Entropic force

In physics, an entropic force acting in a system is a macroscopic force whose properties are primarily determined not by the character of a particular underlying microscopic force (such as electromagnetism), but by the whole system's statistical tendency to increase its entropy.

A standard example of an entropic force is the elasticity of a freely-jointed polymer molecule:  if the molecule is pulled into an extended configuration, the fact that more contracted, randomly coiled configurations are overwhelmingly more probable (i.e. possess higher entropy) will result in the chain eventually returning (through diffusion) to such configurations. To the macroscopic observer, the precise origin of the microscopic forces that drive the motion is irrelevant: The observer simply sees the polymer contract into a state of higher entropy, as if driven by an elastic force.

Entropic forces occur in the physics of gases and solutions, where they generate the pressure of the ideal gas and the osmotic pressure of a dilute solution, and in colloidal suspensions, where they are responsible for the crystallization of hard spheres.

Hydrophobic force
A very frequently cited example of entropic force is hydrophobic force. Though hydrophobic force has an enthalpic component, about half of it originates from the entropy of the hydrogen bonded three dimensional network lattice of water molecules at room temperature. Since each water molecule is capable of donating two hydrogen bonds through the two protons and accept two more hydrogen bonds through the two sp3 hybridized lone pairs, a water molecule, unlike Hydrogen fluoride (accept 3 but donate only 1) or ammonia (donate 3 but accept only 1) which mainly form linear chains, can form an extended three dimensional network lattices. Introduction of a non-hydrogen bonding surface disrupts this networks and the rest of the network immediately rearranges itself around that surface so as to minimize the number of disrupted hydrogen bonds. If the introduced surface had ionic or polar nature there would have been hydrogen molecules standing more or less orthogonal to this surface. But a non-hydrogen bonding surface forces the surrounding hydrogen bonds to be tangential and become locked in a clathrate like basket shape. Water molecules involved in this clathrate like basket envelope formation around the non-hydrogen bonding surface are entropically restrained. Thus any event that would minimize this type of surface would be entropically favoured. For example when two such particles comes very close they merge and the water trapped in between would be released from the trapped state and join the free bulk water molecules and lead to increase in entropy. That is the basis of the so called "attraction" between hydrophobic objects in solution. Though when two hydrophobic objects attract when they are very close, there may be a mild repulsion when they are about to come close. This mild repulsion may happen because the water molecules when trapped in between two hydrophobic surfaces coming from different direction are frustrated about whether to orient tangential to one surface or the other. However when the surfaces come further close this repulsion is more than compensated by the great increase in entropy when the water molecules are completely displaced of the clathrate-like sheath.