Theoretical kinetics

However, the general character of the process can be reasonably well modeled with a polyelectrolyte in solution, and an oppositely charged surface where no covalent interaction between the surface and chain occurs. This model for the adsorbed amount of polyelectrolyte at a charged surface is derived from DLVO theory, which models the interaction of charged particles in solution, and mean field theory, which simplifies systems for analysis.^[2]

Using a modified Poisson-Boltzmann equation and mean field equation, the concentration profile near a charged surface is solved numerically. The solution of these equations yields a simple relation for the adsorbed amount, Γ, based on electrolyte charge fraction, ρ, and bulk salt concentration, ${\displaystyle c_{b}}$.

${\displaystyle \Gamma =\int _{0}^{\infty }\!c(x)\,dx\,\approx {\frac {\left\vert y_{s}\right\vert ^{3/2}}{{\lambda _{B}}{a}{p^{1/2}}}}}$

where ${\displaystyle y_{s}}$ is the reduced surface potential:

${\displaystyle y_{s}={\frac {{e}{\psi _{s}}}{{k_{B}}{T}}}\,}$

and ${\displaystyle \lambda _{B}}$ is the Bjerrum length:

${\displaystyle \lambda _{B}={\frac {e^{2}}{4\pi \varepsilon _{0}\varepsilon _{r}\ k_{B}T}},}$

Layer-by-layer adsorption

A simple schematic showing the alternating adsorption of positively and negatively charged polyelectrolytes to a solid surface.

Since charge plays a key role in polyelectrolyte adsorption, the initial rates of polyelectrolyte adsorption to charged surfaces are often rapid, limited only by the rate of mass-transport (diffusion) to the surface. This high rate then quickly drops off as charge accumulation at the surface occurs, and attractive forces are no longer drawing more polyelectrolyte chains to the surface. This drop in adsorption rates can be countered by exploiting the tendency for charge overcompensation to occur.^[3] In the case of a negatively charged solid surface, cationic polyelectrolate chains are adsorbed to the oppositely charged surface. Their large size and high charge densities tend to overcompensate the original negative surface charge, resulting in a net positive charge due to the cationic polyelectrolytes. This solid surface, with its cationic polyelectrolyte film and consequent positive surface charge, can then be exposed to an anionic polyelectrolyte solution, where the process begins again, creating another film with an oppositely charged surface. This process can then be repeated to create several bilayers on the solid surface.

Solvent choice

The interactions between a polyelectrolyte and the solvent it is placed in have a large effect on the conformation of the polymer both in solution and upon deposition onto the substrate. Due to their unique nature, polyelectrolytes have many options for solvents that traditional polymers such as polyethylene, styrene, and others, would not be soluble in. An excellent example of this is water. While water is a high-polarity solvent, it will still dissolve many polyelectrolytes. The conformation of a polyelectrolyte in solution is determined by a balance of the (usually unfavorable) interactions between the solvent and the polymer, and the electrostatic repulsion between the individual repeat units of the polymer. It has been suggested that a polyelectrolyte chain will form an elongated cylindrical globule in order to optimize its energy. Some models go further and postulate that the most efficient configuration is a series of cylindrical globules linking much larger diameter spherical globules in a "necklace" configuration.^[4]

Good solvent

In a good solvent, the electrostatic forces between the repeat units of the polymer and the solvent are favorable. While not entirely intuitive, this causes the polymer to assume a more tightly packed conformation. This is due to the screening the solvent molecules perform between the charged repeat units of the polyelectrolyte, decreasing the electrostatic repulsion the polymer chain experiences. Since the polymer backbone does not repel itself as strongly as it would in a poor solvent, the polymer chain acts more similarly to an uncharged polymer, assuming a compact conformation.

Poor solvent

In a poor solvent, the solvent molecules interact poorly or unfavorably with the charged portions of the polyelectrolyte. The inability of the solvent to effectively screen the charges between repeat units causes the polymer to assume a looser conformation due to electrostatic repulsion of its repeat units. These interactions allow for the polymer to be more uniformly deposited onto the substrate.

Salt concentration

Representation of the effect of salt on a polyelectrolyte molecule in solution. Also, good solvents produce effects on polymers similar to the high salt condition and poor solvents produce effects similar to the low salt condition.

When an ionic compound is dissolved in the solvent, the ions act to screen the charges on the polyelectrolyte chains. The ionic concentration of the solution will determine the layer formation characteristics of the polyelectrolyte as well as the conformation the polymer assumes in solution.

Polymer coatings

Polyelectrolyte multi-layers are a promising area of research in the polymer coating industry because they can be applied in a spray-on fashion at low cost in a water-based solvent. Although the polymers are held to the surface only by electrostatic forces, the multi-layer coatings adhere aggressively under liquid shear. The disadvantage to this coating technology is that the layers have the consistency of a gel and thus are weak against abrasion.

Implant enhancement

Precursor monomers for a base layer of a microbicidal implant-enhancing polyelectrolyte multi-layer. The top is DMLPEI, and bottom is PAA.

Many biomedical devices that come into contact with bodily fluids are susceptible to adverse foreign body response, or rejection and thus, failure of the device. The main mechanism of infection is the formation of a biofilm, which is a matrix of sessile bacteria consisting of around 15% bacterial cells by mass and 85% hydrophobic exopolysaccharide fibers.^[11] One way to eliminate this risk is to apply localized treatment to the area in the vicinity of the implant. This can be done by applying a drug-impregnated polyelectrolyte multi-layer to the medical device prior to implantation. The goal with this technology is to create a combination of polyelectrolyte multi-layers where one multi-layer prevents the formation of a biofilm and another releases a small-molecule drug through diffusion. This would be more effective than the current technique of releasing a high dose of drugs into the body and counting on some of it to navigate to the afflicted area. The base layer for an effective coating for an implant is DMLPEI/PAA, or linear N, N-dodecyl,methyl-poly(ethyleneimine) / poly (acrylic acid).^[7]

Colloid stability

Top: The electrostatic contribution to colloid stability, showing two like-charged particles repelling each other. Bottom: The steric contribution to colloid stability, showing polymer chains opposing being pushed together and confined, causing a repulsion due to the unfavorable decrease in entropy.

Another of the major applications of polyelectrolyte adsorption is the stabilization (or destabilization) of solid colloidal suspensions, or sols. Particles in solution tend to have attractive forces similar to van der Waals forces, modeled by Hamaker theory. These forces tend to cause colloidal particles to aggregate or flocculate. The Hamaker attractive effect is balanced by one or both of two repulsive effects of colloids in solution. The first is electrostatic stabilization, in which like charges of the particles repel one another. This effect is due to the zeta potential that exists due to a particle's surface charge in solution.^[12] The second is steric stabilization, due to steric effects. Drawing particles together with adsorbed polymer chains greatly decreases the conformational entropy of the polymer chains at the surface, which is thermodynamically unfavorable, making flocculation and coagulation more difficult.

The adsorption of polyelectrolytes can be used to stabilize suspensions, such as in the case of dyes and paints. It can also be used to destabilize suspensions by adsorbing oppositely charged chains to the particle surface, neutralizing the zeta-potential and causing flocculation or coagulation of contaminants. This is used heavily in waste-water treatment to force suspensions of contaminants to flocculate, allowing them to be filtered. There are a variety of industrial flocculants that are either cationic or anionic in nature for targeting particular species.

Encapsulation of liquid cores

An application of the additional stability a polyelectrolyte multi-layer will grant a colloid is the creation of a solid coating for a liquid core. While polyelectrolyte layers are generally adsorbed onto solid substrates, they may also be adsorbed to liquid substrates such as oil in water emulsions or colloids. This process has much potential, but is rife with difficulty. Since colloids are generally stabilized by surfactants, and often ionic surfactants, the adsorption of a multi-layer that is similarly charged to the surfactant causes problems due to the electrostatic repulsion between the polyelectrolyte and the surfactant. This can be circumvented by using non-ionic surfactants; however, the solubility of these non-ionic surfactants in water is greatly decreased compared to ionic surfactants.

These cores, once created, can be used for things such as drug delivery and microreactors. For drug delivery, the polyelectrolyte shell would break down after a certain amount of time, releasing the drug and helping it travel through the digestive tract, which is one of the biggest barriers for the effectiveness of drug delivery.