Weak and Strong Gels and the Emergence of the Amorphous Solid State.

Jack Douglas

doi:10.3390/gels4010019

Abstract

Gels are amorphous solids whose macroscopic viscoelastic response derives from constraints in the material that serve to localize the constituent molecules or particles about their average positions in space. These constraints may either be local in nature, as in chemical cross-linking and direct physical associations, or non-local, as in case of topological “entanglement” interactions between highly extended fiber or sheet structures in the fluid. Either of these interactions, or both combined, can lead to “gelation” or “amorphous solidification”. While gels are often considered to be inherently non-equilibrium materials, and correspondingly termed “soft glassy matter”, this is not generally the case. For example, the formation of vulcanized rubbers by cross-linking macromolecules can be exactly described as a second order phase transition from an equilibrium fluid to an equilibrium solid state, and amorphous solidification also arises in diverse physical gels in which molecular and particle localization occurs predominantly through transient molecular associations, or even topological interactions. As equilibrium, or near equilibrium systems, such gels can be expected to exhibit universal linear and non-linear viscoelastic properties, especially near the “critical” conditions at which the gel state first emerges. In particular, a power-law viscoelastic response is frequently observed in gel materials near their “gelation” or “amorphous solidification” transition. Another basic property of physical gels of both theoretical and practical interest is their response to large stresses at constant shear rate or under a fixed macroscopic strain. In particular, these materials are often quite sensitive to applied stresses that can cause the self-assembled structure to progressively break down under flow or deformation. This disintegration of gel structure can lead to “yield” of the gel material, i.e., a fluidization transition, followed by shear thinning of the resulting heterogeneous “jelly-like” fluid. When the stress is removed, however, the material can relax back to its former equilibrium gel state, i.e., gel rejuvenation. In contrast, a non-equilibrium material will simply change its form and properties in a way that depends on processing history. Physical gels are thus unique self-healing materials in which the existence of equilibrium ensures their eventual recovery. The existence of equilibrium also has implications for the nature of both the linear and non-linear rheological response of gel materials, and the present paper explores this phenomenon based on simple scaling arguments of the kind frequently used in describing phase transitions and the properties of polymer solutions.

Highlights

Gels are ubiquitous—many foods, consumer products and industrial products can be defined as belonging to a rheologically-defined class of materials termed “gels”
The present work mainly focuses on the “critical” regime in which a liquid transform at equilibrium into a solid material, regardless of the specific interactions giving rise to the particle or molecular localization underlying gelation. This dynamical transition has many special physical and mathematical features that are not generally appreciated by physical scientists working with gels, and the present paper focuses on summarizing results that are dispersed in the fundamental physics, mathematics, and experimental polymer science and colloidal science literatures
It is emphasized that amorphous solidification at equilibrium necessitates a “universal” power-law stress relaxation response near the point where the gel state first emerges [10] and the occurrence of this dynamical transition is suggested to rationalize the rather general observation of power-law relaxation near the gel point in diverse forms of condensed matter

Summary

Introduction

Gels are ubiquitous—many foods (e.g., gelatin, cheese, ketchup), consumer products (e.g., toothpaste, cosmetics, shaving cream, etc.) and industrial products (e.g., adhesives, asphalt) can be defined as belonging to a rheologically-defined class of materials termed “gels” (see gel reviews cited below). Gels exhibit universal viscoelastic properties under the thermodynamic conditions in which the gel state first emerges, and this dynamical phase transition generally gives rise to a power-law scaling of the shear stress relaxation function G(t) with time t (see below), along with other scaling properties associated with an underlying dynamic phase transition [10] These scaling relations are often observed in real gel materials (general reviews on this phenomenon are indicated below), and lately these scaling relations have been ascribed generally to the non-equilibrium nature of gels [8,9]. The general tendency of physical gels, and viscoelastic pre-gel solutions of self-assembled molecules and particles, to approach an equilibrium state after a sufficient time has many implications for both the linear and non-linear rheological properties of this class of materials, and the present paper explores this phenomenon based on scaling arguments of the kind frequently used in describing phase transitions and polymer solution properties. We focus on the effect shear flow on the properties of this type of physical gel

Definition of “Weak” and “Strong” Gels

Simple Models of the Non-Linear Rheology of Pre-Gels and Gels

Conclusions