The Freundlich and Langmuir equations used for adsorption will also describe ion exchange. However, the BET equation is not applicable because multiple layers do not form; electrical charge must balance. The Donnan membrane equilibrium discussed in the section about membranes is also relevant to ion exchange because the charges on the resin backbone are localized in an situation analogous to charged proteins than cannot pass through membranes.
Synthetic ion exchange resins are usually cast as porous beads with considerable external and pore surface where ions can attach. Whenever there is a great surface area, adsorption plays a role. If a substance is adsorbed to an ion exchange resin, no ion is liberated. Testing for ions in the effluent will distinguish between removal by adsorption and removal by ion exchange. Of course, both mechanisms may be significant in certain cases, and mass balances comparing moles removed with moles of ions liberated will quantify the amounts of adsorption and ion exchange.
This next material is taken from a brochure about Dowex resins.
The more highly crosslinked a resin, the more difficult it becomes to introduce additional functional groups. Sulfonation is carried out after the crosslinking has been completed and the sulfonic acid groups are introduced inside the resin particle as well as over its surface. Likewise, the quaternary ammonium groups are introduced after the polymerization has been completed and they too are introduced both inside the particle as well as on its surface. Fewer functional groups can be introduced inside the particles when they are highly crosslinked and hence the total capacity on a dry basis drops slightly.
This situation is reversed when a wet volume basis is used to measure
the capacity on a resin. Although fewer functional groups are introduced
into a highly crosslinked resin, these groups are spaced closer together
on a volume basis because the volume of water is reduced by the additional
crosslinking. (See above figure). Thus the capacity on a wet volume basis
increases as cross-linking increases. The next figure describes the changes
in capacity as crosslinking is changed.
In general, the larger the ion or molecule diffusing into an ion exchange
particle, or the more highly crosslinked the polymer, the longer will be
the time required to reach equilibrium conditions.
|
|
Diameter of Particles | |
| 20 - 50 | 0.0331-0.0117 Inches | 840-297 Micrometers |
| 50 - 100 | 0.0117-0.0059 | 297-149 |
| 100 - 200 | 0.0059-0.0029 | 149-74 |
| 200 - 400 | 0.0029-0.0015 | 74-38 |
| minus 400 | < 0.0015 | < 38 |
(a) Equilibration Rate
The
particle size of an ion exchange resin influences the time required to
establish equilibrium conditions. There are two types of diffusion that
must be considered in an ion exchange equilibrium. The first is called
film diffusion or the movement of ions from a surrounding solution to the
surface of an ion exchange particle. The second is called internal diffusion
and is the movement of ions from the surface to the interior of an ion
exchange particle. Film diffusion is usually the controlling reaction in
dilute solutions whereas internal diffusion is controlling in more concentrated
solutions. The particle size of an ion exchange resin affects both film
diffusion and internal diffusion. A fine mesh particle presents more
surface area for film diffusion and also contains less internal volume
through which an ion must diffuse. A decrease in particle size thus shortens
the time required for equilibration. This figure illustrates the shortening
of equilibration times for decreases in particle sizes.
Ion
exchange processes are usually carried out in columns with the resin resting
on a suitable support. Liquids may be processed either up-flow or down-flow
through such columns. The spherical particles of ion exchange resin resist
the flowing of a liquid through or around them. The smaller the particle
size, the greater will be this resistance against which a liquid must flow.
This resistance goes up very rapidly when particles smaller than 100 mesh
are employed. This figure illustrates the decrease in flow rates with decreasing
particle sizes.