Chapter
22
Modified Frontal Chromatographic Method for Water Sorption Isotherms of Biological Macromolecules Seymour G. Gilbert Food Science Department, Cook College, Rutgers, The State University, New Brunswick, NJ 08903 The conventional inverse gas chromatography (IGC) i s based on equations that assume equilibrium i s e s t a b l i s h ed during the course of the chromatograph. Consequentl y , those stationary phases that exhibit marked hysteres i s i n sorption/desorption give IGC sorption data at considerable variance with long-term gravimetric methods. A modified f r o n t a l procedure was developed that avoids the assumption of equilibrium to enable studies of interaction k i n e t i c s of gas phase components with a stationary phase, such as a biopolymer, having entropic as well as enthalpic relations affected by concentration s h i f t s and time dependent parameters.
Methods for determining sorption isotherms by gas chromatography have been published by various authors(.1-5.). The methods used have been elution and frontal chromatography. The first combines sorption and desorption so that any hysteresis i n the equilibrium transport from gas to stationary phase and back to the gas phase can produce corresponding e r r o r s . The Kiselev-Yashin equation, as shown i n Figure 1, A = (Mp/m)(x/y) (1) A = p a r t i t i o n i n g/g solute/solvent Mp = mass solute input m • mass solvent x = prepeak area y • peak area does not necessarily correct for non-linear, non-equilibrium chromatography, despite the p a r t i a l cancellation of errors i n desorption by use of prepeak area r a t i o to peak area r a t i o . Since time i s part of the area c a l c u l a t i o n , any d i f f u s i o n a l or other k i n e t i c factors may induce errors (6.). The use of f r o n t a l chromatography would appear to avoid the errors produced by hysteresis i n that the sorption and desorption processes can be separated i n time. An extensive study of t h i s method for water sorption, using freeze-dried coffee as a 0097-6156/89/0391-0306$06.00/0 • 1989 American Chemical Society
22.
GILBERT
Water Sorption Isotherms of Biological Macromolecules
where: A B C X Y h Figure
• • • = « «• 1.
point ol injection point of emergence of unsorbed peak (air) point of emergence of probe peak prepeak area peak area height of peak Illustration
of
Pulse
Analysis.
307
308
INVERSE GAS CHROMATOGRAPHY
stationary substrate, was conducted by Apostolopolous and Gilbert (7.)* and a study on desorption on starch and sugars was conducted by Paik and Gilbert (&). Paik and Gilbert found discrepancies between f r o n t a l IGC for sorption compared to a s t a t i c method that used a long-term water sorption from saturated salt solutions (Figure 2 ) . They also showed that i f a s u f f i c i e n t l y high temperature r i s e was used, following apparent complete desorption, the area formed from the temperature pulse adds the strongly bound water to the eluate to provide a correction factor for the difference between water sorption by the static weighing and dynamic IGC f r o n t a l methods (Figure 3 ) . Apostolopolous and Gilbert (7.) showed that the divergence was greatest at the lowest temperatures and lowest mass absorbed (maximum bound water conditions), and least divergent at high temperature and high mass sorbed. Gilbert (9.) designated the high water content region at low temperature as the clustered water region i d e n t i f i able with free water, but not with c a p i l l a r y water unless solutions of low molecular weight solutes are present. In t h i s case, the cluster integral of Zimm and Lundberg (10) for water-water interactions i s high enough to approach the vapor pressure of pure water as a l i m i t and fugacity equal to 1. At lower water contents, the water vapor pressure i s the sum of the fugacities of water at a l l s i t e s . This sum includes d i f f e r ing enthalpies of the f i r s t water molecule sorbed and that of any clusters of water at such s i t e s . The same fugacity average can be obtained from a number of combinations of the degree of heterogeneity, the frequency d i s t r i b u t i o n of such enthalpies and t o t a l number of such s i t e s per unit of s o l i d phase. Desorption w i l l d i f f e r from sorption i n proportion to the degree and d i s t r i b u t i o n of such heterogeneity of enthalpies since the entropic relations are different i n a s o l i d , depending on the d i r e c t i o n of the concentration gradient as i t affects the k i n e t i c factors of density and d i f f u s i v i t y within the matrix. These considerations are p a r t i c u l a r l y important for non-linear or concentration dependent relations and non-equilibrium condit i o n s , such as those found i n chromatographic systems showing markedly skewed peaks (6.). As these authors have shown, there i s no i d e n t i f i a b l e solution to the problem of the thermodynamic properties of the highly skewed chromatogram peak. Thus, the elution method i s only v a l i d for equilibrium chromatography. B i o l o g i c a l l y derived macromolecules are highly heterogeneous in s i t e d i s t r i b u t i o n from composition differences i n monomers and where amorphous/crystalline regions are present. The differences previously found i n sorption are related to the difference i n equilibrium time for s t a t i c and chromatographic methods ( 8 ) . A method to circumvent t h i s dilemma was sought by Ferng (11). An extensive and detailed study of s t a t i c sorption methodology was first conducted to provide a basis of reproducible data for starches of different macromolecuiar structure. This was followed by studies of sorption isotherms by IGC with different GC conditions including zero loads with empty and supposedly inert support material (diatomaceous earth). The data showed that the response of the thermal conductivity detector (TCD) to controlled chromatographic conditions of temperature, flow rate, and p a r t i a l water vapor
Water Sorption Isotlierms of Biological Macromolecules
22. GILBERT
309
25
4* frontal analysis method 20
•
static aethod
5
10 Partial
15
Pressure
o f Water
25
20 (mmHg)
Figure 2. S o r p t i o n Isotherm o f Corn Starch Determined a t 25°C by S t a t i c Method.
25
4. modified frontal analysis 20
# static method
15
10
5
10 Partial
Pressure
15 o f Water
20 (mmHg)
F i g u r e 3. S o r p t i o n Isotherm o f S t a r c h Determined a t 25°C by M o d i f i e d F r o n t a l A n a l y s i s and F r o n t a l Method.
310
INVERSE GAS CHROMATOGRAPHY
concentration was highly reproducible and linear with mass and temperature. Thus, the area response discrepancies were produced by incomplete e l u t i o n . This conclusion was reinforced by using a pulse of high temperature to desorb the water from sites of high negative enthalpy of binding (Figure 4). Under these conditions, the mass/ area r a t i o (Ka) of eluted solute of empty, blank and substrate loaded columns were equal (Figure 5)• When coated or highly dispersed starch substrates were used to reduce d i f f u s i v i t y e f f e c t s , the mass/area r a t i o of the prepeak region of the chromatogram was equal to that of the peak area i n the low mass region, reaching a plateau with no change i n area as the substrate became saturated for a highly dispersed, freeze dried high amylose starch. When three dimensional p a r t i c l e s were used instead of coatings, the d i f f u s i o n a l and structural k i n e t i c s showed marked d i f f e r ences i n the rates of mass to area i n the concentration dependent regions of p a r t i t i o n c o e f f i c i e n t (lower temperature and mass sorbed). Thus, the fundamental assumption of the Kiselev Yashin equation that the mass/area r a t i o was equal for prepeak and peak regions was not met, and agreement with s t a t i c data was fortuitous at best. The same considerations apply to the prepeak area of the f r o n t a l method. The eluted peak represents the unabsorbed mass, which i s proportional to the integration of the advancing front over e l u t i o n time. However, there i s an error from incomplete e l u t i o n reducing the prepeak area, since the response height was asssumed to be equal to the water vapor pressure i n equilibrium with a s p e c i f i c amount of water i n the s o l i d phase i n the derivat i o n of equation (1). The error then i s proportional to the hysteres i s , since the water i n the s o l i d phase i s equivalent to a higher vapor pressure i f equilibrium has been attained. A mass balance approach was developed that used a defined input mass with the non sorbed water mass calculated from the front peak area and sorption by difference (12). This produced agreement at the lower concentration stage of the isotherm since the uneluted mass was accounted f o r . The d i f f i c u l t y was that a large number of mass increments was required to determine a strong non-linear (for example, sigmoid) isotherm. This increased the operating time and complexity of the method, as did the Paik and Gilbert procedure (.8). Since the product of flow rate, time and concentration equal the input mass, a constant input concentration permits the c a l c u l a tion of mass from either time or retention volume. Empty columns provide an e s s e n t i a l l y constant r a t i o of input mass to time at constant flow rate with the concentration of water vapor fixed by the temperature of the c a r r i e r gas saturated with water vapor (100% RH or Aw of 1 see Figure 6 ) . This state can be achieved with substrates that do not dissolve i n water when saturated (for example, starches and many proteins), or when the r e l a t i v e humidity i s constant but i n s u f f i c i e n t to allow uptake to produce a highly multilayered or clustered water state i n the substrate equivalent to a continuous water phase or solution. This condition requires a source of humidified gas as i n (7.)* The sorption isotherm equation is then given by A - (tcKt - Yc Ka)/m (2)
22. GILBERT
Water Sorption Isotherms of Biological Macromolecules
Injected Amount vs Peok Area (50cc/min)
15 -i
0
311
2
4
6 •
8
Injected Amount (ul) Empty A
10
12
14
16
Blank
C a l i b r a t i o n curve o f water a t d i f f e r e n t i n j e c t i o n amounts v e r s u s peak area from empty and blank column a t 30°C. Figure
4.
C o n c e n t r a t i o n P r o f i l e Formed During Modified
Frontal
IGC.
Operation
of
312
INVERSE GAS CHROMATOGRAPHY
22. GILBERT
Water Sorption Isotherms ofBiological Macromolecules
313
314
INVERSE GAS CHROMATOGRAPHY
G«i«
Chromatography
| Amplifier
j
1
IBI1 PC/XT I AO/OA C o n v e r t e r
T
L»b Not(Book J
L
r
Disk D r i v e
I Lotus 1 - 2 - 3 J
II
Color Graphic Adaptor! I Input/Output Card
Color Graphic Monitor
j Plotter"^
| Prlntor j
Figure 7. Block Diagram of Data Acquisition System.
22. GILBERT
Water Sorption Isotherms of Biological Macromolecules
315
316
INVERSE GAS CHROMATOGRAPHY
(hc/ho)Po o r (he/ho) = Aw (mass/area) c o n s t a n t (mass/time) c o n s t a n t time a t d e f i n e d h e i g h t he • f ( P l ) a r e a o f peak a t t c water vapor p r e s s u r e a t t c maximum h e i g h t a t s a t u r a t i o n = f ( P o ) s a t u r a t i o n vapor p r e s s u r e o f water equilibrium vapor p r e s s u r e a t a s p e c i f i c water c o n t e n t i n t h e s o l i d phase he = response h e i g h t a t a s p e c i f i c f r o n t a l t i m e , t c , and peak a r e a , Y c . A = mass o f sorbed s o l u t e (water) i n s t a t i o n a r y phase a t time, t c . When h y s t e r e s i s produces a water vapor p r e s s u r e (Pd) f o r d e s o r p t i o n a t a s p e c i f i c mass ( A ) , which i s g r e a t e r than t h e o b s e r v ed P c , t h e peak a r e a c a l c u l a t e d by t h e above e q u a t i o n r e p r e s e n t s an a r e a d i f f e r e n c e p r o p o r t i o n a l t o ( P d - P c ) t c . The t o t a l mass e n t e r e d i n t o t h e column a t t c i s t h e p r o d u c t t c K t , which i n c r e a s e s t o t h e s a t u r a t e d s t a t e response a t s a t u r a t i o n o r Aw=l. The d i f f e r e n c e between t h i s t o t a l mass and t h a t r e l a t e d t o t h e e l u t e d peak a r e a i s g i v e n above as t h e mass o f water sorbed a t P c . The a c q u i s i t i o n and m a n i p u l a t i o n o f t h e m o d i f i e d frontal chromatogram i s f a c i l i t a t e d by i n t e r f a c i n g t h e GC system response t o a n a p p r o p r i a t e computer system t h a t p r o v i d e s h i g h speed s t o r a g e and i n t e g r a t i o n o f d a t a from t h e d e t e c t o r . An a p p r o p r i a t e s e t o f a l g o r i t h m s a l l o w f o r c o n v e r s i o n o f t h e raw d a t a i n t o s o r p t i o n i s o t h e r m s w i t h f u r t h e r c a l c u l a t i o n o f t h e a p p r o p r i a t e thermodyna m i c s and c l u s t e r d i s t r i b u t i o n f u n c t i o n s ( F i g u r e 7 ) . C a l c u l a t i o n o f c u r v e - f i t t i n g constants permit s t a t i s t i c a l e v a l u a t i o n o f complex i s o t h e r m s by d e t e r m i n i n g t h e v a r i a n c e o f such c o n s t a n t s (11 and 12). A complete s o r p t i o n i s o t h e r m i s o b t a i n e d w i t h i n two hours w i t h t h i s c o m b i n a t i o n o f GC and m i c r o p r o c e s s o r . I f t h e s u b s t r a t e i s s t a b l e under t h e GC c o n d i t i o n s , a f a m i l y o f i s o t h e r m s c a n be p r o d u c ed w i t h i n two days o r w i t h i n one i f automated t o o p e r a t e on a 24-hour day. A r e p r e s e n - t a t i v e chromatogram i s shown i n F i g u r e 8. K i n e t i c f a c t o r s can be p r e s e n t and dominate s o r p t i o n r a t e ( d e s o r p t i o n o f c r y s t a l s t r u c t u r e , c h a i n f o l d i n g o r u n f o l d i n g , and s t r u c t u r a l s h i f t s on s w e l l i n g ) . I n such cases t h e d i s c r e p a n c i e s between s t a t i c and IGC methods r e f l e c t t h e t i m e - r e l a t e d d i f f e r e n c e and n o t c o n c e n t r a t i o n dependency o f t h e i s o t h e r m ( 1 3 ) . The s u g g e s t ed procedure w i l l n o t r e s o l v e such d i f f e r e n c e s u n l e s s s u f f i c i e n t l y low f l o w r a t e s a r e u s e d . These d i s c r e p a n c i e s a r e o f g r e a t impor tance i n t i m e - r e l a t e d s t u d i e s , i n c l u d i n g storage l i f e s t a b i l i t y under d i f f e r e n t e n v i r o n m e n t s , as p r o v i d e d by p a c k a g i n g systems o f d i f f e r e n t p e r m e a b i l i t y t o water v a p o r . Some o f t h e p o s s i b l e a p p l i c a t i o n s o f t h i s new method were d i s c u s s e d i n another s t u d y ( 1 4 ) . where:
Pc Ka Kt tc Yc Pc ho Po PI
= » = • = • • =
Acknowledgment s Paper number D-10535-8-88 o f t h e J o u r n a l S e r i e s , New J e r s e y A g r i c u l t u r a l Experiment S t a t i o n , Cook C o l l e g e , Rutgers The S t a t e U n i v e r s i t y , Department o f Food S c i e n c e , New B r u n s w i c k , New J e r s e y
22.
GILBERT
Water Sorption Isotherms of Biological Macromolecules
317
08903. T h i s work was s u p p o r t e d i n p a r t by S t a t e funds and t h e Center f o r Advanced Food Technology (CAFT), a New J e r s e y Commission on S c i e n c e and Technology C e n t e r . Literature Cited 1. Gregg, S.J.; Stock R. (1958). In Gas Chromatography D.H. Desty, Ed. pg. 90, Butterworth, London. 2. Conder, J.R.; Purnell J.H. Trans. Faraday Soc. 1969, 65. 824848. 3. Eberly, P. E. Jr. J. Phys. Chem. 1961, 65, 1261-1265. 4. Kiselev, A.Y.; Yashin Ya.I. (1969). "Gas Adsorption Chromatography." Plenum Press, New York. 5. Gray, D.G.; G u i l l e t , J.E. Macromolecules 1972 ,5, 1972, 316320. 6. Conder J.R.; McHale, S.; Jones, M.A. Analyt. Chem. 1986, 58, 2663. 7. Apostolopoulos, D.; Gilbert, S.G. (1984). Instrumental Analysis of Foods. Vol 2. G. Charalombous and G. Inglett, eds. Academic Press. New York. 8. Paik, S.W.; G i l b e r t , S.G. J. Chromatography. 1986, 351-417. 9. G i l b e r t , S.G. i n The Shelf L i f e of Foods and Beverages, ed. G. Charalambous. Elsevier Science Publishers B. V.,Amsterdam. 10. Zimm, B.H.; Lundberg, J.L. J. Phys. Chem. 1956, 60, 425-428. 11. Ferng A.L. (1987). A study of Water Sorption of Corn Starch from Various Genotypes by Gravimetric and Inverse Gas Chromatographic Method, Ph.D. Thesis. Rutgers University. New Brunswick, New Jersey. 12. G i l b e r t , S.G.; Ferng, A.L. 1987. New method for Sorption Isotherms by Gas Chromatography. 47th Annual IFT Meeting Las Vegas, Nevada. 13. Il, Barbara; Daun, H.; G i l b e r t , S.G. 1987. Water Sorption of G l i a d i n . J . Food Science, paper i n preparation. 14. G i l b e r t , S.G. 1988. Applications f o r Research i n Kinetic and Thermodynamic Problems i n Food Science. ACS Symposium, Toronto, Canada. R E C E I V E D December5,1988
