# Lengthscales in everyday materials

If you are a non-science major; a scientist or just plain interested in understanding the science in everyday phenomena then you are in the right place. We hope that understanding everyday experiences as materials will unlock a whole new world. The underlying theme in this course is the emergence of everyday phenomena from building blocks at smaller constituent scales. This is the first fundamental insight that will be borrowed from centuries of research and fundamental breakthroughs in material science.

Why is the material point of view so insightful? More than two centuries of materials science has revealed that building blocks at extremely small scales lead to the emergence of material properties such as elasticity, hardness, brightness, durability, etc. We also understand how and why transitions from one phase to another like solid → liquid or liquid → gas occur. And while there are all sorts of materials, we know that for the most part, all of them fall into one of 3 categories: solid/liquid/gas (in the next chapters we will explain how many materials actually have a combination of the 3 categories). While Diamond and ice are completely different, statistical mechanics tells us that they are solids for the same universal reasons. Whether a material is solid liquid or gas is not something decided externally. The macroscopic material property emerges because at lower temperatures, molecules stop jumping around as much as they do at higher temperatures, and instead prefer to get closer to their neighboring molecules. This in turn makes molecules arrange in neat crystalline configurations, and they become a solid.

What you might not have known is that even though materials are extremely predictable e.g. water always boils at 1000 C under normal conditions; each individual water molecule is not at all predictable. In fact, molecules behave randomly - they keep jumping around all over the place. If you have seen dust floating on a sunny day - that's pretty much what molecules do, they bump into other molecules and bounce around. But because there are so many molecules in materials, on average material properties are predictable. This brings us to the second fundamental insight. Many times, a sufficient number of individual unpredictable actors can lead to predictable emergent macroscopic phenomena. Take traffic for example: individuals drive erratically, while traffic patterns are surprisingly predictable.

This book is organized into mini chapters that reflect various scales of phenomena in the physical world as shown in the image.

## Building blocks at tiny length scales

In regular materials, material properties emerge from interactions at very small length scales ranging from the nuclear scale (10-15m) to the atom (10-11m) and the atomic lattice (10-10m) scale. For those of you unfamiliar with scientific notation, 10-1m = 1/10 m or 0.1m; 101m = 10m; and 100m = 1m. It's just a convenient way of writing numbers that have a lot of zeros. The size of the nucleus for example is very long to write - 10-15m = 1/1,000,000,000,000,000 m or 0.000000000000001m! It's very easy to make mistakes, and for calculations it's much easier to think in terms of the scientific notation. Further, this length scale does not denote the absolute value. The Hydrogen atom has a diameter of approximately 10-10m, whereas the Carbon atom has a diameter of 3 x 10-10m. 10-10m denotes the order of magnitude. Often while dealing with such varied length scales the order of magnitude is more important than the actual numeric value.

It is precisely the composition of nucleus and atoms as well as arrangement of these atoms that give materials their properties. Hydrogen for example is the most abundant chemical element, and the lightest element in the periodic table. It is extremely reactive because of it's atomic structure. Carbon on the other hand is more stable due to its atomic structure. However, all Carbon forms are not the same. The main reason Diamond is so different from Graphite even though they are both composed of Carbon atoms is because of the arrangement of these Carbon atoms. Diamond takes atleast 1 Billion years to form at extremely high pressures; which makes it into a highly compact 3D arrangement of Carbon atoms. Graphite on the other hand is organized into sheets of Carbon atoms, with weak links between sheets and is very different from diamond. This highlights that the various scales of building blocks in materials are all important, and need to be considered together.

## Building blocks at intermediate lengthscales

Soap is an essential part of our lives both for cleaning dirt and for having fun! But why are soap bubbles stable? It's because they contain special large soap molecules that are 10-9m in size - an order of magnitude larger than typical single element atoms like Carbon. These soap molecules have 2 ends. The head end likes water, whereas the tail end like oil. By sitting at the water - air or water - oil interface, these molecules stabilize soap bubbles. Without them, it wouldn't even be possible to have bubbles. Imagine a life without bubbles!

Another example of a material whose properties arise from building blocks at the intermediate length scale is ice cream. Ice cream is fluffy due to air bubbles at the 10-6m scale. How important are these air bubbles? Well if you've ever kept ice cream out for a few hours, and put back in the freezer, only to have it the next day and find that it's flat - well that is because the ice cream lost much of the trapped bubbles.

## Building blocks at large lengthscales

Finally we come to the largest scale wherein collective human and animal experiences lie. As a concrete example, take traffic. Above a certain number of vehicles/km/lane (around 50 cars/km/lane); traffic jams emerge naturally due to human driver interactions. Above this density, vehicles can't react quick enough to the vehicle in front, and just because of this you can get traffic jams (for no apparent reason!). Moreover, just like atoms bumping around; drivers are also unpredictable. Just ask anyone or reflect on your experiences in traffic. Someone whizzes past doing 20 mph over the speed limit. Another person is distracted by their cell phone. However, in the same vein as materials, traffic patterns are much more predictable. In fact, the transition from 3 Am traffic to rush hour traffic can be thought of in the same vein as phase transitions in materials! However unlike in materials, the key building blocks of traffic are at the scales of vehicles and traffic infrastructure. The well established framework of materials offers a way to understand how macroscopic behaviors emerge from constituent building blocks in our everyday lives.

After this course, you too will hopefully never see the world the same and routine everyday experiences will seem fascinating. The opposite might happen as well - seemingly unpredictable features in our everyday world might seem to make more sense. Unlike other traditional science texts on fields like physics, chemistry, biology; this will be interdisciplinary. And rather than first covering concepts and then application, this will be focused on different material themes. Along the way, we will describe any scientific content that is required to understand the subject matter. This first chapter is a good example. It is titled length scales in everyday materials. Rather than first introducing scientific notation, I embedded it when discussing how material properties emerge from different scales. Personally, I learn something new the best when it's part of a larger goal. Here the goal is understanding everyday phenomena as emerging from key building blocks. The knowledge you gain is not limited to materials, but is more of developing an inquisitive and analytical frame of mind. Breaking down complex problems into their building blocks and solving; regardless of what the problem is.

Finally, this book is far from a comprehensive review on the subject. One huge benefit of understanding the emergence of everyday phenomena from interactions at relevant length scales lies in predicting the future. Let's go back to the example of predictable traffic jams above a particular vehicle density around 50 cars/km/lane. In the near future, we will have autonomous vehicles driving in smart cities. It's still an open question if we can alleviate traffic jams by modifying vehicles or road infrastructure such as traffic lights, all of which are the key building blocks for traffic. The science of materials could offer powerful analogies and frameworks to understand and predict these and more phenomena. Thus building a better, safer, and more resilient future. And hey, you might be hungry for more after reading this and become a pioneer! Reach me at: svivek@ggc.edu

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