Anal. Chem. 2003, 75, 1548-1551
Correspondence
Determination of Molecular Weight Distributions of Diblock Copolymers with Conventional Size Exclusion Chromatography Helmut Schlaad*,† and Peter Kilz‡
Max-Planck-Institut fu¨r Kolloid- und Grenzfla¨chenforschung, Abteilung Kolloidchemie, Am Mu¨hlenberg 1, D-14476 Golm, Germany, and Polymer Standards Service GmbH, In der Dalheimer Wiese 5, D-55120 Mainz, Germany
A convenient method that enables determination of molecular weight distributions of diblock copolymers with conventional size exclusion chromatography (SEC) without referring to any kind of calibration curve or molar mass-sensitive detecting devices is described. It is based on the well-established procedure to calculate the numberaverage molecular weight of copolymers from their chemical composition and the molar mass of the first block segment (precursor), applied on an ensemble of monodisperse copolymer fractions. The chemical composition of SEC fractions is calculated from their UV and RI detector traces, and the number-average molecular weight of the precursor, which is to be known from independent measurements, is taken as the molar mass of the first block segment. The molecular weight distributions and averages obtained by this method for selected copolymer samples were found to be in reasonably good agreement with the ones determined by NMR and SEC with on-line viscosity or multiangle laser light scattering detection. Many macromolecules that are of academic or industrial interest are copolymers with some kind of regular block, star, or graft architecture. Thanks to modern synthetic polymer chemistry, the list of available copolymers is rapidly expanding, and the targeted structures are getting more and more complex. However, even with sophisticated analytical techniques,1,2 it remains very difficult to determine the true molecular nature of such copolymer materials, mainly because of the fact that most analytes are polydisperse in various respects, such as molar mass, chemical composition, and structure. Among liquid chromatographic methods, it is 2-dimensional chromatography that enables a simultaneous tracing of molar mass and compositional distributions and, thus, provides the most detailed information on complex molecular structures.3,4 However, * Corresponding author. Phone: +49-(0)-331-567-9514. Fax: +49-(0)-331-5679502. E-mail:
[email protected]. † Max-Planck-Institut. ‡ Polymer Standards Service GmbH. (1) Kilz, P.; Pasch, H. In Encyclopedia of Analytical Chemistry; Meyers, R. A., Ed.; Wiley: Chichester, 2000; p 7495. (2) Kilz, P. In Encyclopedia of Chromatography; Cazes, J., Ed.; Dekker: New York, 2001; p 195.
1548 Analytical Chemistry, Vol. 75, No. 6, March 15, 2003
this method requires special equipment and knowledge and is, therefore, available to only a few people. Size exclusion chromatography (SEC) is more commonly used, but in order to determine absolute average molecular weights and distributions of copolymers, it needs on-line molar mass-sensitive detectors in addition to conventional concentration detectors (such as UV/vis and RI).1,5-7 Such differential viscosity (DV) and multiangle laser light scattering detecting devices (MALLS) are expensive and also require special knowledge of the correct treatment of raw data. SEC-DV data are transformed into molecular weights via a universal calibration curve,8 and it was demonstrated that this methodology can provide reliable molecular weight averages for linear block copolymers and blends.9,10 SEC with on-line MALLS detection should provide absolute molecular weights of polymer fractions without referring to any calibration curve. However, this is true only for copolymers that are rather monodisperse with respect to chemical composition.11,12 In the case of chemically disperse samples, refractive index increments (dn/dc) might be different for every copolymer fraction, making it very difficult to evaluate LS data. In addition, to determine the true concentration of polymer chains, which is essentially needed for the evaluation of DV and MALLS data, the UV or RI optical detector signals must be corrected according to the different response of comonomers. It would be very much desirable if there were a more convenient way to determine molecular weight distributions of copolymers by SEC without being dependent on molar-mass (3) Kilz, P.; Kru ¨ ger, R.-P.; Much, H.; Schulz, G. In Chromatographic Characterization of Polymers; Provder, T., Ed.; ACS Advanced in Polymers Series 247; American Chemical Society: Washington, DC, 1995; p 223. (4) Pasch, H.; Trathnigg, B. HPLC of Polymers; Springer: Berlin, 1997. (5) Yau, W. W.; Kirkland, J. J.; Bly, D. D. Modern Size Exclusion Chromatography; Wiley: New York, 1979. (6) Mori, S.; Barth, H. G. Size Exclusion Chromatography; Springer: Berlin, 1999. (7) Wintermantel, M.; Schmidt, M.; Becker, A.; Dorn, R.; Ku ¨ hn, A.; Lo ¨sch, R. Nachr. Chem. Technol. Lab. 1992, 40, 331. (8) Benoıˆt, H.; Rempp, P.; Grubisic, Z. J. Polym. Sci. 1967, B5, 753. (9) Yau, W. W. Chemtracts, Macromol. Chem. 1990, 1, 1. (10) Goldwasser, J. M. ACS Symp. Ser. 1993, 521, 243. (11) Runyon, J. R.; Barnes, D. E.; Rudel, J. F.; Tung, L. H. J. Appl. Polym. Sci. 1969, 13, 2359. (12) Gores, F.; Kilz, P. In Chromatography of Polymers; Provder, T., Ed.; ACS Symposium Series 521; American Chemical Society: Washington, DC, 1993; p 122. 10.1021/ac026002e CCC: $25.00
© 2003 American Chemical Society Published on Web 02/20/2003
sensitive detectors. The basic idea behind the following SEC data evaluation method is to use the well-established procedure of calculating the number-average molecular weight of a block copolymer from its composition and the molar mass of the first block segment (the so-called copolymer precursor)13 and applying it on an ensemble of monodisperse diblock copolymer fractions. The chemical composition of fractions can be determined from the SEC traces of two concentration detectors, as described by Kilz14,15 and Trathnigg,16 and the number-average molecular weight of the precursor is taken as the molar mass of the first block segment in every fraction (note that this homopolymer precursor is always available when block copolymers are synthesized by the most commonly applied sequential monomer addition technique, in research as well as industrial applications). These data are then used to calculate the molar mass of every copolymer fraction, which finally allows determination of the molecular weight distribution of the complete sample. Description of the New SEC-UV/RI Data Evaluation Method. The sensitivity of optical detectors is known to be dependent on the type of comonomer, which is, in our case, due to different extinction coefficients (UV) and refractive index increments (RI). Hence, in general, the measured UV and RI traces of copolymer samples are not a direct measure of the concentration of eluting chains and need to be corrected according to the comonomer-specific detector response. The relationship between the UV and RI signal intensities S and the eluting mass m of repeating units A and B in any slice i of a chromatogram is given by
(1a)
RI RI SRI i ) χA mA,i + χB mB,i
(1b)
UV RI RI χUV A , χB , χA , and χB denote specific detector response factors, the values of which are accessible by a calibration of the detectors with A and B homopolymer samples. Solving this system of equations yields
mB,i )
RI RI UV χUV B Si - χB Si
(2a)
UV RI UV χRI A χB - χB χA UV RI χRI - χUV A Si A Si
(2b)
UV RI UV χRI A χB - χB χA
The mole fraction f of either repeating unit in every chromatographic fraction is then calculated by
(
fB,i ) 1 - fA,i ) 1 +
(
M′i ) 1 +
)
MB fB,i M h MA fA,i PA
)
MB mA,i MA mB,i
-1
(3)
MA and MB denote the molar mass of A and B repeating units, respectively. Provided that the number-average molecular weight (13) Elias, H.-G. Makromoleku ¨ le - Struktur, Synthese, Eigenschaften; Hu ¨ thig & Wepf: Basel, Heidelberg, New York, 1990. (14) Kilz, P. GIT Fachz. Lab. 1990, 34, 656. (15) Johann, C.; Kilz, P. J. Appl. Polym. Sci., Symp. 1991, 48, 111. (16) Trathnigg, B. J. Chromatogr. 1991, 552, 507.
(4)
Fitting of this set of data with an appropriate polynom (optional) yields a specific calibration curve, log M′ vs elution volume, for a given copolymer sample. (Note that since the distribution of the first block segment is not considered by eq 4, M′i is only an apparent but close to absolute molecular weight.) The concentration of copolymer chains is given by
ci )
mA,i + mB,i ∆V
(5)
with ∆V as the volume of chromatographic fractions () constant). From the data obtained from the latter two equations, the molecular weight distribution and with it number- and weightaverage molecular weights can be calculated.
∑c M hn≡
i
i
∑
(6a)
ci/M′i
i
∑c M′ i
UV SUV ) χUV i A mA,i + χB mB,i
mA,i )
of the precursor block segment, M h PA, is known from independent measurements, such as osmometry or SEC, one can determine the molar mass of every copolymer fraction.
M hw≡
i
i
∑c
(6b) i
i
Examples. We analyzed three linear diblock copolymer samples, namely a polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA, 1), a polystyrene-block-polybutadiene (PS-b-PB, 2), and a polystyrene-block-poly(Z-L-lysine) (PS-b-PZL, 3), with the new SEC-UV/RI method. The SEC chromatograms of these samples are depicted in Figure 1 (for experimental conditions and molecular characteristics of the corresponding polystyrene precursors, see bottom of Table 1). As seen from Figure 2A, sample 3 exhibits a strong chemical gradient, whereas the other two are homogeneous with respect to chemical composition (not shown). In Figure 2, the major steps of the SEC-UV/RI data evaluation process are exemplarily shown for sample 3. The obtained values of M h n and M h w for all three copolymers are listed in Table 1 (the calibration of detectors was performed with standard solutions of PS, PMMA, PB, and PZL homopolymers). Also included in Table 1 are the results from independent NMR measurements (f M h n) and SEC with on-line differential viscosity (SEC-UV/RI/DV) and multiangle laser light scattering (SEC-UV/RI/MALLS) detection (f M h n and M h w) (the characterization of samples 1 and 2 with DV and MALLS was previously reported in ref 12). It is seen from the data in Table 1 that NMR results agree well with the M h n values obtained by SEC-UV/RI; deviations are usually
