Modified DIX model for ion-exchange equilibrium of L-phenylalanine on a strong cation-exchange resin☆

Jinglan Wu,Pengfei Jiao,Wei Zhuang,Jingwei Zhou,Hanjie Ying,4,*

1College of Biotechnology and Pharmaceutical Engineering,Nanjing Tech University,Nanjing 211816,China

2National Engineering Technique Research Center for Biotechnology,Nanjing 211816,China

3Jiangsu National Synergetic Innovation Center for Advanced Material,Nanjing 210009,China

4State Key Laboratory of Materials-Oriented Chemical Engineering,Nanjing 210009,China

1.Introduction

Amino acids are important biomolecules.They can be used as precursors of proteins and other metabolic products,and also contribute to the production of metabolic energy by oxidative degradation.All human proteins are different connection sequences of twenty types of amino acids encoded by DNA.Currently,all the amino acids have been marketed and their use in pharmaceutical,health and food industries has increased Significantly[1–3].L-phenylalanine is a non-polar aromatic amino acid,classified as essential,and extensively used as an ingredient in food,pharmaceutical and nutrition industries.It is used in a large quantity for the synthesis of artificial sweetener aspartame,which is an ingredient in diet-labeled drinks and food[4].

Ion-exchange chromatography has been used in the separation and purification of L-phenylalanine from fermentation broths since 1960s[5].The optimal design of fixed-bed exchangers requires accurate modeling for ion-exchange equilibrium[6].So far,the Myers and Byington model is usually used to predict exchange equilibrium data of L-phenylalanine on ion-exchange resins.In this model the ion exchange is treated as an adsorption process and deviations from the ideal behavior are explained in terms of the energetic heterogeneity of functional groups in the ion exchanger[7–9].Dye et al.[10]used this model to predict equilibrium uptake of amino acids on a cation-exchange resin,Amberlite 252,in single-and multi-component systems.Their calculations agreed well with the experimental data.Moreira and Ferreira extended this model to evaluate ion-exchange equilibrium of phenylalanine and tyrosine on both cation-and anion-exchange resins[8].They successfully simulated the dynamic breakthrough curves[1]and cyclic adsorption/desorption separation processes of amino acids in a fixed-bed ion-exchange column[11].However,this model assumes that the coions are completely excluded from the resin phase and the non-ideal behavior of selectivity is attributed to the solute–adsorbent rather than solute–solute interactions[12].As a result,this model can only be applied for prediction of the equilibrium uptake of L-phenylalanine in low concentration range,e.g.less than 20 mmol·L?1[8].

The ion-exchange uptake of amino acids has also been predicted with a rigorous model(the Donnan ion-exchange model,DIX model)developed by Jansen et al.[12].This model is based on equilibrium thermodynamics including the Donnan equilibrium.Compared to the Myers and Byington model,the DIX model is more advantageous because it takes into account the uptake of all species,counterions, coions,and neutral species, especially when weak electrolytes are involved and when electrolyte concentrations greatly exceed the resin capacity[12].Consequently,this model can give a convenient description for ion exchange of both strong and weak electrolytes over a wide range of concentration and pH values.Nevertheless,since an ideal behavior is still assumed for both coexisting phases, resin and surrounding aqueous phase,the mode may lead to erroneous results for liquid-phase equilibrium calculations and prediction of intraparticle properties,such as pH or other component activity[13].Bellot et al.extended the DIX model to actual electrolyte systems by introducing activity[13],in which the activity of each component in the liquid phase is evaluated for short-range interactions by using the modified Universal Functional Activity coefficient(UNIFAC)group-contribution model and long-range electrostatic interactions by adding the extended form of the Debye–Hückel equation to the UNIFAC equation,while the behavior of the polymeric phase is described in the framework of the extended Flory–Huggins model.This model has been evaluated by prediction of binary and multicomponent exchange equilibrium data for some amino acids(phenylalanine,alanine,proline,and glutamate)on a strong-acid cation-exchange resin[13].The L-phenylalanine concentration has been extended to 60 mmol·L?1.

The equilibrium uptake of L-phenylalanine strongly depends on the pH and ionic strength of the adsorbate solution[8,14].The concentration of L-phenylalanine in the fermentation broth is higher than 100 mmol·L?1.Hence the Myers and Byington model is not a proper model to describe the sorption behavior of L-phenylalanine on the ion-exchange resins.The most suitable equilibrium model is the Bellot model,but it is too complex.Three equilibrium uptake isotherms of L-phenylalanine on a strong cation-exchange resin were simulated at Cl?concentrations of 1.0,10,and 660 mmol·L?1to validate the model[13],but the model parameters were not given,which impedes its general use.Moreira and Ferreira used the Myers and Byington model to predict the uptake of L-phenylalanine on PK220 at Cl?concentrations of 0.0 and 100 mmol·L?1,with the L-phenylalanine concentration of 20.0 mmol·L?1.The model fitted the experimental results well[8].With the same model,Dye et al.extended the L-phenylalanine concentration to 80 mmol·L?1at Cl?concentrations of 0.0,2.0,7.0 and 170 mmol·L?1,and the deviation was obvious for the concentration of L-phenylalanine higher than 30 mmol·L?1at Cl?of 170 mmol·L?1[10],indicating that the model is not suitable.

The optimal operating pH,at which the equilibrium uptake of L-phenylalanine has a maximum value, plays an essential role in the separation and purification of L-phenylalanine from the fermentation broth.Saunders et al.extended the Myers and Byington model to investigate the effect of pH on uptake of L-phenylalanine.Their model prediction agreed well with the experimental results at L-phenylalanine concentration of 6.07 mmol·L?1[7].With regard to high L-phenylalanine concentration,the effect of pH on uptake of L-phenylalanine has not been reported.Thus a modified DIX model is established in this work to predict the L-phenylalanine(with concentration of 120 mmol·L?1)uptake on a strong cation-exchange resin SH11 at various solution pH values.This model is an extension of Donnan membrane equilibrium theory[12]and is suitable to predict the equilibrium uptake at high concentrations of adsorbate.The objectives of this work are as follows:(i)Obtain the optimal operating pH for L-phenylalanine sorption at the concentration of its fermentation broth.(ii)Predict the uptakes of all species of L-phenylalanine,i.e.,positive-,negative-,and zwitter-ions,at various solution pH values by the proposed model.(iii)Provide the parameters of the proposed model as the fundamental information for the dynamic simulation in the future work.

2.Theory

The DIX model for ion-exchange equilibrium is based on the Donnan membrane equilibrium theory. In the model, the resin phase is considered as a homogeneous phase.The solvent and solutes distribute freely over the two phases.The phase boundary is visualized as a semipermeable membrane,permeable to all species except the functional groups,which are covalently linked to the matrix and stay in the resin phase[12].The electrostatic interactions between fixed charges(functional groups)and mobile charges(ions)in the resin are long-range ones.The modified Debye–Hückel activity coefficient function is used to represent the activity in the liquid phase while the activity in the solid phase is obtained empirically.

At equilibrium the chemical potential(electrochemical potential for electrolytes)of each component i,μi,is equal in both phases,which leads to

where Δμ0is the electrochemical potential difference between the resin and liquid phase at the standard state,R the gas constant,T the temperature,α the activity,ν the partial molar volume assumed to be constant,π the pressure difference or osmotic pressure,z the valence,F the Faraday constant,and ΔΦ is the electrical potential difference between the resin and liquid phase(Donnan potential).Indexes R and L denote the resin phase and the liquid phase,respectively.This equation is the basis for calculating the resin-phase composition from known liquid phase concentrations.It is set up for phase equilibrium in general without limiting assumptions concerning partitioning of neutral species and exclusion of coions,so it applies to counter-ions,co-ions,and neutral species[12].

For both phases the concentrations of component i are related to its activity via the activity coefficient γias follows.

Starting from Eq.(1),the concentration of each component in the resin phase can be calculated by the following equation,in which index cat and an denote cation and anion ions,respectively.The details of model equations are given elsewhere[12].

In the traditional DIX model[12],a thermodynamically ideal system is assumed,so the activity equals to the concentration.In this study,the mean ionic activity coefficient[15]is introduced to describe the activity.

The cation and anion concentrations in the resin phase are written explicitly as

Once the selectivity constants of ion pairs(S)and the mean ionic activity coefficient ratio(γ)are known,complete composition of the resin phase can be calculated from the known concentrations of the liquid phase.In this study,the concentration of L-phenylalanine is less than 40 g·L?1(242.11 mmol·L?1).Thus the mean ionic activity coefficient in the liquid phasecan be calculated by modified Debye–Hückel activity coefficient function(Eq.(13)),which assumes that only electric attraction exists among the ions in the solution and the short range interaction can be ignored[16,17].

where I is the ionic strength,and AD–His the Debye–Hückel constant.Both of them can be obtained by the following equations[18].

In the resin phase,it is difficult to calculate the mean ionic activity coefficient for molar ratios are unknown variables.The value of γ±Ris therefore treated as one of the model parameters.Besides,Scat,H+and San,OH?are also the model parameters.These parameters are obtained with SAS 8.2(Statistical Analysis System).The Levenberg–Marquardt algorithm is used for estimation.The residual error SSresis minimized by adjusting the parameters.

where SSresis the sum of squares of the residuals,Visthevolume,and c0is the initial liquid phase concentration of the component.

3.Materials and Methods

3.1.Materials

The an hydrate form of L-phenylalanine was purchased from Sigma-Aldrich.All the chemicals used were of analytical grade.L-phenylalanine solutions were prepared by dissolving precisely measured amounts(±0.1 mg)of L-phenylalanine in deionized water.The gel-type strong cation exchange resin(SH11resin)was kindly provided by National Engineering Research Center for Biotechnology.The physical properties of the resin are summarized in Table 1.

Table 1 Physicochemical properties of resin SH11

3.2.Ion-exchange capacity of SH11 resin

The to talion-exchange capacity of SH11resin,Q,was determined by equilibrating a sample of the resin in the hydrogen form with an excess volume of NaOH.At equilibrium,the excess NaOH was titrated with 0.1 mol·L?1HCl using an 848 Titrino Plus apparatus with an 801 Magnetic stirrer(Switzerland).The capacity was determined based on the material balance.

3.3.Ion-exchange equilibrium experiments

The equilibrium uptake of L-phenylalanine was determined by contacting the hydrogen from of SH11 resin with a stock solutioncontaining a fixed concentration of L-phenylalanine.The ion-exchange equilibrium experiments were performed at 298 K.The SH11 resin(0.5 g)was added to 30 ml of the solutions in 100 ml flasks.The flasks were completely sealed and shaken for 12 h at an agitation speed of 150 r·min?1in an incubator shaker at a preset temperature to ensure the equilibrium.The mass balance was used to determine the equilibrium compositions of the resin.The amount of L-phenylalanine adsorbed onto the resin was calculated.

Table 2 Parameters of the modified DIX model

where c0and ceare the initial and equilibrium L-phenylalanine concentrations in the solution,respectively,V the solution volume,ρ the resin density,and m the mass of adsorbent.Consequently,qerepresents the equilibrium adsorption capacity corresponding to ceat the present temperature.

To study the effect of pH on L-phenylalanine uptake on theres in,the pH value of L-phenylalanine solution was adjusted by addition of small amount of 2 mol·L?1HCl or 2 mol·L?1NaOH to the solution prior to experiments.The initial L-phenylalanine concentration was fixed at 0.12 mol·L?1,approximately the same concentration in the fermentation broth.At the end of each experiment,after equilibrium was reached,the pH was measured and the L-phenylalanine uptake was calculated.The concentration of OH?was determined from the solutionp H.A SX723 pH meter(Sanxin,Shanghai)was used for pH measurements.All the experiments were carried out in duplicate and the average values are presented.

3.4.High-performance liquid chromatography analysis

The concentrations of L-phenylalanine were determined by high performance liquid chromatography(Agilent Technologies 1200 Series,USA)equipped with a Sepax HP-C18 column(4.6 mm × 250 mm,5 μm,Sepax(Jiangsu)Technologies,Inc.,Changzhou,China).The mobile phase was 30 vol%methanol.The column temperature was 25°C and the flow rate was 1.0 ml·min?1.The detector wavelength was set at 260 nm.

4.Results and Discussion

4.1.Dissociation equilibria of L-phenylalanine in solution

L-phenylalanine is an amphoteric molecule.In aqueous solution it dissociates into different ionic species depending on the pH value.As a result,the following dissociation equilibrium takes place.

whereis the concentration of positively charged L-phenylalanine,is the concentration of zwitterions,whileis the concentration of negatively charged form,ctrepresents the total concentration of L-phenylalanine,andis the concentration of hydrogen ion.The total concentration of L-phenylalanine in the solution is

When the concentration of L-phenylalanine in a solution containing HCl is known,the Cl?concentration may be expressed as

The values of equilibrium constants and isoelectric point(pI)for L-phenylalanine under study are shown in Table 2.The distribution coefficient(δ)calculated by Eq.(20)is shown in Fig.1(a).At the pH value below 2.0,the ratio of L-phe+is the highest.As the pH value increases from 2.0 to 6.0,the ratio of L-phe+decreases and the ratio of L-phe±increases.The ion exchange bet ween L-phenylalanine and counter-ions of the cation exchange resin may take place at the pH value below 6.0.As a result,the cation exchange resin can be used to adsorb L-phenylalanine in this pH range.

Fig.1.Theoretical distribution coefficients for different ionic components of L-phenylalanine in the solution (a) and the mean ionic activity coefficient of solution at different concentrations of L-phenylalanine and different pH values (b).

4.2.The mean ionic activity coefficient of L-phenylalanine in liquid phase

The mean ionic activity coefficientcalculated by Eqs.(13)–(16)at different L-phenylalanine concentrations and pH values is presented in Fig.1(b).The value ofis not equal to unit even at very low concentration(3 g·L?1).The value ofdeclines as the concentration of L-phenylalanine increases.Consequently,if the activity is considered equal to the concentration,there would be some errors between the calculated results and experimental data.

The solution pH has a Significant influence on the mean ionic activity coefficient.As can be observed in Fig.1(b),when the pH is in the range of 2–9 the mean ionic activity coefficienthas the highest value and remains almost constant.However,when the pH is lower than 2 or higher than 12,thevalue reduces greatly.This is because the zwitterions L-phe±are dominant in the solution in the pH range of 2–9(see Fig.1),whereas HCl is added to the L-phenylalanine solution for pH ＜ 2.Consequently,besides L-phe+ions,Cl?ions are in the solution as well,increasing the ionic strength I.Thus the mean ionic activity coefficientdecreases.The same is in the case of pH ＞ 12.NaOH is added to the solution to adjust the solution pH.Consequently,in addition to L-phe?ions,Na+ions exist in the solution as well.This causes the decrease ofwith the increase of pH.The solution pH influences notonly the dissociation equilibrium of L-phenylalanine,but also the mean ionic activity coefficientSignificantly.Investigation on the effect of pH on the L-phenylalanine uptake onto the ion-exchanger is therefore of great importance.

4.3.Effect of solution pH on L-phenylalanine uptake by resin

The influence of solution pH on the L-phenylalanine uptake on the strong-acid ion-exchanger SH11 is shown in Fig.2.The modified DIX model gives an excellent prediction.The values of(L-phenylalanine concentration in the solid phase) calculated by the model and experimentally determinedare listed in Table 3.The relative deviations are all less than 3%,which indicates that the model proposed in this work is reliable.

Fig.2.Concentrations of components in the resin phase at different pH values of solution(point:experimental value;curves,calculated values by the modified DIX model).

Model parametersare presented in Table 2.The value of 0.9694 for γ±Ris very close to those for(see Table 3).It is reasonable because in our study the concentration of L-phenylalanine is around 120 mmol·L?1and pH is between 1–6.The solution concentration and pH have in Significant effect on the L-phenylalanine activity.The value ofis as high as 66.06 whileis only0.251.InJansens et al.'work[12],was 0.241 whilewasin the range of 3.41–64.0.It indicates that the selectivity between cation ions and H+could be much higher than that between anion ions and OH?.As a result,the values ofandare reasonable.The values ofandare close to each other,which is also reasonable.

Table 3 Comparison of the simulation results with experimental data

The in fl uence of solution pH on the uptake ofand total L-phewith the uptake ofHand,is presented in Fig.2.increases to a maximum value and then decreases with the increase of solution pH.Saunders et al.[7]also measured the L-phenylalanine uptake at various solution pHs and gave the same trend,indicating that the results in our work are reasonable.The highestvalue is at pH 2.0.For pH below 2.0,concentrations of H+and Cl?ions are high and adsorbed onto the resin,which has a great effect on the adsorption of L-phe+.Thus the concentration of L-phe+in the resin phase declines with the decrease of pH value.However,for pH above 2.0,higher pH value leads to the decrease of L-phe+concentration and the increase of L-phe±in the solution.Since the concentration of L-phe in the resin phase is proportional to that in the liquid phase in the concentration range studied,the proportion of L-phe±in the resin phase gradually increases with pH.However,the electrostatic attraction between L-phe+and the resin is stronger than the interaction between L-phe±and resin,so that the adsorption ability of SH11 resin for L-phe+is stronger than that for L-phe±.Hence,the total concentration of L-phenylalanine absorbed in the resin phase decreases with the increase of pH value.For pH in 4.5–6.0,the proportion of L-phe±to L-phenylalanine is almost 100%(see Fig.1(a)).The resin-phase concentration of L-phenylalanine retains at a low and stable value in this pH range.

In all,the solution pH plays an important role in the L-phenylalanine adsorption process.According to the above results,pH 2.0 is the optimum condition for adsorbing L-phenylalanine.

5.Conclusions

A modified DIX model for ion exchange equilibrium of L-phenylalanine is established on the basis of DIX model and the Debye–Hückel activity coefficient model.The mean ionic activity coefficient is introduced to reduce the deviation between activity and concentration.It is con firmed by calculation that the mean ionic activity coefficients of resin and liquid phase are not equal to 1 in this research scope.The L-phenylalanine concentration and solution pH have Significant effect on the mean ionic activity coefficient.

The modified DIX model is successfully used to calculate the resin-phase composition from known liquid-phase concentration at various pH values.It is demonstrated that the pH value of the solution has a strong influence on the adsorption process.The highest concentration of L-phenylalanine in the resin phase obtained is at pH of 2.0.

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