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Polymer adsorption and its effect on the stability of hydrophobic colloids. III. Kinetics of the flocculation of silver iodide sols
Polymer Adsorption and Its Effect on the Stability of Hydrophobic Colloids III. Kinetics of the Flocculation of Silver Iodide Sols 1 G. J. F L E E R ANn J. L Y K L E M A Laboratory for Physical and Colloid Chemistry of the Agricultural, University, De Dreijen 6, Wageningen, The Netherlands
Received June 3, 1975; accepted November 5, 1975 In a previous study on the flocculation of silver iodide sols by polyvinyl alcohol (PVA) it was demonstrated that the extent of flocculation depends critically on the way in which sol particles and polymer are mixed. Optimal flocculation was shown to occur if a two-portion method of mixing is applied in which equal numbers of polymer-covered and uncovered particles are brought together. The observations could be fully explained by a bridging model of flocculation. In this study the kinetics of the flocculation process has been investigated with a stopped flow spectrophotometer. The coagulation of AgI-sols by low molecular weight electrolytes was found to be a bimolecular process. Critical coagulation concentrations were found that matched closely those reported in the literature. The floccMation of sol by polymer brought about by mixing of polymer-covered and uncovered particles, follows also bimolecular kinetics. In this case only 50% of the collisionsleads to aggregation and the fast flocculation rate is just half the rate of fast coagulation. In accordance with previous results, the critical floccu]ation concentration of electrolytes with univalent and bivalent counterions was shown to be much lower than the corresponding critical coagulation concentration. Comparison of the kinetics of our two-portion method with the one-portion method (in which the total amount of polymer is added to the total amount of sol) leads to the conclusion that absorbing PVA molecules need a few seconds to form a layer that can effectivelyprotect the sol particles. Thus, the rate of flocculation can provide information on the rate of adsorption. This study underlines again that the way of mixing is a very important parameter in the flocculation of hydrophobic sols by polymers. INTRODUCTION The stability of hydrophobic colloids in the presence of polymers is of wide-spread importance in a variety of applications. I n addition, polymer stabilization and flocculation~ are quite interesting from a theoretical point of view. I n recent years considerable progress has been made towards a qualitative understanding of the processes involved (2, 3). xPresented at the 49th National Colloid Symposium, Potsdam, New York, June 16-18, 1975. Following La Mer's original proposal (1), we distinguish in this paper between flocculation (aggregation of colloidal particles by polymers) and coagulation (aggregation by low molecular weight electrolytes).
While q u a n t i t a t i v e descriptions of stabilization by polymers have recently been developed (4, 5), a q u a n t i t a t i v e t r e a t m e n t of flocculation b y polymers has hardly initiated as yet. To obtain a better insight in the interaction of polymers with colloids, and to provide data that are amenable to quantitative analysis, the present s t u d y has been undertaken. As a model the silver iodide sol-polyvinyl alcohol (PVA) system has been used. The double layer characteristics of AgI have been studied extensively (6), also in the presence of low molecular weight alcohols (7-9) and polymers (10). Using this information in combination with data from adsorption isotherms, elec-
228
Journal of Colloid and InlerJace Science, Vol.55, No. 1, April 1976
Copyright ~) 1976by AcademicPress. Inc. All rights of reproductionin any form reserved.
POLYMER ADSORPTION trophoresis, and viscosity measurements of AgI in the presence of adsorbed PVA, we were able to establish the effective thickness of the adsorbed layers and the distribution of segments over trains and loops. This is described in part I of this series (11) and in (10). In part II (12), the flocculation of AgI by PVA has been studied. It was demonstrated that the order of mixing of sol and polymer is a critical feature, and that the most efficient flocculation is obtained if equal amounts of nearly completely polymer-covered particles and uncovered particles are mixed. The results could be explained quite convincingly in terms of bridging of different particles through polymer loops and/or tails. The key feature of the mixing procedure is that it requires the simultaneous occurrence of long protruding loops, capable of bridging the gap between two particles, and free surface at which those loops can attach. The extent of flocculation attained by this mixing method and the optimal polymer dosage are closely related to the characteristics of the polymer adsorption process. Especially the high affinity character of the adsorption isotherms and the apparent irreversibility of adsorption are important features. These previous flocculation experiments (12) have been carried out in test tubes with flocculation times of the order of hours. For the sake of argument we denote this procedure as the static method. However, for a better understanding of colloid stability, measurements in the very first seconds after mixing are indispensable because these results are more suitable to interpretation in terms of particle-particle interactions than those obtained by a static method (13-15). For this reason we undertook the present study, dealing with flocculation by polymers under very rapid mixing conditions, further denoted as the kinetic method. Hitherto, only a few kinetic studies on flocculation have been reported in the literature (16, 17). It is generally accepted [e.g., (15)~ that the coagulation of colloidal systems by electrolytes is a bimolecular process. Hence, as the
229
first purpose of this study we investigated whether this conclusion would apply also for flocculation. In addition, one of the important results of this kinetic study turned out to be that vaIuable information regarding the rates of polymer adsorption and reconformation during the very first seconds can be obtained from the initial flocculation rate. This type of information is not easily accessible by other means. Two types of measurement have been used in this work.
(1) Stopped Flow Measuremenls In this technique, which was used earlier for the study of the coagulation rate of colloidal systems (18, 19), the absorbance of the flocculating system is recorded in the very first seconds (or fractions of a second) after fast, reproducible mixing. As a first step, rates of coagulation by salts have been measured as a basis for comparison with the flocculation rates. Next, measurements of flocculation rates were carried out. From these it followed that also with this kinetic method the flocculation efficiency, using a two-portion method of mixing, is much greater than with a oneportion method (in which all the polymer is mixed at once with all the sol). Then it was demonstrated that flocculation is indeed a bimolecular process, both with respect to the sol concentration C~oland to the ratio between covered and uncovered particles. The critical flocculation concentration (CFC) of salts, needed to obtain fast flocculation, was found to be independent of c~ol.
(2) Static Measurements Using the static method, it was found that, at constant flocculation time, the critical salt concentration (c½, see below) depends on C~ol. Making use of the bimolecular nature of the flocculation, it was possible to vary the flocculation time in such a way as to lead to a constant total number of particle collisions at varying C~ol. The results indicated that under Journal of Colloid and Interface Science, Vol. 5S, No. 1, April 1976
230
FLEER AND LYKLEMA
these conditions of Csol.
c½ becomes
independent
EXPERIMENTAL
Materials The AgI sols used have been described before (11, 20). The sol particles were negatively charged (pI ~ 5), the average particle radius was 50 nm. The polymer used was PVA 13-98.5, with a viscosity averaged molecular weight of 56 000 and containing about 1.5% of unhydrolyzed acetate groups in the molecule.
Stopped Flow Apparatus A Durrum stopped flow spectrophotometer with a 2-cm path length cell was used in the measurements. In this apparatus the solutions to be mixed are contained in two syringes. By a pressure operated actuator, equal volumes (~0.2 ml) are reproducibly mixed within a very short time (~10 msec for dilute aqueous solutions). The transmittance of the mixture can be recorded on a storage oscilloscope, or (as in our case) on an attached recorder. The percentage transmittance T, was transformed into the absorbance A using A --- 2 - a°log T. The wavelength in these experiments was 650 nm; at this wavelength only scattering occurs (12, 20).
Methods 1. Kinetic method. In the coagulation experiments, one of the syringes of the stopped flow apparatus contained the sol, the other the salt solution. In the flocculation experiments using the one-portion method, the sol was mixed with a solution of PVA and electrolyte of the desired composition. In flocculation experiments with the two-portion method, one syringe was filled with untreated AgI sol, the other with polymer-covered AgI particles in a dilute salt solution. The latter solution was prepared by adding the PVA to the sol (using a buffering water layer between sol and polymer (12)) 1 day before the experiment, whereas the salt was added immediately prior to the kinetic measurements. Journal of Colloid and Interface Science, Vol. 55, No. l, April 1976
In most of the two-portion experiments, the sol concentrations in both syringes were identical, hence ¢1 = 0.5, ¢1 being the fraction of uncovered particles. The only exception to this occurred in the measurement of the flocculation rate as a function of ¢2. 2. Static method. This method has been described extensively in part II. The twoportion method was used in which, after a contact time tl between the polymer and the colloidal particles, the (covered) half of the sol particles was added to the other (untreated) half. The absorbance at 430 nm of the supernatant (obtained by mild centrifuging) was taken as a measure of the extent of flocculation. The allowed flocculation time t2 was of the order of hours. The critical salt concentration c½ was defined as that salt concentration at which, after a given flocculation time, the absorbance of the supernatant was reduced to half of its original value (Arol = 0.5). RESULTS
AND DISCUSSION
Coagulalion by Salts Figure 1 shows some typical results of the coagulation of AgI sols by KNO3. In this figure &A is the increase of the absorbance per centimeter path length due to the coagulation. The salt concentrations indicated in this figure are the final concentrations after mixing. The absorbance increases continuously as a function of time, but already in the first few seconds a slight deviation from the theoretical (15, 21) straight line occurs. The deviation probably can be accounted for by the nonvalidity of the assumption that the scattering of an aggregate is the same as that of a spherical particle with the same total weight. Treatments are available to eliminate this assumption (22), but for the present purpose it suffices to consider only relative values of the initial slopes of the 2~A - - t curves. For the same reason we do not have to take into account possible hydrodynamic effects (23, 24). With increasing salt concentration, the initial slope increases until finally a concentration region is attained where the coagulation rate
231
POLYMER ADSORPTION 10"&A I(3
cm '
CSO =L
tm[~
/
210rnN
~1813
/J
8
2portions m PVA Pl = 2 5 ~ AgI ~ ~
I
2
3
~
5
3 0 r a n KN03
5
Fro. i. The increase of the absorbance of AgI-so]s with time due to coagulation by KNOa. 2M is the increase in absorbance per centimeter path length. The abscissa scale is in seconds. Sol concentration I raM, The final KNO~ concentration is indicated• The dashed curve is an example of a fast flocculation experiment with the two-portion method (4,~=0.5; p~=2.5 m g PVA 13-98.5/mmole AgI; Cl~NO3 = 30 raM).
becomes independent of the salt concentration. This is the region of fast coagulation, beyond the critical coagulation concentration (CCC). The CCC is most easily determined (15, 21) by plotting the logarithm of the reciprocal slope (log dt/dA) against log c,, where c, is the salt concentration. This has been done in Fig. 2. The dashed curve in Fig. 1 reflects the fast flocculation rate using the two-portion method of mixing. In anticipation of the discussion to be presented below, we note that the rate of fast coagulation is about twice the rate of fast flocculation. Figure 2 shows log dt/dA versus log c, plots for three sol concentrations and three salts with counterion valencies z = 1, 2 and 3. The quantity dt/dA is proportional to the stability ratio W (14, 15). All graphs consist essentially of two intersecting straight lines as is usually observed (15, 21). The intersection points are identified as the CCC values. We found 174, 4.0, and 0.11 mM for KNO3, Ca(NO3)2, and La(NQ)3, respectively. These
values are higher than those reported for classical test tube experiments (25). This should be expected since in our experiments the coagulation times are only of the order of seconds and orthokinetic coagulation is absent. In the scope of the present article we do not need to discuss the slopes of the descending branches of the plots. At a given c~ol, the fast coagulation rate is roughly, but not completely, independent of the counterion valency (Fig. 2). The slightly lower coagulation rate at higher z could possibly be accounted for by a different distribution of charge in the Stern layer, as first suggested by Kruyt and Troelstra (26). Again this point, although interesting, is not very pertinent for the present article. Fast coagulation being a bimolecular process, its rate should be proportional to the square of the sol concentration. It follows from the levels of the horizontal branches in Fig. 2 that the measured coagulation rates at high c~,,1are slightly too low in comparison to those at low c~,,~. We found similar differences before (19). This behavior is possibly due to an experimental artifact of the used stopped flow spectrophotometer. Because of too wide an angle of acceptance of the photomultiplier, the unmodified instrument that Ct/dA La{N031:i
~Ca(N01) 2
,•
o
i ' 011raM -~
. . . .
T
i -3
L0rnM
i -2
N°3 • ~ s0L C2mmote/t A t , .. 05 I0
.,
\%-
% , ~27--, -1 tog %'M/
0
Fla. 2. Coagulation kinetics. T h e dependence of (dt/dA)t...o on the electrolyte concentration for three
salts and three sol concentrations. T h e breaks (indicated by arrows) give the critical coagulation concentrations. Journal of Colloid and Interface Science, Vol. 55, No. 1, April 1976
232
FLEER AND LYKLEMA
we used records also part of the secondarily scattered light, giving rise to too low an absorbance (and thus, dA/dt) especially at higher sol concentrations. Indeed it was found by Lichtenbelt et al. (27) using the same instrument that narrowing the angle of acceptance solves the problem, at least for polystyrene latices. Allowing for this instrumental artifact, the results indicated in Fig. 2 may be interpreted as being within experimental error in agreement with the bimolecular nature of the coagulation process.
Flocculation, One-Portion Method In the one-portion method, a solution of PVA containing a low concentration of electrolyte is mixed with silver iodide sol. Some of the results are shown in Fig. 3 as absorbance against time curves. These experiments have been done in 30 mM KNOa. Higher salt concentrations do not alter the flocculation rate, so that these results refer to fast flocculation with respect to the salt concentration. Note the different abscissa scale of Fig. 3 as compared to that of Fig. 1. The curve for the two-
102&A f
cm~l | 2port=ons
t l ~ =25mgPVA/mm'teAgl ~
2
~
p = 50 rngPVA mmoteAgI
125
]
1I
20
t
Fla. 3. T h e increase of the absorbance of AgI-sols with time due to flocculation by PVA. One-portion method. T h e polymer dosage p is indicated, c~ol = 1 raM; CKNOa = 30 m M . T h e dashed curve is the same as that in Fig. 1. dournal of Colloid and Interface Science, Vol. 55, No. I, April 1976
1
JdA
l& - cm-ls 1
//
,2
'
o
5
O8
0 ~,
1
2
3 mgPVA/mmoLe Agl
FIG. 4. Flocculation rate after different time intervals as a function of polymer dosage. One-portion method. T h e flocculation time is indicated. Conditions as in Fig. 3.
portion method in Fig. 3 is the same as that in Fig. 1. It follows from Fig. 3 that a small degree of flocculation occurs with the one-portion method, at least initially. With increasing polymer dosage p (expressed in mg PVA added per mmole of AgI) the initial slope increases until a maximum rate is reached of about 1.3 X 10-* cm-1 sec-I. From the data of Fig. 1, a maximum rate of initial coagulation at the same C~otof about 25 X 10-3 cm -I sec-1 can be deduced. Thus, if any initial flocculation occurs with the one-portion method, it is very slow. There is another remarkable difference with the curves of Fig. 1. Although for polymer dosages p > 1.5 mg/mmole the initial slopes remain constant, the corresponding slopes after some time (>5-10 sec) decrease with increasing p, and eventually become zero. This decrease of the flocculation rate with time in the one-portion method is more dearly expressed in Fig. 4, where the slopes of the curves of Fig. 3 at fixed times are plotted as a function of the polymer dosage. Except for the very beginning of the flocculation process, the flocculation rate passes through a maximum around p = 1.5 mg/mmole, dropping to zero for sufficiently high dosage. This last mentioned fact is in agreement with the results obtained with the static
233
POLYMER ADSORPTION
method (part II). In the latter case, with flocculation times of the order of hours, no flocculation at all could be detected with the one-portion method (4~, = 0, or qh = 1). Apparently, the slight initial flocculation occurring in the very first seconds after mixing cannot be detected with the static method, because the aggregates formed are not separated by centrifuging. An explanation of this slight initial flocculation can be offered in terms of the bridging mechanism given before (part II). Two ilnportant prerequisites for the occurring of flocculation are (i) the presence of long loops and/or tails, extruding from one particle, and (ii) the availability of free surface on other particles onto which these loops and trains can attach themselves. Obviously, only in the very first seconds free surface sites are available for bridging. The extent of bridging is a maximum if p -- 1.5 mg/mmole. This is about half the maximum adsorption (11, 12). The occurrence of a flocculation optimum at half coverage has been proposed by La Mer (1). After longer times, especially at high p, polymer molecules are adsorbed on all particles to such an extent that no available surface sites are left. Moreover, protection due to extended polymer layers on all the particles then starts to develop itself. Thus, this inference of the rate of polymer adsorption may be drawn from these flocculation experiments: Within a few seconds most of the polymer molecules are attached to the surface, most of the available surface is then occupied and the adsorbed layer is capable of effective protection. This does of course not imply, that no further rearrangements could take place, nor that the adsorbed amount and layer thickness could not further increase with time.
Flocculalion, Two-Portion Method In the two-portion method covered sol particles are mixed with uncovered ones. An example of a case of fast flocculation is given by the dashed curve in Fig. 1; the same curve appears also in Fig. 3. Note that in this case
the polymer dosage is expressed as pl, the amount of PVA added per mmole of the first portion of sol, whereas the dosage p in the oneportion method is expressed per lotal amount of AgI. Thus the curves for pz = 2.5 rag/ mmole (one-portion) and for p = 1.25 mg/ mmole (two-portion) refer to the same final composition of the mixture. It is useful to compare the rates of fast flocculation (i.e., in the region where further addition of salt does not increase the rate) using either way of mixing with each other and with the fast coagulation rate. It follows then that the rate of fast flocculation by the twoportion method is lower by about a factor of two than the rate of fast coagulation, whereas the rate of fast flocculation by the one-portion method is very much lower. Figure 5 shows log dt/dA against log c., plots for the two-portion method of mixing. Figure 5 strongly resembles Fig. 2 for the coagulation. The slopes of the lines below the CFC seem to be lower than those in the case of coagulation. That the slopes should be different is quite conceivable, because the interaction energy between an uncovered
~L I
L~(NO,5,
,~
I
,,
"CalNO~],
•
,~
\~i
i
\
c;,, G;mrTol%Zl .,
O,
,.
'° KNO I
I 5
T
t
Ol~,n~ ~
T
16ram -
3
IS.,M 12
-1
-Log % / ~
3
FIG. 5. Flocculation kinetics, two-portion method. The dependence of (dt/dA)e~o on the electrolyte concentration. The sol concentration is indicated. The polymer dosage Pl equals 2.5 mg PVA per mmole AgI of the first portion. The number of covered particles is equal to that of uncovered ones (4L = 0.5). The intersection points of the straight lines (indicated by the arrows) are taken as the critical flocculation
concentrations. Journal of Colloid and Interface Science, Vol. 55, No. 1, April 1976
234
FLEER AND LYKLEMA
and a polymer covered particle contains, in addition to the classical electrostatic repulsion and the Van der Waals attraction, also a contribution due to the polymer bridging. As yet the effect of this polymer contribution on the stability ratio is largely unknown. In a next contribution (28) in this series we intend to investigate in some detail the interaction energy between uncovered and polymercovered particles. It can be deduced from Fig. 5 that the rate of fast flocculation is nearly proportional to the square of the sol concentration, as was the case for the coagulation. The observed slight deviation from this proportionality can again be ascribed to the same instrumental artifact, discussed above. Thus, also for the two-portion method the flocculation process is bimolecular within experimental error. At constant C~ob the fast flocculation levels in Fig. 5 are about 0.3 units higher than the corresponding ones in Fig. 2. Thus, the rate of fast flocculation is lower than the fast coagulation rate by about a factor of two. The reason is that with the two-portion method only half of the possible particle encounters can lead to aggregation: Collisions between two covered particles (due to protective action) and between two uncovered particles (due to electrostatic repulsion) are not effective for flocculation. Another way of demonstrating this is as follows. In a bimolecular coagulation process, the initial rate of fast coagulation is given by (13, 15). - d u / d t = K v 2,
[1]
where v is the initial number of particles and K is the rate constant. If we have vu uncovered and vc covered particles (with v = vu + vc), the flocculation rate can be written as:
-
-
dv -- = dt
dvu
d~,c
dt
dt
- Kuuvu 2 + Kucvcv~ + K~vo ~ + Kc,v~vu.
[2"]
If the numbers of uncovered and covered particles are equal, v, = v~ -- ½v. As only collisions between dissimilar particles are effective, Journal of Colloid and Inlerface Science, Vol. 55, No. 1, April 1976
Kuu = Kcc = 0 and K~c = K,u = K , so that the fast flocculation rate becomes
-d~/dt = ~K~,
E3~
which is half of the fast coagulation rate. In using Kuc = K, it is assumed that a possible change in the collision diameter of a covered particle is exactly counterbalanced by the change in the diffusion constant, K being proportional to the product of the diffusion constant and collision diameter. In a preliminary report (20), this factor of a half was not found. This conclusion was based on too small a number of measurements and is herewith corrected. From Fig. 5, it follows that the critical flocculation concentrations (CFC's) for KNO3, Ca(NO3)2, and La(NO,)3 are 18, 1.6, and 0.11 mM, respectively. The CFC's are independent of C~ol and higher than those found with the static method (see (12), and Fig. 8 and Table I, below). This is to be expected because the time scale is much shorter with the kinetic method. As mentioned above, similar differences are usually found with coagulation experiments. The CFC's are, at least for KNO3 and Ca(NO3)2, much lower than the corresponding CCC's, indicating that the polymer definitely causes an attractive interaction between two particles. The behavior of La(NO3)3 is an exception, in that the CFC approximately equals the CCC. Nevertheless, it is not allowed to look upon the flocculation in the presence of La(NO3)3 as a coagulation mechanism, the flocculation rate is definitely lower than the coagulation rate. If in this case simultaneous coagulation of uncovered particles would occur due to the high valence of the counterion, Eq. [21 would predict a rate which is ¼ of that of fast coagulation. However, the experimental results point out that also with La(NOa)a the factor ½ (or even slightly less) is found, so that this possibility may be ignored. We have no clear explanation to offer for the results with La(NO3)3. Perhaps they are partly due to the competitive adsorption of polymer train segments and (either or not
POLYMER ADSORPTION hydrolyzed, although hydrolysis is unlikely around p H - 6) La 3+ ions on the AgI surface. At any rate, the effect of the polymer seems to be much more pronounced with monovalent and bivalent counterions than with trivalent ones. In Fig. 6, examples are given of two-portion flocculation rates after fixed times as a function of p~. These results apply to C~o~= 0.2 m M and a KNO3 concentration of 15 mM. The dA/dt has been divided by C~o12to facilitate the comparison with the data of Fig. 4. The salt concentration is just below the CFC. The following is observed. The flocculation rate is maximal around pt = 3.0 mg/mmole, in close agreement with the optimal dosage of 2.5 mg/mmole as found with the static method (see (12, Figs. 7 and 9)). This very dosage provides the best compromise between the production of sufficiently long loops (required for bridging) and leaving only little polymer in the solution (which would decrease the number of available attachment sites on the surface of the originally bare particles). Comparing Figs. 4 and 6, it is concluded that at the optimal p~ the flocculation rate with the two-portion method is at least a factor 10 higher than with the one-portion method, already in the first seconds. After longer times this ratio increases strongly. At low dosage (to the left in Fig. 6) the flocculation rate increases with increasing pv The reason is the increasing layer thickness. A significant difference with the corresponding part of Fig. 4 is that in this region dA/dt falls off much slower with time than in the oneportion method. At polymer dosages beyond the maximum (to the right in Fig. 6) the flocculation rate decreases strongly with increasing time also with the two-portion method. We recall that, using the static method, no flocculation could be detected beyond pl -- 3.5 mg/mmole (see (12, Fig. 7)). This is because the excess polymer adsorbs onto the (originally) bare particles, decreasing the number of available surface sites for bridges to be formed. With the kinetic method (Fig. 6) a
235
~03,j,~ dt . CssF crn-I s ~ 12
o
~." of °-°-° ,~.J--.^
,
/
2
J
o
o
o 0s
2~
\\,.
/°
o
0
2
L
6 rng/mrnoi.e Pt
FIG. 6. Flocculation rate at different flocculation times as a function of the polymer dosage pt using the two-portion method, pl is expressed in mg PVA/mmole AgI of the first portion of sol. C,ol = 0.2 mM; cK~o~ = 15 mM. To facilitate comparison with Fig. 4, dA~dr has been divided by C~ol2. slight initial flocculation is found, which slows down very rapidly. Again it can be concluded that within about 20 sec the adsorption of polymer molecules on the second portion of sol particles has proceeded far enough to prevent further attachments and to induce protective action. In Fig. 7, results are shown for experiments with varying fractions of covered (4,1) and ~0 dA
30 - crC ~ gl
20
/ . /
~
/ o
e-
0
02
06
0g
¢~
I0
Fro. 7. Initial flocculation rate w i t h the two-portion
method of mixing as a function of 4~, the fraction of AgI-sol in the first portion, c~ol= 0.2 raM; C~NO~ = 15 raM; pl = 2.5 mg PVA/mmole AgI of the first portion of sol. Journal of Colloid and Interface Science, V o l . 55, N o . 1, A p r i l 1976
236
FLEER AND LYKLEMA
uncovered (i - ~bl) particles. In this case the total sol concentration is constant so that there are no complications in the measurement due to secondary scattering. In a bimolecular flocculation process, the rate must be proportional to 4~1 (1 -- 4~1). As shown in Fig. 7, the experimental points lie within experimental error on a parabola, corroborating the bimolecular nature of the flocculation in the two-portion method.
which q is determined in a situation where half of the material is flocculated (Arol = 0.5). I t is not difficult to forward a qualitative explanation for the observed trends. (1) Increasing the flocculation time at a given sol concentration results in more collisions, and thus, in a greater extent of flocculation. (2) If the concentration of the sol is increased, the number of Brownian encounters per second increases, leading to a higher proportion of focculated material in a given period. (3) Since we have identified c~ as the salt concentration required to obtain a given absorbance within a preset time, the decrease of c½ with increasing C,ol can be attributed to the fact that in the region of slow flocculation the effect of increased double layer repulsion is offset by that of an increased number of collisions per second.
Slatic Melhod A number of experiments has also been carried out using the static method. The difference between the results of these experiments and those of the kinetic method supplement the conclusions arrived at above. The main variables studied are the sol concentration C~ol and the flocculation time t2. The following trends have been observed (1) At given c~ and C~ob the flocculation effÉciency increases with increasing flocculation time t2. (2) At given c, and 12, the flocculation becomes much more efficient with increasing
This last point can be worked out further. If the considerations given above are correct, it must be possible to adjust 12 to c~ot in such a way that the flocculation efficiency and q Csol. become independent of Csol. This adjustment (3) At given t2, the critical salt concencan be brought about since we know that the tration c½ decreases strongly with increasing flocculation is bimolecular. According to biC~ol. Some typical values due to this effect are molecular kinetic theory (13, 15), the number given in Table I in the columns labeled of j-fold aggregates after a flocculation time t2 = 1 hr. 12 is a function of t~/t~ only, where t,~ is the time The fact that c½ depends so strongly on C~oz during which the number of particles is just is a consequence of our way of measuring in halved, t½ can be shown to be inversely proTABLE I Critical Salt Concentrations c½(mM) at Different Sol Concentrations (mM) and Varying Flocculation Time t~; pl = 2.5 mg PVA/mmole AgI; 4,1 = 0.5° KNOa c~,,l
0.2 0.5 1
3
Ca (NOa) ~
q
La (NOs) 3
q
q
(t2 = 1 hr)
(t.., = 3/c~,,1 hr)
(t~ = 1 hr)
(t~ = 3/C~o~ hr)
(12 = 1 hr)
(12 = 3/c~,,i lit')
10.0 6.3 5.0 3.5
4.0 4.1 3.9 3.5
1.05 0.70
0.42 0.40
0.092 0.060
0.040 0.042
0.37
0.37
0.037
0.037
- The contact time It between the polymer and the first portion of sol was 1 day. Journal of Colloid and Interface Science, V o l . 55, N o . 1, A p r i l 1976
POLYMER ADSORPTION
237
portional to c~o~.We recall that our criterion in the static method for the extent of flocculation is the relative absorbance Are1 (with respect to the original sol) of the supernatant after mild centrifugation. This absorbance is a function of the numbers of 1 to j~r-fold particles in the supernatant, where fir is the highest j value of aggregates remaining in the supernatant, j ~ is determined by the time and rate of centrifugation. It follows that for fast flocculation the value of A r~l should depend solely on t2/t~. If a certain repulsion exists between the particles, the flocculation rate is retarded by a factor W, the stability ratio (14, 15). W depends inter alia on the electrolyte concentration and valency, and for polymer flocculation also on the polymer contribution to the interaction free energy. The quantity t½ has now to be replaced by Wt~. Ar~ is now determined completely by t2/Wt½ or by t2C~ol/W. At a constant value of W (i.e., at constant electrolyte concentration and polymer conformation on the surface) Ar~l should therefore be independent of C~ol provided t2c~ol is constant. Conversely, the stability ratio W and thus the critical salt concentration c½ (measured at Arol = 0.5) should be independent of c~ol if t2 is chosen inversely proportional to Csol. The validity of this conclusion is demonstrated in the data of Table I. Indeed the values of q, greatly different at a constant flocculation time t2, become approximately constant if t2 is adjusted so as to make t2c~ot constant (see the columns with t2 = 3/C~o~). I t confirms that the dependence of c~ on the sol concentration has a kinetic origin.
protected by polymer and no free surface sites are available any more, so that bridging is effectively impeded. I t follows that the time scale of the attainment of an adsorbed polymer layer, capable of effective protection is also of the order of a few tens of seconds. In experiments using the two-portion method of mixing, the flocculation is much more effective. The rate of fast flocculation is about half of the rate of fast coagulation, because only half of the particle collisions can lead to aggregation. The flocculation follows bimolecular kinetics, both with respect to the effect of the total sol concentration, and to the ratio of covered and uncovered sol particles. In the two-portion method, a low but nonzero concentration of electrolyte is still needed to produce flocculation. The critical flocculation concentration, as measured by the kinetic method, is independent of the sol concentration, and much lower than the critical coagulation concentration. The critical salt concentration, as measured by a static method could be made independent of the sol concentration by adapting the flocculation time inversely proportional to the sol concentration to attain a constant total number of collisions over a preset period. The main point we wish to make is that this kinetic study underlines the importance of the mixing procedure of sol and polymer. I t may be expected that this procedure deserves attention in any system where the time scales of polymer adsorption and rate of aggregation are of comparable order of magnitude.
CONCLUSIONS
The authors thank Miss G. A. M. Swinkels for carrying out the stopped flow measurements.
This study shows that the way of mixing is an important parameter in flocculation of hydrophobic sols by polymers. With the (usual) one-portion method of mixing, the rate of flocculation was shown to be very low, even in the very first seconds. After some tens of seconds the flocculation process stops completely. By that time all the sol particles are
ACKNOWLEDGMENTS
REFERENCFS 1. LAMER,V. K. ANDHEALY,T. W., Rev. Pure Appl. Chem. 13, 112 (1963). 2. KITCH~:NER,J. A., Brit. Polym. J. 4, 217 (1972). 3. VI~CCE~T,B., Ad~,an. Colloid Interface Scl. 4, 193 (1974). 4. MEIER, D. J., J. Phys. Chem. 71, 1861 (1967). dcurnel of Colloid and Interface Science, Vol. 55, No. 1, April 1976
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FLEER AND LYKLEMA
5. HESSEL1NK, F. TH., VRII, A., AND OVERBEEK, J. TH. G., J. Phys. Chem. 75, 2094 (1971). 6. LYKLEMA,J. AND OVERBEEK, J. TH. G., J. Colloid Sci. 16, 595 (1961) ; LYKLEMA,J., Trans. Faraday Soc. 59, 418 (1963). 7. BIJSTERBOSCH,B. H. AND LYKLEMA,J., f . Colloid Interface Sci. 20, 665 (1965). 8. VINCENT,g., BIJSTERBOSCH,B. H., AND LYKLEMA, J., J. Colloid Interface Sci. 37, 171 (1971). 9. DE WIT, J. N. AND LYKLEMA, J., d. Electroanal. Chem. 41,259 (1973). 10. KOOPAL,L. K. AND LYKLEMA,J., Faraday Discuss. Chem. Soc. 59, 230 (1975). 11. FLEER, G. J., KOOPAL, L. K., AND LYKLEMA, J., Kolloid Z. Z. Polym. 250, 689 (1972). 12. FLEER, G. J. AND LYKLEMA,J., J. Colloid Interface Sci. 46, 1 (1974). 13. VON SMOLUCHOWSKI,M., Physik. Z. II, 557, 585 (1916); Z. Physik. Chem. 92, 129 (1917). 14. Fucas, N., Z. Physik, 89, 736 (I934). 15. OVEaBEEI~,J. TH. G., in "Colloid Science," (H. R. Kruyt, Ed.), Vol. 1, Chap. VII, VIII. Elsevier, Amsterdam (1952). 16. WILLIAMS,D. J. A. AND OTTEWILL,R. H., Kolloid Z. Z. Polym. 243, 141 (1971).
Journal of Colloid and Interface Science, Vol. 55, No. 1. April 1976
17. GREGORY,J., J. Colloid Interface Scl. 42, 448 (1973). 18. OTTEW1LL,R. H., RASTOGI,M. C., ANDWATANABE, A., Trans. Faraday Soc. 56, 866 (1960). 19. FLEER, G. J. AND LYKLEMA,J., J. Colloid Interface S c i . 29, 171 (1969). 20. FLEER, G. J., Thesis, Agricultural Univ. Wageningen, 1971; Meded. Landbouwhogesch. Wageningen 71-20 (1971) ; available on request. 21. REERINK, H. AND OVERBEEK, J. TH. G., Discuss. Faraday Soc. 18, 74 (1954). 22. LIvs, A., S~ART, C., AND WILLJS, E., Trans. Faraday Soc. 67, 2979 (1971). 23. SPIELMAN,L. A., J. Colloid Interface Sci. 33, 562 (1970). 24. HoNm, E. P., ROEBERSEN, G. J., AND WIERSEMA, P. H., J. Colloid Interface Sci. 36, 97 (1971). 25. OVERBEEK, J. Tm G., in "Colloid Science," (H. R. Kruyt, Ed.), Vol. 1, Chap. VIII. Elsevier, Amsterdam (1952). 26. KRUYT,H. R. AND TROELSTRA,S. A., Kolloidchem. Beihefte 54, 225 (1943). 27. LICHTENBELT,J. W. TH., PATnMAMANOHARAN,C., AND WIERSEMA, P. H., Y. Colloid Interface Sci. 49, 281 (1974). 28. FLEER, G. J., to appear.
Received June 3, 1975; accepted November 5, 1975 In a previous study on the flocculation of silver iodide sols by polyvinyl alcohol (PVA) it was demonstrated that the extent of flocculation depends critically on the way in which sol particles and polymer are mixed. Optimal flocculation was shown to occur if a two-portion method of mixing is applied in which equal numbers of polymer-covered and uncovered particles are brought together. The observations could be fully explained by a bridging model of flocculation. In this study the kinetics of the flocculation process has been investigated with a stopped flow spectrophotometer. The coagulation of AgI-sols by low molecular weight electrolytes was found to be a bimolecular process. Critical coagulation concentrations were found that matched closely those reported in the literature. The floccMation of sol by polymer brought about by mixing of polymer-covered and uncovered particles, follows also bimolecular kinetics. In this case only 50% of the collisionsleads to aggregation and the fast flocculation rate is just half the rate of fast coagulation. In accordance with previous results, the critical floccu]ation concentration of electrolytes with univalent and bivalent counterions was shown to be much lower than the corresponding critical coagulation concentration. Comparison of the kinetics of our two-portion method with the one-portion method (in which the total amount of polymer is added to the total amount of sol) leads to the conclusion that absorbing PVA molecules need a few seconds to form a layer that can effectivelyprotect the sol particles. Thus, the rate of flocculation can provide information on the rate of adsorption. This study underlines again that the way of mixing is a very important parameter in the flocculation of hydrophobic sols by polymers. INTRODUCTION The stability of hydrophobic colloids in the presence of polymers is of wide-spread importance in a variety of applications. I n addition, polymer stabilization and flocculation~ are quite interesting from a theoretical point of view. I n recent years considerable progress has been made towards a qualitative understanding of the processes involved (2, 3). xPresented at the 49th National Colloid Symposium, Potsdam, New York, June 16-18, 1975. Following La Mer's original proposal (1), we distinguish in this paper between flocculation (aggregation of colloidal particles by polymers) and coagulation (aggregation by low molecular weight electrolytes).
While q u a n t i t a t i v e descriptions of stabilization by polymers have recently been developed (4, 5), a q u a n t i t a t i v e t r e a t m e n t of flocculation b y polymers has hardly initiated as yet. To obtain a better insight in the interaction of polymers with colloids, and to provide data that are amenable to quantitative analysis, the present s t u d y has been undertaken. As a model the silver iodide sol-polyvinyl alcohol (PVA) system has been used. The double layer characteristics of AgI have been studied extensively (6), also in the presence of low molecular weight alcohols (7-9) and polymers (10). Using this information in combination with data from adsorption isotherms, elec-
228
Journal of Colloid and InlerJace Science, Vol.55, No. 1, April 1976
Copyright ~) 1976by AcademicPress. Inc. All rights of reproductionin any form reserved.
POLYMER ADSORPTION trophoresis, and viscosity measurements of AgI in the presence of adsorbed PVA, we were able to establish the effective thickness of the adsorbed layers and the distribution of segments over trains and loops. This is described in part I of this series (11) and in (10). In part II (12), the flocculation of AgI by PVA has been studied. It was demonstrated that the order of mixing of sol and polymer is a critical feature, and that the most efficient flocculation is obtained if equal amounts of nearly completely polymer-covered particles and uncovered particles are mixed. The results could be explained quite convincingly in terms of bridging of different particles through polymer loops and/or tails. The key feature of the mixing procedure is that it requires the simultaneous occurrence of long protruding loops, capable of bridging the gap between two particles, and free surface at which those loops can attach. The extent of flocculation attained by this mixing method and the optimal polymer dosage are closely related to the characteristics of the polymer adsorption process. Especially the high affinity character of the adsorption isotherms and the apparent irreversibility of adsorption are important features. These previous flocculation experiments (12) have been carried out in test tubes with flocculation times of the order of hours. For the sake of argument we denote this procedure as the static method. However, for a better understanding of colloid stability, measurements in the very first seconds after mixing are indispensable because these results are more suitable to interpretation in terms of particle-particle interactions than those obtained by a static method (13-15). For this reason we undertook the present study, dealing with flocculation by polymers under very rapid mixing conditions, further denoted as the kinetic method. Hitherto, only a few kinetic studies on flocculation have been reported in the literature (16, 17). It is generally accepted [e.g., (15)~ that the coagulation of colloidal systems by electrolytes is a bimolecular process. Hence, as the
229
first purpose of this study we investigated whether this conclusion would apply also for flocculation. In addition, one of the important results of this kinetic study turned out to be that vaIuable information regarding the rates of polymer adsorption and reconformation during the very first seconds can be obtained from the initial flocculation rate. This type of information is not easily accessible by other means. Two types of measurement have been used in this work.
(1) Stopped Flow Measuremenls In this technique, which was used earlier for the study of the coagulation rate of colloidal systems (18, 19), the absorbance of the flocculating system is recorded in the very first seconds (or fractions of a second) after fast, reproducible mixing. As a first step, rates of coagulation by salts have been measured as a basis for comparison with the flocculation rates. Next, measurements of flocculation rates were carried out. From these it followed that also with this kinetic method the flocculation efficiency, using a two-portion method of mixing, is much greater than with a oneportion method (in which all the polymer is mixed at once with all the sol). Then it was demonstrated that flocculation is indeed a bimolecular process, both with respect to the sol concentration C~oland to the ratio between covered and uncovered particles. The critical flocculation concentration (CFC) of salts, needed to obtain fast flocculation, was found to be independent of c~ol.
(2) Static Measurements Using the static method, it was found that, at constant flocculation time, the critical salt concentration (c½, see below) depends on C~ol. Making use of the bimolecular nature of the flocculation, it was possible to vary the flocculation time in such a way as to lead to a constant total number of particle collisions at varying C~ol. The results indicated that under Journal of Colloid and Interface Science, Vol. 5S, No. 1, April 1976
230
FLEER AND LYKLEMA
these conditions of Csol.
c½ becomes
independent
EXPERIMENTAL
Materials The AgI sols used have been described before (11, 20). The sol particles were negatively charged (pI ~ 5), the average particle radius was 50 nm. The polymer used was PVA 13-98.5, with a viscosity averaged molecular weight of 56 000 and containing about 1.5% of unhydrolyzed acetate groups in the molecule.
Stopped Flow Apparatus A Durrum stopped flow spectrophotometer with a 2-cm path length cell was used in the measurements. In this apparatus the solutions to be mixed are contained in two syringes. By a pressure operated actuator, equal volumes (~0.2 ml) are reproducibly mixed within a very short time (~10 msec for dilute aqueous solutions). The transmittance of the mixture can be recorded on a storage oscilloscope, or (as in our case) on an attached recorder. The percentage transmittance T, was transformed into the absorbance A using A --- 2 - a°log T. The wavelength in these experiments was 650 nm; at this wavelength only scattering occurs (12, 20).
Methods 1. Kinetic method. In the coagulation experiments, one of the syringes of the stopped flow apparatus contained the sol, the other the salt solution. In the flocculation experiments using the one-portion method, the sol was mixed with a solution of PVA and electrolyte of the desired composition. In flocculation experiments with the two-portion method, one syringe was filled with untreated AgI sol, the other with polymer-covered AgI particles in a dilute salt solution. The latter solution was prepared by adding the PVA to the sol (using a buffering water layer between sol and polymer (12)) 1 day before the experiment, whereas the salt was added immediately prior to the kinetic measurements. Journal of Colloid and Interface Science, Vol. 55, No. l, April 1976
In most of the two-portion experiments, the sol concentrations in both syringes were identical, hence ¢1 = 0.5, ¢1 being the fraction of uncovered particles. The only exception to this occurred in the measurement of the flocculation rate as a function of ¢2. 2. Static method. This method has been described extensively in part II. The twoportion method was used in which, after a contact time tl between the polymer and the colloidal particles, the (covered) half of the sol particles was added to the other (untreated) half. The absorbance at 430 nm of the supernatant (obtained by mild centrifuging) was taken as a measure of the extent of flocculation. The allowed flocculation time t2 was of the order of hours. The critical salt concentration c½ was defined as that salt concentration at which, after a given flocculation time, the absorbance of the supernatant was reduced to half of its original value (Arol = 0.5). RESULTS
AND DISCUSSION
Coagulalion by Salts Figure 1 shows some typical results of the coagulation of AgI sols by KNO3. In this figure &A is the increase of the absorbance per centimeter path length due to the coagulation. The salt concentrations indicated in this figure are the final concentrations after mixing. The absorbance increases continuously as a function of time, but already in the first few seconds a slight deviation from the theoretical (15, 21) straight line occurs. The deviation probably can be accounted for by the nonvalidity of the assumption that the scattering of an aggregate is the same as that of a spherical particle with the same total weight. Treatments are available to eliminate this assumption (22), but for the present purpose it suffices to consider only relative values of the initial slopes of the 2~A - - t curves. For the same reason we do not have to take into account possible hydrodynamic effects (23, 24). With increasing salt concentration, the initial slope increases until finally a concentration region is attained where the coagulation rate
231
POLYMER ADSORPTION 10"&A I(3
cm '
CSO =L
tm[~
/
210rnN
~1813
/J
8
2portions m PVA Pl = 2 5 ~ AgI ~ ~
I
2
3
~
5
3 0 r a n KN03
5
Fro. i. The increase of the absorbance of AgI-so]s with time due to coagulation by KNOa. 2M is the increase in absorbance per centimeter path length. The abscissa scale is in seconds. Sol concentration I raM, The final KNO~ concentration is indicated• The dashed curve is an example of a fast flocculation experiment with the two-portion method (4,~=0.5; p~=2.5 m g PVA 13-98.5/mmole AgI; Cl~NO3 = 30 raM).
becomes independent of the salt concentration. This is the region of fast coagulation, beyond the critical coagulation concentration (CCC). The CCC is most easily determined (15, 21) by plotting the logarithm of the reciprocal slope (log dt/dA) against log c,, where c, is the salt concentration. This has been done in Fig. 2. The dashed curve in Fig. 1 reflects the fast flocculation rate using the two-portion method of mixing. In anticipation of the discussion to be presented below, we note that the rate of fast coagulation is about twice the rate of fast flocculation. Figure 2 shows log dt/dA versus log c, plots for three sol concentrations and three salts with counterion valencies z = 1, 2 and 3. The quantity dt/dA is proportional to the stability ratio W (14, 15). All graphs consist essentially of two intersecting straight lines as is usually observed (15, 21). The intersection points are identified as the CCC values. We found 174, 4.0, and 0.11 mM for KNO3, Ca(NO3)2, and La(NQ)3, respectively. These
values are higher than those reported for classical test tube experiments (25). This should be expected since in our experiments the coagulation times are only of the order of seconds and orthokinetic coagulation is absent. In the scope of the present article we do not need to discuss the slopes of the descending branches of the plots. At a given c~ol, the fast coagulation rate is roughly, but not completely, independent of the counterion valency (Fig. 2). The slightly lower coagulation rate at higher z could possibly be accounted for by a different distribution of charge in the Stern layer, as first suggested by Kruyt and Troelstra (26). Again this point, although interesting, is not very pertinent for the present article. Fast coagulation being a bimolecular process, its rate should be proportional to the square of the sol concentration. It follows from the levels of the horizontal branches in Fig. 2 that the measured coagulation rates at high c~,,1are slightly too low in comparison to those at low c~,,~. We found similar differences before (19). This behavior is possibly due to an experimental artifact of the used stopped flow spectrophotometer. Because of too wide an angle of acceptance of the photomultiplier, the unmodified instrument that Ct/dA La{N031:i
~Ca(N01) 2
,•
o
i ' 011raM -~
. . . .
T
i -3
L0rnM
i -2
N°3 • ~ s0L C2mmote/t A t , .. 05 I0
.,
\%-
% , ~27--, -1 tog %'M/
0
Fla. 2. Coagulation kinetics. T h e dependence of (dt/dA)t...o on the electrolyte concentration for three
salts and three sol concentrations. T h e breaks (indicated by arrows) give the critical coagulation concentrations. Journal of Colloid and Interface Science, Vol. 55, No. 1, April 1976
232
FLEER AND LYKLEMA
we used records also part of the secondarily scattered light, giving rise to too low an absorbance (and thus, dA/dt) especially at higher sol concentrations. Indeed it was found by Lichtenbelt et al. (27) using the same instrument that narrowing the angle of acceptance solves the problem, at least for polystyrene latices. Allowing for this instrumental artifact, the results indicated in Fig. 2 may be interpreted as being within experimental error in agreement with the bimolecular nature of the coagulation process.
Flocculation, One-Portion Method In the one-portion method, a solution of PVA containing a low concentration of electrolyte is mixed with silver iodide sol. Some of the results are shown in Fig. 3 as absorbance against time curves. These experiments have been done in 30 mM KNOa. Higher salt concentrations do not alter the flocculation rate, so that these results refer to fast flocculation with respect to the salt concentration. Note the different abscissa scale of Fig. 3 as compared to that of Fig. 1. The curve for the two-
102&A f
cm~l | 2port=ons
t l ~ =25mgPVA/mm'teAgl ~
2
~
p = 50 rngPVA mmoteAgI
125
]
1I
20
t
Fla. 3. T h e increase of the absorbance of AgI-sols with time due to flocculation by PVA. One-portion method. T h e polymer dosage p is indicated, c~ol = 1 raM; CKNOa = 30 m M . T h e dashed curve is the same as that in Fig. 1. dournal of Colloid and Interface Science, Vol. 55, No. I, April 1976
1
JdA
l& - cm-ls 1
//
,2
'
o
5
O8
0 ~,
1
2
3 mgPVA/mmoLe Agl
FIG. 4. Flocculation rate after different time intervals as a function of polymer dosage. One-portion method. T h e flocculation time is indicated. Conditions as in Fig. 3.
portion method in Fig. 3 is the same as that in Fig. 1. It follows from Fig. 3 that a small degree of flocculation occurs with the one-portion method, at least initially. With increasing polymer dosage p (expressed in mg PVA added per mmole of AgI) the initial slope increases until a maximum rate is reached of about 1.3 X 10-* cm-1 sec-I. From the data of Fig. 1, a maximum rate of initial coagulation at the same C~otof about 25 X 10-3 cm -I sec-1 can be deduced. Thus, if any initial flocculation occurs with the one-portion method, it is very slow. There is another remarkable difference with the curves of Fig. 1. Although for polymer dosages p > 1.5 mg/mmole the initial slopes remain constant, the corresponding slopes after some time (>5-10 sec) decrease with increasing p, and eventually become zero. This decrease of the flocculation rate with time in the one-portion method is more dearly expressed in Fig. 4, where the slopes of the curves of Fig. 3 at fixed times are plotted as a function of the polymer dosage. Except for the very beginning of the flocculation process, the flocculation rate passes through a maximum around p = 1.5 mg/mmole, dropping to zero for sufficiently high dosage. This last mentioned fact is in agreement with the results obtained with the static
233
POLYMER ADSORPTION
method (part II). In the latter case, with flocculation times of the order of hours, no flocculation at all could be detected with the one-portion method (4~, = 0, or qh = 1). Apparently, the slight initial flocculation occurring in the very first seconds after mixing cannot be detected with the static method, because the aggregates formed are not separated by centrifuging. An explanation of this slight initial flocculation can be offered in terms of the bridging mechanism given before (part II). Two ilnportant prerequisites for the occurring of flocculation are (i) the presence of long loops and/or tails, extruding from one particle, and (ii) the availability of free surface on other particles onto which these loops and trains can attach themselves. Obviously, only in the very first seconds free surface sites are available for bridging. The extent of bridging is a maximum if p -- 1.5 mg/mmole. This is about half the maximum adsorption (11, 12). The occurrence of a flocculation optimum at half coverage has been proposed by La Mer (1). After longer times, especially at high p, polymer molecules are adsorbed on all particles to such an extent that no available surface sites are left. Moreover, protection due to extended polymer layers on all the particles then starts to develop itself. Thus, this inference of the rate of polymer adsorption may be drawn from these flocculation experiments: Within a few seconds most of the polymer molecules are attached to the surface, most of the available surface is then occupied and the adsorbed layer is capable of effective protection. This does of course not imply, that no further rearrangements could take place, nor that the adsorbed amount and layer thickness could not further increase with time.
Flocculalion, Two-Portion Method In the two-portion method covered sol particles are mixed with uncovered ones. An example of a case of fast flocculation is given by the dashed curve in Fig. 1; the same curve appears also in Fig. 3. Note that in this case
the polymer dosage is expressed as pl, the amount of PVA added per mmole of the first portion of sol, whereas the dosage p in the oneportion method is expressed per lotal amount of AgI. Thus the curves for pz = 2.5 rag/ mmole (one-portion) and for p = 1.25 mg/ mmole (two-portion) refer to the same final composition of the mixture. It is useful to compare the rates of fast flocculation (i.e., in the region where further addition of salt does not increase the rate) using either way of mixing with each other and with the fast coagulation rate. It follows then that the rate of fast flocculation by the twoportion method is lower by about a factor of two than the rate of fast coagulation, whereas the rate of fast flocculation by the one-portion method is very much lower. Figure 5 shows log dt/dA against log c., plots for the two-portion method of mixing. Figure 5 strongly resembles Fig. 2 for the coagulation. The slopes of the lines below the CFC seem to be lower than those in the case of coagulation. That the slopes should be different is quite conceivable, because the interaction energy between an uncovered
~L I
L~(NO,5,
,~
I
,,
"CalNO~],
•
,~
\~i
i
\
c;,, G;mrTol%Zl .,
O,
,.
'° KNO I
I 5
T
t
Ol~,n~ ~
T
16ram -
3
IS.,M 12
-1
-Log % / ~
3
FIG. 5. Flocculation kinetics, two-portion method. The dependence of (dt/dA)e~o on the electrolyte concentration. The sol concentration is indicated. The polymer dosage Pl equals 2.5 mg PVA per mmole AgI of the first portion. The number of covered particles is equal to that of uncovered ones (4L = 0.5). The intersection points of the straight lines (indicated by the arrows) are taken as the critical flocculation
concentrations. Journal of Colloid and Interface Science, Vol. 55, No. 1, April 1976
234
FLEER AND LYKLEMA
and a polymer covered particle contains, in addition to the classical electrostatic repulsion and the Van der Waals attraction, also a contribution due to the polymer bridging. As yet the effect of this polymer contribution on the stability ratio is largely unknown. In a next contribution (28) in this series we intend to investigate in some detail the interaction energy between uncovered and polymercovered particles. It can be deduced from Fig. 5 that the rate of fast flocculation is nearly proportional to the square of the sol concentration, as was the case for the coagulation. The observed slight deviation from this proportionality can again be ascribed to the same instrumental artifact, discussed above. Thus, also for the two-portion method the flocculation process is bimolecular within experimental error. At constant C~ob the fast flocculation levels in Fig. 5 are about 0.3 units higher than the corresponding ones in Fig. 2. Thus, the rate of fast flocculation is lower than the fast coagulation rate by about a factor of two. The reason is that with the two-portion method only half of the possible particle encounters can lead to aggregation: Collisions between two covered particles (due to protective action) and between two uncovered particles (due to electrostatic repulsion) are not effective for flocculation. Another way of demonstrating this is as follows. In a bimolecular coagulation process, the initial rate of fast coagulation is given by (13, 15). - d u / d t = K v 2,
[1]
where v is the initial number of particles and K is the rate constant. If we have vu uncovered and vc covered particles (with v = vu + vc), the flocculation rate can be written as:
-
-
dv -- = dt
dvu
d~,c
dt
dt
- Kuuvu 2 + Kucvcv~ + K~vo ~ + Kc,v~vu.
[2"]
If the numbers of uncovered and covered particles are equal, v, = v~ -- ½v. As only collisions between dissimilar particles are effective, Journal of Colloid and Inlerface Science, Vol. 55, No. 1, April 1976
Kuu = Kcc = 0 and K~c = K,u = K , so that the fast flocculation rate becomes
-d~/dt = ~K~,
E3~
which is half of the fast coagulation rate. In using Kuc = K, it is assumed that a possible change in the collision diameter of a covered particle is exactly counterbalanced by the change in the diffusion constant, K being proportional to the product of the diffusion constant and collision diameter. In a preliminary report (20), this factor of a half was not found. This conclusion was based on too small a number of measurements and is herewith corrected. From Fig. 5, it follows that the critical flocculation concentrations (CFC's) for KNO3, Ca(NO3)2, and La(NO,)3 are 18, 1.6, and 0.11 mM, respectively. The CFC's are independent of C~ol and higher than those found with the static method (see (12), and Fig. 8 and Table I, below). This is to be expected because the time scale is much shorter with the kinetic method. As mentioned above, similar differences are usually found with coagulation experiments. The CFC's are, at least for KNO3 and Ca(NO3)2, much lower than the corresponding CCC's, indicating that the polymer definitely causes an attractive interaction between two particles. The behavior of La(NO3)3 is an exception, in that the CFC approximately equals the CCC. Nevertheless, it is not allowed to look upon the flocculation in the presence of La(NO3)3 as a coagulation mechanism, the flocculation rate is definitely lower than the coagulation rate. If in this case simultaneous coagulation of uncovered particles would occur due to the high valence of the counterion, Eq. [21 would predict a rate which is ¼ of that of fast coagulation. However, the experimental results point out that also with La(NOa)a the factor ½ (or even slightly less) is found, so that this possibility may be ignored. We have no clear explanation to offer for the results with La(NO3)3. Perhaps they are partly due to the competitive adsorption of polymer train segments and (either or not
POLYMER ADSORPTION hydrolyzed, although hydrolysis is unlikely around p H - 6) La 3+ ions on the AgI surface. At any rate, the effect of the polymer seems to be much more pronounced with monovalent and bivalent counterions than with trivalent ones. In Fig. 6, examples are given of two-portion flocculation rates after fixed times as a function of p~. These results apply to C~o~= 0.2 m M and a KNO3 concentration of 15 mM. The dA/dt has been divided by C~o12to facilitate the comparison with the data of Fig. 4. The salt concentration is just below the CFC. The following is observed. The flocculation rate is maximal around pt = 3.0 mg/mmole, in close agreement with the optimal dosage of 2.5 mg/mmole as found with the static method (see (12, Figs. 7 and 9)). This very dosage provides the best compromise between the production of sufficiently long loops (required for bridging) and leaving only little polymer in the solution (which would decrease the number of available attachment sites on the surface of the originally bare particles). Comparing Figs. 4 and 6, it is concluded that at the optimal p~ the flocculation rate with the two-portion method is at least a factor 10 higher than with the one-portion method, already in the first seconds. After longer times this ratio increases strongly. At low dosage (to the left in Fig. 6) the flocculation rate increases with increasing pv The reason is the increasing layer thickness. A significant difference with the corresponding part of Fig. 4 is that in this region dA/dt falls off much slower with time than in the oneportion method. At polymer dosages beyond the maximum (to the right in Fig. 6) the flocculation rate decreases strongly with increasing time also with the two-portion method. We recall that, using the static method, no flocculation could be detected beyond pl -- 3.5 mg/mmole (see (12, Fig. 7)). This is because the excess polymer adsorbs onto the (originally) bare particles, decreasing the number of available surface sites for bridges to be formed. With the kinetic method (Fig. 6) a
235
~03,j,~ dt . CssF crn-I s ~ 12
o
~." of °-°-° ,~.J--.^
,
/
2
J
o
o
o 0s
2~
\\,.
/°
o
0
2
L
6 rng/mrnoi.e Pt
FIG. 6. Flocculation rate at different flocculation times as a function of the polymer dosage pt using the two-portion method, pl is expressed in mg PVA/mmole AgI of the first portion of sol. C,ol = 0.2 mM; cK~o~ = 15 mM. To facilitate comparison with Fig. 4, dA~dr has been divided by C~ol2. slight initial flocculation is found, which slows down very rapidly. Again it can be concluded that within about 20 sec the adsorption of polymer molecules on the second portion of sol particles has proceeded far enough to prevent further attachments and to induce protective action. In Fig. 7, results are shown for experiments with varying fractions of covered (4,1) and ~0 dA
30 - crC ~ gl
20
/ . /
~
/ o
e-
0
02
06
0g
¢~
I0
Fro. 7. Initial flocculation rate w i t h the two-portion
method of mixing as a function of 4~, the fraction of AgI-sol in the first portion, c~ol= 0.2 raM; C~NO~ = 15 raM; pl = 2.5 mg PVA/mmole AgI of the first portion of sol. Journal of Colloid and Interface Science, V o l . 55, N o . 1, A p r i l 1976
236
FLEER AND LYKLEMA
uncovered (i - ~bl) particles. In this case the total sol concentration is constant so that there are no complications in the measurement due to secondary scattering. In a bimolecular flocculation process, the rate must be proportional to 4~1 (1 -- 4~1). As shown in Fig. 7, the experimental points lie within experimental error on a parabola, corroborating the bimolecular nature of the flocculation in the two-portion method.
which q is determined in a situation where half of the material is flocculated (Arol = 0.5). I t is not difficult to forward a qualitative explanation for the observed trends. (1) Increasing the flocculation time at a given sol concentration results in more collisions, and thus, in a greater extent of flocculation. (2) If the concentration of the sol is increased, the number of Brownian encounters per second increases, leading to a higher proportion of focculated material in a given period. (3) Since we have identified c~ as the salt concentration required to obtain a given absorbance within a preset time, the decrease of c½ with increasing C,ol can be attributed to the fact that in the region of slow flocculation the effect of increased double layer repulsion is offset by that of an increased number of collisions per second.
Slatic Melhod A number of experiments has also been carried out using the static method. The difference between the results of these experiments and those of the kinetic method supplement the conclusions arrived at above. The main variables studied are the sol concentration C~ol and the flocculation time t2. The following trends have been observed (1) At given c~ and C~ob the flocculation effÉciency increases with increasing flocculation time t2. (2) At given c, and 12, the flocculation becomes much more efficient with increasing
This last point can be worked out further. If the considerations given above are correct, it must be possible to adjust 12 to c~ot in such a way that the flocculation efficiency and q Csol. become independent of Csol. This adjustment (3) At given t2, the critical salt concencan be brought about since we know that the tration c½ decreases strongly with increasing flocculation is bimolecular. According to biC~ol. Some typical values due to this effect are molecular kinetic theory (13, 15), the number given in Table I in the columns labeled of j-fold aggregates after a flocculation time t2 = 1 hr. 12 is a function of t~/t~ only, where t,~ is the time The fact that c½ depends so strongly on C~oz during which the number of particles is just is a consequence of our way of measuring in halved, t½ can be shown to be inversely proTABLE I Critical Salt Concentrations c½(mM) at Different Sol Concentrations (mM) and Varying Flocculation Time t~; pl = 2.5 mg PVA/mmole AgI; 4,1 = 0.5° KNOa c~,,l
0.2 0.5 1
3
Ca (NOa) ~
q
La (NOs) 3
q
q
(t2 = 1 hr)
(t.., = 3/c~,,1 hr)
(t~ = 1 hr)
(t~ = 3/C~o~ hr)
(12 = 1 hr)
(12 = 3/c~,,i lit')
10.0 6.3 5.0 3.5
4.0 4.1 3.9 3.5
1.05 0.70
0.42 0.40
0.092 0.060
0.040 0.042
0.37
0.37
0.037
0.037
- The contact time It between the polymer and the first portion of sol was 1 day. Journal of Colloid and Interface Science, V o l . 55, N o . 1, A p r i l 1976
POLYMER ADSORPTION
237
portional to c~o~.We recall that our criterion in the static method for the extent of flocculation is the relative absorbance Are1 (with respect to the original sol) of the supernatant after mild centrifugation. This absorbance is a function of the numbers of 1 to j~r-fold particles in the supernatant, where fir is the highest j value of aggregates remaining in the supernatant, j ~ is determined by the time and rate of centrifugation. It follows that for fast flocculation the value of A r~l should depend solely on t2/t~. If a certain repulsion exists between the particles, the flocculation rate is retarded by a factor W, the stability ratio (14, 15). W depends inter alia on the electrolyte concentration and valency, and for polymer flocculation also on the polymer contribution to the interaction free energy. The quantity t½ has now to be replaced by Wt~. Ar~ is now determined completely by t2/Wt½ or by t2C~ol/W. At a constant value of W (i.e., at constant electrolyte concentration and polymer conformation on the surface) Ar~l should therefore be independent of C~ol provided t2c~ol is constant. Conversely, the stability ratio W and thus the critical salt concentration c½ (measured at Arol = 0.5) should be independent of c~ol if t2 is chosen inversely proportional to Csol. The validity of this conclusion is demonstrated in the data of Table I. Indeed the values of q, greatly different at a constant flocculation time t2, become approximately constant if t2 is adjusted so as to make t2c~ot constant (see the columns with t2 = 3/C~o~). I t confirms that the dependence of c~ on the sol concentration has a kinetic origin.
protected by polymer and no free surface sites are available any more, so that bridging is effectively impeded. I t follows that the time scale of the attainment of an adsorbed polymer layer, capable of effective protection is also of the order of a few tens of seconds. In experiments using the two-portion method of mixing, the flocculation is much more effective. The rate of fast flocculation is about half of the rate of fast coagulation, because only half of the particle collisions can lead to aggregation. The flocculation follows bimolecular kinetics, both with respect to the effect of the total sol concentration, and to the ratio of covered and uncovered sol particles. In the two-portion method, a low but nonzero concentration of electrolyte is still needed to produce flocculation. The critical flocculation concentration, as measured by the kinetic method, is independent of the sol concentration, and much lower than the critical coagulation concentration. The critical salt concentration, as measured by a static method could be made independent of the sol concentration by adapting the flocculation time inversely proportional to the sol concentration to attain a constant total number of collisions over a preset period. The main point we wish to make is that this kinetic study underlines the importance of the mixing procedure of sol and polymer. I t may be expected that this procedure deserves attention in any system where the time scales of polymer adsorption and rate of aggregation are of comparable order of magnitude.
CONCLUSIONS
The authors thank Miss G. A. M. Swinkels for carrying out the stopped flow measurements.
This study shows that the way of mixing is an important parameter in flocculation of hydrophobic sols by polymers. With the (usual) one-portion method of mixing, the rate of flocculation was shown to be very low, even in the very first seconds. After some tens of seconds the flocculation process stops completely. By that time all the sol particles are
ACKNOWLEDGMENTS
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FLEER AND LYKLEMA
5. HESSEL1NK, F. TH., VRII, A., AND OVERBEEK, J. TH. G., J. Phys. Chem. 75, 2094 (1971). 6. LYKLEMA,J. AND OVERBEEK, J. TH. G., J. Colloid Sci. 16, 595 (1961) ; LYKLEMA,J., Trans. Faraday Soc. 59, 418 (1963). 7. BIJSTERBOSCH,B. H. AND LYKLEMA,J., f . Colloid Interface Sci. 20, 665 (1965). 8. VINCENT,g., BIJSTERBOSCH,B. H., AND LYKLEMA, J., J. Colloid Interface Sci. 37, 171 (1971). 9. DE WIT, J. N. AND LYKLEMA, J., d. Electroanal. Chem. 41,259 (1973). 10. KOOPAL,L. K. AND LYKLEMA,J., Faraday Discuss. Chem. Soc. 59, 230 (1975). 11. FLEER, G. J., KOOPAL, L. K., AND LYKLEMA, J., Kolloid Z. Z. Polym. 250, 689 (1972). 12. FLEER, G. J. AND LYKLEMA,J., J. Colloid Interface Sci. 46, 1 (1974). 13. VON SMOLUCHOWSKI,M., Physik. Z. II, 557, 585 (1916); Z. Physik. Chem. 92, 129 (1917). 14. Fucas, N., Z. Physik, 89, 736 (I934). 15. OVEaBEEI~,J. TH. G., in "Colloid Science," (H. R. Kruyt, Ed.), Vol. 1, Chap. VII, VIII. Elsevier, Amsterdam (1952). 16. WILLIAMS,D. J. A. AND OTTEWILL,R. H., Kolloid Z. Z. Polym. 243, 141 (1971).
Journal of Colloid and Interface Science, Vol. 55, No. 1. April 1976
17. GREGORY,J., J. Colloid Interface Scl. 42, 448 (1973). 18. OTTEW1LL,R. H., RASTOGI,M. C., ANDWATANABE, A., Trans. Faraday Soc. 56, 866 (1960). 19. FLEER, G. J. AND LYKLEMA,J., J. Colloid Interface S c i . 29, 171 (1969). 20. FLEER, G. J., Thesis, Agricultural Univ. Wageningen, 1971; Meded. Landbouwhogesch. Wageningen 71-20 (1971) ; available on request. 21. REERINK, H. AND OVERBEEK, J. TH. G., Discuss. Faraday Soc. 18, 74 (1954). 22. LIvs, A., S~ART, C., AND WILLJS, E., Trans. Faraday Soc. 67, 2979 (1971). 23. SPIELMAN,L. A., J. Colloid Interface Sci. 33, 562 (1970). 24. HoNm, E. P., ROEBERSEN, G. J., AND WIERSEMA, P. H., J. Colloid Interface Sci. 36, 97 (1971). 25. OVERBEEK, J. Tm G., in "Colloid Science," (H. R. Kruyt, Ed.), Vol. 1, Chap. VIII. Elsevier, Amsterdam (1952). 26. KRUYT,H. R. AND TROELSTRA,S. A., Kolloidchem. Beihefte 54, 225 (1943). 27. LICHTENBELT,J. W. TH., PATnMAMANOHARAN,C., AND WIERSEMA, P. H., Y. Colloid Interface Sci. 49, 281 (1974). 28. FLEER, G. J., to appear.