Depletion force
[3] More generally, depletants can include polymers, micelles, osmolytes, ink, mud, or paint dispersed in a continuous phase.
The underlying consequence of the hard-sphere potential is that dispersed colloids cannot penetrate each other and have no mutual attraction or repulsion.
[4] The positive change in entropy lowers the Helmholtz free energy and causes colloidal flocculation to happen spontaneously.
The system of colloids and depletants in a solution is modeled as a canonical ensemble of hard spheres for statistical determinations of thermodynamic quantities.
In these instances, the intricate balance of interactions between the solution components results in the net exclusion of cosolute from macromolecule.
This exclusion results in an effective stabilization of the macromolecule self-association, which can be not only enthalpically dominated, but also entropically unfavorable.
[1] Because the canonical ensemble is an athermal system at a constant volume the Helmholtz free energy is written where
The system's net gain in entropy is positive from increased volume, thus the Helmholtz free energy is negative and depletion flocculation happens spontaneously.
is equal to the change in Helmholtz free energy with distance between two large spheres and is given by[7] The entropic nature of depletion forces was proven experimentally in some cases.
For example, some polymeric crowders induce entropic depletion forces that stabilize proteins in their native state.
When colloids get sufficiently close, that is when their excluded volumes overlap, depletants are expelled from the interparticle region.
[4][7] The resulting density gradient gives rise to an osmotic pressure that is anisotropic in nature, acting on the outer sides of the colloids and promoting flocculation.
As a result, the force acting on the plates increases with the length of the rods until it becomes equal to the osmotic pressure.
[5] In this context, it is worth mentioning that even the isotropic-nematic transition of lyotropic liquid crystals, as first explained in Onsager's theory,[19] can in itself be considered a special case of depletion forces.
[7] This effect was convincingly demonstrated in experiments with vibrofluidized granular materials where attraction can be directly visualized.
However, if an external potential is applied to a solution, then the uniform particle density is disrupted, making Asakura and Oosawa's assumption invalid.
When applied to depletion forces, the grand canonical potential calculates the local particle densities in a solution.
If the intermolecular potentials also include repulsive and/or attractive terms, and if the solvent is considered explicitly, the depletion interaction can have additional thermodynamic contributions.
The notion that depletion forces can also be enthalpically driven has surfaced due to recent experiments regarding protein stabilization induced by compatible osmolytes, such as trehalose, glycerol, and sorbitol.
This effect was generally thought to be an entropic force, in the spirit of the original Asakura–Oosawa model and of macromolecular crowding.
However, thermodynamic breakdown of the free-energy gain due to osmolyte addition showed the effect is in fact enthalpically driven, whereas entropy can even be disfavorable.
This method uses a focused laser beam to apply an attractive or repulsive force on dielectric micro and nanoparticles.
The relatively small size of dispersed particles in waste water renders typical filtration methods ineffective.
Therefore, coagulants and flocculants are typically introduced to waste water which create these depletion forces between the dispersed particles.
These particles typically consist of carbohydrates, pigmentation molecules, or proteins which may adversely affect the taste and purity of the wine.
The table below lists common flocculants along with their chemical formulas, net electrical charge, molecular weight and current applications.
[28] With concentrations of large molecules such as proteins or carbohydrates in the extracellular matrix, it is likely some depletion force effects are observed between cells or vesicles that are very close.
However, due to the complexity of most biological systems, it is difficult to determine how much these depletion forces influence membrane interactions.
[28] Models of vesicle interactions with depletion forces have been developed, but these are greatly simplified and their applicability to real biological systems is questionable.
Depletion forces in colloid-polymer mixtures drive colloids to form aggregates that are densely packed locally.
