摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.

ISSN:0014-7672    

DOI:10.1039/TF94036FP001

出版商:RSC    

年代:1940

数据来源: RSC

摘要:

THE ELECTRICAL DOUBLE LAYER. GENERAL DISCUSSION.* Dr. M. H. Gorh (New York) (with regard to the paper of Tiselius and Svensson page 16) In comparing the procedures of obtaining the net charge of proteins by membrane potentials and titration curves two points arise. Titration curves primarily give information about acid and base binding and cannot without further assumptions be used to furnish information about specific interaction of the protein with other ions in the system. On the other hand in the ideal sense membrane potentials should give this information and therefore should yield an unequivocal value of the net charge. However in the presence of con-siderable electrolyte and protein some uncertainties are present in the interpretation and corrections involved in the calculation of the net charge from membrane potentials.Titration data on the other hand, obtained in regions not far removed from neutrality yield definite in-formation about changes in acid and base binding for the titration correction in the change in hydrogen ion of the solvent is usually negligibly small under these conditions. The method introduced by Abramson 1 for determining the net charge from titration curves in the neighbourhood of the isoelectric point involves the assumption that in this region the binding of ions other than hydroxyl and hydrogen is approximately independent of PH. This assumption appears to be ordinarily justifiable since the non-specific interaction of ions with protein should be expected to depend on the total charge of the protein rather than upon its net charge.In addition this assumption also has justification because of its success in correlating experiment with theory. The two methods (titration curve and membrane potential) cannot be directly compared in the case of the very valuable data of Tiselius and Svensson for the measurements are so far removed from the isoelectric point that the assumption involved in applying the titration curve analysis would be open to question. In comparing however the conclusions of Tiselius and Svensson based on the present data and the conclusions of Moyer and Abels 2 on some of Tiselius’ older data in the neighbourhood of the isoelectric point there remains a discrepancy of 20 yo. It was shown3 that in order to get agreement with the equation that a value of the radius of 3 2 .6 ~ . had to be assumed. On the other hand Tiselius and Svensson were able to get agreement using membrane potential data by assuming a value of 27-5 A. for the radius. This amounts to about a 20 yo difference in the predicted mobility from the same data. * On papers published in this volume at pages I et seqq. 1 H. A. Abramson J . Gen. PhysioZ. 1932 15 575 ; Electrokinetic Phenomena, 3 €3. A. Abramson M. H. Gorin and L. S. Moyer Chem. Reviews 1g39,24,345. New York 1934 Chapter V. Mover and Abels J . Bid. Chem. 1937 121 331. 26 7x 712 GENERAL DISCUSSION The comparison above of course is made at ionic strength of 0.02. The discrepancy between the two methods would undoubtedly disappear at infinite. It would be of interest to apply the more complete equation 3 where vi is the “ average ” radius of electrolyte ions in the solution to the data of Tiselius and Svensson.The term (I +- KYJ would be of con-siderable importance a t the higher ionic strengths (for v i = 3.0 A., I + K Y ~ = 1-437 a t p = 0 . 2 0 ) . Prof. G. S. Adair (Cambridge) Dr. Gorin has expressed doubt as t o the values of the valence of egg albumin quoted by Tiselius and Svenson 4 on the grounds that the conditions are unfavourable for the application of Abramson’s method of calculation. It would appear that he has over-looked the fact that these values for the valence of egg albumin are sup-ported by an extensive series of measurements of membrane potentials with different concentrations of protein different ionic strengths of buffers and varying proportions of bivalent and univalent phosphates.More-over confirmatory evidence has been obtained from determinations of osmotic pressures and the distribution of ions across the membranes.6 No colloidal electrolyte is known to me for which the evidence for the value of the valence (2,) is better established. Prof. H. A. Abramson (New York) (on the same paper) It is always a pleasure to hear from Professor Tiselius. There are several points in his paper which are of interest to me a t this time. Prof. Tiselius mentions that Moyer and I have studied the relation between the migration velocity of protein-coated particles and the titration curves of the respective proteins. I would like to add that we have not only studied the migra-tion velocity of protein-coated particles but we also have compared the electric mobility of dissoEved protein with the titration curves of the protein.Examples of this type of comparison on the electric mobility of dissolved protein and the titration curves of dissolved protein were given at the symposium and have also been published elsewhere. The data for the dissolved proteins were those taken from Tiselius’ own work. In addition the effects of gelatin and deaminized gelatin coated quartz particles in aqueous media and in alcoholic media have been definitely correlated with the titration curves. Indeed the titration curve of deaminised gelatin has been predicted from electric mobilities. All of these data both for dissolved proteins and adsorbed proteins fit in with the notion that the titration curves are certainly very useful in handling problems dealing with the net charge of proteins and that the titration curves within the limits of experimental error and within boundaries of reasonable assumptions still may function to aid in the explanation of electrokinetic data.6 Investigators who publish data on the microscopic method of electro-phoresis should give a value for some standard particle obtained by their technique.In this way a better basis for discussing the theory of electro-phoresis will be obtained. Many measurements appearing in the literature are not quantitative, although quantitative conclusions are frequently drawn. May I therefore suggest that the human red cell be adopted as a standard when suspended in M / I ~ phosphate buffer at $H 7-4 ? This solution has a specific resistance Tiselius and Svenson Trans.Farad. SOC. 1940 36 16. 5Adair and Adair ibid. 2 3 . 6 See for example H. A. Abramson J. Gen. Physiol. 1932 15 575 ; J. Daniel ibzd. 1933 r6 457 ; L. S. Moyer and J. C. Abels J. Bzol. Chem. 1937, 121 331 ; L. S. Moyer and H. A. Abramson ibid. 1938 123 391; M. H. Gorin, L. S. Moyer and H. A. Abramson Chem. Rev. 1939 24,2 GENERAL DISCUSSION 713 of approximately 126 ohms. The value for the electrical mobility of the red cell which I obtained about ten years ago has been confirmed by Moyer and also by other investigators a t the General Electric Company. Dr. J. J. Bikerman (Glasgow) on the papers of Abramson and of Powney and Wood (pp.15’59)- The charge-concentration curves of Abramson (p. 15) are calculated neglecting the effect of the surface conductance on mobility. In order to show the magnitude of this effect Fig. i opposite has been drawn. I t is based on Fig. I in the paper of Powney and’Wood (p. 59)’ and refers to their curve for NaC1. The normality of NaCl is plotted on the abscise. Curve 2 shows the 4 potential calculated from equa-tion (8) on page 157 and has to be com-pared with curve I which represents the uncorrected values of 6 and is identical with the NaCl curve of Powney and Wood. It is seen that 6 in water (whose conductivity was Z - I O - ~ ohm-’ cm.-1) was about 0.093 volt ; according to Smoluchowski this value would correspond to the mobility of 7.4 p/sec.per volt. /cm. Consequently the introduction of the surface conductance lets disappear the maxima of 5 for NaHCO and Na,CO,; only NaOH considerably increases the poten-tial of paraffin oil droplets. The little pre-cision of the calculation does not warrant a decision on the maxima of the curves for Na,SiO and Na4P207. Curve 3 represents the surface charge densities u ((in arbitrary units) based on curve I and starting like Abranison’s curves, from nothing a t concentration = 0. When the corrected values of t are used and the o*oos FIG. i. ions present in water are-taken into account curve 4 results. It is seen that the increase of charge on an addition of electrolytes is less pro-nounced than Fig. 10 on page 15 would let one believe.Prof. A. Frumkin (Moscow) (on the paper of Powney and Wood) It is of interest to mention the paper of A. Gilman and N. Bach,7 who ob-served that a gas bubble acquires a negative electrokinetic charge in a solution of sodium palmitate and a positive one in a solution of tetra-isoamyl-ammonium chloride. Prof. H. A. Abramson (New Yovk) (in reply to Dr. Bikerman) The charge concentration curves calculated by Dr. J. J. Bikerman are of great interest and I am very pleased to see that the general shape of Bikerman’s O-c curve agrees with that already published. Unquestionably Dr. Bikerman’s correction in the lower concentration range is of immediate importance. Also pertinent to our discussion is the fact that the shape of Dr. Bikerman’s curve approaches our curves at higher concentrations of salt where the correction for surface conductance becomes very small.There is one point which I believe should be clarified. Dr. Bikerman has stated that my curves start from zero where the concentration is equal to zero. As a matter of fact all of the u-c curves which I have published here and elsewhere have been corrected as far as possible for the ions present in the water itself. This is done in the following way It is assumed that at room temperature there are about I x I O - ~ moles per litre of carbonic acid dissolved. Since k’, of carbonic acid is of the order of 7 Acta Physicochimica U.R.S.S. 1938 9 27 714 GENERAL DISCUSSION 3 x XO-' a solution in equilibrium with the carbon dioxide of the air has approximately 2 x 10-* moles of H+ and HC0,-.In order to calculate the change of the net charge due to added salts the value of the net charge in this equilibrium water should be first estimated. Therefore if uT is the charge due to the ions of dissolved carbonic acid and the added salt and aW that due to the ions of the carbonic acid alone the charge due to the salt is evidently u = uT - OW. This relationship has been used to calcu-late the values of u given in all of my curves both in the paper presented at this meeting and elsewhere. Of course it is possible that the effect of the carbonic acid ions varies with the ionic strength but that effect should be quite unimportant compared with other corrections which are proposed by Dr. Bikerman. I shall look forward to seeing calculations made by Dr.Bikerman's equation and the simpler form with comparison of the two types of curves. In this case the correction for the ionic strength of water should be the same. Dr. J. Powney and Dr. L. J. Wood (London) (in reply to Professor Frumkin) Although we have no data for cataphoretic mobilities in solu-tions of tetra-isoamyl ammonium chloride it is perhaps worth mentioning that we have recently found that 0.2 yo tetra-methyl ammonium iodide produces no reversal of charge on Nujol droplets the small decrease in mobility (towards the anode) being comparable with that produced by the addition of sodium chloride. The interfacial activity of 0.2 yo tetra-methyl ammonium iodide is only slight ( y xylene = 34 dynesjcm. at 20' C.) . Dr. S. R. Craxford (London) (on Ham and Dean's paper p.52) The Gouy-Debye-Huckel equation for the diffuse part of the double layer allows the charge density a either to increase or to decrease as g decreases, according to how K is changing b u t Drs. Ham and Dean appear to reject the theory as unnatural when it allows a to increase while 5 decreases. From their results in Table I therefore they consider the theory to break down above a concentration of about 0-OOOOI but yet according to the results in Table I1 it holds good up to 0.005 m. Actually for these exceed-ingly small potentials there is no reason for the Debye-Huckel-Gouy equation to break down seriously below about 0-001 m. They also say that as the amount of LaC1 added increases and a increases while 5 becomes very small then if the LaC1 had been a little more active 5 would have become zero and hence a would have had suddenly to decrease from a high value to zero which would be improbable.Here it seems that it is the supposition which is itself improbable because 5 is only approaching zero asymptotically and will never reach it. Hence a may go on steadily increasing (up to the limit of applicability of the theory). Finally Ham and Dean rightly accept the Stern theory of the double layer in spite of the fact that it contains this Gouy equation for the diffuse part of the layer and degenerates to it for very dilute solutions and very small poten-tial differences. Dr. J. J. Bikerman (Glasgow) (on the same paper) Paraffin oil emul-sions coagulate when their c potential falls below about 0.03 volt.Is any explanation forthcoming of why the octadecane sols were stable at 4 = 0-001 volt ? It is true that the measurements were carried out some degrees below the freezing point of octadecane but this fact alone cannot account for the extraordinary difference of stabilities. Dr. A. J. Ham (Liverpool) in reply The experience of this laboratory is that the critical 5 potential of 0.03 volt claimed by Powis* has little significance for much work on hydrocarbon-water emulsions. Other hydrocarbons have given results closely analogous to those which we quoted for octadecane and it appears that the time factor is all important. 8 2 . physik. Chem. 89 186 GENERAL DISCUSSION 715 All such emulsions will coagulate eventually and Powis’ data refer to ap-preciable changes in turbidity over a matter of days as “ rapid coagulation.” I n our experiments emulsions were prepared and left for 24 hours when particles of approximately uniform size remained coarser particles leaving the emulsion.Various salts were then added to such emulsions -in some cases rendering 5 as low as 0.001 volt-and a mobility deter-mination made ; the salts did not affect the stability of the emulsions in the time during which temperature equilibrium was being reached and determinations of mobility carried out which in no case exceeded one hour. Dr. J. J. Bikerman (Glasgozu) (on the paper of Prof. Gortner p. 66) : I agree with Professor Gortner that the high streaming potentials ob-served in his laboratory “ can only be accounted for by assuming a transfer of ions from one electrode to the other.’’ I vJould only suppress the word “ high ” as it is difficult to envisage a constant current produced by displacement of dipoles only.If we admit that streaming potentials (and the 5 potentials derived from them) are due to ions then the ions present in the organic liquids (as distinct from the liquids themselves) xi11 be responsible for the observed effects. Some ions may have contam-inated the liquid before it has been placed in the streaming cell some others may enter the liquid from the cellulose or alumina membranes ; in a few cases the electrolytic dissociation of the liquid may also produce ions. The relative importance of these va.rious sources of ions can be estimated when the specific conductivity of the liquid both outside and in the diaphragm is known.Table I is obviously misprinted as the ratio 5 8e is not always the same for cellulose and Al,O,. Prof. R. A. Gortner (Minnesota) in reply to Dr. J. J. Bikerman The origin of the potentials is unquestionably due to “ the transference of ions from one electrode to the other,” but the real problem is why there are sign reversals in a given solid-liquid homologous series. With such reversals the sign of the potential can hardly be due to ions derived from the solid phase. Since such reversals are shown where both cellulose and Al,O are the solid phase and since certain systems give rise to a different sign against a cellulose surface than is the case for an A1,0 surface it would appear from our studies that the solid surface has a specific influence upon the “ dissociation ” of the liquid.It was this possibility which led me to suggest ‘ I that a specific surface forces a dissociation of these organic mole-cules.” I doubt very seriously whether the ionic behaviour can be estimated by comparing only the specific conductivity of the liquid outside and in the diaphragm. Certainly such studies would not reveal the sign of the potential nor apparently the magnitude of the potential. “ Surface conductance ” 9 is relatively im-portant in cellulose-organic liquid systems ie. the conductance in the diaphragm is much larger than conductance of the liquid in bulk. 136.3 ductance in Al,O,-organic liquid ~ - ~ $ $ ~ ~ h o l . 101.3 systems is not an important factor.iso-propyl alcohol 112.8 1 am indeed grateful to Dr. n-butyl alcohol . 265.2 Bikerman for calling attention to iso-butyl alcohol 66.4 certain gross errors in the calcula- n-hexyl alcohol . I 18.4 tion of some of the data in the n-heptyl alcohol. 18.8 table on page 66. 6e of all of the alcohols in contact with cellulose with the exception of heptyl alcohol are in error by a misplacement of the decimal point and should be ten times as great as printed. I have recalculated the original data with the results shown in Table I. TABLE I. Cellulose-liquid Interface 6c (e.s.u. x 108). Organic Liquid. On the other hand surface con- hiethY1alcohol * 464.1 The values for Colloid Symposium Morzograph VI 41-52 1928 716 GENERAL DISCUSSION for as -In recalculating the original table two other errors were found.6e I n-propionic acid A1,0 should be 16.0 x I O - ~ instead of 16.7 x I O - ~ printed and the {-potential for ethyl n-propionate Also should be 19.1 mv. instead of - 10.8 mv. as printed. With the above corrections the ratios of { to 6e are all within satis-Minor differences in the ratios are accounted for by factory agreement. normal experimental errors. Dr. J. J. Bikerman (Glasgow) to the paper of Rutgers pp. 71 76: Equation (8) on p. 71 assumes that the walls of the capillary are perfectly smooth. In reality every glass surface and especially that cleaned by strong acids etc. is rough and the ratio 52 S of the circumference of the capillary to its cross-section is larger than 2 / ~ Y being the radius of the capillary.Fortunately a reasonable increase of the factor 2/r alters the value of 5 (see equation (15)) by a few per cents. only but it strongly re-duces the value of the surface conductance U (see equation (14)). If the real surface area of the capillaries was 4 times as large as their geo-metrical area then the values of U for very dilute KCl solutions would agree with the theoretical values. But there is certainly no agreement between the theory and the high values of uW in more concentrated KC1 solutions Maybe the more detailed account of the experiments by Mr. Verlende will help to clear up this discrepancy. I t is of course, obvious that the error made when calculating U from equation (14) is the higher the nearer are the values of {3 and Prof.A. J. Rutgers (Ghent) ir reply I do not think that Eqn. (8) assumes that the walls of the capillary are perfectly smooth. From Eqn. (8) it follows that uW is the surface conductance per cm. of circum-ference of the capillary this circumference being measured with the ordinary macroscopic means. The only supposition made is that this urn will be the same for walls of capillaries of different diameters which seems a very pIausibIe assumption. As a consequence of this I think that Eqn. (14) and Eqn. (15) need no correction. The point raised by Dr. Bikerman becomes important as soon as we try to compare experimental and theoretical values of u ,. Nevertheless I think that the big ratio of calculated and theoretical values of urn can only partially be explained by the lack of smoothness of the wall ; this ratio e.g.depends strongly on the concentration of electrolyte and it is difficult to understand why the correction factor provided by the lack of smoothness-which is of a geometrical nature-should depend so strongly on concentration. Dr. J. J. Bikerman (Glasgow) to the papers of Craxford Frumkin and Barclay and Butler pp. 89 125 and 129 The capacity of the double layer calculated from the theory of Gouy is 250 p.F/sq. cni. according to Craxford (p. 89) 240 pF/sq. cm. according to Barclay and Butler (p. I Z ~ ) and 2-36 pF/sq. cm. according to Frumkin (p. 125). I find in agreement with Frumkin 2-3 pF/sq. cm. for the minimum of the capacity curve in a I O - ~ N solution a t 20°. At the potential 0.233 volt (the potential at the minimum is assumed to be zero) Gouy’s capacity is 24 pF/sq.cm. whilst the lowest curve of Fig. 4 (p. 124) gives 15 and 27 pF/sq. cm. In view of the fact that Gouy’s theory is perfectly general and contains no adjustable constants the agreement is rather convincing. I t would be futile to expect a closer agreement here or an agreement a t still higher potentials or higher concentrations as Gouy’s derivation neglects the inter-ionic forces; already at 0.233 volt in 1 0 - 4 N solutions the concentration of “ counter-ions ” a t the mercury-solution boundary is about I N that is SO large that individual properties of ions (their apparent radius etc.), can no longer be neglected. An extension of Gouy’s theory so as to include the inter-ionic forces would be more satisfactory than the cutting of the potential field in two independent parts like those assumecl by the theory of Stern GENERAL DISCUSSION 717 May I also correct a statement repeated in several papers ? Helmholtz’s dcuble layer does not consist of two condenser plates ; that is the picture suggested by Lamb.There is no contrast between Helmholtz’s and Gouy’s theories but Gouy determined the relation between potential and distance which was indefinite in Helmholtz’s equations. Prof. A. Frumkin (Moscow) on the paper by Craxford p. 93 Dr. Craxford quotes my paper in 2. Physikal. Chem. 1923 as supporting the concentration polarisation theory of electrocapillarity which he rejects. I think this indication is incorrect. I never expressed the opinion that the surface conditions of mercury in the capillary electrometer are deter-mined in a kinetic sense by the volume concentration of mercurous ions regardless of the value of this latter.The kinetic mechanism is not dis-cussed in the paper quoted bclt considering in another paper the mechanism of the dropping electrode,’@ I make just the same distinction between the behaviour of mercury in solutions containing high and low concentrations of mercurous ions as Dr. Craxford. The use of thermodynamic symbols relating to mercurous ions in the solution in the derivation of Lippmann’s equation appears to me legitimate as far as an idealised equilibrium system is concerned ; the results obtained must be certainly correct independently of the physical meaning of the concentrations involved.Besides the difficulty encountered in deriving Lippmann’s equation from the equation of Gibbs if there is any can be avoided if the mercurous ion is considered as a component of the metallic phase. The equilibrium conditions axe certainly not strictly realised in the capillary electrometer and it is impossible to say afiriori without further experiments whether the result of the thermodynamic theory can be applied to the experimental electrocapillary curve but the same can be said if Lippmann’s equation is derived from the conception of a com-pletely polarisable electrode. Dr. S. R. Craxford (London) in reply It is very gratifying to receive Professor Frumkin’s unambiguous statement that he also rejects the con-centration polarisation theory as the kinetic basis of the behaviour of a polarised mercury solution interphase.But in spite of this he is still prepared to use this admittedly false assumption as the basis of the thermo-dynamical theory of the interphase I ‘ as far as an idealised equilibrium system is concerned ”. Since thermodynamics is merely another way of writing the results of the kinetic theory it cannot be sound to apply thermo-dynamic equations to systems of such low concentration that the usual kinetic theory equations become meaningless. His use of the thermo-dynamic theory of concentration polarisation for such cases made it not unreasonable to suppose that he also believed the assumptions underlying those equations to be true. Dr. S . R. Craxford (London) in reply to Dr.Bikerman I had not stressed the point about the high capacities obtained from Gouy’s theory of the diffuse layer since that theory is only important nowadays as a special case of Stern’s theory. But since Dr. Bikerman Capacit ylcrn.2 has questioned the figure I quoted I will & ~ ~ ~ ~ ~ ; ~ & . microfarads. supplement it by Table z recalculated from Gouyl’ for N/IO .solutioss. For similar TABLE 2. 0.0 74 0.176 77 surfzce charges these capacities are all very 3‘31 85 much bigger than the experimental value 12.8 131 of 19-5 microfarads. It is not surprising 26.0 202 that Dr. Bikerman’s results in 0.0004 N 4I.3 2 72 solutions agree with Gouy’s theory because I3I-O 590 for such dilute solutions Stern’s cquation approximates to Gouy’s. But however Gouy’s theory is elaborated by taking inter-ionic forces into account it will still be impossible to make l o Erg.e x . Nalzcrwfss. 1928 7 243 11 Ann. Physique 1917 7 163 718 I. 11. Na + I -Solution z $ 1 Solid of NaI Na + I - AgI N a + I -GENERAL DISCUSSION III. represented as in Table 3. When considered in this way it is difficult to see anything in the argument on pp. 113 and 114 more profound than the bald Ag assumption that the change in ‘Am+ on adding excess of a foreign electrolyte is equal to the Soli GENERAL DISCUSSION decreased by subsequent adjust-(iji) It is decreased by specific adsorption of the foreign electro-lyte more I- having to enter the layer from the bulk of the soh-ment of the adsorbed layer. I. Solution of NaI and foreign salt Na -F Na 4-719 11.111. I - "lid "lid I - Agl -ti& to maintain the potential. I I Professor Kruvt neglects lil and (iij) and the; in &der to 'explain the experimental fact that a',- is less than a,- he assumes that (iib) out-weighs (iia). This is equivalent to saying that the electrostatic capacity of the diffuse layer is less than that of the adsorbed layer which is incorrect. (See my reply to Dr. J. J. Bikerman in this discussion.) Dr. J. J. Bikerman (Glasgow) on same paper I am unable to under-stand the method of De Bruyn and hope his own publication will contain a more detailed justification of equation (4). In the meantime I would like to have a clear picture of the experimental side. The e.m.f. of a cell AgI (solid) /suspension of AgI + some NaI /liquid junction/reference elec-trode is measured ; then to the suspension a large excess of a nitrate is added and the e.m.f.determined again. The difference between both values of the e.m.f. is supposed to be equal to the 5 potential of the AgI suspension before addition of the nitrate. Is this a fair account of De Bruyn's method ? Prof. A. Frumkin (Moscow) on paper by Barclay and Butler p. 132 : The significance of the two flat stages on the curve expressing the rela-tion between the potential and the charge of the electrode in presence of amyl alcohol can be readily explained. As it is known from electro-capillary data amyl alcohol is not adsorbed with sufficiently high positive charges of the mercury surface.If the positive potential is decreased the adsorption sets in at a fairly definite value of the potential and a unimolecular layer of amyl alcohol is formed. With further negative polarisation we can reach another limit of the existence of this layer the transition being in this case less sharply pronounced as on the positive branch. A molecular theory of this transition has been given elsewhere.la As the transitions from a surface covered only by an ionic double layer to one covered by a layer of amyl alcohol molecules and vice versa necessitate a large change of the surface charge and a corresponding consumption of the polarising current two flat stages on the oscillogram must appear. In the first stage a large part of the initial positive charge of the mercury is removed and in the second a part of the negative charge is communicated.If instead of measuring the charge of the electrode we measure the capacity as a function of the potential two maxima must appear on the resulting curves corresponding to the two flat stages on the oscillogram given on p. 132. Such measurements have been carried out with octyl alcohol solutions by Proskurnin and Frumkin Is and with la Frumkin 2. Physik 1926 35 792. 13 Trans. Favaday SOC. 1935 31 115. 26 720 GENERAL DISCUSSION buytl alcohol solutions by Ksenofontov Proskurnin and Gorodetzkaja.14 Fig. I taken from the latter paper shows that this maxima occur indeed at potentials which correspond to the limits of the adsorption region of the organic molecules marked on the electrocapillary curves by well pronounced breaks.Dr. J. J. Bikerman (Glasgow) on paper of Audubert p. 1 4 6 The equations used by Professor Audubert are rather empirical than theoret-ical since the theory underlying them does not apply to colloids. As I have already pointed out 16 the impossibility of transferring Debye's equa-tions to sols I will restrict these remarks to a comparison between the observed mobilities and those given by equation (3). From Fig. 6 and 7 i t is seen that r/aA is about 5 0 . 1 0 - 3 ; hence a A d P =- I when d p > 50 . I O - ~ . At the concentrations involved a A d ; obviously is less than I . Equation ( 3 ) requires then an almost linear increase of mobility with the radius a of the particle. This is in contra-diction with experiments.If a is large and aA is over 1000 (see Table IV) equation ( 3 ) shows that the mobility is almost independent of the con-centration above say d p = 0.01 ; this is not confirmed by experiments. The particles of the As,S sol used by Freundlich and Zeh were invisible in ultra-microscope and therefore very probably less than 1-43 . 10-6 cm. On the other hand mastic sols usually have larger particles of the order of magnitude of I O - ~ cm. (see Table 4). Prof. R. Audubert (Paris) in reply ( I ) In agreement with the remark of Bikerman the data recorded in Table I are not intended to represent real radii of the particles of the systems investigated. Indeed, the calculation gives only average radii since the listed sols and suspensions are heterodisperse , (2) Equation (3) questioned by Bikerman is confirmed only in the case when the hypotheses on which it is based are valid (E = 4m20).That is the reason why it was preferred to take for the variable instead of the mobility u the relative change u/u of the mobilities see equation (4). This relation is not experimental ; it is an expansion of the theories of Debye to disperse systems. Experience shows that it is indeed confirmed in the range of small concentrations; the agreement is the better the smaller is the valency of the ions. Equation (4) assumes that the charge E is constant. The observed disagreement between the relative mobilities calculated from (4) and those measured can be interpreted as due to a variation of E. When applied to mastic granules this hypothesis is con-firmed by experiments (equation ( 1 3 ) Table IV).We believe therefore that the theory of Debye and Hueckel in its simple form is applicable to disperse systems at very large dilutions only ; a t smaller dilutions it is necessary to assume a variation of E with the ionic strength of the intermicellar liquid. In the range of high concentra-tions the classical theory of Debye cannot be used as it is not allowed, then when developing the exponential function to neglect the terms of an order higher than unity. The values recorded in Table I are not convincing. Prof. L. S . Moyer (Minnesota) on paper of Bikerman p. 157 In re-gard to the statement of Bikerman that the values previously obtained by Moyer and Bull 16 for the charge density at cellulose surfaces will be altered by consideration of the surface conductance it may be well to mention that our calculations were based on streaming potential data of Bull and Gortner.17 In their data corrections for the influence of surface 14 Acta Physicochimica U.R.S.S.1938 9 41. 15 J. J. Bikerman 2. Electrochem. 1933 39 526. 16 L. S. Moyer and H. B. Bull J. Gen. Pltysiol. 1935. 19 239. 17 H. B. Bull and R. A. Gortner J. Physic. Chem. 1931 35 309 456 700 GENERAL DISCUSSION 72 1 conductance had been introduced by measurement of the specific con-ductance within the pores of the diaphragm. The procedure used was that of Briggs.ls Dr. S. R. Craxford (London) on Guggenheim’s paper p. 1 3 9 For a double layer of unspecified ionic distribution the equation for electro-osmosis for example is obtained by combining the Poisson equation with the Stokes-Navier law and is D D 4 TT 47v u = - +J = - .5 . This involves a number of assumptions one of which is that D the dielectric constant is constant throughout that part of the double layer that is responsible for electrokinesis. If D were not constant there is no reason to suppose that the electro-osmotic equation would take the above form. Dr. Guggenheim considers the equivalent condenser with capacity charge D’ * ( 2 ) K = - = -5 4TS and assumes in his turn firstly that the electro-osmotic equation has the form of ( I ) in spite of the variable D and secondly that D in (I) is the same as D in (2). He is thus enabled to eliminate D and 5 and replace them by the moment of a condenser equivalent to that part of the double layer responsible for electrokinesis.His equation therefore seems to be no freer from assumptions than (I) and it would be difficult to maintain that the moment of the equivalent condenser gives a clearer picture of electro-kinetic phenomena than the potential difference across the diffuse and slipping double layer. The argument that the moment comes in directly and naturally if the electrokinetic equations are derived from the concept of a parallel plate condenser at the interphase as was done first by H. Lamb is not 19 valid because the fact that the correct equation can be derived from a false assumption does not make the derivation correct. It is therefore without importance that in this erroneous derivation Dr.Guggenheim’s equation occurs first and equation ( I ) can subsequently be obtained from it. Dr. E. A. Guggenheim (London) It seems to me that Craxford has put the cart before the horse. The main point of my paper is that my formula (3.1) does not involve Poisson’s equation whereas Craxford’s formula (I) does. The derivation of my formula (3.1) is actually extremely simple. Denoting velocity parallel to the field by u and considering a thin strip of liquid we have as a condition of steady motion qdu = Xdr. . * (4 u = XTfT. . * (B) f = WZU . * (C) Integrating from the wall to the interior we obtain for the velocity u in the interior of the liquid In a tube of circular cross-section the flow f expressed as volume per unit time is given by where Y is intermediate between the radius Y of the tube and the radius Y~ of the cylinder of liquid whose velocity differs inappreciably from u.In practice the distinction between ye yi and Y is trivial. Substituting (B) into (C) we fecover my formula (3.1) f = W~XTf7). . - (3.1) D. R. Briggs. J . Physic. Chew. 1928,32 641. Phil. Mag. 1888 25 52 722 GENERAL DISCUSSION To transform formula (B) into Craxford's formula (I) we have to use my formula (3-3) which is the integral of Poisson's equation. I think that Craxford agrees with me that this substitution is meaningless unless D is constant across the layer. { = ~ P T / D . * (3'3) Dr. J. W. Wrzeszinski (London) on Venvey's paper p. 192 I have I differ from He states that emulsifying agents can be classified into two main (a) colloidal electrolytes and lyophilic colloids ; * (b) finely divided solids ; been investigating the role of emulsifiers for some time.Verwey's conclusions on a few points. groups-and furthermore that both have the effect of giving the drops properties comparable with those of solid particles and of shifting the double layer potential drop towards the outer phase. While it is certainly correct to say that finely divided solids acting as emulsifying agents have the effect of imparting to the dispersed globules properties comparable to those of solids i t is in my view less clear whether the same can be said regarding the stabilising action of colloidal electro-lytes e.g. soaps and of lyophilic colloids such as saponin and agar agar (for O/W emulsions).From results obtained in this laboratory it would appear that the action of a given electrolyte on an emulsion depends very much on whether the emulsion has been prepared with the aid of a finely divided solid or a substance which gives a colloidal solution in the dispersion medium. Using fairly concentrated O/W emulsions the actual con-centrations were kept between 80 and go per cent. of oil,-I observed that emulsions stabilised by substances like sodium oleate and saponin remained unaffected by the addition of the sulphates of the alkali metals but were broken by the corresponding thiocyanates and iodides while exactly the reverse was true of emulsions stabilised by finely divided solids e.g., alumina bentonite. The effect of these salts on the solutions or disper-sions of the emulsifying agents was next studied and was found to cor-respond exactly to the action of the salts on the emulsions prepared with the aid of the emulsifying agents under investigation.These observations show that the stability of stabilised emulsions is very closely related to the state of the solution (or dispersion) of the emulsifying aged used and, moreover that the resistance to inorganic salts is different with emulsions prepared with colloidal solutions on the one hand and those stabilised by (solid) suspensions on the other. The second function of emulsifying agents is said to be to shift the double layer potential drop towards the outer phase. I find it somewhat difficult to attribute a change in the stability of a stabilised emulsion to a change in the potential drop however determinative this be for the stability of an oil-hydrosol.I investigated the influence of electrolyt 3s on the cataphoretic mobility of the dispersed particles in stabilised O/W emul-sions. Using various emulsifying agents I obtained results which closely resembled those published by Dr. Limburg.20 Like Limburg I found that although the influence of electrolytes on the electrokinetic properties of a stabilised emulsion may be frequently very similar to their influence on the cataphoretic velocity of oil-hydrosols there was no similarity in the change of stability on the addition of electrolytes. No minimum of stability was observed at the isoelectric point. I have been led to the conclusion that with a sufficiently high concentra-tion of emulsifying agent-o-6 to 0.7 per cent.(calculated on the internal * See Corrigenda p. 732. "Limburg Rec. trav. chim. 1926 45 772 854 GENERAL DISCUSSION 723 phase) in a great many cases-the electrical behaviour of an emulsion will bear a relatively insignificant relation to its stability. This is also exemplified by the high resistance such emulsions are able to offer to the addition of electrolytes. It is understood that there is no chemical reaction between the emulsifying agent and the electrolyte added If this happens the emulsion is immediately rendered unstable irrespective of the con-centration of emulsifying agent. This question has been considered before in greater detail.21 Excluding chemical interaction emulsions will be stable if the agent used is present in sufficient concentration.If the concentration of emulsifying agent is lowered the mechanical rigidity of the protective film is materially decreased and the smaller the con-centration becomes the more will the properties of the emulsion resemble those of a lyophobic colloid whose stability is mainly determined by the charge on the particles. Dr. E. J. W. Verwey (Eindlzoven) in reply The object of my paper was to point out first of all that in order to understand completely the action of emulsifying agents we must understand the fact that emulsions without emulsifiers are never stable. In this respect the emulsions differ fundamentally from other lyophobic colloids. It seems to me that this fundamental problem is for the main part solved by the considerations in my paper on the stability of emulsions.I do not claim that the few remarks a t the end of the paper are more than provisional suggestions about the phenomena underlying the action of emulsifiers. I understand that Dr. W. distinguishes between O/W emulsions and oil-hydrosols the latter being the more diluted systems. It may be that in some types of highly concentrated emulsions especially when stabilised by a suificiently high amount of emulsifiers the stability conditions are rather complicated. It may be that apart from the double layer also another stability factor plays a part such as solvatation like in the case of lyophilic colloids. Writing about emulsions however I had in mind the work of Ellis Powis Limburg and others about which has been reported again in the paper by Eilers and Korff.Here we are dealing with systems where the stability of the oil droplets with respect to co-agulation and the electrophoretic mobility are clearly correlated. Even if no special emulsifiers had been added deliberately to these systems the very fact of the high zeta-potentials of their particles proves according to the arguments given in my paper that their particles were stabilised by some emulsifying agent. These substances had undoubtedly the effect that the double layer assumed properties as at solid particles and the double layer potential drop was shifted towards the outer phase. Prof. L. S. Moyer (Minnesota) on paper by McFarlane pp. 258 and 261 I was much interested in the observations of McFarlane on the remarkable behaviour of this unusual virus.However I am unwilling to agree with McFarlane that " the work of Abrahamson (should be Abramson) and Moyer suggests that the mobility of the proteins is accounted for solely by the ionisation potential and consequently that the adsorption of salt ions must be negligible in amount ". As a matter of fact in our papers we have been careful to state referring to this citation that " this will probably be found to be not true in general for some process tanta-mount to adsorption of ions of the salt may occur the shape of the LJ - c curve remaining essentially the same but shifted because of the effect of salts on the isoelectric point ".22e*s To assume that " in normal working conditions the molecules of soluble proteins in general may not associate with the wall of the Tiselius U-tube " is not supported by what we know of their behaviour.Abramson and I among many others have pointed B1 King and Wrzeszinski Trans. Favaday SOC. 1939 35 741. rnH. A. Abramson J . Gen. Physiol. 1933 16 593. ?3 L. S. Moyer and J. C. Abels J . Biol. Chem. 1937 121 331 724 GENERAL DISCUSSION out repeatedly 24s 25 that with the possible exception of red cells 24 or particles already coated with certain proteins 26 surfaces (including glass or quartz) readily adsorb all sorts of soluble proteins egg albumin the serum proteins casein insulin gelatin gliadin etc. upon immersion of the surface in their solutions and thereupon become endowed with their electrokinetic properties.I believe that another explanation must be looked for to explain the anomalous boundaries observed with vaccinia virus. Dr. A. S. McFarlane (London) communicated By contrast with Moyer’s above quotation relating to the effect of adsorbed salt ions on the mobility of proteins there is the recent statement by Abramsoa Gorin and Moyer 27 “ For if a t constant ionic strength in simple systems the average charge of the molecule is known to be almost completely deter-mined by the average number of equivalents of hydrogen or hydroxide ions bound it follows that changes in the isoelectric point incidental to surface film formation must be directly correlated with changes in the relative strengths of the amino and carboxyl groups ”. I am therefore grateful to Prof.Moyer for now making it quite clear that he and his collaborators accept the view that adsorbed salt ions contribute to the mobility of proteins. Their claim however that the contribution of these ions is a constant over the $H range in which protein mobilities are usually determined affecting neither the slope nor the shape of the $m-mobility curve is difficult to accept. It is based on the following procedure 27 : “ In a plot with the number of equivalents of acid (base) bound per gram of protein as ordinate and the PH as abscissa the zero point on the ordinate is found by shifting in co-ordinates vertically until the curve goes through zero at the isoelectric point as determined by electrophoresis. The mobility data are then compared with the titration data by taking any single point on the smoothed mobility curve and multiplying the mobility by a factor that will make the two curves correspond.If when all the experimental points are multiplied by this same factor they fall on the titration curve within the limits of error this proportionality is to be considered as demonstrated.” The mobility curve is thus rotated about the isoelectric point until its mean slope is arbitrarily made to coincide with the mean slope of the titration curve and the presence of any factors (other than acid or base ionisation) which affect the mobility of a protein in a linear manner with changing PH could not be detected by examination of these superimposed curves. At present there seems to be as much evidence for the view that the absorption of salt ions on proteins varies progressively with PH as for the view that there is a fixed degree of salt adsorption over a wide PH range.The presence of non-linear changes of salt adsorption with PH would presumably be demonstrated by deviations of the mobility curve froin the superimposed titration curve but the signi-ficance of such deviations can only be assessed in relation to the experi-mental errors involved in the determinations of mobility and acid (base) binding capacity and these are not discussed by the authors. I note with interest Moyer is not in favour of the suggestion that in normal working conditions soluble proteins may not associate with the wall of the Tiselius U-tube. It would be interesting to know what alternative explanation can be offered for the complete absence of any signs of endosmotic flow a t the walls o f the U-tube containing protein materials including the very large plant virus molecules other than vaccinia.24 H. A. Abramson Electrokinetic Phenomena New York 1934. 25 L. S. Moyer Cold Spring Harbor Sym$osia on Quantitative Biology 1938 6, 26 L. S. Moyer and E. Z. Moyer J. Biol. Chem. 1940 132 357 373. 27 H. A. Abramson M. H. Gorin and L. S. Moyer Chew Rev. 1939, 228. 24 345 GENERAL DISCUSSION 725 Dr. S. Levine on the papers of Hamaker p. 188 Derjaguin pp. 208-10, Levine and G. P. Dube pp. 215-19 (Coagulation of Hydrophobic Sols and minimum in Electrical Energy). Objections of an apparently serious nature to our expression for the interaction of two colloidal particles have been raised by Hamaker and Derjaguin.These relate to our minimum which I believe is of paramount importance in hydrophilic sols so that it becomes necessary to answer their criticisms. The question arises as to whether the minimum influences the coagulation process of hydrophobic sols. I shall try to show that at least for small particles the minimum cannot be the position where the particles coalesce although it does affect the rate of coagulation. Firstly in order to explain slow coagulation it seems essential that there exists an energy barrier over which the colliding particles must pass before forming secondary particles. Secondly the position of the minimum srnh (in units of the radius) is in many cases too far out.As examples if we consider the critical coagulation points illustrated in Figs. I and 4 (pp. 218 and 223) for the three electrolyte types 1-1 2-1 and 3-1 the radius being a = 15 mp then 7 = K a = 10.0 2-74 and 1-22 and Smh = 2-13 2.6 and 3-5 respectively. These values are readily obtained from the formulz and numerical results given in our earlier papers. For larger particles of radius 50 m p a t the same critical precipitation values for the three electrolytes the corresponding values of 7 are 32.9 9-00 and 4-03 and those of s w 2-04 2-14 and 2.36 respectively. In truly hydrophobic sols such as gold and platinum very little water is carried down by the precipitate and it is unlikely that the particles are separated by distances of the order 2-5 times the radius.For the smaller particles therefore the minimum cannot be the position of flocculation, although for the larger particles the situation is not so clear. However this last problem is partially solved by examining the depth of the minimum Fmb in the electrical energy which may not be large enough to yield a stable position permitting coagulation. Thus returning to the two sets of examples referred to above and assuming the same critical potentials as in Fig. I p. 218 (45 m.v. for the 1-1 type and 25 m.v. for the 2-1 and 3-1 types) F w / k T o is equal to 4-5 0-93 and 0-44 when a = 15 mp and to N 20 4.6 and 4-0 when a = 50 mp for the three electro-lytes 1-1 2-1 and 3-1 respectively. The only value of F a that seems to cause trouble is that for the 1-1 type with a = 50 mp.One may compare the effect of a minimum even of depth 5kT in dilute sols to that of the van der Waals attractive energy between molecules in a gas. It should be noted that two atoms forming a stable molecule have an energy of binding of the order of I electron volt w 4okT,,. When we come to large particles there arises a difficulty which is pointed out by Hamaker and which was already known to us. For large 7 it can be shown that s d m 2 + I - I ~ / T and w- 0-085.5~Da (asymptotically) which is directly proportional to the radius as illus-trated by Hamaker in Fig. 2 p. 188. At D = 80 a = 50 mp and 5 = IOO mv. for example F h =- 94kTo. This implies that all large spherical particles should coagulate rapidly in the position of the minimum and indeed cannot form stable sols (suspensions or emulsions) at variance with experiment as remarked by Hamaker.Further this appears to contradict our conclusion on p. 220 concerning the absence of an upper limit to the particle radius in stable sols which was based on the properties of the energy at contact and of the energy maximum. Thus it becomes necessary to remove this discrepancy between our theory and experiment. It might be thought at first that the approximation used here which is reliable for small values of T leads to a considerable error for large T but the fol!owing illustration suggests that this does not solve the difficulty. Consider two spherical particles from which we have cut away spherical caps of depth I / K so placed that the two circular plane sections (discs) are parallel to one another a t a distance I/K apart (Fig.ii). Neglecting the influence of the rest of the spheres we will assume this model t 726 GENERAL DISCUSSION approximate to two large particles almost in contact (the radius a > I / K ) . In one of the earlier papers a we applied our method to calculate the electrical energy per unit area associated with two infinite parallel plates and found it to be always negative assuming that the surface charge den-sity on the plates remains constant. Noting that the angle 8 in Fig. ii is given by a cos 8 + I / K = a i.e. by cos 8 = (T - I ) / T the area of each disc is was sins 8 w 2 m u a / ~ for 7 9 I. Substituting this expression for the area and also I / K for the distances between the two plates into formuk (40) and (38) in the above mentioned paper the electrical interaction energy of our model becomes - 0.036 52Da yielding the same order of magnitude as our asymptotic form for the minimum energy for two particles.Using the original Debye-Hiickel equation Corkill and Rosenhead 29 recently computed the electrical forces between two parallel plates and found that there was an attraction when either the charge or potential on the plates is kept constant. Only when the difference of potential between the surface of the plates and the median plane is kept constant do the electrical forces become repulsive. This suggests one source of error in our results namely that the charge on the particles should not be con-stant independent of the separation. However whereas in the case of two parallel plates it is not difficult to suggest other conditions this is not so simple in the case of two spherical particles.A discussion of this problem has already been given by us 1 and its solution appears difficult. Mde/. for /urge purhihs. FIG. ii. FIG. iii. Effect of Surface Irregularities. It is well known that the surface of a crystal has irregularities which are at least of the order of I mp in depth (and length). Particularly crystal growth pro-ceeds in a random fashion when there are impurities which is usually the case during the formation of colloidal particles. If the uneven char-acter of the particle surface is taken into account colliding particles will usually touch at the projecting points. This receives confirmation from the surprisingly small values of the van der Waals constant A that we obtained in our paper.Further the charge will tend to concentrate a t these protuberances on the surface,*O which indeed are the active spots proposed by Kruyt and Verwey.81 To illustrate the influence of these active spots on the form of the electrical energy for large particles we return to the model in Fig. ii for two particles of say IOO mp in radius and cover each disc with a layer of smaller particles of radius I mp such that neighbouring particles are about 10 m p apart yielding about 60 particles on each disc (Fig. iii). (The following argument does not hold if the density of small particles is so high that they are say 4 mp apart but this would imply an Corkill and Rosenhead Proc.Roy. SOC. London ( A ) 1939 172 410. Verwey Chem. Rev. 1935 16 363. I wish to suggest another solution to this dilemma. 28 Levine and Dube Trans. Faraday Soc. 1939 35 1125. so According to Jeans Electricity and Magnetism p. 194 this is the case for a hemispherical boss on a plane conducting surface GENERAL DISCUSSION 727 extremely rough surface.) Assuming an electrolyte concentration of I mMol./l. so that T = 10 and 0.1 for the large and small particles re-spectively and taking 5 = roo mv. we readily calculate that the minimum electrical energy of pairs of large and small particles axe - 150 kTo and - 0.023 kTo respectively whereas the corresponding values of the energy at contact are 210 kTo and 10 kTo. If the charge is all concentrated on the adhering small particles in our model this implies that the equivalent of 6500 pairs of small particles (say 81 on each disc) must simultaneously be in their position of minimum electrical energy in order to attain a total minimum energy of - 150 kTo which is not possible.On the other hand only 21 pairs of small particles in contact give the contact energy for the spherical large particles. Since this model is an extremely crude one we can only reach a very qualitative conclusion namely that the presence of an uneven surface may reduce the minimum electrical energy by as much as a factor of 5 or 10 whexeas the change in the electrical energy a t contact is rather uncertain. The implication of this discussion is rather far reaching namely that no large particles which are truly spherical can form stable sols suspensions or emulsions.It is well known that emulsions which contain large particles (and often coarse suspensions also) are stable only when protected by a layer of smaller particles which may be either colloids certain organic ions such as alkali soaps or very finely divided particles. This is the type of model for large colloidal particles that we have postulated above. In the case of a soap emulsifier the surface would hardly be uneven if a closely packed monolayer of the soap molecules had formed on the par-ticles. However there is no real evidence to disprove the assumption that before this takes place an appreciable part of a second layer has al-ready been deposited producing an irregular ~ u r f a c e .~ ~ Verwey claims that an unprotected emulsion is unstable because a sufficiently high ( potential can never be reached. Lack of space prevents me from com-paring in greater detail his explanation with the alternative one put forward here. The general effect of surface indentations would be to diminish the rapidity with which the van der Waals energy and (to a lesser extent) the electrical energy fall off with particle separation compared to the case of two hypothetical truly spherical particles whose radius is equal to the average radius of the real particles. This would tend to move both the maximum and minimum farther out from particle contact and would account for example for the difficulty mentioned in our paper in footnote 14 on p. 225. We shall discuss this phenomena in more detail in another paper.On first sight the preceding analysis appears to invalidate the ex-planation in our paper for the dependence of the stability properties of sols on the particle radius. However it appears that for large particles the change in the electrical interaction energy a t the maximum as a result of surface imperfections is much less than that in the minimum, and we have based our conclusions on the properties of the former. Furthermore the fact that we are getting qualitative agreement with ex-periment suggests that we cannot be far wrong. It must be remembered that a mathematical treatment of particles of irregular shape would be quite difficult and the best that we can do is to work with idealised cases, at least in the initial stages of the investigation.Mutual Free Energy of Particles. There is another source of error in our calculations which is the object of attack by Derjaguin namely that the free energy and not the ordinary internal electrical energy associated with the double layers should be 32 I am indebted to Dr. A. S. C. Lawrence for this suggestion and also for lengthy discussions on the properties of gels 728 GENERAL DISCUSSION calculated. Derjaguin asserts that the free energy of an electrolyte should be obtained by charging all the ions proportionally when Debye’s method is used. However Onsager s3 and Halpern 34 have shown that one can charge the ions in any manner provided the solution is kept electrically neutral and certain conditions of self-consistency are satisfied which is the case with the approximate Debye-Huckel solution.When the original Debye-Huckel is used this is no longer true but Muller showed that two simple methods of charging the ions namely those of Debye-Hiickel and of Guntelberg lead to ionic activity coefficients which were only slightly different. The method of charging the ions and colloidal particles described on p. 179 in the second of our papers,*@J to which Derjaguin is referring was chosen as an illustration to show that K may be kept constant during the charging process. However we may also use Debye’s method of charging and still obtain a term expressing the work of charging the ionic atmospheres of the colloidal particles which Derjaguin wishes to omit. The problem is to find the mutual free energy of the colloidal particles which are all assumed to have fixed positions.The particles may then be considered as external fields acting on the ions over whose positions we must average. Then the free energy of such a system is obtained by charging both the particles and ions. The fact that the macroscopic state of this system is independent of the positions of the ions does not imply that we must not charge the ions ; otherwise we could not charge the ions in an ordinary electrolyte to obtain its free energy. Since the external field exerted by the particles changes with the relative position of the particles the work of charging the ions will vary with these posi-tions so that we must have a contribution to the interaction energy of the particles which comes from charging the ions.This is still true when the Debye method of charging is employed. To avoid the difficulty of dealing with a sol which is not electrically neutral in his thermodynamic argument Derjaguin is compelled to introduce a hypothetical large con-ductor which would change the thermodynamic system under considera-tion. Finally I have not been able to verify Derjaguin’s equation (IS) the Gibbs-Helmholtz relation. Our derivation of the work function expressing the interaction of the particles is based on keeping K constant which cannot be valid for concentrated sols (e.g. gels). It turns out that this assumption leads to the ordinary average electrical energy when the approximate Debye-Hiickel equation is used. On using their original equation however there is an appreciable difference between the internal energy and our work function as shown in an earlier paper.87 It should be instructive to recon-sider the work of Corkhill and Rosenhead from this point of view.Also, it would be desirable to investigate the error involved in assuming K constant. The relation of our theory to that of Langmuir s* has already been discussed.22 No such conductor exists in actual sols. Role of Minimum in Hydrophilic Sols ; Gelation. No conclusive evidence could be found to prove that the minimum need exist a t all in order to explain the stability properties of hydrophobic sols. Consequently i t becomes imperative to seek for properties of hydro-philic sols which suggest the existence of the minimum.I believe that the phenomena of gelation and in particular of thixotropy can be attributed, at least partially to the minimum in the electrical energy. Now gels 33Onsager Chem. Rev. 1933 13 73. 34Halpern J . Chem. Physics 1934 2 85. 35Muller Physzk. Z. 1927 28 324. 3fiLevine Proc. Roy. SOC. A 1939 170 165 37 Levine J . Chem. Physics 1939 7 831. 38 Langmuir ibid. 1938 6 873 GENERAL DISCUSSION 729 usually consist of non-spherical particles and are quite concentrated so that the computation of the mutual energy of two spherical particles can hardly lead to a detailed theory of gel structure. Hence only a brief and qualitative discussion can be presented here. At present there are three theories of gelation the first based on the existence of layers of bound water the second on a network of particles in actual contact and the third on long range forces between the particles.The first theory that of solvation is not supported by both experimental 3 and theoretical 40 work on the change of dielectric constant of water with field strength (a measure of the saturation or solvation effect) which is shown to be quite weak because of the strong coupling between the water molecules preventing orientation in an external electric field. This does not refer to the water absorbed by short range forces inside the particles or in tbe cracks on the surface of the particles but to the layers of water surrounding the particle. The absence of bound water receives further confirmation from recent work on viscosity which shows that the anomalous viscosity of dilute hydrophilic sols is mainly due to the asymmetric shape of the particles.41 It is proposed that for hydrophobic sols whose particles have " hard " surfaces the van der Waals energy of interaction brings about coalescence a t coagulation whereas in hydFo-philic sols whose particles are per-meated with water the van der Waals energy is quite small and the only " coalescence " which can occur is at the minimum (process of gela-tion) unless the water is removed from the interior of the particles by the addition of sufficient electrolyte (salting out).I therefore assume with Hamaker42 that the funda-mental difference between hydro-phobic and hydrophilic sols can be represented by the mutual energy curves for two particles as shown in Fig.iv the intensity of the van der Waals attraction being the deter-mining factor. This permits of a 4 2! A Hy&ophod/i So/. graduL1 transition from truly hydrophobic to truly hydrophilic sols de-pending on the amount of water imbibed by the particles. One of the chief difficulties of the second theory of gelation the link or scaffolding theory,43 is to reconcile the failure of the (hydrophilic) particles to coalesce in dilute sols with their apparent ability to make contact in the more concentrated state (gelation) the electrolyte concen-tration being the same in the cases. The scaffolding theory was proposed chiefly to explain why rod-like particles in relatively dilute coiicentrations can form gels more readily than particles of other shapes whereas spherical particles seldom form gels.However the theory of long range forces (based on our minimum) can also explain this property in the following manner. Since hydrophilic particles are usually quite small and the energy minimum is roughly proportional to the minimum it is not easy to form a stable lattice of small spherical particles. However a rod-shaped particle may be compared to a rigid row of small spherical particles, and when two of these are parallel to one another assuming as a first approximation that the electrical energy is additive we shall have a much Malsch Physik. Z. 1929 30 836. 40 Debye ibid. 1935 36 193 ; Piekara Proc. Roy. SOC. A 1939 172 360. I1 Cf. Robinson Proc. Roy. SOC. A 1939 170 519. 42 Hamaker Rec.Trav. Chinz. Pays-Bas 1936 55 1015 ; 1937 56 I 727. 43 Cf. Goodeve Trans. Faraday Soc. 1939 35 342 730 GENERAL DISCUSSION deeper minimum which is roughly proportional to the length of the rods. This suggests that a gel should consist of minute clusters of parallel par-ticles which form a stable configuration and which overlap in some way.4* This receives confirmation from the existence of tactoids and from the work of Ekrnal and Fankuchen 45 on virus proteins and from that of Hauser 48 on bentonite. Further the gel still remains optically empty although when the gel is sufficiently concentrated it may become birefringent when the possibility of larger tactoids exists. The fact that orientating the particles does not ordinarily produce gelation can be attributed to the sensitivity of the position of the minimum to electrolyte concentration and also to particle size.It would be accidental if the concentrations of sol and electrolyte were just right so as to bring all the particles into their equilibrium position on alignment. Brownian motion must bring the particles close enough together and then orientate them so as to form clusters the orientation process apparently being facilitated by rolling or tapping (rheopexy) . The difference between thixotropic and non-thixotropic gels is perhaps only one of the energy of binding a t the minimum, which is greater for the smaller particles. I t seems quite natural to assume that the same electrical forces which act in thixotropic gels should continue to do so in ordinary gels.Of course it is likely that there are many gels which have a scaffolding structure but it should not be assumed a przori that this is true of all gels or even of the majority of them. (My remarks have been confined to water as the dispersion medium and need not hold with other liquids.) I wish to emphasize that this proposed theory of gelation is tentative, and that a considerable amount of theoretical work is necessary before it can be adequately tested. However I thought the preceding discussion necessary to counteract any tendency to lightly dismiss the existence of minima in the mutual energy of colloidal particles. It is hoped to in-vestigate the properties of hydrophilic sols in greater detail in a later paper. Prof. B. Derjagsl (addendum to pafier by author fip.203-11) The calculations of the rate of the slow coagulation of lyophobe colloids, included in my paper,&’ were carried out without making the necessary allowance for the London-van der Waals forces. We may easily fill in this gap however by limiting ourselves to the case of particles with a large radius Y . For this purpose making use of Hamaker’s formula for the energy of the van der Waals attraction U,(H) of two spheres,48 we supplement the expression for the total energy of interaction U(H) of two spherical particles : U(H) = U,(H) + U,(H) = KTn and A is the constant of van der Waals energy.2 The expression for U(H) will disclose one minimum and left of it a maximum if the value for m is less than a certain value m, roughly taken to be equal to 0.5 (see Table I).At m > m0 U(H) decreases monotonically with a decrease in H consequently in this case the colloid system is unstable without any doubt. 44The idea that gels consist of minute tactoids was suggested to me by 45 Bernal and Fankuchen Nature 1937 139 923 ; Bernal ibid. 1939 143, 46 Hauser and Reed J . Physic. Cham. 1937 41 911. 47 B. Derjaguin Trans. Faraday SOC. 1940. 36 203. 48 Hamaker Physica 1937 IV 10 1058. Prof. J. D. Bernal. 663. Cf. Langmuir Zoc. cit GENERAL DISCUSSION m . K ( Z ) ~ ~ = . K(z)min -73 1 0.15 0.2 0.3 0'4 0'5 (2) 1-32 1.21 1.13 1-02 absent (I) 1 4 8 1 0.97 0.96 0.94 z:: absent Employing formula (21) of our communication in a slightly altered form instead of (22") we obtain : Thus the emulsion will be sufficiently stable under the condition that m < 0.15, or in accordance with (1') approximately under the condition : The criterion of the stability which we developed theoretically is in agreement with the empirical rule obtained by H. Eilers and I. Korff 4O : 49 Eilers and Korff Trans. Faraday SOC. 1940 36 229. K (IV) cc2 - = const = C . where (, is the critical value of the zeta-potential. In particular the above authors found that relation (IV) describes very well Povis's experi-ments with emulsions of cylinder oil in water (H. Eilers and I. Korff, Table IV) as well as with the hydrosol As,S (ebenda Table VI) if a value of the order of 10-3 is assumed for C when is expressed in millivolts, and a value of the order of 10-14 when To is expressed in c.g.s.E. Upon equating Go with go in (IV) and making use of these values of C, from (111) and (IV) we obtain the following value for A : which agrees with the " mean " value of this constant.m It should be noted that these computations being based on the simpli-fied Debye-Huckel equation hold strictly speaking only while the values of the quantity A - 1 0 - 1 2 . (V) where z is the valence of the ith ion are not large-f the order of unity. By the way the critical values of this quantity were of the order of 1.5-2.0 in Povis's experiments. Thus the results obtained particularly relation IV cannot lay claim to a great degree of accuracy. A more exact calculation based on the complete Debye-Huckel equation will form the subject of the following paper

ISSN:0014-7672    

DOI:10.1039/TF9403600711

出版商:RSC    

年代:1940

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.

ISSN:0014-7672    

DOI:10.1039/TF940360732b

出版商:RSC    

年代:1940

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No.13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions.Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.

ISSN:0014-7672    

DOI:10.1039/TF9403600733

出版商:RSC    

年代:1940

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.

ISSN:0014-7672    

DOI:10.1039/TF9403600749

出版商:RSC    

年代:1940

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No.13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions.Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.

ISSN:0014-7672    

DOI:10.1039/TF9403600752

出版商:RSC    

年代:1940

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No.13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions.Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.

ISSN:0014-7672    

DOI:10.1039/TF9403600766

出版商:RSC    

年代:1940

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.

ISSN:0014-7672    

DOI:10.1039/TF9403600780

出版商:RSC    

年代:1940

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.

ISSN:0014-7672    

DOI:10.1039/TF9403600781

出版商:RSC    

年代:1940

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.

ISSN:0014-7672    

DOI:10.1039/TF9403600785

出版商:RSC    

年代:1940

数据来源: RSC