Coagulation rate of silica dispersions investigated by single-particle optical sizing

COLLOIDS AND Colloidsand Surfaces A: Physieochemicaland EngineeringAspects106(1996) 213-221

ELSEVIER

A

SURFACES

Coagulation rate of silica dispersions investigated by single-particle optical sizing Sandor Barany a,., Martien A. Cohen Stuart b, Gerard J. Fleer b a University of Miskolc, 3515 Miskolc-Egyetemvaros, Hungary b Agricultural University, Wageningen, Dreijenplein 6, 6703 HB Wageningen, The Netherlands

Received 16 June 1995; accepted 10 August 1995

Abstract

Using a single-particle optical sizer, the kinetics of the rapid coagulation of monodisperse silica particles of radius 265 nm in KC1 and CaCI2 solutions was studied. The rate constant kll of the process is 1.7 × 10 12cm 3 s 1, which is three times smaller than the Smoluchowski value for the overall rate constant. This discrepancy is explained by the retardation effect of viscous interactions and the existence of long-range attractive forces between particles. For suspensions with an initial particle concentration between 2.5 × 10s and 2.4 x 10 9 c m -3, the kll values are independent of the pH value (in the range 7-10) and of the particle number concentration. The ratio between the coagulation concentrations of monovalent and bivalent counterions is 50, under both perikinetic and orthokinetic conditions, which indicates that this silica suspension is electrostatically stabilized. This is in contrast to literature data for very small S i O 2 particles. We propose that the so-called "structural" forces are much less important for large silica particles. Keywords: Coagulation rate; Dispersions; Silica; Single-particle optical sizing

1. Introduction In the classical theory of rapid coagulation developed by Smoluchowski [ 13, every collision between colloiding particles is assumed to be effective when the particles have approached one another to within a distance at which the attraction forces become dominant. The process is considered to be diffusion controlled. The main assumptions of the original theory are: (1) the primary particles are monodisperse, (2) the rate of coagulation for different aggregation steps is equal, even though the size and morphology of the aggregates are different, (3) the binary collisions between particles (aggregates) are considered, (4) the aggregation

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process is irreversible, and (5) only the steady-state process is taken into account. Several methods have been used for determining the rate constants of aggregation: ultramicroscopy [23, flow ultramicroscopy [33, flow ultramicroscopy in combination with single-particle light scattering [4], single-particle optical sizing [5], photon correlation spectroscopy [6], dynamic light scattering [7], etc. The kinetics of aggregation of different colloidal systems (Au, Se, AgI, SiO2, Fe203, kaolinite, graphitized carbon, latex particles, etc.) has been investigated. Some of the data are summarized in Refs. [8] and [9]. The experimentally determined overall rate constant of fast aggregation (i.e. at high electrolyte concentrations) is usually found to be less than (approximately half of) the theoretically predicted value of Von Smoluchowski theory, except for

214

S. Barany et al./Colloids Surfaces A: Physicochem. Eng. Aspects 106 (1996) 213-221

some old data on the coagulation of gold particles [2]. This deviation has been explained by the influence of hydrodynamic interactions and longrange van der Waals forces [10-13] or by a reversibility of the aggregation process [14,15]. There are few data on the kinetics of aggregation of silica particles. However, dispersions of SiOz play an important role in many technological processes. Ludwig and Peschel [6,7] determined the rate constants for rapid and slow coagulation of SiO 2 particles of different sizes in the presence of LiC1 and CsC1 using dynamic light scattering and photon correlation spectroscopy. The smallest particles were shown to be the most stable, and for large particles the aggregation in the secondary minimum should be taken into account. Some authors consider that SiO 2 dispersions are electrostatically stabilized systems [16], whereas others stress the essential role of "structural" forces (hydration forces) in the mechanism of the stabilization of sols and suspensions of silica or quartz [17,18]. Obviously, this mechanism could be different for different pH values of the medium, i.e. for particles with different surface charge density, We describe below the results of a study of the kinetics of rapid coagulation ofmonodisperse silica suspensions in electrolyte solutions at different pH values and different initial number concentrations. We used the single-particle optical sizer (SPOS) developed in the Laboratory of Physical and Colloid Chemistry of the Agricultural University of Wageningen [5,8].

and [21]. For the perikinetic experiments, a small bottle (diameter 2.5 cm, height 4.7 c m ) w a s filled with 5.0 ml of colloidal dispersion, and another with an equal volume of electrolyte solution. Coagulation was induced by simply pouring the solution into the colloidal dispersion and turning the mixture end-over-end just once. The mixture was then allowed to stand for a given period. In the orthokinetic experiments we used the procedure described in Ref. [21 ]: the mixed dispersion as described above was poured rapidly into an empty bottle of the same size. This operation was repeated 20 times, i.e. until the mentioned number of mixing steps was reached. After the last mixing the sample was kept at rest for 1 min and then diluted into a 20-fold volume of distilled water, in order to "freeze" the size distribution of aggregates. The rates of coagulation were measured by counting the total number of particles as well as the number of singlets, doublets and triplets (we have not determined larger aggregates) as a function of time using the SPOS method. This instrument counts the number of particles of different size in a colloidal dispersion. The principles of the operation and performance of the SPOS have been described in detail elsewhere [5,8].

3. Results A typical size distribution of an aggregated SiO2 dispersion is shown in Fig. 1. Before introducing 300

2. E x p e r i m e n t a l

Monodisperse silica particles were prepared by hydrolysis of a solution of Si(OEt)4 according to the method described in Ref. [19]. The particle radius was 265 nm, and the point of zero charge was at pH 2.3 from titration experiments. These particles have a rather high surface charge density due to a somewhat porous gel-like surface structure. Potassium and calcium chloride were used as the coagulating electrolyte. Coagulation experi . ments were performed in both perikinetic and orthokinetic regimes, using the methods of mixing suspension and salt solution described in Refs. [20]

~

250

~

~

oinqle~s

2oo

~ z

150 lOO 50 0 -5o

.

.

do.b~e~s

~ 0 .

2oo

~

~ 60o 8o0 tter~,q i..... ity ~ .... 4oo

t 000

Fig. 1. Size distribution of singlets, doublets and triplets in a s i 0 2 suspension at a KC1 content of 0.75 M, 1 h after the start

of coagulation. Perikineticregime.

S. Barany et al./Colloids Surfaces A: Physicochem. Eng. Aspects 106 (1996) 213-221

the suspension into the flow system it was filtrated from dust, such that the number of dust particles did not usually exceed 2-3% (in exceptional cases 5%) of the number of particles to be measured. In Fig. 2 the change of the total number of particles per cm 3 vs. time as well as the time evolution of the number of singlets, doublets and triplets in 0.75 M KC1 are shown. Our experiments show that the transition from slow to rapid coagulation occurs at a KC1 concentration of approximately 0.5 M (see below), and hence the salt content of 0.75 M was adequate to induce fast aggregation, The early stages of aggregation can be treated as a set of consecutive reactions, and the change in the concentration of singlets, doublets and triplets is described by the following set of differential equations [9]: d N ~ = _kI1N2_k12NIN2_k13N1N3 dt

(1)

215

dN2 1 dt - - 2 k11N~ -k12N1N2- k22N~- k23N2N3 (2) dN3 dt -

klzN1Nz_k13N1N 3 _kz3N2N3_k33N23 (3)

where N1, N2 and N 3 are the number concentrations of singlets, doublets and triplets, respectively, and t is the time. In Eqs. (1)-(3) we have ignored aggregates bigger than triplets. These non-linear differential equations cannot be solved analytically, but the experimental data (Nx, N2, N3 as a function of time) can be fitted to a numerical integration of the equations. Using this, the fitting parameters (kH, k22, etc.) can be found by iteration [4,8]. A much simpler way to determine the overall rate constant kij is to assume that all the rate constants are equal to kH. Such an assumption

N crn-3

x.

109

8

__x

•

A~?

4 ~¢~.4.~ ~

nglets doublets

trivets 108

total

~

'

'

10

30

x J

60

--

t . rain

Fig. 2. Time evolution of the number of singlets, doublets and triplets, and of the total number of particles in an SiO 2 suspension at 0.75 M KCI. pH = 8.0, No = 2.4 x 109 cm -3. Perikinetic regime.

216

S.

Barany et al./Colloids Surfaces A: Physicochern. Eng. Aspects 106 (1996) 213-221

was made by Von Smoluchowski, who then found for the decrease of the primary particles vs. time: N1 =No(1 + k11Nof/2) -2 (4)

polystyrene latex [9,24-27], etc. Our experimental value of kit is three times smaller than Smoluchowski's value for the overall constant of rapid perikinetic coagulation defined by dN/dt = - k s N 2, where N is the total particle concentration. This rate constant has the value

For the case of rapid coagulation of polystyrene lattices it was shown that the errors introduced by using the Smoluchowski equation are very small, of the order of 2% [5,8]. For the experiment presented in Fig. 2, we plotted (N0/N1) t / 2 - 1 as a function of (1~2)Not in Fig. 3. It can be seen that the experimental data indeed follow linear behaviour according to the Smoluchowski equation. The calculated value of kit is 1.7 x 10 12 cm 3 s - t which is very close to the rate constant (1.9 x 10 t2 cm 3 s-~) of rapid coagulation of SiOz particles with d = 180 nm as determined by photon correlation spectroscopy [6]. Our k~l value is also in good agreement with the experimentally determined rate constants for other colloidal particles: (1.6-2.5) x 10-x2 cm -3 s 1 for AgI [22], (0.5-2.0) x 10 -12 cm 3 s ~ for Fe203 [23], (1.3-3.4) x 10-12cm3s t for

ks = 4kbT/3tl (=5.43 x 1 0 - t 2 c m 3 s - t i n water at T = 2 9 3 K ) ( 5 ) where ~/is the viscosity of the medium, and kb is the Boltzmann constant. This discrepancy may be due to viscous (hydrodynamic) interactions and/or to long-range attractive forces. McGown and Parfitt [10] took into consideration the effect of long-range attractive forces on the stability ratio W (the ratio between the most rapid rate of coagulation and the actual, slower rate). Derjaguin and Muller [11] and later Spielman [12] developed a method to calculate the reduction in coagulation rate (which can be characterized a s f = kr/k s, where k r is the calculated rate constant without

( No / NI)I121

1.2

1,0

0.8

o

o

0.2

I

i

20

40

_ _

/

60

_

i

80

1/2 Not 10-10 s cm-3

F i g 3 Plot of (No/N1) 1/2, where N1 is the number of singlets at time t and N o is that at t = 0, against Not/2, according to E q (4) The d a t a were t a k e n from Fig. 2.

s. Baranyet al./ColloidsSurfacesA: Physicochem.Eng. Aspects106 (1996) 213-221 and ks that with retardation effects) as a result of viscous interactions and long-range attractive forces. It was shown that viscous effects can lower the coagulation rate by almost an order of magnitude, and that Hamaker constants A estimated from measured coagulation rates under negligible repulsion can be greatly in error if viscous interactions are ignored. According to Spielman [12], the ratio W/Wvisc between stability coefficients without and with viscous interactions W/W,,isc typically ranges from 0.6 to 0.7 for A/6kT between 1 and 20. However, there is a much greater effect of viscous interactions in the presence of an energy maximum; in this case W/Wviscranges from 0.1 to 0.15 [12]. Similar results were obtained by Honig et al. [ 13] who also evaluated the hydrodynamic interaction between colloidal particles, but improved on the previous treatment by Derjaguin and Muller [11] by numerical integration of the complete Hamaker equation over a wide range of A values, It was shown that the relative difference between the dimensionless rate constants, with and without taking hydrodynamic interaction into account, is larger for smaller Hamaker constant values. The numerical result of Honig et al. [ 13 ] and those of Spielman [12] are practically the same. According to Refs. [ 1 1 - 1 3 ] the coefficient of retardation f can be calculated as i

[3(u)H-Ze vt~m/kbr dH f=

2,

(6)

i fl(u)H--2eVAOt)/kbr d H 2a The hydrodynamic correction term [l(u) is represented by

fl(u)-

6u2+ 1 3 u + 2 6u2+ 4u

(7)

where u is the dimensionless distance between the particles, defined by u=(H--2a)/a (8) In Eq. (6), Vt is the energy of interaction of two

217

spherical particles of radius a, VA is the attractive potential energy, and H is the shortest distance between two spherical particles. The literature values for the Hamaker constants A for SiO2 range between 2 x 10 -21 and 8 x 10 -21 J [6], so it is useful to compare the effect of hydrodynamic interaction and long-range attractive forces for two limiting values of A. We c h o s e 10 -21 J and 5 x 10 -21 J. Calculations using Eqs. (6), (8) and (10) of Ref. [ 13] show a decrease in the constant of rapid coagulation in comparison with the Smoluchowski value; for A = 5 x 10 -21 J the theory gives a decrease in the coagulation constant by a factor of 1.9 (kll = 2.86 x 10 -12 cm 3 s 1), whereas for A = 10 -21 J this becomes a factor of 2.3 (kll--2.36 x 10 12 cm 3 s-1). These magnitudes are closer to the value predicted from Eq. (5), but are still too low by a factor of about 2. This discrepancy could be caused by the influence of structural forces owing to the presence of adherent hydration layers on the surface, which would create a weak repulsion between SiO2 particles with compressed electrical double layers. As shown by Spielman [ t 2 ] , even a small repulsion can have a strong effect on the value of f. Another explanation for the faster experimental rate could be that the process of coagulation of the silica suspension is not purely perikinetic: during the initial mixing of the suspension with an electrolyte solution some orthokinetic effects might have been introduced. We have also investigated the effect of the initial number of particles and of the pH on the rate constant. Our experiments show that for suspensions with N O= 2.5 x 108, 5.5 x l0 s and 2.4 x 109 c m 3, respectively, the coagulation rate constant is in the range (1.7-1.9) x 10 -12 cm 3 s -1. Hence, it is practically independent of the initial particle number, as should be expected from Von Smoluchowski theory. Similar behaviour was found by Lichtenfeld et al. [20] for the rapid coagulation of poly(vinyl acetate) particles in the range No=(0.3-2.6) x 108 cm 3. However, in Ref. [28] it was reported that the coagulation rate constant depended on the initial particle concentration, and that the aggregation constant increased with N O. No reasonable explanation was given.

218

S. Barany et aL/Colloids Surfaces A: Physicoehem. Eng. Aspects 106 (1996) 213-221

It is of interest to compare the coagulation values of electrolytes with counterions of different charge to obtain insight into the mechanism of stabilization and coagulation of this particular system, Results for the aggregation of SiO 2 suspensions in the presence of CaC12 are given in Fig. 4. The time dependence of the total number of particles and that of singlets and doublets was found to proceed similarly to that in the presence of KC1 (Fig. 2). The only difference is that the total number of particles decreases faster with increasing electrolyte concentration than in the case of KC1. Fig. 5 shows the change in the total number of particles as a function of electrolyte concentration at different time intervals after mixing the S i O 2 suspensions with salt solutions. After 10 min we only have weak coagulation, even in a solution as concentrated as 1 M KC1 or higher. After 30 min there is much faster aggregation, and after 60 min or more the total number of particles no longer depends on the electrolyte concentration, provided this is above a threshold value of about 0.5 M. This is the critical coagulation concentration (ccc) of KC1, i.e. the electrolyte concentration at which

the transition from slow to rapid coagulation occurs. It was also shown that this transition is sharper in the presence of divalent counterions: the decrease in particle concentration takes place within a relatively narrow CaC12 concentration interval. The ccc of calcium chloride (1 h or more after mixing) is 10 mmol/1-1. This means that the ratio between the ccc of KC1 and CaC12 is approximately 50, which is close to the theoretical ratio (z6= 64) predicted by DLVO theory for the concentration coagulation of highly charged colloidal particles. It follows that the silica particles are stabilized electrostatically, and that their coagulation occurs according to the classical picture. Several authors [-17,18,29] have suggested that silica and quartz (as well as other oxide suspensions at their point of zero surface charge) are stabilized mainly by structural (hydration) forces, and that aggregation only occurs when the surface hydration layers are destroyed. The latter is achieved by the addition of electrolytes in high concentration, by dehydrating agents (for example alcohols), or by heating. The S i O 2 suspension under consideration reveals different behaviour. At pH 2.5, which is near to the point of zero charge, the majority (about 70%) of particles are aggregated, and the

N • 10 9

o-n-3

÷

2 /

+

o

~ o

/

~

singlets doublets

* ~

108 20

z,O

60

80

100

t , rnin.

Fig. 4. Time evolution of the number of singlets and doublets, and of the total number of particles in a SiO 2 suspension at 0.01 M CaCI2. Perikinetic coagulation.

S. Barany et al./Colloids Surfaces A: Physicochem. Eng. Aspects 106 (1996) 213-221

219

N cm-3

4 c ~ ~ 2

" ~

.

~

° ' - - - - - - - - - . - . . o ~ o

40 rain.

~

~

60 rnin.

o

o

--~

o 120 rain.

108

I

i

0,5

~,0

i

1,5

•

Cl~cl (M)

Fig. 5. Dependence of the total number of particles in a SiO 2 suspension on KC1 concentration, at different time intervals after the start of aggregation. Perikinetic regime.

shape of the curves giving the particle number as a function of KC1 concentration is different from that observed for pH 7 or pH 10 (Fig. 6). At pH 7 the total number of particles remains constant after an initial slight drop (which corresponds to a factor of approximately 1.5 in particle number). The ccc of KC1 decreases from 0.5 M (in the range pH 7-10) to 0.3 M. At pH 2.5 the coagulation occurs through a HC1/KC1 electrolyte mixture, Consequently, at pH 2.5 strong stabilization of SiOa suspensions by structural forces does not occur. It seems that for these large particles, where the attractive forces are relatively strong and operate at long distances, the structural forces are weak and unable to stabilize the system. However, for dispersions with small hydrophilic particles these forces could become a much stronger stabilizing factor. This consideration might explain the discrepancies between the literature data and our results: according to some literature data [-16-18] SiO2 sols are stable in acidic media, whereas our system with much larger particles was found to aggregate strongly,

We finally comment on the coagulation under orthokinetic conditions. Shear affects the aggregation owing to the action of several factors, such as bulk convection, Brownian diffusion, hydrodynamic interactions, etc. The kinetics of coagulation of polystyrene latices in turbulent mixing has been analysed recently by Adachi et al. [30]. Here we note only that the simultaneous (and according to some authors additive) effect of these factors leads to a substantial decrease of the stability of the system with aggregation. Repeatedly pouring a dispersion into an empty bottle and back leads to a steeper decrease of the particle number vs. electrolyte concentration in comparison with the perikinetic process, and the aggregation takes place at lower salt content (Fig. 7). The orthokinetic ccc values of KC1 and CaC12 are 0.3 tool 1-1 and 6 mmol 1-1, respectively, which is 40% lower than under perikinetic conditions, but the ratio between these two coagulation thresholds remains the same (= 50). Hence, shear affects the rate of coagulation, but not the mechanism.

S. Barany et al./Colloids Surfaces A. Physicochem. Eng. Aspects 106 (1996) 213-221

220

N .10B

era-3

o

o

,:,

~,

~

pH = 2,5

x

2

~

,

"

~

pH=lO

I

I

I

0,5

1,0

1,5

--

CKCI (M)

Fig. 6. Perikinetic coagulation of an SiO2 suspension by KC1, 100 min after the start of coagulation at pH 2.5 and 10.

t

N .10 8

N. 108

cm-3

,~

8

o

10 6

\ 8 7

t,

\

o -..-._o

2

J

I

5

10

o

o----

l

J

I

15

2O

25 Ccact2

~o

6

o

o

~

.

mmol/I

o

t

i

i

i

0,2

0,4

0,8

1.2

t

CKCI , m o U I

Fig. 7. Dependence of the total number of particles in an SiO 2 suspension on KCI and CaCI2 concentration under orthokinetic conditions, pH 6.8. The time of mixing was 20 × 1.36 s, after which the dispersion was allowed to stand for 30 min (explanation in the Experimental section).

S. Barany et al./Colloids Surfaces A." Physicochem. Eng. Aspects 106 (1996) 213-221

Acknowledgements W e t h a n k M r . A.J. v a n d e r L i n d e for p r o v i d i n g the silica d i s p e r s i o n s , a n d M r . R. F o k k i n k for h e l p in u s i n g the S P O S i n s t r u m e n t . S.B. t h a n k s the

Commission of the European Community for f i n a n c i a l s u p p o r t of his f e l l o w s h i p at W a g e n i n g e n .

References

[13 M. Von Smoluchowski, Z. Phys. Chem., 92 (1917) 129. [2] R. Zsigmondy, Z. Phys. Chem., 92 (1917) 600. [3] N.M. Kudrayvtseva and B.V. Derjaguin, Colloid J. USSR, 25 (1963) 739. [4] N. Buske, H. Gedan, W. Katz, H. Lichtenfeld and H. Sonntag, Colloid Polym. Sci., 258 (1980) 1303. [5] E.G.M. Pelssers, M.A. Cohen Stuart and G.J. Fleer, J. Colloid Interface Sci., 137 (1990)350. [6] P. Ludwig and G. Peschel, Progr. Colloid Polym. Sci., 76 (1988) 42. [7] P. Ludwig and G. Peschel, Progr. Colloid Polym. Sci., 77 (1989) 146. [8] E.G.M. Pelssers, Single Particle Optical Sizing, Dissertation, Agricultural University Wageningen, 1988. [9] H. Gedan, H. Lichtenfeld, H. Sonntag and H. Krug, Colloids Surfaces, 11 (1984)199. [103 D.N.L. McGown and G.D. Parfitt, J. Phys. Chem., 71 (1967) 449. [11] B.V. Derjaguin and V.M. Muller, Dokl. Akad. Nauk SSSR, 176 (1967) 869. [12] L.A. Spielman, J. Colloid Interface Sci., 33 (1970) 562.

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[ 13] E.P. Honig, G.J. Robertson and P.H. Wiersema, J. Colloid Interface Sci., 36 (1971) 97. [14] B.V. Derjaguin and N.M. Kndrayvtseva, Colloid J. USSR, 26 (1964) 61. [15] H. Sonntag and V.N. Shilov, Colloids Surfaces, 20 (1986) 303. [16] N.A. Shabanova, V.V. Popov and Yu.G. Frolov, Colloid J. USSR, 46 (1984)986. [ 17] Yu.M. Chernoberezhkii, E.V. Golikova and V.I. Kutchuk, Vestn. Leningr. Univ., 1 (1987) 38. [18] H. Yotsumoto and R.-H. Yoon, J. Colloid Interface Sci., 157 (1993) 434. [19] W. Str6ber, A. Fink and E. Bohn, J. Colloid Interface Sci., 165 (1994) 62. [20] H. Lichtenfeld, H. Sonntag and Ch. Duff, Colloids Surfaces, 54 (1991) 267. [213 Y. Adachi, M.A. Cohen Stuart and R. Fokkink, J. Colloid Interface Sci., 167 (1994) 346. [223 N.H.G. Penners and L.K. Koopal, Colloids Surfaces, 28 (1987) 67. [23] R.H. Ottewill and M.C. Rastogi, Trans. Faraday Soc., 56 (1960) 866. [24] B.A. Matthews and C.T. Thodes, J. Pharm. Sci., 57 (1968) 557. [253 A. Lips and E.J. Willis, J. Chem. Soc., Faraday Trans. 1, 69 (1973) 1226. [26] W. Hatton, P. McFadyen and A.L. Smith, J. Chem. Soc., Faraday Trans. 1, 70 (1974) 655. [27] A. van der Scheer, A. Tanke and C.A. Smolders, Faraday Discuss. Chem. Soc., 65 (1978). [28] J.G. Rarity and K.J. Randle, J. Chem. Soc., Faraday Trans., 81 (1985) 285. [29] A.A. Baran, I.M. Solomentseva and O.D. Kurilenko, Colloid J. USSR, 37 (1975)219. [30] Y. Adachi, M.A. Cohen Stuart and R. Fokkink, J. Colloid Interface Sci., 165 (1994) 310.