- Email: [email protected]
Initial Stage Dynamics of Bridging Flocculation of Polystyrene Latex Spheres with Polyethylene Oxide
Journal of Colloid and Interface Science 229, 148–154 (2000) doi:10.1006/jcis.2000.6964, available online at http://www.idealibrary.com on
Initial Stage Dynamics of Bridging Flocculation of Polystyrene Latex Spheres with Polyethylene Oxide Y. Adachi1 and T. Wada Institute of Agricultural and Forest Engineering, Tsukuba University, Tsukuba-shi, Ibaraki 305-8572, Japan Received January 18, 2000; accepted May 8, 2000
The kinetics of bridging flocculation of polystyrene latex (PSL) particles induced by addition of excess polyethylene oxide (PEO) in the initial stage was studied using standardized mixing flow generated in an end-over-end rotation apparatus. To clarify the effect of the rate of polymer supply, flocculation experiments were performed by changing polymer concentration (Cp ). As was found in previous investigation, the progress of flocculation is divided into two stages. The first stage is characterized by an enhancement of the rate of flocculation by polymer addition. The increase in polymer concentration results in a higher enhancement but in a shorter duration for this stage. In the second stage, the flocculation is essentially stopped due to the appearance of steric stabilization. It was found that the ultimate degree of flocculation goes through a maximum against Cp . That is, when Cp > = 1.0 ppm, the ultimate degree of flocculation decreases with increased Cp . In this region, a clear crossover from the first stage to the second stage was observed. In the extreme case, evidence of a slight setback of flocculation was confirmed, which implies the breakup of metastable bridges by the application of additional fluid shear. When Cp < = 1.0 ppm, the ultimate degree of flocculation decreases with decreased Cp . The crossover from the first stage to the second stage appears more gradual at lower Cp . These results were observed irrespective of ionic strength. This result was interpreted as the elimination of a bare surface due to the spreading of a steric layer of adsorbed polymer. The characteristic time for reconformation of the polymer at a bare colloidal surface was estimated to be a few seconds. ° C 2000
Academic Press
Key Words: bridging flocculation; polystyrene latex; polyethylene oxide; standardized mixing flow; polymer adsorption; dynamics of polymer at surface.
1. INTRODUCTION
Flocculation of colloidal particles is fundamental to many industrial processes and to environmental science. It is well known that the addition of a dissolving polymer with an affinity for the surface of colloidal particles dramatically influences the stability of colloidal dispersion. That is, when a polymer chain attaches to more than two particles at the same time, the chain will act as a 1
To whom correspondence should be addressed.
0021-9797/00 $35.00
C 2000 by Academic Press Copyright ° All rights of reproduction in any form reserved.
bridging material and induce bridging flocculation (1–3, 17, 18). When a dense layer of adsorbed polymers is formed around the colloidal particles, it will act as a steric barrier against the approach of other colloidal particles, and thus the dispersed state of colloidal suspension is sterically protected (4–6). Since the formation of bridges between colloidal particles and the formation of steric layers around colloidal particles proceed simultaneously under conditions of turbulent mixing when colloidal particles and polymer flocculant are put together in the same solution, we propose that induction of bridging flocculation is competitive with polymer adsorption (7). This theory has been emphasized in our series of previous investigations in which the kinetics of flocculation induced by excess addition of polymer flocculant in the initial stage was extensively analyzed in terms of a collision process in the normalized mixing (8–10). As a result, we found that flocculation started very rapidly but slowed down abruptly after a while. Analysis of the rate of flocculation in the very initial period of incubation reveals the role of polymer conformation close to the dissolving state in the formation of bridges between colloidal particles. Using a polyelectrolyte as a flocculant, we have also elucidated the importance of polymer chain dynamics in the transient process of adsorption from a coil-like solution state to the flattened conformation of the adsorbed state on the bare surface of colloidal particles (11, 12). However, the experimental results obtained with polyelectrolyte are strongly influenced by electrostatic interactions. That is, adsorption is greatly enhanced by an electrostatic attractive force acting between the surfaces of colloidal particles and the charged segments, and the conformation and flexibility of polyelectrolytes change remarkably as a function of ionic strength. These factors raise other questions that are essentially important for the flocculation induced by polyelecrolytes. For analysis of polymer folding on a colloidal surface, it is beneficial to use data that are free of factors complicated by charged polymers. In the present study, we conducted a series of flocculation experiments with polystyrene latex (PSL) particles induced by the addition of polyethylene oxide (PEO). The experiments were designed to examine the effects of the rate of polymer supply and of the thickness of the electrical double layer of colloidal particles.
148
149
BRIDGING FLOCCULATION OF POLYSTYRENE LATEX
coagulation, β, as
2. RATE OF COLLISION IN A TURBULENT FLOW
The principle of analysis used in the present study is the same as that used in our previous series of investigations (9–12). It is based on the rate of collision, which is determined from the flow conditions of turbulent mixing. This can be obtained from measurement of the rate of rapid coagulation of well-defined colloidal particles. If we assume that (i) the hypothesis of isotropic turbulence proposed by Kolmogorov is applicable, (ii) the size of the collision radius is sufficiently small in comparison with the size of the smallest eddy of the turbulence, (iii) all particles move following fluid motion, (iv) all collisions lead to coagulation and coagulated flocs will never be broken up, (v) the effects of Brownian motion and sedimentation are negligibly small, (vi) the coagulation is in the early stage where most particles remain as singlets of radius a0 , we can derive the equation for the temporal variation of the number concentration of colloidal particles (19, 20), N (t), as r d N (t) 8πε = −αT (2a0 )3 N (t)2 , dt 15ν
γ =
(a0 + δHe )3 , αT a03
[1]
[4]
where δHe denotes the effective protruding length of attached polymer on the colloidal surface. Hence, if we measure the rate of flocculation with and without polymer flocculants under certain fixed conditions of mixing, we can estimate the value of δHe from β. The effective shear rate obtained from the rate of rapid coagulation can be also used to estimate the flux of polymer molecules onto the colloidal surface. Because the size of the dissolving polymer is small, the contribution due to Brownian motion should be taken into account. Assuming simple additivity of the contributions from Brownian motion and turbulent motion, we can derive the equation for the rate of polymer supply to a colloidal particle, Jp , as r
where ε and ν denote the rate of energy dissipation per unit mass and the kinematic viscosity of the fluid, respectively. Equation [1] implies that the coagulation in the turbulent flow can effectively be treated as a sort of shear coagulation with an effective shear rate r
β=
Jp = 4π (D0 + Dp )(a0 + ap )Np +
8π ε (a0 + ap )3 Np , [5] 15ν
where D, a, and N denote the diffusion constant, the radius, and the number concentration, and subscripts p and 0 denote the polymer and the colloidal particle, respectively. 3. EXPERIMENTAL
(a) Materials 4ε . 15νπ
[2]
αT is the correction factor that takes into account the effect of hydrodynamic interaction between colloidal particles when they collide. This value can be approximated by substituting Eq. [2] into the numerical result of van de Ven and Mason (21) as r µ Á ¶ 4ε 3 0.18 , a0 αT = A 36πµ 15πν
[3]
where A and µ denote the Hamaker constant and the viscosity of the fluid (19, 20). When the collision between colloidal particles with attached polymer takes place, the collision radius effectively increases, reflecting the protruding part of the attached polymer on the colloidal surface. Accordingly, the rate of flocculation will be enhanced due to the increased collision radius. Therefore, comparison of the rate of flocculation induced by addition of polymer flocculant with the rate of salt-induced rapid coagulation will provide information on the effective length of the protruding polymer. If we assume that the highly porous and permeable structure of a polymer chain eliminates the necessity of correcting for hydrodynamic interaction, we can write the ratio of the enhanced rate of flocculation to the rate of salt-induced rapid
Monodisperse polystyrene latex particles with a diameter of 1356 nm, denoted PSL1356 in our previous papers, were again used in the flocculation experiment. A commercially available PEO, with a nominal molecular weight of 5 × 106 g/mol (Aldrich Co. Ltd.), was used as flocculant. In the previous study (9), aggregate formation by the PEO made the preparation of a stable solution difficult. In the present study, an effort was made to avoid this effect by incubating the stock solution (100 ppm) in 1 × 10−4 M KCl solution for 1 day. To determine the size of the polymer in solution, the relative viscosity was measured as a function of polymer concentration. Analysis on the basis of the Einstein equation for viscosity and the nominal molecular weight gave the radius of the polymer as a0 = 105 nm. This was consistent with the prediction of the Mark–Houwink–Sakurada equation: [η] = 5.94 × 10−4 M0.66 W .
[6]
No distinctive difference in the viscosity data as a result of the change in salt concentration from 1 × 10−4 to 1 × 10−2 M was detected. (b) Procedure Flocculation was induced by the standard procedure of colloid mixing. The solution was mixed with the same amount
150
ADACHI AND WADA
of colloidal dispersion using a standard end-over-end rotation apparatus with a forked flask. Initially, one side was filled with 5.0 ml of colloidal dispersion and the other with an equal volume of electrolyte or PEO solution. Mixing was started by pouring the dispersion into the electrolyte or PEO solution. The mixed dispersion was then poured back into the emptied side. This operation was repeated periodically until the predetermined number of mixing steps (t) was reached. The duration of one step was fixed to 1 s throughout this investigation. The rate of flocculation was measured by counting the total number concentration of clusters, N (t), with a Coulter counter as a function of the number of mixing steps. During the monitoring, the flocculated dispersion was sucked up gently using a specially made pipette, poured into the pure electrolyte solution of the same ionic strength as the dispersion, and then diluted again with the isoton, which is the strong electrolyte prepared for the Coulter counter measurement.
4. RESULTS
The total number of clusters per unit volume for salt-induced coagulation is plotted as a function of the number of mixing steps in Fig. 1. The linear relation between ln(N (t)/N (0)) and t verifies the validity of the applied method. From the slope of this plot, the rate of energy dissipation, ε, of the applied mixing was estimated as 8.20 × 10−2 J s−1 kg−1 . Results of polymerinduced flocculation for differing ionic strengths are shown in Figs. 2 and 3. For a clear comparison between the rate of saltinduced coagulation and the rate of polymer-induced flocculation, the linear part of the first stage is magnified in Figs. 4 and 5.
FIG. 2. ln(N (t)/N (0)) vs t for flocculation induced with an application of PEO. The background solution of KCl is 1.0 × 10−4 M. N (0) = 7.7 × > 1 ppm). (b) 107 (1/cm3 ). (a) The results for higher polymer concentration (Cp = The result for lower polymer concentration (Cp < 1 ppm). The solid line rep= resents the regression line of the result of salt-induced coagulation taken from Fig. 1. Cp = (+) 0.25 ppm, (3) 0.5 ppm, (j) 1 ppm, (s) 2 ppm, (m) 4 ppm, (∗) 8 ppm.
5. DISCUSSION
FIG. 1. Temporal variation of the total number of clusters per unit volume for salt-induced coagulation as a function of the number of mixing steps (t). N (0) = 7.7 × 107 (1/cm3 ), [KCl] = 1.17 M.
A schematic diagram representing the pattern of temporal variation of the total number concentration of clusters, N (t), relative to the initial concentration, N (0), is presented in Fig. 6. As illustrated in this figure, flocculation progresses in two stages. The first stage is characterized by rapid flocculation. The initial rate of flocculation is strongly enhanced by the application of
BRIDGING FLOCCULATION OF POLYSTYRENE LATEX
151
FIG. 4. Magnification of ln(N (t)/N (0)) vs t in the beginning stage for KCl = 10−4 M.
phase to the colloidal surface by calculating the collision flux of polymer toward the surfaces of colloidal particles. Substitution of experimentally obtained data for the polymer size, by viscometry, and the rate of energy dissipation, by the rate of salt-induced coagulation, into Eq. [5] allows crude estimation of Jp . For Cp = 1.0 ppm, Jp is estimated at 22.1 PEO molecules/PSL particles/s, whereas saturated adsorption of the PEO onto PSL particles (0sat ) was reported as 0.5 mg/m2 (9), which corresponds to 347 PEO molecules/ PSL particle. The ratio 0sat /Jp is calculated as 15.7 s, which agrees with the duration of the first stage as estimated for Cp = 1.0 ppm. This agreement confirms the validity
> 1 ppm. KCl = 10−2 M FIG. 3. (a) ln(N (t)/N (0)) vs t for the case, CP = and N (0) = 7.7 × 107 (1/cm3 ). Symbols for each polymer concentration are the same as those used in Fig. 2. (b) ln(N (t)/N (0)) vs t for the case, CP < = 1 ppm. KCl = 10−2 M and N (0) = 7.7 × 107 (1/cm3 ).
PEO; however, soon after the first stage, flocculation abruptly comes to a halt, and the second stage, the establishment of steric stabilization by the adsorbed polymer, begins. In the following, we focus on three points to elucidate the dynamics of polymer adsorption and reconformation on the surfaces of colloidal particles. (i) Time Required to Establish Steric Stabilization We can confirm that the progress of the initial stage is limited by the hydrodynamic transportation of polymer from the bulk
FIG. 5. Magnification of ln(N (t)/N (0)) vs t in the beginning stage for KCl = 10−2 M.
152
ADACHI AND WADA
than that predicted only by the hydrodynamic transportation. This prediction agreed with the experimental results observed for lower Cp . In addition, a more gradual shift from the first stage to the second stage at lower Cp can be explained if we assume that the time scale of invasion is a few seconds. Because we could not find any differences with respect to ionic strength, we expect that the polymer layer formed by spreading is already thicker than 30 nm, which is the Debye reciprocal length for the experimental condition at the lower ionic strength (KCl = 1.0 × 10−4 M). This fact also means that the theory of polymer inactivation by the folding of the protruding chain into the inside of the electrical double layer proposed by Pelssers et al. (17) is not the case for our system. On the basis of the difference in the resulting layer thicknesses due to the means of polymer addition, Polverari and van de Ven (29) concluded that the adsorption of PEO onto PSL particles is kinetically controlled. This conclusion is qualitatively consistent with our findings. (ii) Effective Thickness of Polymer Layer
FIG. 6. Schematic diagram of the progress of flocculation with PEO.
of the analysis on the basis of hydrodynamic transportation. In addition, in the region of higher Cp (Cp > = 1.0 ppm), the first stage becomes shorter with increased Cp . From this result, we can conclude that the appearance of steric stabilization is limited by hydrodynamic transportation of the polymer toward the surface. This conclusion is the same as that clearly demonstrated with the flow reflectometoric technique (22) in which the rate of supply of PEO to the flat surface of a silicon wafer is strictly calculated. However, another source that contributes to stabilizing colloids can be found in the results at lower polymer concentrations (Cp < = 1.0 ppm). As was discussed under Results, the ultimate degree of flocculation was found to go through a maximum, i.e., the ultimate degree of flocculation decreased with decreased polymer concentration for Cp < = 1.0 ppm. In addition to the decrease in the ultimate degree of flocculation, the first stage is not sufficiently long to guarantee limitation by hydrodynamic transportation alone. Since these phenomena are commonly observed irrespective of ionic strength, stabilization due to the electrostatic interaction is denied. One possible explanation is the elimination of a bare surface due to the spread of polymers on the colloidal surface. That is, attached polymers that arrive earlier on the colloidal surface will flatten their conformation. Accordingly, the area of the “bare” surface that can accommodate newcomers will decrease and finally will be lost. In accordance with the decrease in the probability of finding bare surface, the probability of successful collision between colloidal particles is expected to decrease. The effect of invasion of the spread polymer is expected to shorten the duration of the first stage more
The effective length of the protruding polymer on the colloidal particle, δHe , can be calculated using the difference of the initial slopes indicated in Figs. 4 and 5 on the basis of Eq. [4]. In some cases, δHe calculated for lower polymer concentrations was estimated to be negative. This unrealistic result is due to neglecting to correct for the decrease of capture efficiency stemming from the hydrodynamic interaction between two colliding particles with this polymer layer. However, no exact answer is available for this correction. We simply skip this unrealistic case, and only the results with positive valules are indicated in Table 1. The value of δHe obtained for high Cp is larger than the diameter of PEO molecules determined by viscometry. The two reasons that can be considered so far are the extension of PEO molecules by fluid shear (24) and the formation of PEO aggregates (9, 25–27). For the former, it should be noted that the critical shear rate above which a polymer chain yields to the stretched form is much higher than the effective shear rate estimated using Eq. [2]. For the latter, although we are not able to deny completely its possibility, as was pointed out by our previous work, the time scale involved in the present study is much shorter than the time scale of hysteresis due to the formation of PEO aggregate observed in the surface force measurement (25–27). TABLE 1 Estimated Adsorbed Layer Thickness KCl 1 × 10−4 M
KCl 1 × 10−2 M
PEO (ppm)
β
δHe (nm)
β
δHe (nm)
0.25 0.5 1.0 2.0 4.0 8.0
1.7 2.9 5.7 10 14 18
— — 160 330 450 550
2.8 3.8 6.5 — 22 26
53 200 — 630 710
BRIDGING FLOCCULATION OF POLYSTYRENE LATEX
It should also be noted that Polverali and van de Ven (29) reported that hydrodynamic layer thickness decreased when the measurement was performed in the presence of PEO aggregate in the solution. Therefore, it is difficult to determine the effect of the formation of PEO aggregate. It is important and also interesting to compare the values of δHe with those obtained by previous researchers (23, 28–31). The available data were mostly obtained using hydrodynamic methods for PEO of lower molecular weight. Their measurements were performed in the final state of adsorption, i.e., after sufficiently long periods of incubation. The estimate based on extension to the molecular weight of the polymer used in the present study is always smaller than our maximum value, which was obtained with the highest polymer concentration. The reason is probably that our δHe data reflect the collision radius in the transient state, while the reported values are those for the final state. It is of interest to express δHe as a function of characteristic time involved in adsorption. One important characteristic time is defined by the interval of polymer supply to the surfaces of colloidal particles. Because the flux of polymer is given by Eq. [5], the time scale can be given simply by choosing the cross-sectional area which is involved in adsorption phenomena. In Fig. 7, δHe is plotted as a function of the interval of polymer supply, taking the representative area as 210 × 210 nm2 , where 210 nm is equivalent to the diameter of polymer molecules in solution estimated by viscometry. As is demonstrated in this figure, the decay of δHe with a time scale of a few seconds is illustrated. (iii) Setback of Flocculation In Fig. 8, we extract the results obtained for higher polymer concentrations. As addressed in this figure and in Fig. 3a, one of the more interesting characteristics found in the system of higher polymer concentrations is the slight setback of floccu-
153
FIG. 8. ln(N (t)/N (0)) vs t obtained for higher polymer concentrations extracted from Fig. 2.
lation which appears at the boundary between the first and the second stage. The setback means the breakup of bridges by an application of hydrodynamic shear. The bridges formed in the earlier stage can be considered to be involved with more segment-surface contacts. In other words, in the initial short period when most portions of colloidal surfaces remain bare, it is relatively easy to find appropriate segmentsurface contacts to form the anchors of bridges. However, in the later stage when the surface becomes relatively crowded, it also becomes relatively difficult to find stable contacts for the formation of bridges due to hindrance by preadsorbed polymers. In this situation, bridges are formed in an unstable state with fewer segment-surface contacts. This results in the breakup of bridges, which is seen as a setback of flocculation. It is interesting that the time scale of the setback is a few seconds which corresponds to the characteristic time of δHe decay. However, it is much shorter than the characteristic time of the quenching of polymer adsorption reported for another system (13–16). 6. CONCLUSIONS
Initial stage dynamics of bridging flocculation of PSL particles with PEO were precisely monitored by the particle-counting technique. Flocculation experiments were performed in a turbulent flow generated by an end-over-end rotation apparatus. The obtained results shed light not only on the kinetics of flocculation but also on the kinetics of formation of adsorbing polymer layers, both of which depend strongly on the rate of polymer supply. FIG. 7. δHe as a function of interval polymer supply toward the colloidal surface with considered area cross section of polymer coil (h) KCl = 1 × 10−2 , (d) KCl = 1.0 × 10−4 .
(1) The effective thickness of the adsorbed layer of PEO on the PSL particle was expressed as a function of the rate of
154
ADACHI AND WADA
polymer supply to the colloidal surface. The result suggested relaxation from a solution state to an adsorbed state with a time scale of a few seconds. (2) A slight setback of flocculation was confirmed for the system of higher polymer concentrations. The time scale involved in this relaxation again turned out to be a few seconds. (3) The ultimate degree of flocculation reached a maximum at Cp = 1.0 ppm. The decrease in the region of lower Cp was interpreted as a result of the elimination of bare surfaces by the spread of the polymer which arrived earlier at the surface. ACKNOWLEDGMENTS This work was partly funded by a Grant-in-Aid for Scientific Research (0946105) and a General Research Grant of the Nestle Science Promotion Committee.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
Ruehrwein, R. A., and Ward, D. W., Soil Sci. 73, 485 (1952). La Mer, V. K., and Healy, T. W., Rev. Pure Appl. Chem. 13, 112 (1963). Fleer, G. J., and Lyklema, J., J. Colloid Interface Sci. 52, 228 (1974). Napper, D. H., “Polymeric Stabilization of Colloidal Dispersions” Academic Press, London, 1983. Scheutjens, J. M. H. M., and Fleer, G. J., Macromolecules 18, 1882 (1985). De Genne, P. G., Macromolecules 15, 492 (1982). Gregory, J., Colloids Surf. 31, 231 (1988). Adachi, Y., Cohen Stuart, M. A., and Fokkink, R., J. Colloid Interface Sci. 165, 310 (1994).
9. Adachi, Y., Cohen Stuart, M. A., and Fokkink, R., J. Colloid Interface Sci. 167, 346 (1994). 10. Adachi, Y., Adv. Colloid Interface Sci. 1, 56 (1995). 11. Adachi, Y., and Matsumoto, T., Colloids Surf. A 113, 229 (1996). 12. Matsumoto, T., and Adachi, Y., J. Colloid Interface Sci. 204, 328 (1998). 13. Buijs, J., Van den Berg, P. A. W., Lichtenbelt, J. W. Th., Norde, W., and Lyklema, J., J. Colloid Interface Sci. 178, 594 (1996). 14. Pefferkorn, E., and Elaissari, A., J. Colloid Interface Sci. 138, 187 (1990). 15. Van Eijk, M. C. P., and Cohen Stuart, M. A., Langmuir 13, 5447 (1997). 16. Zhu, P. W., and Napper, D. H., J. Colloid Interface Sci. 214, 389 (1999). 17. Pelssers, E. G. M., Cohen Stuart, M. A., and Fleer, G. J., J. Chem. Soc., Faraday Trans. I 86, 1355 (1990). 18. Ash, S. G., and Clayfield, E. J., J. Colloid Interface Sci. 55, 645 (1976). 19. Kobayashi, M., Adachi, Y., and Ooi, S., Langmuir 15, 4351 (1999). 20. Kobayashi, M., and Adachi, Y., Nogyo Doboku Gakkai Ronbunshu 191, 111 (1998). 21. van de Ven, T. G. M., and Mason, S. G., Colloid Polym. Sci. 255, 468 (1977). 22. Dijt, J. C., Cohen Stuart, M. A., Hofman, J. E., and Fleer, G. J., Colloids Surf. A 51, 141 (1990). 23. Kato, T., Nakamura, K., Kawaguchi, M., and Takahashi, A., Polym. J. 13, 103 (1981). 24. Perkins, T. T., Smith, D. E., and Chu, S., Science 276, 2016 (1997). 25. Boils, D., and Hair, L., J. Colloid Interface Sci. 157, 19 (1993). 26. Israelachvili, J. N., Tandon, R. K., and White, L. R., J. Colloid Interface Sci. 78, 430 (1980). 27. Klein, J., and Luckham, P., Nature 300, 429 (1982). 28. Killmann, E., and Sapuntzjis, P., Colloids Surf. A 86, 229 (1994). 29. Polverari, M., and van de Ven, T. G. M., Colloids Surf. A 86, 209 (1994). 30. Cohen Stuart, M. A., Waajen, F. H. W. H., Cosgrove, T., Vincent, B., and Crowley, T. L., Macromolecules 17, 1825 (1984). 31. van der Beek, G. P., and Cohen Stuart, M. A., J. Phys. F. 49, 1449 (1988).
Initial Stage Dynamics of Bridging Flocculation of Polystyrene Latex Spheres with Polyethylene Oxide Y. Adachi1 and T. Wada Institute of Agricultural and Forest Engineering, Tsukuba University, Tsukuba-shi, Ibaraki 305-8572, Japan Received January 18, 2000; accepted May 8, 2000
The kinetics of bridging flocculation of polystyrene latex (PSL) particles induced by addition of excess polyethylene oxide (PEO) in the initial stage was studied using standardized mixing flow generated in an end-over-end rotation apparatus. To clarify the effect of the rate of polymer supply, flocculation experiments were performed by changing polymer concentration (Cp ). As was found in previous investigation, the progress of flocculation is divided into two stages. The first stage is characterized by an enhancement of the rate of flocculation by polymer addition. The increase in polymer concentration results in a higher enhancement but in a shorter duration for this stage. In the second stage, the flocculation is essentially stopped due to the appearance of steric stabilization. It was found that the ultimate degree of flocculation goes through a maximum against Cp . That is, when Cp > = 1.0 ppm, the ultimate degree of flocculation decreases with increased Cp . In this region, a clear crossover from the first stage to the second stage was observed. In the extreme case, evidence of a slight setback of flocculation was confirmed, which implies the breakup of metastable bridges by the application of additional fluid shear. When Cp < = 1.0 ppm, the ultimate degree of flocculation decreases with decreased Cp . The crossover from the first stage to the second stage appears more gradual at lower Cp . These results were observed irrespective of ionic strength. This result was interpreted as the elimination of a bare surface due to the spreading of a steric layer of adsorbed polymer. The characteristic time for reconformation of the polymer at a bare colloidal surface was estimated to be a few seconds. ° C 2000
Academic Press
Key Words: bridging flocculation; polystyrene latex; polyethylene oxide; standardized mixing flow; polymer adsorption; dynamics of polymer at surface.
1. INTRODUCTION
Flocculation of colloidal particles is fundamental to many industrial processes and to environmental science. It is well known that the addition of a dissolving polymer with an affinity for the surface of colloidal particles dramatically influences the stability of colloidal dispersion. That is, when a polymer chain attaches to more than two particles at the same time, the chain will act as a 1
To whom correspondence should be addressed.
0021-9797/00 $35.00
C 2000 by Academic Press Copyright ° All rights of reproduction in any form reserved.
bridging material and induce bridging flocculation (1–3, 17, 18). When a dense layer of adsorbed polymers is formed around the colloidal particles, it will act as a steric barrier against the approach of other colloidal particles, and thus the dispersed state of colloidal suspension is sterically protected (4–6). Since the formation of bridges between colloidal particles and the formation of steric layers around colloidal particles proceed simultaneously under conditions of turbulent mixing when colloidal particles and polymer flocculant are put together in the same solution, we propose that induction of bridging flocculation is competitive with polymer adsorption (7). This theory has been emphasized in our series of previous investigations in which the kinetics of flocculation induced by excess addition of polymer flocculant in the initial stage was extensively analyzed in terms of a collision process in the normalized mixing (8–10). As a result, we found that flocculation started very rapidly but slowed down abruptly after a while. Analysis of the rate of flocculation in the very initial period of incubation reveals the role of polymer conformation close to the dissolving state in the formation of bridges between colloidal particles. Using a polyelectrolyte as a flocculant, we have also elucidated the importance of polymer chain dynamics in the transient process of adsorption from a coil-like solution state to the flattened conformation of the adsorbed state on the bare surface of colloidal particles (11, 12). However, the experimental results obtained with polyelectrolyte are strongly influenced by electrostatic interactions. That is, adsorption is greatly enhanced by an electrostatic attractive force acting between the surfaces of colloidal particles and the charged segments, and the conformation and flexibility of polyelectrolytes change remarkably as a function of ionic strength. These factors raise other questions that are essentially important for the flocculation induced by polyelecrolytes. For analysis of polymer folding on a colloidal surface, it is beneficial to use data that are free of factors complicated by charged polymers. In the present study, we conducted a series of flocculation experiments with polystyrene latex (PSL) particles induced by the addition of polyethylene oxide (PEO). The experiments were designed to examine the effects of the rate of polymer supply and of the thickness of the electrical double layer of colloidal particles.
148
149
BRIDGING FLOCCULATION OF POLYSTYRENE LATEX
coagulation, β, as
2. RATE OF COLLISION IN A TURBULENT FLOW
The principle of analysis used in the present study is the same as that used in our previous series of investigations (9–12). It is based on the rate of collision, which is determined from the flow conditions of turbulent mixing. This can be obtained from measurement of the rate of rapid coagulation of well-defined colloidal particles. If we assume that (i) the hypothesis of isotropic turbulence proposed by Kolmogorov is applicable, (ii) the size of the collision radius is sufficiently small in comparison with the size of the smallest eddy of the turbulence, (iii) all particles move following fluid motion, (iv) all collisions lead to coagulation and coagulated flocs will never be broken up, (v) the effects of Brownian motion and sedimentation are negligibly small, (vi) the coagulation is in the early stage where most particles remain as singlets of radius a0 , we can derive the equation for the temporal variation of the number concentration of colloidal particles (19, 20), N (t), as r d N (t) 8πε = −αT (2a0 )3 N (t)2 , dt 15ν
γ =
(a0 + δHe )3 , αT a03
[1]
[4]
where δHe denotes the effective protruding length of attached polymer on the colloidal surface. Hence, if we measure the rate of flocculation with and without polymer flocculants under certain fixed conditions of mixing, we can estimate the value of δHe from β. The effective shear rate obtained from the rate of rapid coagulation can be also used to estimate the flux of polymer molecules onto the colloidal surface. Because the size of the dissolving polymer is small, the contribution due to Brownian motion should be taken into account. Assuming simple additivity of the contributions from Brownian motion and turbulent motion, we can derive the equation for the rate of polymer supply to a colloidal particle, Jp , as r
where ε and ν denote the rate of energy dissipation per unit mass and the kinematic viscosity of the fluid, respectively. Equation [1] implies that the coagulation in the turbulent flow can effectively be treated as a sort of shear coagulation with an effective shear rate r
β=
Jp = 4π (D0 + Dp )(a0 + ap )Np +
8π ε (a0 + ap )3 Np , [5] 15ν
where D, a, and N denote the diffusion constant, the radius, and the number concentration, and subscripts p and 0 denote the polymer and the colloidal particle, respectively. 3. EXPERIMENTAL
(a) Materials 4ε . 15νπ
[2]
αT is the correction factor that takes into account the effect of hydrodynamic interaction between colloidal particles when they collide. This value can be approximated by substituting Eq. [2] into the numerical result of van de Ven and Mason (21) as r µ Á ¶ 4ε 3 0.18 , a0 αT = A 36πµ 15πν
[3]
where A and µ denote the Hamaker constant and the viscosity of the fluid (19, 20). When the collision between colloidal particles with attached polymer takes place, the collision radius effectively increases, reflecting the protruding part of the attached polymer on the colloidal surface. Accordingly, the rate of flocculation will be enhanced due to the increased collision radius. Therefore, comparison of the rate of flocculation induced by addition of polymer flocculant with the rate of salt-induced rapid coagulation will provide information on the effective length of the protruding polymer. If we assume that the highly porous and permeable structure of a polymer chain eliminates the necessity of correcting for hydrodynamic interaction, we can write the ratio of the enhanced rate of flocculation to the rate of salt-induced rapid
Monodisperse polystyrene latex particles with a diameter of 1356 nm, denoted PSL1356 in our previous papers, were again used in the flocculation experiment. A commercially available PEO, with a nominal molecular weight of 5 × 106 g/mol (Aldrich Co. Ltd.), was used as flocculant. In the previous study (9), aggregate formation by the PEO made the preparation of a stable solution difficult. In the present study, an effort was made to avoid this effect by incubating the stock solution (100 ppm) in 1 × 10−4 M KCl solution for 1 day. To determine the size of the polymer in solution, the relative viscosity was measured as a function of polymer concentration. Analysis on the basis of the Einstein equation for viscosity and the nominal molecular weight gave the radius of the polymer as a0 = 105 nm. This was consistent with the prediction of the Mark–Houwink–Sakurada equation: [η] = 5.94 × 10−4 M0.66 W .
[6]
No distinctive difference in the viscosity data as a result of the change in salt concentration from 1 × 10−4 to 1 × 10−2 M was detected. (b) Procedure Flocculation was induced by the standard procedure of colloid mixing. The solution was mixed with the same amount
150
ADACHI AND WADA
of colloidal dispersion using a standard end-over-end rotation apparatus with a forked flask. Initially, one side was filled with 5.0 ml of colloidal dispersion and the other with an equal volume of electrolyte or PEO solution. Mixing was started by pouring the dispersion into the electrolyte or PEO solution. The mixed dispersion was then poured back into the emptied side. This operation was repeated periodically until the predetermined number of mixing steps (t) was reached. The duration of one step was fixed to 1 s throughout this investigation. The rate of flocculation was measured by counting the total number concentration of clusters, N (t), with a Coulter counter as a function of the number of mixing steps. During the monitoring, the flocculated dispersion was sucked up gently using a specially made pipette, poured into the pure electrolyte solution of the same ionic strength as the dispersion, and then diluted again with the isoton, which is the strong electrolyte prepared for the Coulter counter measurement.
4. RESULTS
The total number of clusters per unit volume for salt-induced coagulation is plotted as a function of the number of mixing steps in Fig. 1. The linear relation between ln(N (t)/N (0)) and t verifies the validity of the applied method. From the slope of this plot, the rate of energy dissipation, ε, of the applied mixing was estimated as 8.20 × 10−2 J s−1 kg−1 . Results of polymerinduced flocculation for differing ionic strengths are shown in Figs. 2 and 3. For a clear comparison between the rate of saltinduced coagulation and the rate of polymer-induced flocculation, the linear part of the first stage is magnified in Figs. 4 and 5.
FIG. 2. ln(N (t)/N (0)) vs t for flocculation induced with an application of PEO. The background solution of KCl is 1.0 × 10−4 M. N (0) = 7.7 × > 1 ppm). (b) 107 (1/cm3 ). (a) The results for higher polymer concentration (Cp = The result for lower polymer concentration (Cp < 1 ppm). The solid line rep= resents the regression line of the result of salt-induced coagulation taken from Fig. 1. Cp = (+) 0.25 ppm, (3) 0.5 ppm, (j) 1 ppm, (s) 2 ppm, (m) 4 ppm, (∗) 8 ppm.
5. DISCUSSION
FIG. 1. Temporal variation of the total number of clusters per unit volume for salt-induced coagulation as a function of the number of mixing steps (t). N (0) = 7.7 × 107 (1/cm3 ), [KCl] = 1.17 M.
A schematic diagram representing the pattern of temporal variation of the total number concentration of clusters, N (t), relative to the initial concentration, N (0), is presented in Fig. 6. As illustrated in this figure, flocculation progresses in two stages. The first stage is characterized by rapid flocculation. The initial rate of flocculation is strongly enhanced by the application of
BRIDGING FLOCCULATION OF POLYSTYRENE LATEX
151
FIG. 4. Magnification of ln(N (t)/N (0)) vs t in the beginning stage for KCl = 10−4 M.
phase to the colloidal surface by calculating the collision flux of polymer toward the surfaces of colloidal particles. Substitution of experimentally obtained data for the polymer size, by viscometry, and the rate of energy dissipation, by the rate of salt-induced coagulation, into Eq. [5] allows crude estimation of Jp . For Cp = 1.0 ppm, Jp is estimated at 22.1 PEO molecules/PSL particles/s, whereas saturated adsorption of the PEO onto PSL particles (0sat ) was reported as 0.5 mg/m2 (9), which corresponds to 347 PEO molecules/ PSL particle. The ratio 0sat /Jp is calculated as 15.7 s, which agrees with the duration of the first stage as estimated for Cp = 1.0 ppm. This agreement confirms the validity
> 1 ppm. KCl = 10−2 M FIG. 3. (a) ln(N (t)/N (0)) vs t for the case, CP = and N (0) = 7.7 × 107 (1/cm3 ). Symbols for each polymer concentration are the same as those used in Fig. 2. (b) ln(N (t)/N (0)) vs t for the case, CP < = 1 ppm. KCl = 10−2 M and N (0) = 7.7 × 107 (1/cm3 ).
PEO; however, soon after the first stage, flocculation abruptly comes to a halt, and the second stage, the establishment of steric stabilization by the adsorbed polymer, begins. In the following, we focus on three points to elucidate the dynamics of polymer adsorption and reconformation on the surfaces of colloidal particles. (i) Time Required to Establish Steric Stabilization We can confirm that the progress of the initial stage is limited by the hydrodynamic transportation of polymer from the bulk
FIG. 5. Magnification of ln(N (t)/N (0)) vs t in the beginning stage for KCl = 10−2 M.
152
ADACHI AND WADA
than that predicted only by the hydrodynamic transportation. This prediction agreed with the experimental results observed for lower Cp . In addition, a more gradual shift from the first stage to the second stage at lower Cp can be explained if we assume that the time scale of invasion is a few seconds. Because we could not find any differences with respect to ionic strength, we expect that the polymer layer formed by spreading is already thicker than 30 nm, which is the Debye reciprocal length for the experimental condition at the lower ionic strength (KCl = 1.0 × 10−4 M). This fact also means that the theory of polymer inactivation by the folding of the protruding chain into the inside of the electrical double layer proposed by Pelssers et al. (17) is not the case for our system. On the basis of the difference in the resulting layer thicknesses due to the means of polymer addition, Polverari and van de Ven (29) concluded that the adsorption of PEO onto PSL particles is kinetically controlled. This conclusion is qualitatively consistent with our findings. (ii) Effective Thickness of Polymer Layer
FIG. 6. Schematic diagram of the progress of flocculation with PEO.
of the analysis on the basis of hydrodynamic transportation. In addition, in the region of higher Cp (Cp > = 1.0 ppm), the first stage becomes shorter with increased Cp . From this result, we can conclude that the appearance of steric stabilization is limited by hydrodynamic transportation of the polymer toward the surface. This conclusion is the same as that clearly demonstrated with the flow reflectometoric technique (22) in which the rate of supply of PEO to the flat surface of a silicon wafer is strictly calculated. However, another source that contributes to stabilizing colloids can be found in the results at lower polymer concentrations (Cp < = 1.0 ppm). As was discussed under Results, the ultimate degree of flocculation was found to go through a maximum, i.e., the ultimate degree of flocculation decreased with decreased polymer concentration for Cp < = 1.0 ppm. In addition to the decrease in the ultimate degree of flocculation, the first stage is not sufficiently long to guarantee limitation by hydrodynamic transportation alone. Since these phenomena are commonly observed irrespective of ionic strength, stabilization due to the electrostatic interaction is denied. One possible explanation is the elimination of a bare surface due to the spread of polymers on the colloidal surface. That is, attached polymers that arrive earlier on the colloidal surface will flatten their conformation. Accordingly, the area of the “bare” surface that can accommodate newcomers will decrease and finally will be lost. In accordance with the decrease in the probability of finding bare surface, the probability of successful collision between colloidal particles is expected to decrease. The effect of invasion of the spread polymer is expected to shorten the duration of the first stage more
The effective length of the protruding polymer on the colloidal particle, δHe , can be calculated using the difference of the initial slopes indicated in Figs. 4 and 5 on the basis of Eq. [4]. In some cases, δHe calculated for lower polymer concentrations was estimated to be negative. This unrealistic result is due to neglecting to correct for the decrease of capture efficiency stemming from the hydrodynamic interaction between two colliding particles with this polymer layer. However, no exact answer is available for this correction. We simply skip this unrealistic case, and only the results with positive valules are indicated in Table 1. The value of δHe obtained for high Cp is larger than the diameter of PEO molecules determined by viscometry. The two reasons that can be considered so far are the extension of PEO molecules by fluid shear (24) and the formation of PEO aggregates (9, 25–27). For the former, it should be noted that the critical shear rate above which a polymer chain yields to the stretched form is much higher than the effective shear rate estimated using Eq. [2]. For the latter, although we are not able to deny completely its possibility, as was pointed out by our previous work, the time scale involved in the present study is much shorter than the time scale of hysteresis due to the formation of PEO aggregate observed in the surface force measurement (25–27). TABLE 1 Estimated Adsorbed Layer Thickness KCl 1 × 10−4 M
KCl 1 × 10−2 M
PEO (ppm)
β
δHe (nm)
β
δHe (nm)
0.25 0.5 1.0 2.0 4.0 8.0
1.7 2.9 5.7 10 14 18
— — 160 330 450 550
2.8 3.8 6.5 — 22 26
53 200 — 630 710
BRIDGING FLOCCULATION OF POLYSTYRENE LATEX
It should also be noted that Polverali and van de Ven (29) reported that hydrodynamic layer thickness decreased when the measurement was performed in the presence of PEO aggregate in the solution. Therefore, it is difficult to determine the effect of the formation of PEO aggregate. It is important and also interesting to compare the values of δHe with those obtained by previous researchers (23, 28–31). The available data were mostly obtained using hydrodynamic methods for PEO of lower molecular weight. Their measurements were performed in the final state of adsorption, i.e., after sufficiently long periods of incubation. The estimate based on extension to the molecular weight of the polymer used in the present study is always smaller than our maximum value, which was obtained with the highest polymer concentration. The reason is probably that our δHe data reflect the collision radius in the transient state, while the reported values are those for the final state. It is of interest to express δHe as a function of characteristic time involved in adsorption. One important characteristic time is defined by the interval of polymer supply to the surfaces of colloidal particles. Because the flux of polymer is given by Eq. [5], the time scale can be given simply by choosing the cross-sectional area which is involved in adsorption phenomena. In Fig. 7, δHe is plotted as a function of the interval of polymer supply, taking the representative area as 210 × 210 nm2 , where 210 nm is equivalent to the diameter of polymer molecules in solution estimated by viscometry. As is demonstrated in this figure, the decay of δHe with a time scale of a few seconds is illustrated. (iii) Setback of Flocculation In Fig. 8, we extract the results obtained for higher polymer concentrations. As addressed in this figure and in Fig. 3a, one of the more interesting characteristics found in the system of higher polymer concentrations is the slight setback of floccu-
153
FIG. 8. ln(N (t)/N (0)) vs t obtained for higher polymer concentrations extracted from Fig. 2.
lation which appears at the boundary between the first and the second stage. The setback means the breakup of bridges by an application of hydrodynamic shear. The bridges formed in the earlier stage can be considered to be involved with more segment-surface contacts. In other words, in the initial short period when most portions of colloidal surfaces remain bare, it is relatively easy to find appropriate segmentsurface contacts to form the anchors of bridges. However, in the later stage when the surface becomes relatively crowded, it also becomes relatively difficult to find stable contacts for the formation of bridges due to hindrance by preadsorbed polymers. In this situation, bridges are formed in an unstable state with fewer segment-surface contacts. This results in the breakup of bridges, which is seen as a setback of flocculation. It is interesting that the time scale of the setback is a few seconds which corresponds to the characteristic time of δHe decay. However, it is much shorter than the characteristic time of the quenching of polymer adsorption reported for another system (13–16). 6. CONCLUSIONS
Initial stage dynamics of bridging flocculation of PSL particles with PEO were precisely monitored by the particle-counting technique. Flocculation experiments were performed in a turbulent flow generated by an end-over-end rotation apparatus. The obtained results shed light not only on the kinetics of flocculation but also on the kinetics of formation of adsorbing polymer layers, both of which depend strongly on the rate of polymer supply. FIG. 7. δHe as a function of interval polymer supply toward the colloidal surface with considered area cross section of polymer coil (h) KCl = 1 × 10−2 , (d) KCl = 1.0 × 10−4 .
(1) The effective thickness of the adsorbed layer of PEO on the PSL particle was expressed as a function of the rate of
154
ADACHI AND WADA
polymer supply to the colloidal surface. The result suggested relaxation from a solution state to an adsorbed state with a time scale of a few seconds. (2) A slight setback of flocculation was confirmed for the system of higher polymer concentrations. The time scale involved in this relaxation again turned out to be a few seconds. (3) The ultimate degree of flocculation reached a maximum at Cp = 1.0 ppm. The decrease in the region of lower Cp was interpreted as a result of the elimination of bare surfaces by the spread of the polymer which arrived earlier at the surface. ACKNOWLEDGMENTS This work was partly funded by a Grant-in-Aid for Scientific Research (0946105) and a General Research Grant of the Nestle Science Promotion Committee.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
Ruehrwein, R. A., and Ward, D. W., Soil Sci. 73, 485 (1952). La Mer, V. K., and Healy, T. W., Rev. Pure Appl. Chem. 13, 112 (1963). Fleer, G. J., and Lyklema, J., J. Colloid Interface Sci. 52, 228 (1974). Napper, D. H., “Polymeric Stabilization of Colloidal Dispersions” Academic Press, London, 1983. Scheutjens, J. M. H. M., and Fleer, G. J., Macromolecules 18, 1882 (1985). De Genne, P. G., Macromolecules 15, 492 (1982). Gregory, J., Colloids Surf. 31, 231 (1988). Adachi, Y., Cohen Stuart, M. A., and Fokkink, R., J. Colloid Interface Sci. 165, 310 (1994).
9. Adachi, Y., Cohen Stuart, M. A., and Fokkink, R., J. Colloid Interface Sci. 167, 346 (1994). 10. Adachi, Y., Adv. Colloid Interface Sci. 1, 56 (1995). 11. Adachi, Y., and Matsumoto, T., Colloids Surf. A 113, 229 (1996). 12. Matsumoto, T., and Adachi, Y., J. Colloid Interface Sci. 204, 328 (1998). 13. Buijs, J., Van den Berg, P. A. W., Lichtenbelt, J. W. Th., Norde, W., and Lyklema, J., J. Colloid Interface Sci. 178, 594 (1996). 14. Pefferkorn, E., and Elaissari, A., J. Colloid Interface Sci. 138, 187 (1990). 15. Van Eijk, M. C. P., and Cohen Stuart, M. A., Langmuir 13, 5447 (1997). 16. Zhu, P. W., and Napper, D. H., J. Colloid Interface Sci. 214, 389 (1999). 17. Pelssers, E. G. M., Cohen Stuart, M. A., and Fleer, G. J., J. Chem. Soc., Faraday Trans. I 86, 1355 (1990). 18. Ash, S. G., and Clayfield, E. J., J. Colloid Interface Sci. 55, 645 (1976). 19. Kobayashi, M., Adachi, Y., and Ooi, S., Langmuir 15, 4351 (1999). 20. Kobayashi, M., and Adachi, Y., Nogyo Doboku Gakkai Ronbunshu 191, 111 (1998). 21. van de Ven, T. G. M., and Mason, S. G., Colloid Polym. Sci. 255, 468 (1977). 22. Dijt, J. C., Cohen Stuart, M. A., Hofman, J. E., and Fleer, G. J., Colloids Surf. A 51, 141 (1990). 23. Kato, T., Nakamura, K., Kawaguchi, M., and Takahashi, A., Polym. J. 13, 103 (1981). 24. Perkins, T. T., Smith, D. E., and Chu, S., Science 276, 2016 (1997). 25. Boils, D., and Hair, L., J. Colloid Interface Sci. 157, 19 (1993). 26. Israelachvili, J. N., Tandon, R. K., and White, L. R., J. Colloid Interface Sci. 78, 430 (1980). 27. Klein, J., and Luckham, P., Nature 300, 429 (1982). 28. Killmann, E., and Sapuntzjis, P., Colloids Surf. A 86, 229 (1994). 29. Polverari, M., and van de Ven, T. G. M., Colloids Surf. A 86, 209 (1994). 30. Cohen Stuart, M. A., Waajen, F. H. W. H., Cosgrove, T., Vincent, B., and Crowley, T. L., Macromolecules 17, 1825 (1984). 31. van der Beek, G. P., and Cohen Stuart, M. A., J. Phys. F. 49, 1449 (1988).