Probing Colloidal Particle Aggregation by Light Scattering

772 CHIMIA 2013, 67, Nr. 11 Polymers, Colloids, and interfaCes

doi:10.2533/chimia.2013.772 Chimia 67 (2013) 772–776 © Schweizerische Chemische Gesellschaft Probing Colloidal Particle Aggregation by Light Scattering

Gregor Trefalt, Istvan Szilagyi, Tamas Oncsik, Amin Sadeghpour, and Michal Borkovec*

Abstract: The present article reviews recent progress in the measurement of aggregation rates in colloidal suspensions by light scattering. Time-resolved light scattering offers the possibility to measure absolute aggregation rate constants for homoaggregation as well as heteroaggregation processes. We further discuss the typical concentration dependencies of the aggregation rate constants on additives. Addition of simple salts containing monovalent counterions leads to screening of the electrostatic repulsion of the charged particles and a transition from slow to rapid aggregation. Addition of salts containing multivalent counterions may lead to a charge reversal, which results in a sequence of two instability regions. Heteroaggregation rates between oppositely charged particles decrease with increasing salt level. This decrease is caused by screening of the electrostatic attraction between these particles. Keywords: Coagulation · Latex particles · Light scattering · Multivalent ions · Particle aggregation · Simple ions

Introduction Fig. 1. Scheme of different par- Aggregation in colloidal particle sus- ticle aggregates. pensions is a relevant process in a wide Homoaggregation (top) and heteroag- range of systems and phenomena.[1–6] In gregation (bottom). papermaking or wastewater treatment, rapid aggregation of particles must be induced to obtain the desired product or appropriate degree of water purification. Stable suspensions are needed to obtain sufficient shelf-life of consumer products or to main- tain easily flowing particle slurries. Particle aggregation can be controlled concentrations, they will eventually be in- tively high particle concentration, and in by addition of appropriate chemicals. fluenced by gravitational forces, and sedi- this situation early stages of the aggregation Depending on the envisioned application, ment or cream. When the particle concen- are difficult to probe. For larger particles, they are referred to as coagulants, floccu- tration is sufficiently high, the clusters will this technique can be used in a straight- lants, or stabilizers.[2,4,6] When aggregation fill the available space, interlink, and form forward fashion, but the optical proper- is induced in an initially stable particle a colloidal gel.[12,13] ties of the particles used must be known suspension, one obtains particle dimers When aggregation occurs between accurately. In single particle counting, the first (Fig. 1).[4,7–9] Thereby, one refers to identical (or similar) particles, one may aggregating suspension is passed through the early stages of the aggregation pro- refer to homoaggregation.[4,9–11] When one a narrow capillary.[22,23] Thereby, the pas- cess. Since the aggregation process is ir- deals with a mixture of dissimilar particles, sage of each individual cluster is recorded reversible, larger clusters will form as time this fact is stressed by referring to hetero- by means of a suitable detection scheme, proceeds, and one refers to late stages. aggregation.[14–17] Large irregular clusters such as electric conductivity or light scat- Clusters in the late stages have irregular, may form, but they are typically more tering. The technique offers excellent reso- fractal structures.[10,11] At lower particle ramified than the ones obtained in homo- lution, but to which extent the clusters have aggregation. More recently, small hetero- been disturbed by the high shear fields in aggregates of colloidal particles have been the capillary cannot be easily addressed. synthesized and these are referred to as Time-resolved light scattering is proba- colloidal molecules.[18–20] Such entities in- bly the most versatile technique, which can troduce directionality into the interactions be used in the static as well as the dynamic between such particles and might eventu- mode.[7,9,15,24–26] This technique operates ally lead to novel functional materials. entirely in situ, permits to access a wide Particle aggregation can be probed by range in particle sizes, typically from ten various techniques, in particular, turbidity nanometers up to a micrometer. Moreover, measurements, single particle counting, the technique enables us to distinguish *Correspondence: Prof. M. Borkovec and light scattering. Widely used are tur- various types of aggregates formed. Recent Department of Inorganic and Analytical Chemistry University of Geneva bidity measurements with a spectropho- progress in its utilization to probe early Sciences II tometer.[8,21] However, the results obtained stages of the aggregation will be summa- 30, Quai Ernest-Ansermet with this technique cannot be always easily rized here. Typical results how the aggre- CH-1211 Geneva 4 interpreted. When the particle size is small, gation rate coefficients are influenced by Tel.: +41 22 379 6405 E-mail: [email protected] an easily measurable signal requires a rela- various salts will be equally discussed. Polymers, Colloids, and interfaCes CHIMIA 2013, 67, Nr. 11 773

Aggregation Kinetics by Light drodynamic radius R though the diffusion and the corresponding kinetic law is given Scattering coefficient, which is obtained from the dy- in Eqn. (6): namics of the fluctuations of the scattered light. The doublet formation rate coeffi- Colloidal particles aggregate irrevers- dc ibly to larger clusters, whereby the elemen- cient can be measured with SLS from the AB = kcc (6) dt AB AB tary step is:[4] initial relative rate of change of the scattering intensities by means of Eqn. (3):[7] In the early stages of the aggregation

AA A2 (1) of a binary particle mixture, one may have dIln SkFq() two homoaggregation processes and one dt AA AA heteroaggregation process occurring si- t0 (3) The early stages of the aggregation, Iq() multaneously. The relative rate of change kc 2 1 when monomers and dimers dominate, can AA 0 2(Iq) of the scattering intensity has additive be described by the kinetic law: 1 contributions from all three processes, namely:[17] where c is the initial particle number con- dc k 0 AA AA c2 centration, I (q) and I (q) are the scatter- A (2) 1 2 SkFq() dt 2 ing intensities of a monomer and a dimer, AA AA (7) 2(kF qk)(Fq) respectively. Thereby, q denotes the mag- AB AB BB BB where c and c are the number concen- nitude of the scattering vector, which can A AA trations of monomers and dimers, t the be adjusted through the scattering angle. where F (q) refers to the symmetric dou- AA time, and k the aggregation rate coeffi- A similar expression can be obtained in blets AA and represents a generalization AA cient. When only monomers and dimers the case of DLS for the initial relative rate of Eqn. (3) for a mixed system, F (q) to BB dominate, one refers to the early stages of of change of the apparent hydrodynamic symmetric doublets BB, and F (q) to the AB the aggregation. radius:[7] analogous expression for the asymmetric The kinetics of colloidal aggregation doublets AB. The factors F (q) play the ij can be conveniently followed by time-re- role of basis functions, and by means of solved light scattering (Fig. 2). One may dRln their different angular dependencies one DkHq() AA AA can distinguish the different contributions use static light scattering (SLS), dynamic dt t0 light scattering (DLS), and sometimes it (4) from homoaggregation and heteroaggrega- 1 Iq2 () may be advantageous to combine both. kcAA 0 1 tion within an angle-dependent measure- 2(Iq) SLS measures the average scattering inten- 1 ment. For DLS, one can derive an entirely sity I, while DLS gives access to the hy- analogous expression:[17] where α denotes the hydrodynamic factor, which is the ratio of the diffusion coeffi- DkHq() AA AA (8) (a) cients of the dimer and the monomer. Since 2(kH qk)(Hq) 1.4 58° the scattering intensities can be estimated AB AB BB BB 83.5° 109° from the approximate theory of Rayleigh, 1.2 where H (q) are similar basis functions as Debye, Gans (RDG) of more accurate ij T-matrix approaches,[27–29] Eqns (3) and introduced in Eqn. (7). Fig. 4 illustrates Intensity 1.0 (4) can be used to measure the aggrega- how this approach can be used to measure tion rate coefficients. This comparison is heteroaggregation rate constants. The ini-

Relative 0.8 made in Fig. 3 for the aggregation of sul- tial apparent rates measured by SLS and fate and amidine latex particles of diam- DLS are compared. At low electrolyte eters of 200 nm and 300 nm in 1 M KCl concentration, only the heteroaggregation 0 1000 2000 3000 4000 solution. One observes that RGD theory process occurs (Fig. 4a) and the measured Time (s) works well for smaller particles, while the angular dependence is solely determined T-matrix has to be used to accurately de- by the asymmetric AB dimers. At high 1.6 (b) 58° scribe the angular dependence for larger electrolyte concentration, all different di-

Radius 1.5 83.5° particles. Under these conditions, one finds mers AA, AB, and BB are forming, and 109° a rate coefficient of 2.7×10–18 m3/s for the their different contributions are indicated 1.4 sulfate particles and 4.0×10–18 m3/s for the (Fig. 4b). For such measurements, one 1.3 amidine particles. The measured hydrody- can separate these different contributions, 1.2 namic factors are 1.46 and 1.34, which is in and determine the heteroaggregation rate Hydrodynamic good agreement with the theoretical value unambiguously. From these experiments, 1.1 of 1.39. one finds from SLS a heteroaggregation 1.0 When one deals with the same (or simi- rate coefficient 7.0×10–18 m3/s at 10–4 M Relative –18 3 0 1000 2000 3000 4000 lar) colloidal particles, one refers to homo- and 4.9×10 m /s at 1 M, while compa- aggregation. When different particles are rable values are obtained from DLS. Time (s) involved, one refers to heteroaggregation. Fig. 2. Relative change in the scattering inten- In early stages, the elementary step in the heteroaggregation process is:[17] Tuning Particle Aggregation by sity and apparent hydrodynamic radius with Additives time during particle aggregation normalized to the initial value. (a) Scattering intensity and (b) In their seminal work, Derjaguin, apparent hydrodynamic radius. For some scat- AB AB (5) tering angles, the scattering intensity may also Landau, Verwey, and Overbeek (DLVO) decrease as the aggregation proceeds. recognized that particle aggregation rate is 774 CHIMIA 2013, 67, Nr. 11 Polymers, Colloids, and interfaCes Apparent ) -1

s 250 (a) SLS DLS ) -6 T-matrix 140 -1 ) s 200 RDG -1 AB -6 s Experiment 80 Experiment (a) (x10 Dynamic SLS -6 200 150 120 T-matrix T-matrix DLS 150 (x10 (x10 60 Rate 100

100 100 Rate Rate Rate AA+BB+AB 50 40 AB Static 80 50 AA+BB+AB

(x10 BB

0 Static

0 Dynamic 20

-50 -6 AA AA 60 s BB Apparent -1 -50

) 0 0 40 80 120 160 Apparent Apparent Angle (°) 0 40 80 120 160 0 40 80 120 160 Angle (°) Angle (°) ) -1 ) Apparent s -1 ) Experiment Experiment (b) -6 s 250 -1 120 -6 s 400 (b) 200 T-matrix T-matrix

-6 T-matrix 200 (x10 100

RDG 180 (x10 AB 300 150 AB (x10 SLS Dynamic AA+BB+AB 80 160 Rate AA+BB+AB 200 DLS Rate 100 AA 60 AA Rate 140 50 BB 40 Static

100 Rate 120 0 Dynamic 20 BB Static 0 -50 100 (x10 0 Apparent

80 Apparent -100 -6 0 40 80 120 160 0 40 80 120 160 s Apparent -1

) Angle (°) Angle (°) 0 40 80 120 160 Angle (°)

Fig. 3. Apparent aggregation rates measured Fig. 4. Apparent aggregation rates measured by time resolved SLS (left) by time-resolved SLS and DLS as a function and DLS (right) as a function of the scattering angle for heteroaggrega- of the scattering angle for homoaggregation in tion in a mixture of oppositely charged sulfate (A) and amidine latex par- 1 M KCl solution and pH 4.0. Note that static ticles (B) of diameters of 200 nm and 300 nm, respectively, at a number and dynamic rates are proportional, and thus fraction of 0.75 of the sulfate particles at pH 4.0. Lines represent the best can be plotted within the same graph. The fits to the T-matrix model whereby the contributions of the particular type dashed and solid lines presents the best fits to of dimers AA, BB, and AB are indicated. (a) Aggregation at an electrolyte the RDG and T-matrix model, respectively. (a) concentration of 10-4 M where only AB aggregates are forming, and (b) Sulfate latex particles of 200 nm in diameter aggregation at an electrolyte concentration of 1 M where all types of ag- and (b) amidine latex particles of 300 nm in gregates form simultaneously. diameter. determined by mutual diffusion of the two ity, and a the particle radius. The above re- cient in the fast aggregation regime. Thus, particles in their potential energy profile:[4] lation applies to homoaggregation of simi- a small stability ratio around unity refers lar particles, while an analogous relation to fast aggregation, while a larger value to can be used to evaluate the rate coefficient slow aggregation.

VVvdWdVl (9) for heteroaggregation. Therefore, the rate Let us now discuss the typical depen- coefficients can be estimated from the so- dencies of the stability ratio in some rel- lution composition and particle properties, evant situations. Fig. 5 illustrates the sta- with two main contributions, namely the such as their size and surface characteris- bility ratio for homoaggregation for nega- van der Waals energy V and the energy tively charged carboxylated latex particles vdW tics. due to the overlap of the electrical double The DLVO theory predicts two distinct with a diameter of 300 nm at pH 4.0 in the layers V . presence of linear aliphatic polyamines. dl aggregation regimes. When the interaction These two contributions can nowa- potential is attractive, the aggregation is Thereby, the number of amine groups is days be estimated with good accuracy. rapid since the approach of the particles indicated. These polyamines are almost From the energy profile, the rate coef- process is mainly controlled by their mu- fully protonated, and thus represent a con- ficient can be obtained from the known tual diffusion. In this case, one refers to the venient model system to study the major expression for diffusion controlled reac- fast aggregation regime. When the inter- effects of valence on colloidal aggregation. tions, namely:[4,9] action potential features an intermediate The first characteristic situation occurs barrier, the aggregation is slow, since the for counterions of low valence. At low salt particles must overcome this barrier by concentrations, aggregation is very slow 4kT B and the suspension is stable. Increasing kAA thermal activation. In this case, one refers 3a to the slow aggregation regime. Instead of the salt concentrations, the stability ratio 1 (10) Br() reporting rate coefficients, one often refers decreases steeply, until the plateau at unity exp[Vr()/(kT)] dr r 2 B to the stability ratio defined as is reached. Increasing the salt level further, 2a the rate coefficient remains independent of k the concentration. The transition between where r is the center-to-center separation, W fast (11) the slow and fast aggregation regimes is ij k B(r) is the hydrodynamic resistance func- ij referred to as the critical coagulation con- tion, k is the Boltzmann constant, T the centration (CCC). This transition is caused B absolute temperature, η the solvent viscos- where k is the aggregation rate coeffi- by the progressive screening of the elec- fast Polymers, Colloids, and interfaCes CHIMIA 2013, 67, Nr. 11 775

Fig. 5. Stability and dicting the observed trends relatively well (a) charging characteris- (Fig. 5a). The surface potentials were es- tics of carboxylated timated from electrophoretic mobilities latex particles of a and a Hamaker constant of 4.5×10–21 J was diameter of 307 nm used. This value is somewhat smaller than versus the concentra- –21 tion of linear aliphatic the theoretical estimate of 9.0×10 J for [37] polyamines at pH 4.0. polystyrene, probably due to roughness Ratio 100 The number of amine and retardation effects. The discrepancy groups is indicated. for N1 is probably related to short range N1 (a) Experimental sta- hydration forces, while the discrepancies Stability bility ratios where the near the restabilization maximum for N4 solid lines are predic- and N6 are thought to originate from sur- Ratio 10 tions of DLVO theory. face charge heterogeneities. The experi- (b) Electrophoretic mentally observed fast aggregation rate mobility results with –18 3

Stability constant is 3.1×10 m /s, while the DLVO N2 solid lines, which theory predicts 7.1×10–18 m3/s. This some- 1 serve to guide the eye only. what larger value probably originates from

Ratio inaccuracies in the hydrodynamic resis- 3 4 5 10 10 10 tance function at small separations. Much less quantitative information is

Stability available on heteroaggregation. However, N4 the case of two oppositely charged particles has been investigated in some de- tail in the presence of monovalent salt.[17] The corresponding data were measured with the multi-angle techniques described above and they are presented in Fig. 6. One observes that the corresponding stability ratio increases with increasing electrolyte concentration, but the effect is much more N6 modest than for homoaggregation. This in- crease originates from the screening of the mutual electrostatic attraction of the two oppositely charged particles. The over- all trend can be again well described by DLVO theory. Thereby, the surface potentials of both particles have been estimated (b) from electrophoresis.

Conclusion N6 N4 Our capabilities to measure aggregation rates in colloidal suspensions by light scat- N2 N1 tering have recently evolved substantially. By measuring the angular dependence of the light scattering signal in a time-re-

trostatic double layer interactions by the that is induced by the adsorption of the ions Ratio dissolved salt ions.[4,25,26] of higher valence. This charge reversal can

When the valence is increased, one ob- be demonstrated by electrophoresis (Fig. Stability serves that the CCC shifts towards lower 5b). Similar effects involving screening concentrations.[25,30,31] This dependence and charge reversal were also observed is referred to as the Schulze-Hardy rule, with positively charged particles and mul- which states that the CCC scales as the in- tivalent anions.[25,30,32] However, anions verse six power of the valence.[4] The data appear to induce a charge reversal more shown in Fig. 5 obey this scaling rather easily than cations. Reversal of charge represents a key mechanism in destabilization Fig. 6. Heteroaggregation rate coefficients well. However, another characteristic fea- between sulfate and amidine latex particles of ture becomes apparent for higher valence, of colloidal suspensions, and can be impor- diameters 277 nm and 160 nm, respectively, namely the restabilization at intermediate tant in amphoteric systems, surfactants, or versus the ionic strength adjusted with KCl concentrations. This restabilization is re- polyelectrolytes.[33–36] electrolyte at pH 4.0. The line shows calculated lated to the charge reversal of the particles The DLVO theory is capable of pre- results with DLVO theory. 776 CHIMIA 2013, 67, Nr. 11 Polymers, Colloids, and interfaCes

[22] H. Holthoff, A. Schmitt, A. Fernandez-Barbero, solved fashion, the absolute aggregation [1] D. Horn, F. Linhart, ‘Retention Aids’, Blackie M. Borkovec, M. A. Cabrerizo-Vilchez, P. rates can be measured. In particular, the an- Academic and Professional, London, 1996. Schurtenberger, R. Hidalgo-Alvarez, J. Colloid [2] B. Bolto, J. Gregory, Water Res. 2007, 41, 2301. gular dependence permits simultaneously Interface Sci. 1997, 192, 463. [3] R. Nystrom, K. Backfolk, J. B. Rosenholm, K. occurring homoaggregation as well as het- [23] H. Lichtenfeld, H. Stechemesser, H. Möhwald, Nurmi, J. Colloid Interface Sci. 2003, 262, 48. J. Colloid Interface Sci. 2004, 276, 97. eroaggregation to be distinguished. These [4] W. B. Russel, D. A. Saville, W. R. Schowalter, [24] S. H. Behrens, M. Borkovec, P. Schurtenberger, techniques permit the study of aggregation ‘Colloidal Dispersions’, Cambridge University Langmuir 1998, 14, 1951. rates in various systems. Homoaggregation Press, Cambridge, 1989. [25] I. Szilagyi, A. Sadeghpour, M. Borkovec, [5] P. G. de Gennes, Nature 2001, 412, 385. of charged colloidal particles in the pres- Langmuir 2012, 28, 6211. [6] M. Elimelech, J. Gregory, X. Jia, R. A. ence of ions of low valence is influenced [26] C. Schneider, M. Hanisch, B. Wedel, A. Jusufi, Williams, ‘Particle Deposition andAggregation: M. Ballauff, J. Colloid Interface Sci. 2011, 358, by screening the electrostatic repulsion Measurement, Modeling, and Simulation’, 62. between the charged particles, and leads Butterworth-Heinemann Ltd., Oxford, 1995. [27] M. I. Mishchenko, D. W. Mackowski, J. Quant. [7] H. Holthoff, S. U. Egelhaaf, M. Borkovec, P. to a sharp transition between slow and fast Spectrosc. Radiat. Transf. 1996, 55, 683. Schurtenberger, H. Sticher, Langmuir 1996, 12, aggregation. With increasing valence, this [28] H. Holthoff, M. Borkovec, P. Schurtenberger, 5541. Phys. Rev. E 1997, 56, 6945. transition point shifts towards lower con- [8] S. H. Xu, Z. W. Sun, Soft Matter 2011, 7, 11298. [29] P. Galletto, W. Lin, M. I. Mishchenko, M. centrations. However, a restabilization can [9] M. Kobayashi, F. Juillerat, P. Galletto, P. Bowen, Borkovec, J. Chem. Phys. 2005, 292, 139. be observed in the presence of multivalent M. Borkovec, Langmuir 2005, 21, 5761. [30] A. Sadeghpour, I. Szilagyi, M. Borkovec, Z. [10] P. Sandkuhler, M. Lattuada, H. Wu, J. Sefcik, ions when their valence is sufficiently Phys. Chem. 2012, 226, 597. M. Morbidelli, Adv. Colloid Interface Sci. 2005, high. This restabilization originates from [31] I. Szilagyi, D. Rosicka, J. Hierrezuelo, M. 113, 65. Borkovec, J. Colloid Interf. Sci. 2011, 360, 580. a charge reversal induced by the adsorp- [11] M. Y. Lin, H. M. Lindsay, D. A. Weitz, R. C. [32] P. Sinha, I. Szilagyi, F. J. M. Ruiz-Cabello, P. tion of these ions. Heteroaggregation rates Ball, R. Klein, P. Meakin, Nature 1989, 339, Maroni, M. Borkovec, J. Phys. Chem. Lett. 360. between oppositely charged particles de- 2013, 4, 648. [12] T. Gisler, R. C. Ball, D. A. Weitz, Phys. Rev. crease with increasing salt level, and this [33] M. Schudel, S. H. Behrens, H. Holthoff, R. Lett. 1999, 82, 1064. Kretzschmar, M. Borkovec, J. Colloid Interface decrease can be explained by screening the [13] L. F. Rojas, R. Vavrin, C. Urban, J. Kohlbrecher, Sci. 1997, 196, 241. electrostatic attraction between these par- A. Stradner, F. Scheffold, P. Schurtenberger, [34] T. Hiemstra, W. H. van Riemsdijk, Langmuir ticles. All these trends can be well ratio- Faraday Discuss. 2003, 123, 385. 1999, 15, 8045. [14] R. O. James, A. Homola, T. W. Healy, J. Chem. nalized by DLVO theory, even though this [35] M. Borkovec, G. Papastavrou, Curr. Opin. Soc. Farad. Trans. I 1977, 73, 1436. theory often predicts stronger dependen- Colloid Interface Sci. 2008, 13, 429. [15] W. L. Yu, E. Matijevic, M. Borkovec, Langmuir [36] L. Liang, J. J. Morgan, Aquat. Sci. 1990, 52, 32. cies than observed experimentally. With 2002, 18, 7853. [37] M. A. Bevan, D. C. Prieve, Langmuir 1999, 15, these experimental and theoretical tools, [16] A. M. Puertas, A. Fernandez-Barbero, F. J. de 7925. the stability of colloidal suspensions can las Nieves, J. Chem. Phys. 2001, 114, 591. be controlled in a much more detailed fash- [17] W. Lin, M. Kobayashi, M. Skarba, C. Mu, P. Galletto, M. Borkovec, Langmuir 2006, 22, ion than was possible so far. 1038. [18] Y. S. Cho, G. R. Yi, J. M. Lim, S. H. Kim, V. Acknowledgement N. Manoharan, D. J. Pine, S. M. Yang, J. Am. This research was mainly supported by Chem. Soc. 2005, 127, 15968. Swiss National Science Foundation, University [19] D. J. Kraft, J. Groenewold, W. K. Kegel, Soft of Geneva. Partial support by the COST Action Matter 2009, 4, 1302. CM1101 is also acknowledged. [20] E. Duguet, A. Desert, A. Perro, S. Ravaine, Chem. Soc. Rev. 2011, 40, 941. [21] A. Puertas, J. A. Maroto, F. J. de las Nieves, Received: June 9, 2013 Colloids Surf. A 1998, 140, 23.