Sue Lee, Week #1

My first week at MIT has been exciting and full of new challenges. On my first day, I stumbled into building 36, also known as the Research Laboratory of Electronics (RLE) building, slightly overwhelmed and quite nervous. Dr. Berggren’s lab was located on the second floor, and was pretty easy to locate among the many labs in the building, being the first lab in the hallway. It was 9AM on a Monday morning, and only a few other members in the lab were present. The postdoctoral fellow that I had been contacting via email soon arrived and instructed me to go to the Atlas Service Center to get my ID, leaving me with a map of the campus (he had to run to a meeting). I got my ID, and found my way back to the my information center of the RLE department, where the guy at the desk inputed my information into the system and gave me a little welcome package. I went back to the lab, where Dorothy, a sweet lady and the administrative assistant of Dr. Berggren’s lab, tagged me onto the lab email address and gave me an info packet about the lab. Soon thereafter I was introduced to the graduate student I was assigned to work with, Brian, and we went into the conference room so that he could explain the logistics of his project to me. I felt pretty good that I could actually understand most of what he said, based on the literature reviews I have read beforehand, and that I could finally understand the parts I failed to understand on my own. By the time the meeting was over and I finally had time to grab lunch, it was 3:30PM. I didn't even realize how hungry I was because of all the adrenaline rushing through me.

Brian's research is mainly focused on using the Ising model to simulate the process of block copolymer self assembly. Firstly, the Ising model is a mathematical model dealing with magnetism that is actually used very commonly in the field of statistical mechanics. The model allows the identification of phase transitions by using the magnetic dipole moments of atomic spins that are either in the state of +1 or -1. When the temperature is high, the state of the atomic spins are randomly oriented. As the temperature is decreased, the spins become oriented into two ways: ferromagnetic and antiferromagnetic. Ferromagnetic means that the spins are aligned in one direction (all +1 or all -1) and antiferromagnetic means that spins are in alternating directions (+1 -1 +1 -1…). The first step of the project was to create a code that would create a 100x100 array/matrix of +1 or -1 states that would ultimately, through copious iterations, reach an array of entirely +1 or -1 states. To accomplish this, I used the Hamiltonian equation:

which calculates the energy of the system with the given pairs of magnetic spins. In any given system, the total energy is reduced to its minimum, which is favorable due to increased stability. In the equation, the J and the h are constants which I set as 1 and 0 in my code for the sake of simplicity (we will look into the significance/impact of these values later on). The sigma i and sigma j represent the "spin" values of the nearest neighbors (top, left, bottom, right) of a randomly chosen point (row_chosen, col_chosen) within the array. The energy between the points in the array, as well as the energy of the points themselves are summed to calculate the total energy, H(sigma).
You may ask, how exactly can the Ising model be applied to directed self assembly of block copolymers, an incredibly complex technology with many possible deviations? Indeed, the model represents a much simplified version of the process of self assembly. However, this is the beauty of the model: the different “spins” represent the existence of a bond between two neighboring posts in the template of block copolymers. The +1 magnetic spin symbolizes a connection between two posts, while the -1 spin symbolizes the lack thereof of such connection. Thus, a binary code of +1 and -1 is used to create a model of the pattern of block copolymers. (I will be further getting into this this coming week.)

We wanted to create a code that would create a continuous array, much like a sphere, so that each chosen point would have all four nearest neighbors (top, left, bottom, right). This meant taking into account each extraneous case of having a random point chosen on either one of the four edges of the square array. This took a a good amount of trial and error, but after a few days of rerunning my code and barraging my grad student with questions, I succeeded in creating the code. Now, all I had to do was incorporate the Hamiltonian equation to determine which values (of the randomly selected points) would be inverted (switch signs) or not, which depended on the temperature (T) of the system and thus the probability given by the equation P= exp(H-H1)/T. Lastly, I was required to test different values for my three variables (iter, iter2, and a) to determine which combination of numbers would yield the most successful, most effective algorithm. After another few days of testing hundreds of combinations and analyzing the resulting data, I succeeded in achieving an entirely +1/-1 array after approximately 20 million iterations, which takes about 3 minutes for each run. We can visualize the effectiveness of the code by an image of black and white pixels which represent the +1 and -1 values of the array. I have made a presentation with the visualizations, which I will be presenting to Professor Berggren this week.

I met Diana and her family at the MIT graduation on Thursday, which was definitely one of the many highlights of the week. During my first weekend, my mom, me and my brother went on the famous duck tour that tours the landmarks of Boston on land and on the Charles River, ate one of the best lobster rolls I’ve ever had in my life, and sat next to Ban Ki-moon, former Secretary General of the United Nations, at a restaurant named Koreana. Yes, Ban Ki-moon was sitting right next to me! I wondered why he was sitting at one of the tables out in the open, but figured out that it must have been because the restaurant didn't take reservations. Right before we left, I gathered the courage to tell him that I have admired him, which is an understatement, since I was in elementary school, and asked him if I could have his autograph. He thanked me, shook my hand, and wrote in Korean: “To Sue, I hope that you will achieve greater advancements in the future.”

I am very excited for all the pleasant surprises in store for me here at Cambridge, and to finally get to learn how to fabricate BCP templates in the lab next week!