Everyday entropy: hydrophobia

The following excerpt is significant both because it illustrates the importance of configuration for the way bodies appear to behave and because it describes a classical view of entropy as a measure of disorder, so that decreased entropy is more orderly, without ever settling on a clear understanding of order.  Arieh ben-Naim would not be pleased, but, however you conceive of order and entropy, what is clear is that a hydrophobic boundary increases the energy that can be absorbed by the configuration of water.  Whether it does so by seeding a tighter lattice or inspiring longer bonding periods, it makes the configuration more predictable, which I think is how ben-Naim would explain it.
H2O, a biography of water, by Philip Ball, page 240


“Small, wholly hydrophobic molecules such as methane and krypton (a self-contained one-atom molecule) don’t form hydrogen bonds, and they don’t have electric dipoles that enable them to exploit favourable electrostatic interactions with a polar solvent like water.  At face value it would seem that, if you put molecules like this into water, all you are doing is breaking up part of the network of hydrogen bonds to make room for it, without getting any energetic stabilization back in return.  No wonder, then, that these gases are not very soluble in water.

But if we look more carefully, we see that this is not really what happens at all.  When methane dissolves in water, the water warms up: energy is released.  That’s a sign that ‘bonds’ are formed in the broadest sense – that the methane molecules are welcomed by favourable interactions.  In other words, inserting a methane molecule into water’s hydrogen-bonded network does not just break bonds without recompense – there is a considerable payback.  Any breaking of hydrogen bonds as the methane forces out a cavity in the network is more than balanced out by other favourable interactions, which can only be due to van der Waals forces, between the methane and the surrounding water.
And yet despite all this, methane is still pretty insoluble in water.  Why so, if it seems to be energetically favourable to surround methane molecules with water?  The answer is that the heat change is only half the story.  The other half concerns entropy, a measure of disorder in a system.  In a crystal all of the atoms are regularly arranged, whereas ina gas they can go anywhere, so long as they don’t overlap.  So there is more disorder – more entropy – in a gas, and a substance’s entropy increases when it is vaporized.
Whether or not a process of change will occur depends on the balance between the change in heat and the change in entropy it entails.  By ‘a process of change’, I mean anything: the reaction of two chemical compounds, the freezing of water, the toppling of a tree, the formation of a star.  The scales that govern all change in the Universe weigh up one of these two quantities against the other.
Methane does not dissolve well in water because the favourable heat change – the fact that heat is released – is counteracted by an unfavourable entropy change: the entropy decreases.  This tells us that when methane dissolves in water the two substances are together more orderly overall than they were in isolation.  The presence of a hydrophobic molecule like methane amidst the random hydrogen-bonded networks of liquid water somehow increases its order.
No one truly knows how to interpret this fact in terms of molecular structure.  Indeed, it remains one of the most debated issues in physical chemistry.
How else can one account for hydrophobic interactions, if not by increased structuring of water?  The decrease in entropy – the loss of disorder – when hydration occurs might be accounted for partly by the fact that the water molecules in the hydration shell become less free to rotate, rather than because they shift into new, more orderly positions.  There is some indication that water molecules around a hydrophobic particle are oriented with their O-H bonds tangential to the particle’s surface, as if the water molecules are resting an arm on the particle.  Maybe the water molecules thereby accommodate the particle not by increasing their degree of structure but by steadfastly maintaining it: a little reorientation of the molecules could be all that is needed to avoid sacrificing hydrogen bonds.  But here we are in the realm of speculation and can, at present, venture no further.
But the biggest controversies rage around water at hydrophobic surfaces.  In the 1980s, when sensitive methods for measuring the forces between two very close surfaces were developed, evidence began to emerge that two hydrophobic surfaces with water between them attract one another over distances of up to 300 nanometres.  That may sound like a short range  – it is hundreds of times smaller than the width of a human hair – but it is far, far longer than the range of any known interactions between neutral molecules, which don’t extend beyond ten nanometres at most.  An attractive force extending over 300 nanometres between hydrophobic surfaces in water is almost absurdly long-ranged – it must be mediated by something like a thousand intervening water molecules.  To understand how surprising this is, imagine how you’d feel if you were to be knocked over in Central Station at rush hour by a porter striding past on the opposite side of the hall.”

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