# The Chemistry of Relationships/Friendships

There is a reason why we call friendships “bonds”. It’s an incredible thing to think about, and I’ve been pondering about this topic for a few years, since high school. First, I must give mad props to Joyce for helping me polish this idea in my talks with her. Now before we delve deeper into this [surprisingly complex] topic, we have some preliminary stuff to take care of.

We begin by considering the idea of change. I’ve already set this discussion up here. Recall that we can think about a change as a difference in states – $\Delta A$. But we can take the limit of $\Delta A$ for small deltas – we can take the instantaneous change and track that through the interval of $\Delta A$. This is idea of integrating $dA$ to obtain $\Delta A$.

In life the difference between $dA$ and $\Delta A$ is encapsulated in this: “Do the means justify the ends?” $\Delta A$ skips everything in between. It is path-independent; it specifies just the beginning and end states. On the other hand, in examining $dA$ we look at the path between states and how we get from A to B. So we ask, does the path, do the means, matter? Or is the change between State B and State A the more dominant question?

In chemistry the state-oriented vs. the path-oriented mindset separates thermodynamics from kinetics. Chemical kinetics looks at the rates of reactions, which is highly dependent on the mechanism – the path the reaction takes. On the other hand, chemical thermodynamics studies the relative favorabilites of reaching different states.

So now we can look at the idea of interpersonal relationships through the eyes of chemistry. Bonds don’t just form out of thin air, after all. They require favorable thermodynamics – state B must have lower energy than state A. They also require favorable kinetics – the reaction path must not have too many bumps or barriers. Likewise, friendships form only when the conditions are right. And there are two ways to examine why friendships happen: from a kinetic viewpoint, and from a thermodynamic viewpoint. We will take a look at both in more detail now.

1. THE KINETIC VIEWPOINT

We have a bunch of atoms, each with some kinetic energy. Now according to collision theory, atoms must have the right orientation and the right amount of kinetic energy, known as the activation energy, for a reaction to occur. Once the reaction occurs, the atoms form what is known as the activated complex, which can undergo a transformation either backwards, reforming the original atomic constituents, or forwards, entering a product state.

Initial social interaction works the same way. Through the course of our lives, we meet many many people. And in many cases, we will not have enough energy to form an activated complex. Or maybe our “orientations” aren’t right – there is some steric hindrance, the alignment of atomic orbitals just isn’t ideal, or maybe one atom only sideswiped another. For instance, if I talk with someone on an airplane for a couple of hours, I will probably never see them again. The conditions just aren’t ripe. (This actually did happen to me – I met a very nice lady with a poodle on my plane ride home from Berkeley last summer. But of course, I never saw her again.)

Now, sometimes two people hit it off very well and become acquaintances, because everything went right. I guess the best way to describe the activated complex is the awkward phase in between friendship and stranger. You’re definitely not familiar enough with this person to invite him/her out to a meal, or to do any “friend” stuff. It’s not a comfortable phase. Not surprisingly, the activated complex is a high energy state. And physics doesn’t like high energy states. Many times, you lose contact with the acquaintance, and you go back to what you were originally: strangers. But sometimes, you go forward, and enter your friendship product state.

Some remarks follow. Collision theory states that the rate constant, which is proportional to the reaction rate, is exponential in the activation energy. A small change in activation energy does wonders for how fast the reaction proceeds. That’s what catalysts, such as enzymes, do – by lowering the activation energy just a tad, they increase the reaction rate by many orders of magnitude. The activation energy for stranger to friendship transformation is immense; reaction rates are slow, initial awkwardness is high. Catalysts are almost always essential for friendship formation. Sometimes these catalysts are other friends (chemistry example: the presence of a functional group that polarizes a covalent bond is essential for an organic reaction to occur; hydrocarbons themselves are relatively nonreactive). Other times, they are shared experiences or shared interests. A very dull person with few experiences requires high activation energies to reach an activated state. The presence of a common interest provides an alternative pathway for people to connect.

This was one of my first discoveries when I first looked at the social interaction problem in high school. The people who were popular had stuff to talk about, and ways to connect with people. They had all types of catalysts that lowered the activation energy of reactions. I didn’t. So that made me sad for awhile.

Thankfully however, I soon discovered another aspect of chemical reactions – thermodynamics.

2. THE THERMODYNAMIC VIEWPOINT

The thermodynamics of a reaction, abstracted by the Gibbs Free Energy $\Delta G$, is intrinsically linked with the reaction’s equilibrium constant, defined as the ratio of the population in the product state to the population in the original state at steady-state, zero-forcing conditions. Now, the kinetics state the pathway that gets you to steady-state conditions, but we are going to ignore that for now. We aren’t going to ask how we get to friendship. We’re going to ask how many times we get there, assuming the path is laid out for us.

Picture someone who is affable. Who do you think about? I think of all the people on the floor I live on. If I were to redo my experience with “6th floor”, the probability of my entering a friendship state with the people here would be very high. But then think about all the jerks you’ve met. What is the probability in that case?

This is the essence of the thermodynamic viewpoint. For a friendship to occur, good orientations and shared experience catalysts are not enough. The two sides must “jive” together if they meet, and this happens every time regardless of circumstance (read: kinetics). Sometimes the energetics is very favorable, as was with me and Vicki, and you feel comfortable with them immediately – you enter a lower energy state fast. Personally, I find low $\Delta G$ in people who are bubbly, smiling, and enthusiastic. Not surprisingly, some of my best friends I’ve met at Berkeley fit that description. People look for different things in other people, which makes $\Delta G$ between pairs of people difficult to calculate.

Nevertheless, some personalities are naturally low in Gibbs Free Energy – they are naturally more sought after. Remember the jerks? People typically don’t like jerks. I discovered in high school was that being nice and smiling actually netted me friends. As did knowing calculus and science – people looked up to me for academic assistance, which I gladly gave. What I lacked in kinetics, I overcame with a heaping helping of thermodynamics. And that is the good news about thermodynamics. Kinetics (aside from catalysts) are often out of our control – you still have to collide with the right circumstances to form friendships. But thermodynamics are something we can control. If you want more friends, you can always improve your thermodynamics so as to increase the probability of forming and sustaining a friendship when you meet a new person.

One final thing about thermodynamics – in general, we live our lives interacting and friending people (not on FB, in real life). Likewise, the almost all the world is made of bonded chemicals. The sum of all the free energies of bonded states on Earth must therefore be less than the sum of all the free energies of the non-bonded states. Back in the friendship scheme of things, this means we have natural affinity towards social interaction and friendship forming in general. Most of your encounters will be of the near-zero or negative $\Delta G$ type. Only kinetics stops you.

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Finally, to conclude, we will examine the extrovert vs. introvert problem. For the longest time I thought extroverts had more friends, because they liked to talk with people more. But then I found an article that claimed extroverts and introverts have similar amounts of close friends. And then I met Joyce – who has many friends due to her bubbly, happy personality. But she is nevertheless an introvert. How can this be?

The extrovert/introvert problem is one of kinetics. Extroverted people have more kinetic energy and so are more likely to reach activation energy. They like to talk to people and interact. On the other hand, introverted people have less kinetic energy and so do not interact/collide as much. The physically equivalent idea is Temperature ($\propto$ kinetic energy). In fact, the rate constant is goes by exp(1/T), where T is the temperature, so extroversion helps a lot, just like shared experiences. But neither guarantees friendships – that is the job of $\Delta G$ once the kinetic barrier has been breached. Meanwhile, temperature does not affect the energetics*, so the amount of good low $\Delta G$ product states will be about the same for both the high- and low- temperature environments.

The extrovert/introvert problem provides some of the most compelling evidence for the chemistry of relationships/friendships, and some of the best applications too. I think it is astounding that we can draw as many parallels as we have done here. There is still much to be figured about the dynamics of friendships.

* For those more familiar with chemistry, we ignore entropic effects. Since $\Delta G = \Delta H - T \Delta S$, the temperature dependence vanishes if we drop the $\Delta S$ term, which is allowed here since entropy has little to do with our analysis.

P.S. 1700+ words, ~3 pages single-spaced on a Word doc. Yay!