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An indirect measurement of negative adsorption
Colloids and Surfaces, 24 (1987) 51-58 Elsevier Science Publishers B.V., Amsterdam -
51 Printed in The Netherlands
An Indirect Measurement of Negative Adsorption M.C.H. MOUAT Grasslands Division, DSIR, Private Bag, Palmerston North (New Zealand) (Received 8 August 1986; accepted 15 October 1986)
ABSTRACT A method is described for the measurement of negative adsorption by measurement of the concentration of sequential rinses of the adsorbant-solution system. Equilibrium conditions need not be attained between rinses. The method allows the determination of negative adsorption without the need for direct measurement of the concentration associated with the inner solution, or the requirement that the material be initially free of the ion under test. Results show good agreement with the generally accepted method of measuring the increase in concentration of the outer solution through introduction of ion-free negative adsorbant.
INTRODUCTION
The negative adsorption of ions, or ion exclusion, by charged particles has been measured by many workers since Schofield (1947) demonstrated its aplication for measuring the surface area of clays. The methods of measuring negative adsorption fall into two general modes, a direct measurement of the concentrations of both the solution ambient to the charged surface (Ci) and the solution in equilibrium with that solution (CO) (Schofield, 1947; Bower and Goertzen, 1955; Bolt and Warkentin, 1956), and measurement of the increase in concentration of an external solution (Co) of a system enclosing a charged phase over the concentration when the charged phase is not present (C,) (De Haan, 1964; Van den Hul, 1983). From the direct measurement method, negative adsorption per unit mass of charged particle ( y’ ) may be deduced from y’=Vi
(Co-Ci)/?TZ
where Vi is the volume of solution containing the exclusion volume. In the method employing the increase in concentration, r’=v,
(CO-C*)/m
where Vt is the total volume of added solution of anion concentration, C,. The direct measurement method requires an identifiable Vi and a method of
0166-6622/87/$03.50
0 1987 Elsevier Science Publishers B.V.
52
removing, for analysis, all the anions from this volume without contamination from like anions not associated with the solution at the time of equilibrium. The increased concentration method requires that the colloidal material be totally free of the anion under test. Accurate measurements of C, and C, are critical as the difference in their concentrations are less than the C,,- Ci of the direct measurement method. In many cases, particularly those with biological materials, the requirements that the colloid be free of the anion under test or that the anion can be quantitatively eluted cannot be met. In these cases, the only measurement available for analysis is the concentration of the outer, equilibrating solution. This solution of volume ( V, ) and concentration (CO) is at equilibrium with a volume ( Vi) of concentration (Ci) associated with the exclusion volume and which may be partially eluted by continual withdrawal of the anion from the outer solution. The partial elution is a rinsing involving a sequential removal of V, and replacement with an equal volume of water. True equilibria cannot be obtained between these rinses, but since the attaining of equilibrium is a function of time, f(t) , it is possible to measure the concentration (Ci) initially associated with the volume ( Vi) in a manner similar to that used to measure the reserve concentration of adsorbed phosphate in soils (Mouat, 1983 ) . Consider a system at equilibrium of total volume, V,, from which a volume V, is rinsed by being removed and replaced with water. The unrinsed volume, Vi, includes the solution in association with the colloidal fraction and the volume of exclusion. These volumes remain constant and are known. The time, t, between rinses is constant and known. Then letting k the number of successive rinse, subscript k the measurement associated with the kth rinse, C, the concentration of anion under test in solution (volume, V,) removed at rinsing, and Ci the apparent concentration of solution (volume Vi) remaining, CS,=
(Ci,_1
-C&J
Vi/V,
(1)
and (2)
C,, =C,, f(t) where C,, is the equilibrium concentration Thus, C*kcf(t)
Cik-1
Vi/V,
of C, for the lath rinse, C+_, Vi/V,. (3)
Then, since V, = V, - Vi, (4)
then
53
where the subscript 0 refers to the initial, equilibrium state before rinsing commenced, and, U=[(l-f(t))Vt+f(t)Vj]/V,
(5a)
Then, from Eqn (1) , C,, = ( CioUk-l -CioUk) Vi/V,
(6)
i.e., ln(C,,V,/Vi)=ln[C&(l-a)]+(12-1)lnc
(7)
By regression, the intercept, A = In [ Ci, (1 - a) ] and slope, B = In a, of Eqn ( 7) may be evaluated and hence, the initial, equilibrium concentration of Vi, C, =eA/(l-eB)
(8)
may be derived. Through this regression, the exclusion of anions from the charged surface may be found from
(9) where m is the mass of colloid, without the necessity of quantitative elution of electrolytes form the inner volume, nor the requirement that the initial concentration of the anion be known. METHOD
All experiments were conducted in cylindrical, perspex half-cells of 10 mm length and 10 mm radius backed by a plane wall and coupled together with a membrane of dialysis paper (E.H. Sargent & Co. Parchment) separating the inner half-cell, containing the charged colloid, from the outer half-cell, containing solution only. The back wall of the inner cell was lined with cellotape adhesive to which 0.01 g of H+ Amberlite IRC-50 was fixed. No special effort was made to obtain an even spread of resin. The outer half-cell had a sealed, 5 mm, sample-port to allow the removal and replacement of solution. For all experiments, the cells were held at 25°C and in darkness except for brief sampling periods. To test the consistency of the time dependence on the equilibrium between the half-cells, 2.5 ml of 80 pmol 1-l P as Ca (H,PO,) 2 were added to the inner half of 38 cells coupled to 2.5 ml water in the outer half-cell. At various times over three days, the phosphate which had diffused into the outer chamber was measured in a 2 ml sample taken from the outer chamber. Negative adsorption of phosphate was measured by both the increase in concentration method and by the method of regression of the depleting solution. Phosphate solutions of 100,80,60,40 and 20 pmol 1-l P as Ca (H,PO,) 2 were
0
1000
2000
time
3000
Imin)
4000
5000
Fig. 1. Time course of phosphate diffusion to outer half-cell.
added at 2.5 ml per side to both sides of the cells and allowed to equilibrate for 21 days. A 2 ml sample was then removed from the solution (outer) chamber and analysed for the outer (Co or C,,) concentration of phosphate for both methods. The 2 ml was replaced with water - the first (k= 1) rinse of the depletion sequence. At precise 3 day intervals, a 2 ml sample was removed for analysis and replaced with water. This was repeated for 5 rinses. Phosphate analyses were made by the method of Murphy and Riley (1962). RESULTS
The consistency of the time function on phosphate diffusion across the cells is illustrated in the excellent fit of an inverse exponential time relationship with phosphate diffusion data in the time-course experiment (Fig. 1). The fitted line is [P] = (44.5~1.01)(1-e-(0.000803~0.0000387)t) where [P
]
represents the concentration
(10)
of phosphate in the outer cell at time
t.
All regressions of data according to Eqn (7) gave highly significant slopes and intercepts (p < 0.001) for the determination of Ci by the depleting solution method. Linear correlations for all were < - 0.98. Representative regressions of all concentrations are shown in Fig. 2. The equilibrium outer concentration (C,) and the phosphate exclusion per g colloid calculated both from the increase in concentration of C, over the
55
0
co
=
117
x
co
=
89
b Co =
67
co
47
l
=
rco=
umol/l .
21
0
2
8
4
(k -
1)
Fig. 2. Linear regressions at 5 initial, outer, equilibrium concentrations lation of the initial inner concentration ( Ci) .
(C,,) used for the calcu-
concentration added, and calculated from the regression of the depleting solutions are given in Table 1. Standard errors are given for both determinations as is the recovery of phosphate measured by depleting solutions. The standard errors shown are in no way indicative of the relative reproducibility of results of the two methods as the “regression” method contained self-replication in its determination while individual determinations of the “increase in concentration” method were unreplicated in this trial. TABLE 1 Comparison of results from the indirect regression method with those of the method of increase in concentration. Means of 5 measurementa with standard errors Phosphate added, C. @moI I-‘)
Outer Equil. cont., C. (,mnol I-‘)
Inner cont. by regression Ci (FmoI 1-l)
Y’ regression (wool fr’)
y ’ by cont. increase two1 g-1)
Recovery % by regression method
100 80 60 40 20
115.0 91.8 66.2 43.9 21.3
90.0 74.3 53.2 33.8 13.3
7.55 + 0.25 5.26 + 0.57 3.82 k 0.18 3.04+0.19 2.41 +O.lO
7.52 f 1.15 5.90 + 1.07 3.10+0.62 1.98 + 0.43 0.68f0.19
99.9 101.4 97.9 94.6 81.2
56 1
Ideal Ca = 100 * Ca = 60 0 Ca = 60 ACa= 40 x Ca = 20 q
l
II .F: 0.E cl 2 AJ G :! : 0.6 .2 -r( .Y h
0.4
0 k .d CI :
0.2
k
2
Rinse
Lnber
4
5
6
Fig. 3. Rinsing decay curves of phosphate concentration from ideal equilibrium rinses and from sub-equilibrium rinses of cells exhibiting negative adsorption and from a soil exhibiting positive phosphate adsortion. C, values are of initial phosphate concentration added (pm01 1-l). DISCUSSION
The results shown in Table 1 show that the indirect method of measuring negative adsorption from the regression of a depletion series given measurements comparable with those of the increase in concentration method. There appeared to be a divergence in the results of the two methods at the lowest concentration tested but errors here were large as the sensitivity of phosphate detection at these levels was low. The drop in sensitivity had a greater effect on the increase in concentration method as indicated by the standard errors, and this may have caused the drop in y ’ with respect to fi at low concentrations. The accuracy of both methods would have been improved had 32P been tagged to the solution, but the method under test is intended for biological material which cannot be subjected to the rigour of absolute isotopic exchange. The validity of the indirect method is dependent on the linearity of the regression of Eqn (7). The high correlations obtained shows this to be so, as does the visual expression of Fig. 2; however, the slope of these lines (In a) is not constant over all regressions. The parameter “a” includes all effects pertaining to the attainment of a true equilibrium following a dilution period. In the case of the phosphate supply of the inner volume being changed during the
57
0 initial x initial A initial “0
1000
2000
time
PI = 20 umol/l [PI = 40 umol/l [PI = 80 umol/l 3000
4000
5000
Imin)
Fig. 4. Time course of phosphate concentration in outer half-cell from inner half-cell of initial concentration of 20,40 and 60~011-‘. Values for 40 and 60~011-’ have been multiplied by 0.5 and 0.25, respectively, for ready comparison. Fitted curves are of [P] =A(l-e”‘), where A=12.6?0.423, for 20 b= -0.000513f0.0000331 j&no1 1-l; A = 12.2 f 0.273, b= -0.000544If:0.0000544 for 0.5~40 pmol 1-l; A = 11.9kO.304, b= -0.000557f0.0000286 for 0.25~60~011-‘.
depletion series, it includes the effect of desorption of adsorbed phosphate in increasing the phosphate available for removal during rinsing, or conversely it accounts for the increase phosphate exclusion with decrease in concentration during the depletion series. Thus, it allows the measurement, through summation of the quantity of labile posphate released by an adsorbent surface under continual removal of solution phosphate (Mouat, 1983) as well as the quantity of phosphate present in solution at an exclusion surface. This quantity is expressed as a virtual concentration of a fixed “inner” volume. It is not a true concentration; rather it is the total quantity which can be released in solution from a fixed “inner volume” by exhaustive depletion. For convenience of measurement, the volume is fixed and the quantity expressed as a concentration in a manner similar to earlier expressions of anion exclusion which expressed exclusion as a virtual volume of fixed concentration (Schofield, 1947). The effect of desorption of phosphate and exclusion of phosphate on the depletion sequence is shown in Fig. 3 where the depletion series of the four concentrations of the negative adsorption cells and the depletion of a phosphate-adsorbing soil (Mouat, 1983) are compared with the ideal, nonadsorbing, equilibrium depletion series of 40% removal per rinse. The virtual nature of Ci precludes the sensible solution of Eqn (5a) but the value for “a” will
58
remain constant for the depletion series of a given initial concentration as the time course for the attainment of equilibrium is not affected by the inner volume. This was tested at three phosphate concentrations at 20’ C in a manner similar to the time course described above. No discernible difference in the inverse exponential regressions was found (Fig. 4). The indirect determination of negative adsorption through the regression of a depletion series can provide a method for measuring the exclusion of anions from biological and like material where neither the inner, equilibrium concentration nor the total initial concentration (requirements for orthodox negative adsorption measurements) can be obtained with certainty.
REFERENCES Bolt, G.H. and Warkentin, B.P., 1956.6th Congr. Sci. Sol (Paris), 1.5,33. Bower, C.A. and Goertzen, J.O., 1955. Soil Sci. Sot. Am. Proc., 19: 147. De Haan, F.A.M., 1964. J. Phys. Chem., 68: 2970. Mouat, M.C.H., 1983. N.Z. J. Agric. Res., 26: 321. Murphy, J. and Riley, J.P., 1962. Anal. Chim. Acta, 27: 31. Schofield, R.K., 1947. Nature (London), 160: 408. Van den Hul, H.J., 1983. J. Colloid Interface Sci., 92: 217.
51 Printed in The Netherlands
An Indirect Measurement of Negative Adsorption M.C.H. MOUAT Grasslands Division, DSIR, Private Bag, Palmerston North (New Zealand) (Received 8 August 1986; accepted 15 October 1986)
ABSTRACT A method is described for the measurement of negative adsorption by measurement of the concentration of sequential rinses of the adsorbant-solution system. Equilibrium conditions need not be attained between rinses. The method allows the determination of negative adsorption without the need for direct measurement of the concentration associated with the inner solution, or the requirement that the material be initially free of the ion under test. Results show good agreement with the generally accepted method of measuring the increase in concentration of the outer solution through introduction of ion-free negative adsorbant.
INTRODUCTION
The negative adsorption of ions, or ion exclusion, by charged particles has been measured by many workers since Schofield (1947) demonstrated its aplication for measuring the surface area of clays. The methods of measuring negative adsorption fall into two general modes, a direct measurement of the concentrations of both the solution ambient to the charged surface (Ci) and the solution in equilibrium with that solution (CO) (Schofield, 1947; Bower and Goertzen, 1955; Bolt and Warkentin, 1956), and measurement of the increase in concentration of an external solution (Co) of a system enclosing a charged phase over the concentration when the charged phase is not present (C,) (De Haan, 1964; Van den Hul, 1983). From the direct measurement method, negative adsorption per unit mass of charged particle ( y’ ) may be deduced from y’=Vi
(Co-Ci)/?TZ
where Vi is the volume of solution containing the exclusion volume. In the method employing the increase in concentration, r’=v,
(CO-C*)/m
where Vt is the total volume of added solution of anion concentration, C,. The direct measurement method requires an identifiable Vi and a method of
0166-6622/87/$03.50
0 1987 Elsevier Science Publishers B.V.
52
removing, for analysis, all the anions from this volume without contamination from like anions not associated with the solution at the time of equilibrium. The increased concentration method requires that the colloidal material be totally free of the anion under test. Accurate measurements of C, and C, are critical as the difference in their concentrations are less than the C,,- Ci of the direct measurement method. In many cases, particularly those with biological materials, the requirements that the colloid be free of the anion under test or that the anion can be quantitatively eluted cannot be met. In these cases, the only measurement available for analysis is the concentration of the outer, equilibrating solution. This solution of volume ( V, ) and concentration (CO) is at equilibrium with a volume ( Vi) of concentration (Ci) associated with the exclusion volume and which may be partially eluted by continual withdrawal of the anion from the outer solution. The partial elution is a rinsing involving a sequential removal of V, and replacement with an equal volume of water. True equilibria cannot be obtained between these rinses, but since the attaining of equilibrium is a function of time, f(t) , it is possible to measure the concentration (Ci) initially associated with the volume ( Vi) in a manner similar to that used to measure the reserve concentration of adsorbed phosphate in soils (Mouat, 1983 ) . Consider a system at equilibrium of total volume, V,, from which a volume V, is rinsed by being removed and replaced with water. The unrinsed volume, Vi, includes the solution in association with the colloidal fraction and the volume of exclusion. These volumes remain constant and are known. The time, t, between rinses is constant and known. Then letting k the number of successive rinse, subscript k the measurement associated with the kth rinse, C, the concentration of anion under test in solution (volume, V,) removed at rinsing, and Ci the apparent concentration of solution (volume Vi) remaining, CS,=
(Ci,_1
-C&J
Vi/V,
(1)
and (2)
C,, =C,, f(t) where C,, is the equilibrium concentration Thus, C*kcf(t)
Cik-1
Vi/V,
of C, for the lath rinse, C+_, Vi/V,. (3)
Then, since V, = V, - Vi, (4)
then
53
where the subscript 0 refers to the initial, equilibrium state before rinsing commenced, and, U=[(l-f(t))Vt+f(t)Vj]/V,
(5a)
Then, from Eqn (1) , C,, = ( CioUk-l -CioUk) Vi/V,
(6)
i.e., ln(C,,V,/Vi)=ln[C&(l-a)]+(12-1)lnc
(7)
By regression, the intercept, A = In [ Ci, (1 - a) ] and slope, B = In a, of Eqn ( 7) may be evaluated and hence, the initial, equilibrium concentration of Vi, C, =eA/(l-eB)
(8)
may be derived. Through this regression, the exclusion of anions from the charged surface may be found from
(9) where m is the mass of colloid, without the necessity of quantitative elution of electrolytes form the inner volume, nor the requirement that the initial concentration of the anion be known. METHOD
All experiments were conducted in cylindrical, perspex half-cells of 10 mm length and 10 mm radius backed by a plane wall and coupled together with a membrane of dialysis paper (E.H. Sargent & Co. Parchment) separating the inner half-cell, containing the charged colloid, from the outer half-cell, containing solution only. The back wall of the inner cell was lined with cellotape adhesive to which 0.01 g of H+ Amberlite IRC-50 was fixed. No special effort was made to obtain an even spread of resin. The outer half-cell had a sealed, 5 mm, sample-port to allow the removal and replacement of solution. For all experiments, the cells were held at 25°C and in darkness except for brief sampling periods. To test the consistency of the time dependence on the equilibrium between the half-cells, 2.5 ml of 80 pmol 1-l P as Ca (H,PO,) 2 were added to the inner half of 38 cells coupled to 2.5 ml water in the outer half-cell. At various times over three days, the phosphate which had diffused into the outer chamber was measured in a 2 ml sample taken from the outer chamber. Negative adsorption of phosphate was measured by both the increase in concentration method and by the method of regression of the depleting solution. Phosphate solutions of 100,80,60,40 and 20 pmol 1-l P as Ca (H,PO,) 2 were
0
1000
2000
time
3000
Imin)
4000
5000
Fig. 1. Time course of phosphate diffusion to outer half-cell.
added at 2.5 ml per side to both sides of the cells and allowed to equilibrate for 21 days. A 2 ml sample was then removed from the solution (outer) chamber and analysed for the outer (Co or C,,) concentration of phosphate for both methods. The 2 ml was replaced with water - the first (k= 1) rinse of the depletion sequence. At precise 3 day intervals, a 2 ml sample was removed for analysis and replaced with water. This was repeated for 5 rinses. Phosphate analyses were made by the method of Murphy and Riley (1962). RESULTS
The consistency of the time function on phosphate diffusion across the cells is illustrated in the excellent fit of an inverse exponential time relationship with phosphate diffusion data in the time-course experiment (Fig. 1). The fitted line is [P] = (44.5~1.01)(1-e-(0.000803~0.0000387)t) where [P
]
represents the concentration
(10)
of phosphate in the outer cell at time
t.
All regressions of data according to Eqn (7) gave highly significant slopes and intercepts (p < 0.001) for the determination of Ci by the depleting solution method. Linear correlations for all were < - 0.98. Representative regressions of all concentrations are shown in Fig. 2. The equilibrium outer concentration (C,) and the phosphate exclusion per g colloid calculated both from the increase in concentration of C, over the
55
0
co
=
117
x
co
=
89
b Co =
67
co
47
l
=
rco=
umol/l .
21
0
2
8
4
(k -
1)
Fig. 2. Linear regressions at 5 initial, outer, equilibrium concentrations lation of the initial inner concentration ( Ci) .
(C,,) used for the calcu-
concentration added, and calculated from the regression of the depleting solutions are given in Table 1. Standard errors are given for both determinations as is the recovery of phosphate measured by depleting solutions. The standard errors shown are in no way indicative of the relative reproducibility of results of the two methods as the “regression” method contained self-replication in its determination while individual determinations of the “increase in concentration” method were unreplicated in this trial. TABLE 1 Comparison of results from the indirect regression method with those of the method of increase in concentration. Means of 5 measurementa with standard errors Phosphate added, C. @moI I-‘)
Outer Equil. cont., C. (,mnol I-‘)
Inner cont. by regression Ci (FmoI 1-l)
Y’ regression (wool fr’)
y ’ by cont. increase two1 g-1)
Recovery % by regression method
100 80 60 40 20
115.0 91.8 66.2 43.9 21.3
90.0 74.3 53.2 33.8 13.3
7.55 + 0.25 5.26 + 0.57 3.82 k 0.18 3.04+0.19 2.41 +O.lO
7.52 f 1.15 5.90 + 1.07 3.10+0.62 1.98 + 0.43 0.68f0.19
99.9 101.4 97.9 94.6 81.2
56 1
Ideal Ca = 100 * Ca = 60 0 Ca = 60 ACa= 40 x Ca = 20 q
l
II .F: 0.E cl 2 AJ G :! : 0.6 .2 -r( .Y h
0.4
0 k .d CI :
0.2
k
2
Rinse
Lnber
4
5
6
Fig. 3. Rinsing decay curves of phosphate concentration from ideal equilibrium rinses and from sub-equilibrium rinses of cells exhibiting negative adsorption and from a soil exhibiting positive phosphate adsortion. C, values are of initial phosphate concentration added (pm01 1-l). DISCUSSION
The results shown in Table 1 show that the indirect method of measuring negative adsorption from the regression of a depletion series given measurements comparable with those of the increase in concentration method. There appeared to be a divergence in the results of the two methods at the lowest concentration tested but errors here were large as the sensitivity of phosphate detection at these levels was low. The drop in sensitivity had a greater effect on the increase in concentration method as indicated by the standard errors, and this may have caused the drop in y ’ with respect to fi at low concentrations. The accuracy of both methods would have been improved had 32P been tagged to the solution, but the method under test is intended for biological material which cannot be subjected to the rigour of absolute isotopic exchange. The validity of the indirect method is dependent on the linearity of the regression of Eqn (7). The high correlations obtained shows this to be so, as does the visual expression of Fig. 2; however, the slope of these lines (In a) is not constant over all regressions. The parameter “a” includes all effects pertaining to the attainment of a true equilibrium following a dilution period. In the case of the phosphate supply of the inner volume being changed during the
57
0 initial x initial A initial “0
1000
2000
time
PI = 20 umol/l [PI = 40 umol/l [PI = 80 umol/l 3000
4000
5000
Imin)
Fig. 4. Time course of phosphate concentration in outer half-cell from inner half-cell of initial concentration of 20,40 and 60~011-‘. Values for 40 and 60~011-’ have been multiplied by 0.5 and 0.25, respectively, for ready comparison. Fitted curves are of [P] =A(l-e”‘), where A=12.6?0.423, for 20 b= -0.000513f0.0000331 j&no1 1-l; A = 12.2 f 0.273, b= -0.000544If:0.0000544 for 0.5~40 pmol 1-l; A = 11.9kO.304, b= -0.000557f0.0000286 for 0.25~60~011-‘.
depletion series, it includes the effect of desorption of adsorbed phosphate in increasing the phosphate available for removal during rinsing, or conversely it accounts for the increase phosphate exclusion with decrease in concentration during the depletion series. Thus, it allows the measurement, through summation of the quantity of labile posphate released by an adsorbent surface under continual removal of solution phosphate (Mouat, 1983) as well as the quantity of phosphate present in solution at an exclusion surface. This quantity is expressed as a virtual concentration of a fixed “inner” volume. It is not a true concentration; rather it is the total quantity which can be released in solution from a fixed “inner volume” by exhaustive depletion. For convenience of measurement, the volume is fixed and the quantity expressed as a concentration in a manner similar to earlier expressions of anion exclusion which expressed exclusion as a virtual volume of fixed concentration (Schofield, 1947). The effect of desorption of phosphate and exclusion of phosphate on the depletion sequence is shown in Fig. 3 where the depletion series of the four concentrations of the negative adsorption cells and the depletion of a phosphate-adsorbing soil (Mouat, 1983) are compared with the ideal, nonadsorbing, equilibrium depletion series of 40% removal per rinse. The virtual nature of Ci precludes the sensible solution of Eqn (5a) but the value for “a” will
58
remain constant for the depletion series of a given initial concentration as the time course for the attainment of equilibrium is not affected by the inner volume. This was tested at three phosphate concentrations at 20’ C in a manner similar to the time course described above. No discernible difference in the inverse exponential regressions was found (Fig. 4). The indirect determination of negative adsorption through the regression of a depletion series can provide a method for measuring the exclusion of anions from biological and like material where neither the inner, equilibrium concentration nor the total initial concentration (requirements for orthodox negative adsorption measurements) can be obtained with certainty.
REFERENCES Bolt, G.H. and Warkentin, B.P., 1956.6th Congr. Sci. Sol (Paris), 1.5,33. Bower, C.A. and Goertzen, J.O., 1955. Soil Sci. Sot. Am. Proc., 19: 147. De Haan, F.A.M., 1964. J. Phys. Chem., 68: 2970. Mouat, M.C.H., 1983. N.Z. J. Agric. Res., 26: 321. Murphy, J. and Riley, J.P., 1962. Anal. Chim. Acta, 27: 31. Schofield, R.K., 1947. Nature (London), 160: 408. Van den Hul, H.J., 1983. J. Colloid Interface Sci., 92: 217.