Znd. Eng. Chem. Res. 1995,34, 4486-4493
4486
Evaluation of Kinetic and Thermodynamic Parameters of Amino Acids on Modified Divinylbenzene-Polystyrene Resins Using a Liquid Chromatography Technique Mercedes Martinez, Alejandro Carrancio, Jose Luis Casillas, and Jose Aracil* Departamento de Zngenieria Quimica, Facultad de Ciencias Quimicas, Universidad Complutense, 28040 Madrid, Spain
Liquid chromatography has been used to evaluate the sorption and diffusion characteristics of DL-tryptophan, DL-phenylalanine, L-DOPA, DL-glUtamiC acid, and DL-lySine in modified divinylbenzene-polystyrene resins. All amino acids adsorbed quite rapidly, but there were significant differences in both equilibrium constants and diffusivities. On the modified resins, the values of equilibrium constants decreased with decreasing molecular weight. Diffisivity values increased with temperature and decreased with molecular weight for both resins. 1. Introduction
There is a high demand for biologically-produced molecules. Amino acids, peptides, and proteins'play a very important role in industry and are among the main products of biotechnology. These compounds often have an extremely high value and must be produced with considerable purity. Nowadays selective fermentation with genetically selected bacterial strains is the main production route. Fermentation products generally undergo a sequence of separation steps in which cell mass and high molecular weight compounds are removed first and more difficult separations are carried out last. The industrial-scale separation and purification of fermentation products using modified resins have been previously examined (Aracil et al., 1992). The adsorption capacity and selectivity of the resin were modified by changing the chemical properties and structure of the polymer surface. A particular type of these resins was selected from chromatography studies on their adsorption properties. The present study reports the extension of the liquid chromatography previously developed for the study of liquid adsorption and diffusion in divinylbenzenepolystyrene materials using the moment method. The use of the chromatographic method makes it possible to determine both thermodynamic and kinetic transport parameters. From the first moment the following parameters can be obtained: adsorption equilibrium constant and heat of adsorption. From the second moment the pore mass transfer coefficient is calculated. The chromatographic method has been applied to adsorbate-adsorbent systems that produced elution peaks with a shape close to Gaussian and with only a small degree of tailing. The parameters obtained this way allow one to simplify the rigorous methods to design the purification operation in both batch and fmed-bed processes. As a result, the computing time necessary for the calculations is considerably reduced. For highly asymmetric peaks, the method of moments has not been applied because the evaluation of the second moment is subject to significant error. There are two main objectives in the present study. First objective is to further verify the applicability and reliability of the liquid chromatography in the deter-
* Author t o whom correspondence is addressed. Fax: 34.1.13944114. E-mail:
[email protected].
mination of kinetic and thermodynamic parameters of adsorption in two different porous adsorbents. The second aim of this work is to investigate the effect of both the chemical nature of the liquid adsorbate and the physical properties of the porous adsorbent on the adsorption parameters. We have studied the thermodynamics and kinetics of adsorption of DL-tryptophan, DL-phenylalanine,L-DOPA, DL-glutamic acid, and DL-lysine. An evaluation was carried out to investigate the influence of polarity on the process over modified Amberlite XAD-2 and XAD-4 resins, XAD-2-1 and XAD-4-1 (Aracil et al., 1992). 2. Experimental Section
2.1. Apparatus. A liquid chromatography metering pump (Perkin-Elmer LC-100 column oven) provided a steady flow of eluent through a liquid sampling valve (Rheodyne), and hence t o the adsorbent column and Perkin-Elmer LC-75 spectrophotometric detector with variable W wavelength equipped with flow cells. The high-pressure pump was equipped with flow controllers and a digital flow meter, which could provide flow rates up to 5 cm3 min-l at pressures up to 1.0 x lo7 Pa. 2.2. Column Preparation and Temperature Control. The XAD-2 and XAD-4 modified resins, XAD-2-1 and XAD-4-1, synthesized in our laboratory by halogenation of commercial divinylbenzene-polystyrene resins and the experimental procedure have been previously described (Martinez et al., 1988). The resins were ground and wet-sieved to obtain suitable portions of particles of diameter between 30 and 45 pm. The resin thus prepared was slurried in neutrally dense acetic acid in a high-pressure vessel and packed into a column (20 x 0.22 cm) by sweeping the slurry in a stream of high-pressure distilled deaerated water into the column containing a 4 ,um frit at one end. The resin temperature was controlled by the column oven. To ensure that the eluent temperature at the bed entrance did not differ significantly from the bed temperature, the eluent was routed through a preheat tube, held in a constant temperature water bath upstream of the injection valve. 2.3. Reagents and Buffer. The Amberlite XAD-2 and XAD-4 were supplied by Rohm and Haas Co. The monomer trapped in the resin pores was removed by Soxhlet extraction using methanol as a solvent. The eluent of controlled pH (3.0) and ionic strength (0.1 M) was prepared by dissolving known quantities
0888-5885l95I2634-4486~Q9.QQlQ0 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34, No. 12, 1995 4487 The physical properties of modified resins and amino acids and the experimental conditions are given in Tables 1 and 2, respectively.
3. Mathematical Model
//
0
/ FLOW RATE (xi0 ' m i'I
0
2.6
6
7.6
10
Figure 1. Pressure drop across a column bed with the flow rate for the HPLC system employed.
of analytically pure Na2HP04, KH2P04, and NaCl in distilled deionized water in proportions specified by Perrin (1963). High-purity grade DL-tryptophan, DLphenylalanine, L-DOPA,DL-glutamic acid, and DL-lySine were supplied by Sigma Chemical Co. Solutions of the compounds were prepared by dissolving milligram quantities in 25 cm3 of buffered eluent. The solutions were stored in air-tight vessels at low temperature. The eluent was degassed using an ultrasonic bath and delivered via a 4 pm filter to the column. It is known that adsorption is linear when such low concentrations are used (Iskaudarari and Pretrizyk, 1981). 2.4. Operating Procedure. The column was eluted with a buffer solution of chosen pH overnight, prior to each experimental run. The temperature of the water bath was raised t o the desired point, and the eluent flask and preheat tube were immersed in the bath. About 1 h was allowed for thermal steady state t o be attained. Samples of solution of 20 p L volume were injected into the column. The response of the on-line U V detector to an eluted peak was monitored on a chart recorder, amplified, and converted from analogical to digital form by an A/D card, PCLD-7115 REV Al, before reaching the computer system. The pulse samples for the experiment varied from 0.1 to 1.5 x mol L-l. After acid washing, the dead time to, and therefore the dead volume of the adsorption system, was estimated by injecting an appropriately buffered solution of NaNO3 into the column and recording its chromatogram. The chromatograms thus obtained were analyzed by calculating the first and second moments with the aid of a computer program. In order to check the integrity of the packing procedure, the porosity of the bed was determined by pumping distilled sodium nitrate through the bed at flow rates within 0.5-5.0 cm3 min-l (Reynolds number x 1.0). The pressure drop across the column was monitored as a function of the flow rate. For laminar flow, the well-known Kozeny-Carman equation shows that the value of ep is constant, for each value of pressure, only depending on the geometric parameters of column packing. A plot of these data as the Kozeny-Carman relationship (Figure 1)showed that bed porosities were 0.63 and 0.64 for XAD-2 and XAD-4 modified resins, respectively. Furthermore, the porosities of the wet particles (ep)were estimated from these values, and the dead time was calculated according to eq 2. Experiments in which the bed was bypassed showed that the contribution of the interconnecting pipe to t o and peak spreading was negligible and that eq 2 was valid.
When a pulse of an adsorbate solute is introduced into a liquid chromatography column packed with spherical or pseudospherical pellets of resin, the characterization of the adsorption properties of a system can be obtained by the chromatographic moments. Analysis of chromatographic adsorption by considering only the first two moments has been treated in detail elsewhere (Shah and Ruthven, 1977). The first moment (LA) and the second central moment (a2)may be calculated by numerical integration or may be estimated from the geometric shape parameters of the peak. By assuming the absence of any chemical reaction, a linear adsorption isotherm (i.e., adsorption equilibrium limited to the Henry law region), and an instantaneous injection pulse, the previously mentioned relationships for the first moment (mean) can be written as:
i')kI
"[
p=t,+-l+u
(1)
where to, the dead time, was estimated by analyzing the NaN03 peak as described above: to =
t[€+
+
(1
(2)
€)Ep]
(3) The column eficiency may be evaluated from the height equivalent t o a theoretical plate (HETP). In chromatography analysis, the HETP is expressed in terms of the moments as:
(4) and
-2
The first and second moments, used for the estimation of kinetic parameters, have been corrected using the dead volume determined from NaNO3 tests. 4. Results
The linearity of the adsorption isotherm can be verified on a typical chromatogram (Figure 2). The shape of the peak is almost symmetrical and typical of linear adsorption. This was confirmed by varying the adsorbate concentration in the pulse and measuring retention times. The values of kads obtained were independent of peak areas. The instantaneous pulse is verified by the results that showed that the retention time was independent of the injection volume of the adsorbate in the linear region of adsorption. The amino acid samples were of very low concentration (0.5 wt %) and were further diluted in the column since the sample
4488 Ind. Eng. Chem. Res., Vol. 34, No. 12, 1995
Table 1. Physical Properties of the Modified Resins and Compounds resin
surface area (m2g-l)
average pore volume (cm3 9-1)
average pore diameter (A)
% halogen
XAD-2-1 XAD-4-1
168.63 493.68
0.50 0.63
119.35 51.45
30.48 33.45
compound DL-tryptophan
mol wt 204.23
volume (A3) 227.8
L-DOPA
197.19
196.0
polarity
formula
I
HO
DL-phenylalanine
165.19
189.9
low
DL-glutamic acid
147.13
138.4
high
"2
HOOC-CH~-CH~-CH-COOH
I
"2
DL-lySine
146.15
168.6
high
H~N-CHZ-CH~-CH~-CH~-CH-COOH
I
"z
Table 2. Summary of Experimental Conditions resin compound temperature (K) flow rate (cm3min-') PH ionic strength (M)
XAD-2-1,XAD-4-1 DL-tryptophan, L-dopa, DL-phenylalanine, DL-glutamic acid, DL-lysine 293,303,313,323 0.5, 1.0, 1.5 3.0 0.1
volume used was small compared to the column volume. Experiments were repeated under the same conditions of temperature and velocity to confirm the reproducibility of the system. The results showed that temperature and velocity did not significantly affect the retention time of NaN03 within a 5% error. 4.1. Bed Voidage and Axial Dispersion. Figure 3 shows a plot of the first moment of the response against Llv for sodium nitrate. Since the NaN03 molecule is small enough to penetrate freely into the pores of the modified resins, there cannot be significant diffusion or adsorption ( k a & = 0). According to eq 1, the plot should be linear through the origin with a slope equal to the bed voidage ( E ) . For the columns used in the present study the void values determined this way are 0.63 for XAD-2-1 and 0.64 for XAD-4-1 resins, in agreement with the results obtained with the KozenyCarman equation. Studies of axial dispersion of liquids in packed beds have shown that Ddv is essentially independent of fluid velocity at low Reynolds number. Under conditions of axial dispersion control, the HETP is given by Ddu and should therefore be essentially constant and the same for all the adsorbents. Since NaN03 molecules are small, they penetrate freely and rapidly with no significant mass transfer resistance, and the HETP value should represent the axial dispersion contribution and should be independent of both velocity and temperature. Figure 4 shows the HETP data for NaN03 plotted against the interstitial velocity. It can be observed that the HETP is approximately constant (Wdu = 0.60 for XAD-4-1and 0.40 for XAD-2-1) and independent of fluid velocity and temperature over the range of 40 values examined. 4.2. Evaluation of Thermodynamic Parameters. The plots of the first moment against the reciprocal of the interstitial flow velocity as Llv for all the amino acids in both columns are essentially linear, and the
1.2 1
r
1
A
0.6
0
1
1.S
2
2.1
3
3.6
4
4.S
TIME (mid Figure 2. Typical experimental HPLC chromatogram of phenylalanine using a modified XAD-4 resin at 293 K.
0
0.2
0.4
0.8
0.8
6 DL-
1
L/v (mid Figure 3. Variation of first moment with L l v for NaN03 at 293 K in HPLC system.
data can be well represented by single straight lines for the temperature range 293-322 K. Figure 5 shows a typical plot for DL-phenylalanine. The adsorption equilibrium constants (kads), summarized in Tables 3 and 4, were derived from the slopes of the plots for the different sorbates according to eq 1. The differences in the kads values obtained for all the amino acids examined may be explained in terms of
[nd. Eng. Chem. Res., Vol. 34, No. 12,1995 4489 1.d
0.0
1 1
P (mid 0.6
o.o
t
-0
0 io
20
l0
20
ao 40 v (cm min")
eo
eo
70
60
00
70
0.1
0.2
0.a
0.4
0.6
L/v (mid
b
0.0
0.0
HETP (cm) 0.4
0.2
0 0
SO
40
v (cm min") Figure 4. (a)Variation of HETP with v for in an HPLC system using modified XAD-2 resins at 293 K. (b) Variation of H E W with v for NaN03 in an HPLC system using modified XAD-4 resins at 293 K.
three factors: compound molecular weights, polarities, and physicochemical properties of the resins. On the two modified resins, the values of adsorption constant, k&, decrease in the following order: DL-tryptophan > DL-phenylalanine > L-DOPA > DL-glutamic acid > DL-lySine This decreasing order corresponds to decreasing molecular weight, as is to be expected, except for the L-DOPA. This compound, having higher molecular weight, is less strongly adsorbed. The lower adsorption constant value observed for L-DOPA in comparison with DL-phenylalanine, which has lower molecular weight, can be explained by the difference in polarity. In fact, the increase in the polarity of the adsorbate can drastically decrease the adsorption equilibrium constant, with the most polar adsorbates, DL-glutamic acid and DL-lysine, being the least adsorbed. For three adsorbates, L-DOPA,DL-glUtamiC acid, and DL-lysine, the values of adsorption constant, ka&, were similar in the two modified resins. This can be explained in terms of interaction forces among the polar groups in the adsorbates and those of the resins, with the functionalization degree being similar for both of the resins tested. These forces are higher for L-DOPA because the number of polar groups in the amino acid is larger. The pore diameter also decreases in the above order,. and the surface area increases in the same order. The difference in the surface area may explain that DL-
Figure 5. (a) Variation of the first moment with L l v for DL-phenylalanine using modified XAD-2. (b) Variation of the first moment with L l v for DL-phenylalanine using modified XAD-4.
tryptophan is adsorbed on the XAD-4 modified resin and not on the XAD-2 modified resin. The van't Hoff type equation:
K = KOexp(-AHIRT)
(6)
has been used to correlate the equilibrium adsorption constants a t different temperatures with the heat of adsorption. The logarithmic plots of the adsorption constant against reciprocal temperature were linear for all adsorbates and the two adsorbents (Figure 6). This suggests that effects of heat capacity variation with temperature are negligible in the range of temperature studied. The heats of adsorption calculated are presented in Tables 3 and 4 and show moderate exothermic adsorption for all compounds except for DL-tryptophan. In general, the heats of adsorption increase with increasing molecular weight for both resins, except for DL-lysine. The heat of adsorption of DL-lysine is larger than expected and has the same value on both modified resins. This is due to the protonated structure of the two amino groups of the adsorbate a t the pH of the experiment (3.0). The heat of adsorption of DL-glutamic acid is smaller that of DL-lysine, although both amino acids have similar molecular weight. This is due to the fact that DL-glutamic acid is less strongly adsorbed. There is no significant temperature dependence for the equilibrium constant, ha&, for DL-glutamic acid, since this amino acid has only one protonated amino group. It can be concluded that this amino acid is contained within pores but is not significantly adsorbed on the pore walls.
4490 Ind. Eng. Chem. Res., Vol. 34,No. 12, 1995
Table 3. Thermodynamic and Kinetic Parameters of Amino Acids Using a Modified XAD-2 Resin amino acid temperature (K) C.F. kads AS' (kJ mol-') -AH (kJ mol-l) D, (lo6cm2 s-l) DL-tryptophan
L-DOPA
DL-phenylalanine
DL-glUtamiC acid
DL-lysine
293 303 313 323 293 303 313 323 293 303 313 323 293 303 313 323 293 303 313 323
3.27 3.19 3.12 3.91 14.1 12.9 10.9 8.25 3.03 2.88 2.78 2.75 2.69 2.63 2.51 2.30
4.95 4.75 4.60 3.95 12.50 11.40 9.75 8.05 4.05 4.00 3.95 3.90 3.70 3.50 3.30 3.05
-5.60 -5.60 -5.60 -5.60 -18.20 -18.20 -18.20 -18.20 -8.25 -8.25 -8.25 -8.25 -5.70 -5.70 -5.70 -5.70
5.60 5.60 5.60 5.60 11.60 11.60 11.60 11.60 0.98 0.98 0.98 0.98 4.85 4.85 4.85 4.85
3.35 3.45 3.80 4.05 6.55 6.85 7.25 7.85 3.15 3.70 3.80 3.90 3.20 3.70 3.90 4.10
Table 4. Thermodynamic and Kinetic Parameters of Amino Acids Using a Modified XAD-4 Resin amino acid temperature (K) C.F. kads A S (kJ mol-') -AH (kJ mol-') D,(106 cm2 s-') DL-tryptophan
L-DOPA
DL-phenylalanine
DL-glUtamiC acid
DL-lysine
293 303 313 323 293 303 313 323 293 303 313 323 293 303 313 323 293 303 313 323
9.49 7.98 5.39
28.65 22.00 16.80
2.81 2.72 2.68 2.57 3.62 2.51 1.99 1.75 3.22 3.05 2.81 2.50 3.15 2.45 2.36 2.15
4.95 4.70 4.45 4.10 6.30 5.50 5.15 5.05 3.90 3.80 3.75 3.60 3.70 3.60 3.30 3.10
-41.30 -41.30 -41.30 -41.30 -3.60 -3.60 -3.60 -3.60 -4.40 -4.40 -4.40 -4.40 -4.10 -4.10 -4.10 -4.10 -6.10 -6.10 -6.10 -6.10
The change in entropy of adsorption, AS,has been calculated using the following equation:
A S = -R In&) + AH/T
(7)
Assuming constant concentration a t given sites on a modified resin, values of the adsorption constant and heat of adsorption obtained for all compounds, shown in Tables 3 and 4, have been explained in terms of AS'. Using modified resins, there are differences in the AS' values calculated for the amino acids, except for DLlysine. The values obtained on modified XAD-2 are approximately double the AS' values on modified XAD4, probably due t o changes in the adsorption mechanism. The DL-lysine can adopt a six-ring member conformation, depending on the pore diameter of the resins. All values of AS' are negative for all the amino acids. This phenomenon can be explained in terms of the conformational changes in the DL-lysine molecule during the mechanism of adsorption. The chemical nature of the adsorbates and the surface area and pore diameter of the adsorbent seem t o be the predominant factor in determining the values of the adsorption constant. Increasing the polarity and decreasing the molecular weight of the adsorbent lead to a decrease in the adsorption equilibrium constant. 4.3. Evaluation of Kinetic Parameters. For significant mass transfer resistance, the HETP should
20.25 20.25 20.25 20.25 4.90 4.90 4.90 4.90 5.70 5.70 5.70 5.70 2.10 2.10 2.10 2.10 5.00 5.00 5.00 5.00
DdR,* (lo3 s-l)
9.53 9.81 10.81 11.51 18.60 19.40 20.60 22.32 8.95 10.55 10.80 11.09 9.10 15.20 11.09 11.66
DJRD2(lO3s-l)
8.50 11.60 13.40
24.17 32.99 38.11
2.50 2.80 3.00 3.10 6.15 6.50 6.76 6.95 3.00 3.10 3.30 3.50 3.00 3.10 3.25 3.45
7.11 7.96 8.53 8.81 17.49 18.49 19.23 19.76 8.55 8.81 9.38 9.95 8.55 8.81 9.24 9.81
increase linearly with interstitial liquid velocity, as expected from eq 5. The slope and intercept should yield the mass transfer resistances and the axial dispersion coefficient, respectively. For systems where very rapid and strong adsorption occurs, like a gas-solid system, there can be a significant additional contribution to the axial dispersion, arising from direct transport through the solid. In the present work, the axial dispersion contribution (2Ddu) was found to have values of 0.40 and 0.60 for XAD-2-1 and XAD-4-I, respectively (Casillas et al., 1992). These values were obtained by plotting HETP versus the interstitial liquid velocity for all amino acids for both modified resins. The order of magnitude of the external mass transfer coefficient, kf, at a low Reynolds number, has been estimated from Wakao and Funazkri's correlation (Wakao and Funazkri, 1978). The external mass transfer resistance term (Rd3kf) in eq 5 may be neglected in comparison with the macropore diffusion resistance term (RP2/15@,) since kf (approximately cm s-l) is about 3 orders of magnitude larger than D, (approximately cm s-l). Assuming that macropore diffusion is the controlling resistance, the diffusional time constant DdRP2,and hence the pore diffusivity D,, can be derived from the slopes of plots of HETP against
Ind. Eng. Chem. Res., Vol. 34,No. 12, 1995 4491
-
0.s
HETP (om)
-
0.26
3
3.2
3.1
3.3
3.4
3.s
0
l0
30
20
v
1000/T d/K)
40
SO
60
70
SO
60
70
(cm mln“)
1-
It
-a
*
I OL-TRYPTOPHAN
+
Oc-LYSlWE
-B’ DL-OLUTAMIC ACID
-A
L-DOM
0.6
-
DL-CHlNVLALANINf
I c
9.1
3.2
3.3
9.4
3,s
1000/T d/K)
Figure 6. (a) Variation of In(&,) with inverse of temperature for all amino acids using modified XAD-2. (b) Variation of ln(k,d,) with inverse of temperature for all amino acids using modified XAD-4.
liquid velocity:
6)(
slope = 2(1 -l&)( 1
+
&r
(8)
The axial dispersion (2Ddu)value was subtracted from the measurement of HETP for the amino acids, and the difference was plotted against the interstitial liquid velocity. Reasonably linear plots passing through the origin were obtained, but some data showed some scatter. This is probably due to the relative error in the second moment calculated, which is usually less consistent than the first moment. The increasing trend of the slope with velocity is clear in all compounds for both resins. A typical plot for DL-phenylalanine is shown in Figure 7. The time constants and diffusivity constants derived from the slope are summarized in Tables 3 and 4 and are on the order of magnitude cm2 s-l. This confirms the validity of the assumption of this work. Significant differences in diffusivity values are observed, and they increase with temperature and decrease with molecular weight for, both columns. This indicates that the diffusivity values are more affected by the chemical nature of sorbates and adsorbents than by the geometric structure of the adsorbents. The values of macropore diffisivity obtained in both columns are very similar. It is observed that the HETP increases with decreasing temperature and increasing liquid velocity, suggesting, as expected, higher mass transfer resistance at lower temperature and higher liquid velocity.
0
10
30
20
49,
v
(em mln Figure 7. (a) Variation of HETP with interstitial liquid velocity (u) for DL-phenylalanine using modified XAD-2. (b)Variation of HETP with interstitial liquid velocity (u) for DL-phenylalanine using modified XAD-4.
The number of transfer units, as calculated from the HETP values obtained from the experimental work, varies between 20 and 60 for XAD-2-1 and between 25 and 60 for XAD-4-I. 5. Discussion
Adsorption Constant. Aromatic Amino Acids. For similar polarity, the highest values found for the adsorption constant correspond to amino acids of larger molecular weight. In this case the mechanism of adsorption in the polymeric “matrix” is carried out by physical retention caused by the size of the molecule of adsorbate. The smallest molecule (DL-phenylalanine) shows weaker interaction with both resins than DLtryptophan, which is the largest molecule studied. Regardless of the molecular weight and size of the molecule, less polar compounds present higher values of the adsorption constant than polar ones. The DLtryptophan molecule is probably entrapped in the XAD-2 resin, and desorption does not occur. Therefore, the adsorption constant values of DL-tryptophan could not be determined. Aliphatic Amino Acids. DL-Glutamic acid and DLlysine are molecules with similar molecular weight and high polarity, this being smaller than that of the aromatic amino acids. As can be expected, the adsorption constants have moderate values. This can be explained in terms of the nonpolar interactions between the adsorbate and the adsorbent. Considering this low adsorption, DL-glutamic acid presents a higher value of the adsorption constant than DL-lysine,probably due to
4492 Ind. Eng. Chem. Res., Vol. 34, No. 12,1995
the less polar carboxylic group of DL-glUtamiC acid in comparison with the amino group of DL-lySine. This is in agreement with the facts that have been explained above, i.e., for equal molecular weight, the less polar amino acid presents the highest adsorption constant. Adsorption Enthalpy. Aromatic Amino Acids. The calculated values of the adsorption enthalpy for the two resins used show the same behavior as the adsorption constant. This can be explained by the same reasons cited above concerning polarities and the size of the adsorbate. Aliphatic Amino Acids. Considering this amino acid series, the two compounds have the same molecular weight values. DL-Lysine, which shows a slightly higher polarity than DL-glutamic acid, has a higher enthalpy of adsorption. This can be explained by the high volume of the molecule, and, in consequence, the energy necessary to separate it from the polymeric matrix when it is already adsorbed will be higher. Adsorption Entropy. Aromatic Amino Acids. In general, the more negative AS is, the more ordered the system is. This can be observed from results using XAD-2 modified resin, since this resin has the largest pore diameter values and the smallest surface area. The maximum difference in the values of AS for the two resins was obtained for DL-phenylalanine (-18.22 in modified XAD-2 and -4.40 in modified XAD-41, the least polar of the aromatic amino acids compared. Aliphatic Amino Acids. Adsorption entropy values obtained with the two resins are quite similar for the less polar amino acid, DL-lysine, and for the amino acid with the lowest volume, DL-glutamic acid. Pore Diffusion Coefficient. Aromatic Amino Acids. Considering an aromatic amino acid and the two resins tested, intraparticle diffusion has high values when the temperature increases and, within the series of compounds studied, increases when the adsorption constants increase. As has been explained above, this is due to two different factors: polarity and molecular weight of the compound. For aromatic amino acids the contribution of diffusional resistance to mass transfer is smaller than that for aliphatic amino acids. Aliphatic Amino Acids. The values of the diffusion coefficient were calculated for both amino acids tested. DL-Glutamic acid and DL-lysine values are similar, due to the fact that these compounds have similar molecular weight and polarity. In all the experiments, and for the two resins, the dependence between temperature and the diffusion coefficient is as explained above. Influence of the Adsorbent. Aromatic Amino Acids. The values obtained for the adsorption constant, enthalpy, entropy and pore diffusion coeMicient using modified XAD-2 are higher than those obtained using modified XAD-4. The difference is more significant in the values of the adsorption constant, enthalpy, and entropy obtained for less polar compounds. In the case of the polar compound L-DOPA,the difference is small because of the possible mechanisms of adsorption. Aliphatic Amino Acids. Similar values have been found for the adsorption constant, enthalpy, entropy, and pore diffusion coefficient using both resins, except when DL-glutamic acid was used as adsorbate. In this case the entropy value obtained for modified XAD-2 is 2 times smaller than the value obtained for modified XAD-4. This can be explained by considering that it has the smallest volume and the lowest polarity.
6. Conclusions
An experimental method using moment analysis of chromatographic elution curves was applied to determine the thermodynamic and kinetic parameters for adsorption of five types of amino acids in a bed with modified resins AMBERLITE XAD-2 and XAD-4. In this paper, the method of data analysis that was followed was based on the use of the first two moments of the chromatographic peak for different liquid flow velocities and temperatures. The intraparticle void fraction in the bed was determined from the first moment of sodium nitrate data. The capacity factor, adsorption equilibrium constant, adsorption enthalpy, and values proportional to adsorption entropy were determined from the first moment. The second moment gave information on pore diffusivity, diffusional time constants, and height equivalent to a theoretical plate (HETP). On the two modified resins, the values of adsorption constant decrease with decreasing molecular weight, except for L-DOPA. This amino acid, having higher molecular weight, is less strongly adsorbed. This could be explained by differences in polarity. An increase in the polarity of the adsorbent produces a decrease in the adsorption equilibrium constant. The difference in the surface area of the two resins may explain that tryptophan is adsorbed on the XAD-4 modified resin and not on the XAD-2 modified resin. The heats of adsorption increase with increasing molecular weight for both two resins, except for DLlysine, due to compensation effects. There are differences in the entropy of adsorption using different modified resins. The values obtained for XAD-2 are 2 times larger than those measured on modified XAD-4, except for DL-lysine. The diffusivity values increase with temperature and decrease with molecular weight for both columns. The height equivalent to a theoretical plate (HETP) increases with decreasing temperature and increasing liquid velocity. It can also be concluded that, since in a liquid system axial mixing is determined by the flow pattern in the bed rather than by molecular diffusion, the value of axial dispersion should be approximately the same for all the sorbates eluting through the same column under similar conditions, in our work 0.60 and 0.40 for XAD4-1 and XAD-2-1, respectively.
Acknowledgment The authors thank CICYT (Project BIO 93-694) and Universidad Complutense of Madrid for financial support.
Nomenclature C: adsorbate concentration in the mobile phase, mmol g-1 D,: intracrystalline diffusivity, cm2 DL:axial dispersion coefficient, cm2 s-l Dp: pore mass transfer coefficient, cm2 k: apparent constant ka& adsorption equilibrium constant kf: external fluid film mass transfer coefficient, cm L: length of packing in the column, cm q : amount adsorbed by the resin particle, mg g-l R,: radius of the resin particle, cm r,: crystal radius, cm T absolute temperature, K t : time, s u : interstitial flow velocity, cm s-1
Ind. Eng. Chem. Res., Vol. 34, No. 12, 1995 4493 Lw: heat of adsorption, kJ mo1-l AS': change in entropy on adsorption, kJ mol-'
Greek Letters bed porosity cp: porosity of the particle p : first moment 02:second moment E:
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Received for review March 28, 1995 Accepted July 13, 1995@ IE9502087
* Abstract published in Advance ACS Abstracts, October 15, 1995.
