Entropic force

The Entropiekraft or entropic force is caused by the thermal motion of the particles under an externally applied force.

Mathematical formulation

In the canonical ensemble is the entropic force that is associated with the macro-state, given by the negative gradient of the entropic energy contribution to the free energy:

With

• The observed macrostate
• The temperature
• The entropy associated with the macro state.

Thus, the entropic force acts along the steepest ascent for the entropy in the space of macrostates.

The same applies to the isothermal- isobaric ensemble with the free energy as an adapted optimally themodynamischen potential.

Examples

Polymers

The tensile force of a rubber or of a single polymer is based on the entropy, so indirectly on the energy of the heat bath, in contrast to a hard spring, which force is caused by distortion of the stored energy. For polymers of coercion is given by the fact that it is stretched due to the external force and thus less microscopic configurations are available.

The Entropiekraft can from the underlying polymer model have a different representation dependent. Common to all is that Hooke's law is valid for moderately stretched polymers with temperature-dependent spring constant. At the temperature that is applied to a polymer having segments of the effective length, and the end-to -end distance of the force

Osmotic pressure

Another example of entropic forces of osmotic pressure. It is based on varying concentrations of a chemical substance in areas, which are spatially separated by a semi-permeable ( semipermeable ) wall. The constraint here is given by the semi-permeable wall. The movement of the particles and their desire to produce a concentration equilibrium, the osmotic pressure builds up. Again, the configuration space for the non-permeable particles is limited.

Hydrophobic effect

The hydrophobic effect can be understood by the effect of an entropic force.