Progr Colloid Polym Sci (1998) 110:105 109 © SteinkopffVerlag 1998 A. Schmitt A. Fern~ndez-Barbero M.A. Cabrerizo-Vilchez R. Hidalgo-,~lvarez On the identification of bridging flocculation: An extended collision efficiency model A. Schmitt (1~)' M.A. Cabrerizo-Vilchez R. Hidalgo-Alvarez Grupo de Fisica de Fluidos y Biocoloides Departamento de Fisica Aplicada Universidad de Granada Campus de Fuentenueva E-18071 Granada Spain A. Fernfindez-Barbero Grupo de Fisica de Fluidos Complejos Departamento de Fisica Aplicada Universidad de Atmeria Cafiada de San Urbano s/n E-04120 Almeria Spain Abstract A new generalized collision efficiency model for bridging floc- culation was developed. It comprises the La Mer, the Moudgil and the Molski models. The extended model allows to separate and quantify the contributions of the different aggregation mechanisms (slow coagulation, weak flocculation and bridging flocculation). The model was tested for polystyrene particles covered with different amounts of bovine serum albumin (BSA). Single- cluster light scattering was employed to study the aggregation kinetics and to obtain the initial aggregation rate constant. It was found that the simple La Mer model cannot explain the experimental results whilst the Molski model gives reasonably good results for fast but fails for slow aggregation processes, Only the extended model works for slow and fast aggregation processes, Key words Colloidal aggregation light scattering bridging floc- culation - single-particle detection - collision efficiency Introduction Colloidal aggregation may be controlled by a wide variety of different mechanisms. The addition of salt to an elec- trostatically stabilized colloidal dispersion leads to a com- pression of the electric double layer and therefore, to salt- induced coagulation. The stability of the colloid may also be affected by macromolecules which irreversibly absorb onto the surface of colloidal particles. At high surface coverage, steric effects usually impede flocculation and ensure an increased colloidal stability. Neverthless, some weak flocculation may occur even for totally covered par- ticles. At lower surface coverage, bridges of macro- molecules may form between the particles and, thus, give rise to bridging flocculation [-1 3]. Bridging flocculation takes place only when a covered part of the surface of one particle collides with the un- covered part of another particle. In this case, the aggrega- tion rate should depend on the degree of surface coverage 0, i.e. the fractional coverage of the particle surface by adsorbed molecules. La Mer assumed the rate ks of pure bridging flocculation to be proportional to the number of free sites on one particle and the number of occupied sites on the other. He postulated [4-6] that ks ~ 0(1 - 0). (1) This relationship implies that maximum flocculation should occur at half surface coverage (0max = 50%) and no flocculation at all for uncovered and totally covered par- ticles, respectively. This simplified approach to bridging flocculation, however, cannot be entirely true since it as- sumes that bridging flocculation is the only mechanism of aggregation. It does not take into account that many dispersed systems are significantly unstable in the absence of absorbed molecules (coagulation) as well as when par- ticles are completely covered (weak flocculation) [7]. More detailed models were proposed by Hogg [8], Ash and Clayfield [9], Moudgil [10] and Molski [7]. Neverthe- less, all of them show the common feature that bridging