This post is a collection of thoughts on the principles of entropy, energy and equilibrium expressed in the context of self assembly of surfactant molecules . Let us begin by asking what a surfactant is. For the purposes at hand, a surfactant is a molecule with a small head that likes water and a long tail that hates water as shown in the cartoon alongside. What “loves” means in the following is that the entity can lower its energy by being in contact with water and what “hates” means is that it costs the system a lot of energy when it is in contact with water . Now, we put a bunch of these surfactant molecules in water and allow them to come to “equilibrium”. What do they do?
To understand this question, we have to first clarify what a system will like to do. The equilibrium state of the system will be one where it can do the maximum number of things it likes. The first thing the system likes to do is lower its energy as much as it can. On the other hand, the system likes to have as much disorder as possible, technically speaking, “maximize its entropy”. If I call the energy of the system E and the entropy of the system S, then the system likes to have a minimum value for the quantity F = E – TS, and this is called the free energy of the system. Don’t let this little jargon scare you. What follows is simple enough even if you don’t remember this. Also, before we can guess what the system will like to do, we need to know one more thing about the surfactant molecules. If two surfactant molecules come close to each other, what would they do? The tails of these molecules are such that they are happiest when they are as close to each other as they can get, for they lower their energy by reducing their interaction with water and increase their entropy as well . The heads of these molecules are such that they want to stay as far away from each other, because these heads are usually charged and like charges repel right? So they lower their energy by staying away from each other.
With that, we have all the ingredients we need to answer the question we asked. It is now all about a competition between love and hate. Suppose the heads love water way more than the tails hate it. Then the equilibrium state of the system will be a solution of the surfactant molecules in water, with all the molecules well separated from each other and doing their own thing . Next, suppose the circumstances are that the hate of the tail wins. Also, suppose that the heads are wide objects so that the overall shape of the surfactant molecule is a cone (see figure). Then, the molecules are happiest when they form micelles. Micelles are objects that are spheres, with the polar heads outside near the water and the tails inside, talking only to each other and protected from the water by the polar heads. Note that, in order to form micelles, you need a given amount of surfactant in the water (If you have fewer surfactant molecules, entropy wins and they stay in the form of the solution). The everyday situation under which micelles are formed is when you wash your clothes with soap. The dirt on the clothes form nucleating centers for the micelles and the micelle itself being water soluble, dissolves in the water when you rinse your clothes.
The more interesting case is when the heads are not fat, i.e., the surfactant molecule is a cylinder rather than a cone (see figure) and still the hate of the tails wins. In this case, the system forms what are called “lipid bilayers”. This is just two layers of surfactant molecules assembled such that the tails of each layer face each other (effectively, it is like having a layer of oil trapped between two layers of polar heads). Now, in this structure, the tails in the middle are clearly happy for all their neighbors are fellow hydrocarbons. But, just as clearly, the tails at the edge of the structure are unhappy because they have to talk to the surrounding water. One way to eliminate this is for this bilayer to fold on itself to form a spherical shell (see figure, which displays a cross section of such a structure). This way, there is no surface of tails talking to the water. But the trade off comes at the cost of forcing the heads in the inner layer to be more close to each other than they like. But, if the hate of the tails for water is large enough, this happens and the resulting stable structure is now a vesicle!
The interesting things to note here are twofold. One, in spite of the language I am using, in the actual experiment, all I did was take a spoonful of surfactant molecules and put it in water. All the structures mentioned above self assembled! I did not have to do a thing. The second thing to note is that, the above vesicle is essentially a minimal cell membrane, the first step towards the process that converts an auto catalytic chemical reaction into what we call now as life!
So, if we can make this membrane functional, namely, make sure that the chemical machinery required for life is trapped inside the vesicle, make appropriate “holes” so the membrane is suitably permeable (i.e., it lets some stuff in (raw material for making food) and some other stuff out (waste products) and not vice versa), we would have made an artificial cell! Some first steps in this direction have already been taken. See for example, this PNAS article reporting the use of “directed self assembly” to make a bio reactor, which is to say it is not quite a cell yet, and this article entitled “Towards an artificial cell based on gene expression in vesicles” . We are not very far from making what can only be termed as artificial life, in a physics lab, in a test tube. And the reason I started thinking along these lines was to be able to ask the question – “Intelligent design anyone??” :) .
Caveats and disclaimers
 The aim is to try and keep things simple, focusing on the primary ideas and suppressing all but the bare essentials in terms of details and subtleties.
 The jargon is that the head of a surfactant molecule is a polar group like sodium sulfate and hence this ionizes in water and hence is hydrophilic. The tail is a covalently bonded hydrocarbon polymer and hence hates the high dielectric constant medium of water and is hydrophobic.
 The entropy of a polymer would be given by the number of configurations they have. They can fluctuate better and sample their accessible phase space better in the lypophilic environment of other tails, than in water, where any fluctuation will result in an energy cost.
 It is clearly an oversimplification. The question is truly one of entropy versus energy. So, this will be a strong function of the concentration of the surfactant and the temperature of the water. At low enough concentrations or high enough temperature this will always be the default state with no possibility of self assembled structures.
 This is actually a frivolous statement. The stumbling block that people have to overcome is the complexity of a real biological membrane, which has embedded proteins and is active and what not. But from a physicist’s point of view, it is but self assembly, but takes a lot of time. I say this in spite of the fact that from what knowledge we have of the primordial soup and pre-life conditions on earth, there appear to have been singular events that precipitated the emergence of life in nature and we do not know either way, the probability of such singular events occurring from random initial conditions.