The conditions for maximum values of these two properties have been formulated. It is pointed out that the progressive addition of acid to a system containing a non-diffusible weak base should not cause the value of the membrane potential to rise, pass through a maximum, and fall, but should only cause it to diminish. It is shown that the theory predicts slight differences in the effect of salts on the ion ratio in such systems, the effect increasing with the valence of the cation.

THE COMBINATION OF SALTS AND PROTEINS. I

1. It has been found that the ratios of the total concentrations of Ca, Mg, K, Zn, inside and outside of gelatin particles do not agree with the ratios calculated according to Donnan's theory from the hydrogen ion activity ratios. 2. E.M.F. measurements of Zn and Cl electrode potentials in such a system show, however, that the ion activity ratios are correct, so that the discrepancy must be due to a decrease in the ion concentration by the formation of complex ions with the protein. 3. This has been confirmed in the case of Zn by Zn potential measurements in ZnCl(2) solutions containing gelatin. It has been found that in 10 per cent gelatin containing 0.01 M ZnCl(2) about 60 per cent of the Zn(++) is combined with the gelatin. 4. If the activity ratios are correctly expressed by Donnan's equation, then the amount of any ion combined with a protein can be determined without E.M.F. measurements by determining its distribution in a proper system. If the activity ratio of the hydrogen ion and the activity of the other ion in the aqueous solution are known, then the activity and hence the concentration of the ion in the protein solution can be calculated. The difference between this and the total molar concentration of the ion in the protein represents the amount combined with the protein. 5. It has been shown that in the case of Zn the values obtained in this way agree quite closely with those determined by direct E.M.F. measurements. 6. The combination with Zn is rapidly and completely reversible and hence is probably not a surface effect. 7. Since the protein combines more with Zn than with Cl, the addition of ZnCl(2) to isoelectric gelatin should give rise to an unequal ion distribution and hence to an increase in swelling, osmotic pressure, and viscosity. This has been found to be the case.