Phase Transitions

We are all familiar with phase transitions from our commonplace experiences boiling water, or watching a popsicle melt on a hot day. The melting of a solid and the boiling of a liquid are sufficiently quotidian that those events are more or less synonymous with the term 'phase transition'. Through this we come to understand that there different phases of matter, and that under the right conditions, that matter can change phase, wherein its properties change in a distinct and readily apparent manner. Liquids can flow, solids are firm, and gases fill all the space they are given. These are certainly different phases, but from our earliest education in science, we are taught that they are the only phases, and a phase transition refers to a change from one of the three to another. The study of statistical mechanics and condensed matter physics shows that the nature of phase transitions is much richer than this simple picture, and that the difference between phases is often extremely subtle.

We know that phase transitions occur in matter, but what is the distinguishing feature of matter that allows phase transitions to occur? Can a phase transition occur in a single atom? When exactly does the phase transition occur, and what does it signify? That is, what is the meaning behind the words phase transition.

In this brief introduction we will consider commonalities among phase transitions, and in particular, how to identify them despite their sometimes exotic and disparate nature. We will learn how physicists think about phase transitions, and in particular, how they use the ideas of statistical mechanics to classify and understand them. Additionally, we will examine the phase transition found in diblock copolymers as a means of identifying the key features of a phase transition in a slightly more exotic capacity.
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