Ind. Eng. Chem. Fundam. 1985, 2 4 , 108-112
108
COMMUNICATIONS Size Exclusion Parametric Pumping A new parametric pumping method, size exclusion parametric pumping, was developed based on changes in the physical structure of the gel when temperature is varied. Experimental results for batch and continuous parametric pumping are reported for Blue Dextran 2000 and nickel nitrate in water with Sephadex G 2 5 and Bio-Gel P-2 gels. The two gels have qualitatively different behavior. The two solutes are easily fractionated with Sephadex G-25. Also, a novel two-bed parametric pump utilizing both gels is developed.
Introduction
Over the past 15 years there has been considerable interest in cyclic separation methods such as parametric pumping, cycling zone adsorption, and pressure swing adsorption. These methods were reviewed by Wankat (1981), and parametric pumping was reviewed by Rice (1976). Size exclusion chromatography (SEC) is now a generally accepted routine laboratory technique. Operating methods and the literature are discussed in a variety of articles and books (Reiland, 1971; Yau et al., 1979). Although the major phenomenon occurring in SEC is exclusion based on molecular size, many other effects also influence the separation. Ionic strength, pH, interaction between solvent and solute, temperature change, and sorption are included. Parametric pumping usually works on the basis of change in degree of adsorption. However, in this paper a totally different mechanism based on the cyclic change of the physical structure of gel with temperature change is used. SEC is commonly used for desalting proteins. However, this dilutes the protein solution during the processing. Thermal parametric pumping can both desalt and concentrate proteins. Temperature effects in SEC have been explored but not exploited to produce separation. Chitumbo and Brown (1973) used a thermodynamic argument based on assumed solventsolute, solvent-gel, and solute-gel interactions to explain temperature effects in Sephadex and cellulose gels. In rigid gels, increasing the temperature will decrease adsorption effects (Cantow et al., 1967; Mori and Suzuki, 1980), and the volumetric expansion of the solvent will decrease observed retention times. These studies led us to study the effects of temperature in SEC. Preliminary experiments showed that solute velocities are significantly affected by temperature. Because of this, we were able to develop size exclusion parametric pumping. In this research, batch parametric pumping experiments were carried out with Sephadex G-25 and Bio-Gel P-2 gels, and continuous parametric pumping was done with Sephadex G-25. An aqueous solution of Blue Dextran 2000 and nickel nitrate, whose properties are relatively wellknown, is chosen as a model system for protein desalting. Experimental Studies of Retention Volume The effect of temperature in SEC was studied for Sephadex G-25 (50-150 Km), Sephadex G-100 (40-120 bm), and Bio-Gel P-2 (100-200 mesh). A jacketed Pharmacia column with adjustable plungers was used. The swollen 0196-4313/85/ 1024-0108$01.50/0
gel was allowed to settle under gravity and then was further compressed. We defined the degree of compression c as t = (column length while compressed)/(column length for gravity settled) I 1.0 (1) If e is too large, a void space will appear when the flow is started. Different gels have different ranges of operable t.
The column was operated at 5 or 45 "C. Feed was initially at room temperature. A feed pulse of 0.2 wt % aqueous solution of Blue Dextran 2000 (a polydextran of molecular weight about 2000000) or 10 wt % aqueous solution of Ni(NO&6H20 was injected for 10 or 30 s, respectively. Deaerated distilled water was used as the eluent. The volumetric flow rate was maintained a t 0.45 ("t 0.01) mL/min with a Milton-Roy minipump. The peaks were detected with an on-line spectrophotometer at 256 or 617 nm for Blue Dextran 2000 and 306 nm for nickel nitrate. The peaks were symmetric. Results for Sephadex G-25 are shown in Table I while results for Bio-Gel P-2 are in Table 11. The solute velocities were calculated from the retention volumes as follows
US u=--vR/
(2)
vT
For Sephadex G-25 (Table I) the retention volume for Blue Dextran 2000 increased as temperature increased, while retention volume decreased with increased compression (smaller values of E) as expected. This latter result agrees with that of Edwards and Helft (1970). A t higher temperatures and higher e , the Blue Dextran 2000 moves more slowly. For Bio-Gel P-2 (Table 11) the retention volumes for both solutes decrease as temperature increases. Thus both solutes move faster as temperature is increased. The velocities of the solutes change significantly with temperature. The change is significantly more than the volume expansion of water. The two gels clearly behave differently for Blue Dextran 2000, which should be totally excluded from the gels. This difference is probably due to different swelling behavior of the gels, which can be explained by Flory's theory (Flory, 1953). Since the changes for the two solutes are in opposite directions with Sephadex (2-25, most of the parametric pumping experiments were done with this gel as it simplifies solute fractionation. Parametric Pumping Experiments
Direct thermal mode parametric pumping experiments for separating nickel nitrate and Blue Dextran 2000 have
0 1985
American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 24, No. 1, 1985
109
Table I. Column Elution Studies for Sephadex G-25 (50-150 pm)O t
= 0.928
5 "C
t
45 "C
= 0.893
5 "C
t
45 "C
= 0.825
5 "C
t
45 "C
= 0.777
5 "C
45 "C ~
~~
Retention Volume, mL nickel nitrate Blue Dextran
18.70 7.81
17.40 8.15
nickel nitrate Blue Dextran
0.65 1.56
0.72 1.52
17.82 6.89
16.50 7.67
16.25 5.51
14.91 6.00
14.92 4.61
13.70 5.02
0.64 2.00
0.73 1.82
0.67 2.16
0.74 2.02
Calculated Velocity, cm/min 0.66 1.71
0.72 1.55
"Column length for gravity settling was 29.1 cm. Flow rate ranged from 0.44 to 0.46 mL/min. Table 11. Column Elution Studies for Bio-Gel P-2 (100-200 mesh)" L = 0.937 t = 0.894 5°C 45°C 5 O C 45°C Retention Volume, mL nickel nitrate 22.88 18.21 22.04 17.75 Blue Dextran 6.54 5.18 5.81 4.71
1
0 Q
- - RIGHT
W
1,
NICKEL NITRRTE BLUE OEXTRRN
0.47 1.65
0.60 2.11
0.47 1.80
a.
.0900
U + Lz
w .O60Cu 3
m LL
.
.om a z
"Column length for gravity settling was 25.4 cm. Flow rate ranged from 0.45 to 0.46 mL/min. 0.000
,
1 0.00
reservoir
Left
Right
Product
product
I
1
N~UOFER OF cvc"L"i"s"
10.00
0.0000 50.00
YO .no
Figure 2. Concentration changes in batch parametric pumping: Sephadex G-25 (50-150 pm); t = 0.817 (= 26/31.8); V , = 6 mL; V , = 20 mL; V , = 10 mL. 10.00
,
I OISPLRCEUENT V0L.lMLi
Figure 1. Schematic diagram for parametric pumping system.
been studied. Cross-linked dextran gel (Sephadex G-25, 50-150 pm) from Pharmacia Fine Chemicals and polyacrylamide gel (Gio-Gel P-2,100-200 mesh) from Bio-Rad Laboratories were used as the stationary phases. A 1-cm i.d. chromatographic column, equipped with adjustable plungers and a water jacket (Column SR 10/50), manufactured by Pharmacia Fine Chemicals, was used for all experiments. The apparatus shown in Figure 1 was used. For batch operation the feed and product lines were shut off. The swollen gel was packed at room temperature into the vertically mounted column. The evenly packed gel column was left to stand for 10 min. This is the column length for gravity settling used in eq 1. Then the gel length was adjusted to the desired length with the plungers. Feed and effluents were pumped by a high-pressure Elalex pump and Milton-Roy minipumps. The entire system was operated automatically with the aid of three-way solenoid valves, pneumatically driven Cheminert six-position rotary valves and Chrontrol timers. Elution volumes and concentrations of nickel nitrate and Blue Dextran 2000 in aqueous solution were determined on and off line, respectively, with a Perkin-Elmer Lambda 1 single-beam spectrophotometer at wavelengths of 306 and 617 nm, respectively. The concentrations of both solutes were calculated by nonlinear regression since they both adsorb at both wavelengths. Batch Parametric Pumping with Sephadex G-25. A series of batch parametric pumping experiments was carried out with Sephadex G-25 gel, with water as the solvent. In batch parametric pumping experiments, both of the reservoirs and the gel column are initially loaded with the feed mixture with known concentrations of Blue Dextran and nickel nitrate. The closed system was operated cyclically, with the temperature of the column at 5 "C when the flow moves to the right and at 45 "C when it
-
t
0.58 2.11
Right
5 w
Calculated Velocity, cm/min nickel nitrate Blue Dextran
,1200;
RESERVOIR
iIi
5.2
0
6.0
X 4
15.0 11.0 19.0
*
% Q C
6.00
0 U lL
z
2 (L U
2
Y.00
m W
2.00
0.00
L 0.00
I
10.00
1
I
1
20.00 NUMBER 3&OOcvcL~~~O0
50.00
60.00
Figure 3. Separation factors for Blue Dextran with displacement volume as a parameter in batch parametric pumping: Sephadex G-25 (50-150 pm); t = 0.817 (= 26/31.8); V, = 20 mL; V , = 10 mL.
moves to the left. Ten minutes without flow was allowed for heat transfer after each temperature shift. Equal displacement volumes were used for each half-cycle. The concentration changes of solutes in each reservoir are shown in Figure 2. As predicted by the preliminary studies on Sephadex G-25 (Table I), the two solutes move in the opposite directions and accumulate in different reservoirs. Separation performance for Blue Dextran as displacement volume VD changes are shown in Figure 3. The separation factor for a single component was defined as (concn of solute i in one reservoir) ai = (3) (concn of solute i in other reservoir)
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Ind. Eng. Chem. Fundam., Vol. 24, No. 1, 1985
t;
E
E2
6.30
a
/
A
0.0000 25.05
Figure 6. Concentration changes in batch parametric pumping: Bio-Gel P-2 (100-200 mesh); t = 0.870 (= 20.7/23.8); V, = 4 mL; VL = 6.6 mL; VR = 5.3 mL.
?.@O
3 00
c
'
, 00
I
10 00
8.ooo
1
~FOOcvc~~sOO
50 00
300C
EC 3C.
Figure 4. Separation factors for nickel nitrate with displacement volume as a parameter in batch parametric pumping: Sephadex (3-25 (50-150 pm); t = 0.817 (= 26/31.8); V , = 20 mL; V R= 10 mL.
s-*ve--e--y-+-
2 000 r
30
5 oc
,
IC 00~ " N B E R I&CCCYCLES
, 20 00
25 00
'
0 0000
30 00
Figure 7. Separation performance in continuous parametric pumping: Sephadex G-25 (50-150 Wm); e = 0.817 (= 26/31.8); V, = 15 mL; VR = 15 mL.
-
1 I u.00
Y
1 0.00
L
5 .,20
10.00
SISPLACENEhT VEL. :ML
IJ.OC
23.co
Figure 5. Separation of Blue Dextran from nickel nitrate in batch parametric pumping: Sephadex G-25 (50-150 pm); e = 0.817 (= 26/31.8); VL = 20 mL; V, = 10 mL.
For Blue Dextran, the degree of separation increases as the number of cycles increases for VD up to 6 mL. For VD larger than 6 mL, the separation factor increases and then remains constant after a certain number of cycles. When VD exceeds 10 mL, the separation factor approaches 1, which means no separation of Blue Dextran. These results are expected since some of the Blue Dextran in one reservoir is transferred to the other during each half-cycle if the displacement volume is larger than both retention volumes a t the two temperatures. Since the retention volume of nickel nitrate at 5 "C is 17.86 mL, which is larger than that a t 45 O C , we would expect the separation factor for nickel nitrate to increase with increasing number of cycles if VD < 17.86. This agrees with the results shown in Figure 4. For the case of double solute separation, the separation factor was defined as ~ B = N
(CB/CN)Prod
1
(cB/cN)Prod
2
(4)
Separation factors calculated by eq 4 are shown in Figure 5. Separation between Blue Dextran and nickel nitrate is much better when VD is less than 10 mL. The low
separation factor when VD is larger than 10 mL is due to the poor separation on the part of Blue Dextran. Batch Parametric Pumping with Bio-Gel P-2. Batch parametric pumping was also done with Bio-Gel P-2 following the same procedure used with Sephadex G-25. The concentrations of Blue Dextran and nickel nitrate in each reservoir as a function of number of cycles are shown in Figure 6. As expected by the preliminary studies of Bio-Gel P-2 (Table 11),both of the solutes are concentrated in the left reservoir, which is quite different from the Sephadex G-25 runs. Continuous Parametric Pumping with Sephadex G-25. In the continuous parametric pumping experiments, both of the reservoirs and the gel column are filled with water initially. The feed mixture of Blue Dextran and nickel nitrate was introduced into the left end of the column as a pulse. While the mixture was pushed toward the right, the temperature of the column was kept at 5 "C. The right product, which is abundant in the fast-moving Blue Dextran, was then withdrawn from the right end of the column. After 10 min with no flow to warm the column to 45 "C, the direction of flow was reversed. Withdrawing the left product from the left end, which is abundant in nickel nitrate, completed the cycle. After 10 min to cool the column down to 5 "C, the feed mixture was injected to the left end of the column to initiate the next cycle. The separation performance of the continuous parametric pump is shown in Figure 7. Note that Blue Dextran and nickel nitrate are concentrating in different reservoirs. As the cycles are repeated, nickel nitrate contaminates the right product to decrease the separation factor. The results
Ind. Eng. Chem. Fundam., Vol. 24, No. 1, 1985 Left reservoir
111
.
Rotary
CDC
Right reservoir
Feed Left product
Middle product
Figure 8. Schematic diagram for continuous parametric pumping with coupled columns. Table 111. Experimental Data for Continuous Parametric Pumping with Coupled Columns run A run B run C feed, mL/cycle 1.27 1.27 1.27 product, mL/cycle left 0.47 0.60 0.70 middle 0.44 0.44 0.44 solvent recovery, mL/cycle 0.36 0.23 0.13 Separation Factor UN
= CN,L/~N.M
UB = C B . M / ~ B , L ~ B = N (CB/~N)M
-a
-
4.4 33 145
76 24 1824
(CB/CN)L a
Not steady state.
approach a repeating steady state or limit cycle. Continuous Parametric Pumping with Coupled Columns. Parametric pumping with coupled columns was done continuously to take advantage of the differences in behavior of Sephadex G-25 and Bio-Gel P-2. Two columns are coupled together as shown in Figure 8. The columns were at 5 "C while flow was to the right. From the preliminary elution studies of these gels, Blue Dextran would be expected to concentrate at the junction of the two columns and nickel nitrate in the left reservoir. Since both solutes move leftward in the Bio-Gel column, pure solvent is recovered from the right end of the Bio-Gel column. A series of continuous parametric pumping experiments was done with changes in the amount of solvent recovered. Operational data and separation performances are shown in Table I11 and Figure 9. Products were withdrawn by the same time schedule as the continuous parametric pumping with a single column. The three runs differ because the amount of left product was changed. At the beginning of run A, 0.36 mL of pure solvent was recovered out of 1.27 mL of feed per cycle. After 50 cycles, the solvent, recovered from the right end of the right column, was contaminated by Blue Dextran. There was also an undesirable increase of nickel nitrate in the middle product. In run B, the amount of solvent recovered was decreased to 0.23 mL per cycle to prevent the contamination in the right reservoir. The withdrawing period for the middle product was also changed to catch the maximum peak of Blue Dextran which was accumulated during run A. The concentration of Blue Dextran decreased sharply and approached its steady state at around the 170th cycle. The concentration of nickel nitrate in the left product also decreased because the amount of the left product was increased to 0.60 mL. Toward the end of run B, a small amount of Blue Dextran was detected in the solvent in the right reservoir. Decreasing the amount of solvent recovery to 0.13 mL/cycle completely eliminated the contamination of the right reservoir by Blue Dextran in run C. After the first 50 cycles in run C, concentrations of nickel nitrate and Blue Dextran were constant in both products. The sepag ~1824. The mass ration factor of the two solutes, ~ r was balances of both solutes were met within 5% for the last
2.00
e 0 I
31
c
El
:
+ec e,
:Le-
,
"_
"
30
:
120.3
UUMSIR :F
15:
0
CYCLES
!?C c
210
:
--
2°C 3
~
:.m
PC.0
Figure 9. Separation performance in continuous parametric pumping with coupled column: Sephadex G-25 (50-150 pm); e = 0.808 (= 25.7/31.8); Bio-Gel P-2 (100-200 mesh); e = 0.837 (=41.7/ 49.8).
cycles of both runs B and C.
Discussion and Conclusion The experiments done in this study show that size exclusion can be exploited for cyclic separation systems. The results of the batch parametric pumping experiments agreed with the preliminary studies of the elution volumes of the solutes with different gels. Each solute moves in a different direction with Sephadex G-25 and in the same direction with Bio-Gel P-2. In continuous experiments, especially those using coupled columns, large separation factors were obtained. At least seven different phenomena can be hypothesized to cause the observed temperature effects. Thus, changing the temperature could change the (1)solvent volume, (2) solvent-solute interactions, (3) adsorption, (4)electrostatic attraction or repulsion, (5) size of hydrated species, (6) porosities between particles and inside a particle, and (7) hindered diffusion. For Blue Dextran 2000, which is totally excluded, the only explanations which seem possible are (1) and (6). Since the observed effects were much larger than changes in solvent volume, the gel structure appears to be changing and thus changing the porosities. For nickel nitrate, all of the explanations could contribute. Thus more experiments are needed to determine what is causing the observed change in velocity of small solutes. The durability of the gel was excellent. There were no observable changes in the properties of Sephadex G-25 even after 400 temperature cycles. Acknowledgment Discussions with Bill Priedeman and Shankar Nataraj were helpful. This research was partially supported by NSF Grant CPE-8006903. Nomenclature C = solute concentration, w t '70 U = solute wave velocity, cm/min Us = superficial velocity, cm/min V , = displacement volume, mL V , = retention volume, mL V , = total packed volume, mL Greek Letters ai= separation factor for one solute, eq 3 "BN = separation factor for two solutes, eq
e = degree of compression, eq 1
Subscripts B = Blue Dextran 2000 i = i component L = left product M = middle product N = nickel nitrate
4
Ind. Eng. Chem. Fundam. 1905, 2 4 , 112-1 14
112
R = right product Registry No. Nickel nitrate, 13138-45-9;blue dextran 2000, 9049-32-5; Sephadex G-25, 9041-35-4; Bio-Gel P-2, 60407-73-0.
Literature Cited Cantow, M. J. R.; Porter, R. S.; Johnson, J. F. J . Poly" Sci. Part A-1, 1987, 5 ,987. Chitumbo, K.; Brown, W. J. Chromatogr. 1973, 8 7 , 17. Edwards, V. H.; Helft, J. M. J . Chromatogr. 1970, 4 7 , 490. Flory. P. J. "Principles of Polymer Chemistry"; Cornell University Press: Ithaca and London, 1953; p 579. Morl, S.; Suzuki, T. Anal. Chem. 1980, 52, 1625. Reiland, J. In "Methods in Enzymology", Jakoby, W. E., Ed., Vol. 22; Academic: New York, 1971; p 287.
Rice, R. G. Sep. Purif. Methods 1978, 5 , 139. Yau, W. W.; Kirkland, J. J.; Bly, D. D. "Modern Size Exclusion Liquid Chromatography"; Wiley: New York, 1979. Wankat, P. C. In "Percolation Theory and Apllications", Rodrigues. A. E.; Tondeur, D., Ed.; Sijthoff and Noordhoff: Alphen aan den Rijn, Netherlands, 1981; pp 443-516.
School o f Chemical Engineering P u r d u e University W e s t L a f a y e t t e , Indiana 47907
Yoon-Mo Koo Phillip C. Wankat*
Received f o r review June 15, 1983 Revised manuscript received April 23, 1984 Accepted July 19, 1984
Prediction of Vapor Pressures for Substituted Benzenes by a Group-Contribution Method A new group-contribution method is developed for prediction of vapor pressures of substituted benzenes. Good representation is obtained for vapor pressure data of 48 substituted benzenes in the region 1.33-199.98 kPa. The model may be useful to predict vapor pressures of substituted benzenes for which experimental data are not available.
Introduction Vapor pressures of pure substances are the most important and fundamental physical properties. Recently, the need of vapor pressure data for high-molecular-weight (HMW) hydrocarbons has rapidly increased. However, sufficient experimental data are not available mainly because of experimental difficulties. A method for prediction of vapor pressures for such HMW hydrocarbons is desired. Of the empirical methods, a group-contribution method based on only a limited number of data for such components is chosen as the most suitable approach. This method has wide applicability for predicting the physical properties of pure compounds such as the critical constants (Lydersen, 1955), the standard heat of formation at 25 "C (Verma and Doraiswamy, 1965), the liquid molar volume at 25 "C (Hoshino et al., 1979), the refractive index a t 25 "C (Hoshino et al., 1979), the latent heat of vaporization a t the normal boiling point (Hoshino et al., 1978, 1979), acetric factor of alkanes (Hoshino et al., 1982), and the entropy of vaporization at the normal boiling point (Hoshino et al., 1983). Macknick and Prausnitz (1979) proposed a group-contribution method for determination of two adjustable parameters of the Abrams-Massaldi-Prausnitz (AMP) vapor-pressure equation (Abrams et al., 1974; Macknick et al., 1977) for HMW hydrocarbons such as paraffins, aromatics, and naphthenics. Edwards and Prausnitz (1981) extended it to nitrogen- and sulfur-contaning groups, and Ruzicka (1983) also developed a method for naphthenic 5-membered ring groups and condensed naphthenic groups. In these works, the group contributions were reduced directly from experimental vapor-pressure data in the range 1.33-199.98 kPa. In the present work, the Antoine equation is adopted to predict vapor pressures. It has three adjustable parameters A , B, and C, and they are determined from boiling temperatures at three specified pressures (1.33, 101.32, and 199.98 kPa). The new group-contribution method is developed to calculate the boiling temperatures of substituted benzenes a t specified pressures and, consequently, the parameters of the Antoine equation are determined for each compound. For 48 substituted benzenes (1296 data points), the average error between 0196-4313/85/ 1024-01 12$01.50/0
calculated and experimental vapor pressure is only 3.7%. Proposed Group-Contribution Method The group-contribution method of Macknick and Prausnitz (1979) could not account for the distinction of fine molecular structures such as the position of substituents in substituted benzenes. The present method takes account of such a distinction of substituted benzenes. As pointed out by Macknick and Prausnitz (1979),many kinds of vapor-pressure equations have been derived from the Clapeyron equation coupled with simplifying or semiempirical assumptions. The equations often contain at least three or more adjustable parameters, with no clearly physical significance, and generally it is difficult to analyze these parameters by use of the group-contribution approach. The Antoine equation adopted here also contains three such kinds of parameters, but it has been widely used in vapor pressure predictions in the range of 1.33-199.98 kPa as mentioned by Reid et al. (1977). To resolve its difficulty, a new group-contribution method for the Antoine equation has been developed. Instead of an attempt to calculate Antoine's parameters directly, a new group-contribution method for estimating three boiling temperatures a t three specified pressures has been developed. These pressures are 1.33,101.32, and 199.98 kPa. The pressure of 101.32 kPa is equal to atomospheric pressure and many experimental data of boiling temperatures are available. Pressures of 1.33 kPa and 199.98 kPa are adopted as the applicable limits of the Antoine equation. Substituted benzenes may contain six kinds of functional groups: -CH3, -CH2-, XH-,>C
