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Molecular Dynamics Primer: Introduction (Non-technical)

*Work in Progress*

Molecular Dynamics (MD) is a set of mathematical tools that enable researchers to investigate small-scale structures and processes. Here, "small-scale" typically refers to nanoscale objects. Along the line, we will study the use, scope of limitations of MD further. 

Let's look at the big picture. Your computer, for example, consists of thousands of parts. Each part again consists of few to few million even smaller components. If we dive deep, we will end up with these:
  • Transistors (Too many of them, they are the heart of electronic systems)
  • Resistors and capacitors (Basic electric circuit component, resists or stores charge)
  • Copper or Aluminium wires (Typically embedded inside the Printed Circuit Board for electrical connections)
  • Plastic and inorganic compounds (Used as case materials, keys etc. Some high-end ones will give you more metal)
So far so good. Now suppose you are an engineer and your boss asks you to modify the thermal design of the laptop to reduce the maximum temperature during peak load. How would you do that? One approach would be-
  1. Run the laptop as it is now.
  2. Record temperature at different parts of the laptop under different load.
  3. Identify hot spots.
  4. Open the back cover and observe the configuration of the heat pipes and fan.
  5. You may simplify and model the system in a Finite Element software, like COMSOL and simulate different scenarios.
  6. Take some decision based on your observation. For example, is the conductivity of the heat pipe too low? Or is it not in the vicinity of the hot spots? Maybe the fan is not powerful enough or the intake and exhaust ports are partially blocked.
  7. Compare your proposed approach against the limitations. Maybe you can't use Copper heat pipe because it is too expensive or maybe a more powerful fan will produce too noise.
  8. Once a solution is chosen, build a prototype and re-evaluate.
Now, let's look at another problem. Say you want to understand how your coffee mug breaks when it drops. Coffee mugs are, generally, made from some ceramic material. As you may already know, these materials tend to break suddenly, also known as the brittle failure, as opposed to tearing of rubber band. You can drop a lot of mugs and use a highspeed camera to see the crack initiation and propagation, but that is surely not the best way to go. As a start, you can look at the material instead of the coffee mug as a whole. Standardized test results of various ceramic-like material are available in the literature. You will find that after a certain stress, the crack propagates from micro-scale crack points already present in the material (mostly occurs during manufacturing phase).

If you want to predict some more interesting properties of ceramic or perhaps a novel material, you can perform even more tests. However, these tests have some limitations. Apart from being time-consuming, there is a limit of how small can you go. From the coffee mug, you can go to a broken piece, then you can make an even smaller piece from there. If you are persistent, you can make a good sample, put it under a microscope and look at what is called the crystal structure. With modern equipment, you can even perform lots of tests at that scale. But there is a limit, be it time, money, or opportunity.

Let's compare your coffee mug to your laptop now. Your coffee mug is made of ceramic, it can be divided (or broken!) into parts, each part has more tiny pieces glued together etc. etc. At the very end, you will meet the atoms, and after that the elementary particles. Similar to the laptop process, we are trying to solve a problem. In this case, we are interested in how the coffee mug breaks or how the crack initiation and propagation mechanism works.

First, let's simplify our problem. Look at the coffee mug and choose a small area to study (How small? More on that later). In general, there will be lots of microcracks all over the mug, so any area is OK for now. This small area will be our hot spot. We can look at it very closely and ignore all the rest. Since most of the areas are similarly filled with crack, crack propagation will work quite similarly for these spots too. And that is STEP 3 from laptop problem. 

Now, you can look at it under the microscope again to find some pattern. But you have been there already. So, let's try something else. We are going to simulate it. And we will use Molecular Dynamics (MD) to simulate this problem. Before doing that, we have to tackle two big questions:

1. Why simulate?
Experiment at small scale is still not very feasible. You will need specialized types of equipment that are very costly. Further, there are many things that are not simply accessible via experiment. For example, if you want to measure the shear stress at an internal point of a solid object experimentally, your will be in trouble. Simulation offers a very good alternative to these sort of proble and the predictions are quite good.

2. Why MD?
What do we understand by the term "simulation"? We are mathematically modeling a system or process and solving the resulting equations. The equation can be as simple as x+y = 3 and y = 9; solve for x & y, and voila! Or the problem can involve complicated differential or integral equations. If you are simulating a macro-scale (everyday life) fluid system (say air flow within your laptop), you may solve the Navier-Strokes equation using Finite Difference or Finite Element like methods. For elasticity problems, you may solve coupled equilibrium and the constitutive equations. For electronic structure, you may solve Schrodinger's equation! Each method has their strength and weakness. If the equations are too complicated, it will take a long time to solve them (for example, Schrodinger's eqn). If the equations are too simplified, the model may not correctly represent the physical system in question. For reference, many macroscopic systems can be solved using Finite Element based methods with adequate accuracy and speed but this method is hardly suitable as the system becomes microscopic or involve quantum mechanics. These limitations stem from the nature of equations under consideration and the mathematical techniques being used to solve them. For a molecular system, for example- a protein, molecular dynamics offers a good balance between accuracy and speed.

There are different flavors of MD. In classical MD, we consider each particle as hard spheres (forget proton and electrons!). We then write Newton's equation of motion, F = ma for all the particles and solve all the equations. This enables us to calculate the trajectory of all the atoms. For the coffee mug, we can essentially calculate the movement of atoms as the crack propagates and visualize every atom in the hot spot! Apart from visualization, we can also calculate many interesting properties related to these sort of problems. From the analyses, you may come up with some new theory of crack propagation!

That was our STEP 5. The MD software instruction set will take care of STEP 4. If the experimental results for the problem you are studying are already available, you can check your results against that one or you may convince someone to do the experiment to validate your findings. Or you may compare your findings with currently accepted views. That is somewhat comparable to STEP 6 & 7. And since it's a computer study, we can skip the last step.

Now, we (briefly) covered why we might want to simulate something using a procedure called MD, we will look at the basic of MD itself in the next article.


Updated: May 07, 2018

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