Density Programming in Capillary Supercritical Fluid Chromatography

Journal of Chromatographic Science, Vol. 21, May, 1983

Density Programming in Capillary Supercritical Fluid Chromatography J.C. Fjeldsted, W.P. Jackson, P.A. Peaden, and M.L. Lee* Department of Chemistry, Brigham Young University, Provo, Utah 84602

Abstract Various aspects of mobile phase density programming in capillary supercritical fluid chromatography were investigated. Linear pressure programming, linear density programming, and asymptotic density programming were evaluated for the separation of components in a polystyrene oligomer mixture with an average molecular weight of 2000. The asymptotic density program effected elution of oligomers in a homologous series at regular time intervals.

Introduction In the last fifteen years, there has been a growing interest in the field of supercritical fluid chromatography (SFC) because of the need to analyze non-volatile and thermally labile compounds. Polymers represent one class of non-volatile compounds which can be analyzed using SFC. Since a wide molecular weight range of oligomers is usually present in a polymer mixture, pressure programming is necessary in order to both separate and elute all components. Pressure programming is important in achieving the separation of oligomers because of its ability to significantly change the solvating properties of the mobile phase during a chromatographic analysis. The resolution of oligomers in a polymer mixture during pressure programming occurs because higher mobile phase densities are required in order to cause successive members of an oligomer series to dissolve to the same extent. Three important factors which affect the separation of successive oligomers during pressure programming are the shapes of the pressure-density isotherms (1), the sensitivity of successive oligomer solubilities to mobile phase density (2-4), and the column pressure drop (1,5). In past work, problems associated with each of these factors have been overcome by using slow linear pressure programming rates (6,7), large particle column packings (to minimize pressure drops), and high operating temperatures (to make pressure-density isotherms less steep) (1,8). "Author to whom correspondence should be addressed

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The majority of published papers discuss retention in terms of pressure and pressure programming. This is because of the ease with which column inlet and outlet pressures can be measured. However, the retention of solutes in SFC is primarily dependent on mobile phase density. Figure 1 shows the relationship between density and pressure for «-pentane near its critical point. Since density is not directly proportional to pressure near the critical point, linear pressure programming is not preferred for resolving components of mixtures having a wide molecular weight range. In order to study the effects of different density profiles during pressure programming, computer control of the pressure based on pressure-density isotherms of the mobile phase can be used. Under these conditions, density programming is possible. Computer control also allows programming to be performed in a manner to account for the increasing sensitivities of successive oligomer solubilities to the mobile phase density. In this study, a capillary column was used to study the elution of a polystyrene oligomer mixture under different programmed elution conditions. The extremely low pressure gradient along the column allowed the assumption that the entire column was at the same mobile phase density and, therefore, the column pressure drop need not be considered in arriving at an efficient elution program.

Experimental The supercritical fluid chromatograph used in this study has been described elsewhere (9). The mobile phase was delivered by a liquid chromatographic syringe pump (Varian 8500) to the column which was housed in a gas chromatographic oven (Hewlett-Packard 5710). The sample to be analyzed was introduced into the capillary column by means of a 0.2-/*l internal sample volume valve (Valco Instruments) in conjunction with an inlet splitter. The detector was a variable wavelength UV monitor (Kratos SF770). In order to maximize sensitivity, while at the same time preserving efficiency, the outlet end of the 0.1-mm i.d. capillary column was coupled to a larger diameter (0.25-mm i.d.) fused silica capillary which served as the detector flow cell. The capillary column was allowed to pass into the larger diameter fused silica capillary, terminating just

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short of the point of detection to minimize dead volume. The mobile phase linear velocity was initially set at 4 cm s 1 , and the mass flow rate during the chromatographic run was held constant by maintaining a set pressure drop across the column restrictor (40-m x 0.04-mm i.d. glass capillary). Mass flow control was accomplished by regulating a back pressure of nitrogen gas at the outlet of the column restrictor. The computer interface consisted of a multiple channel digitalto-analog converter capable of controlling the pressure of the LC pump reservoir and also the mobile phase flow controller at the outlet of the column. The micro-computer (Apple II Plus with 48K RAM) was interrupt-driven from a quartz time base to ensure accuracy in the time dependence of the software driven elution program. All hardware and software were developed in-house. The capillary column was a 10-mxO.l-mm i.d. fused silica column coated with 50% phenyl methylphenylpolysiloxane polymer which was then free-radical crosslinked to prevent extraction by the supercritical mobile phase (10). Nanograde npentane was used as the mobile phase. The polystyrene standards were supplied by Pressure Chemical, Inc. Since the density of the mobile phase is the primary factor involved in the partitioning of a solute between the stationary and mobile phases in SFC, pressure-density isotherms were calculated (11) at several temperatures for /i-pentane as well as for other mobile phases. From the pressure-density data, nth order polynomial regression analysis gave a satisfactory 6th order polynomial approximating the pressure-density relationship of the mobile phase. Using appropriate software control, any desired density was easily established in the column. Linear pressure, linear density, and asymptotic density programming were investigated. The results of the three elution programs were compared on the basis of resolution of components of an oligomer mixture with an average molecular weight (MW) of 2000.

sum of a constant times the time and the starting density. Inserting this into Equation 3, letting tn represent the elution time for component n, and combining constants, the following equation is obtained: K' n

Fq. 4

In this equation, tn is the elution time for an oligomer containing n monomer units, t^, is the elution time as n — oo, and K ' is a new constant, the value of which is dependent on the density programming rate. This equation predicts that, in linear density programming, successive oligomers will be eluted closer together and all oligomers will be eluted by the time t^. is reached. Figure 2 illustrates that this does indeed occur. If it is desired to have members of a homologous series elute at regular time intervals, n becomes equal to some constant times the sum of the time, t, and a reference time, t'. The reference

70 -i 60 E "c5

_

• 50 ID CC CO 4 0 CO LU CC

0.30

20 10 0.1

0.2 DENSITY - g ml

1 0.3

0.4

Figure 1. Pressure versus density isotherms of n-pentane corresponding to T = 1 . 0 1 (201°C), 1.03 (210°C), 1.05 (220°C), 1.07 (229°C), 1.09 (239°C), and 1.11 (248°C)

Results and Discussion The elution of compounds in a homologous series is described by the equation: In k ' = A + B o n - m n e

Eq. 1

where A, B o , and m are constants, n is the number of monomeric units in the oligomer being eluted, and Q is the mobile phase density (4). From Equation 1, it can be shown that: B0-ITIQ

dn

Eq. 2

mn

Solving for Q and n in Equation 2 results in the expression: Bo m

1 mF 'n

Eq. 3

The value of B 0 /m is simply the convergence density, e a , at which all members of a homologous series coelute. F ' is the constant of integration. When pressure programming is performed in a manner that yields a linear mobile phase density program, Q is equal to the

Figure 2. Linear density programmed elution of 2000 MW polystyrene oligomer mixture on a 10-mx0.1-mm i.d. fused silica capillary column coated and bonded with 50% phenyl methylphenylpolysiloxane stationary phase operated at 210°C with n-pentane carrier at a program rate of 0.002 g c r r r 3 min~ * from a density of 0.10 g c m " 3

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time, t ' , is necessary since no compound can elute before the dead time. It also allows one to start the regular time elution of homologs with values of n >1 earlier in a chromatographic run. With these criteria, Equation 3 can be expressed in terms of time as: K

Eq. 5

t + t'

Both K and t ' determine the spacing and retention of components as they elute. Larger values for K along with larger values for t ' will cause members of a homologous series to elute farther apart. There are two convenient methods for obtaining values for e a . One method (4,5) arises from the relationship: ln« = Bo — mg

min. The result was a 120 min chromatographic run with good spacing of the oligomers. Lengthening the value of t ' , as well as increasing K to maintain the same starting density, yielded increased analysis time and improved resolution while maintaining good oligomer spacing (Figure 4). This can be explained by realizing that each oligomer experienced increased retention with a resulting increase in the number of effective theoretical plates. The higher numbers of effective theoretical plates resulted in better resolution of successive oligomers. By slightly lowering the value set as the asymptotic density to 0.46 g cm ' in the density program, the time of analysis was also lengthened without significant change in the equal spacing of

Eq. 6

By making a few constant density chromatographic runs and plotting lna against the mobile phase density, the density at which « = 1 can be determined. This value of Q, when a= 1, is equal to g a . Equation 5 provides the second means for calculating g a . If the elution density for a series of oligomers is plotted against 1/n in a linear density run, g a is found by extrapolating I/n — 0. This second method was used to determine e a in the work shown here. Table I gives the values of elution densities for oligomers 11 to 34 of a 2000 MW polystyrene standard. Linear least squares curve-fitting of the reciprocal of oligomer chain length versus elution density gave an intercept of 0.467 ± 0.004 g cm ' which corresponds to the density at which all oligomers would coelute. This value correlates well with experimental results. Figure 3 shows the elution of the same polystyrene sample in which the computer was programmed to produce a density ramp according to Equation 5 where e a = 0.480 g cm \ K = 18.0 g cm ' min ', and t ' = 50

i

'

t

TIME - hours

Table 1. Mobile Phase Elution Density for Polystyrene Oligomers Number of

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Monomer Units (n)

1/n

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

0.0909 0.0833 0.0769 0.0714 0.0667 0.0625 0.0588 0.0556 0.0526 0.0500 0.0476 0.0454 0.0434 0.0416 0.0400 0.0384 0.0370 0.0357 0.0344 0.0333 0.0322 0.0312

0.0303 0.0294

Figure 3. Asymptotic density programmed elution according to Equation 5 where t ' = 5 0 min, K=18.0 g cm~ 3 min~ 1 , e a =0.48 g c m " 3 , and initial density = 0.12 g c m " 3 ; otherwise same as Figure 2

Mobile Phase Elution Density (g cm~ 3 ) 0.256 0.267 0.276 0.286 0.295 0.304 0.313 0.322 0.330 0.337 0.344 0.350 0.357 0.362 0.369 0.372 0.376 0.380 0.384 0.388 0.391 0.394 0.397 0.400

i I

Figure 4. Same as Figure 3 with t'=80 min, K=28.8 g cm" 3 mm"1, and ea=0.48 g cm" 3


the eluting oligomers (Figure 5). This demonstrated some latitude in establishing the asymptotic density constant, ga. However, values for e a which differed by more than approximately 0.02 gem" 1 from those calculated failed to maintain uniform spacing of the oligomers throughout the run. Finally, it was of some interest to compare asymptotic density programming to linear pressure programmed elution (Figure 6). Rather large spacing occurred during the first part of the run because of the relatively slow increase in density with increasing pressure at the lower pressure range. Oligomers 10 through 20 eluted closer together because the mobile phase density increased rapidly during this period. The last several peaks were more equally spaced as the compressibility of the supercritical fluid was reduced, resulting in a lower change in mobile phase density with increased pressure. A similar separation was

achieved by Schmitz and Klesper (8) using a 20-cm x4.6-mm i.d. column packed with 10-/im particles. By operating at a higher temperature (240°C) where the pressure-density isotherm is more linear, they obtained an approximate equal spacing of oligomers throughout the chromatogram. These results indicate that density is the controlling factor in the partitioning of solutes between stationary and mobile phases in SFC. In the separation of a homologous series, it is important that a suitable density program be established which accounts for a limiting density where alpha becomes unity.

Acknowledgments This work was supported by the U.S. Department of Energy Grant No. DE-FG22-81PC40809 and by the Gas Research Institute, Contract No. 5081-260-0586. Any opinions, findings, conclusions, or recommendations expressed herein are those of the authors and do not necessarily reflect the views of DOE or GRI.

References

r Figure 5. Same as Figure 3 with t'=50 min, K=17.0 g crrr 3 mirr 1 , and ca=0.46 g crrr 3

Figure 6. Linear pressure programmed elution from 34.6 atm (0.12 g cm"3) at 0.15 atm mirr 1 ; otherwise same as Figure 2

1. J.A. Graham and L.B. Rogers. Effects of column length, particle size, flow rate, and pressure programming rate on resolution in pressure-programmed supercritical fluid chromatography. J. Chromatogr. Sci. 18: 75-84 (1980). 2. J.E. Conaway, J.A. Graham, and L.B. Rogers. Effects of pressure, temperature, adsorbent surface, and mobile phase composition on the supercritical fluid chromatographic fractionation of monodisperse polystyrenes. J. Chromatogr. Sci. 16: 102-10 (1978). 3. L.M. Bowman, Jr., M.N. Myers, and J.C. Giddings. Supercritical fluid (dense gas) chromatography/extraction with linear density programming. Sep. Sci. Technol. 17: 271-87 (1982). 4. P.A. Peaden and M.L. Lee. Supercritical fluid chromatography: methods and principles. J. Liquid Chromatogr. 5: (Suppl. 2): 179-221 (1982). 5. P.A. Peaden and M.L. Lee. Theoretical treatment of resolving power in open tubular supercritical fluid chromatography. J. Chromatogr. 259: 1-16(1983). 6. E. Klesper and W. Hartmann. Apparatus and separations in supercritical fluid chromatography. Eur. Polym. J. 14: 77-88 (1978). 7. J.A. Nieman and L.B. Rogers. Supercritical fluid chromatography applied to the characterization of a siloxane-based gas chromatographic stationary phase. Sep. Sci. 10:517-45 (1975). 8. F.P. Schmitz and E. Klesper. Separation of styrene oligomers by supercritical fluid chromatography (SFC) using a modified HPLC-instrument. Polym. Bull. 5: 603-08 (1981). 9. P.A. Peaden, J.C. Fjeldsted, M.L. Lee, S.R. Springston, and M. Novotny. Instrumental aspects of capillary supercritical fluid chromatography. Anal. Chem. 54: 1090-093 (1982). 10. P.A. Peaden, B.W. Wright, and M.L. Lee. The preparation of nonextractable methylphenylpolysiloxane stationary phases for capillary column gas chromatography. Chromatographia 15: 335-40 (1982). 11. G.N. Lewis and M. Randall. Thermodynamics. McGraw-Hill, New York, 1961, pp. 605-16.

Manuscript received July 21, 1982; revision received December 1, 1982.

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