The rate of ion exchange depends on the rates of the chemical (ionic) reactions in the ionic exchange material (membranes, dispersions, beads, pellets, etc.), but it is often limited by the diffusion processes. The ion exchange process maybe primarily controlled by diffusion, which is dependent upon the material layers, structure, thickness and reactant rate of contact on the surface of the material. This blog post introduces the factors to consider when thinking about the kinetics of the ion exchange reactions.
Mechanism of Ion Exchange Processes
A common ion-exchange system is an ion exchange polymer swollen with water submerged in an aqueous solution. The exchange of ions is accomplished via the transfer of ions to and from the polymer material. Between the aqueous solution and polymer material is an interface boundary, which is a thin film of solution that should be analyzed separately. The properties in this interface layer will be different from both the surrounding solution and inside the ion exchange material. There are steps that can be taken to minimize this interface layer film thickness, but this film will always be present.
Figure 1 shows a simple illustration of the ion exchange mechanism. Ion 1 is inside the polymer ion exchange material, and Ion 2 is floating in the aqueous solution. Ion 2 travels comes in contact with the interface layer by chance. Once Ion 2 reaches the interface, it travels though the interface film into the polymeric material. Ion 1 diffuses out of the polymer, through the film, and into solution. The replacement of Ion 1 with Ion 2 is called ion exchange. In order for the ion exchange mechanism to occur, a stoichiometric equivalent of counterions must replace an equivalent amount of other counterions due to the electroneutrality requirement of all systems in nature. When a counterion crosses the interface layer, an electric potential is created between the two phases. That potential is compensated by the movement of another counterion in the opposite direction.
As detailed in Figure 2, the following steps occur during the ion exchange process:
- Step 1: The dissolved complexes dissociate in the aqueous solution.
- Step 2: The ion diffuses from the solution to the interphase layer. This step can be manipulated through agitation of a liquid or pressure of a gas to increase the ion transfer.
- Step 3: The ion diffuses through the interface boundary layer. Agitation can be used to reduce this film thickness. The method of transport in Step 3 is solely the mobility of the ion.
- Step 4: After the transfer of the ion through the boundary layer, the ion diffuses into the ion exchange material due to a concentration gradient.
- Step 5: The first ion associates with the functional group of the ion exchange material.
- Step 6: To fulfill the electroneutrality principle, the second ion dissociates from the functional group on the ion exchange material.
- Step 7: The second ion diffuses from the bulk of the ion exchange material to the surface.
- Step 8 and 9: The second ion diffuses from the interface layer to bulk of the solution.
- Step 10: The second ion associates with a molecule in the solution phase.
Of course, the process of ion exchange only occurs if an ion is capable of stoichiometrically replacing another ion and there is adequate flux for ion exchange. The mass transport kinetics is limited by diffusion of the slowest ion. We have simplified the ion exchange process in Figure 2; however, the actual ion exchange process can be more complex. Theoretically, the ion with the fastest mobility will diffuse at the highest rate, but there is a balance of charges throughout the material that affects the diffusion of the ions. This charge balance may slow the faster ion and accelerate the slower ions.
The mechanism of ion exchange consists of many steps which take place in the solution/interface layer/ion exchange material system. If we examine our system using a chemistry-based kinetic approach, we can predict the rate based upon the rate of the slowest step. We can create a kinetic description based upon the equations developed for homogeneous systems. We can scientifically explain the processes in Figure 2:
- Mass transfer (diffusion) in the solution or in other external medium (steps 2 and 9): These processes can be assisted by hydrodynamic turbulences (i.e., stirring) and thus, is not considered as a possible limiting step for ion exchange.
- Mass transfer (diffusion) through the film surrounding the ion exchanger (steps 3 and 8): The film is a solution zone with a certain thickness. The mass transport through this layer is dependent upon the diffusion rate constant (diffusion coefficient). The layer thickness can be reduced through agitation.
Mass transfer (diffusion) in the ion exchange phase (steps 4 and 7): This process depends upon the properties of the ion exchange material and cannot be changed unless the properties of the material are altered.
Reactions between counterions and fixed groups (ion-pair association/dissociation) (steps 5 and 6): These processes are the actual chemical reactions that affect the overall rate of ion exchange.
Complex dissociation and formation in solution (steps 1 and 10): These processes are not part of the ion exchange process but can cause a bottleneck with the mass transfer.
As you can see from these descriptions, the majority of the ion exchange processes are actually diffusion phenomena. If you are creating a mathematical model of the ion exchange kinetics, the majority of the steps can be described using diffusion equations. A mathematical description of each step can be expressed as a kinetic equation with a rate constant; however, there are no actual chemical reactions for the majority of these steps. In many models, the interface layer is considered negligible because the diffusion through the ion exchange material is usually rate limiting due to the chemical structure and much greater thickness. However, it is included in detailed models because it can have a significant affect and does have a different mode of transport. The concentration gradient in the interface layer is defined by the concentrations in the bulk liquid and at the ion exchange surface. Therefore, for an ion entering the ion exchange phase, the difference cannot exceed the ion concentration in the bulk solution. The driving force in the ion exchange material is the concentration at the surface and in the material. The concentration difference can be due to a greater concentration of fixed ionic groups compared with the concentration of the surrounding medium or vice versa. The rate limiting step may be different for either case.
The most common rate limiting steps are either the (1) diffusion of ions inside of the material, or (2) diffusion of ions through the interface boundary layer. In both of these cases, the ion migration is due to the properties of the system; therefore, the rate cannot be changed without altering the chemical or physical properties of the system. The factors which favor an increased rate of diffusion in the ion exchange material and reduce the diffusion rate in the film are:
A high concentration of exchange sites in the material
Low degree of cross-linking
Dilute ionic solution
Small particle sizes
When studying ion exchange systems, the concentration of the external medium or the agitation rate could be a rate limiting step, so a simple increase in solution concentration, agitation rate, or ion exchange material thickness may shift the rate limiting step in the system.
Most ion exchange systems can be improved if the ion exchange rates are increased. A fast way to increase the diffusion rate is to select materials with a low degree of crosslinking or choose a thinner ion exchange layer (or smaller bead of ion exchange material). Thicker layers or larger beads require longer distances for the ions to travel through the material. The ion exchange rate can also be enhanced through solution agitation or increasing the temperature of the system. Another consideration is the high selectivity of the functional groups towards certain ions, which can cause reduced rates of exchange. The kinetics of most ion exchange systems are due to the material properties, ion selectivity, diffusion in the various parts of the system, and the ion exchange rates.