Directed percolation identified as equilibrium pre-transition towards non-equilibrium arrested gel states

Abstract

The macroscopic properties of gels arise from their slow dynamics and load-bearing network structure, which are exploited by nature and in numerous industrial products. However, a link between these structural and dynamical properties has remained elusive. Here we present confocal microscopy experiments and simulations of gel-forming colloid–polymer mixtures. They reveal that gel formation is preceded by continuous and directed percolation. Both transitions lead to system-spanning networks, but only directed percolation results in extremely slow dynamics, ageing and a shrinking of the gel that resembles synaeresis. Therefore, dynamical arrest in gels is found to be linked to a structural transition, namely directed percolation, which is quantitatively associated with the mean number of bonded neighbours. Directed percolation denotes a universality class of transitions. Our study hence connects gel formation to a well-developed theoretical framework, which now can be exploited to achieve a detailed understanding of arrested gels.

Critical properties of the susceptible-exposed-infected model on a square lattice

“…The exponents δ, ν , β, and ψ [respectively in Eqs. (17), (21), (22) and (23)], were also computed in those models [43,46,49] and are numerically equal. Thus, the critical behavior of SEI model here studied is in the same infinite-noise universality class of the contact process in d = ∞.…”

“…An important and thoroughly studied universality class of absorbing phase transitions is the "ubiquitous" directed percolation (DP) universality class [12][13][14][15][17][18][19]. For many years it has evaded experimental confirmation [5,[20][21][22]. Earlier, it was thought that one possible reason was due to quenched disorder as the DP universality class is perturbatively unstable against it for d < 4 [23][24][25].…”

“…(d) The critical exponents β and ν for many values of γ. The solid lines are the predictions to β and ν Eqs (22). and(21).…”

Self-assembly of complex structures in colloid-polymer mixtures

“…A system that is well-studied in theory and simulation and in addition can be realized and investigated experimentally is a charge-stabilized colloid-polymer mixture which intrinsically involves multiple length scales as the colloids effectively attract each other close to contact due to depletion interactions while being repulsive on larger length scales because of screened electrostatic repulsions. Experimental and theoretical studies have been performed to understand the nature of colloid-polymer mixtures [33][34][35][36][37][38][39][40][41][42][43][44] some of which exhibit glassy states [36,37], gels [38][39][40][41][42], and cluster formation [41,43,44]. The phase behavior concerning the gas, liquid, and trivial solid phase has been investigated in [45][46][47][48][49][50][51][52][53][54][55].…”

Reversible Formation of Thermoresponsive Binary Particle Gels with Tunable Structural and Mechanical Properties

“…6,7 Despite decades of research into gelating colloids, a full understanding of the kinetics of these systems has proven elusive. 8 Research points towards a gel formation that follows a path of spinodal decomposition and subsequent arrest, 9,10 while the formation kinetics and final structure have proven hard to predict. 11,12 Similar arrest kinetics are also observed in glasses, which show similarities to gels in structure and dynamics 13 and the subject of caging effects is relevant to understanding both glassy and gel properties.…”