Report
Characterizing Polymers by MPC
T
his year marks the 90th anniverUsing commercially sary of the publication of Tswett's papers describing a new available instrumen- techniqueseminal called chromatography for separating plant pigments. For nearly a centation, molecular tury since, thousands of researchers, and "real" chemists have develprobe chromatographyteachers oped applications for chromatography would have seemed incredible to the can provide useful that founding father. Among the oddest and most valuable of these is the use of GC to information on the investigate the morphology of crystalline and amorphous polymers by "probing" physical and chemical the interior and interfacial regions of pure mixed polymers with various moleproperties of polymers orcules In most cases the polymer is used as a thin stationary-phase film coated on a solid sunnnrt (packed columns'! or on the
0003-2700/97/0369-229A/$14.00/0 © 1997 American Chemical Societv
walls of fused-silica capillary columns, and the probes are volatile solutes that may or may not be good solvents for the polymer. In 1969, Guilletfirstsuggested using GC to measure the glass transition temperature Tg of polymers (I). In a later paper, he proposed the term "molecular probes" to describe these chromatographic solutes because they were similar to the molecular beams then in development (2). Despite repeated attempts to get the name "molecular probe chroma-
Jon F. Parcher Rebecca R. Edwards Kwang S. Yun University of Mississippi
Analytical Chemistry News & Features, April 1, 1997 229 A
Report Data analysis schemes
The type of analysis scheme used to interpret MPC data is often dictated by the specific application. For example, one of the most commonly used chromatographic schemes for determining glass transition temperatures, melting points, and crystallinity of polymers involves a van't Hoff-type plot of the logarithm of the retention volume of a probe solute as a function of the reciprocal temperature. A typical example is shown in Figure 1 for several probe solutes using a poly(methyl methacrylate) (PMMA) column at temperatures of 40 to 200 °C The S-shaped plot with linear regions at high and low temperatures, that is, when the polymer is a rubber or a glass, is commonly observed for many polymers; however, the plot details vary with solute and polymer. The van't Hoff plots are particularly useful because the slope of the curve at any temperature is proportional to the enthalpy of transfer of the solute from the mobile to the polymeric stationary phase. Linear regions of the plot indicate temperature ranges where the enthalpy of transfer is constant (independent of temperature) and a positive slope indicates an exothermic
tography" adopted in the literature, it was never accepted. Instead, the designation "inverse GC"—first coined by workers studying asphalt (2)—became widely yccepted. This terminology is unfortunate because there is nothing "inverse" about the technique. It is carried out with polymeric stationary phases and common GC instrumentation and procedures. Molecular probe chromatography (MPC) is a much more descriptive term and will be used throughout this discussion. The technique has undergone a renaissance recently, and several reviews (3, 4) have discussed the myriad applications developed to date. The experimental technique is deceptively simple; however, interpretation of the chromatographic results can be disturbingly complex, and such interpretation is often inappropriately simplified by many practitioners. Experimentally, the initial step in any MPC application is the preparation of a GC column with the polymer uniformly distributed as a thin film acting as a nor-
mal chromatographic stationary phase. This step is the most critical and timeconsuming. The rest of the procedure simply involves injecting different probe solutes at various temperatures. The probes can be selected to interrogate different regions of the polymers—for example, the bulk or interfacial regions—and the retention times can be shortened by using low molecular weight solutes. Thus, most common MPC experiments require only a few minutes for the complete elution of the probe solutes at each temperature MPC has been used to measure various physical parameters of diverse polymers such as glass transition temperature (5), melting point (6), liquid-crystal mesophase transitions (7), polymer crystallinity and kinetics (6), solute-polymer interaction parameters (6), polymerpolymer interaction parameters (8), diffusion coefficients of solutes in polymers (9), and surface properties and adsorption isotherms (10).
230 A Analytical Chemistry News & Features, April 1, 1997
Guillet originally proposed the most commonly accepted model for the interpretation of such plots (2). The basic postulate is that the retention mechanism for the probe solutes changes from adsorption on the surface of glassy polymers at low temperatures (less than T ) to absorption of the solute into the bulk polymer in a rubbery state at higher temperatures. The intermediate (endothermic) region represents a nonequilibrium state in which both retention mechanisms operate concurrently. The retention volume equation V =V m + V holdd for rny rubbery polymer whereas the governing firm wniilrl W n m p V - V A- K LJUII vvuuiu ucLUiiic VR
A
v m "i"-^adsorptiorr^-s
for the same oolvmer in a dassv state In eauations if reDresentsaneauilibrium cnn«;tant and W snH d arpth^vnlsurface area of the resnertivelv T h e enuilihrium constants ' for arr'r'nn ri ad nrnt' n be similar
in magnitude; however, the volume and surface area of a polymer can differ dramatically to produce the sharp change in VR close to 7„. Such changes in retention i
'
i
i
i-
i
mechanism, and hence retention volume,
could account for the unusual variations shown in Figure 1. Over the years, however, this model has been repeatedly criticized, as well as corroborated, by many workers using different polymers and probes. One of the major difficulties with determining Tg by MPC is probe dependence, that is, how the shapes of the plots vary with the nature of the probe solute (Figure 1). It has been found that the T of a polymer measured by differential scanning calorimetry often corresponds to the first point of deviation of the chromatographic data from the linear region of a van't Hoff plot at low temperatures, at which the polymer is in a glassy state. These points are marked with arrows in Figure 1 and vary over a range of 40 °C The T determined from differential scanning calorimetry for this narticular batch of PMMAwas 90-100 °C So i i this snerifir case the hydrocarbon probe 2-butanone
produced the most reliable from the van't Hoff plot This probe dependence is a commonly observed phenomenon with MPC (8) and brings into question the idea of simple ad/absorption processes as the dominant retention mechanisms. Some investigators, most recently Romdhane and coworkers (9), have even suggested that absorption of the solute into the bulk polymer was the only retention mechanism operative in polymeric systems and that the characteristic shape of the van't Hoff plots was caused solely by the variation of the diffusion coefficient of the probe in the polymer with the temperature and physical state of the polymer In particular it was suggested that the controlling factor was the ratio of the carrier gas flow
Figure 2. MPC of n - d e c a n e w i t h a PMMA c o l u m n . Blue, T< 7" ; red, T> T .
(which determines the contact time of the solute with the polymer) to the diffusion coefficient (11). If this ratio is low, ,hat ts, if the flow rate is low and the diffusion coefficient high, then the elution peaks would be symmetric and the retention times high; on the other hand, if the ratio is high, then the peaks would be asymmetric (because of slow diffusion) and the retention times low. Others have proposed that the nonlinear van't Hoff plots are an artifact of dataanalysis schemes in which the retention time was measured from the peak maxima (12). The first moment and peak maximum are equivalent for symmetric elution peaks; for asymmetric peaks, however, the statistically valid first moment differs from the peak maximum. If, for example, the retention times are measured from the true first moment of the asymmetric elution peaks for chloroform with polystyrene, the van't Hoff plots become linear throughout the temperature range encompassing the glass transition temperature (12) Other investigators have questioned the validity of all of the proposed mechanisms and suggested that
neither slow diffusion nor surface ad-
cnrption w a s r e e n n n s i b l e for ttip nhcprverl
chromatographic behavior (13) The uncertainty in the retention mechanism is primarily caused by the observed asymmetry of the elution peaks of most probe solutes with glassy polymers. Figure 2 illustrates the skewed elution peaks obtained with «-decane and PMMA. In this example, the elution peaks are wider and less symmetric at temperatures close to T Rhan aa tither highee ro rowee remperatures. This dramatic change in peak shape at temperatures near T is illustrated in detail for another system M-decane with polystyrene in Figure 3 Polystyrene has a T of about 100 °C; it can be that fV»e retention time of the peak maximum is minimal at T and the peak shape and show anomalous variations with temperature Asymmetric peaks are normally characteristic of chromatographic systems that are either not at equilibrium or else dominated by adsorption processes with nonlinear isotherms. In most cases, it is difficult—if not impossible—to chromatographically distinguish between these two phenomena for any given solute when the polymer is in a glassy state.
Despite these problems, MPC has significant advantages over other experimental methods for the characterization of polymeric systems. The polymer can be studied in a pure state because the chromatographic solutes are present at vanishingly low concentrations. Experimental procedures are fast, accurate, and simple; can be carried out over a wide temperature range; and can use commercially available instrumentation. Also the duration of the experiment is determined solely by the elution time of the probe solute (s). The systems rapidly equilibrate because the polymer is present thin film in forced flow of carrier gas Multiple solutes with different chemical properties can be used to simultaneously probe the bulk and interfacial rpcrions of the polymer
(This advantage however is tempered by the problem of probe dependence ) Moreover, it is difficult to investigate many polymers by classical gravimetric or volumetric techniques because of their low volatility and often low solubiilty. Measurement of diffusion coefficients and interaction parameters by these techniques is often laborious andtime-consuming.For these reasons, MPC has been used in a wide variety of applications. Glass, liquid crystal, and melting transition temperatures
Without a doubt, the most widely used application of MPC is determining firstand second-order phase-transition temperatures of polymeric materials such as pure polymers, blended polymers, and liquidcrystal polymers. The values for Tg are
Analytical Chemistry News & Features, April 1, 1997 231 A
Report universally determined from a van't Hofftype plot, such as Figure 1. The problem of probe dependence persists along with other problems, so in addition to specific applications, many fundamental studies have been carried out to determine the effect of various parameters on the accuracy of the determination of phase-transition temperatures. Some of the pertinent parameters investigated include the nature and solvent strength of the probe solutes (14), the magnitude of the carrier gas flow rate (15 16) the polymerfilmthickness (17 18) and the amount of probe solute injected (13 19) The effect of probe concentration is especially critical because a probe solute could possibly plasticize the oolvmer inadvertently and lower T
(Iff)
Others, however, have claimed to observe the opposite effect, that is, the chromatographically measured Tg values were too high when measured with certain probes (20). The newcomer to this technique should be aware that such apparent contradictions are rife within the fundamental studies cited above and that the major source of such problems is the use of broad comparisons between widely diverse polymer and solute systems or the interpretation of such complex systems with relatively simplistic models The chromatographic technique for measuring T is nonetheless very useful for many systems However it is doubtful that it will ever supplant differential
Figure 4. MPC determination ot tne degree of crystallinity of PEO. Inset is percent crystallinity; Tm1 and Tm2 are melting temperatures for two different compounds. (Adapted from ref. 21.) 232 A
rimetry for the characterization of pure polymers. Crystallinity and crystallization kinetics
The melting point of a semicrystalline polymer can be measured from a van't Hoff plot. In this case, however, the nonlinearity of such a plot is not caused by a change in retention mechanism but rather from a loss of amorphous regions of the polymer caused by crystallization. Presumably, the crystalline regions are not accessible to the probe solutes, and thus the retention volume of the probe diminishes as crystallization occurs. Figure 4 illustrates these types of measurements for the semicrystalline polymer polyethylene oxide (PEO) doped with lithium (21). The degree of crystallinity can be determined from 1 - [T^/^(amorphous)] (2), where F°(amo hous) is the specific retention volume of the hypothetical, completely amorphous polymer represented by the extrapolated line in Figure 4, in which T indicates die melting temperature of the two crystalline materials. In mis case, two crystalline regions are observed: one of PEO at low temperatures and another at intermediate temperatures containing some amount of salt The percent of crystalUnity is shown as a function of temperature in the inset of Ficnire 4
This unique method has been used extensively to study semicrystalline polymers. Predictably, there are also some problems with this approach, such as the physically unrealistic maxima that are often observed in crystallinity versus temperature plots. Furthermore, the model assumes a single partition-retention mechanism, so liquid surface adsorption invalidates the measurements. Finally, extensive extrapolation of data from high temperatures such as those in Figure 4 introduces large uncertainties in the calculated degree of crystallinity at low temperatures However the technique has all the advantages of any MPC method and does not require a complpfrply crvQtalline nnlymer for referenrp By suddenly dronning the temperature from above T to a lower temperature and injerrinp- the probe solute reneatedly while the pol mer is crystalli inp- the
kinetics of the crystallization process can also be investigated (22).
Analytical Chemistry News & Features, April 1, 1997
Diffusion coefficients of probe solutes in molten polymers
Temperature-dependent diffusion coefficients of molecular species in polymers are critical parameters for the design of many polymeric processes. Experimental determination of these quantities by classical methods is extremely difficult, and as a result, a great deal of effort has been expended developing chromatographic methods to make these measurements. However, the major problems with chromatographic methods are the need to either accurately the second ment of the elution peaks numerically fit elution peak profiles or fit retentionvolume data to theoretical or empirical models by curve-fitting techniques Each of these processes is fraught with diffiriilty and suhiect to lartre errors
Two independent methods for the determination of diffusion coefficients from MPC experiments have been proposed. The first is a classic approach based on the resistance to mass transfer term C of the van Deemter equation. Under certain rigorous experimental conditions, where slow diffusion of the probe solute in the polymer is the dominant spreading mechanism and partitioning is the only retention mechanism, C is given by C = (q)(t /Ds)[k'/(l+k') ]
(1)
where q is a shape factor, x is the thickness of the polymer film, Ds is the diffusion coefficient of the probe solute in the polymer, and k' is the chromatographic capacity factor. The q value depends on the physical distribution of the polymer film. It is 2/3 for a planar film, 1/12 for a film concentrated at the contact point between two spheres, and 8/re2 for a sphericalfilm.Using the definition of the height equivalent to a theoretical plate, H= c2z/L, where a2. is the second moment of the elution peak with respect to distance and L is the column length, Equation 1 can be expressed in terms of the ratio of the second moment with respect to time to the adjusted first moment tR - tm as A. =
tfT2[#R-y/o2t]
(2)
The most recent work in this area (23, 24) has involved polymer-coated spherical glass beads and used Equation 1 with a
shape factor of 8/rc2. Other investigators took advantage of the unique properties of fused-silica capillary columns using Equation 1 with a shape factor of 2/3, and Laurence derived a version of Equation 2 for capillary columns (25-27). Danner and co-workers (9,28) have used this technique to evaluate the free-volume model of polymers with D data measured by chromatographic methods over a range of temperatures encompassing T Although this approach is theoretically sound, it is extremely difficult to achieve the necessary experimental conditions with glassy polymeric liquids in which only a single mechanism (diffusion in the polymer) controls the second moment and only one mechanism (partition) determines thefirstmoment. Thefirstand second moments must be accurately determined to calculate D , as indicated by Equation 2. In addition, the exact value of x is difficult to determine because the polymerfilmthickness may vary from point to point within the column. The second method for measuring Ds from MPC data was developed by Schreii ber (15,29) in order to avoid the measurement of second moments and to correct for the effect of adsorption of the probe solutes on the surface of the polymer. The latter effect can be quite pronounced in some chromatographic experiments because of the thin film distribution of the polymer when coated on a solid support or on the walls of a capillary column. This method is based on the hypothesis that partitioning of the solutes into the bulk of the polymer is minimized at high flow rates (caused by low residence time) and that the dominant retention mechanism becomes liquid surface adsorption under these conditions Thus at lower flow iime of a Qnlute shniild Hprrea^p with in/"•t**aaoifirr flrrtw trnirQivl a Imw^i* l i m i t " i"*afl*v*t
ine onlv liauid surface adsorotion The oronosed empirical eauation is (15)
[1 - k exp(- n Dst/ix )]
(3)
where VN is the net retention volume of the solute; (VN)S is the net retention volume due to the surface adsorption, which is assumed to be instantaneous and independent of flow rate; (VN)b° is the hypothetical net retention volume at zero flow
rate, caused by partitioning of the solute into the bulk polymer; k is an empirical constant; and t is the time the solute is adsorbed on the surface. The authors assumed that the time available for the solute to diffuse into the polymer was determined by thetimethe solute was adsorbed at the surface. If k is known, then (V )a can be evaluated from the ertention data at high flow rates and Ds can be determined from the flow-rate dependence of the net retention volume. In this approach, the operative equation is empirical; however, the rigorous assumption of a single retention mechanism is obviated, and the method does not
The results from MPC are worth the effort required to ensure the validity of the experiment.
MPC is that the polymer can be probed by a solute effectively at infinite dilution (^ -> 0), so no solute-solute interactions are manifest, yielding In (ax/wj° = In (V(/v2) + [l-(l/r)] + jte
(5)
where w is the weight fraction, v is the specific volume of each component, and (a^Wj)" is the weight-based activity coefficient that tan be eetermined ffom MPC data using an equation presented in Reference 30. Manipulating equations gives an explicit expression for x12™ , the erobepolymer interaction parameter, from chromatographic retention volume data, namely, X12 = m (^7SRv2/r1v1vg2) (P\/RT)(Bn - Fj) - [1 - (1/V)]
(6)
in which P°lt Bu, and V1 are the vapor pressure, virial coefficient, and liquidphase molar volume, respectively, of component 1. The specific retention volume of component 1 in the polymer (component 2) is V 2- Thus, the eolute-polymee interaction parameter can be determined from a single chromatographic experiment. However, to estimate polymer-polymer require the measurement of the second interactions, three distinct chromatomoment of an elution peak. Only the flowgraphic measurements are required the rate dependence of the first moment is retention volume of the infinite dilution required for the estimation of Ds. solute in polymer 2, the same data for a second polymer 3 (V^3), and the same Flory interaction parameters data for a blend of polymers 2 and 3. MPC has been used to determine many Equation 6 then orovides a basis for detertypes of interaction parameters, including mining solute-polvmer interaction paramthose between a solute and a polymer, those between two polymers in a polymer eters from the measured specific retention volumes. blend, and the degree of cross-linking within a pure polymer. These parameters In addition to using this technique for are particularly difficult to measure by solute parameters, several researchers conventional techniques because of the have used it to measure the interaction need for a vanishingly small concentration parameter X23 betweee two oolymers with of the solute. For a pure linear polymer, no solute. Recently, this concept has been the basic theoretical model is the Floryextended to include the determination of Huggins equation for the activity a of a the extent of cross-linking within a polysolute (component 1) mer network (31,32), which necessitates using an extended version of the FloryInaj = lnc|> + [L I (l/r)]§2 + Xy$2 (4) Huggins model for cross-linked polymers. Applying the same limits used to derive Equation 5 a simple relation can be deas a function of the volume fraction f, in rived between the degree of cross-linking which r is the size ratio of the polymer to and the interaction parameters for a solute the solute and %12 is the interactton paand a linear polymer v °° ana the rameter between the solute and the polysolute with a cross-linked network polymer. One of the significant advantages of Analytical Chemistry News & Features, April 1, 1199 233 A
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mer (31,32), assuming that the rvalue is the same for the linear and cross-linked polymers. These approaches are theoretically sound; however, the chromatographic methods for determining %23 and the effective number of cross-links per gram of polymer are still plagued with the problem that the values obtained depend on the probe solute used. Probe dependence has been addressed by many (8,33), yet no single solution has proven entirely satisfactory thus far. Caveat emptor MPC can provide unique and particularly useful information regarding the physical and chemical properties of polymers and polymer blends. The experiments are simple, the instrumentation is commercially available, the theoretical models are relatively tractable, and the data analysis schemes 3.re cosily performed. However, the analyst must be continuously aware of the pitfalls of extrapolating MPC results from one system to predict the properties of a different polymeric system. In particular variables such as flow rate sample size temperature and especially the chemical nature of the probe solutes and polymers must be carefully studied to determine the effects on each system Very ofrpn a trend nh^prvpH with one solutp—nnlymer rnmbination will hp the onnnsite of that T
obtained from worth the effort required to ensure the validity of the experimental results.
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(7) Price, G. J.; Shillcock, I. M. Can. J. Chem. 1995, 73,1883-92. (8) Etxeberria, A; Iriarte, M.; Uriarte, C; Iruin, J. J. Macromolecules 1s95,282 7188-95. (9) Romdhane, I. H.; Danner, R. P.; Dudaa J. L. Ind. Eng. Chem. Res. 1995,34, 2833-40. (10) Gavara, R; Catala, R; Aucejo, S.; Cabedo, D.; Hernandez, R / Polym. Sci., Polym. Phys. Ed. 1196,34,1907-15. (11) Courval, G. J.; Gray, D. G. Macromolecules 1975,8,916-20. (12) Wang, J.-Y.; Charlet, G. Macromolecules 1989,22,3781-88. (13) Glass, A S.; Larsen, J. W. Macromolecules 1993,26,6354-58. (14) Al-Saigh, Z. Y; Munk, P. Macromolecules 1984,27,803-09. (15) Qin, R Y; Schreiber, H. P. Langmuir 1994,10,4153-56. (16) Card, T. W.; AllSaigh, Z. Y; Munk, P. Macromolecules 1985,18,1030-34. (17) Braun, J. M.; Guillet, J. E. Macromolecules 1975,8, 882-88. (18) Courval, G. J.; Gray, D. G. Macromolecules 1975,8,326-31. (19) Munk, P.; Al-Saigh, Z. Y; Card, T. W. Macromolecules 1985,18,2196-22010 (20) Llorente, M. A; Menduina, C; Horta, A / Polym. Sci., Polym. Symp. 1980, 68, 229-37. (21) Dexi, W.; Song, H.; Parcher, J. F.; Murray, R. W. Chem. Mater. 1919,1, 357-62(22) Gray, D. G; Guillet, J. E. Macromolecules 1971,4,129-33. (23) Hu, D. S.; Han, C. D.; Stiel, L. I./. Appl. Polym. Sci. 1987,33,551-76. (24) Munk, P., et al. Macromolecules 1987, 20,1278-85. (25) Pawlisch, C. A; Macris, A; Laurence, R L. Macromolecules 1987,20,1564-78. (26) Pawlisch, C. A; Brie, J. R; Laurence, R L. Macromolecules 1988,21,1685-98. (27) Arnould, D.; Laurence, R. L. .n Inverse Gas Chromatography, Lloyd, D. R, et ,l., Eds.; American Chemical Society: Washington, D.C., 1989, pp 87-106. (28) Faridi, N.; Romdhane, I. H.; Danner, R. P.; Duda, J. L. Ind. Eng. Chem. Res. 1994, 33,2483-91. (29) Mukhopadhyay, P.; Schreiber, H. P. Macromolecules 1993,26,6391-96. (30) Patterson, D.; Tewari, Y B.. Schreiber, H. P.; Guillet, J. E. Macromolecules 1971, 4,356-59. (31) Price, G. J.; Siow, K. S.; Guillet, JJ E. Macromolecules 1989,22, 3116-19. (32) Price, G. J.; Guillet, J. E. Polym. Mater. Sci. Eng. .199, 70,421-22. (33) Schuster, R H.; Grater, H.; Cantow, H.-J. Macromolecules 1984,17,619-25.
References (1) Smidsrod, O; Guillet, J. E. Macromolecules Jon Parcher and Kwang Yun are professors 1969,2,272-77. (2) Guillet, J. E.; Stein, A. N. Macromolecules of chemistry, and Rebecca Edwards si a 1970,3,102-05. Ph.D. candidate at the University of Missis(3) Munk, P. In Macromolecules 1992; Kahovec, J., Ed.; VSP-BH: The Netherlands, sippi. Yun and Parcher have collaborated in the study of the fundamental processes 1993, pp 185-206. governing retention mechanisms for vari(4) Al-Saigh, Z. Y. Polym. News 1914,19, 269-79. ous types of chromatography. Address corre(5) Wang, J.-Y.; Charlet, G. Macromolecules spondence to Parcher at Chemistry Depart1993,26,2413-19. (6) Al-Saigh, Z. Y; Chen, P. Macromolecules ment, University ofMississippi, University, MS 38677 (
[email protected]). 1991,24, 3788-95.
