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Dynamics of initial stage flocculation of polystyrene latex spheres with polyelectrolytes
COLLOIDS
AND Colloids and Surfaces
ELSEVIER
A
SURFACES
A: Physicochemical and Engineering Aspects 113 (1996) 229-236
Dynamics of initial stage flocculation of polystyrene latex spheres with polyelectrolytes Y. Adachi *, T. Matsumoto Institute of Agricultural and Forest Engineering, Tsukuba University, Tsukuba City, Ibaraki 305, Japan Received 12 October 1995; accepted 23 March 1996
Abstract
An end-over-end rotation apparatus was created in order to obtain reproducible mixing suitable for the study of the kinetics of flocculation. The validity was verified by measuring the rate of coagulation of monodispersed polystyrene latex particles with simple electrolytes by means of a Coulter Counter. The method was applied to the analysis of the initial behavior of flocculation induced by the addition of excess polyelectrolyte flocculant with a nominal molecular weight of 4.5 million. In contrast to coagulation with a simple electrolyte, the rate of flocculation in the initial stage was remarkably enhanced and then decreased abruptly after certain mixing steps. The degree of the initial stage of enhancement and the duration of this stage were found to be dependent on the concentration of the polyelectrolyte. Ascribing the enhancement to the increase in the effective collision radius of the colloidal particles due to the attached polymer layer, the thickness of this layer, ~ne, was calculated. Analyses showed that ~He increases as polymer concentration increases up to a layer thickness of 500 nm, which correlates with the size of the polymer in the solution. However, an analysis of the collision process between particles and polyelectrolytes implied that the kinetics of polymer adsorption in the initial stage are limited by transportation until near saturation. Taking into account the data on electrophoretic mobility, we concluded that our results are consistent with the picture of kinetically-controlled polymer adsorption proposed by De Witt and van de Ven [J.A. De Witt and T.G.M. van de Ven, Langmuir, 8 (1992) 788].
Keywords: Flocculation; Initial stage; Kinetics; Polyelectrolyte; Polystyrene latex
1. Introduction
It is well known that colloidal dispersions can be brought to flocculation by the addition of small amounts of adsorbing polymer. The mechanism of this destabilization is recognized as the formation of macromolecular bridges between the colloidal particles. It is necessary to study the behavior of adsorbed polymers on a single surface as well as that between two surfaces for a better understanding of this process, and many years of study have been devoted to this point. On the theoretical * Corresponding author. 0927-7757/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved PII S0927-7757 (96) 03649-0
side, the classical statistical thermodynamic theory of polymer solutions [1] has been extended to a description of the behavior of polymer chains located in the vicinity of the surface. There are two main groups of theories: the application of the scaling concept [ 2] and a more detailed calculation based on the mean field approximation [3]. The prediction of polymer conformations at various interfaces under various conditions is now possible because of these works. Applications of small angle neutron scattering [4], N M R [ 5 ] and surface force apparatus [6] have been reported to confirm the theoretical predictions. As a result, a great deal of knowledge concerning the equilibrium proper-
230
Y. Adachi, "12 Matsumoto / Colloids Surfaces A: Physicochem. Eng. Aspects 113 (1996) 229-236
ties of polymer chains at interfaces is now available [7]. Nevertheless, theory and experimentation on the basis of equilibrium thermodynamics is not sufficient to predict the behavior of flocculation. That is, in most practical cases, flocculation is also irreversibly controlled by kinetic factors. The importance of this aspect has already been recognized in the pioneering work of Ruehrwein and Ward [8] and has been underlined by many experimentalists E9-13]. Because the formation of a bridge, in addition to polymer adsorption, is usually performed under mixing conditions which are difficult to specify clearly, it seemed impossible to quantify elementary processes such as the rate of collision between colloidal particles, the rate of collision of polymer molecules onto the colloidal surface and the rate of reconformation of polymer on the surface. However, recent experimental efforts have gradually elucidated the kinetic aspects involved in polymer adsorption and flocculation. By applying the technique of reflectometry under a well-defined hydrodynamic condition, Dijt et al. [14] found that the adsorption of PEO from aqueous phase to silica surface is limited by mass transfer up to about 75% of the maximum adsorption. In a subsequent study, they reported that the desorption of polymer is limited by mass transfer El5]. These are examples of a short term behavior referred to as a local equilibrium condition which appears in the absence of an energy barrier. However, long term behavior, sometimes referred to as surface process, is also involved in the kinetics. Examples can be found in the exchange of adsorbing polymer El6], the temporal change of the adsorbing conformation of polyelectrolytes observed with evansescent wave spectroscopy [ 17,18] and crossover of flocculation from RLA (reaction-limited aggregation) to DLA (diffusion-limited aggregation) as the incubation time of colloidal dispersion in the polymer solution elapses [19]. In a novel experiment, Quali and Pefferkorn 1-20] showed that polymer-bridges flocs will continue to fragment spontaneously for more than several days. These results mean that there are cases in which quite a long time is necessary to reach the state of complete equilibrium after the attainment of an initial metastable condition. Their results are consistent with the results of a kinetic
experiment on polymer adsorption reported by De Witt and van de Ven [-21] which showed that the adsorbed amount, as well as the thickness of the adsorbing layer, increases with an increase in the concentration of added polymer. These results are interpreted in terms of competition between the collision of polymers with the bare surface and the reconformation of adsorbing polymers on the surface. In other words, with low concentrations, slow adsorption leads to a low surface coverage of flattened molecules, while fast adsorption leads to a high surface coverage of unflattened molecules which does not relax into an equilibrium configuration over a short period. The same situation takes place in the initial stage of flocculation induced by the addition of excess polymer flocculant and should be crucial for the analysis of nonequilibrium aspects. In our pervious study [,22], we showed a way to characterize the mixing flow in terms of a collision process between colloidal particles. This method allows us to analyze a rate of ftocculation as short as 1 s from the start of mixing. We found a remarkable enhancement of the rate of flocculation induced immediately after the addition of adsorbing polymer [-23,24] with this technique. Ascribing this enhancement to an increase in the effective collision radius of colloidal particles due to the attached polymer layer, we found that the thickness of the layer correlates with the size of polymer molecules existing in the bulk solution. In the present study, we applied the same technique to probe the transient behaviour of polymer adsorption in the early stage of incubation. We constructed an end-over-end rotation apparatus to obtain consistently reproducible mixing. We monitored the initial behavior of flocculation induced by a highly charged polyelectrolyte by means of a Coulter Counter as a function of the rate of polymer supply to the colloidal surface in the standardized mixing system. The results obtained and the electrophoresis data were qualitatively consistent with the results of a kinetically-controlled adsorption experiment reported by De Witt and van de Ven. Our crude analysis indicates that the time scale of the reconformation of the polyelectrolyte on the bare surface is larger than that
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Y. Adachi, T. Matsumoto / Colloids Surfaces A: Physicochem. Eng. Aspects 113 (1996) 229~36
which is required for a polyelectrolyte to move by self-diffusion in the bulk solution.
2. The rate of collision in turbulent mixing Since the rate of collision between colloidal particles is a function of the mixing intensity, the flow condition of a certain mixing can be evaluated by the measurement of the rate of rapid coagulation, which is equivalent to the rate of collision in the absence of repulsive forces between colloidal particles [22]. In a system with a sufficiently high Peclet number where the contribution of Brownian coagulation can be regarded as negligibly small, the following equation for the temporal evolution of the number of colloidal particles per unit volume, N(t), can be derived assuming that the volume fraction of colloidal particles, ~b,is constant:
( N(t)'] = ~24e a,
(1)
where e, v, a T and t denote the rate of energy dissipation per unit mass, kinematic viscosity, capture efficiency of turbulent coagulation and elapsed time respectively. When colloid particles move with attached polymers, their collision radii are increased by the amount 6he. The collision between colloidal particles is enhanced if the surface of the particle is not fully covered with polymer molecules so that the stabilizing effect does not appear. If we assume that the permeable structure of the polymer layer eliminates the reducing effect of hydrodynamic interaction on the capture efficiency, the enhancement factor, fl, of the rate of flocculation in the turbulent flow can be written as (a 0 --t-~He) 3
fl -
aTa3
(2)
where ao denotes the radius of a primary particle. Hence, if we measure the rate of flocculation of a certain mixing with and without the addition of polymers, we can derive the value of 6m from the ratio of tiThe collision frequency between a colloidal particle and polymer molecules can be estimated in a similar way to that of the collision between
colloid particles. Since the size of the dissolved polymer is small, the contribution from Brownian motion cannot be treated as negligible. The assumption of the simple additivity of Brownian motion and fluid flow [25] leads to the following equation for the rate of collision towards a colloid particle: Jp = 4rr(Do + Dp)(a 0 q- ap)Np q- N / ~ v ( a O + ap)3 Np
(3) where D, a and N denote the diffusion constant, the radius and the number per unit volume respectively. Subscripts "p" and "o" denote polymer molecules and colloidal particles respectively.
3. Experimental
3.1. Materials Monodispersed polystyrene latex (PSL) was prepared by the standard emulsion polymerization of styrene in the absence of surfactant [26]. The diameter of particles was determined by electron microscopy as 1956 nm. The critical coagulation concentration of this latex against KC1 solution was determined as 0.25 M. As a flocculant, a polyelectrolyte based on the salt of dimethylamino ethylmethacrylate, as indicted in Fig. 1 (hereinafter denoted as #820H), with a nominal molecular weight of 4.5 x 106g mo1-1 kindly supplied by Mizusawa Kagaku Co. Ltd. was used. The molecular weight of this polycation was calculated from the M a r k Houwink equation [27]: [~/] = 3.73 × 10 -4 Mw 0"66 from the measurement of intrinsic viscosity in 1 M NaC1 solution. The estimated value of the molecular weight can only be considered as a crude indication because of the expected polydispersity. In order J CH2 - -
cooc.2c¢ ( c.3 • CIo
CH3 -/"
Fig. 1. Chemical structure of the salt of dimethylamino ethylmethacrylate.
Y. Adachi, T. Matsumoto/ ColloidsSurfaces A: Physicochem. Eng. Aspects 113 (1996) 229-236
232
to estimate the effective volume of the dissolved polymer under the same conditions adopted in the flocculation experiment, the viscosity was also measured in a 1 x 1 0 - 4 M KC1 solution. The size of the polyelectrolyte was estimated using Einstein's equation of viscosity. All these properites of the flocculant are listed in Table 1.
3.2. Mixing apparatus and procedure An end-over-end rotation apparatus as illustrated in Fig. 2 was constructed. The framework consisted of two wheels with different diameters connected to a crankshaft to generate a rocking motion in the larger wheel by the rotation of the smaller one. A forked flask was mounted on the larger wheel. The ratio of the two diameters was adjusted to 1.152 throughout the experiment. By turning over the smaller wheel, the rocking motion of the larger Table 1 Physical properties of flocculants Notation #820H
Chemical structure See Fig. 1
[r/] in 1 M NaCI (dlg -1) 8.0
Mw(nominal, g mol- 1)a 4.5 X 10 6
M~ (viscosity, g mol- 1)b 3.7 × 106
[r/] in 1 x 10-4 M KCI (dlg 1)c 68
dp(nm )
320
aThis value was given by the supplier. bThe concentration of #820 was around 10 ppm when viscosity was measured. CThe concentration of #820H was 5 ppm when this value was determined.
I
.:.<,
:\
..~
.
~:
x\\
\\\--i
Fig. 2. Schematic diagram of the end-over-end rotation apparatus: (1) grip; (2) wheel; (3) hinge; (4) crank shaft; (5) forked flask; (6) bearing axle.
wheel let the liquid flow from one side of the flask to the other. Initially, 5.0 ml of PSL dispersion was put into one side of the forked flask and the same amount of electrolyte (2.266 M KC1 solution) or polyelectrolyte (#820H) into the other side. The mixing operation was started by pouring the electrolyte or the polyelectrolyte into the dispersion, followed by pouring the mixed dispersion back into the emptied side, and so on. This operation was continued periodically until the predetermined number of steps (t) was reached. The duration of one step was fixed at 1 s throughout this investigation. In order to evaluate the degree of coagulation or flocculation which occurred during sampling, sampling and dilution of the dispersion were carried out exactly 10 s after the last mixing step. The number of particles was counted using a Coulter Counter and N(t) was obtained by multiplying the factor of dilution. In the case of the flocculation experiment using a polyelectrolyte, the polyelectrolyte as well as the colloidal dispersion were always immersed in a 1 x 10 4 KC1 solution, and thus the ionic strength of the mixture was kept constant.
3.3. Electrophoretic mobility and optimum flocculation concentration In order to obtain information on the state of the polyelectrolyte adsorbed on the colloidal surface, we measured the electrophoretic mobility of colloid polyelectrolyte complex and the optimum flocculation concentration (OFC), i.e. the optimum ratio of the amount of dosed polymer to that of colloidal surface to induce flocculation. Electrophoretic mobility was monitored in the same experiment on the kinetics of flocculation with a mixing stage of at least 10 steps with polyelectrolyte concentrations of 0.5 and 1.5 ppm. These data are presented in Table 2. For OFC, the normal turbidimetry was conducted at a particle concentration of 3.60 x 108 1 cm -3, which was 10 times as high as that used in the experiment on the kinetics of flocculation. O F C was determined by observing the transmittance of the supernatant which was left in a static condition for 2 h after mixing 30 times. The value of O F C was obtained as 0.14 mg m -z (300 polymer molecules per particle)
Y. Adachi, T. Matsumoto/ Colloids Surfaces A." Physicochem. Eng. Aspects 113 (1996)229-236
233
Table 2 Electrophoretic mobility of PSL complex Concentration of #820H (ppm) Mobility in 1 x 10 -4 M KC1 (~tm s-1/V cm 1)a
0 -4.61
0.5 5.1-5.7
1.5 6.9-7.2
aA standardized mixing operation of more than 10 steps was treated. This value was stable for more than 2h, thus demonstrating no evidence of desorption.
which corresponds to the value reported elsewhere 1-28] for the same system. We confirmed the excessive addition of flocculant in each run of the flocculation experiment from these results.
4. Results The total number of clusters per unit volume in the case of salt-induced coagulation of the latex is plotted as a function of the mixing steps in Fig. 3. The linear relation between ln(N(t)/N(O)) and t verifies the validity of the applied method. From this result, the absolute mean value of the velocity gradient of the mixing was estimated as 96 s -t, assuming that the Hamaker constant for polystyrene/water is 6 x 10 -21 J [29]. Results obtained for polyelectrolyte-induced flocculation will be analyzed using these results. In Fig. 4, we
-1.0
0
K
20
~'
I
40
60
Fig. 4. ln(N(t)/N(O)) vs. the number of steps (t) for the case of flocculation induced with polyelectrolyte (#820H). N(0) = 3.60 x 107 1 cm -3, [KC1] = 1.13 M. Concentration of #820H: (D) 1.5 ppm; ( ~ ) 1.0 ppm; (O) 0.5 ppm; (A) 0.25 ppm. The solid represents the regression of the salt-induced coagulation taken from Fig. 3.
show the evolution of flocculation induced with the polyelectrolyte. As can be seen, an excessive addition of polyelectrolytes resulted in a remarkable enhancement of the rate of flocculation in the initial stage followed by an abrupt decrease of the rate in the next stage. Although there is considerable scatter in the data, we could extract a few qualitative characteristics when we applied higher concentrations of the polyelectrolyte, as illustrated in Fig. 5. These were: an increase in the rate of
0-
--0,
Z _0.41
O~-N
S
z .C z
o
°%,0
-- -0.6
~
High
c°lnYce~i~rtrtil0Y~e
-0.8
0
I
I
I
20
40
60
N
80
t
Fig. 3. Temporal variation of total number of clusters per unit volume in the case of salt-induced coagulation as a function of the number of mixing steps (t). N(0) = 3.60 x 107 1 cm -3, [-KCI] = 1.13 M.
mixing steps (t)
Fig. 5. Typical shape of the figure representing the temporal evolution of flocculation with respect to polyelectrolyte concentration. The broken line represents the results of salt-induced coagulation.
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Y. Adachi, T. Matsumoto / Colloids Surfaces A: Physicochem. Eng. Aspects 113 (1996) 229-236
enhancement in the initial stage; a decrease in the duration of the initial stage; a decrease in the degree of flocculation at the end of the initial stage; and a clearer transition to the second stage. However, the slope of the initial stage seems to have a certain asymptotic value with respect to increase in the polyelectrolyte concentration. Since some scatter in the data was observed, we ran experiments four times under the same chemical conditions. Although the characteristics described above were not always reproducible quantitatively, the qualitative tendencies described above were always observed for each run.
5. Discussion The results for the kinetics of salt-induced coagulation provide a mean value of the mixing velocity gradient with which the kinetics of flocculation by polyelectrolytes as well as the kinetics of polyelectrolyte adsorption onto the colloidal surface can be analyzed. One of the most interesting analyses is a comparison of the rates of flocculation with various polyelectrolyte concentrations in the initial stages. On the basis of Eq. (2), the rate of flocculation in the initial stage can be converted to 5He. The calculated values are plotted against the polyelectrolyte concentration in Fig. 6. The error bars denote the range of deviations observed in different runs. Since Eq. (2) is based on the assumption that the capture efficiency of the collision between colloid-polyelectrolyte complexes is unity, it is only valid for the extreme case in which the adlayer is fluffy, allowing sufficient drainage to eliminate hydrodynamic interaction between complexes upon their collision. Therefore, in cases when adlayers are very flat for which the effect of hydrodynamic interaction between complexes does not vanish, the direct usage of Eq. (2) is no longer valid. In our calculations, we have simply discarded the results when we obtained negative values for 6he. Nevertheless, the calculated values of 5he as shown in Fig. 6 show a clear tendency to increase with an increase in polyelectrolyte concentration. It should also be noted that the value of fine correlated with the size of the dissolved polymer calculated from viscometry (Table 1). Since K-1
5He (nm)
500-
t
400-
300-
200-
100-
I
0.5
I
1.0
1.5
(ppm)
Fig. 6. The estimated value of 6no as a function of applied polymer concentration.
(the Debye length) is smaller than the obtained values of 5He by one order of magnitude, the effect of electrostatic repulsion can be regarded as negligibly small. The electrophoretic mobility data listed in Table 2 are noteworthy. Although it is not possible to quantify the exact amount of polyelectrolyte adsorbed on the surface of the colloidal particles from just the results of the mobility experiments, it can be used as a qualitative indication of the amount of positive charge resulting from the adsorption of the polyelectrolyte. The higher mobility observed with the application of a higher polyelectrolyte concentration, equivalent to the higher rate of polyelectrolyte supply to the surface of colloidal particles, means a larger amount of polyelectrolyte was adsorbed on the colloidal particle. This result is consistent with the picture of kinetically-controlled polymer adsorption proposed by De Witt and van de Ven [21]. Therefore, it is reasonable to interpret the results
Y. Adachi, T. Matsumoto/Colloids Surfaces A: Physicochem. Eng. Aspects 113 (1996) 229 236
shown in Fig. 6 as a reflection of kineticallycontrolled polymer adsorption. In order to construct a more quantitative picture, it is also interesting to carry out a crude analysis of the adsorption kinetics of polyelectrolytes moving towards the surace of a colloidal particle. Substituting the values listed in Table 1 into Eq.(3), the flux of polyelectrolytes towards a colloidal particle is calculated as Jp ~ 80 (polyelectrolyte particle s-1) when the polyelectrolyte concentration is 1 ppm. Since the duration of the initial stage is approximately 10 s, the number of polyelectrolytes adsorbed on the particle surface at the end of the initial stage is estimated to be about 800, Higashitani and Kubota [30] reported that the same polyelectrolyte will adsorb onto the surace of PSL particles approximately twice the amount of the OFC. Since the number of molecules of #820H on the PSL at the OFC is estimated to be 300, we may conclude that the adsorption of the polyelectrolyte onto the PSL particle is limited by transportation until near saturation. If the surface area of a colloidal particle is divided by the cross-sectional area of the polyelectrolyte, we get a ratio of ~ 160. On the basis of this ratio and polyelectrolyte flux, we can draw a schematic snapshot of kinetically-controlled polyelectrolyte adsorption with an average interval of 1 s as shown in Fig. 7. We can construct a crude quantification of the kinetically-controlled polyelectrolyte adsorption from this diagram. For instance, when the polyelectrolyte concentration is 1 ppm, approximately 50% of the colloidal surface is hit by a polyelectrolyte in 1 s. In this case, 6he was calculated to ~ 400 nm. The interference from neighboring polyelectrolytes probably disturbs the spreading behavior of the polyelectrolyte on the surface, thus resulting in the large layer thickness. The time scale involved in this process is in the order of 1 s. However, the progress of flocculation when the polyelectrolyte concentration is 0.25 ppm is important when we consider the reconformation of the polyelectrolyte on a surface Which is almost bare. Since we observed intermediate enhancement of the rate of flocculation in the initial stage, the process is still limited by transportation. That is, 6he is at least larger than ~:-~, which is calculated to be 30 nm from the ionic strength. In this case,
235
(~He
15 ppm
450nm
1.0 ppm
®
@®® I /1/
!
~380nm
I
0.5 ppm @
Ill/
@
I
i ~ 200am
0.25ppm I-Z//
I
"t- > 30 nm
Fig. 7. Snapshot with shutter speed of 1 s at PSL surface. The sample area was eight times as large as that of the polyelectrolyte cross-section. The number of polyelectrolytes represents the average number of polyelectrolytes transported to the surface in 1 s.
the flux of polyelectrolyte to the surface is only one-quarter of the previous one. The time scale involved in this relaxation can be considered to be a few seconds. It is also interesting to compare these time scales with that of diffusion. Using the Stokes-Einstein equation and assuming a displacement of 200 nm, the time scale is calculated to be 10 ms, which is smaller than our estimation by two orders of magnitude. This difference implies that there exists a considerable restriction which results in the resistance of the movement of a polyelectrolyte on the surface even though it is in the initial stage of adsorption.
6. Conclusions A reproducible method of colloid mixing carried out in our end-over-end rotation apparatus was normalized in terms of collision processes between colloid particles. The validity of this method was confirmed by measurement of the kinetics of the salt-induced coagulation of PSL. The established procedure was applied to investigate the initial
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stage kinetics of flocculation induced by excessive addition of polyelectrolyte. The kinetics were characterized by an extreme enhancement of the rate of flocculation which levelled off rather abruptly after a certain period of mixing. This process was interpreted as a competition between polymer adsorption and flocculation. Analyses were conducted on the basis of the collision process with which kinetically-controlled polymer adsorption was elucidated. The results for the dependency of the polyelectrolyte concentration indicate that the time scale involved in the polyelectrolyte reconformation on the oppositely charged surface is of the order of ] s in the system studied.
Acknowledgment We gratefully acknowledge Professor Bunichiro Tomita for his kind interest and Dr. Kunio Furusawa for his advice on the particle counting and electrophoresis experiments. This work was partly funded by a Grant-in-Aid for Scientific Research (05806031) from the Japanese Ministry of Education and Project Research of Tsukuba University.
References [1] P.J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY, 1953, Chapter 12. [2] P.G. de Gennes, Adv. Colloid Interface Sci., 27 (1987) 189. [3] J.M.H.M. Scheutjens and G.J. Fleer, J. Phys. Chem., 83 (1979) 1619; 84 (1980) 178. [4] T. Cosgrove and K. Ryan, Langmuir, 6 (1990) 136, [5] T. Cosgrove, T,G. Heath, K. Ryan and T.L. Crowley, Macromolecules, 20 (1987) 1879.
[6] J. Klein and P.F. Luckham, Nature, 308 (1984) 836. I-7] G.J. Fleer, M.A. Cohen Stuart, J.M.H.M. Scheutjens, T. Cosgrove and B. Vincent, Polymers at Interfaces, Chapman & Hall, London, 1993. [8] R.A. Ruehrwein and D.W. Ward, Soil Sci., 73 (1952) 485. [9] G.J. Fleer and J. Lyklema, J. Colloid Interface Sci., 52 (1974) 228. [10] J. Gregory, J. Colloid Interface Sci., 42 (1973) 448. [11] E.G.M Peissers, M.A. Cohen Stuart and G.J. Fleer, J. Chem. Soc., Faraday Trans., 86 (1990) 1355. [12] T.G.M. van de Ven, Adv. Colloid Interface Sci., 48 (1994) 141. [13] V. Chaplain, M.L, Janex, F. Lafuma, C. Graillat and R. Audebert, Colloid Polym. Sci., 273 (1995) 984. [14] J.C. Dijt, M.A. Cohen Stuart, J.E. Hofman and G.J. Fleer, Colloids Surfaces, 51 (1990) 141. [15] J.C. Dijt, M.A. Cohen Stuart and G.J. Fleer, Macromolecules, 25 (1992) 5416. [ 16] E. Pefferkorn, A. Haouam and R. Varoqui, Macromolecules, 21 (1988) 2111. [17] D.J. Neivandt and M.L. Gee, Langmuir, 11 (1995) 1291. [18] M. Trau, F. Grieser, T.W. Healy and L.R. White, J. Chem. Soc., Faraday Trans., 90 (1994) 1251. [19] A. Elaissari and E. Pefferkorn, J. Colloid Interface Sci., 141 (1991) 522. [20] (a) R. Quali and E. Pefferkorn, J. Colloid Interface Sci., 168 (1994) 315. (b) E. Pefferkorn, Adv. Colloid Interface Sci., 56 (1995) 33. [21] J.A. De Witt and T.G.M. van de Ven, Lan~nuir, 8 (1992) 788. [22] Y. Adachi, M.A. Cohen Stuart and R. Fokkink, J. Colloid Interface Sci., 165 (1994) 310 [23] Y. Adachi, M.A. Cohen Stuart and R. Fokkink, J. Colloid Interface Sci., 167 (1994) 346. [24] Y. Adachi, M.A. Cohen Stuart and R. Fokkink, J. Colloid Interface Sci., 171 (1995) 520. [25] Y. Adachi, Adv. Colloid Interface Sci., 56 (1995) l. [26] A. Kotera, K. Furusawa and Y. Takeda, Kolloid Z.Z. Polyrn., 237 (1970) 677. [27] Y. Iwakura, Koubunshi, 11 (1962) 1036. [28] L. Eriksson, B. Alm and P. Stenius, Colloids Surfaces, 70 (1993) 47. [29] T.G.M. van de Ven and S.G. Mason, Colloid Polym. Sci., 255 (1977) 468. [30] K. Higashitani and T. Kubota, Powder Technol., 51 (1987) 61.
AND Colloids and Surfaces
ELSEVIER
A
SURFACES
A: Physicochemical and Engineering Aspects 113 (1996) 229-236
Dynamics of initial stage flocculation of polystyrene latex spheres with polyelectrolytes Y. Adachi *, T. Matsumoto Institute of Agricultural and Forest Engineering, Tsukuba University, Tsukuba City, Ibaraki 305, Japan Received 12 October 1995; accepted 23 March 1996
Abstract
An end-over-end rotation apparatus was created in order to obtain reproducible mixing suitable for the study of the kinetics of flocculation. The validity was verified by measuring the rate of coagulation of monodispersed polystyrene latex particles with simple electrolytes by means of a Coulter Counter. The method was applied to the analysis of the initial behavior of flocculation induced by the addition of excess polyelectrolyte flocculant with a nominal molecular weight of 4.5 million. In contrast to coagulation with a simple electrolyte, the rate of flocculation in the initial stage was remarkably enhanced and then decreased abruptly after certain mixing steps. The degree of the initial stage of enhancement and the duration of this stage were found to be dependent on the concentration of the polyelectrolyte. Ascribing the enhancement to the increase in the effective collision radius of the colloidal particles due to the attached polymer layer, the thickness of this layer, ~ne, was calculated. Analyses showed that ~He increases as polymer concentration increases up to a layer thickness of 500 nm, which correlates with the size of the polymer in the solution. However, an analysis of the collision process between particles and polyelectrolytes implied that the kinetics of polymer adsorption in the initial stage are limited by transportation until near saturation. Taking into account the data on electrophoretic mobility, we concluded that our results are consistent with the picture of kinetically-controlled polymer adsorption proposed by De Witt and van de Ven [J.A. De Witt and T.G.M. van de Ven, Langmuir, 8 (1992) 788].
Keywords: Flocculation; Initial stage; Kinetics; Polyelectrolyte; Polystyrene latex
1. Introduction
It is well known that colloidal dispersions can be brought to flocculation by the addition of small amounts of adsorbing polymer. The mechanism of this destabilization is recognized as the formation of macromolecular bridges between the colloidal particles. It is necessary to study the behavior of adsorbed polymers on a single surface as well as that between two surfaces for a better understanding of this process, and many years of study have been devoted to this point. On the theoretical * Corresponding author. 0927-7757/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved PII S0927-7757 (96) 03649-0
side, the classical statistical thermodynamic theory of polymer solutions [1] has been extended to a description of the behavior of polymer chains located in the vicinity of the surface. There are two main groups of theories: the application of the scaling concept [ 2] and a more detailed calculation based on the mean field approximation [3]. The prediction of polymer conformations at various interfaces under various conditions is now possible because of these works. Applications of small angle neutron scattering [4], N M R [ 5 ] and surface force apparatus [6] have been reported to confirm the theoretical predictions. As a result, a great deal of knowledge concerning the equilibrium proper-
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Y. Adachi, "12 Matsumoto / Colloids Surfaces A: Physicochem. Eng. Aspects 113 (1996) 229-236
ties of polymer chains at interfaces is now available [7]. Nevertheless, theory and experimentation on the basis of equilibrium thermodynamics is not sufficient to predict the behavior of flocculation. That is, in most practical cases, flocculation is also irreversibly controlled by kinetic factors. The importance of this aspect has already been recognized in the pioneering work of Ruehrwein and Ward [8] and has been underlined by many experimentalists E9-13]. Because the formation of a bridge, in addition to polymer adsorption, is usually performed under mixing conditions which are difficult to specify clearly, it seemed impossible to quantify elementary processes such as the rate of collision between colloidal particles, the rate of collision of polymer molecules onto the colloidal surface and the rate of reconformation of polymer on the surface. However, recent experimental efforts have gradually elucidated the kinetic aspects involved in polymer adsorption and flocculation. By applying the technique of reflectometry under a well-defined hydrodynamic condition, Dijt et al. [14] found that the adsorption of PEO from aqueous phase to silica surface is limited by mass transfer up to about 75% of the maximum adsorption. In a subsequent study, they reported that the desorption of polymer is limited by mass transfer El5]. These are examples of a short term behavior referred to as a local equilibrium condition which appears in the absence of an energy barrier. However, long term behavior, sometimes referred to as surface process, is also involved in the kinetics. Examples can be found in the exchange of adsorbing polymer El6], the temporal change of the adsorbing conformation of polyelectrolytes observed with evansescent wave spectroscopy [ 17,18] and crossover of flocculation from RLA (reaction-limited aggregation) to DLA (diffusion-limited aggregation) as the incubation time of colloidal dispersion in the polymer solution elapses [19]. In a novel experiment, Quali and Pefferkorn 1-20] showed that polymer-bridges flocs will continue to fragment spontaneously for more than several days. These results mean that there are cases in which quite a long time is necessary to reach the state of complete equilibrium after the attainment of an initial metastable condition. Their results are consistent with the results of a kinetic
experiment on polymer adsorption reported by De Witt and van de Ven [-21] which showed that the adsorbed amount, as well as the thickness of the adsorbing layer, increases with an increase in the concentration of added polymer. These results are interpreted in terms of competition between the collision of polymers with the bare surface and the reconformation of adsorbing polymers on the surface. In other words, with low concentrations, slow adsorption leads to a low surface coverage of flattened molecules, while fast adsorption leads to a high surface coverage of unflattened molecules which does not relax into an equilibrium configuration over a short period. The same situation takes place in the initial stage of flocculation induced by the addition of excess polymer flocculant and should be crucial for the analysis of nonequilibrium aspects. In our pervious study [,22], we showed a way to characterize the mixing flow in terms of a collision process between colloidal particles. This method allows us to analyze a rate of ftocculation as short as 1 s from the start of mixing. We found a remarkable enhancement of the rate of flocculation induced immediately after the addition of adsorbing polymer [-23,24] with this technique. Ascribing this enhancement to an increase in the effective collision radius of colloidal particles due to the attached polymer layer, we found that the thickness of the layer correlates with the size of polymer molecules existing in the bulk solution. In the present study, we applied the same technique to probe the transient behaviour of polymer adsorption in the early stage of incubation. We constructed an end-over-end rotation apparatus to obtain consistently reproducible mixing. We monitored the initial behavior of flocculation induced by a highly charged polyelectrolyte by means of a Coulter Counter as a function of the rate of polymer supply to the colloidal surface in the standardized mixing system. The results obtained and the electrophoresis data were qualitatively consistent with the results of a kinetically-controlled adsorption experiment reported by De Witt and van de Ven. Our crude analysis indicates that the time scale of the reconformation of the polyelectrolyte on the bare surface is larger than that
231
Y. Adachi, T. Matsumoto / Colloids Surfaces A: Physicochem. Eng. Aspects 113 (1996) 229~36
which is required for a polyelectrolyte to move by self-diffusion in the bulk solution.
2. The rate of collision in turbulent mixing Since the rate of collision between colloidal particles is a function of the mixing intensity, the flow condition of a certain mixing can be evaluated by the measurement of the rate of rapid coagulation, which is equivalent to the rate of collision in the absence of repulsive forces between colloidal particles [22]. In a system with a sufficiently high Peclet number where the contribution of Brownian coagulation can be regarded as negligibly small, the following equation for the temporal evolution of the number of colloidal particles per unit volume, N(t), can be derived assuming that the volume fraction of colloidal particles, ~b,is constant:
( N(t)'] = ~24e a,
(1)
where e, v, a T and t denote the rate of energy dissipation per unit mass, kinematic viscosity, capture efficiency of turbulent coagulation and elapsed time respectively. When colloid particles move with attached polymers, their collision radii are increased by the amount 6he. The collision between colloidal particles is enhanced if the surface of the particle is not fully covered with polymer molecules so that the stabilizing effect does not appear. If we assume that the permeable structure of the polymer layer eliminates the reducing effect of hydrodynamic interaction on the capture efficiency, the enhancement factor, fl, of the rate of flocculation in the turbulent flow can be written as (a 0 --t-~He) 3
fl -
aTa3
(2)
where ao denotes the radius of a primary particle. Hence, if we measure the rate of flocculation of a certain mixing with and without the addition of polymers, we can derive the value of 6m from the ratio of tiThe collision frequency between a colloidal particle and polymer molecules can be estimated in a similar way to that of the collision between
colloid particles. Since the size of the dissolved polymer is small, the contribution from Brownian motion cannot be treated as negligible. The assumption of the simple additivity of Brownian motion and fluid flow [25] leads to the following equation for the rate of collision towards a colloid particle: Jp = 4rr(Do + Dp)(a 0 q- ap)Np q- N / ~ v ( a O + ap)3 Np
(3) where D, a and N denote the diffusion constant, the radius and the number per unit volume respectively. Subscripts "p" and "o" denote polymer molecules and colloidal particles respectively.
3. Experimental
3.1. Materials Monodispersed polystyrene latex (PSL) was prepared by the standard emulsion polymerization of styrene in the absence of surfactant [26]. The diameter of particles was determined by electron microscopy as 1956 nm. The critical coagulation concentration of this latex against KC1 solution was determined as 0.25 M. As a flocculant, a polyelectrolyte based on the salt of dimethylamino ethylmethacrylate, as indicted in Fig. 1 (hereinafter denoted as #820H), with a nominal molecular weight of 4.5 x 106g mo1-1 kindly supplied by Mizusawa Kagaku Co. Ltd. was used. The molecular weight of this polycation was calculated from the M a r k Houwink equation [27]: [~/] = 3.73 × 10 -4 Mw 0"66 from the measurement of intrinsic viscosity in 1 M NaC1 solution. The estimated value of the molecular weight can only be considered as a crude indication because of the expected polydispersity. In order J CH2 - -
cooc.2c¢ ( c.3 • CIo
CH3 -/"
Fig. 1. Chemical structure of the salt of dimethylamino ethylmethacrylate.
Y. Adachi, T. Matsumoto/ ColloidsSurfaces A: Physicochem. Eng. Aspects 113 (1996) 229-236
232
to estimate the effective volume of the dissolved polymer under the same conditions adopted in the flocculation experiment, the viscosity was also measured in a 1 x 1 0 - 4 M KC1 solution. The size of the polyelectrolyte was estimated using Einstein's equation of viscosity. All these properites of the flocculant are listed in Table 1.
3.2. Mixing apparatus and procedure An end-over-end rotation apparatus as illustrated in Fig. 2 was constructed. The framework consisted of two wheels with different diameters connected to a crankshaft to generate a rocking motion in the larger wheel by the rotation of the smaller one. A forked flask was mounted on the larger wheel. The ratio of the two diameters was adjusted to 1.152 throughout the experiment. By turning over the smaller wheel, the rocking motion of the larger Table 1 Physical properties of flocculants Notation #820H
Chemical structure See Fig. 1
[r/] in 1 M NaCI (dlg -1) 8.0
Mw(nominal, g mol- 1)a 4.5 X 10 6
M~ (viscosity, g mol- 1)b 3.7 × 106
[r/] in 1 x 10-4 M KCI (dlg 1)c 68
dp(nm )
320
aThis value was given by the supplier. bThe concentration of #820 was around 10 ppm when viscosity was measured. CThe concentration of #820H was 5 ppm when this value was determined.
I
.:.<,
:\
..~
.
~:
x\\
\\\--i
Fig. 2. Schematic diagram of the end-over-end rotation apparatus: (1) grip; (2) wheel; (3) hinge; (4) crank shaft; (5) forked flask; (6) bearing axle.
wheel let the liquid flow from one side of the flask to the other. Initially, 5.0 ml of PSL dispersion was put into one side of the forked flask and the same amount of electrolyte (2.266 M KC1 solution) or polyelectrolyte (#820H) into the other side. The mixing operation was started by pouring the electrolyte or the polyelectrolyte into the dispersion, followed by pouring the mixed dispersion back into the emptied side, and so on. This operation was continued periodically until the predetermined number of steps (t) was reached. The duration of one step was fixed at 1 s throughout this investigation. In order to evaluate the degree of coagulation or flocculation which occurred during sampling, sampling and dilution of the dispersion were carried out exactly 10 s after the last mixing step. The number of particles was counted using a Coulter Counter and N(t) was obtained by multiplying the factor of dilution. In the case of the flocculation experiment using a polyelectrolyte, the polyelectrolyte as well as the colloidal dispersion were always immersed in a 1 x 10 4 KC1 solution, and thus the ionic strength of the mixture was kept constant.
3.3. Electrophoretic mobility and optimum flocculation concentration In order to obtain information on the state of the polyelectrolyte adsorbed on the colloidal surface, we measured the electrophoretic mobility of colloid polyelectrolyte complex and the optimum flocculation concentration (OFC), i.e. the optimum ratio of the amount of dosed polymer to that of colloidal surface to induce flocculation. Electrophoretic mobility was monitored in the same experiment on the kinetics of flocculation with a mixing stage of at least 10 steps with polyelectrolyte concentrations of 0.5 and 1.5 ppm. These data are presented in Table 2. For OFC, the normal turbidimetry was conducted at a particle concentration of 3.60 x 108 1 cm -3, which was 10 times as high as that used in the experiment on the kinetics of flocculation. O F C was determined by observing the transmittance of the supernatant which was left in a static condition for 2 h after mixing 30 times. The value of O F C was obtained as 0.14 mg m -z (300 polymer molecules per particle)
Y. Adachi, T. Matsumoto/ Colloids Surfaces A." Physicochem. Eng. Aspects 113 (1996)229-236
233
Table 2 Electrophoretic mobility of PSL complex Concentration of #820H (ppm) Mobility in 1 x 10 -4 M KC1 (~tm s-1/V cm 1)a
0 -4.61
0.5 5.1-5.7
1.5 6.9-7.2
aA standardized mixing operation of more than 10 steps was treated. This value was stable for more than 2h, thus demonstrating no evidence of desorption.
which corresponds to the value reported elsewhere 1-28] for the same system. We confirmed the excessive addition of flocculant in each run of the flocculation experiment from these results.
4. Results The total number of clusters per unit volume in the case of salt-induced coagulation of the latex is plotted as a function of the mixing steps in Fig. 3. The linear relation between ln(N(t)/N(O)) and t verifies the validity of the applied method. From this result, the absolute mean value of the velocity gradient of the mixing was estimated as 96 s -t, assuming that the Hamaker constant for polystyrene/water is 6 x 10 -21 J [29]. Results obtained for polyelectrolyte-induced flocculation will be analyzed using these results. In Fig. 4, we
-1.0
0
K
20
~'
I
40
60
Fig. 4. ln(N(t)/N(O)) vs. the number of steps (t) for the case of flocculation induced with polyelectrolyte (#820H). N(0) = 3.60 x 107 1 cm -3, [KC1] = 1.13 M. Concentration of #820H: (D) 1.5 ppm; ( ~ ) 1.0 ppm; (O) 0.5 ppm; (A) 0.25 ppm. The solid represents the regression of the salt-induced coagulation taken from Fig. 3.
show the evolution of flocculation induced with the polyelectrolyte. As can be seen, an excessive addition of polyelectrolytes resulted in a remarkable enhancement of the rate of flocculation in the initial stage followed by an abrupt decrease of the rate in the next stage. Although there is considerable scatter in the data, we could extract a few qualitative characteristics when we applied higher concentrations of the polyelectrolyte, as illustrated in Fig. 5. These were: an increase in the rate of
0-
--0,
Z _0.41
O~-N
S
z .C z
o
°%,0
-- -0.6
~
High
c°lnYce~i~rtrtil0Y~e
-0.8
0
I
I
I
20
40
60
N
80
t
Fig. 3. Temporal variation of total number of clusters per unit volume in the case of salt-induced coagulation as a function of the number of mixing steps (t). N(0) = 3.60 x 107 1 cm -3, [-KCI] = 1.13 M.
mixing steps (t)
Fig. 5. Typical shape of the figure representing the temporal evolution of flocculation with respect to polyelectrolyte concentration. The broken line represents the results of salt-induced coagulation.
234
Y. Adachi, T. Matsumoto / Colloids Surfaces A: Physicochem. Eng. Aspects 113 (1996) 229-236
enhancement in the initial stage; a decrease in the duration of the initial stage; a decrease in the degree of flocculation at the end of the initial stage; and a clearer transition to the second stage. However, the slope of the initial stage seems to have a certain asymptotic value with respect to increase in the polyelectrolyte concentration. Since some scatter in the data was observed, we ran experiments four times under the same chemical conditions. Although the characteristics described above were not always reproducible quantitatively, the qualitative tendencies described above were always observed for each run.
5. Discussion The results for the kinetics of salt-induced coagulation provide a mean value of the mixing velocity gradient with which the kinetics of flocculation by polyelectrolytes as well as the kinetics of polyelectrolyte adsorption onto the colloidal surface can be analyzed. One of the most interesting analyses is a comparison of the rates of flocculation with various polyelectrolyte concentrations in the initial stages. On the basis of Eq. (2), the rate of flocculation in the initial stage can be converted to 5He. The calculated values are plotted against the polyelectrolyte concentration in Fig. 6. The error bars denote the range of deviations observed in different runs. Since Eq. (2) is based on the assumption that the capture efficiency of the collision between colloid-polyelectrolyte complexes is unity, it is only valid for the extreme case in which the adlayer is fluffy, allowing sufficient drainage to eliminate hydrodynamic interaction between complexes upon their collision. Therefore, in cases when adlayers are very flat for which the effect of hydrodynamic interaction between complexes does not vanish, the direct usage of Eq. (2) is no longer valid. In our calculations, we have simply discarded the results when we obtained negative values for 6he. Nevertheless, the calculated values of 5he as shown in Fig. 6 show a clear tendency to increase with an increase in polyelectrolyte concentration. It should also be noted that the value of fine correlated with the size of the dissolved polymer calculated from viscometry (Table 1). Since K-1
5He (nm)
500-
t
400-
300-
200-
100-
I
0.5
I
1.0
1.5
(ppm)
Fig. 6. The estimated value of 6no as a function of applied polymer concentration.
(the Debye length) is smaller than the obtained values of 5He by one order of magnitude, the effect of electrostatic repulsion can be regarded as negligibly small. The electrophoretic mobility data listed in Table 2 are noteworthy. Although it is not possible to quantify the exact amount of polyelectrolyte adsorbed on the surface of the colloidal particles from just the results of the mobility experiments, it can be used as a qualitative indication of the amount of positive charge resulting from the adsorption of the polyelectrolyte. The higher mobility observed with the application of a higher polyelectrolyte concentration, equivalent to the higher rate of polyelectrolyte supply to the surface of colloidal particles, means a larger amount of polyelectrolyte was adsorbed on the colloidal particle. This result is consistent with the picture of kinetically-controlled polymer adsorption proposed by De Witt and van de Ven [21]. Therefore, it is reasonable to interpret the results
Y. Adachi, T. Matsumoto/Colloids Surfaces A: Physicochem. Eng. Aspects 113 (1996) 229 236
shown in Fig. 6 as a reflection of kineticallycontrolled polymer adsorption. In order to construct a more quantitative picture, it is also interesting to carry out a crude analysis of the adsorption kinetics of polyelectrolytes moving towards the surace of a colloidal particle. Substituting the values listed in Table 1 into Eq.(3), the flux of polyelectrolytes towards a colloidal particle is calculated as Jp ~ 80 (polyelectrolyte particle s-1) when the polyelectrolyte concentration is 1 ppm. Since the duration of the initial stage is approximately 10 s, the number of polyelectrolytes adsorbed on the particle surface at the end of the initial stage is estimated to be about 800, Higashitani and Kubota [30] reported that the same polyelectrolyte will adsorb onto the surace of PSL particles approximately twice the amount of the OFC. Since the number of molecules of #820H on the PSL at the OFC is estimated to be 300, we may conclude that the adsorption of the polyelectrolyte onto the PSL particle is limited by transportation until near saturation. If the surface area of a colloidal particle is divided by the cross-sectional area of the polyelectrolyte, we get a ratio of ~ 160. On the basis of this ratio and polyelectrolyte flux, we can draw a schematic snapshot of kinetically-controlled polyelectrolyte adsorption with an average interval of 1 s as shown in Fig. 7. We can construct a crude quantification of the kinetically-controlled polyelectrolyte adsorption from this diagram. For instance, when the polyelectrolyte concentration is 1 ppm, approximately 50% of the colloidal surface is hit by a polyelectrolyte in 1 s. In this case, 6he was calculated to ~ 400 nm. The interference from neighboring polyelectrolytes probably disturbs the spreading behavior of the polyelectrolyte on the surface, thus resulting in the large layer thickness. The time scale involved in this process is in the order of 1 s. However, the progress of flocculation when the polyelectrolyte concentration is 0.25 ppm is important when we consider the reconformation of the polyelectrolyte on a surface Which is almost bare. Since we observed intermediate enhancement of the rate of flocculation in the initial stage, the process is still limited by transportation. That is, 6he is at least larger than ~:-~, which is calculated to be 30 nm from the ionic strength. In this case,
235
(~He
15 ppm
450nm
1.0 ppm
®
@®® I /1/
!
~380nm
I
0.5 ppm @
Ill/
@
I
i ~ 200am
0.25ppm I-Z//
I
"t- > 30 nm
Fig. 7. Snapshot with shutter speed of 1 s at PSL surface. The sample area was eight times as large as that of the polyelectrolyte cross-section. The number of polyelectrolytes represents the average number of polyelectrolytes transported to the surface in 1 s.
the flux of polyelectrolyte to the surface is only one-quarter of the previous one. The time scale involved in this relaxation can be considered to be a few seconds. It is also interesting to compare these time scales with that of diffusion. Using the Stokes-Einstein equation and assuming a displacement of 200 nm, the time scale is calculated to be 10 ms, which is smaller than our estimation by two orders of magnitude. This difference implies that there exists a considerable restriction which results in the resistance of the movement of a polyelectrolyte on the surface even though it is in the initial stage of adsorption.
6. Conclusions A reproducible method of colloid mixing carried out in our end-over-end rotation apparatus was normalized in terms of collision processes between colloid particles. The validity of this method was confirmed by measurement of the kinetics of the salt-induced coagulation of PSL. The established procedure was applied to investigate the initial
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I( Adachi, T. Matsumoto / Colloids Surfaces A: Physicochem. Eng. Aspects 113 (1996) 229-236
stage kinetics of flocculation induced by excessive addition of polyelectrolyte. The kinetics were characterized by an extreme enhancement of the rate of flocculation which levelled off rather abruptly after a certain period of mixing. This process was interpreted as a competition between polymer adsorption and flocculation. Analyses were conducted on the basis of the collision process with which kinetically-controlled polymer adsorption was elucidated. The results for the dependency of the polyelectrolyte concentration indicate that the time scale involved in the polyelectrolyte reconformation on the oppositely charged surface is of the order of ] s in the system studied.
Acknowledgment We gratefully acknowledge Professor Bunichiro Tomita for his kind interest and Dr. Kunio Furusawa for his advice on the particle counting and electrophoresis experiments. This work was partly funded by a Grant-in-Aid for Scientific Research (05806031) from the Japanese Ministry of Education and Project Research of Tsukuba University.
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[6] J. Klein and P.F. Luckham, Nature, 308 (1984) 836. I-7] G.J. Fleer, M.A. Cohen Stuart, J.M.H.M. Scheutjens, T. Cosgrove and B. Vincent, Polymers at Interfaces, Chapman & Hall, London, 1993. [8] R.A. Ruehrwein and D.W. Ward, Soil Sci., 73 (1952) 485. [9] G.J. Fleer and J. Lyklema, J. Colloid Interface Sci., 52 (1974) 228. [10] J. Gregory, J. Colloid Interface Sci., 42 (1973) 448. [11] E.G.M Peissers, M.A. Cohen Stuart and G.J. Fleer, J. Chem. Soc., Faraday Trans., 86 (1990) 1355. [12] T.G.M. van de Ven, Adv. Colloid Interface Sci., 48 (1994) 141. [13] V. Chaplain, M.L, Janex, F. Lafuma, C. Graillat and R. Audebert, Colloid Polym. Sci., 273 (1995) 984. [14] J.C. Dijt, M.A. Cohen Stuart, J.E. Hofman and G.J. Fleer, Colloids Surfaces, 51 (1990) 141. [15] J.C. Dijt, M.A. Cohen Stuart and G.J. Fleer, Macromolecules, 25 (1992) 5416. [ 16] E. Pefferkorn, A. Haouam and R. Varoqui, Macromolecules, 21 (1988) 2111. [17] D.J. Neivandt and M.L. Gee, Langmuir, 11 (1995) 1291. [18] M. Trau, F. Grieser, T.W. Healy and L.R. White, J. Chem. Soc., Faraday Trans., 90 (1994) 1251. [19] A. Elaissari and E. Pefferkorn, J. Colloid Interface Sci., 141 (1991) 522. [20] (a) R. Quali and E. Pefferkorn, J. Colloid Interface Sci., 168 (1994) 315. (b) E. Pefferkorn, Adv. Colloid Interface Sci., 56 (1995) 33. [21] J.A. De Witt and T.G.M. van de Ven, Lan~nuir, 8 (1992) 788. [22] Y. Adachi, M.A. Cohen Stuart and R. Fokkink, J. Colloid Interface Sci., 165 (1994) 310 [23] Y. Adachi, M.A. Cohen Stuart and R. Fokkink, J. Colloid Interface Sci., 167 (1994) 346. [24] Y. Adachi, M.A. Cohen Stuart and R. Fokkink, J. Colloid Interface Sci., 171 (1995) 520. [25] Y. Adachi, Adv. Colloid Interface Sci., 56 (1995) l. [26] A. Kotera, K. Furusawa and Y. Takeda, Kolloid Z.Z. Polyrn., 237 (1970) 677. [27] Y. Iwakura, Koubunshi, 11 (1962) 1036. [28] L. Eriksson, B. Alm and P. Stenius, Colloids Surfaces, 70 (1993) 47. [29] T.G.M. van de Ven and S.G. Mason, Colloid Polym. Sci., 255 (1977) 468. [30] K. Higashitani and T. Kubota, Powder Technol., 51 (1987) 61.