Mechanics of gelation describes processes relevant to sol-gel process. In a static sense, the fundamental difference between a liquid and a solid is that the solid has elastic resistance against a shearing stress while a liquid does not. Thus, a simple liquid will not typically support a transverse acoustic phonon, or

shear wave __NOTOC__ In seismology and other areas involving elastic waves, S waves, secondary waves, or shear waves (sometimes called elastic S waves) are a type of elastic wave and are one of the two main types of elastic body waves, so named because th ...

. Gels have been described by Born as liquids in which an elastic resistance against shearing survives, yielding both viscous and elastic properties. It has been shown theoretically that in a certain low-frequency range, polymeric gels should propagate shear waves with relatively low damping. The distinction between a sol (solution) and a gel therefore appears to be understood in a manner analogous to the practical distinction between the elastic and plastic deformation ranges of a metal. The distinction lies in the ability to respond to an applied shear force via macroscopic viscous flow. In a dynamic sense, the response of a gel to an alternating force (oscillation or vibration) will depend upon the period or frequency of vibration. As indicated here, even most simple liquids will exhibit some elastic response at shear rates or frequencies exceeding 5 x 10⁶ cycles per second. Experiments on such short time scales probe the fundamental motions of the primary particles (or particle clusters) which constitute the lattice structure or aggregate. The increasing resistance of certain liquids to flow at high stirring speeds is one manifestation of this phenomenon. The ability of a condensed body to respond to a mechanical force by viscous flow is thus strongly dependent on the time scale over which the load is applied, and thus the frequency and amplitude of the stress wave in oscillatory experiments.

Structural relaxation

The structural relaxation of a

viscoelastic In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly ...

gel has been identified as primary mechanism responsible for densification and associated pore evolution in both colloidal and polymeric silica gels. Experiments in the viscoelastic properties of such skeletal networks on various time scales require a force varying with a period (or frequency) appropriate to the relaxation time of the phenomenon investigated, and inversely proportional to the distance over which such relaxation occurs. High frequencies associated with ultrasonic waves have been used extensively in the handling of polymer solutions, liquids and gels and the determination of their viscoelastic properties. Static measurements of the shear modulus have been made, as well as dynamic measurements of the speed of propagation of shear waves, which yields the dynamic

modulus of rigidity In materials science, shear modulus or modulus of rigidity, denoted by ''G'', or sometimes ''S'' or ''μ'', is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain: :G \ \stackrel ...

Dynamic light scattering Dynamic light scattering (DLS) is a technique in physics that can be used to determine the size distribution profile of small particles in suspension or polymers in solution. In the scope of DLS, temporal fluctuations are usually analyzed using ...

(DLS) techniques have been utilized in order to monitor the dynamics of density fluctuations through the behavior of the

autocorrelation function Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variabl ...

near the point of gelation.

Phase transition

Tanaka ''et al''., emphasize that the discrete and reversible volume transitions which occur in partially hydrolyzed acrylamide gels can be interpreted in terms of a

phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states o ...

of the system consisting of the charged

polymer A polymer (; Greek '' poly-'', "many" + ''-mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...

network, hydrogen (counter)ions and liquid matrix. The phase transition is a manifestation of competition among the three forces which contribute to the osmotic pressure in the gel: # The positive osmotic pressure of (+)

hydrogen ion A hydrogen ion is created when a hydrogen atom loses or gains an electron. A positively charged hydrogen ion (or proton) can readily combine with other particles and therefore is only seen isolated when it is in a gaseous state or a nearly particle ...

s # The negative pressure due to polymer-polymer affinity # The rubber-like elasticity of the polymer network The balance of these forces varies with change in temperature or

solvent A solvent (s) (from the Latin '' solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usually a liquid but can also be a solid, a gas, or a supercritical fluid. Water is a solvent for ...

properties. The total osmotic pressure acting on the system is the sum osmotic pressure of the gel. It is further shown that the phase transition can be induced by the application of an electric field across the gel. The volume change at the transition point is either discrete (as in a first-order Ehrenfest transition) or continuous (second order Ehrenfest analogy), depending on the degree of ionization of the gel and on the solvent composition.

Elastic continuum

The gel is thus interpreted as an elastic continuum, which deforms when subjected to externally applied shear forces, but is incompressible upon application of hydrostatic pressure. This combination of fluidity and rigidity is explained in terms of the gel structure: that of a liquid contained within a fibrous polymer network or matrix by the extremely large friction between the liquid and the fiber or polymer network. Thermal fluctuations may produce infinitesimal expansion or contraction within the network, and the evolution of such fluctuations will ultimately determine the molecular morphology and the degree of hydration of the body. Quasi-elastic light scattering offers direct experimental access to measurement of the wavelength and lifetimes of critical fluctuations, which are governed by the

properties of the gel. It is reasonable to expect a relationship between the

amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...

of such fluctuations and the elasticity of the network. Since the elasticity measures the resistance of the network to either

elastic Elastic is a word often used to describe or identify certain types of elastomer, elastic used in garments or stretchable fabrics. Elastic may also refer to: Alternative name * Rubber band, ring-shaped band of rubber used to hold objects togeth ...

(reversible) or

plastic Plastics are a wide range of synthetic or semi-synthetic materials that use polymers as a main ingredient. Their plasticity makes it possible for plastics to be moulded, extruded or pressed into solid objects of various shapes. This adaptab ...

(irreversible) deformation, the fluctuations should grow larger as the elasticity declines. The divergence of the scattered light intensity at a finite critical temperature implies that the elasticity approaches zero, or the

compressibility In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility or, if the temperature is held constant, the isothermal compressibility) is a measure of the instantaneous relative volume change of a f ...

becomes infinite, which is the typically observed behavior of a system at the point of instability. Thus, at the critical point, the polymer network offers no resistance at all to any form of deformation.

Ultimate microstructure

The rate of relaxation of density fluctuations will be rapid if the restoring force, which depends upon the network elasticity, is large—and if the friction between the network and the interstitial fluid is small. The theory suggests that the rate is directly proportional to the elasticity and inversely proportional to the frictional force. The friction in turn depends upon both the viscosity of the fluid and the average size of the pores contained within the polymer network. Thus, if the elasticity is inferred from the measurements of the scattering intensity, and the viscosity is determined independently (via mechanical methods such as ultrasonic attenuation) measurement of the relaxation rate yields information on the pore size distribution contained within the polymer network, e.g. large fluctuations in polymer density near the critical point yield large density differentials with a corresponding bimodal distribution of porosity. The difference in average size between the smaller pores (in the highly dense regions) and the larger pores (in regions of lower average density) will therefore depend upon the degree of phase separation which is allowed to occur before such fluctuations become thermally arrested or "frozen in" at or near the critical point of the transition.

References

External links