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Macromolecules 1986, 19, 2618-2621
Chemical Composition and Molecular-Size Factors in Polymer Analysis by Thermal Field-Flow Fractionation and Size Exclusion Chromatography Judy J. Gunderson and J. Calvin Giddings* Department of Chemistry, University of Utah, Salt Lake City, Utah 84112. Received May 20, 1986
ABSTRACT: In this report we show that retention in thermal field-flow fractionation (thermal FFF) can be cleanly broken into two factors: the ordinary (concentration)diffusion coefficientD, which depends almost exclusively on molecular size, and the thermal diffusion coefficient DT, which depends only on polymer composition. The molecular-size factor, reflected in D, is almost identical with that controlling retention in size exclusion chromatography (SEC). Consequently, D values for various polystyrene, polyisoprene, and poly(methy1methacrylate) standards have been obtained by using SEC measurements. With this, the DT values were obtained by measuring the retention of the same samples by thermal FFF. The composition effect tied to DT was found to be substantial,equivalent in one case (polyisoprene/poly(methyl methacrylate))to a fivefold variation in molecular weight. It is shown by comparing thermal FFF and SEC runs on the same sample pairs that the composition effect alone is sufficient to provide good resolution. We have consequently suggested that compositionalvariations, such as those found in copolymers and polymer blends, can be evaluated by thermal FFF measurements in which a molecular-size base line is established by SEC.
Introduction Both thermal field-flow fractionation (thermal FFF) and size exclusion chromatography (SEC) are capable of separating polymer fractions at high resolution levels. Since each of these techniques is an elution system, the separation is observed as a difference in the retention (elution) times of individual components undergoing differential migration through the flow channel or column. For any given polymer family, the separation process unfolds according to differences in the size or molecular weight of the component polymer molecules. In a recent paper we examined the relative effectiveness of the size or molecular weight fractionation in thermal FFF and SEC.' We showed that resolving power can be broken into two elements: selectivity and efficiency. Selectivity,which is the functional change in retention time or volume relative to the fractional change in molecular weight, is much higher in thermal FFF than in SEC. Column efficiency, a measure of band sharpness, attains higher levels for SEC. The combination of these two elements into a single resolution index, when evaluated for these two techniques, shows that thermal FFF generally generates higher resolution levels than SEC. The above-cited study examined fundamental differences in retention behavior, as well as the differences in selectivity and efficiency noted above, in the comparison of thermal FFF and SEC. In this paper we examine another substantial departure between thermal FFF and SEC, which relates to the role of polymer composition in thermal FFF retention and resolution. It has long been known that ideal SEC yields an elution spectrum in which the position of any given component depends on the physical dimensions of the component molecules. This physical size is generally measured in terms of the hydrodynamic radius or volume. The hydrodynamic radius does not (and cannot) rigorously control retention in all situations,2 but it represents size effects well enough that any two species having identical hydrodynamic volumes, even if picked from different polymer families, will elute at almost the same position from an SEC column. Consequently, retention and separation are based primarily on molecular size; differences in chemical constitution have only second-order effects and enter solely to the extent that they influence physical size. 0024-9297/86/2219-2618$01.50/0
Thermal FFF is based on a different mechanism, yielding a substantially different outcome. From thermal FFF theory it is known that retention can be expressed in terms of two physicochemical parameters: the ordinary concentration diffusion coefficient D and the thermal diffusion coefficient DT. Parameter D, however, depends (inversely) upon hydrodynamic radius, so this parameter will experience the same relative increments upon going from one polymer molecule to another as will the hydrodynamic radius. (Despite a common dependence on D, a given increment in D will lead to different fractional shifts in elution volume and even to different directions of the shift, positive for SEC and negative for thermal FFF.) However, the additional dependence of elution volume in thermal FFF on DT adds a major new dimension not influencing retention in SEC. In this paper we show that DT is sensitive to the chemical nature of the polymeric sample material. We will examine the magnitude of this chemical sensitivity and note its possible uses in cases where there is a compositional variation, as in polymer blends and copolymers. In particular, we will examine the way in which thermal FFF and SEC provide complementary information when applied to samples of different polymer types. For example, concurrent runs by thermal FFF and SEC should identify the chemical composition of the polymer under study and provide the molecular weight distribution as well.
Theory Separation Mechanism in SEC. The universal calibration method introduced by Benoit3 employs the hydrodynamic radius or volume of the polymer as the key separation parameter. The hydrodynamic volume may be expressed as a constant multiplied by the product of the intrinsic viscosity [ T ] and the molecular weight M . Thus the calibration curves for a variety of polymers will collapse toward a single curve when plotted as log ([7]M) vs. elution volume V , rather than the usual log M vs. V,. The intrinsic viscosity is related to the molecular weight of the polymer through the empirical Mark-Houwink equation [ q ] = KM"
where values for the Mark-Houwink coefficients, K and 0 1986 American Chemical Society
Macromolecules, Vol. 19, No. 10, 1986
a, vary with polymer type and solvent. These constants have been determined for a wide variety of polymer/solvent s y ~ t e m s . ~ 9 ~ The diffusion coefficient a t infinite dilution is given by the Stokes-Einstein equation, which can be related to the intrinsic viscosity by the expressione
where R is the gas constant, T i s the temperature, 71 is the carrier viscosity, and N is Avogadro's number. Equation 2 relates the diffusion coefficient to the product M [ v ] , which is the "hydrodynamicvolume" parameter commonly used in the universal calibration of SEC. This means that components emerging with the same elution volume in SEC have comparable diffusion coefficients. This will become an important consideration in the next section, where the separation parameters in thermal FFF are discussed. Separation Mechanism in FFF. The extent to which a sample is retained in an FFF channel is specified by its retention ratio R, equal to the displacement velocity of the sample relative to that of the carrier. The parameter R is related as follows to the mean thickness 1 of the sample cloud or layer compressed against the wall of a channel with parabolic flow:' R = V o / V , = Gl/w[coth ( ~ / 2 1 -) 2 1 / ~ N ] 6 ( l / w ) (3) where Vo is the volume of the channel, V , is the volume necessary to elute the sample, and w is the channel thickness. This equation is correct only to a first approximation for thermal FFF due to the secondary influence of the applied temperature gradient, which perturbs the parabolic flow by causing a variation in the carrier viscosity across the channel. This perturbation has been examined and corrections have been applied.s The mean thickness 1 of the sample layer is a function of the applied temperature gradient and of the two diffusion coefficients, D and DT, of the polymer/solent system7
where y is the thermal expansion coefficient (generally negligible) and dT/dx is the temperature gradient. At a constant temperature gradient, retention then depends on (and increases with) the ratio of the thermal diffusion coefficient DT to the ordinary diffusion coefficient D. It has been shown that DT has a very weak dependence, if any, on molecular eight.^ Thus in any one polymer family, differences in retention in thermal FFF are due primarily to changes in D. This separation parameter, by virtue of eq 2, also underlies retention in SEC. Thus for any given polymer series, thermal FFF and SEC will both fractionate samples according to the distribution of D values. However, separation mechanisms are different in the two cases, leading to opposite elution orders (high-D molecules appearing first in thermal FFF and last in SEC), different p e a k widths, and generally comparable but not identical resolution 1evels.l If the sample mixture varies in composition as well as molecular weight, then separation in thermal FFF is influenced additionally by D p We will show how DT varies from one class of polymers to another.
Experimental Section The thermal FFF system used in this study has been described elsewhere.' T h e channel is 0.0762 mm (0.003 in.) thick, 2.0 cm
Polymer Analysis by Thermal Field-Flow Fractionation 2619 Table I Polymer Standards Used for This Study Mwx Mw/Mn polymer (max) source 107 1.10 poly(methy1 Pressure Chemical methacrylate) 240 1.09 Pressure Chemical poly(methy1 methacrylate) 86 1.05 Chrompack polyisoprene polyisoprene 210 1.10 Chrompack polystyrene 50 1.06 Pressure Chemical polystyrene 100 1.06 Pressure Chemical polystyrene 110 1.06 Pressure Chemical polystyrene 200 1.06 Pressure Chemical polystyrene 233 1.06 Pressure Chemical polystyrene 300 1.06 Pressure Chemical 411 1.10 Mann Research Labs polystyrene polystyrene 498 1.20 Pressure Chemical 600 1.10 Pressure Chemical polystyrene polystyrene 860 1.20 Mann Research Labs
in breadth, and 45 cm long. The channel volume is approximately 0.75 mL. The channel was pressurized to approximately 100 psi, allowing the system to be run with the hot wall near the normal boiling point of the carrier. The hot wall for these experiments was kept a t 62 "C while the cold wall was kept at 22 "C. The SEC column is a commercial Ultrastyragel column (Waters Chromatography Division, Millipore Corp., Milford, MA). The column is 30 cm long and has an inner diameter of 7.8 mm. The particle diameter is 7 pm and the pore size is reported as lo5 A. The column is described as applicable over the molecular weight range 50 X lo3 to 4000 X lo3. Spectrophotometry grade tetrahydrofuran was used as the carrier solvent. The same auxiliary equipment was used for both separation units. A Waters Model 6000A pump was used for solvent delivery. The channel effluent from each column was detected by a refractive index detector Model 1037A (HewlettPackard, Palo Alto, CA). A two-pen Goertz Metrawatt (Nurnberg, Germany) recorder monitored the output from the detector. The polymer samples used in this study are listed in Table I along with their suppliers and reported maximum polydispersity values. The polystyrene and polyisoprene samples were diluted to a concentration of 0.1% (weight/volume) and the poly(methy1 methacrylate) samples were diluted to a concentration of 0.3% prior to injection. The samples were introduced into the column via a sample injection valve fitted with a 10-pL sample loop.
Results and Discussion The ordinary and thermal diffusion coefficients, D and DT, for the polymer samples shown in Table I were determined in order to examine the variations with chemical composition and molecular weight. The D's were calculated from eq 2 by using measured retention volumes and the universal calibration curve for the SEC column. The latter curve was determined from polystyrene standards using the Mark-Houwink coefficients K = 1.5 X lo4 dL/g and a = 0.7.5 A comparison of D values for polystyrene standards calculated from eq 2 with the above MarkHouwink coefficients for determination of the intrinsic viscosity relative to those values determined from light scatteringgJOis shown in Figure 1. The agreement is good. We assume that the D and DT values calculated from both SEC and thermal FFF approximate the values a t infinite dilution. This assumption was examined by calculating the concentration of sample effluent from the thermal FFF column and correcting the D value assuming a linear concentration dependen~e.~JO It was found for polystyrene samples that the corrected D varied less than 5% in the most extreme case from the value at infinite dilution, thus justifying the infinite dilution approximation. With D values established by SEC measurements, the DT values of Table I1 were determined from thermal FFF retention by using eq 4 and an expression related to eq 3
Macromolecules, Vol. 19, No. 10, 1986
2620 Gunderson and Giddings
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Figure 4. Runs with 2.4 X lo5 MW poly(methy1methacrylate) and 2.0 X lo5 MW polystyrene by thermal FFF and SEC. Experimental conditions: SEC flow rate = 1.0 mL/min; thermal FFF T , = 21 "C, Th = 62 "C, and flow rate = 0.13 mL/min. Figure 2. Separation of 2.1 X lo5 MW polyisoprene and 3.0 X lo5MW polystyrene pair by thermal FFF compared to unresolved run by SEC. Experimental conditions: SEC flow rate = 1.0 mL/min; thermal FFF cold-wall temperature T, = 22 "C, hot-wall temperature Th = 62 "C, and flow rate = 0.13 mL/min. Table I1 Determination of Ordinary Diffusion Coefficient D and Thermal Diffusion Coefficient D Tfrom Thermal FFF and SEC Experimental Results for a Variety of Polymer Standards: Poly(methy1 methacrylate) (PMMA), Polyisoprene (PI), and Polystyrene (PS) D x 107, D~ x 107, uolvmer mol w t R llw cm2 s-l cm2 s-I K-I 5.36 1.24 PMMA 107000 0.485 0.112 1.31 240 000 0.326 0.072 3.67 PMMA 0.51 4.19 PI 86 000 0.716 0.210 0.51 3.00 PI 210000 0.588 0.150 0.87 PS 5.42 100000 0.618 0.160 0.95 4.84 PS 110000 0.540 0.131 0.92 3.85 PS 200 000 0.474 0.108 0.93 300 000 0.340 0.075 2.70 PS
but accounting for the nonparabolic flow profile. Table I1 confirms our expectation that DT has only a negligible dependence on molecular weight. However, DT varies significantly from one polymer family to another. For example, DT is approximately 2.5 times larger for poly(methyl methacrylate) than for polyisoprene. Equation 4 and the final approximate expression of eq 3 show that this difference is associated with a shift of comparable magnitude in retention ratio R and retention volume V,. Such a retention shift corresponds approximately to that found for a fivefold difference in molecular weight. Thus, the influence of polymer composition on DT is substantial. This influence should be great enough to discern chemical differences when thermal FFF is used in conjunction with SEC. The potential for utilizing the composition effects appearing in DT is examined in Figures 2-4. These figures show the results for several binary mixtures made up from different polymer families and run on both the thermal
FFF and SEC systems. In none of these runs can the binary pair be resolved by SEC due to the closeness of molecular dimensions as reflected in the similarity of the two D values. In each case these pairs are resolved or partially resolved by thermal FFF. For these three cases, the D values, as shown by Table 11, differ by no more than 10% for the binary pair, an inadequate increment to produce observable resolution. Clearly, the successful resolution by thermal FFF can only be due to the different compositional factors reflected in the DT values. The resolution demonstrated for thermal FFF in Figures 2-4 is reasonably high despite the fact that we have not used a binary polyisoprene/poly(methyl methacrylate) pair, which differ the greatest (by a factor of 2.5) in DT values (see Table 11). In the case of Figure 2, high resolution is found for a polyisoprene/polystyrene pair with a DT ratio of 1.8. In Figures 3 and 4, where different polystyrene/poly(methyl methacrylate) pairs are run, the DT ratio is only 1.4. For the lower molecular weight sample pair, shown in Figure 3, this ratio is not adequate to fully resolve the two components. However, resolution generally increases both with increasing molecular weight and with steeper temperature gradients.' The improved resolution in Figure 4 relative to that shown in Figure 3 is largely due to the higher molecular weight of the samples, although there is a small contribution from a small but favorable increment in the D values. If it were necessary to fully resolve the lower molecular weight mixture, the applied temperature gradient could be increased until the needed level of resolution was met. We note that the inverse case in which components coelute in thermal FFF but are well resolved in SEC could also be studied. However, we believe that the interpretation of the results is more direct when observing coeluting components in SEC, which, because of the single property ( D ) determining elution volume in SEC as opposed to the two properties (D and DT) involved in thermal FFF, leads to a constant value of the first property ( D )with the property (DT) to be distinguished in the thermal FFF
Macromolecules 1986,19, 2621-2632 run. In the inverse case, the coeluting components would differ in both D and DT,which is less straightforward in interpretation.
Conclusions There are many examples in which two analytical techniques have been combined in order to acquire information both on molecular-size distribution and on chemical composition parameters. These combinations have been used primarily in copolymer studies. In some cases an SEC procedure is used in combination with some other separation process, including thin-layer chromatography," liquid chromatography,12or even SEC with another s01vent.l~ Also, SEC has been combined with detector systems yielding more than one channel of information, including sequential pairs of unlike detectors14and multiwavelength diode array d e t e ~ t 0 r s . l ~ The results of this study show that thermal FFF has very good qualifications for entering this stable of combined techniques. In many ways thermal FFF represents an ideal combination with SEC because thermal FFF retention is cleanly divided into two factors, one representing the same molecular-size effects that control retention in SEC, and the other representing chemical composition effects. Furthermore, the composition effects appear to be pronounced. Further work is being done in our laboratory to establish this trend for a wider variety of polymer families. The possibility also exists that one thermal FFF procedure could be combined with another using a different carrier solvent. Unlike the combination of two SEC procedures using two solvents, one would not risk troublesome adsorption effects with the thermal FFF pair. However, again, the feasibility of this approach cannot be evaluated
262 1
until additional work is done with different carrier liquids. Hopefully, this short study will establish a foundation from which polymer compositional variations can be examined through the application of thermal FFF methodology. The high resolving power and versatility of thermal FFF systems should aid considerably in implementing this approach to polymer characterization.
Acknowledgment. This work was funded by Grant No. CHE-8218503 from the National Science Foundation. Registry No. Poly(methy1methacrylate), 9011-14-7; polyisoprene, 9003-31-0;polystyrene, 9003-53-6. References and Notes (1) Gunderson, J. J.; Giddings, J. C. Anal. Chim. Acta, in press. (2) Giddings, J. C.; Kucera, E.; Russell, C. P.; Myers, M. N. J . Phys. Chem. 1968, 72,4397.
(3) Grubisic, Z.; Rempp, P.; Benoit, H. J. Polym. Sci., Part B 1967, 5, 753. (4) Bandrup, J.; Immergut, E., Eds. Polymer Handbook; Wiley: New York, 1975. (5) Yau, W. W.; Kirkland, J. J.; Bly, D. D. Modern Size-Exclusion Liquid Chromatography; Wiley: New York, 1979. (6) Rudin, A.; Johnston, H. K. J. Polym. Sci., Part B 1971,9,55. (7) Giddings, J. C.; Caldwell, K. D.; Myers, M. N. Macromolecules 1976, 9, 106. (8) Gunderson, J. J.; Caldwell, K. D.; Giddings, J. C. Sep. Sci. Technol. 1984, 19, 667. (9) Mandema, W.; Zeldenrust, H. Polymer 1977, 18, 835. (10) McDonnel, M. E.; Jamieson, A. M. J . Macromol. Sci., Phys. 1977, B13(1),67. (11) Teramachi, S.; Hasegawa, A,; Yoshida, S. Macromolecules 1983, 16, 542. (12) Mori, S.; Uno, Y.; Suzuki, M. Anal. Chem. 1986, 58, 303. (13) Rubio. L. H.: MacGreeor. J. F.: Hamielec. A. E. Adu. Chem. Ser. 1983, NO. 203, 317. ' (14) Balke. S. T.: Patel. R. D. Adv. Chem. Ser. 1983. No. 203. 281. (15) Nicholson, J. C.; Meister, J. J.; Patil, D. R.; Field, L. R. Anal. Chem. 1984,56, 2447.
Equilibrium Morphology of Block Copolymer Melts Takao Ohta* and Kyozi Kawasaki Department of Physics, Kyushu University, Fukuoka 812, Japan. Received February 28, 1986 ABSTRACT The microphase separation of diblock copolymers is studied by means of the mean field theory originally introduced by Leibler. The long-range interaction of the local monomer concentration deviation $(r),which arises from zero osmotic compressibility of the pure block copolymer systems, is shown to be very important for the morphology of the ordered structures. In the strong-segregationlimit, where the interfacial thickness 5 is sufficiently small compared to a domain dimension D, the 2/3 power law D Wl3,with N the polymerization index, is derived for planar, cylindrical, and spherical geometries of the ordered structure. The transitions from a lamellar structure to a cylindrical structure and from cylindrical to spherical are also investigated. The approximations employed are the random phase approximation in the derivation of the free energy function 411.)and the local approximation for the higher order vertex functions in F{$).
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1. Introduction Block copolymers have been studied for many years by polymer chemists mainly because of their technological interest.' When two sequences of monomers A and B, forming a copolymer molecule, are incompatible with each other, the copolymer melt undergoes a spatial segregation a t low temperatures. However, a macroscopic phase separation, which occurs, e.g., in a polymer blend, cannot occur since the two sequences are chemically connected a t a junction point. The phase separation is on a mesoscopic scale where the microdomains of A-rich and B-rich regions emerge. In thermal equilibrium those microdomains are 0024-9297/86/2219-2621$01.50/0
regularly arranged. In fact the periodic structures of lamellar, cylindrical, and spherical domains have been observed by changing the molecular weight ratio f of the A and B These various structures provide new thermal and mechanical properties that are not seen in homopolymers formed by only A or B monomers. After the pioneering work by Meier,5 Helfand and WassermarP developed the statistical mechanical theory of the microphase separation in a bulk block copolymer above a glass transition temperature. They studied the equilibrium morphology of the ordered structures in the strong-segregation limit where the interface thickness $. 0 1986 American Chemical Society
