Eur. Phys. J. Special Topics 223, 2297–2306 (2014)
https://doi.org/10.1140/epjst/e2014-02265-0

Review

Relaxation dynamics near the sol–gel transition: From cluster approach to mode-coupling theory

¹ CNR-SPIN, Dipartimento di Scienze Fisiche, Università di Napoli “Federico II”, Complesso Universitario di Monte Sant'Angelo, via Cintia, 80126 Napoli, Italy
² Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre RS, Brazil
³ Dipartimento di Ingegneria Industriale e dell'Informazione, Seconda Università di Napoli, Real Casa dell'Annunziata, 81031 Aversa (CE), Italy

^a e-mail: coniglio@na.infn.it

Received: 18 April 2014
Revised: 18 August 2014
Published online: 24 October 2014

Abstract

A long standing problem in glassy dynamics is the geometrical interpretation of clusters and the role they play in the observed scaling laws. In this context, the mode-coupling theory (MCT) of type-A transition and the sol–gel transition are both characterized by a structural arrest to a disordered state in which the long-time limit of the correlator continuously approaches zero at the transition point. In this paper, we describe a cluster approach to the sol-gel transition and explore its predictions, including universal scaling laws and a new stretched relaxation regime close to criticality. We show that while MCT consistently describes gelation at mean-field level, the percolation approach elucidates the geometrical character underlying MCT scaling laws.