Computer Simulation of Elution Behavior of Probes in Inverse Gas

chamber, etc. Computer Simulation. Diffusion of the probe in the gas and polymer phases, and adsorption on the support and on the polymer surface (bot...
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Chapter 4

Computer Simulation of Elution Behavior of Probes in Inverse Gas Chromatography Comparison with Experiment Paul Hattam, Qiangguo Du , and Petr Munk

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Department of Chemistry and Center for Polymer Research, University of Texas, Austin, TX 78712 In order to f a c i l i t a t e the analysis of the shape and p o s i t i o n of e l u t i o n curves i n inverse gas chromatography, such curves were generated i n a computer f o r many well-defined s i t u a t i o n s . The e f f e c t s of d i f f u s i o n in the gas phase, of slow d i f f u s i o n in the polymer phase (compared to an instantaneous e q u i l i b r a t i o n of the probe), and of surface adsorption (Langmuir type) were simulated. A set of evaluation guidelines was established and was applied t o several model experiments.

The use of inverse gas chromatography (IGC) to study the properties of polymers has greatly increased i n recent years (1,2). The shape and p o s i t i o n of the e l u t i o n peak contain information about a l l processes that occur i n the column: d i f f u s i o n of the probe i n the gas and the polymer phases, p a r t i t i o n i n g between phases, and adsorption on the surface of the polymer and the support. T r a d i t i o n a l IGC experiments aim a t obtaining symmetrical peaks, which can be analyzed using the van Deemter (_3) or moments method U ) . However, the behavior of the polymer-probe system i s also r e f l e c t e d i n the asymmetry of the peak and i t s t a i l . A method that could be used to analyze a peak of any shape, allowing e l u c i d a t i o n of a l l the processes on the column, would be of great use. I t i s d i f f i c u l t to separate the e f f e c t s of the various processes contributing to the shape and p o s i t i o n of an experimental e l u t i o n peak because, i n most instances, i t i s not obvious which factors are a t play i n any p a r t i c u l a r experiment. Hence, i t i s useful to analyze various models of chromatographic processes t h e o r e t i c a l l y and follow t h e i r e f f e c t on the e l u t i o n peak. However, the d i f f e r e n t i a l equations describing these models Permanent address: Materials Science Institute of Fudan University, Shanghai, People's Republic of China 0097-6156/89/0391-0033$06.00/0 « 1989 American Chemical Society Lloyd et al.; Inverse Gas Chromatography ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

INVERSE GAS C H R O M A T O G R A P H Y

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may be solved a n a l y t i c a l l y only f o r the simplest models. I t i s possible t o cast these d i f f e r e n t i a l equations i n the form of difference equations and follow the development of the system by a computer. This paper reports the results of our computer simulations f o r some simple systems and compares the r e s u l t s with appropriate experimental data. T r a d i t i o n a l Analysis of E l u t i o n Curves The commonly used method of analysis postulates that i d e a l e l u t i o n curves are symmetrical and Gaussian. The time a t the p o s i t i o n of the peak maximum, t , i s a measure of the d i s t r i b u t i o n c o e f f i c i e n t of the probe between the stationary and mobile phases; peak spreading i s expressed by the height equivalent to one t h e o r e t i c a l plate H, which may be written as H = L/N, N being the number of t h e o r e t i c a l plates and L the column length. Furthermore we may write

Downloaded by CORNELL UNIV on October 20, 2016 | http://pubs.acs.org Publication Date: April 24, 1989 | doi: 10.1021/bk-1989-0391.ch004

R

N

P

= (t /W^) R

2

8 In 2

(1)

denotes the peak width a t half height; and subscript P denotes a parameter obtained from peak dimensions. The extended (_5) van Deemter equation (_3) may be written i n a general form as H = A + 2

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A

f

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1

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20

25

30 L0G A Figure 2. Dependence of the f i r s t moment on the amount of probe i n j e c t e d . (A) probe i n j e c t e d as a l i q u i d ; (•) probe injected as a vapor. l0

i l l u s t r a t e s the dependence of t ^ / t ^ and fy/i^ on l o g M ^ j f o r the simulation a t several Z values and with Z = 0. In Figure 3 we present the same dependence f o r the experimental data of acetone ( i n t h i s instance the dependence i s on l o g i Q A , peak area). While the simulation covers an extensive range of concentrations t h i s may not be possible experimentally. Small i n j e c t i o n s are l i m i t e d by the low detector s i g n a l (broad peaks magnifying t h i s e f f e c t ) , while large i n j e c t i o n s are l i m i t e d by non-linear detector response. However, even with the experimental range of concentrations covered, a comparison of the curves i n Figures 1 and 3 i s u s e f u l . I t indicates that the r e s u l t s are i n the region of moderately s i z e d i n j e c t i o n s (for the number of a c t i v e s i t e s on the column). At 100°C Z i s small, aproximately 1 or 2, whereas a t 40 C Z i s greater by an order of magnitude. Although the precise value of Z cannot be determined as the i n j e c t i o n s i z e i s f a r from the l i m i t of i n f i n i t e d i l u t i o n , the value of F^t approaches unity with increasing amount of probe. This trend indicates that the retention i s due to the surface of the support. Overall, the surface simulation and the experimental r e s u l t s compare favorably. Current work i s focused on acquiring more data, both from experiment and from simulation. At t h i s time i t seems l i k e l y that i n the future i t w i l l be possible to determine the capacity of the packing material f o r various probes. This w i l l permit c o r r e c t i o n of probe retention data f o r the e f f e c t of the a c t i v e surface s i t e s on the support. w

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Lloyd et al.; Inverse Gas Chromatography ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

Downloaded by CORNELL UNIV on October 20, 2016 | http://pubs.acs.org Publication Date: April 24, 1989 | doi: 10.1021/bk-1989-0391.ch004

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INVERSE GAS CHROMATOGRAPHY

0

1

2

3

4

L0G A |0

Figure 3. Dependence of t ^ / t ^ (•) and fy/t^ (•) on Log^A, peak area, f o r acetone on an uncoated column a t 40°C and 100°C. Data a t 100 C plotted twice f o r comparison. #

Conclusions The following conclusions were drawn from t h i s research. 1. While the simulations do not predict exactly the r e s u l t s of experiment, they are extremely useful i n predicting behavior trends. 2. The f i r s t moment can be used i n the determination of c h a r a c t e r i s t i c numbers provided c a r e f u l data a c q u i s i t i o n and experimental procedure are followed. Use of higher moments should be handled with great caution. 3. Comparison of the e l u t i o n time a t peak maximum and the f i r s t moment i s extremely informative as to what processes are a f f e c t i n g the retention of the probe. 4. By following the dependence of e l u t i o n parameters on the amount of probe injected, i t i s possible t o d i s t i n g u i s h between surface adsorption and bulk adsorption of the probe. Acknowledgment The authors are g r a t e f u l f o r the f i n a n c i a l support of the National Aeronautics and Space Administration, (Grant No. NAG9-189) and the National Science Foundation, (Grant No. DMR-8414575).

Lloyd et al.; Inverse Gas Chromatography ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

4.

HATTAMETAL.

Computer Simulation of Elution Behavior

Literature Cited. 1. 2. 3. 4. 5.

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6. 7. 8. 9. 10.

Laub, J. R.; Pecsok, R. L. Physicotchemical Applications of Gas Chromatography; Wiley: New York, 1978. Aspler, J. S. I n Pyrolysis and GC i n Polymer Analysis; Chromatographic Science Series, Vol. 29: Liebman, S. A.; E. J. Levy Eds.; Dekker: New York, 1985. Chapter IX. van Deemter, J. J.; Zuderweg, F. J.; Klinkenberg, A. Chem. Eng. Sci. 1956, 5, 271. Vidal-Madjar, C.; Guiochon, G. J . Chromatogr. 1977, 61, 142. Golay, M. J. E. Gas Chromatography;Coates, V. J.; Noebles, H. J.; Fagerson, I. S. Eds.; Academic Press, New York 1958. Munk, P; Card, T. W.; Hattam, P.; El-Hibri, M. J.; Al-Saigh, Z.Y. Macromolecules 1987, 20, 1278. Giddings, J. C. J . Chromatogr. 1961, 5, 49. McQuarrie, M. J . J. Chem. Phys. 1963 38 ,437. Hattam, P.; Munk, P. Macromolecules 1988, 21,2083. McNally, M. E.; Grob, R. L. Amer. Lab. 1985, 17, 106.

RECEIVED November2,1988

Lloyd et al.; Inverse Gas Chromatography ACS Symposium Series; American Chemical Society: Washington, DC, 1989.