Salt
Figure1. Sodium Chloride or salt. At room temperature, salt is a crystal based on sodium and chlorine atoms, which are arranged in a lattice [1]. Salt grains are rigid and have high elastic constants. They do not flow and are able to retain their shape.By contrast, liquids like water or oil, have no rigidity; they flow and are unable to retain their shape.

Introduction to Squishy Physics
Alberto Fernandez-Nieves
School of Physics Georgia Tech

We are all familiar with crystalline materials, such as aluminum, ice or salt. They are what we would call hard materials: They are elastic, like springs, and return to their original state after strained a bit. They do not flow and are thus able to retain their shape. Microscopically, if we were to look inside and see the atoms or molecules on which they are based, we would realize that they are all located in very well defined positions, on average. We say the atoms are arranged in a certain structure or lattice (Figure 1). Crystals are thus ordered materials: The atoms are only located in lattice sites and nowhere else.

By contrast to these crystalline materials, liquids flow and do not have a specific shape; in fact, they adopt the shape of the container in which they are kept. At a microscopic level, liquids are very different from crystals. In a liquid, the atoms or molecules are completely disorganized and arranged in a random fashion. We say that the liquid is disordered: The atoms are located anywhere in space without any precise arrangement.

Interestingly, many of the healthcare and personal care products we use every day, many of the foods we eat every day, and many of the materials we see every day in technological applications are neither a crystal nor a liquid; in fact, we might say they have characteristics of both a liquid and a solid. Think about mayonnaise, for example. You can carry it around on your spoon and pass it onto your dish. It looks solid: It does not flow; it retains its shape and behaves elastically, since it recovers its original shape after you have poked it a bit. However, it is very easy to spread: Once you apply a force that is large enough, it behaves like a liquid: It changes shape, it flows and it does not recover its original shape after doing this. Materials like mayonnaise are squishy materials. They are soft and thus easy to deform, but what is most important, they can behave like solids or liquids depending on how you treat them. In most cases, these soft materials are based on mixtures of phases: Small particles in a liquid to form colloidal suspensions, like milk, drops in a liquid to form emulsions, like some salad dressings, and bubbles in a liquid to form foams like shaving cream (Figure 2).

Figure 2
Figure 2. Foams are dispersions of bubbles in a liquid. The image on the left is a picture of a foam made with water, soap and regular air. Red dye is added for easier visualization. At the top, the foam has drained and is drier, while at the bottom the foam is wetter. The image is taken from [2]. Shaving cream is an example of a dense foam. As many other soft materials, shaving cream is easy to deform, but once it is spread on your face it exhibits solid-like properties: It retains its shape and does not flow. In the ocean, air is entrained in salty water to make visually appealing foams; in this case, the density of bubbles is less than in shaving cream and the forces applied on the foam large enough for it to behave pretty much like a liquid.

The interactions between the particles, the drops or the bubbles, together with the number of them that are present per unit volume determine the rich and varied behavior of these materials. For example, in the presence of an attraction between the suspended particles, milk can form yoghurt; and mayonnaise simply results from a very dense emulsion of oil drops in egg yolk.

Liquid crystals, like those used in the screens of most calculators, digital wrist watches and laptops, are also intermediate between a crystal and a liquid. They are interesting states of matter that are not as organized as a crystal, nor as disorganized as a liquid. As a result, they are also not as rigid as solid materials nor do they flow like simple liquids. Typically, the origin to this behavior arises from the shape of the molecules in which they are based. For example, if the molecules are elongated like rods, they can arrange themselves in what we call a nematic phase: They all point in the same direction, but they are not spatially arranged in a lattice. As a result, nematics have what we call orientational order, since all molecules point in the same direction, but lack translational order like that of any crystal. They have some elasticity, but not so much, as they are not fully organized materials, and thus are easy to deform and to manipulate. It is precisely this mixture of solidlike and liquidlike properties that render liquid crystals so useful in so many technological applications.

In this web page, we hope to bring some of these materials to your attention and briefly describe their behavior. Understanding their properties is not only relevant for applications, but also poses fundamental problems that we are still trying to solve. In some cases we use them as models of more complicated materials, like biological materials, whose behavior we wish to describe and eventually predict. In other cases, we use them to explore challenging scientific problems. For instance, J. J. Thomson [3], the discoverer of the electron, wondered in 1904 how a certain number of these negatively charged particles would arrange themselves on the surface of a sphere (Figure 3).

Figure 3
Figure 3. J. J. Thomson, the discoverer of the electron, asked in 1904 what the configuration of N electrons would be if they were arranged on the surface of a sphere, in an attempt to explain the periodic table. By coating an emulsion drop with tiny colloidal particles, scientists have gained enormous insight into this centenary problem [4].

As it turns out, this question still remains largely unknown and is included in the list of sixteen mathematical problems for the XXI century compiled by the famous mathematician, S. Smale [5]. In this same list, one also finds, that we have not yet proven that the maximum volume a collection of spheres occupies when organized in a random fashion is 64% of the total available volume. Despite the fact that we know this from experience, since we can easily measure, for example, the free space left between sugar grains in a container, we still have not been able to show this theoretically. We can design squishy materials to address some of these and other fundamental questions. Through the use of experimentation we hope to make you think about materials and problems that you encounter every day, but that perhaps, you have not thought about deeply enough. Squishy physics can be used to show physics questions arising from everyday life and to convey the excitement of current research [6].

References

[1] C. Kittel, Introduction to solid state physics (John Wiley & Sons Inc. 1996).
[2] E. R. Weeks, Soft jammed materials, in Statistical physics of complex fluids, eds. S. Maruyama, M. Tokuyama (Tohoku University Press, Sendai, Japan, 2007).
[3] J. J. Thomson, Phil. Mag. 7, 237 (1904).
[4] A. R. Bausch, M. J. Bowick, A. Cacciuto, A. D. Dinsmore, M. F. Hsu, D. R. Nelson, M. G. Nikolaides, A. Travesset, and D. A. Weitz, Science 299, 1716 (2003).
[5] S. Smale, Math. Intelligencer 20, 7 (1998).
[6] P. Habdas, E. Weeks, D. G. Lynn, The Physics Teacher 44, 276 (2006).