have a great influence on electrostatic interactions because these affect the "magnitude of electrical charge" in solution. As can be seen from the above equation, the repulsion energy depends on the square of the Debye length. From the equation for the Debye length, it is demonstrated how ionic strength can ultimately affect the electrostatic interactions in a solution. Bjerrum length Naturally, the question of the distance at which these electrostatic interactions become important arises. This can be discussed using the Bjerrum length. The Bjerrum length is the distance at which the electrostatic interaction between two charges is comparable to the thermal energy, . The distance is given by eq. 2: where = elementary charge, = vacuum permittivity, = relative dielectric constant. Surface Charge Density The factors discussed above can influence the charge on the surface of the polyelectrolyte. The surface charge density of these surfaces, at low surface potentials, can be modeled using a simplified version of the Grahame equation (eq. 3): where = surface potential. Examples of polymers and their surface charge densities can be found in the table below. Applications Deflocculation Depending on the situation, polyelectrolytes can function as either flocculants or deflocculants. In order to stabilize emulsion, deflocculant polyelectrolytes are required. When repulsive forces between particles overcome the intermolecular forces in solution and the loose flocculated aggregates separate, deflocculation occurs. As opposed to the loose and easily separated sediments formed in flocculation, sediments formed in deflocculation are tightly packed and difficult to redisperse. The repelling forces in a deflocculation increase the zeta potential, which in turn reduces the viscosity of the suspension. Because of this reduction in viscosity, deflocculants are sometimes referred to as “thinning agents”. These thinning agents are usually alkaline and raise the pH of the suspension, preventing flocculation. Deflocculants are used as thinning agents in molding plastics, making glassware, and creating clay ceramics. Petroleum Waste Treatment Polyelectrolytes can also act as flocculants, separating solids (flakes) and liquids in industrial processes such as solubilization and oil recovery and they usually have a large cationic charge density. Using organic materials to refine petroleum instead of iron or aluminum coagulated would greatly decrease that amount of inorganic waste produced. The waste consists of stable oil-in-water emulsions. The addition of various polyelectrolytes to petroleum waste can cause the oil to coagulate, which will make it easier to remove and dispose of, and does not significantly decrease the stability