## Abstract

The paper is devoted to the problem of the kinetic study of aggregation of particles with several active sites (so called “patchy particles”) using turbidimetry. Patchy particles are known as chemically-anisotropic reactants, and the kinetics theory of their interaction is far from complete. In this work we theoretically derived and experimentally verified analytical expressions, which are convenient for the treatment of the turbidimetric data on the overall optical density change (due to light scattering of the particles) of the aggregating patchy colloid. Light scattering cross sections of the aggregates were calculated using the superposition T-matrix method. Particularly, we used an analytical approximation for the diffusion-limited rate constants of Smoluchowski equations of aggregation of chemically-anisotropic particles (or clusters) with several small active sites assuming that the clusters are of fractal structure. In order to account for the case of a small (<10) number of active sites on particles we used Monte Carlo stochastic algorithm of Gillespie method. For the verification, we carried out experiments on kinetic turbidimetric study of the immunoagglutination of 65 nm polystyrene particles covered by anti-CRP IgG antibodies in the water solution of C-reactive protein (CRP). Good agreement of experimental data and theoretical simulations allowed us to evaluate the average number of active antibody molecules per particle as 9.0 ± 2.2 and the affinity of the antigen-antibody complex as 5.5 ± 1.5 × 10^{7} M^{−1}. A significant kinetic effect of the small number of active sites per particle was found.

Original language | English |
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Pages (from-to) | 72-79 |

Number of pages | 8 |

Journal | Colloids and Surfaces A: Physicochemical and Engineering Aspects |

Volume | 516 |

DOIs | |

Publication status | Published - 5 Mar 2017 |

## Keywords

- Biospecific binding
- Colloid aggregation kinetics
- Fractal clusters
- Gillespie algorithm
- Latex immunoagglutination
- Monte-Carlo simulation
- Patchy particles
- Rate constant
- Turbidimetric assay
- MATRIX
- SIZE
- LIGHT-SCATTERING
- ANTIBODY
- MODEL
- RATE-CONSTANT
- CHEMICAL-REACTIONS
- NANOPARTICLES
- COAGULATION
- LIMITED AGGREGATION