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Materials science

Soft is strong

Nature volume 462, pages 4546 (05 November 2009) | Download Citation

The mechanisms that govern the rate at which glasses soften on heating have long been a mystery. The finding that colloids can mimic the full range of glass-softening behaviours offers a fresh take on the problem.

For hundreds of years, scientists have wondered how glass-forming liquids solidify without crystallizing as they cool — or indeed without undergoing much change in structure at all. Glass artists take advantage of this continuous rigidification process to create and preserve liquid 'form' and 'action', fascinating onlookers as they turn glowing globs of hot molten glass into elegant shapes. The artists take care to use a glass-former that converts to a solid over a wide range of temperatures, so that they have time to work their magic. Other glass compositions make the transition from fluid to solid much more suddenly, and it would be impossible to work with them.

Glass-forming liquids that soften quickly on heating are described as being fragile, whereas those that don't are 'strong'. The same distinction is made to describe the behaviour of liquids under compression — fragile liquids 'jam up' suddenly into glasses under pressure, and strong ones don't. But we don't know why. On page 83 of this issue, Mattsson et al.1 report that the same pattern of strength and fragility holds for certain colloidal suspensions, and that they do know why. This offers hope that colloids could be used as model systems to help describe liquid behaviour.

To explain Mattsson and colleagues' findings, we first need to remind ourselves of the difference between colloids and liquids. Liquids are composed only of molecules (or atoms or ions), which ceaselessly collide, oscillate and diffuse. The fissures and gaps that form transiently in liquids are empty of matter. Colloidal suspensions, on the other hand, consist of microscopic chunks of matter, usually — but not necessarily — spherical in shape, suspended in a liquid medium. The suspended matter would settle slowly to the bottom of the colloid if it were not for the impacts it makes with the endlessly oscillating molecules of the liquid. Instead, the particles undergo Brownian motion, diffusing randomly, much like molecules, and providing a source of wonder for generations of science students peering down microscopes. To describe all of this, one can measure the viscosity of the colloid, the diffusivity of the particles (a measurement of the particles' ability to diffuse through a particular medium) and the corresponding relaxation process that occurs when shear stress in the fluid is dissipated by viscous flow of liquid molecules or colloidal particles.

In most colloids that have been studied, the suspended particles are as solid as rock. As the concentration of the particles is increased (and so too the percentage of the colloid's volume that is occupied by particles, known as the packing fraction), the relaxation times of the colloids increase dramatically. The relaxation time reaches 100 seconds — the relaxation time that defines the glass transition point of a material — at a packing fraction of 0.58. This value is called the glass transition packing fraction by analogy with the glass transition temperature. The behaviour of such colloids is remarkably similar to that of 'hard-sphere fluids' (the classical model of liquids in which the liquid particles are thought of as non-compressible spheres), for which the maximum packing fraction seems to be 0.64–0.65 (refs 2,​3,​4,​5). The behaviour of hard-particle colloids turns out to be the fragile extreme of colloidal behaviour.

To get the equivalent of strong behaviour, Mattsson et al.1 had to make their colloid particles soft. Such particles deform as they are packed closer together, tending to become cuboidal instead of spherical — a process brought about by a redistribution of the solvent inside the particles. To study the effects of different degrees of softness, the authors made three different kinds of particle from polymer networks that had different cross-linking densities. They were thus able to observe the effect of particle softness on the relaxation times of the colloids. The authors found that the variation of colloidal relaxation times with respect to particle concentration changes distinctively as the particles become harder (Fig. 1a).

Figure 1: Colloidal relaxation times are analogous to liquid fragility.
Figure 1

a, Mattsson et al.1 report that the variation of colloidal relaxation time, τα, with respect to colloidal particle concentration, ζ, (scaled by the particle concentration at glass transition, ζg), depends on the softness of the particles. k is a scaling factor. b, The variation of viscosity, η, with volume, V (scaled by the volume V* at glass transition) for certain glass-forming liquids was previously reported by King and colleagues7, some of whose data are reproduced here. The trends observed in a are strikingly similar to those of the viscosity–volume relationships: τα of the 'hard' colloids varies like the viscosity of fragile liquids (such as isopropylbenzene, shown); τα of colloids of intermediate softness varies like the viscosity of intermediate liquids (which have viscosities somewhere between fragile and strong, such as glycerol, shown). No comparable data for the viscosities of strong liquids are available. Viscosities were reported in centipoise.

So how do these data1 connect with the fragility of glass-forming liquids? To find out we must go back to the 1990s, when King and colleagues6,7 studied the effect of volume compression on the viscosity of certain non-crystallizing liquids. In a series of heroic experiments, they suspended balls of nickel in tiny volumes of liquid inside high-pressure diamond-anvil cells, then whirled the cells around in circles so that huge centrifugal forces acted on the balls. By measuring the distance rolled by the balls in a known period of time, King and colleagues calculated the viscosities of many liquids, over enormous ranges of viscosity and pressure, all with high precision (Fig. 1b). The variation in colloidal relaxation times measured by Mattsson et al.1 is strikingly similar to that of King and colleagues' viscosity data6,7. In particular, the trends observed by Mattsson et al. in the variation of relaxation time with particle concentration as colloidal particles become harder are the same as the trends in the viscosity–volume relationships of increasingly fragile liquids (Fig. 1).

So, hard colloids are analogous to fragile liquids, whereas soft colloids can be compared to strong liquids. But why is soft strong? Mattsson et al.1 offer the attractive explanation that the elastic energy of colloidal particles — the energy stored when the particles are distorted — determines the fragility of colloids. This meshes nicely with other elasticity-based theories8 that have been proposed to explain the behaviour of glass-forming materials. Nevertheless, we should remember that a strong correlation exists between volume and entropy, and that entropy-based theories of liquid dynamics9 have been very successful10. Energy cannot be stored elastically under pressure without loss of entropy, so it is reasonable to expect a unified theory for fragile behaviour in soft matter to emerge in due course, thus bringing an explanation of the differing fragilities of liquids a step closer.

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  1. C. Austen Angell and Kazuhide Ueno are in the Department of Chemistry, Arizona State University, Tempe, Arizona 85287-1604, USA.  caa@asu.edu; kzueno@ynu.ac.jp

    • C. Austen Angell
    •  & Kazuhide Ueno

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