Critical Dynamics of the Sol-Gel Transition

Abstract

The dynamics of the sol-gel transition is probed by use of quasielastic light scattering. A type of critical dynamics is observed that is associated with a divergent friction, rather than a singularity in a thermodynamic quantity. Several novel effects are reported, including power-law time decay of the intensity autocorrelation function, critical slowing down of the average relaxation time, and observation of a fractal time set in the scattered field.PACS numbers: 82.70. Gg, 61.41.+e A gelling solution at the sol-gel transition is a unique state of matter that is neither liquid nor solid, but rather is in transition between these states. For example, the viscosity of the incipient gel is infinite, but the modulus is zero. Recently we have come to appreciate the unusual dynamics of this transition state by using the technique of quasielastic light scattering x to probe the relaxation of density fluctuations of wave vector q by the autocorrelation function of the scattered intensity, l(q,t) =(1(0)/(/)). In many systems the decay of density fluctuations can be described by a single relaxation time (exponential time decay). More complex materials, such as polymeric melts near the glassy transition temperature, exhibit a spectrum of relaxation times that gives a "stretched" exponential decay, exp[ -(t/r) b ] where 0 < b < 1. Regardless of the form, all known I(q,t) can be described by some characteristic time T. In this paper we demonstrate that in a gelling solution the characteristic time diverges at the sol-gel transition. This observation is unexpected and must not be confused with the usual critical slowing down in second-order thermodynamic phase transitions, since scattered-intensity measurements show that the compressibility does not diverge at the gel point. The fact that a critical slowing down should not be observed in quasielastic light scattering at the gel point has been elaborated by de Gennes, 2 who points out that the longitudinal modes observed in a quasielastic light-scattering experiment should be insensitive to the formation of a weak gel phase.The observation of an infinite characteristic time implies two possible modes of decay. First, the decay can be described by a function that is scaled by a divergent characteristic time, e.g., an exponential decay with r-• <». This is precisely the description of critical slowing down in second-order phase transitions. Second, the form of the decay can be independent of the time scale, at least on times short compared with the characteristic time. This is possible if the decay is described by a function that does not contain a time scale-a power law. In fact, we will show that at the gel point a decay of the form I(q,t)~-\/t 021 is observed over the experimentally accessible 5 decades in time. Before the gel point, this power-law decay is truncated by a stretched-exponential tail, at a certain divergent characteristic time. A simple description of these phenomena is proposed, and we show that the detected photons divide the time axis in a selfsimilar wa...

Critical dynamics of gelation

“…Colby et al 36 report values 1.4 ≤ k ≤ 1.7 and Martin et al obtained k = 1.4 ± 0.2 from viscoelastic measurements 37 and k = 1.5±0.2 rather indirectly from measurements of the incoherent scattering function. 2 The origin of the scatter of the experimental data is not clear. A splitting of the static universality class into different dynamic ones has been suggested.…”

“…2 In the sol phase, a stretched exponential of the autocorrelation was observed, S t (q) ∼ exp{−(t/t q ) α } with α = 0.65 ± 0.05. The experimentally determined timescale t q is diffusive and diverges as the gelation transition is approached t q ∼ (c crit −c) −2.2 .…”

“…There are strong precursors of the gelation transition in the fluid-like sol phase: The decay of correlations is not exponential, but follows a Kohlrausch law. 2 This indicates a spectrum of relaxation times extending to arbitrary large values.…”

Director dynamics in liquid-crystal physical gels

“…However, in the present study, the scattered light arises primarily from fluctuations in the orientation of the nematic director, not density fluctuations as in the previous lightscattering studies of gelled systems [23][24][25][26][27][28][29] . Therefore, structural changes such as micellar diffusion or concentration fluctuations in the polymer network are revealed indirectly by their effect on the nematic-director dynamics.…”

Synthesis and characterization of nanocrystalline hydroxyapatite gel and its application as scaffold aggregation

“…The results show strong similarities with the theory of the structural glass transition 23 . The gelling solution at the sol-gel transition is a unique state of matter that is neither liquid nor solid, but rather is in transition between these states 24 . The resulting structure after the gel formation and shown in the ESEM image (Figure 3) is similar with the theoretical images obtained by colloidal route 25,26 .…”