Aggregation Rate Measurements by Zero-Angle Time-Resolved Multiangle Laser Light Scattering Ke Wang, Anup K. Singh, and John H. van Zanten* Chemical Engineering Department, North Carolina State University, Raleigh, North Carolina 27695-7905, and Chemical & Radiation Detection Laboratory, Sandia National Laboratories, Livermore, California 94550 Received July 31, 2001. In Final Form: December 18, 2001 A new method for determining second-order aggregation rate constants via time-resolved multiangle laser light scattering is introduced. A major advantage of this approach is that second-order aggregation rate constants are determined without any assumptions regarding the dimer intraparticle interference or form factor. The second-order aggregation rate constants are calculated from the temporal variation of the zero-angle excess Rayleigh ratio within the context of von Smoluchowski’s well-established model of colloidal aggregation. The new method is illustrated with two systems: (1) GM1-bearing liposomes aggregated in the presence of the cholera toxin B subunit and (2) sulfonated polystyrene latex aggregated in the presence of CaCl2. Whereas the method is demonstrated to be particularly well-suited for investigating slow aggregation processes, rapid aggregation processes are also accessible if proper precautions are taken. Introduction The stability and aggregation kinetics of liquid- dispersed colloidal particles lies at the heart of many technological processes including ceramic, magnetic, opti- cal, and electrical material manufacturing; wastewater treatment; pharmaceutical formulation; and paint, coating and ink development. The kinetic stability of colloidal dispersions is of great significance to all colloid science. For instance, stability studies are often utilized in investigations of fundamental interparticle forces and hydrodynamic interactions. These stability studies are typically focused on investigations of aggregation or coagulation processes, particularly during their earliest stages, which facilitates the interpretation of the experi- mental measurements. Colloidal aggregation phenomena have been studied by a wide variety of techniques. The most unambiguous methods involve direct counting via ultramicroscopy or particle counting. 1-4 Unfortunately, these approaches are tedious and, as such, are not suitable for routine inves- tigations of colloidal stability. Whereas turbidimetry provides a rapid means of qualitatively assessing ag- gregation phenomena, 5,6 difficulties remain with quan- titatively interpreting these measurements, although it should be noted that work is proceeding in this area. 7,8 Additionally, static 9,10 and dynamic 11,12 light scattering methods are frequently used to monitor colloidal stability. However, when considered individually, these previous light scattering methods require a priori knowledge of the dimer intraparticle interference or form factor, which is typically approximated by the Rayleigh-Gans-Debye method. This approximation was recently shown to be erroneous for sufficiently large scattering angles. 13 Swiss researchers recently described a combined dynamic and static light scattering method that obviates the need for assuming an analytical form for the dimer form factor. 14 One potential downfall of their proposed method is its economic viability, as it requires simultaneous dynamic and static light scattering measurements to be made at several angles, which is a potentially expensive under- taking if one considers the cost of purchasing multiple autocorrelators. Therefore, an alternative dimer-form- factor-independent method for determining second-order aggregation rate constants would be attractive. In this paper, a new method for determining second- order aggregation rate constants from time-resolved multiangle laser light scattering is reported. The second- order aggregation rate constants are determined from the temporal variation of the excess Rayleigh ratio at zero scattering angle analyzed within the framework of von Smoluchowski’s aggregation model. The primary advan- tage of this method is that it does not require a priori knowledge of the dimer intraparticle interference or form factor, unlike other individual light scattering methods. The method’s utility is demonstrated with two completely different types of colloidal aggregation processes: (1) cholera toxin B subunit-induced aggregation of GM1- bearing liposomes and (2) CaCl 2 -induced aggregation of sulfonated polystyrene latex particles. The method is shown to be particularly useful for monitoring relatively slow aggregation processes. Materials and Methods Materials. Ganglioside GM1, L-R-distearoylphosphatidyl- choline (DSPC), cholesterol, and cholera toxin B subunit were obtained from Sigma Chemical Co. (St. Louis, MO). Unilamellar liposomes with a composition of DSPC/cholesterol/GM1 in a 47.5: * Corresponding author. E-mail: john_vz@ncsu.edu. (1) Sonntag, H.; Strenge, K. Coagulation Kinetics and Structure Formation; Plenum Press: New York, 1987. (2) Swift, D. L.; Friedlander, S. K. J. Colloid Sci. 1964, 19, 621. (3) Matthews, B. A.; Rhodes, D. T. J. Colloid Interface Sci. 1970, 32, 332. (4) Broide, M. L.; Cohen, R. J. J. Colloid Interface Sci. 1992, 153, 493. (5) Ottewill, R. H.; Shaw, J. N. Discuss. Faraday Soc. 1966, 42, 154. (6) Lichtenbelt, J. W. Th.; Pathmamanoharan, C.; Wiersema, J. J. Colloid Interface Sci. 1974, 49, 281. (7) Maroto, J. A.; de las Nieves, F. J. Colloid Polym. Sci. 1997, 275, 1148. (8) Maroto, J. A.; de las Nieves, F. J. Colloids Surf. A 1998, 132, 153. (9) Lips, A.; Smart, C.; Willis, E. J. Chem. Soc., Faraday Trans. 1971, 67, 2979. (10) van Zanten, J. H.; Elimelech, M. J. Colloid Interface Sci. 1992, 154, 1. (11) Novich, B. E.; Ring, T. A. Clays Clay Miner. 1984, 32, 400. (12) Virden, J. W.; Berg, J. C. J. Colloid Interface Sci. 1992, 149, 528. (13) Holthoff, H.; Borkovec, M.; Schurtenberger, P. Phys. Rev. E 1997, 56, 6945. (14) Holthoff, H.; Egelhaaf, S. U.; Borkovec, M.; Schurtenberger, P.; Sticher, H. Langmuir 1996, 12, 5541. 2421 Langmuir 2002, 18, 2421-2425 10.1021/la011207o CCC: $22.00 © 2002 American Chemical Society Published on Web 02/21/2002