Ion-Exchange Equilibria of Amino Acids on a Strong Acid Resin

Accordingly, all the ionic forms of the amino acid which contain a positively charged basic group are allowed to be exchanged. Each of these exchange ...
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Ind. Eng. Chem. Res. 1996, 35, 1912-1920

Ion-Exchange Equilibria of Amino Acids on a Strong Acid Resin Stefano Melis, Jozef Markos,† and Giacomo Cao*,‡ Dipartimento di Ingegneria Chimica e Materiali, Universita´ degli Studi di Cagliari, Piazza d’Armi, I-09123 Cagliari, Italy

Massimo Morbidelli* Laboratorium fu¨ r Technische Chemie, ETH-Zentrum, CAB C40, Universita¨ tstrasse 6, CH-8092 Zurich, Switzerland

The exchange equilibria of several amino acids, with particular emphasis on those displaying two basic groups, on a strong-acid cation exchange resin (Amberlite IR120) are investigated. The behavior of the experimental data is described through a mathematical model which takes into account the dissociation equilibria of amino acids in aqueous solution, the electroneutrality condition, and an ion-exchange isotherm recently proposed in the literature. In the latter, by assuming ideal behavior for both the solution and the solid phase, the exchange process is treated on the basis of the mass action law, while the existence of a distribution of two types of functional groups with different energies is assumed in order to describe the resin heterogeneity. The developed model is then used in order to satisfactorily correlate binary uptake data and to predict with good accuracy the uptake of amino acids in multicomponent systems. 1. Introduction Amino acids are extensively used for the synthesis of several products for pharmaceutical and health industries. Several steps are, in general, required in order to separate individual amino acids from the mixtures obtained at the end of the production stage. As discussed in the literature (cf. Yu et al., 1987; Agosto et al., 1989; Saunders et al., 1989), owing to the amphoteric character of amino acids, ion-exchange resins can be used in order to develop chromatographic techniques suitable for both analytical and industrial separation purposes. These techniques exploit the differences in the ionization constants and therefore require an accurate control of the pH of the feed solution. In addition, also the specific affinities of the charged amino acid molecules toward the resin are important. Thus, in order to properly design fixed-bed ion-exchange equipments, a reliable simulation of multicomponent equilibria of the involved amino acids on the ion-exchange resin is needed. Several attempts were made in the literature in order to systematically study the equilibrium sorption of amino acids on ion-exchange resins and understand how pH and salt concentrations, which play a fundamental role when developing large-scale processes, affect these equilibria. Yu et al. (1987) and Wang et al. (1989) quantitatively described the equilibrium uptake of neutral, basic, and acidic amino acids on a AG50W-X8 cation-exchange resin through a model where it is assumed that the exchange reaction is determined by the presence of the aminic cation independently of the net charge of the molecular species. Accordingly, all the ionic forms of the amino acid which contain a positively charged basic group are allowed to be exchanged. Each of these exchange equilibria is described by a single constant * Author to whom correspondence should be addressed. † Present address: Department of Chemical and Biochemical Engineering, Slovak Technical University, Radlinskeho 9, 812 37 Bratislava, Slovak Republic. ‡ Fax: + 39-70-675-5067. E-mail: [email protected]. § Fax: + 41-1-6321082. E-mail: [email protected].

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through the assumption of a constant separation factor (cf. Helfferich, 1962). This results, for neutral, acidic, and basic amino acids, in two, four, and six separation factors, respectively, which are then incorporated, together with the corresponding dissociation constants, in a single apparent separation factor, which refers to the total concentrations of amino acid in all its forms. This factor is expressed as a function of pH, which is assumed to be known experimentally, as it is indeed the case of buffered solutions. This approximate model has the noticeable advantage of predicting a constant apparent separation factor for buffered systems, which significantly simplifies the calculations of multicomponent column dynamics (cf. Helfferich and Klein, 1970). From the satisfactory comparison of model results with experimental data, at least in the investigated range of compositions, it was concluded that the presence of a negatively charged -COO- on the amino acid, in either the ionic or zwitterionic form, strongly diminishes its affinity for the cation-exchange resin. Subsequently, Helfferich (1990) proposed a model where only amino acids in cationic form were considered to be exchangeable and the exchange equilibrium was described in terms of mass action law. Anionic species were excluded from the resin based on the Donnan effect, and for the nonionic species, a simple sorption with no exchange was considered. A rather comprehensive study on ion-exchange equilibria in multicomponent systems involving primarily amino acids has been reported by Carta and co-workers (i.e., Saunders et al., 1989; Dye et al., 1990; Jones and Carta, 1993). An equilibrium model was developed by coupling the usual description of the dissociation equilibria in the aqueous phase, with a model for the multicomponent exchange equilibria originally developed by Myers and Byington (1986). This model (Saunders et al., 1989) accounts for variable selectivities in ion exchange by introducing an energetic heterogeneity of the functional groups of the ion exchanger, which involves three adjustable parameters per binary system, namely, the average adsorption energy, the standard deviation, and the skewness of the energy distribution. The equilibrium uptake of several amino acids on © 1996 American Chemical Society

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various commercially available ion-exchange resins has been measured. The binary exchange data have been fitted to estimate the model adjustable parameters which have then been used to predict multicomponent equilibrium data. On the whole, the obtained agreement is rather satisfactory. The model above has the limitation that it cannot be applied to amino acids which contain two basic groups, since these can form both mono- and divalent cations. In this case, the adopted ion-exchange equilibrium model (cf. Saunders et al., 1989) is not valid, and the other approaches available (cf. Dye et al., 1990; for lysine) do not account for deviations from ideal behavior or resin heterogeneity. In this work we present an equilibrium model which can be applied to all amino acids and accounts for variable selectivities. This is based on, besides the dissociation equilibria in the aqueous phase, a recently developed model for ion exchange equilibria (Melis et al., 1995). This model accounts for the heterogeneous nature of the ion exchanger, as the Myers and Byington (1986) model, while it describes the exchange equilibrium of every single site through the law of mass action. As a result the equilibrium model can be applied to any kind of amino acid, including amino acids with two basic groups, and properly accounts in this case for the important effect of the solution normality. The validation of the model has been accomplished using equilibrium data of several mixtures of amino acids on a commercial strong-acid cation-exchange resin. The amino acids considered were either neutral or acidic or basic and included specifically L-proline (Pro), L-phenylalanine (Phe), L-tyrosine (Tyr), L-glutamic acid (Glu), L-histidine (His), L-lysine (Lys), L-arginine (Arg), and L-cystine (Cys). Emphasis was placed on amino acids with two basic groups and on the role of the solution normality. Moreover, the ability of the model in predicting multicomponent equilibria has been considered. The model parameters have been estimated by fitting binary exchange data relative to the equilibrium between each one of the components and a reference counterion. With these, multicomponent equilibria have been calculated and compared with experimental data. 2. Experimental Section The resin used in this work (Amberlite IR120 by Rohm & Haas) is a strong-acid cation exchange resin with gellular structure, constituted of a sulfonated styrene-divinylbenzene copolymer. The total ionexchange capacity of the resin, q0, was determined by contacting a sample of the resin (3-5 g) in hydrogen form with 100 mL of a 0.1 N solution of sodium hydroxide containing 5% by weight of sodium chloride for 24 h at constant temperature. After equilibrium was reached, the excess sodium hydroxide left in the solution was measured by titration using phenolphthalein as an indicator and the ion-exchange capacity (q0 ) 5.49 mmol/g of dry resin) was determined by mass balance. The ratio between dry and hydrated resin weights (ω ) 0.45) was obtained by determining the weight loss of a hydrate sample of the resin dried in vacuum at 110 °C. Before starting this procedure, the resin was converted into the hydrogen form and filtered in a vacuum funnel in order to remove the interstitial water. The dry resin density has been measured as equal to Fp ) 0.57 g of dry resin/cm3. The amino acids considered in this work were all L form, with purity greater than 99%, and were used without further purification, while all the other chemicals were reagent grade.

The experimental equilibrium measurements were carried out in a temperature-controlled shaker (30 °C) by contacting known weights (1-2 g) of the resin in hydrogen form with 100 cm3 of solution of known solute concentration and pH. The desired co-ion concentration (Cl-) was reached by adding hydrochloric acid. The flasks were sealed and shaken for 3 h, which were proved experimentally to be sufficient for reaching equilibrium. Finally, the solutions were sampled in order to determine the equilibrium solute concentrations and pHs. The equilibrium solute concentration in the resin phase qi [mmol/g of dry resin] is determined as the amount which is not present in the bulk after equilibrium is achieved, through the following mass balance:

qi ) V(Ci0 - Ci)/ωW

(1)

where V and W represent the volume of solution and the mass of hydrated resin, respectively, while Ci0 and Ci are the initial and final concentrations of solute i in solution. The experimental values of amino acid concentrations were determined using an HPLC, equipped with a UV diode array detector and a column (Chromsphere C8) with reverse phase packed with C8 hydrocarbons on silica gel (particle size 5 µm, column length 25 cm, internal diameter 4.6 mm). The column, which was operating at room temperature, was fed with a flow rate of 1.5 mL/min. The elution was performed using a buffer solution of sodium acetate and acetic acid at pH ) 5.6. The sodium concentration was determined by a Video 12 spectrophotometer, while the chloride concentration was not measured, since it was assumed to not participate in the exchange process. 3. Equilibrium Model Amino acids are characterized by amphoteric behavior and thus can be present in aqueous solution in different ionic forms, depending upon solution pH. On the basis of the number of carboxylic and basic groups present in the side chain of the molecule (in addition to one R-aminic group and one R-carboxyl group which are always present), amino acids are classified into three groups: neutral (no functional groups on the side chain or both one carboxylic group and one basic group on the side chain), acidic (one carboxylic group on the side chain), and basic (one basic group on the side chain). In order to quantitatively describe the dissociation equilibria of amino acids in aqueous solution, the following equilibrium reactions are taken into account:

A2+ T A+ + H+

(2.1)

A+ T A( + H+

(2.2)

A( T A- + H+

(2.3)

A- T A2- + H+

(2.4)

All the reactions above are simultaneously present only for amino acids containing both a carboxylic group and a basic group on the side chain (e.g., cystine) and not for other types of amino acids. In particular, only reactions (2.1-2.3) occur in the case of basic amino acids, reactions (2.2-2.4) apply to acidic amino acids, and reactions (2.2) and (2.3) describe the behavior of the neutral ones without functional groups on the side chain.

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Table 1. Solution Equilibrium Parameters at 25 °C amino acid

pKa2

pKa1

pKb1

1.77 2.18 2.01 1.04

2.16 2.0 2.2 2.1 6.1 8.95 9.04 2.05

9.13 10.6 9.11 4.07 9.18 10.53 12.48 8.0

L-phenylalanine L-proline L-tyrosine L-glutamic

acid

L-histidine L-lysine L-arginine L-cystine

pKb2

pI

ref

5.5 6.3 5.7 3.2 7.5 9.7 11.2 5.0

10.07 9.47

10.25

a b b b b b b b

a

Lange’s Handbook of Chemistry, 1973. b CRC Handbook of Chemistry and Physics, 1978.

By assuming ideal behavior for the aqueous phase, the dissociation constants for the reactions (2.1-2.4), whose numerical values for the amino acid considered in this work are summarized in Table 1, are expressed by

Ka2 ) CA+CH+/CA2+

(3.1)

Ka1 ) CA(CH+/CA+

(3.2)

Kb1 ) CA-CH+/CA(

(3.3)

Kb2 ) CA2-CH+/CA-

(3.4)

where CA2+, CA+, CA(, CA-, and CA2- represent the concentration of the different ionic forms of the generic amino acid, A: dicationic, cationic, zwitterionic, anionic, and dianionic form, respectively. Obviously, when one or more of the reactions (2.1-2.4) do not occur, the corresponding expression for the equilibrium constant becomes meaningless. The total “analytical” concentration of the amino acid, CA, is given by

CA ) CA2+ + CA+ + CA( + CA- + CA2-

(4)

By combining eqs 3 and 4, the following expressions for the concentrations of the different ionic forms can be obtained as a function of the hydrogen ion concentration, CH+, and of the analytical concentration, CA:

in the general case of neutral amino acids like cystine, when all the dissociation reactions (2) are present. However, they can be used also for the other amino acids, once the appropriate values for the dissociation constants of the missing reactions are chosen (i.e., Ka2 ) ∞ and/or Kb2 ) 0). The concentrations of positively and negatively charged species in solution are related by the electroneutrality condition which may be written in the following general form:

∑π[Piπ+] ) ∑θ[Rjθ-]

(10)

where [Piπ+] and [Rjθ-] represent the concentration of the cationic and anionic species, respectively. This equation allows us to evaluate the last remaining unknown, i.e., the hydrogen ion concentration, CH+. Thus, from the appropriate forms of eqs 5-10, which depend upon the specific amino acid under examination, one can obtain the concentration of all positively and negatively charged species if the values of CA and of the concentrations of the possibly present inorganic species, e.g., CNa+ and CCl-, are known. Note in this regard that complete dissociation of hydrochloric acid and sodium hydroxide is assumed. It is worth mentioning that, in the case where pH is known experimentally, it is also possible to neglect eq 10 and use directly the measured value of CH+ in the remaining equations. This is typically the case of buffered solutions, as considered, for example, by Wang et al. (1989) and Helfferich (1990). The equilibrium uptake of the generic species Sνi i+ by the hydrogen form of the resin can be described by coupling the solution dissociation equilibria above with a suitable model for the ion exchange. In the case of a multicomponent system containing Nc counterions, by selecting the hydrogen ion as a reference counterion, we can consider Nc - 1 independent exchange reactions between hydrogen and each one of the system components:

CA2+ ) Ka2 Ka2Ka1 1+ + + CH+ (C +)2

CA Ka2Ka1Kb1 (CH+)3

H

CA+ )

Ka2Ka1Kb1Kb2 +

(CH+)4

CA Ka1Kb1

CH+ Ka1 Ka1Kb1Kb2 1+ + + + 2 Ka2 CH+ (C +) (CH+)3 H

C A( )

(5)

CA (CH+) CH+ Kb1 Kb1Kb2 1+ + + + Ka2Ka1 Ka1 CH+ (C +)2

(6)

(7)

H

C A- )

CA 3

(CH+) (CH+)2 CH+ Kb2 1+ + + + Ka2Ka1Kb1 Ka1Kb1 Kb1 CH+

(8)

νi+ + Sνisi+ + νiH+ r T Sir + νiHs

CA 4

(CH+) (CH+)3 (CH+)2 CH+ 1+ + + + Ka2Ka1Kb1Kb2 Ka1Kb1Kb2 Kb1Kb2 Kb2

(9)

It is again worth mentioning that eqs 5-9 are derived

(11)

where νi is the charge of the counterion Sνi i+ and the subscripts r and s refer to resin and solution phases, respectively. In order to describe quantitatively the exchange equilibria represented by eqs 11, we considered the model developed by Melis et al. (1995) where both phases are assumed to be ideal while the heterogeneity of the resin functional groups is accounted for by considering a given distribution of the standard-free energy change of the ion-exchange process, ∆G°. In particular, this has been approximated through a population of two equally abundant different types of functional groups. Thus, for the generic ith equilibrium reaction (11) occurring on functional groups of type j, the equilibrium constant Kj,i can be written as:

Kj,i )

CA2- )

i ) 1, Nc - 1

(Qj,i)(CH+)νi (Ci)(Qj,H+)νi

(qj,i)(CH+)νi

)

i ρ1-ν j) p (Ci)(qj,H+)νi 1, 2 and i ) 1, Nc - 1 (12)

where Ci and Qj,i ()Fpqj,i) represent the concentration of the species Sνi i+ in the liquid and on the jth type of functional groups of the resin, respectively. Let us now

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introduce the ionic fractions of the generic ionic species, Sνi i+:

νiCi

Xi )

νiCi

(13)

) N

Nc

∑ νkCk

k)1

νiqj,i

Yj,i )

νiqj,i

(14)

) q0,j

Nc

∑ νkqj,k

k)1

where N is the total ionic concentration in the solution phase or solution normality and q0,j is the total exchange capacity of the resin functional groups of the jth type. Substituting in eq 12, we obtain

Kj,i )

( )

(Yj,i)(XH+)νi ρpq0,j (X )(Y +)νi N j

j,H

1-νi

j ) 1, 2 and i ) 1, Nc - 1 (15)

Combining eqs 15 together with the congruence conditions (i.e., the sum of the ionic fractions equals unity both in solution and on each type of functional group), it is possible to obtain all the unknown ionic fractions, Yj,i (and hence the loadings qj,i), once the equilibrium constants Kj,i and the values of q0,j are known. Note in this regard that, owing to the assumption of equally abundant functional groups, q0,j is equal to half of the total exchange capacity of the resin, and therefore it is readily calculated from the measured value of q0, i.e., q0,j ) 2.745 mmol/g of dry resin. The overall composition of the resin phase can now be evaluated by summing up the resin loadings relative to each type of functional group: Nf)2

qi )

∑ j)1

qj,i

(16)

or, alternatively, by summing up the weighted ionic fractions on each type of functional group: Nf)2

Yi )

∑ j)1

Nf)2 Y q0,j j,i Yj,i ) q0 j)1 2

∑

(17)

where, of course

Yi )

νiqi

νiqi )

Nc

∑ νkqk

q0

(18)

k)1

As discussed in Melis et al. (1995), the parameters Kj,i can be directly related to the average value and the variance of the distribution of the Gibbs free energy change associated to the exchange reaction (11):

exp

[

]

-(∆G°i) )K h i ) (K1,iK2,i)1/2 RT

(19)

-σi ) γi ) (K1,i/K2,i)1/2 RT

(20)

exp

[ ]

Hence, in the following, we will always refer to K h i and γi as the model parameters. It should also be pointed out that, since the model herein considered assumes ideality in both phases, multicomponent systems containing Nc counterions can be described on the basis of only the Nc - 1 binary equilibria of each exchangeable species with a reference counterion, i.e., the triangle rule holds. In other words, there is no need to study all the possible equilibria between each couple of counterions, i.e., Nc(Nc - 1)/2, as in the case of nonideal models (cf. Shallcross et al., 1988). It is finally worth noting that, since amino acids can be simultaneously present in solution with different cationic forms, the total solute concentration in the resin phase is given by

qA ) qA+ + qA2+

(21)

where qA+ and qA2+ can be computed from the corresponding ionic fractions in the resin phase through eqs 13-16. Thus, summarizing, in order to describe the behavior of amino acids which display two basic groups, four parameters, two for each ionic form, have to be obtained. In the following, these parameters will be indicated as K h +, γ+, K h ++, and γ++. For amino acids which contain a single cationic form in solution the model parameters are only K h + and γ+. 4. Comparison with Experimental Data 4.1. Binary Equilibria. The equilibrium uptake isotherms of phenylalanine, proline, tyrosine, glutamic acid, lysine, histidine, arginine, and cystine with the hydrogen form of the resin are quantitatively described in this section using the model presented in the previous section. Let us consider the following the case of amino acids containing one and two basic groups, separately. Amino Acids with One Basic Group. In this case we refer to acidic and some neutral amino acids, i.e., those with no carboxylic or basic groups on the side chain. Since in solution these produce only monovalent cations, the ion-exchange equilibrium models developed by Myers and Byington (1986) and Melis et al. (1995) become coincident. Accordingly, the present treatment becomes equivalent to that of Dye et al. (1990). Moreover, when neglecting the heterogeneity of the resin functional groups, thus considering groups of only one type (i.e., γ ) 1 in eq 20), these models reduce to the constant selectivity treatment of Wang et al. (1989). Thus, in order to appreciate the importance of nonconstant selectivity effects, in the following we will compare the experimental data of each system with the results of both the model developed in this work and its ideal version (i.e., γ ) 1). The equilibrium uptake of phenylalanine is shown in Figure 1a in terms of amino acid concentration in the resin phase as a function of its analytical value in solution for different values of the co-ion concentration CCl-. It can be seen that, if the latter is small or zero, the uptake of the amino acid approaches the total exchange capacity of the resin, even for small values of its analytical concentration. When increasing the coion concentration, the uptake of amino acid is reduced, because of the increased competition from hydrogen ions. The same experimental data of Figure 1a are represented in terms of ionic fractions in the resin phase as a function of the ionic fraction in solution in Figure 1b. It may be seen that the uptake process depends only

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Figure 1. (a) Uptake of Phe as a function of the total Phe concentration in solution at various chloride concentrations; (b) Ion-exchange equilibrium for Phe/H+. Table 2. Values of the Adjustable Parameters of the Model and Corresponding Average Percentage Errors in Reproducing Binary Equilibrium Dataa system

K h+

γ+

Phe/H+

6.04 (5.9) 2.08 (2.62) 2.98 (4.55) 1.12 (1.12) 0.65 (0.67) 1.47 (4.03) 0.27 (0.24) 4.96 (4.76) 1.32 (1.32)

2.56 4.88 3.19 1.0 2.71 6.61 16.1 1.12 1.0

Pro/H+ Tyr/H+ Glu/H+ His/H+ Lys/H+ Arg/H+ Cys/H+ Na+/H+

K h ++

13.4 (14.6) 28.5 (30.0) 22.8 (23.6) 24.0 (24.0)

γ++

1 1 1.14 1.26

 (%) 1.9 (3.2) 4.2 (14.5) 5.5 (8.8) 4.5 (4.5) 5.7 (6.1) 3.4 (3.7) 5.1 (9.3) 5.0 (5.0) 4.1 (4.1)

a The values of parentheses refer to the ideal version of the model, i.e., γ ) 1.

upon the ionic fraction of the amino acid cation, and it is independent of both co-ion and total amino acid concentrations. It is also apparent that the separation factor, which for exchange of amino acid cations and hydrogen ions is defined as:

SA,H ) YAXH/YHXA

(22)

remains fairly constant, as observed also by Dye et al. (1990) for a different ion-exchange resin, i.e., Dowex 50W-X8. The experimental data above can be quantitatively correlated using the equilibrium model developed in the previous section. Since phenylalanine contains only one cationic group, the model requires only two adjustable parameters: K h + and γ+. These have been estimated by fitting directly the experimental data through a nonlinear least-squares procedure. The comparison between model results (solid curves) and experimental data is also shown in parts a and b of Figure 1, while the estimated values of the model parameters are summarized in Table 2, together with the corresponding average percentage error, . The broken curves in the same figures represent the results of the ideal version of the model, where only one parameter has been fitted (K h ) 5.9) while the other one

Figure 2. (a) Uptake of Pro as a function of the total Pro concentration in solution at various chloride concentrations; (b) Ion-exchange equilibrium for Pro/H+.

has been kept constant, i.e., γ ) 1. The objective function used in the fitting procedure is given by the squared relative deviations of the experimental and calculated values of the resin phase concentrations, qi. Analogous results can be obtained for the other neutral amino acid considered in this section, i.e., proline, as may be seen from parts a and b of Figure 2, where experimental data are compared with model results, whose parameter values are also reported in Table 2. From Figure 2b, it appears that, in contrast to the previous case, proline displays a nonconstant separation factor which, in particular, decreases from values that are well above unity when the ionic fraction in solution is small to values smaller than unity when XA approaches 1. As expected, the performance of the ideal model (K h ) 2.62) in this case is quite poor. For the category of acidic amino acids, the equilibrium uptakes of glutamic acid and tyrosine are considered. Actually, tyrosine is not an acidic amino acid in the usual meaning, since it does not display any carboxylic group on the side chain. Nevertheless, we included tyrosine in the class of acidic amino acids because of the presence of a hydroxyl group on the side chain, which provides an acidic character to the molecule and leads to the formation, at high values of the pH, of a dianionic form, according to the dissociation reaction (2.4). For the case of glutamic acid, it is seen from Figure 3a that the uptake increases when decreasing the coion concentration because the competition from hydrogen ions is reduced. Moreover the Y-X diagram for glutamic acid shown in Figure 3b indicates that, also in this case, the data at different co-ion concentration and pH values fall on the same curve. The experimental data for tyrosine reported in parts a and b of Figure 4 involve only low amino acid concentrations due to its limited solubility in aqueous solution. Similar data for tyrosine and for glutamic acid are reported by Saunders et al. (1989) on Amberlite 252 and by Dye et al. (1990) on Dowex 50W-X8, respectively.

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Figure 5. Uptake of Lys as a function of the total Lys concentration in solution at various chloride concentrations.

Figure 3. (a) Uptake of Glu as a function of the total Glu concentration in solution at various chloride concentrations; (b) Ion-exchange equilibrium for Glu/H+. Figure 6. Uptake of His as a function of the total His concentration in solution at various chloride concentrations.

Figure 7. Uptake of Arg as a function of the total Arg concentration in solution at various chloride concentrations.

Figure 4. (a) Uptake of Tyr as a function of the total Tyr concentration in solution at various chloride concentrations; (b) Ion-exchange equilibrium for Tyr/H+.

Model results are compared with experimental data in Figures 3 and 4. The corresponding values obtained for the adjustable parameters are reported in Table 2, together with the values of the average relative error. The ideal version performs poorly in the case of tyrosine (K h ) 4.55), while for glutamic acid it is completely equivalent to the complete model, for which the fitted value of γ equals unity (see Table 2). Amino Acids with Two Basic Groups. In this group, we consider basic and neutral amino acids which in solution lead to both mono- and divalent cations.

Accordingly, in this case the model involves four parameters per each amino acid, i.e., K h +, γ+, K h ++, and γ++. Note that the approach based on the model of Myers and Byington (1986) cannot be applied in this case. The experimental data of equilibrium uptake of some basic amino acids, lysine, histidine, and arginine, are shown in Figures 5-7, respectively, together with the corresponding model results. The obtained values of model parameters and average percentage errors, , are reported in Table 2. From Figures 5-7, it may be seen that, for high values of co-ion concentration, as the total amino acid concentration increases, the uptake initially increases, then remains constant at a value of amino acid concentration in resin phase approximatively equal to half of the total resin capacity q0, and eventually rises again, approaching the value of q0 at large total amino acid concentrations. This behavior may be explained by considering that the dicationic form is present in a significant amount for total concentrations of amino acid lower than co-ion

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Figure 8. Calculated uptake of different ionic forms of His as a function of the total His concentration in solution at zero chloride concentration.

concentration. Under these conditions, because of electroselectivity, almost only this form of the amino acid is sorbed and therefore the maximum uptake of each amino acid is limited to half of the total resin capacity. When increasing the total amino acid concentration, the divalent cationic form disappears and the monovalent one becomes predominant. Thus, each mole of the dicationic form of the amino acid is exchanged for 2 mol of the monocationic form and hence the total uptake increases. When the co-ion concentration is small or zero, it is apparent from Figures 5-7 that the behavior of the basic amino acids is similar to that of neutral ones. This is so because, under these conditions, the concentration of divalent cations is always rather small, and thus the uptake is dominated by the stoichiometric exchange of monovalent cations and hydrogen. It is worth noting, however, that only when considering the case of lysine the total resin capacity is actually reached. For this amino acid, in fact, the concentration of the divalent form is negligible as compared to that of the monovalent form. This is not true for the case of histidine, as may be seen from Figure 6. For this amino acid, the contributions of monovalent and divalent forms to the total resin loading are shown separately in Figure 8 for CCl- ) 0 and for the same parameter values used in Figure 6. It appears that the contribution of the divalent form is predominant at very low total amino acid concentrations, while at larger values it becomes smaller but not negligible. This behavior remains unchanged also for non zero co-ion concentration values as well as for arginine. It is worth noting that the curve related to q(A++) shown in Figure 8 does approach zero as the total amino acid concentration goes to zero. In particular, it reaches a maximum value of 2.637 mmol/g of dry resin at about 0.0009 mmol/L. The capability of the ideal version of the model in correlating the uptake data of basic amino acids is also illustrated in Table 2. It may be seen that in this case the average percentage errors in reproducing the experimental data are very similar to those of the complete model, except for arginine. This result can be justified by noting that, at least in the range of compositions investigated, the equilibrium is mainly governed by the exchange reaction of the divalent cation, which exhibits modest deviations from ideal behavior. This conclusion, which applies only to the systems considered in this work, is apparent from the values of the heterogeneity parameter of the divalent cations, γ++, which, as shown in Table 2, are always close to unity, while this is not the case for the other heterogeneity parameter, γ+. Finally, note that the equilibrium uptake data of Figures 5-7 are not represented in terms of ionic

Figure 9. Uptake of Cys as a function of the total Cys concentration in solution at various chloride concentrations.

Figure 10. Ion-exchange equilibrium for Na+/H+.

fractions, in contrast to what we did earlier for amino acids with only one basic group. In fact, although the contribution of monovalent and divalent ions can be separately accounted for from the theoretical point of view, as shown in Figure 8, this is not possible for the experimental data, since the individual concentrations of the different ionic forms of the amino acid in the resin phase composition cannot be measured independently. For the category of neutral amino acids we consider cystine. The experimental data shown in Figure 9 can only be obtained at low amino acid concentration due to its limited solubility in aqueous solution. For this reason, the plateau in the equilibrium uptake curve which was present in Figures 5-7 for basic amino acids has not been evidenced in this case. The corresponding model results are also shown in Figure 9, while the values of model parameters are reported in Table 2, together with the results of the ideal model, which, as in the case of basic amino acids, provides a good accuracy in correlating the experimental data. 4.2. Multicomponent Equilibria. In order to further test the model reliability, multicomponent uptake measurements have been also carried out for the systems Pro/Na+/H+, Tyr/Na+/H+, Cys/Na+/H+, Pro/Glu/ H+, Cys/Tyr/H+, and Cys/Tyr/Na+/H+. Since these systems include the inorganic species sodium, its equilibrium exchange behavior has to be characterized. The corresponding experimental data for exchange with the hydrogen ion are compared with model results in Figure 10, where it may be seen that it displays an ideal behavior (i.e., γ ) 1). The multicomponent experimental data are compared with model results in Figure 11 in terms of experimental versus calculated values of resin phase composition. From these figures we can conclude that the developed model provides reliable predictions of multicomponent equilibria by using model parameters fitted from binary equilibrium data, as may also be seen from the average error values reported in Table 3. In contrast, the ideal version of the model does not predict satisfactorily the experimental data, particularly

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Figure 11. Comparison of experimental and predicted uptakes of proline and sodium for Pro/Na+/H+ (a); tyrosine and sodium for Tyr/ Na+/H+ (b); cystine and sodium for Cys/Na+/H+ (c); proline and glutamic acid for Pro/Glu/H+ (d); tyrosine and cystine for Tyr/Cys/H+ (e); and cystine, tyrosine, and sodium for Cys/Tyr/Na+/H+ (f). Table 3. Multicomponent Systems Investigated and Average Percentage Errors in Predicting Their Equilibrium Behaviora system: 1/2/3/H+

1

Pro/Na+/H+ Tyr/Na+/H+ Cys/Na+/H+ Pro/Na+/H+ Cys/Na+/H+ Cys/Tyr/Na+/H+

7.2 (19.4) 3.0 (6.5) 7.0 (7.0) 14.3 (26.1) 10.6 (11.2) 8.5 (9.0)

2

3

15.1 (18.4) 19.2 (19.4) 16.7 (16.8) 13.6 (10.6) 12.6 (13.8) 8.3 (10.5) 22.0 (22.6)

global (%) 11.15 (18.9) 11.0 (13.0) 11.9 (11.9) 14.0 (18.4) 11.6 (12.5) 12.9 (14.0)

a  refers to the errors in the concentration values of the ith i counterion. Values in parentheses refer to the ideal version of the model.

when some of the species involved display a significant deviation from the ideal behavior, e.g., proline. Therefore, as already concluded by Dye et al. (1990), a nonideal model is necessary to interpret multicomponent equilibrium data.

5. Concluding Remarks The equilibrium uptake of various amino acids by the hydrogen form of a cation-exchange resin is studied. It

is found that the exchange process occurs due to the stoichiometric exchange of amino acid cations for hydrogen ions. Emphasis is placed on the analysis of amino acids, which can form both mono- and divalent cations, i.e., basic and neutral with one carboxylic and one basic group on the side chain. The equilibrium data are quantitatively correlated by taking into account a comprehensive mathematical model which couples the description of solution dissociation equilibria with the exchange process as described by an ion-exchange equilibrium model developed by Melis et al. (1995), which accounts for the resin heterogeneity by assuming a symmetrical distribution of functional groups with different energies. The proposed model can describe with sufficient accuracy the ion-exchange equilibria of each amino acid in all ranges of concentrations and solution normality values. In particular, it is found that the equilibrium of both acidic and neutral amino acids (limited to those containing only one aminic group) is not affected by solution normality or total amino acid concentration and depends only on the relative ionic fraction in the aqueous solution, in agreement with the results of Dye et al. (1990). On the other hand, the marked nonideal behavior of some of the amino acids considered, e.g.,

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proline, clearly demonstrates that the assumption of a constant separation factor (cf. Wang et al., 1989; Helfferich, 1990) does not yield satisfactory results. In the case of amino acids (whether basic or neutral) containing two basic groups, the equilibrium behavior depends strongly on the solution normality. This cannot be explained through the model originally proposed by Myers and Byington (1986) and used by Carta and coworkers. The use of a nonideal model which also accounts for the effect of solution normality (i.e., Melis et al., 1995) is then needed. The developed model has also been used to predict multicomponent equilibria using the adjustable parameter values obtained by fitting the appropriate binary exchange data (see Table 2). The agreement with the experimental data is satisfactory. Nomenclature Ci ) concentration of species i in solution, mmol/L ∆G° ) average value of standard Gibbs free energy of the ion-exchange process Ka ) dissociation constant, mol/L Kb ) dissociation constant, mol/L Kj,i ) thermodynamic equilibrium constant between ion i and the reference counterion on functional groups of type j K h i ) average equilibrium constant between ion i and the reference counterion N ) total ionic concentration or solution normality qi ) concentration of species i in the resin phase, mmol/g of dry resin qj,i ) concentration of species i on resin functional groups of type j, mmol/g of dry resin q0 ) total ion-exchange capacity, mmol/g of dry resin q0,j ) ion-exchange capacity of functional groups of type j, mmol/g of dry resin Qj,i ) concentration of species i on resin functional groups of type j, mmol/L R ) ideal gas constant Si,j ) separation factor between ions i and j T ) temperature, K Xi ) ionic fraction of species i in solution V ) solution volume, mL W ) mass of hydrated resin, g Yi ) ionic fraction of species i in resin Yj,i ) ionic fraction of species i in resin on functional groups of type j Greek Letters γ ) heterogeneity parameter defined by eq 20  ) average percentage error νi ) stoichiometric coefficient Fp ) dry resin density, g/L σ ) standard deviation of exchange process energy distribution ω ) ratio between dry and hydrated resin weights, g of dry resin/g of hydrated resin Superscripts 0 ) initial conditions

+ ) monovalent cation ++ ) bivalent cation Subscripts r ) resin s ) solution

Acknowledgment This work was financially supported by the Italian Consiglio Nazionale delle Ricerche (Progetto Strategico “Technologie Chimiche Innovative”), Italy. We gratefully acknowledge the fellowship awarded to J.M. by TEMPUS Program 1125/91. The assistance of Mr. A. Viola and Mr. R. Orru´ in setting up the analytical method is also acknowledged. Literature Cited Agosto, M.; Wang, N. H. L.; Wankat, P. Moving Withdrawal Liquid Chromatography of Amino Acids. Ind. Eng. Chem. Res. 1989, 28, 1358-1364. CRC Handbook of Chemistry and Physics, 59th ed.; Weast, R. C., Ed.; CRC: Boca Raton, FL, 1978; p C756. Dye, S. R.; De Carli, J. P., II; Carta, G. Equilibrium Sorption of Amino Acids by a Cation Exchange Resin. Ind. Eng. Chem. Res. 1990, 29, 849-857. Helfferich, F. Ion exchange; McGraw-Hill: New York, 1962. Helfferich, F. Ion Exchange Equilibria of Amino Acids on Strongacid Resins: Theory. React. Polym. 1990, 12, 95-100. Helfferich, F.; Klein, G. Multicomponent Chromatography; Marcel Dekker: New York, 1970. Jones, L.; Carta, G. Ion Exchange of Amino Acids and Dipeptides on Cation Resins with Varying Degree of Cross-linking. 1. Equilibrium. Ind. Eng. Chem. Res. 1993, 32, 107-117. Lange’s Handbook of Chemistry, 11th ed.; Dean, J. A., Ed.; McGraw-Hill: New York, 1973; p 512. Melis, S.; Cao, G.; Morbidelli, M. A New Model for the Simulation of Ion Exchange Equilibria. Ind. Eng. Chem. Res. 1995, 34, 3916-3924. Myers, A. L.; Byington, S. Thermodynamics of Ion Exchange: Prediction of Multicomponent Equilibria from Binary Data. In Ion Exchange: Science and Technology; Rodrigues, A. E., Ed.; NATO Advanced Study Institute Series E107; Martinus Nijhoff: Dordrecht, The Netherlands, 1986; pp 119-145. Saunders, M. S.; Vierow, J. B.; Carta G. Uptake of Phenylalanine and Tyrosine by a Strong-acid Cation Exchanger. AIChE J. 1989, 35, 53-68. Shallcross, D. C.; Herrmann, C. C.; McCoy, B. J. An Improved Model for the Prediction of Multicomponent Ion Exchange Equilibria. Chem. Eng. Sci. 1988, 43, 279-288. 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 Acids Mixtures. React. Polym. 1987, 6, 33-44.

Received for review September 14, 1995 Revised manuscript received February 9, 1996 Accepted February 21, 1996X IE950569M

X Abstract published in Advance ACS Abstracts, April 15, 1996.