J . Chem. SOC., Faraday Trans. I, 1984, 80, 1553-1566 Adsorption of Ions at the Cellulose/Aqueous Electrolyte Interface Part 3.-Calculation of the Potential at the Surface of Cellulose Fibres BY THELMA M. HERRINGTON* AND BRIAN R. MIDMORE Department of Chemistry, University of Reading, Reading RG6 2AD Received 14th September, 1983 The zeta potential, (, for cotton linters and bleached sulphate pulp has been calculated from measurement of the streaming potential. The measurements were taken at the same electrolyte and pH conditions as the charge/pH isotherms of Part 1. A comparison is made of the surface potential calculated under the same conditions from the charge/pH isotherms, negative adsorption experiments, polyelectrolyte theory and streaming potential measurements. It is shown that the [ potential is not a good relative measure of the surface charge and cannot be used for qualitative comparison between such similar materials as bleached sulphate pulp and cotton linters.Since the discovery of electrokinetic phenomena in the early nineteenth century, extensive data have been accumulated in this field. This has been partly for historical reasons and partly because of the relative ease with which electrokinetic phenomena may be studied. Electrokinetic phenomena involve the tangential displacement of a liquid along what is known as the slipping plane. From theoretical considerations it is possible to calculate the potential at this slipping plane from measurement of electrokinetic phenomena. This potential is known as the zeta potential. The zeta potential, [, has a different character from v0, the surface potential, generally being considerably smaller in magnitude.It has often been approximated to vS, the potential of the diffuse double layer, implying that the slipping plane coincides more or less with the first layer of adsorbed i0ns.l However, c only gives exact quantitative information about the nature of the double layer if the position of the slipping plane is known, which is in turn only determinable from knowledge of both [ and vS. It might appear from these considerations that the extensive data accumulated in the field of electrokinetics were unjustified, taking into account that the absolute value of [ only has relevance within the context of electrokinetic phenomena. However, it has always been thought that c has a semi-quantitative significance, potentials within a given system (or different types of similar material) being comparable with each other.The ‘isoelectric point’, where [ = 0, is also determinable and allows a comparison with the point of zero charge from the charge/pH isotherms. Moreover, the measurement of the [ potential gives information about the nature of the diffuse layer which is totally independent of adsorption phenomena and therefore provides a very useful and independent comparison with values of I,U determined from charge/pH isotherms or negative-adsorption data. THEORY When a liquid is forced through a compacted plug of particles a convection current is produced because of the removal of excess counter-ions from the double layer by the 15531554 THE CELLULOSE/AQUEOUS ELECTROLYTE INTERFACE flowing fluid.In order to maintain electrical neutrality this convection current is balanced by a conduction current in the opposite direction, which induces the ‘streaming potential’ between either side of the plug. The interpretation of these streaming potentials depends upon the following assumptions : (1) only external fibre surfaces are involved, (2) each portion of fibre is electrokinetically identical, (3) the flow is lamellar, (4) the velocity gradient or shear rate at the plane of shear is constant throughout the pad and ( 5 ) the internal pore network is statistically uniform throughout the pad. The Helmholtz-Smoluchowski equation for streaming potential is given by where is the pore factor. (Other terms are defined at the end of the paper.) It is related to the conductivity of the bulk liquid and the conductivity of the surface by r = 1 /(&+2As/r).Eqn (1) applies to single capillaries, and its extension to porous plugs presents problems when the surface conduction becomes important, i.e. at low concentrations of electrolyte. The surface-conduction problem can be overcome by measuring streaming current since surface conduction is not involved : I, = - ~ a P c / q L . (3) This formula would apply to plugs composed of granular particles of fairly uniform size and shape. Chang and Robertson2 worked with compressible plugs of beaten and unbeaten cellulose fibres, nylon, dacron, etc., and found that a plot of In (I, q/&P) against c was linear, i.e. (4) where c is the concentration of solid material in the plug.In terms of the streaming potential ( 5 ) so that the pore factor c is given by c = exp (-Jc)/(A,+ 2Ls/r), and the slope of a plot of E, against P would depend on the density of the plug. However, we found that it was only possible to alter the packing density of the plug within narrow limits, but within these limits the slope was independent of the plug density at constant electrolye concentration. Thus it was decided to use eqn (2) and to eliminate < by the method of Brigg~.~ At high concentrations of electrolyte (0.1 mol dm-3 KCl) < = l/Ao = R,/L. At low electrolyte concentrations Is = - EaPc exp (- Jc)/qL ESP = E c exp ( - Jc)/h(A, + 2AsIr)l = l/(Ao+2As/r) = R/L.Then Es/P = ERc/vA,, R, = ERc/qK (4) where K is the cell constant. EXPERIMENTAL The potassium chloride and sodium chloride used were A.R. grade. The hydrochloric acid and sodium hydroxide solutions used for adjusting the pH were prepared as in Part 1, as were the fibre slurries. The streaming-potential apparatus is described in detail el~ewhere.~ It consisted of two reservoirs connected by two-way taps to the streaming-potential cell. The streaming solution was forced through the base of one reservoir, through the cell and into the other reservoir via a vertical glass tube, which ensured that the hydrostatic head opposing theT. M. HERRINGTON AND B. R. MIDMORE 1555 flow of solution remained constant. Two smaller vessels were connected to the side of each reservoir and enabled the pH, conductivity and temperature of the solution to be determined.The solution was forced from one reservoir to the other using C0,-free nitrogen. All joints were either Teflon-sleeved cone-and-socket or else Sovril. The fibre was formed between two perforated platinum discs covered with nylon mesh. Platinum wire attached to the discs was used to measure the resistance, R, of the pad. Ag,AgCl electrodes were positioned either side of the platinum discs to measure the streaming potential. These were the same as used in the titration work. The streaming potential was determined using a Vibron electrometer model 62 A (Electronic Instruments, Richmond, Surrey). The conductivity of the solution and pad was determined by means of a Wayne-Kerr bridge, model B605 (Wilmot-Breeden Electronics, Bognor Regis, Sussex) and the pH of the solution was determined using a pH meter, model pHM 64 (Radiometer, Copenhagen), with glass and calomel electrodes. The fibre pad was formed from a slurry in demineralized water.The settling of the fibre was accelerated by suction; care was taken to keep the pad wet and free of air bubbles. Fibre concentrations of ca. 0.15 g The cell constant of the fibre pad was determined by repeatedly passing fresh KC1 solution (0.1 mol dm-3) through the pad until the resistance, R,, of the pad remained constant. The temperature of the solution was recorded. From tables of the conductivity of KCl solutions at that temperat~re,~ the cell constant, K, of the pad was calculated. To measure the streaming potential, the 0.1 mol dm-3 KCl solution was replaced with the streaming solution mol dm-3 NaCl).Again the plug was washed with solution until a constant resistance of the plug was recorded. Some of the solution was then forced into a side vessel and its pH and temperature were determined. The conductivity was also determined in the side vessel as a check to ensure adequate washing of the plug. The pH was varied using sodium hydroxide and hydrochloric acid. All the plots of E, against P were linear. The electrophoresis measurements were carried out using the Rank mark I1 electrophoresis apparatus (Rank Bros, Bottisham, Cambridge). The silica flat cell, fitted with a double- platinum-electrode system, was used. The cellulose fines were obtained by beating a 1 % slurry in a single-rotor blender; after filtering, the fines were collected by centrifugation and kept in wet storage at 4-6 "C. were used.mol dm-3 or RESULTS Streaming-potential measurements were made for cotton linters and bleached sulphate pulp over the whole pH range (2-10.5) in mol dm-3 NaCl. The zeta potential was determined from the linear plots of E, against P. Data for the whole pH range in 10-2moldm-3 NaCl were also determined for cotton linters. The variation of c with pH is shown in fig. 1 for cotton linters and in fig. 2 for bleached sulphate pulp. Electrophoresis data were also determined for cotton linters, and the zeta potential so obtained is shown by way of comparison in fig. 1. The data are in agreement within experimental error.the variation of potential with distance from the surface is given by According to the analysis of Gouy and exp ( - K X ) = tanh [zery(x)/4kTl/tanh (zeryd/4kT) (7) where ~ ( x ) is the potential of the double layer at a distance x from the surface, which is equal to c at the plane of shear. Now as is low for cellulose fibres (< 25 mV) then tanh (ze[/4kT) ze[/4kT. (8) Thus at pH a exp ( - Icx,) = sit, 4k T (9)1556 THE CELLULOSE/AQUEOUS ELECTROLYTE INTERFACE / 1 I4 12- 10. 0 . -S/mV - 6. 4 - 2 - 0.. PH Fig. 1. Variation of the zeta potential with pH for cotton linters from measurements of streaming potential. 0 , l 0-3 mol dm-3 NaCl ; 8 , l 0-2 mol dm-3 NaCl ; , 1 0-2 mol dm-3 NaCl (micro-electrophoresis data) ; ----, [, values (see text). - 0- _ _ - - - 4 - - - / / //020Y /’ .6’ /4.r P ” / / / / , A I . 2 3 4 5 6 7 8 9 10 I I where t , = tanh (zey/f/4kT); x,, [, and y/$ refer to the distance of the plane of shear, the zeta potential and the surface potential at pH a. Similarly for a second pH at the same effective ionic strength, pH b:T. M. HERRINGTON AND B. R. MIDMORE 1557 Table 1. Electrokinetic data for cotton linters in mol dm-3 NaCl from streaming- potential measurements 10.64 12.0 9.52 11.0 7.98 9.3 6.42 8.9 4.83 7.5 4.34 6.4 3.09 2.0 2.24 0.3 - - 24.0 1.563 13.9 - - 18.8 1.188 10.6 - - 17.2 1.083 9.6 - - 1 5.9a 1.000 8.9 0.843 4.10 11.7 0.729 6.5 0.719 3.93 8.9 0.552 4.9 0.225 3.63 3.4 0.208 1.9 0.034 3.70 a vs(NA) = - 10.5 mV at pH 6.5 estimated from negative-adsorption experiments assuming S = 130 m2 g-l. If the position of the plane of shear does not change on altering the pH, then x, = X b and This equation enables a quantitative comparison between zeta potential and surface potential without an accurate estimate of c necessarily being known, as this is eliminated in the ratio.Also, if tya is low (a condition that is fulfilled in the case of cotton linters in lov2 mol dm-3 NaCl where rys < 25 mV) then [eqn (14) below]. Thus if the acid group is totally dissociated at pH b, then l a / T b = a (13) where a is the degree of dissociation at pH a. This allows values of pK to be calculated at different values of the pH. A plot of pK against a gives pKo from electrokinetic data. The values of pK are given for cotton linters in mol dm-3 NaCl in table 1.A plot of pK against a extrapolates to a pKo of 3.65. [This compares with a pKo of 4.05 for mol dm-3 NaCl (fig. 6 of Part 1) using values for a calculated from the charge/pH isotherm.] Alternatively values of aa were obtained from the chargelpH isotherm for cotton linters in mol dm-3 NaCl (fig. 2 of Part 1). Taking cb as - 8.9 mV at the point of neutralisation (pH 6.42), then la can be calculated from eqn (13). These values are also given in table 1 and they are plotted as a dashed line in fig. 1. To show that the approximation for eqn (12) is valid, values of tys were calculated from the Gouy-Chapman equation : od = ( 2ni k Tc)42 sinh (zi e tya/2k T ) (14) assuming that 06 = oo and thus tya x ry,(GC). The nitrogen-adsorption surface area of 130 m2 g-l for cotton linters was used to estimate od from the Sao/pH isotherm (fig.2 of Part 1). As is shown in table 1, the values of rya are c 25 mV. mol dm-3 NaCl, tyo(GC) calculated in this way is much higher, and eqn (1 1) must be used to calculate la. These values are given in table 2 and are plotted in fig. 1. In the case of bleached sulphate pulp in mol dm-3 NaC1, For cotton linters in1558 THE CELLULOSE/AQUEOUS ELECTROLYTE INTERFACE Table 2. Electrokinetic data for cotton linters in mol dm-3 NaCl using streaming- potential measurements 10.03 8.46 7.31 6.34 6.18 6.08 4.81 4.50 3.78 3.10 2.71 2.15 24.1 22.8 22.8 21.5 20.6 20.2 16.8 15.7 8.9 4.3 1.2 0.2 55.6 47.4 42.0 37.2b 36.3 35.5 21.7 15.7 6.9 4.3 1.147 1 .ooo 0.900 0.805 0.788 0.771 0.484 0.353 0.144 0.096 26.1 22.8 20.5 18.4 18.0 17.6 11.0 8.0 3.3 2.2 a vANA) = - 17.1 mV at pH 6.5 if estimated from negative-adsorption measurements assuming S = 130 m2 g-l.* tb = 0.4307. Table 3. Electrokinetic data for bleached sulphate pulp in lop3 mol dmP3 NaCl using streaming-potential measurements 10.31 8.55 6.53 5.82 4.78 4.08 3.44 2.51 13.9 13.5 12.4 12.2 10.4 7.6 4.9 1.6 110.8 107.5 99.9 89.2 69.7 42.4 15.8 2.2 1.015 1 .ooo 0.962 0.897 0.756 0.501 0.196 0.028 13.7 13.5 13.0 12.1 10.2 6.8 2.6 0.4 the nitrogen-adsorption surface area of 190 m2 g-' was used to calculate yS. Values of [, from eqn (1 1) are given in table 3 and plotted in fig. 2. Values of tyS (NA) were calculated from the negative-adsorption results at pH 6.5 for cotton linters in low2 and mol dmP3 NaC1. The values are given in tables 1 and 2.DISCUSSION COTTON LINTERS The value of the zeta potential in mol dm-3 NaCl and pH 7.0 agrees reasonably well with results obtained by other workers. Zeta potentials of between 25 and 30 mV have been previously determined for cotton.8 The suppression of the double layer onT. M. HERRINGTON AND B. R. MIDMORE 1559 increasing the electrolyte concentration is clearly seen by comparing the zeta potentials at lop3 and The low surface charge density on the cotton linters will almost certainly lead to an over-estimation of the effective surface potential, yd, using the Gouy-Chapman eqn (14). This problem is not encountered if yd is calculated from the negative- adsorption experiments as then only the ‘effective’ surface potential is registered.It is therefore interesting to note the better agreement between the zeta and the surface potential calculated from the negative-adsorption data at both sodium chloride concentrations. This would indicate that for cotton linters the zeta potential calculated from electrokinetic phenomena is a reasonable estimate of the effective surface potential. The zeta potential [, predicted from the charge/pH isotherms is shown as a broken line in fig. 1. The general form of both isotherms is the same. This is clearly shown in the case of 10-2mol dm-3 NaC1. Again this is additional evidence that the adsorption of hydroxide ions is responsible for the double layer. The ‘isoelectric’ point is also close to the point of zero charge (P.z.c.) (pH 2.0 compared with pH 1.5-2.5 for the adsorption isotherm), which is good evidence for the mutual source of the two phenomena.mol dm-3 NaCl. BLEACHED SULPHATE PULP The general form of the predicted zeta potential, CS, is close to that of the measured values (fig. 2), and together with a good comparison between the ‘isoelectric’ point and P.Z.C. (pH 2.0 and 1.7) this provides good evidence that the adsorption of hydroxide ions at the cellulose surface is the source of the surface charge and hence double layer. However, the zeta potential is very much smaller than the calculated surface potential. Indeed it is lower than in the case of cotton linters in spite of an increased surface charge density. This phenomenon, of the zeta potential being lowered on increasing the charge, has previously been observedg and has been used as an argument against adsorption of hydroxide ions being the source of the surface charge.1° The weight of evidence for the ionogenic source of the surface charge shown in this work discounts such an argument.Our work shows quite dramatically that the [ potential is not a measure of the surface charge and cannot be used for a comparison of the surface charge of even very similar materials. Note that the zeta potential is reduced as the swelling in the fibre increases. Thus the swollen volume of bleached sulphate pulp is 2.50 cm3 g-l compared with 1.10 cm3 g-l for cotton.1° It seems probable therefore that, because of the swelling of amorphous cellulose or perhaps carboxylated cellulose chains at the surface, the position of the shear plane is shifted further out into the double layer, thereby reducing the zeta potential.This model was first postulated by Goring and Mason.ll Indeed such micro-fibrils at the surface of cellulose have been detected in electron-microscope images of the surface of unswollen fibres. A value of 8 nm for the position of the shear plane was calculated from eqn (7) for bleached sulphate pulp in lop3 mol dmp3 NaCl at pH 6.5 and the data of table 3. SWELLING IN CELLULOSE FIBRES Grignon and Scallan12 interpreted the swelling in cellulose fibres in terms of gel theory. They considered the swelling to be caused by an osmotic pressure differential and used the Donnan theory to describe the distribution of the ions. The osmotic pressure is caused by a difference in concentration of mobile ions between the interior of the fibre and the external solution.An alternative model to explain the swelling is advanced here using double-layer theory. The repulsive pressure, nR, at the midpoint1560 1500- 1000- ? -u 500- THE CELLULOSE/AQUEOUS ELECTROLYTE INTERFACE 0’ 2 3 4 5 6 j 8 PH 0- 60 50 40 ? “a 20 10 Fig. 3. Comparison of observed and theoretical swelling in pulps. The upper figure shows the experimentally observed swelling in carboxymethylated cotton (a super absorbent pulp). The lower figure shows the calculated swelling assuming the repulsive double-layer overlap model. [NaCl]/mol dm-3 as follows: 0, 2.5 x loF2; m, 2.5 x 10-I; 0, 0, 10-l; +, 1. of two flat overlapping double layers is equal to the osmotic pres~ure.~ If it is assumed that the attractive pressure, nA, between adjacent lamellae follows Hook’s law then (1 5 ) nA = 2dY where Y is Young’s modulus and 2d is the lamella separation. At equilibrium nA = nR, so that exp (ey/,/2kT)- 1 exp (ey/,/2kT) + 1 2dY = 64nikTexp(-22icd) Now yo can be estimated from eqn (14) and so for a given K and Y, d may be calculated.The effect of ionic strength and pH on d was calculated for the unbleached sulphate pulp (sample A of Part 2). Y was calculated by taking the d value of 70.1 A (obtained in Part 2) in mol dmP3 NaCl at pH 6.0. The results are shown in fig. 3.T. M. HERRINGTON AND B. R. MIDMORE 1561 The experimentally observed swelling for a super-absorbent pulp (carboxymethyl- ated cotton) is shown by way of comparison.12 The water-retention values given as grams of water per gram of fibre are converted to an interlamellar spacing by assuming that the volume of water is equal to dS and S is 200 m2 g-l.This model is at least satisfactory on a semi-quantitative level. The plots are both of the same general form, which is similar to the chargelpH isotherms. The swelling of the super-absorbent pulp drops by 50% between 0.025 and 0.25 mol dm-3 NaCl, whereas that of the unbleached sulphate pulp drops by 54% between This pore closure offers a plausible explanation for the lowering of charge found in 1 mol dm-3 NaCl for both the cotton linters and bleached sulphate pulp (fig. 2 and 3 of Part 1). As the pores close up, through suppression of the double layers with increasing electrolyte concentration, then the smallest pores become less accessible to hydroxide ions, thereby reducing the number of carboxy groups available for reaction.and 10-1 mol dm-3 NaCl. CONCLUSIONS POTENTIAL AT THE CELLULOSE/ WATER INTERFACE There are four ways of estimating the surface potential using the data obtained in this series of papers: (1) the Gouy-Chapman equation using the surface charge density So,, (2) negative-adsorption measurements using the surface area determined from negative or nitrogen adsorption, (3) potentiometric titrations and polyelectrolyte theory and (4) use of the zeta potential determined from electrokinetic data. (1) THE GOUY-CHAPMAN EQUATION In eqn (14) So, is known from the chargelpH isotherms, so if it is assumed that oh = oo then all that is needed is a value for S .Two are available from negative and nitrogen adsorption. The negative-adsorption value might be regarded as the most appropriate as it is determined in aqueous solution. It does not detect the small pores which are inaccessible to ions but accessible to nitrogen. Now o,, may only be approximated to od if there is little or no cation adsorption in the Stern layer. The concept of the Stern layer was invoked, as at a high potential (w,, = 200 mV) and high electrolyte concentration (0.1 mol dm-3 NaCl) at 25 "C the concentration of counter- ions at the surface would be greater than that of solid sodium chloride. By assuming a Stern layer or molecular condenser, the potential can drop to reasonable values. In the case of cellulose near the neutralisation point, the surface charge is approximately constant at all electrolyte concentrations.Now if the potential is high eqn (14) becomes o6 = (2ni EkT)iexp (eyd/2kT) but n, = n,exp(ewd/kT) (18) n, = $/2~kT (19) < ot/2~kT. (20) For the bleached sulphite pulp o, = -2.50 x C m-2 at pH 6.5 (fig. 3 of Part 1 and S = 120 m2 g-l) and hence n+ is 0.18 mol dm-3, which is well below the solu- bility of sodium chloride at 25 "C. Thus it seems reasonable to assume that it is not necessary to define a Stern layer and oo can be assumed to be a good approximation to os, the charge at the start of the diffuse double layer. Eqn (14) then gives a value of w,, which will be designated vo(GC). therefore1562 THE CELLULOSE/ AQUEOUS ELECTROLYTE INTERFACE Table 4. Comparison between the surface potentials calculated from negative-adsorption and surface-charge measurements for bleached sulphate pulp in different concentrations of sodium chloride, n, ni/10-2 mol dm-3 -y/j20(NA)/mV -y/i2*(GC)/mV -y/jgO(NA)/mV - y/$gO(GC)/mV 8.81 27.0 32.8 15.3 21.9 6.56 40.6 36.7 21.7 24.3 4.46 53.6 42.5 27.5 28.8 2.08 57.9 57.1 28.6 39.8 0.875 85.5 75.0 36.9 54.5 0.694 78.4 79.0 35.0 59.3 a &)(NA) = potential determined by negative adsorption assuming surface area S.y/iS)(GC) = potential determined from charge/pH isotherms assuming surface area S. (2) CALCULATION OF SURFACE POTENTIAL FROM NEGATIVE ADSORPTION From eqn (9) of Part 2 S = A VB2/n,[ 1 - exp (etys/2k T)]-l (21) so that if S and A V are known, then lys can be calculated. Values of SW for the oxidised pulp (when tps is effectively infinite) and SW from nitrogen adsorption are used to calculate AVW and then [l -exp(etys/2kT)] = A V / A P .(22) These values of tys will be designated y/ANA). (3) CALCULATION OF SURFACE POTENTIAL USING POLYELECTROLYTE THEORY From eqn ( 5 ) of Part 1 pK = pKo + 0.434AG(a)/kT (23) y/ = kT(pK-pKo)/0.434e. (24) where AG = ety. Thus The potential determined in this way will be designated tyel. (4) CALCULATION OF SURFACE POTENTIAL FROM ELECTROKINETICS It has been shown in the discussion section of this paper that the zeta potential is not a good estimate of the surface potential at least for bleached sulphate pulp. COMPARISON BETWEEN THE SURFACE POTENTIALS CALCULATED BY METHODS (I), (2) AND (3) BLEACHED SULPHATE PULP The negative-adsorption measurements were carried out over a range of chloride concentrations, but only at one pH, 6.5.The surface-charge/pH isotherms were determined over a range of pH but only four chloride concentrations (fig. 3 of Part 1). Interpolation of the isotherms enabled So, to be estimated at the same chloride concentrations as were used in the negative-adsorption experiments. To calculate both tyo(GC) and tys(NA), there is a choice of two values for S. One obtained from negative-adsorption measurements on the oxidised pulp, assuming no change in poreT. M. HERRINGTON AND B. R. MIDMORE 1563 Table 5. Comparison between the surface potentials calculated from polyelectrolyte theory, yel, and surface-charge measurements, y0(GC) (S = 190 m2 g-l), for bleached sulphate pulp in sodium chloride solutions 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Wac11 = loF3 mol dm-3 0 0 10.1 20.5 23.7 38.5 33.7 53.3 43.2 65.4 53.3 75.5 65.1 84.1 77.0 91.5 94.7 98.0 124.3 103.8 [NaCl] = 10-l mol dm-3 0 0 0.6 2.1 2.1 4.2 3.3 6.3 4.7 8.4 6.5 10.5 8.3 12.6 11.2 14.6 17.8 16.6 33.7 18.6 [NaCl] = mol dm-3 0 0 1.5 6.7 3.0 13.2 4.5 19.6 10.1 25.7 18.9 31.4 30.8 36.9 43.2 42.0 58.6 46.7 81.7 51.3 [NaCl] = 1 mol dm-3 0 0 0.6 0.7 1.2 1.3 1.5 2.0 2.4 2.7 2.9 3.3 4.7 4.0 8.8 4.7 14.8 5.3 21.3 6.0 structure (120 m2 g-l), and the other a dry (solvent-exchanged) surface area obtained from nitrogen adsorption (190 m2 g-l).Values of y,(GC) and yB(NA) were calculated for both values of the surface area and are given in table 4.The larger surface area gives lower potentials. The agreement is excellent except for the two lowest chloride concentrations. From the pH/charge isotherms both yo(GC) and yel are calculated. They are compared at the four different sodium chloride concentrations at a range of values of a (i.e. pH) in table 5. For yo(GC) S is taken as 190 m2 g-l. The agreement is reasonable except that y,(GC) tends to be higher than yel at low values of a. This may be explained by the fact that here we do not have a situation where the charge is smeared over the whole surface but consists of discrete point charges so that the Gouy-Chapman theory is not applicable. The reasonable agreement between y,(GC), ya(NA) and yel has a number of consequences. (i) The Gouy-Chapman treatment of the double layer is applicable to the cellulose/wafer interface. The three methods of calculating y rely on the determination of five independent variables and therefore provide each other with mutually supportive evidence. method variables1564 THE CELLULOSE/AQUEOUS ELECTROLYTE INTERFACE Table 6.Comparison between the surface potentials cal- culated from negative-adsorption, y/,(NA), and surface- charge measurements, y/,(GC) ( S = 130 m2 g-l), for cotton linters in different concentrations of sodium chloride, ni nil mol dmb3 - ly,(NA)/mV - v,,(GC)/mV 20.2 9.9 1 1 . 1 4.33 11.0 21.9 3.22 14.6 24.6 0.980 17.1 38.3 0.852 17.5 39.8 (ii) There is little or no adsorption of ions in the Stern layer. As lyb(NA) and probably lyel are estimates of the potential at the start of the diffuse layer, their similarity with ly,(GC) suggests that this is situated more or less at the cellulose/water interface, i.e.the Stern layer is empty. (iii) If lyel, ly8(NA) or ly,(GC) provides a reasonable estimate for the surface potential of bleached sulphate pulp then the zeta potential is a very poor estimate of this potential. COTTON LINTERS Calculated values of ly8(NA) and ly,(GC) are given in table 6 for S = 130 m2 g-l for the range of chloride concentrations used in the negative-adsorption experiments and at pH 6.5. ly,,(GC) and lyel from the charge/pH isotherms are given in table 7 again using S = 130 m2 g-l. The agreement between the different methods of calculating ly is not so good. If the anomalously high values of tyel at mol dm-3 NaCl are ignored, then lye, is in reasonable agreement with ly,(GC).The lower values of lyB(NA) compared with ly,(GC) might be explained by the low charge density, but this is not reflected in a lower lye,, which might be expected to have similar character The discrepancy may lie in an over estimation of the surface area. If 06 is calculated from eqn (14) using the values of lye, at a = 0.8 and electrolyte concentrations of mol dm-3 and low2 mol dm-3, values of -0.0121 C m-2 and -0.0068 C m-2 are obtained, giving an average of -0.0095 C m-2. From the charge/pH isotherms (fig. 2 of Part 1) So, is -0.39 C g-l, so that this suggests an effective surface area of 40 m2 g-l. This indicates that a wet surface area of 48 m2 g-l, obtained from negative adsorption, may be a better estimate of the surface area rather than 130 m2 g-l.This value for the surface area would increase both lys(NA) and lyo(GC) and then even the zeta potentials obtained for the relatively unswollen cotton linters become a poor estimate of tyS. to lyB(NA)- THE ORIGIN OF THE ELECTRICAL CHARGE OF CELLULOSE It has been tacitly assumed throughout Parts 1, 2 and 3 that the origin of the electrical charge on cellulose is the adsorption of hydroxide ions, and that the mechanism for this adsorption is the reaction of these hydroxide ions with occasional carboxy groups in the cellulose structures. It can be asked what justification there is for this. (1) The surface potential calculated from negative adsorption compares very wellT. M. HERRINGTON AND B.R. MIDMORE 1565 Table 7. Comparison between the surface potentials calculated from polyelectrolyte theory, ye,, and surfacecharge measurements, y,(GC) (S = 130 m2 g-l), for cotton linters in sodium chloride solutions 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 [NaCl] = mol dm-3 0.0 0.0 6.0 5.0 12.4 10.0 20.6 14.8 32.5 19.6 44.3 24.1 59.0 28.6 76.8 32.8 97.6 36.8 120.0 40.7 [NaCl] = 10-l mol dme3 0.0 0.0 0.2 0.5 0.4 1 .o 0.5 1.5 0.7 2.0 0.9 2.5 . 1.1 3.0 1.2 3.5 1.4 4.0 1.6 4.5 [NaCl] = mol dm-3 0.0 0.0 1.5 1.6 3.0 3.2 4.1 4.7 6.8 6.3 10.1 7.9 14.8 9.4 20.7 11.0 28.4 12.5 37.6 14.1 [NaCl] = 1 mol dm-3 0.0 0.0 0.0 0.2 0.0 0.3 0.0 0.5 0.0 0.6 0.0 0.8 0.0 1 .o 0.0 1 . 1 0.0 1.3 0.0 1.4 with that calculated from the Gouy-Chapman equation using the charge/pH isotherms.The former method does not rely on any assumption about the origin of the charge on the surface, while the latter relies on the assumption that the adsorption of hydroxide ions is responsible for the surface charge. This is also true for the potential calculated from polyelectrolyte theory. (2) The P.Z.C. and ‘isoelectric point’ (from zeta potential) occur at similar values of the pH for both cotton linters and bleached sulphate pulp, indicating that adsorption of hydroxide ions is responsible for the diffuse double layer. (3) In the sodium adsorption experiment of Part 1 it was found that the adsorption of hydroxide ions is balanced by the adsorption of sodium ions. This would not be true if other negative ions were responsible for the surface charge of cellulose. We are indebted to S.E.R.C.and to Wiggins-Teape Ltd for joint sponsorship of this research. We also thank Dr Th. Tadros for helpful discussions. We would also like to thank the late Dr Heinz Corte, without whose industry, enthusiasm and, above all, inspiration this work would not have taken place. GLOSSARY OF SYMBOLS a area of cell Es streaming potential e charge on electron 4 streaming currentTHE CELLULOSE/AQUEOUS ELECTROLYTE INTERFACE proportionality constant cell constant length of cell concentration of co-ion i in bulk solution concentration of positive ions pressure across cell negative logarithm of ionization constant negative logarithm of ionization constant at a = 0 resistance of pad at low electrolyte concentrations resistance of pad at 0.1 mol dm-3 KCl radius of pore surface area per gram = tanh (zeva/4kT) = tanh (zey8 / 4 k T ) excluded volume Young's modulus valency of ion i, sign included degree of dissociation from charge/pH isotherm surface excess bulk conductivity surface conductivity electrical permittivity of the medium zeta potential viscosity of medium Debye reciprocal length, K = (2ni zf e2/&kT)b attractive disjoining pressure charge in density at surface charge in density at plane of shear pore factor potential at surface potential calculated from the Gouy-Chapman equation potential at the plane of shear potential calculated from negative adsorption potential at distance x from interface i H. R. Kruyt, Colloid Science (Elsevier, Amsterdam, 1952), vol. 1. D. K. Briggs, J . Phys. Chem., 1928, 32, 641. B. R. Midmore, Thesis (Reading University, 1983). C. W. C. Kaye and T. H. Laby, Tables of Physical and Chemical Constants (Longmans, London, 1973). * M. Y. Chang and A. A. Robertson, Pulp and Paper Res. Inst. (Canada), Tech. Rep. No. 485, 1965. 6 G. Gouy, J. Phys. (Paris), 1910, 9, 457. 7 D. L. Chapman, Philos. Mag., 1913, 25, 475. 8 S. G. Mason, Tappi, 1950, 33, 8. lo S. G. Mason, Tappi, 1950,33,413. 11 D. A. Goring and S. G. Mason, Can. J . Res., 1950, 6, 307. S. M. Neale and R. H. Peters, Trans. Faraday Soc., 1946, 41,478. J. Grignon and A. M. Scallan, J. Appl. Polym. Sci., 1980, 25, 2929. (PAPER 3/ 1622)