Transfer of Cationic Polymers from Cellulose Fibers to Polystyrene Latex HIROO TANAKA 1 AND LARS ODBERG 2 Swedish Pulp and Paper Research Institute, Box 5604, S-114 86 Stockholm, Sweden
Received April 3, 1991; accepted July 23, 1991 The transfer of cationic polymers from cellulose fibers to monodisperse polystyrene latex particles (PSL) has been studied using fluorescently labeled (dansylated) cationic polyacrylamides (DC-PAM) of different molecular weights ( M W ) . The rate of transfer after 1 h preadsorption was in the following order: medium MW > high MW > low MW. It is interesting to note that DC-PAM with the highest MW (8 X 10 6) is transferred fairly easily, considering the fact that our previous work has shown that for such a high MW no exchange reaction takes place on PSL or on fibers. These results indicate that protruding segments of the polymer and the hydrodynamic shear play an important role in polymer transfer. Polymers with low MW (2 X 104), on the other hand, can penetrate rapidly into the pores of fibers and transfer is reduced. The charge density of the polymer did not greatly affect the polymer transfer. When the times between adsorption and start of transfer were short (5 min), polymers retransferred from PSL to fibers, and the transferred fraction converged approximately to the ratio of the charge on PSL to the charge on fibers. ¢ 1992AcademicPress,Inc. INTRODUCTION
To be effective as retention aids, the polymers must be adsorbed onto the fibers, fillers, and fiber fragments. Extensive research undertaken in order to understand the adsorption process (1-7) indicates that at least at low ionic strength it can be viewed as an ion-exchange reaction. The conformational change of polymer on the solid surface and the flocculation kinetics have also been studied to promote a better understanding of retention processes (8-13). The levels of addition of polymers are generally low, and particles with various sizes, shapes, and surface characteristics exist in papermaking suspensions. The adsorption of cationic polymers on anionic surfaces takes place quickly (14), since there is no barrier to adsorption but rather an electrostatic attraction at short distances. If the mixing is not very thorough at the point of polymer addition the adsorption of polymers will not occur homogeneously, and surfaces available for polymer adsorption may remain. The added polyelectrolytes will partly flocculate the papermaking stock, but many of the flocs formed will be broken up due to hydrodynamic shear,
Polymers are widely used to modify surface properties and to stabilize or destabilize colloidal dispersions. The behavior of polymers at interfaces is of great importance for a variety of applications. One such important application is as retention aids in papermaking. The stock from which paper is made often contains not only fibers but also filler particles (clay or calcium carbonate) and small fiber fragments. To retain these small particles in the sheet being formed, retention aids are added. These retention aids are expected to flocculate the small particles to the fibers and, since the fibers are easily retained on the wire on which the paper is formed, the fine particles will also be retained. Especially during recent years the need for retention aids has increased, since the speed of the paper machines has been increased and twin-wire formers with high hydrodynamic forces are being used. 1 Permanent address: Department of Forest Products, Kyushu University, Higashi-ku, Fukuoka 812, Japan. 2 To whom correspondence should be addressed. 40 002 1-9797/92 $3.00 Copyright© 1992by AcademicPress,Inc. All rightsof reproductionin any formreserved.
Journalof Colloidand InterfaceScience, Vol. 149,No. 1, March 1, 1992
41
T R A N S F E R OF CATIONIC POLYMERS
which will make possible the transfer of polymers between particles. The transfer of polymers from one solid surface to another is one important aspect of the flocculation process on which there have so far been very few studies. Knowledge in this field is of course not only of interest for papermaking but also for many other processes where flocculation is used, e.g., mineral processing. One of the few reports on the transfer of polymers was presented by Lindstrrm (15 ), who in an extended conference abstract suggested that cationic polyacrylamides (C-PAM) adsorbed initially to fiber fragments (fines) subsequently transferred to the coarse fibers. He found that the electrophoretic mobilities of fines decreased with time and that the radioactivity of fines treated with tritiated CPAM also decreased. The details of these experiments have not, however, been published. The purpose of the present investigation has been to study extensively the transfer of CPAM from fibers to monodisperse polystyrene latex. Fluorescently labeled polymers with different molecular weights and different charge densities were used. EXPERIMENTAL
Materials Cationic polyacrylamides (C-PAM) with various molecular weights (MW) and charge densities (CD) were prepared and fluorescently labeled by dansylation as described previously (16). The degree of labeling was less than 0.5 mol%. At this level, the adsorption of the polymers on cellulosic fiber or latex is not influenced (7), but the fluorescence response is very high. The characteristics of the dansylated C-PAM (DC-PAM) used are listed in Table I. Detailed molecular weight distributions have not been determined for the polymers used in the present study. However, similarly synthesized polymers used in studies of cleavage of polymers during flocculation had Mw/Mn in the range 4-10. These detailed molecular weight distributions will be submitted for publication shortly.
TABLE I Properties of Cationic Polyacrylamides
Code P*l-2 P*2 P*3 P*4 P'5-2
Molecular weight 2 4 4 4 8
X X × × X
104 105 105 105 106
Chargedensity (meq]g) 0.60 0.64 1.42 2.50 0.66
Polystyrene latex (PSL) was synthesized as described in the previous paper (7). The product was a monodisperse latex with a diameter of 985 nm as determined by scanning electron microscopy (SEM) and a CD of 4.0 /seq/g as determined by conductometric titration (17). The cellulosic fibers used were from a neverdried bleached softwood kraft pulp, Imperial Anchor (Iggesunds Bruk, Sweden). The fine material was removed using a Celleco filter (mesh size 100 #m) before use to avoid loss of fibers during the washing steps (see below) and to enable latex particles to be separated from the mixture without contamination by pulp fines. The charge density of the fibers was 28 t~eq/g as determined by conductometric titration (17).
Procedures All experiments were performed in deionized water at room temperature (22 + I°C) with stirring at 200 rpm using a rotary shaker (GFL 3015). The rotary shaker gives lower shear forces than on a paper machine, which makes the transfer process more extended in time. Thirty ml of 0.005 or 0.0012% DC-PAM solution was added to 30 ml of 1.0% pulp suspension. After a given time, the fibers were filtered using a plastic net with a pore size of 10 izm and washed with about 50 ml ofdeionized water until no fluorescence was detected in the filtrate. The filtrate contained no pulp fines. The amount of adsorbed polymer was determined by polyelectrolyte titration (18) Journal of Colloid and Interface Science, Vol. 149,No. 1, March 1, 1992
42
TANAKA AND 0DBERG described above, and the fluorescence intensities were determined. The reason for fixing the concentration is that PSL itself exhibits a slight fluorescence. The SEM pictures of fibers gently shaken with PSL for various periods and washed with deionized water were taken using a Cambridge Stereoscan 200 under standard conditions.
100
IE < fl_ i
50
8
•.
.
o o
,
, I 500
i
i
i
i
I i////
I
1000 Time
I0000 ,
i
I
i
RESULTS AND DISCUSSION
I
Effect of Time between Adsorption and Transfer
30000
rain
FIG. 1. Fraction of DC-PAM (P*l-2) transferred from cellulose fibersto PSL. Effectof time between adsorption of DC-PAM and addition of PSL. Fibers: 0.5%;PSL: 2.0%; DC-PAM: 0.5% on fibers, 22 + I°C, pH 5 + 0.2. Time between adsorption and transfer: O, 5 min; O, 1 h; A, 24 h; A, 2 weeks.
and from the residual fluorescence intensity of the filtrate. The pulp was then suspended in deionized water at a level of 1.0% consistency. The same volume of 4.0% PSL was added and the suspension was shaken continuously. About 5 ml samples of suspension were withdrawn at appropriate time intervals and filtered through the net as described above to separate PSL from fibers. The separated PSL was collected using a Millipore filter ( T y p e D A ) with an average pore diameter o f 0.65 #m. The PSL was then air-dried at r o o m temperature, finely divided, and dried in an evacuated desiccator over P205. The PSL was dissolved in dimethylformamide ( D M F ) at a concentration o f 2% with vigorous stirring, and the fluorescence intensity of this solution was measured using a P e r k i n - E l m e r LS-5 Luminescence spectrometer. The excitation and emission wavelengths used were 333 and 540 nm, respectively. The a m o u n t o f D C - P A M transferred from fibers to PSL was determined by comparing the intensities with calibration curves made as follows. PSL dispersions of concentration 2% with 0.15% D C - P A M adsorbed were prepared. Mixtures of finely divided PSL with and without D C - P A M at various ratios were then prepared and dissolved in D M F as Journal oJColloid and Interface Science, Vol. 149, No. 1, M ar ch 1, 1992
Fibers were treated with DC-PAMs P* 1-2 or P*2 at the level o f 0.5%. The adsorption process took place under shaking for 5 min, 1 h, 24 h and 2 weeks. No D C - P A M was detected in the filtrate, i.e., it was adsorbed completely onto fibers at all times. Figure 1 shows the transfer of polymer P* 12 ( M W = 2 × 104; C D 0.60 m e q / g ) from fibers to latex. Figure 2 gives the results for P*2 with higher M W (4 X 105) but with similar C D (0.64 m e q / g ) , In the case of the polymer with lower MW, the transfer of polymer continued even after 3 weeks (Fig. 1 ), but the effect of time between polymer adsorption and start of transfer, hereafter referred to as the pre-adsorption time, was not very great. The transfer did,
100
.....
. . - o ~ o
i
o
_
--A-
~ so
,5 /
?
e~
~
o
,
o
500
/t
I
,,4
1000 T i m e
10000 ,
I
I
I
I
30000
rain
FIG. 2. Fraction of DC-PAM (P*2) transferred from cellulose fibersto PSL. Effectof time between adsorption of DC-PAM and addition of PSL. Fibers: 0.5%;PSL: 2.0%; DC-PAM: 0.5% on fibers, 22 + I°C, pH 5 + 0.2. Time between adsorption and transfer: O, 5 min; e, 1 h; A, 24 h; A, 2 weeks.
TRANSFER OF CATIONIC POLYMERS
43
FiG. 3. SEM picture of fibersjust after addition of PSL. Verylittle polymertransferhas taken place. DCPAM (P*I-2), MW = 2 X 104. Preadsorptiontime 1 h. however, become more difficult with the increasing pre-adsorption times. For DC-PAM with a medium molecular weight, 4 X 105, the polymer transfer was greatly influenced by the pre-adsorption time as can be seen by comparison of Fig. 1 with Fig. 2. Figure 3 is a SEM picture of fibers for a preadsorption time of 1 h for P * l - 2 just after addition of PSL. At this time very little p o l y m e r transfer has taken place. Very few PSL particles are deposited onto the fibers. The length of a stretched out polymer with weight average M W = 2 X 104 is calculated to be about 35 n m (assumptions: M W of m o n o m e r unit (acrylamide) is 71 and the ratio of weight average M W to number average M W is 2). The length of the polymer is thus around 1 / 30 of the diameter of the PSL particle. It is also well known that cellulose fibers are porous and that there are many wrinkles and cavities on the
fiber surface. With these facts in mind a fiber surface with adsorbed low M W polymers and PSL particles is schematically illustrated in Fig. 4a. When the particles collide with the fibers, the transfer of polymers to PSL should occur from the extreme outer surface of the fibers, because most of the wrinkles or cavities and pores in cell walls are too small for PSL particles to enter. The polymers that are hidden in wrinkles or cavities, although located near the outer surface, or that have penetrated into pores cannot transfer. The molecular weight of the polymer is on the other hand too low to attach the PSL particle to the surface, and transfer will take place directly upon collision. Due to the transfer of cationic polymer the cationic character of the surface is reduced. The polymers located somewhat deeper in the fibers will now start to diffuse to the surface to compensate the negative charges. When the Journal of Colloid and Interface Science, Vol. 149, No. 1, March 1, 1992
44
TANAKA AND 0DBERG
(b)
(~)
F~G. 4. Schematic diagrams showing the size relation between PSL particles and DC-PAM adsorbed on cellulose fiber: (a) DC-PAM ( P * l - 2 ) , M W = 2 × 104; (b) DCP A M ( P * 2 ) , M W = 4 × 105.
time between adsorption and transfer was 5 min, a considerable amount of DC-PAM remained near the surface. Some of these poly-
mers move out to the surface, but some polymers still continue to penetrate into the inner parts of the pores even when polymers on the surface are being transferred. When the time between adsorption and start of transfer was 2 weeks, the polymers were almost evenly distributed over outer and inner surfaces of the fibers. When the polymers on the outer surfaces transfer to other surfaces, the polymers located inside the pores may move out until the equilibrium is achieved. However, since the cationic polymers with lower M W obviously can diffuse rather easily on the surface of fibers, the effect of the pre-adsorption time on polymer transfer is not very great. The time between adsorption and transfer had however a great effect on polymer transfer for polymers with higher M W (4 × 10 5) as shown in Fig. 2. When the time was 5 min, the polymer transfer took place very quickly,
FIG. 5. SEM picture of fibers just after addition of PSL. Very little polymer transfer has taken place. DCP A M ( P * 2 ) , M W = 4 × 10 5. Preadsorption time 1 h. Journal of Colloid and Interface Science, Vol. 149,No. 1, March 1, 1992
TRANSFER OF CATIONIC POLYMERS
especially in an initial stage, and the degree of transfer was about 40% after 50 min, whereas the corresponding transfer for the polymer with low MW (2 × 104) was only 10%. Shortly after adsorption, most of the high molecular weight polymers should be located on the outer surfaces of fibers, with loops and tails available so that the PSL particles can be attached to the fibers. The results obtained suggest that the transfer of polymers takes place when PSL particles are gradually removed from the fibers by the hydrodynamic shear and/or the abrasion induced by the mutual collisions of fibers as the suspension containing fibers, polymers, and PSL was continuously shaken. This interpretation is supported by SEM observations. Figure 5 is a SEM picture of fibers after a pre-adsorption time of 1 h (MW = 4 × 105)just after addition of PSL. Almost all fiber surfaces are covered
45
with deposited PSL particles. As in the case of the low MW polymer described earlier, the fiber surface with adsorbed polymer and PSL particles is schematically illustrated in Fig. 4b. The whole surface of the fibers can be covered with PSL particles as shown in Fig. 5, because enough tails and loops of the polymers remain to bridge between fibers and particles. After shaking the mixture for 100 h, the transfer of polymer almost leveled off. At this stage, the majority of particles were detached from the fiber surface, as can be seen in SEM picture (Fig. 6). Interestingly, PSL particles still remain but only in the fiber lumen and in pits where the hydrodynamic forces must be very weak and no abrasion takes place. When the pre-adsorption time is increased the transfer of the polymer is much less extensive, as can be seen in Fig. 2. There are many reasons for this. The polymer molecules
FIG. 6. SEM picture of fibers after shaking for 4 days. DC-PAM (P*2), MW = 4 × 105. Preadsorption time 1 h. Journal of Colloid and Interface Science, Vol. 149, No. I, March 1, 1992
46
T A N A K A AND 0 D B E R G
will start to penetrate into the pores of the fibers, which will make them less available for transfer and also more firmly anchored to the fiber. Furthermore when some of the molecules have diffused into the fibers, the ones remaining on the surface will adopt a flatter conformation with fewer loops and tails.
Effect of Molecular Weight Three kinds of DC-PAM were used in which the CDs were similar (0.60-0.66 meq/g) but the MW varied widely (2 × 104, 4 × 105, and 8 × 106). The time between adsorption and transfer was I h for all experiments. Figure 7 shows that the degree of transfer was highest for the medium MW and lowest for the low MW. It is quite interesting that the polymers with the highest MW ( 8 × 106) could transfer fairly easily, especially in view of our previous work (19) which showed that for such a high MW polymer exchange reactions between adsorbed polymers and polymers in solution did not take place on cellulosic fibers or on PSL. As discussed in the previous section, it is very likely that protruding segments of polymers and hydrodynamic shear or mutual abrasion between fibers play an important role in the transfer of polymers from one solid to another.
From these results, it is suggested that the degree of turbulence, size, and shape of the particles significantly influence the transfer of polymers. The higher the degree of the turbulence and the larger the particles, the easier should the transfer of polymers take place. During the process of transfer the polymer chains might also be cleaved. Investigations of these points are in progress.
Effect of Charge Densities
As shown in Fig. 8, the effect of CD on polymer transfer was not great in our experiments. It was expected that DC-PAM with higher CD would transfer more slowly because of a flatter conformation of the adsorbed polymer and a higher number of linkages between polymer and fiber. In contrast, DC-PAM with higher CD transferred rather easily during the initial stage. This probably depends on the existence of a distribution of polymer conformations on the fiber surface. The fractions of DC-PAM adsorbed are given in Table II. DCPAM (P*2) with low CD was adsorbed completely, but DC-PAMs (P*3 and P*4) with medium and high CD were adsorbed at the levels 72 and 32%, respectively. In the two latter cases, although the polymer first adsorbing on the fibers can attain a flat conformation, the polymer molecules adsorbed at later stages will probably be forced to take up much more 100 extended conformations. In addition, a polymer with high charge density probably diffuses more slowly into the fibers, which will also favor transfer of the high CD polymers. To avoid such heterogeneous conditions < 50 12when the influence of different pre-adsorption d a times was studied for different CDs, the level of addition of DC-PAM was lowered to 0.12%. The pH was furthermore raised to 7 + 0.2 to promote the dissociation of carboxyl groups m 0 500 1000 10000 30000 0 of the fibers and hence adsorption. Results are Time , rnin ~shown in Fig. 9. FIG. 7. Effect of molecular weight on the fraction of When the pre-adsorption time was 5 min, DC-PAM transferred from cellulose fibers to PSL. Fibers: polymer transfer took place quite easily in the 0.5%; PSL: 2.0%; DC-PAM: 0.5% on fibers, 22 + I°C, pH initial-stage. The influence ofCD of DC-PAM 5 _ 0.2. Time between adsorption and transfer: 1 h. MW: on transfer was, however, small, the transfer, A, 2 × 104 ( P * I - 2 ) ; O, 4 × 105 (P*2); ff], 8 × 106 being somewhat lower for the highest CD. (P'5-2). •
,
,
,
. . . .
,
i
,
i
i
,
i
i//1/
I
I
I
i
I
Journal of Colloid and Interface Science, VoL 149 No, 1, M a r c h 1, 1992
TRANSFER OF CATIONIC POLYMERS
47
lOO
60
d
< lz
50
o_ i u a
6e~
Y
g 0
. . . .
g I
. . . .
500
I
i
/ //
/
1000 Time
I
10000 ,
I
I
I
I
0
30000
500
1000 Time
min
FIG. 8. Effectof charge density on the fraction of DCPAM transferred fromcellulosefibersto PSL. Fibers:0.5%; PSL: 2.0%; DC-PAM:0.5% on fibers, 22 _+ 1°C, pH 5 + 0.2. Time between adsorption and transfer: 1 h. CD (meq/ g): I, 0.64 (P*2); Ell, 1.42 (P*3); ,% 2.50 (P*4). When the pre-adsorption time was 1 week, the polymer transferred very slowly, probably because of penetration of polymers into pores in the fibers. However, the effect of CD on the transfer was very small. This result is again very different from that relating to the polymer exchange rate, which was much slower for the DC-PAM with higher CD (19). These results again m a y suggest that cleavage of polymer chains takes place during the transfer. The transfer of a highly charged polymer can then occur quite easily despite a flat conformation. Further investigations are in progress using size exclusion chromatography. When the pre-adsorption time was 5 min, polymer transfer occurred quickly during an initial stage and reached a m a x i m u m after approximately 1 day (Fig. 9). This means that polymers retransfer from PSL particles to fi-
8 0 0 0 10000 ,
30000
rain
FIG. 9. Fraction of DC-PAMtransferred from cellulose fibers to PSL. Effectsof charge density and time between adsorption of DC-PAMand addition of PSL. Fibers: 0.5%; PSL: 2.0%; DC-PAM:0.12% on fibers, 22 + I°C, pH 7 + 0.2. Charge density (meq/g): t, O, 0.64; A, A, 1.42; II, D, 2.50. Time between adsorption and transfer: e, A, m, 5 rain; O, ~, D, 1 week.
bers. The explanation is probably that remaining polymers on the outer fiber surfaces penetrate into pores with time, and these surfaces become accessible for polymer adsorption. The fraction of DC-PAM transferred with different CDs converged to about 30%. It is particularly interesting that the transferred fraction converged to this level irrespective of whether a short or long pre-adsorption time was used. From the CDs of fibers and PSL, the total number of charges was calculated to be 140 #eq/1 (5 g/1 X 28/~eq/g) on the fibers and 80 #eq/1 (20 g/1 × 4 # e q / g ) on the PSL. If it is assumed that the DC-PAMs are distributed as the ratio of charges, the transferred fraction should be 36% in the equilibrium situation. The fact that the experimental results
TABLE II Adsorption of DC-PAMs with Different Charge Densities onto Cellulose Fibers. Constant Molecular Weight = 4 X 105 Code
Initial conc. of DCPAM (mg/t)
Conc. of DC-PAM after 1 h (mg/1)
DC-PAM adsorbed on fiber (rng/g)
Fraction of DC-PAM adsorbed (%)
P*2 P*3 P*4
25.0 25.0 25.0
0 7.0 17.0
5.0 3.6 1.6
100 72 32
Note.
Adsorption conditions are those given in Fig. 8. Journal of Colloid and Interface Science, Vol. 149, No. 1, March I, 1992
48
TANAKA AND ODBERG
were a little lower, as can be seen in Fig. 9, may be due to PSL particles in the pits and remaining on the fiber surfaces (Fig. 6 ). These results indicate that the adsorption of cationic polymers onto negatively charged surface is mainly governed by ion-exchange reactions at these low electrolyte concentrations, as has also been shown in separate experiments (5,7). ACKNOWLEDGMENTS Financial support from "Cellulosaindustrins Stiftelse f'rr Teknisk och Skoglig Forskning samt Utbildning" is gratefully acknowledged. Dr. Anthony Bristow is thanked for linguistic revision of the manuscript. REFERENCES 1. Marra, J., van der Schee, H. A., Fleer, G. J., and Lyklema, J., in "Adsorption from Solution" (R. H. Ottewill and C. H. Rochester, Eds.). Academic Press, New York, 1983. 2. Furusawa, K., Kanesaki, M., and Yamashita, S., J. Colloid Interface Sci. 99, 341 (1984). 3. Cosgrove, T., Obey, T. M., and Vincent, B., J. Colloid Interface Sci. 111, 409 (1986). 4. Takahashi, A., and Kawaguchi, M., Adv. Polym. Sci. 46, 1 (1982); Kawaguchi, M., Hayashi, K., and Takahashi, A., preprint in "Polymers in Colloidal Systems," p. 4. Eindhoven, The Netherlands, 1987. 5. Winter, L., Whgberg, L., t)dberg, L., and Lindstrrm, T., J. Colloid lnterface Sci. 111, 537 (1986).
Journal of Colloid and Interface Science, Vol. 149, No. 1, March 1, 1992
6. Lindstrrm, T., in "Fundamentals of Papermaking" (C. F. Baker and V. W. Punton, Eds.), p. 311. Mech. Eng. Publ., London, 1989. 7. Tanaka, H., (}dberg, L., W~tgberg,L., and Lindstrrm, T., J. Colloidlnterface Sci. 134, 219 (1990). 8. Tanaka, H., in "Papermaldng Raw Materials" (V. W. Punton, Ed.), p. 841. Mech. Eng. Pub1., London, 1985. 9. Wfigberg, L., Odberg, L., Lindstrrm, T., and Aksberg, R., J. Colloid Interface Sci. 123, 287 (1988). 10. Mtihle, K., J. Colloid Interface Sci. 22, 249 (1987); Colloid Polym. Sci. 263, 660 (1985). 11. Smith, D. K. W., and Kitchener, J. A., Chem. Eng. Sci. 33, 1631 (1978). 12. Pelssers, E. G. M., Cohen Stuart, M. A., and Fleer, G. J., J. Chem. Soc. Faraday Trans. 86, 1355 (1990). 13. Whgberg, L., Odberg, L., and Glad-Nordmark, G., in "Fundamentals of Papermaking (C. F. Baker and V. W. Punton, Eds.), p. 413. Mech. Eng. Publ., London, 1989. 14. Falk, M., Odberg, L., Whgberg, L., and Risinger, G., Colloids Surf. 40, 115 (1989). 15. Lindstrrm, T., Preprint in "International Symposium on Wood and Pulping Chemistry," p. 121. Vancouver, Canada, 1985. 16. Tanaka, H., and tJdberg, L., J. Polym. Sci. Chem. 27, 4329 (1989). 17. Katz, S., Beatson, R. T., and Scallan, A. M., Sven. Papperstidn. 87, R48 (1984). 18. Senju, R., Bull. Chem. Soc. Jpn. 26, 143 ( 1953); Horn, D, Prog. Colloid Polym. Sci. 65, 251 (1978). 19. Tanaka, H., Odberg, L., Whgberg, L., and Lindstr/Sm, T., J. Colloidlnterface Sci. 134, 229 (1990).