I n d . E n g . C h e m . Res. 1993,32, 107-117 Gill, P. E.; Murray, W.; Saunders, M. A.; Wright, M. H. Constrained Nonlinear Programming. Handbook in Operations Research and Management Science; North-Holland: Amsterdam, 1989; Vol. 1, Chapter 3. Henley, E. J.; Seader, J. D. Equilibrium Stage Separation Operation in Chemical Engineering; Wiley: New York, 1981. Holland, C. D.; Liapis, A. I. Computer Methods for Solving Dynamic Separation Problems; McGraw-Hill: New York, 1983. Joseph, B.; Jang, S. S.; Mukai, H. Integrated Model Based Control of Multivariable Nonlinear Systems. IFAC Model Based Process Control; Pergamon Press: New York, 1988; pp 121-128. Luyben, W. L. Process Modeling, simulation and Control for Chemical Engineers; McGraw-Hill: Singapore, 1990. Moore, R. D.; Corripio, A. B. Online Optimization of Distillation Columns in Series. Presented at AIChE Annual Meeting, Chicago, IL, Nov 1990. Naphtali, L.M.; Sandholm, D. P. Multicomponent Separation Calculations by Linearization. AIChE J . 1971, 17, 148.
107
Ohmura, S.; Kasahara, S. New Distillation Method Utilizing Salient Features of Both Shortcut and Tray-by-Tray Method. J . Chem. Eng. Jpn. 1978, 11 (3), 185-193. Powell, M. J. D. A Fast Algorithm for Nonlinearly Constrained Optimization Calculations; Lecture Notes in Mathematics No. 630; Springer-Verlag: Berlin, 1978. Powell, M. J. D. Private communications, 1990. Riggs, J. B. Nonlinear Process Model Based Control of a Propylene Sidestream Draw Column. Ind. Eng. Chem. Res. 1990, 29, 2221-2226. Sairam, V. M. Tech. Dissertation, IIT Kanpur, India, 1991. Stewart, W. E.; Levien, K. L.; Morari, M. Simulation of Fractionation by Orthogonal Collocation. Chem. Eng. Sci. 1985, 40, 409-421.
Received for review January 27, 1992 Revised manuscript received September 15, 1992 Accepted October 5, 1992
SEPARATIONS Ion Exchange of Amino Acids and Dipeptides on Cation Resins with Varying Degree of Cross-Linking. 1. Equilibrium Ida L. Jones and Giorgio Carta* Center for Bioprocess Development, Department of Chemical Engineering, University of Virginia, Charlottesuille, Virginia 22903-2442
The uptake equilibrium of alanine, leucine, phenylalanine, phenylalanylalanine, and phenylalanylphenylalanine is obtained experimentally for sulfonated polystyrene-divinylbenzene resins with the degree of cross-linking from 4 to 10%. The uptake of these solutes by the hydrogen form of the resins is shown to depend upon solution equilibria and ion exchange interactions and is found to occur essentially only through the exchange of amino acid or dipeptide cations for hydrogen ion. The selectivity coefficient for these exchange reactions is found to be related to the hydration of the resin and to the hydrophobic character of the exchanged solute. At low resin loadings with solute, the selectivity coefficient varies modestly with the degree of cross-linking of the resin but increases dramatically with the hydrophobicity of the solute. At higher resin-phase concentrations, on the other hand, steric interactions appear to be dominant for the large iaolutes. This leads to a decrease in the apparent selectivity coefficient with resin loading, and, in extreme cases, hinders a full utilization of the resin ion exchange capacity measured for small inorganic cations. An equilibrium model is successfully used to correlate the uptake equlibria for these solutes, allowing one to compute the resin loading with amino acid or dipeptide as a function of the solution composition.
Introduction Ion exchange resins are used extensively on a large scale for the recovery, separation, and purification of amino acids, peptides, and other compounds found in the food and pharmaceutical industries (Belter, 1984). In these applications involving amphoteric compounds, such as amino acids, ion exchange resins are particularly effective since the net charge on these molecules may vary in magnitude and sign with the pH of the solution. Thus, a solute that has been taken up by a resin at a certain pH at which the molecule has a charge opposite to that of the resin may be efficiently desorbed by changing the solution pH to a value such that the net charge on the molecule is the same as that of the resin. In addition, since the ion-
* Author t o whom correspondence is t o be addressed.
ization properties of these molecules differ from species to species, mixtures of these compounds can often be separated on this basis. Cross-linked polystyrene divinylbenzene resins are most commonly used in these applications with either cation or anion exchange functionalities. These resins are generally available both in gel and in macroreticular (or macroporous) forms. In the former case, the resin is in the form of a water-swollen gel which contains no permanent macropores. In the latter case, the resin particles contain permanent macropores interdispersed through a gel-type structure at the subparticle level. In the past, numerous studies have extensively a d d r d the use of ion exchange resins in analytical applications for amino acids and small peptides (Partridge, 1949;Moore and Stein, 1951; Hamilton, 1966; Niederwieser, 1983; Blackburn, 1983). Only recently, however, has considerable
0888-588519312632-0107$04.00/00 1993 American Chemical Society
108 Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993 Table I. Resin Properties nominal resin % DVB Dowex 50WX4 4 xus-40232" 6 XUS-40260" 8 XUS-43437O 8 HCR-W2 8 xus-40197" 10 HGR-W2 10 a
QO?
me4
(g of dry resin)
6.2 5.6 5.6 5.4 5.3 5.1 5.2
wd, (g of dry resin)/ (g of hydrated resin) 0.31 0.36 0.47 0.48 0.48 0.53 0.53
7,(g of dry resin)/ (g of hydrated resin) 2.23 1.78 1.13 1.08 1.08 0.88 0.88
Pdv
(g of dry resin)/cm3 0.35 0.45 0.57 0.58 0.58 0.65
'Monosphere enhanced performance" resin, Dow Chemical Co.
research been devoted to the study of the fundamental physical-chemical phenomena that affect the ion exchange of these molecules. A number of recent studies have been devoted to the representation of uptake equilibria of amino acids by cation exchange resins as a function of solution composition (Carta et al., 1988, Saunders et al., 1989; Wang et al., 1989; Gosling et al., 1989; Helfferich, 1990; Dye et al., 1990). Saunders et al., for example, have shown that the uptake of phenylalanine and tyrosine by the hydrogen form of macroreticular cation exchange resin occurs via the stoichiometric exchange of amino acid cations, with essentially no contribution deriving from the sorption of zwitterionic or negatively charged species. Similar results have been obtained by Wang et al., who indicated that it is the net charge of an amino acid that determines the uptake by a resin. Zwitterionic species are, thus, prevented from being exchanged because of the spatial proximity of two opposite charges on the molecule. Models to describe the ion exchange equilibria of these molecules have been developed by several authors (Wang et al., 1989; Saunders et al., 1989; Dye et al., 1990). These models, however, invariably contain parameters that have to be determined by fitting experimental results for each resin and exchanged solute. As a consequence, the description of equilibria requires a considerable amount of experimentation. In this respect, thus, a broader knowledge of the behavior of different resins and exchanged solutes is desirable since it might permit the development of a rational methodology for the estimation of equilibrium based upon a knowledge of resin characteristics and molecular properties. Although a number of experimental studies have been reported in the literature, in most cases a single resin, typically with a nominal degree of crosslinking of a%, has been used. Thus, it is difficult to recognize the existence of general trends in the exchange of these solutes. In this paper, we report a study of the ion exchange of three amino acids and two dipeptides with a number of gel-type sulfonated polystyrenedivinylbenzene resins with nominal degrees of cross-linking varying from 4 to 10%. Uptake equilibria of these molecules are obtained in batch experiments, and the results are analyzed taking into account the solution dissociation equilibria An ion exchange equilibrium model that allows for variable selectivity coefficients is then used to fit the measured uptake equilibria, and the model parameters are correlated in terms of the resin hydration and the relative hydrophobicity of the exchanged solutes. The effects of resin characteristics and molecular properties on the rates of intraparticle transport of these molecules are reported in part 2, the following paper in this issue.
Experimental Section Resin Properties. A number of commercially available sulfonated polystyrene-divinylbenzenes have been used in this study, and their relevant properties are given in Table I. All the resins are gel-type and were obtained from
3
I '\
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o ' , 3
"
'
"
"
2
'
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Figure 1. Hydration water of resins in hydrogen form versus the nominal degree of cross-linking.
Dow Chemical Co. (Midland, MI). The resins with the XUS denomination are characterized by a uniquely narrow particle size distribution and are referred to by the manufacturer as "monosphere enhanced performance" resins. As a result of the uniformity of structure, these resins have been shown to posseas a superior osmotic shock resistance when repeatedly exposed to strong acid and base solutions (Jones and Carta, 1991). The other resins cited in this table have instead the broad particle size distribution which is typical of conventional commercial resins. The resin samples were used as supplied by the manufacturer, with no particle size classification attempted. However, prior to use in experiments, the resin samples (each one from a single lot) were pretreated by repeated washes in a column with 1 N NaOH and HC1 solutions, converted to the hydrogen form with 1N HC1, and thoroughly rinsed with distilled-deionized water with a resistivity greater than 10 M Q cm. The total ion exchange capacity of each resin (qo, meq/ (g of dry resin)) was determined by equilibrating resin samples in the hydrogen form with an excess of a NaOH solution. The total capacity was determined by back-titrating the excess NaOH as described by Dye et al. (1990). The dry weight fraction of the hydrated resins in the hydrogen form (wd, (g of dry resin)/(g of hydrated resin)) was also determined, as described by Dye et al., from the weight loas at 115 "C of resin samples from which the interparticle water had been removed. The particle dry resin density (Pd, (g of dry resin)/(cm3 of hydrated resin)) was determined from the bulk density measured with a standard capillary picnometer and from the measured wd values. All of these experiments were conducted at 22 f 3 OC in distilled-deionized water. Sulfonated polystyrene-divinylbenzene resins are normally classified by defining their nominal degree of cross-linking as a percentage of divinylbenzene (DVB). This is not necessarily an exact measure of the true chemical composition of the resin, but it rather reflects the total hydration of the resin in hydrogen form. This definition was adopted t.O characterize the resin samples used in this work. A plot of the measured resin hydration versus the nominal degree of cross-linkingdefined for these resins
Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993 109 Table 11. Amino Acids and Peptide Properties solute MW DK, DK, Af." cal/mol alanine 89 2.34b 9.6gb 500; 1eucin e 131 2.36b 9.62b 1800' phenylalanine 165 2.11d 9.13d 2500' PheAla 236 3.33' 7.42' 2520' PhePhe 312 3.33' 452d "Relative hydrophobicity, Af = 0 for glycine. bMeister (1965). 'Nozaki and Tanford (1971). dSaunders et al. (1989). 'Thia work. 'Calculated from eq 1.
is given in Figure 1. A line representing the data of Reichenberg and McCauley (1955) is also shown giving the measured hydration of similar sulfonated resins as a function of the degree of cross-linking. The results are related essentially in an inversely proportional manner and are in agreement with those of Reichenberg and McCauley. It should be noted, however, that it cannot be concluded that the true degree of cross-linking of our resin samples is indeed equal to the nominal value, since the hydration of a resin could depend to some extent upon the polymerization and functionalization methods employed in the manufacturing process. Uptake Measurements. The uptake equilibrium of three amino acids and two dipeptides was measured for the different resins. The compounds included in this study are given in Table I1 along with some of their relevant molecular properties. The amino acids were obtained in L-form from Ajinomoto USA, Inc., and the peptides from Sigma Chemical Co. The pK values of these amino acids were obtained from various literature sources, as indicated. The pK values of phenylalanylalanine (PheAla) were instead obtained following the titration method of Harris (1923). The basic pK value of phenylalanylphenylalanine (PhePhe) was assumed to be the same as that of PheAla, since the titration method in this case proved inaccurate as a result of the very low solubility of PhePhe in water. The solute hydrophobicity values given in Table I1 are based upon the hydrophobicity scale of Nozaki and Tanford (1971). Although other more general hydrophobicity scales have been proposed (see for example Rekker and deKort (1979)),this hydrophobicity scale has the advantage that it is built directly on the partition behavior of amino acids in a water-organic solvent system. The Af values represent the free energy of transfer from water to an organic solvent for amino acid side chains. Thus in this scale, glycine, which has no side chain, is assumed to have 4 = 0. As suggested by Eiteman and Gainer (1990),the value of the relative hydrophobicity has additive constitutive properties, since in this definition it depends only upon the free energy of transfer of side chains. As a result, the hydrophobicity of a dimer can be estimated as the sum of the hydrophobicities of the constituent monomers, minus the free energy Afw lost by the removal of water in the condensation of the two monomers. Since the relative hydrophobicities of the individual amino acids are known, the hydrophobicity of a peptide containing m amino acids can be calculated from (Eiteman and Gainer, 1990) m
Af = CAfi - (m- l)Afw i=l
(1)
Eiteman and Gainer have estimated a value of Afw = 480 f 40 cal/mol. The values of Af calculated from this equation for PheAla and PhePhe are given in Table 11. Obviously the method could not be applied to large peptides because of the possibility of free energy (in terms of relative hydrophobicity) lost by interactions among the constituent amino acids. For small peptides, on the other
hand, these interactions should have limited importance. The uptake of amino acids by the resins was obtained by allowing samples of the resins in hydrogen form (1-2 g of hydrated resin) to come to equilibrium with dilute HCI solutions (100-200 cm3) containing various initial concentrations of the exchangeable solutes in sealed Erlenmeyer flasks. The flasks were shaken in a constant temperature bath at 25 f 1 "C for 8-24 h. After this period, the solutions in the flasks were sampled and analyzed, and the uptake of solute by the resin was obtained from a mass balance. Achievement of equilibrium was tested by taking several samples at different times for some of the experiments, as well as by allowing the system to reach equilibrium with resin samples preloaded with solute. The same method was used for the peptides, but using 0.1 g of hydrated resin and 10 cm3 of solution in test tubes. The concentrations of alanine and leucine were determined by HPLC with the procedure described by Dye et al. For the other species the concentrations were determined from the UV absorption signal with a spectrophotometer (Beckman, Model DU-50).
Rssults and Discussion Uptake Equilibria. The equilibrium uptake of alanine, leucine, phenylalanine, phenylalanylalanine, and phenylalanylphenylalanine by four of the resins studied with the degree of cross-linking from 4 to 10% DVB is given in Figures 2 4 . Similar data were also obtained for the other resins. Within the accuracy of the experimental method, however, the uptake data obtained for different resins with the same nominal degree of cross-linking were the same. Thus, only a representative set of data is given in full for each degree of cross-linking, The correlated parameter values of an equilibrium model discussed below are nevertheless given for all the resins. The lines shown in these figures are calculated from that model. In all cases, with the exception of PhePhe, the experiments were conducted in such a way as to span a broad range of concentrations, with corresponding resin loadings from very low values to almost complete saturation. This broad range of concentrations was not possible for PhePhe because of ita rather low solubility in aqueous solution. In Figures 2-6, qA is the total uptake of amino acid or peptide by the resin expressed in millimoles per gram of dry resin in hydrogen form. CAis the total (or analytical) concentration of the amino acid or peptide in solution. Since it was desired to measure uptake equilibria without interferences from buffering species, the experiments were carried out in seta with a constant initial concentration of the chloride co-ion. This species is largely excluded from the resins by the Donnan potential effect, and, thus, ita concentration remained essentially constant during each experiment. The pH, in turn, varied from point to point along each curve. Two competing effects determine the behavior observed in these experiments, as pointed out by Saunders et al. (1989). At high chloride concentrations, the pH is low, and most of the amino acid or peptide is present in solution in its exchangeable,positively charged form. A t these low pH values, however, the concentration of the competing hydrogen ion is much larger, and only a modest uptake of the solute is observed. At lower chloride concentrations, on the other hand, the pH is higher, and the fraction of amino acid in positively charged form is lower. At the same time, however, the hydrogen ion concentration is much lower, and the resin takes up a much larger amount of the amino acid or peptide. In fact, as shown by Dye et al. (1990), in the absence of other competing counterions, the uptake of an amino acid by a resin would be maximum at the isoelectric point of that species, which is obtained
110 Ind. Eng. Chem. Res., Vol. 32, No. 1,1993
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resents the ratio of the measured uptake of the amino acid or peptide, qA,and the resin ion exchange capacity qo. In the case of PhePhe, the uptake data were obtained only at high chloride concentrations. For these conditions, since the peptide concentration in solution was very low, the peptide was fully protonated. Thus, ita ionic fraction was approximated by X = CA/CC1-. In all the cases studied, the uptake data obtained a t different co-ion concentrations and pH appear to be correlated by a single line. This indicates that the uptake of these solutes depend solely upon the ionic fraction X,and not upon the total concentration of solute Ck In fact, to obtain the same X value at high and low chloride concentrations, the total concentration CAat a higher chloride concentration has to be much larger than at a lower chloride concentration. Since the same value of Y is obtained in the two cases, we can conclude that the uptake
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occurs as a result of the exchange of amino acid or peptide cations. Similar results have also been obtained by Wang et al. (1989) for the uptake of amino acids by the sodium form of an 8% DVB resin. In this case, the uptake was the result of the exchange of amino acid cations and sodium ions. For the data in Figures 8-12 we may define an apparent selectivity coefficient for the exchange process as
As is apparent from the data in these figures, S is not
constant and varies in magnitude and trend with the percent of DVB and the nature of the exchanged solute. The selectivity coefficient is generally larger for the more
114 Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993
t
-
the site with lower selectivity, with a resulting decrease in the apparent selectivity coefficient. This modeling approach has been later extended to the ion exchange of amino acids in single and multisolute systems by Saunders et al. (1989) and Dye et al. (1990). In their formulation, a binomial distribution of two elements is assumed. For a system containing two counterions, the apparent selectivity coefficient is given by
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Figure 12. Uptake equilibrium of phenylalanylphenylalanine for different resins in terms of ionic fractions: (a) Dowex 50WX4 (4% DVB), (b) XUS 40232 (6% DVB), (c) XUS 40260 (8% DVB), (d) XUS 40197 (10% DVB).
hydrophobic solutes and for the resins with an intermediate percent of DVB. In general S appears to vary with the ionic fraction of the solute. For resins with a low degree of cross-linking this variation is modest. However, at higher values of the percent of DVB, a much more pronounced variation is observed. In this case, S is maximum at low ionic fractions, when the resin is almost completely in the hydrogen form. As the resin becomes saturated with amino acid or peptide, S is reduced to values that, in some cases, are below unity. Correlation of Ion Exchange Equilibria and Discussion. A number of factors may cause the variation of selectivity coefficients in ion exchange that are sometimes observed. If ion exchange is regarded as the equilibrium between two homogeneous phases, the resin phase and the solution phase, then the selectivity coefficient may be assumed to be affected by the activity coefficients within the resin matrix, which, in turn may be affected by the molecular properties of the exchanged solutes and their interactions with the resin. On the other hand, crosslinked, gel-type ion exchange resins are probably more realistically regarded as a highly heterogeneous and constricted environment. In this case we could expect very significant local variations in the nature of the exchange sites and in the environment that immediately surrounds them, such as those caused by non-uniformities in the local degree of cross-linking and in the extent of sulfonation (Myers and Byington, 1986). In addition sieving and steric interaction effects are likely to exist in highly cross-linked resins when the solute size is comparable with the mesh size of the cross-linked polymer (Helfferich, 1962). Myers and Byington have developed a model for in exchange that assumes the existence of a heterogeneous distribution of functional groups having different specific selectivity. In this model, it is assumed that the apparent selectivity results from the combined ion exchange reactions occurring onto each individual functional group. Thus, for example, starting with a resin in the B-form, ion exchange of a solute A would occur initially on the functional groups having greater selectivity, resulting in an initially high apparent selectivity. As the loading of A on the resin increases, however, ion exchange would occur on
As shown by Myers and Byington (1986), S represents an average selectivity coefficient for the entire range of ionic fractions from 0 to 1, W is heterogeneity parameter that depends upon the variance of the distribution of selectivities among the functional groups, and p is the skewness of the assumed binomial distribution of functional groups. All three parameters generally have to be obtained from a fit of experimental data. In the limits of p = 0 or 1,there is only one type of functional group. In this case, eq 10 yields S = S, and the seltctivity coefficient is constant. Similarly, we obtain S = S when W = 1 for any value of p, as, in this case, in the conceptual model all functional groups have the same specific selectivity. Furthermore, setting S = 1 in eq 10 gives x*=
+ WVp] 1 - S(W" + WV) + S2W"+" 1 - S[W"(l - p)
(13)
For certain values of S, W, and p, this equation yields a value of X * between zero and unity, indicating that the modeling approach can be conveniently used to fit ion exchange data exhibiting an apparent selectivity reversal, with values of S above and below unity. Finally, in the limit of X = 0, eq 10 yields a limiting, infinite dilution value, So, which is given by s o =
S[W"(1
- p)
+ WVp]
(14)
Thus,the model appears to possess the necessary flexibility to represent all of the features observed in our experimental measurements. In addition, it should be noted that while the model is formally built on the assumption of a heterogeneous distribution of functional groups, the behavior predicted by these equations is qualitatively consistent with different physical situations. A variation in the apparent selectivity similar to that obtained from these equations would be seen, for example, as the result of steric hindrance effects at high solute loadings in the constricted environment of highly cross-linked resins. The model obviously does not allow a discrimination between these effects but provides, nevertheless, a flexible fitting tool to summarize ion exchange equilibria. The fitting of the uptake data with eq 10 was carried out by first reducing the q A - CAdata to the X - Y form as described above, and then performing a nonlinear regression fit of the three model parameters (3, W, and p) for each resin, using the IMSL subroutine ZXSSQ. The model parameters obtained with this procedure are given in Table III. For PhePhe, only the infiiite dilution values So were determined, since the data were obtained only for
Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993 115 Table 111. Equilibrium Parameter Values resin Dowex 50WX4 XUS 40232 . ..~~~ 5% DVB 4 6 Ala 1.1 1.6 1.0 W 3.0 0.90 P 0.9 3.2 s 2.3 Leu 1.7 W 3.5 0.93 e 0.90 7.4 Phe S 3.7 1.8 W 6.6 0.92 P 0.86 7.1 8 4.8 PheAla 2.0 W 3.8 0.91 P 0.90 22 PhePhe So 29
s
XUS 40260 8 1.6 2.8 0.51 2.9 2.8 0.71 6.9 1.8 0.90
XUS 43437 8 1.7
HCR-W2 8 1.8 2.3 0.50 2.7 2.8 0.69 6.3 2.4 0.85
1.1
0.50 3.0 1.7 0.50 5.8 2.5 0.65
XUS 40197 10 1.2 2.5 0.90 3.3 1.5 0.74 3.4 5.0 0.78 0.51 58 0.62 18
2.2
10 0.82 21
very small values of X. For the other species this infinite dilution value may be calculated from eq 14. Model calculations are shown in Figures 2-12. In all cases the model provided a fit within the accuracy of the experiment error in the determination of the q A values (&lo%). Values of W significantly different from unity were obtained for these resins and organic compounds, indicating that the apparent selectivity decreases with the loading of the solute on the resin. The average selectivity parameter values, S, also vary, increasing with solute size and hydrophobicity for the resins with lower percent of DVB. For the more highly cross-linked resins, however, the average selectivity appears to increase in the order Ala-Leu-Phe, but it then decreases _tomuch lower values for PheAla. This decrease in the S value for PheAla is accompanied by a large increase in the W value, to produce the large apparent selectivity reversal effect seen in Figure llc,d. This effect likely results from steric hindrance within the polymer network that prevents complete loadings of the resin with large solutes. Qualitatively similar effects, in fact, have been previously observed for the ion exchange of large organic ions. Hale et al. (1953), for example, observed that in the ion exchange of tetraethylammonium ion with a sulfonated resin with 15% DVB, the apparent selectivity (relative to hydrogen ion) decreased gradually from a value around 10 at low ionic fractions, to values around at higher ionic fractions. Furthermore, with a resin with 10% DVB, these authors observed that only about 63% of the total ion exchange capacity (measured with NH4+)was accessible by tetraethylammonium ion. This molecule was estimated to have a diameter of the order of 7.5 A. The molecular structure of the amino acids has been determined by Gurskaya (1968) from crystallographic measurements. Although these molecules are far from being spherical, from these measurements it can be estimated that the molecular sizes of Ala, Leu, and Phe are smaller than 7 A, while PheAla and PhePhe are larger. Consistent with the results of Hale et al., we can then conclude that for molecules larger than about 7 A, utilization of the entire ion exchange capacity in resins with a percent of DVB greater than 8 is prevented. In fact, if we assume a molar volume of 133 cm3/mol, corresponding to a spherical molecule 7.5 A in diameter, we can estimate that a resin with an ion exchange capacity of 5.1 meq/ (g of dry resin fully saturated with this solute) would have to contain 0.68 cm3of solute per gram of dry resin. This amounts to about 80% of the total hydration water of a 10% DVB resin, and it appears unlikely that this volume of solute could be accommodated by the stretching of the polymer network. A useful comparison of the behavior of different resins may be obtained by considering the apparent selectivity
HGR-W2 10
3.5 4.6 0.80
100,
0 Ala
- - - - - - h i
1
I 2
8
6
4
10
12
% DVB
Figure 13. Effect of the resin cross-linking on the apparent selectivity relative to hydrogen ion for different amino acids and dipeptides in the infinite dilution limit. 1
35, 30 -
%DVB 0 4
25 -
vp
20
-
15
-
10
-
0 6
~a
A 10
5 -
n Alal
0
Leu
1000
Phe /PheAla
2000 3000 Af (cal/mol)
PhePhe,
4000
5000
Figure 14. Effect of the solute hydrophobicity on the apparent selectivity relative to hydrogen ion for different amino acids and dipeptides in the infinite dilution limit.
-.
coefficient in the infinite dilution limit (Y 0). This value should be representative of the true relative affmity of the solutes for the accessible and most selective functional groups in the resin, free of effects deriving from steric interactions among exchanged solute molecules. The So values calculated from eq 14 are shown in Figure 13 as a function of the percent of DVB in the resins, and in Figure 14, as a function of the relative hydrophobicity values of the solutes given in Table II. From Figure 13 it is apparent that the selectivity coefficient increases for resins with a low degree of cross-linking as the resin percent of DVB is increased, reaching a maximum before decreasing again at a higher percent of DVB. The position of the maximum is shifted toward lower values for the larger solutes, and no maximum is seen for PhePhe. In this case, steric hindrance effects likely dominate the behavior. From Figure 14 it is apparent that the selectivity coefficient increases with the solute hydrophobicity. Note that, while the molecular weights of Phe and PheAla are quite different, the estimated hydrophobicities are nearly the same, and essentially the same selectivity coefficient is obtained for
116 Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993
the different resins. PhePhe, on the other hand, which has a much larger hydrophobicity, exhibits a much larger So-value. In addition, to further corroborate this point, some limited meaurements on the uptake of AlaPhe by the resin XUS 40260 were conducted (Holsinger,1992). In this case the positively charged amino group is on the alanine residue of the molecule. Within the experimental error, however, the same ion exchange behavior as that of PheAla was obtained for AlaPhe, indicating that the ion exchange selectivity is related to the overall hydrophobicity of the dipeptide (which is the same for PheAla and AlaPhe), irrespective of the nature of the amino terminal on the molecule. The behavior observed for the selectivity coefficient of amino acids and dipeptides in these resins is quite different from that seen with inorganic cations. For the latter species the selectivity scale is determined by swelling pressure effects, and the selectivity coefficient increases as the size of the hydrated species is reduced (Helfferich, 1962). Thus, for example, sulfonated resins favor Na+ over Li+ and H+. Furthermore, since swelling pressure effects are more significant in more highly cross-linked resins, the selectivity coefficients for these compounds become increasingly different from unity as the percent of DVB is increased. For the amino acid and dipeptide cations, the selectivity coefficients are larger for the larger species and exhibit only a relatively modest variation with the resin cross-linking. For these compounds in styrenic resins, hydrophobic interactions of the exchanged solutes with the resin polymeric backbone appear to play an important role. Thus,as previously advanced by Dye et al. (1990), although the uptake process appears to occur solely via the exchange of cations, the hydrophobic nature of the exchanged solute determines the selectivity coefficient for the exchange reaction. At high ionic fractions, however, steric interactions among solute molecules within the polymer network become more important and determine the uptake behavior. Conclusions The results of this study, obtained for a practically significantrange of gel-type, sulfonated resins and for some representative amino acids and dipeptides, indicate that in these highly hydrated resins the uptake of these solutes occurs via the stoichiometric exchange of cations. The observed uptake behavior at different co-ion concentrations could, in fact, be explained taking into account the known solution equilibria to reduce the data solely in terms of ionic fractions. The experimental results indicate that the selectivity coefficient for the exchange of amino acid and peptide cations with hydrogen ion varies with solute and resin properties and with the resin loading. The hydrophobic nature of the exchanged solute and the hydration of the resins appear to have significant effects. The selectivity for the exchange with hydrogen ion increases with the hydrophobicity of the exchanged solute and is maximum for an intermediate value of the resin cross-linking. The results were successfully correlated with a model that describes variable selectivity Coefficients by assuming the existence of a heterogenous population of functional groups in the resin. The model makes use of three fitting parameters, S, w, and p , for each3pecies and resin. The average selectivity coefficient, S, appears to vary in a consistent pattern with the nature of the exchanged species and the cross-linking of the resin, as shown in Table 111. At a low percent of DVB, S increases with solute hydrohobicity. On the other hand, at a high percent of DVB, $ is smaller for the larger molecules, since for these resins
steric hindrance prevents a full utilization of the exchange capacity that one observes for small inorganic cations. The trends of W and p are less clear, as there is a greater statistical uncertainty in fitting these parameters. Both W and p , in fact, affect the variability of the apparent selectivity, S, with solute loading. The combined effect of these two parameters is, however, to give rise to a larger variation of S with Y for the larger species and the more highly cross-linked resins. A more exact correlation could be obtained for the infinite dilution selectivity coefficient which is related to the model parameters by eq 14. Its value, So,could be correlated with the resin cross-linking and the solute hydrophobicity. Acknowledgment This research was supported by the Dow Chemical Co., Midland, MI. Nomenclature CA = solution concentration, mol/L 4= free energy of transfer for amino acid side chain, &/mol Atw = free energy lost by removal of water, cal/mol K i= dissociation equilibrium constant, mol/L Kw = ionic product of water, mo12/L2 p = skewness parameter qA = solute concentration in resin, mmol/(g of dry resin) qo = resin total ion exchange capacity, mmol/(g of dry resin) S = apparent selectivity coefficient for exchange with hydrogen ion S = average selectivity parameter So = selectivity at infinite dilution wd = dry weight fraction, (g of dry resin)/(g of hydrated resin) W = heterogeneity parameter X = ionic fraction of amino acid or peptide cations in solution X * = ionic fraction corresponding to S = 1 Y = ionic fraction of amino acid or peptide in the resin Greek L e t t e r s y = Pd =
total hydration water, (g of water)/(g of dry resin) dry resin density, (g of dry resin)/(cm3of hydrated resin)
Literature Cited Belter, P. A. Ion Exchange and Adsorption in Pharmaceutical Manufacture. AIChE Symp. Ser. 1984,80, 110-117. Blackburn, S. Amino Acids and Amines. In Handbook of Chromtography; Zweig, G., Sherma, J., Eds.; CRC Press: Boca Raton, FL, 1983. Carta, G.; Saunders, M. S.; DeCarli, J. P., 11;Vierow, J. B. Dynamics of Fixed-Bed Separations of Amino Acids by Ion Exchange. AIChE Symp. Ser. 1988,84,54-61. Dye, S. R.; DeCarli, J. P., 11; Carta, G. Equilibrium Sorption Amino Acids by a Cation Exchange Resin. Ind. Eng. Chern. Res. 1990, 29, 849-857. Eiteman, M. A.; Gainer, J. L. Peptide Hydrophobicity and Partitioning in Poly(ethy1ene glycol)/Magnesium Sulfate Aqueous Two Phase System. Biotechnol. Prog. 1990, 6, 479-484. Gosling, I. S.; Cook, D.; Fry, M. D. M. The Role of Adsorption Isotherms in the Design of Chromatographic Separations for Downstream Processing. Chem. Eng. Res. Deu. 1989, 67, 232-242. Gurskaya, G. V. The Molecular Structure of Amino Acids. Determination by X-ray Diffraction Analysis; Consultants Bureau: New York, 1968. Hale, D. K.; Packham, D. I.; Pepper, K. W. Properties of Ion Exchange Resins in Relation to Their Structure. Part V. Exchange of Organic Cations. J . Chem. SOC.1953, 844-851. Hamilton, P. B. Ion Exchange Chromatography of Amino Acids. Adu. Chromatogr. 1966, 2, 3-15. Harris, L. J. The Titration of Amino- and Carboxyl-Groups in Amino Acids, Polypeptides, Etc. Parts I-111-Investigations with Aqueous Solutions. Proc. R . SOC.London 1923,95,440-484. Helfferich, F. Ion Exchange; McGraw-Hill: New York, 1962; pp 156-169.
Helfferich, F. Ion Exchange Equilibrium of Amino Acids on Strong-Acid Resins: Theory. React. Polym. 1990, 12, 95-100.
Ind. Eng. C h e m . Res. 1993,32, 117-125 Holsinger, K. J. Experimental Determination of Equilibrium and Transport Properties of Peptides in Dowex Enhanced Performance Resins. Undergradulate Thesis, University of Virginia, Charlottesville, VA, 1992. Jones, I. L.; Carta, G. Ion Exchange Equilibrium and Transport of Amino Acids and Peptides in Enhanced Performance Resins. Paper presented at the AIChE Annual Meeting, Los Angeles, CA, 1991. Meister, A. Biochemistry of the Amino Acids, 2nd ed.; Academic Press: New York, 1965;Vol. I, p 28. Moore, S.; Stein, W. H. Chromatography of Amino Acids on Sulfonated Polystyrene Resins. J. Biol. Chem. 1951, 176, 663-681. Myers, A. L.;Byington, S. Thermodynamics of Ion Exchange: Prediction of Multicomponent Equilibria from Binary Data. In Ion Exchange Science and Technology; Ftodrigues, A. E., Ed.; NATO AS1 Series E No. 107;Nijhoff: Dordrecht, The Netherlands, 1986; pp 119-145. Niederwieser, A. Chromatography of Amino Acids and Oligopeptidea. In Chromutography, 4th ed., Part B Heftmann, E., Ed.; Van Nostrand New York, 1983. Nozaki, Y.;Tanford, C. The Solubility of Amino Acids and Two Glycine Peptides in Aqueous Ethanol and Dioxane Solutions. J. Biol. Chem. 1971,246,2211-2217.
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Partridge, S. M. Displacement Chromatography on Synthetic Ion Exchange Resins: 3. Fractionation of a Protein Hydrolysate. Biochem. J. 1949,44,521-527. Reichenberg, D.; McCauley, D. J. Properties of Ion Exchange Resins in Relation to their Structure. VII. Cation Exchange Equilibrium on Sulfonated Polystyrene Resins of Varying Degree of Crosslinking. J. Chem. SOC.1955,2741-2750. Rekker, R. F.; deKort, H. M. The Hydrophobic Fragment Constant; an Extension to a lo00 Data Point Set. Eur. J. Med. Chem. Chim. Therapeutics 1979,14,479-488. Saunders, M. S.; Vierow, J. B.; Carta, G. Uptake of Phenylalanine and Tyrosine by a Strong-Acid Cations Exchanger. AIChE J. 1989,35,53-68. Wang, N. H.-L; Yu, Q.; Kim, S. U. Cation Exchange Equilibria of Amino Acids. React. Polym. 1989,11,261-277. Yu, Q.; Yang, J.; Wang, N. H.-L. Multicomponent Ion Exchange Chromatography for Separating Amino Acid Mixtures. React. Polym. 1987,6,33-44.
Received f o r review June 25, 1992 Revised manuscript received October 15,1992 Accepted October 27, 1992
Ion Exchange of Amino Acids and Dipeptides on Cation Resins with Varying Degree of Cross-Linking. 2. Intraparticle Transport Ida L. Jones and Giorgio Carta* Center for Bioprocess Development, Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22903-2442
The ion exchange kinetics of alanine, a-aminobutyric acid, leucine, phenylalanine, phenylalanylalanine, and phenylalanylphenylalanine with sulfonated polystyrenedivinylbenzene resins having a degree of cross-linking from 2 to 10% is studied under alkaline desorption conditions. Desorption in a shallow-bed contactor with NaOH concentrations in the range of 50-200 mM is shown to occur in the absence of equilibrium limitations and of external mass-transfer resistance. For these conditions, the desorption rate is controlled by the slow diffusion of amino acid or peptide cations, which appears to be severely hindered in the cross-linked polymer mesh of the resins. The diffusivity values are found to be correlated with a decreasing exponential function of the effective degree of crosslinking of the resin and of the apparent molar volume of the diffusing solute. Intraparticle effective diffusivities obtained from these alkaline desorption measurements are shown to provide an adequate simulation of the rate of uptake of these solutes from acidic solutions.
Introduction In part 1 (the preceding paper in this issue) of this series concerning the equilibrium uptake of amino acids and dipeptides by sulfonated polystyrene-divinylbenzene resins,we have shown that the uptake process occurs via the exchange of amino acid or peptide cations, with no apparent contribution from the sorption of zwitterionic or negatively charged species. The degree of cross-linking of the resin and the hydrophobic character of the exchanged species were found to have significant effects on the apparent selectivity coefficient for the exchange of these compounds for hydrogen ion. In addition, for larger solute9 with highly cross-linked resins, utilization of the entire ion exchange capacity was found to be hindered by steric interaction among the exchanged solute molecules. As a consequence, the selection of an optimum resin system for these applications involving relatively large organic ions requires that one balances the higher total ion exchange capacity (per unit resin volume) of more highly cross-linked resins with the accessibility of this capacity offered by resins with a lower degree of cross-linking. Other factors
* Author to whom correspondence should be addressed.
are of course also important in selecting an optimum resin, such as the chemical and mechanical stability of the resin and its osmotic shock performance. However, more important than any other factor is, perhaps, the rate of intraparticle transport, since for these organic ions, this can be expected to decrease substantially with the cross-linking of the resin. The kinetics of ion exchange of amino acids and small peptides has been addressed in a few systematic studies. Two mass-transfer mechanisms are generally associated with the ion exchange of these molecules: convective transport outside the particle and intraparticle diffusion. Further, intraparticle diffusion may occur either via diffusion through liquid filled macropores, or through the gel structure of a resin, or through both, depending on whether the resin is macroreticular or gel-type (Patell and Turner, 1979;Yoshida and Kataoka, 1985). In the latter case, the relative importance of macropore- and gel-phase transport depends on the magnitude of the diffusivities in the two phases, as well as on the nature of the ion exchange equilibrium. Saunders et al. (1989),for example, have reported a study on the batch kinetics of ion exchange of phenylalanine and tyrosine on a macroreticular cation exchanger with a nominal degree of cross-linking of 12%.
0888-588519312632-0117$04.00/00 1993 American Chemical Society
