Computer Simulation of Elution Behavior of Probes in Inverse Gas

Chapter 4

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

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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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


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

0 -

A

f

*

1

'

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

g

n

p

s

#

s

s

Q

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


44

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).


4.

HATTAMETAL.

Computer Simulation of Elution Behavior

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


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


Computer Simulation of Elution Behavior of Probes in Inverse Gas

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