Entropic force

Diffusion from a microscopic and macroscopic point of view. Initially, there are solute molecules on the left side of a barrier (purple line) and none on the right. The barrier is removed, and the solute diffuses to fill the whole container. Top: A single molecule moves around randomly. Middle: With more molecules, there is a statistical trend that the solute fills the container more and more uniformly. Bottom: With an enormous number of solute molecules, all randomness is gone: The solute appears to move smoothly and deterministically from high-concentration areas to low-concentration areas. There is no microscopic force pushing molecules rightward, but there appears to be one in the bottom panel. This fake-force is called an entropic force.

In physics, an entropic force acting in a system is a phenomenological force resulting from the entire system's statistical tendency to increase its entropy, rather than from a particular underlying microscopic force.

Examples

Polymers

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 system has an increased amount of predictability. But randomly coiled configurations are overwhelmingly more probable; i.e., they have greater entropy. This results in the chain eventually returning (through diffusion) to such a configuration. 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.

Hydrophobic force

Water drops on the surface of grass.

Another example of an entropic force is the hydrophobic force. It comes from the entropy of the 3D network of water molecules (at room temperature). Each water molecule is capable of

• donating two hydrogen bonds through the two protons
• accepting two more hydrogen bonds through the two sp3 hybridized lone pairs

Therefore, water molecules can form an extended three-dimensional network. Introduction of a non-hydrogen-bonding surface disrupts this network. The water molecules rearrange themselves around the surface, so as to minimize the number of disrupted hydrogen bonds. This is in contrast to hydrogen fluoride (which can accept 3 but donate only 1) or ammonia (which can donate 3 but accept only 1), which mainly form linear chains.

If the introduced surface had an ionic or polar nature, there would be water molecules standing more or less normal to the surface. But a non-hydrogen-bonding surface forces the surrounding hydrogen bonds to be tangential and they are locked in a clathrate-like basket shape. Water molecules involved in this clathrate-like basket around the non-hydrogen-bonding surface are constrained in their orientation. Thus, any event that would minimize such a surface is entropically favored. For example, when two such hydrophobic particles come very close, the clathrate-like baskets surrounding them merge. This releases some of the water molecules into the bulk of the water, leading to an increase in entropy. This is the basis of the so-called "attraction" between hydrophobic objects in water.

General chemistry

Entropic forces also occur in the physics of gases and solutions, where they generate the pressure of an ideal gas (the energy of which depends only on its temperature, not its volume), the osmotic pressure of a dilute solution, and in colloidal suspensions, where they are responsible for the crystallization of hard spheres.

Speculative examples

In recent years (especially since 2009) some forces that are generally regarded as conventional forces have been argued to be actually entropic in nature. These theories remain speculative and are the subject of ongoing work.

Gravity

Main article: Entropic gravity

It is generally believed that gravity is a microscopic force (or arguably a pseudo-force in general relativity). However, some speculative work, in particular a 2009 theory due to Erik Verlinde (published in April 2011)., has argued that gravity can be explained as an entropic "force".

For example, when someone throws a ball in the air, it follows a parabolic trajectory (in the absence of wind resistance). Conventionally, it is said that the ball follows a deterministic path dictated by Newton's law of gravity or general relativity. However, in the entropic theory, it is argued that the ball can follow any trajectory and picks a trajectory "at random". A calculation demonstrates that, in the collection of possible trajectories, the overwhelming majority are almost exactly the same as the parabolic trajectory. Therefore the ball is observed to follow a parabola.

Other forces

Other forces have been argued recently to be entropic in origin, including Coulomb's law, the electroweak and strong forces, and dark matter and dark energy.

See also

• Colloids
• Nanomechanics
• Data clustering
• Entropic elasticity of an ideal chain