Heterogeneous Diffusion in a Reversible Gel

Abstract

We introduce a microscopically realistic model of a physical gel and use computer simulations to study its static and dynamic properties at thermal equilibrium. The phase diagram comprises a sol phase, a coexistence region ending at a critical point, a gelation line determined by geometric percolation, and an equilibrium gel phase unrelated to phase separation. The global structure of the gel is homogeneous, but the stress is only supported by a fractal network. The gel dynamics is highly heterogeneous and we propose a theoretical model to quantitatively describe dynamic heterogeneity in gels. We elucidate several differences between the dynamics of gels and that of glass-formers.PACS numbers: 61.43. Bn, 82.70.Gg, 61.20.Lc Although gels are commonly used in everyday life they continue to offer fundamental challenges to research. Their physics is determined by a wide window of lengthscales, from the molecular size of particles in the solvent to macroscopic structures, and by a similarly broad range of timescales: Gels are "complex" fluids [1]. Of particular interest are physical gels which are typically made of molecules forming a stress-sustaining network, with links that have a finite lifetime, as opposed to chemical gels where junctions are permanent and properties follow directly from geometry. The transient character of the network in physical gels results in a complex interplay between structure and dynamics, leading to non-trivial flow properties. Here we propose a model of a reversible physical gel which is microscopically realistic (we are in fact inspired by one particular material), and specifically design a hybrid Monte Carlo / molecular dynamics numerical approach to successfully bridge the gap between microscopic details and macroscopic observations, while offering deep insight on the nature of physical gels.Inspired by recent experimental work on gelation, a variety of "minimal" models have recently been studied to elucidate the connection between gelation and seemingly related phenomena: Geometric percolation [2, 3], glass transition [4,5,6], phase separation [7,8]. Detailed experiments performed with colloidal particles with tunable interactions [9] revealed that a non-trivial interplay between phase separation and kinetic arrest may produce gel-like structures. Associating polymers constitute another well-studied example of reversible gels [1]. In that case, gels can be obtained far from phase separation, producing viscoelastic materials with highly non-linear rheological properties that are not well understood [10,11]. In many cases, a close similarity between gelation and glass formation is reported [1]. We explain below this similarity but discuss also important differences.Our model is inspired by a material described in Ref. [11]. It is a microemulsion of stable and monodisperse oil droplets in water mixed with telechelic polymers, i.e. long hydrophilic chains with hydrophobic end caps. A polymer can form a loop around a single droplet, or, more interestingly, a bridge between two drople...

Relaxation dynamics in a transient network fluid with competing gel and glass phases

“…Denoting by C ij the number of polymers connecting droplets i and j, we have established in Refs. [17,19], that the following interaction is a reasonable coarse-grained representation of this ternary system:…”

“…Our model system is a coarse-grained representation [17] of a transient gel which has been studied in experiments [18]. In this system, an equilibrium lowdensity gel is obtained by adding telechelic polymers to an oil-in-water microemulsion.…”

“…In general, these paths lead to spatially heterogeneous structures. However, in recent times, considerable effort has been made to devise ways by which spatially homogeneous physical gels can be formed [10,[17][18][19][20][21][22][23][24][25][26]. For such gel-forming systems, a wide variety of relaxation functions have been reported: logarithmic [27][28][29][30], stretched [16] or compressed exponentials [21,31].…”

Bond formation and slow heterogeneous dynamics in adhesive spheres with long-ranged repulsion: Quantitative test of mode coupling theory

“…Nonequilibrium origins of the low angle scattering peaks also were suggested by the observation of their time evolution [22,25]. Alternatively, to reach gelation from the fluid, liquid-gas phase separation can be prevented setting a maximum number of bonds per particle [26] or total number of bonds in the system [27]. In these cases, gelation is directly connected to percolation, and the low-q modes facilitate the relaxation of the whole system, due to the lack of stiffness (only two to four neighbours are allowed on average).…”

Ultra-long-range dynamic correlations in a microscopic model for aging gels

“…Gels are lowdensity structures forming percolating networks, with bonds that are either permanent (chemical gels) or transient (physical gels) [1][2][3][4][5][6]. A prevalent method to form physical gels follows a nonequilibrium route by quenching a homogeneous fluid into a phase coexistence region [1,[7][8][9][10][11][12], which generates bicontinuous structures.…”