392 Fermentation and Biochemical Engineering Handbook The selectivity of an ion exchange resin will also depend on its cross linking. The polymer structure of the ion exchange resin can be thought of as collections of coiled springs which can swell or contract during the exchange of ions. 24) The cross-linking of the polymer limits the extent to which the resin may swell--the higher the degree of cross-linking, the lower the extent to which the resin can be hydrated. This limit on resin hydration determines the relative equivalent volumes of hydrated ions which the cross linked polymer network can accommodate. This is shown in Table 3. 25As the resin cross-linking or the fixed ion concentration is lowered, the selectivity of the resin decreases Table 3. Selectivity and Hydration of Cation Resins with Different Degrees of Crosslinking/251 4%DVB 8%DVB 16% DVB Catic K H K H K H 1.00418 1.00211 1.00130 H 1.30431 1.26200 l45136 1.49372 1.88183 2.23113 1.75360 2.22172 3.07106 2.37342 291159 4.15102 736163 194102 5.20229 9.66113 22.285 H- Hydration(g H,O/eq resin) DVB= divinylbenzene
392 Fermentation and Biochemical Engineering Handbook The selectivity of an ion exchange resin will also depend on its crosslinking. The polymer structure of the ion exchange resin can be thought of as collections of coiled springs which can swell or contract during the exchange of The cross-linking of the polymer limits the extent to which the resin may swell-the higher the degree of cross-linking, the lower the extent to which the resin can be hydrated. This limit on resin hydration determines the relative equivalent volumes of hydrated ions which the crosslinked polymer network can accommodate. This is shown in Table 3, [251 As the resin cross-linking or the fixed ion concentration is lowered, the selectivity of the resin decreases. Table 3. Selectivity and Hydration of Cation Resins With Different Degrees of Cros~linking[~~] 4% DVB 8% DVB 16% DVB Cation KH KH K H Li H Na m4 K cs T1 Ag 1.00 418 1.30 431 1.49 372 1.75 360 2.09 341 2.37 342 4.00 289 5.20 229 1.00 211 1.26 200 1.88 183 2.22 172 2.63 163 2.91 159 7.36 163 9.66 113 1.00 130 1.45 136 2.23 113 3.07 106 4.15 106 4.15 102 19.4 102 22.2 85 K = Selectivity compared to Li H = Hydration (g H,O/eq resin) DVB = divinylbenzene
The degree of cross linking can affect the equilibrium level obtained particularly as the molecular weight of the organic ion becomes large. with highly cross-linked resins and large organic ions, the concentration of the organic ions in the outer layers of the resin particles is much higher than in the center of the particle The selectivity of the resin for a given ion is also influenced by dissocia of the functional group covalently attached to the functional groups may not be ionized. This is particularly true if the functional group is a weak acid or base. For cation exchange, the degree of dissociation for the functional group increases as the pH is increased; however, the degree of dissociation for the ions in solution decreases with creasing pH. Therefore, if a cation resin had weak acid functionality,it would exhibit little affinity at any pH for a weak base solute. Similarly,an anion resin with weak base functionality exhibits little affinity at any pH for a weak acid solute The influence of pH on the dissociation constants for resin with a given functionality can be obtained by titration in the presence of an electrolyte Typical titration curves are shown in Fig. 5 for cation resins and in Fig. 6 for anion resins. 126] For sulfonic acid functional groups, the hydrogen ion is a very weak replacing ion andis similar to the lithium ion in its replacing power However, for resin with carboxylic acid functionality, the hydrogen ion exhibits the highest exchanging power. Table 41271[28]summarizes the effect different anion exchange resin functionalities have on the equilibrium ex change constants for a wide series of organic and inorganic anions The selectivity can also be influenced by the non-exchanging ions(co s)in solution even though these ions are not directly involved in the exchange reaction. An example of this influence would be the exchange of calcium ascorbate with an anion resin in the citrate form. Although calcium does not take part in the exchange reaction, sequestering of citrate will provide an additional driving force for the exchange. This effect, of course, would have been diminished had a portion of the ascorbate been added as the sodium ascorbate rather than the calcium ascorbate For nonpolar organic solutes, association into aggregates, perhaps even micelles, may depress solution activity. These associations may be influenced by the co-ions present
Ion Exchange 393 The degree of cross-linking can affect the equilibrium level obtained, particularly as the molecular weight of the organic ion becomes large. With highly cross-linked resins and large organic ions, the concentration of the organic ions in the outer layers of the resin particles is much higher than in the center of the particle. The selectivity of the resin for a given ion is also influenced by the dissociation constants of the functional group covalently attached to the resin (the fixed ion) and ofthe counter-ions in solutions. Since the charge per unit volume within the resin particle is high, a significant percentage of the hctional groups may not be ionized. This is particularly true if the hctional group is a weak acid or base. For cation exchange, the degree of dissociation for the functional group increases as the pH is increased; however, the degree of dissociation for the ions in solution decreases with increasing pH. Therefore, if a cation resin had weak acid functionality, it would exhibit little afiinity at any pH for a weak base solute. Similarly, an anion resin with weak base functionality exhibits little affinity at any pH for a weak acid solute. The influence of pH on the dissociation constants for resin with agiven functionality can be obtained by titration in the presence of an electrolyte. Typical titration curves are shown in Fig. 5 for cation resins and in Fig. 6 for anion resins.[26] For sulfonic acid functional groups, the hydrogen ion is a very weak replacing ion and is similar tothe lithium ion in its replacing power. However, for resin with carboxylic acid functionality, the hydrogen ion exhibits the highest exchanging power. Table 4[271[281 summarizes the effect different anion exchange resin functionalities have on the equilibrium exchange constants for a wide series of organic and inorganic anions. The selectivity can also be influenced by the non-exchanging ions (coions) in solution even though these ions are not directly involved in the exchange reaction. An example of this influence would be the exchange of calcium ascorbate with an anion resin in the citrate form. Although calcium does not take part in the exchange reaction, sequestering of citrate will provide an additional driving force for the exchange. This effect, of course, would have been diminished had a portion of the ascorbate been added as the sodium ascorbate rather than the calcium ascorbate. For nonpolar organic solutes, association into aggregates, perhaps even micelles, may depress solution activity. These associations may be influenced by the co-ions present
394 Fermentation and Biochemical Engineering Handbook 12 SUI 10 PHOSPHONIC D CARBOXYLIC AcID a NAOH PER GRAN RESIN Figure 5. Titration curves of typical cation exchange resins. 126 6 INTERMEDIATE BASE RESIN WEAK BASE RESIN MEQ HCL PER GRAM RESIN Figure 6. Titration curves of typical anion exchange resins (25)
394 Fermentation and Biochemical Engineering Handbook PH 14 12 8 6 - 10 - 8- - 2- 0 I I I I I I 0 2 4 6 8 10 12 L I I I I I I 0 2 4 6 8 10 12 MEQ NAOH PER GRAM RESIN Figure 5. Titration curves of typical cation exchange resins.[26] PH I I I I I 0 2 4 6 8 10 12 MEQ HCL PER GRAM RESIN Figure 6. Titration curves of typical anion exchange resins.[26]
Ion Exchange 395 Table 4. Selectivity Coefficients for Strongly Basic Anion Resin(271(281 Type I Anion Type Il Anion on Anion Salicylate 32.2 salicyl 8.7 C6H5O- 8.7 CHO. 5.2 7.3 HSO 4 4.1 HSO 6.l 38 3.3 Br 2.3 1.6 CN 1.3 HSO3 1.3 HSO3 13 NO2 13 0.32 H 0.65 HCOO 0.22 HPO 034 CH. CO0r 0.17 HCOO 0.22 HNCH.CO0. 0.10 CHCOO 0.18 OH- 0.09 0.09 NCH,COO 10 2.2 Kinetics The overall exchange process may be divided into five sequential steps 1. The diffusion of ions through the solution to the surface of the ion exchange particles 2. The diffusion of these ions through the ion exchange particle 3. The exchange of these ions with the ions attached to the functional group 4. The diffusion of these displaced ions through the particle 5. The diffusion of these displaced ions through the solution
Ion Exchange 395 Table 4. Selectivity Coefficients for Strongly Basic Anion Re~in[~'1[~*1 Type I Anion Type I1 Anion Anion Salicylate I- HSO, NO,- BrCNHSO,- NO,- c1- HCO,- HCOOC,H,OH2p04 CH3COOH2NCH2C 00- OHFKXcl 32.2 8.7 5.2 4.1 3.8 2.8 1.6 1.3 1.2 1 .oo 0.32 0.25 0.22 0.17 0.10 0.09 0.09 Anion KXcl Salicylate I- HSO, NO3- BrCNHSO,- NO; c1- OHHCO,- HCOOCH,COOFH2NCH2COOC,H,OH2PO.4 28 8.7 7.3 6.1 3.3 2.3 1.3 1.3 1.3 1 .oo 0.65 0.53 0.34 0.22 0.18 0.13 0.10 2.2 Kinetics The overall exchange process may be divided into five sequential steps: 1. The diffusion of ions through the solution to the surface of 2. The diffusion of these ions through the ion exchange 3. The exchange of these ions with the ions attached to the 4. The diffusion of these displaced ions through the particle 5. The diffusion of these displaced ions through the solution the ion exchange particles particle hctional group
396 Fermentation and Biochemical engineering handbook be accompanied by an ion of the opposite charge to satisfy the law of electroneutrality ge is usually considered to be controlled by transfer in ion exchange particles or in the immediately surrounding liquid phase. The theory used to describe mass transfer in the particle is based the Nernst-Planck equations developed by Helfferich/2 which accounted for the effect of the electric field generated by ionic diffusion, but excluded convection It is recognized that the Nernst-Planck theory fails to take into account the effect of swelling and particle size changes which accompany ion exchange or to take into account the slow relaxation of the resin network which causes the diffusion coefficient to vary with time. However, the approximations which these equations provide are a reasonable starting point and will most likely be found to be sufficient for the biotechnology engineer Any further refinements would lead rapidly to diminished returns. Likewise the mass transfer in the liquid phase is usually described according to the Nernst film concept using a version 30 of the Nernst-Planck equation or Glueckauf's 31] simpler linear driving force approximation There are five models 32 which can be used to represent the kinetics in ion exchange systems which involve liquid exchange phase mass transfer, solid phase mass transfer, and chemical reaction at the exchange group Model 1. The liquid phase mass transfer with a linear driving force is the controlling element. This model assumes that there are no concentration gradients in the particle, that there is a quasi-stationary state of liquid phase mass transfer, that there is a linear driving force and that there is a constant separation factor at a given solution concentration Model 2. The rate-controlling step is diffusion within the ion exchange particles. This model assumes that there are no concentration gradients in the liquid phase and that there is no convection, either through solvent uptake or release, in the solid phase Model 3. This model is controlled by the exchange reaction at the fixed ionic groups. This model assumes that the slowness of the exchange reaction allows for sufficient time for mass transfer to establish and maintain equilibrium so that no concentration gradient exists in either the ion exchange the liquid phase Model 4. This is a variation of model 3 in which the counter-ion from the solution does not permeate beyond the portion of particle which has been converted to the exchanging ionic form. The boundary of the unreacted core reduces the time such that this is called the shrinking core model. It is this
396 Fermentation and Biochemical Engineering Handbook Each step of the diffusion, whether in the resin or solution phase, must be accompanied by an ion of the opposite charge to satisfy the law of electroneutrality . Kinetics of ion exchange is usually considered to be controlled by mass transfer in ion exchange particles or in the immediately surrounding liquid phase. The theory used to describe mass transfer in the particle is based on the Nernst-Planck equations developed by Helfferi~h[~~] which accounted for the effect of the electric field generated by ionic diffusion, but excluded convection. It is recognized that the Nernst-Planck theory fails to take into account the effect of swelling and particle size changes which accompany ion exchange or to take into account the slow relaxation of the resin network which causes the diffusion coefficient to vary with time. However, the approximations which these equations provide are a reasonable starting point and will most likely be found to be sufficient for the biotechnology engineer. Any further refinements would lead rapidly to diminished returns. Likewise, the mass transfer in the liquid phase is usually described according to the Nernst film concept using a version[30] of the Nernst-Planck equation or Glueckauf d311 simpler linear driving force approximation. There are five models[32] which can be used to represent the kinetics in ion exchange systems which involve liquid exchange phase mass transfer, solid phase mass transfer, and chemical reaction at the exchange group. Model 1. The liquid phase mass transfer with a linear driving force is the controlling element. This model assumes that there are no concentration gradients in the particle, that there is a quasi-stationary state of liquid phase mass transfer, that there is a linear driving force and that there is a constant separation factor at a given solution concentration. Model 2. The rate-controlling step is diffusion within the ion exchange particles. This model assumes that there are no concentrationgradients in the liquid phase and that there is no convection, either through solvent uptake or release, in the solid phase. Model 3. This model is controlled by the exchange reaction at the fixed ionic groups. This model assumes that the slowness ofthe exchange reaction allows for sufficient time for mass transfer to establish and maintain equilibrium so that no concentration gradient exists in either the ion exchange particles or in the liquid phase. Model 4. This is a variation of Model 3 in which the counter-ion from the solution does not permeate beyond the portion of particle which has been converted to the exchanging ionic form. The boundary of the unreacted core reduces the time such that this is called the shrinhng core model. It is this