Mass Spectrometric Inverse Gas Chromatography: Investigation of

The result is a single continuous chromatogram for each probe solute over a range of temperatures encompassing the glass transition temperature, Tg. S...
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Anal. Chem. 1997, 69, 2485-2495

Mass Spectrometric Inverse Gas Chromatography: Investigation of Polymeric Phase Transitions S. Panda, Q. Bu, B. Huang, R. R. Edwards, Q. Liao, K. S. Yun, and J. F. Parcher*

Chemistry Department, University of Mississippi, University, Mississippi 38677

An improved inverse gas chromatographic method involving the use of a mass-specific detector for the determination of the glass transition temperature of polymeric materials is described. The new method allows the use of several probe solutes simultaneously with an automated, closed-loop injector and stepped temperature programming. The result is a single continuous chromatogram for each probe solute over a range of temperatures encompassing the glass transition temperature, Tg. Several different methods for the exact determination of Tg from the chromatogram were investigated, including the classical van’t Hoff-type plots with retention volumes calculated from both the peak maximum and first moment values of the elution peaks. Two new methods are also proposed for the evaluation of Tg from either the temperature dependence of the second moments of the elution peaks for probe solutes or simple inspection of the variation of elution peak height (width) with temperature. All four methods for the determination of Tg are evaluated with three probe solutes and four different polymers, viz., poly(methyl methacrylate), poly(ethylene terephthalate), polycarbonate, and two batches of polystyrene with different molecular weights and Tg values. Three phenomenological models were used to interpret the chromatographic retention mechanisms of the solute probes in glassy and rubbery polymers. These are (i) the classical adsorption/absorption model for glass and rubber polymers, (ii) the single absorption mechanism model, and (iii) a dual-mode model previously used to explain the sorption of gases, such as CO2, in glassy polymers. It is concluded that no single approach is adequate to interpret the experimental results for all of the systems, although each model is adequate for some individual solute/ polymer combinations. The onset of segmental motion in a polymer with increasing temperature often gives rise to a glassfrubber transition characterized by a glass transition temperature, Tg. Glass transition temperatures can be altered and manipulated by the use of polymer blends or plasticizers including liquids, soluble vapors, or compressible fluids, such as CO2. Such experimental manipulation has many technological implications and commercial applications. Control and manipulation of the glass transition temperature of polymers has become significant in such areas as the separation and fractionation of polymers, polymer fabrication, impregnation of polymers with additives and removal of unwanted impurities. However, practical measurement of the glass transition temperature of polymers plasticized with a low molecular weight, S0003-2700(96)00848-7 CCC: $14.00

© 1997 American Chemical Society

perhaps volatile, component is experimentally difficult yet critically important to the development of novel polymeric materials with well-controlled physical and chemical properties. There are several different experimental approaches to the detection of a glass transition in polymeric media. These include the classical calorimetric methods, spectroscopic techniques, elastic modulus measurements and chromatographic techniques. Each of these methods has unique advantages as well as concomitant disadvantages; however, the use of volatile liquids or compressible fluids as plasticizers severely restricts the choice of experimental techniques for measuring Tg. Nevertheless, one of the calorimetric methods, differential scanning calorimetry (DSC) has been used to estimate the effect of dissolved CO2 on the glass transition temperature of poly(methyl methacrylate).1 Also, an elastic modulus method, viz., creep compliance, has been used2,3 to determine the glass transition temperature of a polymer as a function of the pressure of carbon dioxide in contact with the polymer. Ideally, when volatile plasticizers are used, the exact composition of the diluent-polymer mixture should be determined in order to provide a correlation between the glass transition temperature and the composition of such mixtures. However, no classical experimental method has yet been developed which can simultaneously measure both the uptake of a diluent by a polymer and the effect of such sorption on Tg. To date, no chromatographic method has been applied to the measurement and investigation of such complex, multicomponent polymer systems. Some chromatographic methods, in particular inverse gas chromatography (IGC),4-6 have been shown to provide accurate information about the phase transitions of pure polymers7-11 as well as the degree of crystallinity,8,12,13 molecular diffusion coefficients,14-21 and the strength of molecular interactions.22-25 (1) Chiou, J. S.; Barlow, J. W.; Paul, D. R. J. Appl. Polym. Sci. 1985, 30, 26332642. (2) Condo, P. D.; Paul, D. R.; Johnston, K. P. Macromolecules 1994, 27, 365371. (3) Condo, P. D.; Johnston, K. P. J. Polym. Sci., Polym. Phys. Ed. 1994, 32, 523-533. (4) Conder, J. R.; Young, C. L. Physicochemical Measurement by Gas Chromatography; John Wiley & Sons Ltd.: New York, 1979. (5) Inverse Gas Chromatography; Lloyd, D. R., et al., Eds.; ACS Symposium Series 391: American Chemical Society: Washington, DC, 1989. (6) Munk, P. In Macromolecules 1992; Kahovec, J., Ed.; VSP-BH: Zeist, The Netherlands, 1993; pp 185-206. (7) Braun, J. M.; Lavoie, A.; Guillet, J. E. Macromolecules 1975, 8, 311-315. (8) Braun, J. M.; Guillet, J. E. Macromolecules 1977, 10, 101-106. (9) Braun, J. M.; Guillet, J. E. Macromolecules 1976, 9, 340-344. (10) Braun, J. M.; Guillet, J. E. Macromolecules 1975, 8, 882-888. (11) Deshpande, D. D.; Tyagi, O. S. Macromolecules 1978, 11, 746-751. (12) Guillet, J. E.; Stein, A. N. Macromolecules 1970, 3, 102-105. (13) Dexi, W.; et al. Chem. Mater. 1989, 1, 357-362. (14) Hattam, P.; Munk, P. Macromolecules 1988, 21, 2083-2090.

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The chromatographic methods have the advantages of speed, simplicity, and (with a mass-specific detection system) solute specificity.26 Probably the greatest advantage of the chromatographic approach, however, is the ability to investigate solute/ polymer mixtures with the solute present at infinite dilution, i.e., with essentially pure polymer. Unfortunately, however, there are several fundamental problems and experimental uncertainties in the current IGC methodology that must be addressed. The significant weak points of IGC include both the uncertainty of retention mechanism(s) and assumptions regarding the thermodynamic validity of commonly used chromatographic retention parameters at temperatures close to or below Tg. The latter problem is evidenced by an experimentally observed flow rate dependence of the specific retention volume measured from the retention time of the maximum point of an elution peak at temperatures close to Tg.10,11,20,24,27,28 This combination of multiple retention mechanisms and uncertain equilibrium conditions means that the results obtained from a given IGC experiment may depend on the chemical and physical properties of the probe solute as well as those of the polymer.9,29-31 In addition to these fundamental problems, further experimental and mathematical problems exist as well. The experimental problems include the preparation of a packed or capillary GC column with a precisely known amount of polymer as the stationary phase. Another difficulty is the “batch mode” method of operation in which a single solute is studied at one temperature to produce one retention volume datum. This requirement is often imposed by the nonspecific detectors, e.g., FID or TCD, commonly used for IGC experiments. Data analysis also presents some unique problems because of the indirect nature of the IGC experiment. That is, changes in the polymer morphology are detected only by their secondary effect on the solubility and/or diffusion of a volatile probe solute in a given polymer. The experimentally observed changes in probe retention with temperature are often ill-defined and may vary for different solutes, and the experimental elution peaks are often asymmetric, thus augmenting the difficulties of generating valid thermodynamic information. Asymmetric elution peaks for infinite dilution probe solutes are characteristic of polymeric stationary phases which are in or close to their glassy states. In this case, the maximum point on an elution peak may not be an accurate measure of the first moment of that peak, and it is the first moment that is the (15) Xie, L. Q. Polymer 1993, 34, 4579-4584. (16) Romansky, M.; Guillet, J. E. Polymer 1994, 35, 584-589. (17) Pawlisch, C. A.; Macris, A.; Laurence, R. L. Macromolecules 1987, 20, 15641578. (18) Romdhane, I. H.; Danner, R. P.; Duda, J. L. Ind. Eng. Chem. Res. 1995, 34, 2833-2840. (19) Arnould, D.; Laurence, R. L. Ind. Eng. Chem. Res. 1992, 31, 218-228. (20) Qin, R. Y.; Schreiber, H. P. Langmuir 1994, 10, 4153-4156. (21) Faridi, N.; Duda, J. L.; Danner, R. P. Rubber Chem. Technol. 1996, 69, 234244. (22) Du, Q.; Hattam, P.; Munk, P. J. Chem. Eng. Data 1990, 35, 367-371. (23) El-Hibri, M. J.; Cheng, W.; Munk, P. Macromolecules 1988, 21, 3458-3463. (24) Lichtenthaler, R. N.; Liu, D. D.; Prausnitz J. M. Macromolecules 1974, 7, 565-570. (25) Smidsrod, O.; Guillet, J. E. Macromolecules 1969, 2, 272-277. (26) Parcher, J. F.; Bell, M. L.; Lin, P. J. In Advances in Chromatography; Giddings, J. C., Ed.; Marcel Dekker: New York, 1984. (27) Tyagi, O. S.; Deshpande, D. D. J. Appl. Polym. Sci. 1987, 34, 2377-2388. (28) Mukhopadhyay, P.; Schreiber, H. P. Macromolecules 1993, 26, 6391-6396. (29) Etxeberria, A.; et al. Macromolecules 1995, 28, 7188-7195. (30) Olabisi, O. Macromolecules 1975, 8, 316-322. (31) Robard, A.; Patterson, D. Macromolecules 1977, 10, 1021-1025.

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thermodynamically valid parameter. For example, in 1989, Wang and Charlet32 suggested that the classical S-shaped van’t Hoff plots commonly used to determine the glass transition temperature from IGC data were artifacts caused by the use of peak maximum retention times rather than first moment values. Their work showed that a plot of ln Vg0 vs 1/T was linear and independent of flow rate for chloroform with polystyrene if the specific retention volume, Vg0, was calculated from the first moment rather than the peak maximum. In that case, the van’t Hoff plot no longer would serve as a viable tool for the determination of Tg. Their results suggested a single absorption mechanism for both the glassy and rubbery polymer, and thus the classical dual (absorption/adsorption) retention mechanism model was of questionable validity, at least for this particular system. However, these authors also suggested that the temperature dependence of the second moment of the elution peaks could be used to distinguish a polymer in a glassy state from that in a rubbery state. This observation could form the basis for the estimation of Tg from second moment data for systems which do not show a sharp transition in the reciprocal temperature van’t Hoff-type plots. Unfortunately, the application of statistical moment analysis in IGC studies is extremely difficult and uncertain because of the myriad problems encountered in the measurement of the first and especially the second moments of asymmetric chromatographic peaks.33-36 The present investigation was designed to develop an improved experimental procedure for the IGC determination of glass transition temperatures by directly addressing some of the problems cited previously. The described method involves the use of (i) an off-line vapor injector for repetitive, automated injections of probe solutes, (ii) a mass-specific detection system to allow the use of multiple probes in a single experiment, (iii) stepped temperature programming operation to produce a single chromatogram for an IGC experiment over a broad temperature range, i.e., to eliminate batch mode operations, and (iv) information regarding the shape of elution peaks as well as the specific retention volume to determine the exact Tg value for a given polymer. The proposed technique is designed specifically to allow the determination of glass transition temperatures for plasticized polymers in which the plasticizing agent is a volatile liquid or supercritical fluid. EXPERIMENTAL SECTION Materials. The IGC instrumentation and injection system are shown in Figure 1, where the closed-loop injector37 is shown in bold. Briefly, the off-line injector was operated as follows: the isolation valve (9) was switched to allow a gas to sweep the injector loop; the loop was then filled with a gas, such as neon, which served as a dead timer marker; the isolation valve was returned to the position shown in the figure (9) to form a closed loop; and then a mixture of probe solutes in liquid form was injected into the packed column injection port (10) and vaporized at 250 °C in the valve oven (12). The closed loop then acted as a sample reservoir for subsequent injections from the gas sampling valve (11). The capillary injection port for the mass detector (5), (32) Wang, J. Y.; Charlet, G. Macromolecules 1989, 22, 3781-3788. (33) Yau, W. W.; Kirkland, J. J. J. Chromatogr. 1991, 556, 111-118. (34) Yau, W. W.; et al. J. Chromatogr. 1993, 630, 69-77. (35) Anderson, D. J.; Walters, R. R. J. Chromatogr. Sci. 1984, 22, 353-359. (36) Foley, J. P.; Dorsey, J. G. Anal. Chem. 1983, 55, 730-737. (37) Panda, S.; et al. J. Chromatogr. 1995, 715, 279-285.

Figure 1. Mass spectrometric IGC instrumentation. 1, Carrier gas (He); 2, instrument flow controller; 3, flow regulator; 4, pressure sensor; 5, capillary injector; 6, electronic pressure controller; 7, vent; 8, sweep gas (Ne); 9, isolation valve (closed position); 9′, isolation valve (sweep mode); 10, analytical column injector; 11, gas sampling valve (load); 11′, gas sampling valve (injection mode); 12, valve oven; 13, analytical column; 14, fused silica tube; 15, GC oven; 16, mass-specific detector. Table 1. Structure and Physical Properties of the Polymers polymer

average MW

Tg (°C)

polystyrene

190 000

11038

structure of repeat unit CH2 CH

polystyrene (low MW) poly(methyl methacrylate)

50 000 100 000

65 10538

CH3 C CH3 COOCH3

polycarbonate resin

64 000

15039

CH3 O

C

O O C

CH3

poly(ethylene terephthalate)

18 000

8139 O CH2CH2

capillary column (14), and mass-specific detector were part of a commercial GC/MS system, viz., a Hewlett Packard 5971A MSD instrument. The MSD capillary column was replaced by an empty 200 µm i.d. fused silica tube which acted only as a transfer line for the solutes from the packed column to the detector. The packed column injection port, packed column, isolation and gas sampling valves, pressure sensors, and flow controllers were added to the instrument. Flow into the MSD was controlled via the normal inlet splitter (5) and electronic pressure controller of the GC/MS system. The MSD was operated in the selected ion monitor mode to enhance sensitivity and allow the use of truly infinite dilution samples. The MSD also allowed the determination of accurate retention times of multiple probe solutes, even when the solutes were not chromatographically resolved, which was often the case at higher temperatures. The IGC experiments were carried out in a stepped mode by maintaining the temperature of the GC oven (15) containing the packed column constant for a certain period of time to allow an injected peak to elute. After elution of the peak, the temperature

O

O

O

C

C

was quickly ramped before the next injection. The molar flow rate of the carrier gas was maintained constant throughout any run by the flow regulators. The volumetric flow rate at column conditions varied with the column temperature and pressure during a stepped temperature-programmed experiment. The volumetric flow rates were calculated from the ideal gas law for the helium carrier gas. Neon was used as a dead time marker. The polymers used for this investigation, shown in Table 1, were polystyrene and poly(methyl methacrylate), supplied by Polysciences, Inc., and poly(ethylene terephthalate) and polycarbonate, supplied by Aldrich. The molecular weights listed are Mw values. The glass transition temperature for the low molecular weight polystyrene was determined by differential scanning calorimetry. The Tg values for the other polymers were taken from the cited references. (38) Bovey, F. A. Macromolecules: An Introduction to Polymer Science; Academic Press: New York, 1979. (39) Aldrich Catalog/Handbook of Fine Chemicals; Aldrich Chemical Co., Inc.: Milwaukee, WI, 1996.

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The chromatographic columns were prepared by dissolving the pure polymers in a suitable solvent, mixing with DMCS-treated Chromosorb W, and subsequently evaporating off the solvent. The stationary phase was packed in 1/4 in. o.d. copper columns. The percent coating was determined by combustion of the polymer from the solid support. The polymer loadings varied from 3 to 13%. Calculations. The first and second statistical moments of the elution peaks, µ1 and µ2, respectively, were calculated from the detector response, h(t) as a function of time, t, by the equations

µ1 )

∑th(t) ∆t ∑h(t) ∆t

∑(t - µ ) h(t) ∆t ) ∑h(t) ∆t

(1)

2

µ2

1

(2)

The GC/MS system was operated in a selected ion monitor mode with a cycle time, ∆t, of 100-200 ms. Thus, for a typical elution peak with a width of 30 s, the number of data points used for the moment calculations would be in the range of several hundred. Theoretical Models. There are two principal models for the interpretation of the chromatographic retention data of probe solutes with polymers in the glass and rubber states. The primary difference between the models is the relative significance of the role of adsorption on the bulk surface or on the inner surface of microvoids within the polymer in the postulated retention mechanism for the probe solutes. The earliest and most commonly accepted model10,11,40-44 posits absorption (partition) as the dominant retention mechanism for temperatures above Tg but surface adsorption as the primary retention process at lower temperatures. The change in retention mechanism is manifest as an abrupt change of slope in a plot of retention volume vs reciprocal temperature, i.e., a van’t Hoff-type plot. The glass transition temperature is taken as the temperature at which the retention data first show a deviation from linearity at temperatures below Tg.7,10,28,42 The peak asymmetry observed for solutes adsorbed on glassy polymers can probably be attributed to nonlinear adsorption isotherms or slow adsorption kinetics. This model has been discussed extensively in the literature and used successfully to interpret many published IGC investigations of polymeric materials. Recently, however, an alternative, but not necessarily contradictory, theory has been used to interpret certain systems. This model14,45,46 postulates a single absorption process (retention mechanism) for polymers in both glassy and rubbery states. As mentioned previously, several authors18,32 have suggested that the classical S-shaped form of the van’t Hoff plots for polymers in the region of a glassTrubber transition is an artifact caused by the use of the retention time of the maximum point of an elution peak (40) Guillet, J.; et al. In Inverse Gas Chromatography; Lloyd, D., et al., Eds.; American Chemical Society: Washington, DC, 1989; pp 20-32. (41) Braun, J. M.; Guillet, J. E. Macromolecules 1976, 9, 617-621. (42) Braun, J. M.; Guillet, J. E. J. Polym. Sci., Polym. Chem. Ed. 1976, 14, 10731081. (43) Courval, G. J.; Gray, D. G. Macromolecules 1975, 8, 916-920. (44) Courval, G.; Gray, D. G. Macromolecules 1975, 8, 326-331. (45) Pawlisch, C. A.; Bric, J. R.; Laurence, R. L. Macromolecules 1988, 21, 16851698. (46) Edwards, T. J.; Newman, J. Macromolecules 1977, 10, 609-615.

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for the calculation of retention volumes. These authors showed that van’t Hoff plots are linear for some probe solutes with polystyrene over a wide temperature range encompassing Tg if the retention volumes were calculated from the first moment of the elution peak rather than from the peak maximum. A linear van’t Hoff plot for a polymer in both glassy and rubbery states would indicate a single retention mechanism. The observed peak asymmetry for solutes partitioning in the glassy polymer is purportedly caused by slow diffusion processes within the bulk of the polymer. Along with these two chromatographic models, a dual-mode sorption model has been proposed47-49 to account for the unusual sorption behavior of light gases in glassy polymers. This model postulates that the sorption of gases in glassy polymers consists of two separate contributions. One is simple dissolution of the gases in the polymer described by Henry’s law. The other is adsorption of the gases on the inner surface of microvoids (hole free volume) within the polymer. Such adsorption can be described by the Langmuir equation. The overall uptake of the gas at any pressure and temperature (below Tg) is the sum of the two independent mechanisms. At temperatures above Tg, the adsorption mechanism diminishes, and Henry’s law behavior is observed. The experimental results reported in the current investigation will be used to assess the validity and applicability of these three theoretical models to each of the particular systems studied herein. RESULTS AND DISCUSSION To minimize the time required for a complete IGC experiment covering a range of temperatures, probe solutes which eluted very rapidly were selected. Thus, overlapping chromatographic peaks were frequently observed, and a mass specific detector was required. The mass resolution of chromatographically unresolved elution peaks is illustrated in Figure 2 for two probe solutes (pentane and isooctane) and a dead time marker (neon). Part A of Figure 2 depicts the response obtained from the MSD, while parts B and C show the responses that would have been obtained with flame ionization and thermal conductivity detectors, respectively. Four polymers were selected for investigation because they had glass transitions in the experimentally accessible range and were otherwise suitable for chromatographic studies. Three solute probes, chloroform, benzene, and decane, were used to cover a range of chemical types and solvent strength for the applicable polymers. A typical chromatogram is shown in Figure 3, which also illustrates the temperature programming technique for both negative and positive 10 °C steps. The stepped lines in the figure illustrate the temperature increments, referenced to the right-hand scale, and the time intervals used for the experiment. These particular experiments were carried out to determine whether or not there were any hysteresis effects that could influence the chromatographic results. Such hysteresis had been observed with continuous programming techniques. The chromatogram shown in Figure 3 has a unique pattern of peak heights even though the amount of solute injected at each temperature, and thus the peak area, was essentially constant, (47) Barrer, R. M.; Barrie, J.; Slater, J. J. Polym. Sci. 1958, 27, 177-197. (48) Kamiya, Y.; et al. J. Polym. Sci., Polym. Phys. Ed. 1986, 24, 535-547. (49) Kamiya, Y.; et al. J. Polym. Sci., Polym. Phys. Ed. 1989, 27, 879-892.

Figure 3. Chromatograms for repetitive injections of n-decane with polystyrene. Top panel, temperature increments of -10 °C; bottom panel, temperature increments of +10 °C.

Figure 2. Comparison of MSD selected ion response (A) to the hypothetical response for flame ionization (B) and thermal conductivity (C) detectors.

with only a slight (∼3%) loss per injection due to dilution of the sample reservoir with carrier gas.37 Significantly, the elution peak heights do not reflect this constant loss; instead, there is a local maximum in the peak heights at an intermediate temperature close to 100 °C for both temperature programming directions. The heights of the elution peaks are controlled by the peak dispersion mechanisms operative in a given system; however, the classical method for the chromatographic determination of Tg is based on a measure of the retention of a solute, not peak dispersion. The retention data are usually reported in the form of a van’t Hoff-type plot of the log of the specific retention volume vs the reciprocal temperature, and Tg is determined graphically as the first point of deviation from linearity in the plot at low temperatures, i.e., at temperatures where the polymer is in a glassy state. The specific retention volumes can be calculated from retention times measured at the maximum point of the elution curves or from the calculated first moment of the peaks. These two parameters will give different retention volumes for elution peaks which are asymmetric, such as those observed for most solutes with glassy polymers. The results for these calculations with one solute, benzene, and four different polymers are shown in Figure 4. This figure illustrates some of the basic difficulties with IGC investigations of polymers, because each of the van’t Hoff plots is distinct from the others. As previously observed by Wang and Charlet32 for chloroform, the first moment plots for benzene with both batches of polystyrene are linear and distinct from the peak maximum plots. On the other hand, neither of

those observations is true for the other three polymers. Thus, the statement by Wang and Charlet32 that S-shaped van’t Hoff plots are an artifact caused by the use of peak maxima retention volumes rather than first moment seems to hold for only a single polymer, polystyrene. For PMMA, both plots are nonlinear; for PET, the first moment plot is nonlinear, while the peak maxima plot is linear; and for PCR, the first moment and peak maxima are equivalent, and the plots are linear with a very obvious change in slope at Tg. In every case, the first moment and peak maxima data coincide at high temperatures, where the polymer is a rubber. The van’t Hoff plots for chloroform with the four polymers were identical in shape with those for benzene. Thus, only the experimental results for benzene will be discussed herein. Benzene and chloroform are relatively good solvents for most of the polymers. Completely different results are observed, however, for the van’t Hoff plots for different probe solutes, such as n-decane, which is not a good solvent for any of the polymers. The results for this probe solute are shown in Figure 5. In this case, the plots for polystyrene are both nonlinear with the classical S-shape. The same is true for PMMA; however, in this case, the two plots coincide for temperatures where the polymer is a glass, and the same is true for PET. PCR shows coincidence at high temperatures, with a linear but broken first moment plot and an S-shaped peak maxima plot. Linear van’t Hoff plots indicate that a single retention mechanism, usually partition, is dominant, whereas an S-shaped plot indicates that multiple, concurrent mechanisms, such as adsorption and absorption, exist and the relative significance of the contribution to retention of each mechanism depends on the temperature. This lack of consistency has proven to be a major problem for the determination of Tg from chromatographic retention data. The commonly accepted method for determining Tg for van’t Hoff Analytical Chemistry, Vol. 69, No. 13, July 1, 1997

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Figure 4. Van’t Hoff plots for benzene with four polymers. The ordinate for the high molecular weight polystyrene data is on the right-hand side of the plot. O, first moment; b, peak maxima.

plots7,10,28,42 is to specify Tg as the temperature at which the peak maxima data deviate from linearity at low temperatures. These points can be compared with the Tg values, which are marked with arrows in Figures 4 and 5. The assignments are valid for both solutes with PS and PCR. The PET polymer shows no clear break with either solute. PMMA gives a correct value with the alkane probe but a very anomalous value with the benzene probe. It is possible that benzene, which is a very good solvent for PMMA, could plasticize the polymer and lower the Tg value. To test this hypothesis, the sample size was decreased to the lowest limits detectable by the GC/MS system operated in the SIM mode; however, no change in the van’t Hoff plot was observed. In addition to changes in solubility caused by the glass transition in polymers, there is a secondary, but often significant, change in the rate of diffusion of the probe solute in the bulk polymer or adsorption of the solute on the polymer surface or microvoids. This change is reflected in the dispersion of the 2490

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elution peaks rather than the retention volume. Wang and Charlet32 first measured the second moments of the elution peaks for chloroform with polystyrene in the glassy and rubbery states. The parameter actually used was a dimensionless second moment which is the reciprocal of the number of theoretical plates, N:

1/N ) µ2/µ12

(3)

Wang and Charlet32 suggested that Tg could be determined from a plot of 1/N vs temperature as a sharp increase in 1/N with decreasing temperature at the glass transition temperature. This suggestion was predicated on the assumption50 that the diffusion coefficient of the probe solute in the glassy polymer would be much smaller than that in the rubbery polymer, which would (50) Gray, D. G.; Guillet, J. E. Macromolecules 1974, 7, 244-247.

Figure 5. Van’t Hoff plots for n-decane with four polymers.

result in a sudden increase in dispersion, i.e., a sudden decrease in the efficiency of the column expressed as the number of theoretical plates, N. To test this hypothesis with the current data, retention volume data for each system were plotted in the form of 1/N vs temperature. The plot for one system, viz., chloroform with PSsthe same system studied by Wang and Charletsis shown in Figure 6, with the arrow drawn at the position suggested by Wang and Charlet32 to indicate the glass transition temperature. In fact, the current experimental study was extended to lower temperatures than studied previously,32 so a second abrupt change in slope could be observed at 100 °C, which is actually the glass transition point. The decrease in 1/N at low temperatures is due more to an increase in the retention time, µ1, rather than a decrease in µ2. Thus, the use of a dimensionless second moment somewhat obscures the changes in peak shape imposed by a change in diffusion coefficient. Nevertheless, the sharp change in the dimensionless second moment at Tg suggests a means for determining the glass transition temperature from statistical moment data from even asymmetric elution peaks.

Figure 6. Plot of the dimensionless second moment of chloroform with polystyrene.

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Figure 7. Moment ratio plots for benzene with four polymers.

Several investigators have shown17,18,45 that, under certain rather rigorous conditions, the diffusion coefficient, Ds, of a probe solute in a polymer can be measured from the statistical moments of the elution peaks using the relationship

{ }

2df2 µ1 - t0 Ds ) 3 µ2

Analytical Chemistry, Vol. 69, No. 13, July 1, 1997

( ) {

D1 ) D0 exp (4)

where df is the thickness of the polymer film and t0 is the retention time of a solute which is insoluble in the polymeric stationary phase, i.e., the dead time of the system. The necessary conditions are discussed in the original references17,18,45 and are somewhat difficult to achieve, especially with packed columns. However, the function (µ1 - t0)/µ2 should be at least proportional to Ds if partition is the dominant retention mechanism and resistance to mass transfer in the polymer is the predominant dispersion mechanism for the probe solute. In other words, in some cases, this function will have more physical significance than the dimensionless second moment or 1/N. 2492

The temperature dependence of the diffusion coefficient for an infinitely dilute solute (1) in a polymer (2) has been shown18,51 to follow a free volume expression given by eq 5,

}

-γVˆ 2*ξ E exp RT K12[K22 + λ(T - Tg)]

(5)

where D0 is a constant, E is the activation energy for diffusion, γ is an overlap factor, Vˆ 2* is the specific hole free volume of the polymer, and ξ is the ratio of the critical molar volumes of jumping units for the polymer and solvent, i.e.,

ξ)

Mj,1Vˆ 1* Mj,2Vˆ 2*

(6)

Here, Mj,i is the molecular weight of a jumping unit of component i. K12 and K22 are the free volume parameters of the polymer, (51) Vrentas, J. S.; Duda, J. L. J. Appl. Polym. Sci. 1978, 22, 2325-2339.

Figure 8. Moment ratio plots for n-decane with four polymers.

and Tg is the glass transition temperature of the pure polymer. The parameter λ ) 1 for rubbery polymers, and λ ) 0.2-0.3 for glassy polymers.18 The Arrehenius form of eq 5 indicates that a plot of log D1 vs 1/T should be reasonably linear, with a change of slope at the point where the value of λ changes, i.e., at Tg. The same logic should hold for the moment ratio, (µ1 - t0)/µ2. Such plots for benzene are shown in Figure 7. Except for PCR, the plots show a clear change in the function at the glass transition temperature and an upper limit of approximately 100 min-1 at high temperatures. The upper limit is really a lower limit on µ2 imposed by the finite volume of the sampling loop in the injector. That is, the peak width cannot be smaller than the width of the injected pulse. The PMMA polymer shows an anomalous temperature dependence of the moment ratio for benzene at low temperatures, i.e., the function decreases with increasing temperature, indicating that the diffusion is not the dominant dispersion mechanism and that eq 4 is not valid for this system. This conclusion is supported

by the observation that the first moment van’t Hoff plots for this system are nonlinear and multiple mechanisms contribute to both the dispersion and retention of benzene in PMMA. Surprisingly, the break in the moment ratio plot for benzene with PMMA occurs very close to Tg, unlike the first deviation from linearity (Figure 4), which is far too low. The PCR polymer shows no change in the moment ratio for benzene at the glass transition temperature, indicating that the retention mechanism for benzene is the same for both rubbery and glassy PCR polymer. While partition is the dominant retention mechanism for benzene with polystyrene and probably PET as well, adsorption is an important mechanism for long-chain alkanes such as n-decane. The moment ratio results for this probe solute with the same four polymers are shown in Figure 8. In each case, there is a break in the moment ratio plot at or close to the glass transition temperature, and the moment ratio decreases with increasing temperature at temperatures below Tg, indicating that Analytical Chemistry, Vol. 69, No. 13, July 1, 1997

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Figure 10. IGC chromatograms for n-decane with four polymers. Figure 9. IGC chromatograms for benzene with four polymers.

simple partition is not the dominant retention mechanism. Calculation of the second moments of asymmetric peaks is difficult and unreliable; however, the moment ratio provides an auxiliary method for the determination of Tg from IGC experiments for systems in which the van’t Hoff plots are unsatisfactory. The moment ratio and van’t Hoff plots for decane can be interpreted with the classical model of surface adsorption at temperatures below Tg along with bulk partition well above Tg. The intermediate temperature region showing the reversed temperature dependence of the retention volumes represents a transition region in which two retention mechanisms operate concurrently, with the relative significance of each mechanism dependent on the system temperature and the physical state of the polymer. The effects of this retention mechanism change on the shape and retention time of the elution peaks for n-decane with polystyrene are illustrated in Figure 3. The chromatograms for benzene and decane with the other polymers are shown in Figures 9 and 10, where the Tg points are marked with a dot. The patterns of the peak heights (widths) correspond with and reflect the shapes of the van’t Hoff plots, even though the two data analysis schemes measure completely different phenomena, viz., peak dispersion and retention of the solute probe. If the van’t Hoff plot shows an endothermic region, where the retention volume increases with increasing temperature, a maximum is observed in the peak heights, with the first decline in height occurring at the glass transition temperature. This is observed for all three probe solutes with PS and PMMA, although the transition temperature with benzene and PMMA is low (∼70 °C), as shown in the van’t Hoff plot (Figure 4). On the other hand, if the van’t Hoff plots do not show such temperature reversal, then the IGC chromatograms do not show a maximum in the peak heights. This is the case for all three solutes with PET and PCR. In Figure 10, there is some scatter in the peaks heights observed for decane at higher temperatures, but no systematic variation is evident. The effect of a glass transition on the shapes of elution peaks is illustrated in Figure 11, which shows a series of overlapping chromatograms for n-decane with PMMA to illustrate the anomalous temperature dependence of both retention and dispersion at 2494 Analytical Chemistry, Vol. 69, No. 13, July 1, 1997

Figure 11. Detailed IGC chromatograms for n-decane and PMMA from 80 to 150 °C.

temperatures close to Tg. Similar patterns have been observed43 and predicted from mathematical models on the basis of the assumption of a single absorption mechanism14 as well as the classical adsorption/absorption model.43,50 The anomalous pattern of peak shape and retention changes with temperature near Tg is unique and reproducible but provides no clear way to distinguish between the various models for the interaction of solutes with polymers. CONCLUSIONS Mass spectrometric inverse gas chromatography provides an additional tool for the investigation of polymeric systems and is unique in the ability to study such systems with the polymer in essentially a pure state, i.e., with the solute present at infinite dilution. IGC is also useful as a technique to study the effect of polymeric glass transitions on the solubility of probe solutes in the polymer and the diffusion coefficient of the solute in the polymer. The technique complements the more common differential scanning calorimetry, which measures the changes in the heat capacity of a polymer. However, this study, involving a series of polymers and probe solutes, shows that the technique is useful but far from a perfect method for the determination of Tg for polymers. The technique

is indirect, and the effect of a phase transition on the solubility and diffusion coefficient of a probe solute often varies from one polymer or one probe to another. Under carefully controlled conditions, the glass transition temperature may be determined from a van’t Hoff plot, the heights of elution peaks in a chromatogram, or a moment ratio plot. The latter two methods are new and are presented for the first time in this investigation. In most cases, at least one of these data analysis schemes will provide accurate data for Tg; however, the results from any individual scheme may be unsatisfactory. For example, the van’t Hoff and/ or moment ratio plots may not show a clear break at Tg, or the chromatograms may not show a maximum in the peak height at Tg. The major problem is the multiplicity of processes contributing to the chromatographic retention of a solute with a glassy polymeric stationary phase. These mechanisms vary with each polymer and probe, the physical state of the polymer, and the temperature of the system. IGC is, however, one of the few experimental methods available to investigate such complex polymeric systems. With regard to the three possible models for sorption and dispersion of the IGC probe solutes, the data presented herein

are inadequate to establish a single dominant mechanism for all polymer/solute systems. To the contrary, it is most probable that different probes are retained in different glassy polymers by multiple processes which may change dramatically with temperature and/or the physical state of the polymer. Nonetheless, it is possible to determine Tg for many polymeric systems by this technique, and the methodology should be applicable to the investigation of the plasticization effects of volatile gases or vapors on the glass transition temperature of common polymers. ACKNOWLEDGMENT This research was supported by a grant from the National Science Foundation. The authors also wish to express their appreciation to the Hewlett Packard Co. for the donation of the 5971 MSD system. Received for review August 20, 1996. Accepted April 24, 1997.X AC960848Z X

Abstract published in Advance ACS Abstracts, June 1, 1997.

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