Article pubs.acs.org/Macromolecules
Characterization of Branched Polymers by Comprehensive Two-Dimensional Liquid Chromatography with Triple Detection Seonyoung Ahn,† Hyojoon Lee,† Sekyung Lee, and Taihyun Chang* Department of Chemistry and Division of Advanced Materials Science, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Korea ABSTRACT: In the branching analysis by size exclusion chromatography (SEC)/ triple detection (concentration, light scattering, and viscosity detectors) method, the branch number is calculated from the extent of chain size contraction due to chain branching relative to the linear polymer of the same molecular weight (MW). A problem can arise from the fact that polymer chain size depends on both MW and chain branching. Since SEC separates polymers according to the chain size, an SEC fraction of randomly branched polymers may contain polymer species heterogeneous in both MW and chain architecture in general. As a solution of the problem, we propose a separation of polymers by interaction chromatography according to MW first and then measure the chain size distribution of polymers in the homogeneous MW fraction by SEC/triple detection. The analysis scheme is successfully established by online two-dimensional liquid chromatography combining temperature gradient interaction chromatography and SEC/triple detection.
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INTRODUCTION Long chain branching (LCB) is one of the important molecular characteristics which influences processability and performance of polymeric materials significantly.1,2 Therefore, precise characterization of chain branching is a requisite step to understand the relationship between the molecular characteristic and the rheological and mechanical properties of the polymeric materials.3,4 It is nontrivial to characterize LCB precisely. The most widely employed method to characterize the branch distribution is size exclusion chromatography separation coupled with triple (concentration, light scattering, and viscosity) detection (SEC/TD).5−7 The method is based on the theoretical study by Zimm and Stockmayer in 1949, in which they worked out how the chain size (mean-square radius of gyration, Rg2) is affected by chain branching.8 Chain branching reduces Rg2 relative to the linear chain of the same molecular weight (MW) and the ratio of Rg2 values is defined as the chain contraction factor, g g≡
between g and g′ needs to be established to calculate branch numbers since the theoretical chain contraction factor is derived for Rg2, not [η]. The g factor has been derived for a few model branched chain architectures such as regular stars (having uniform MW arms)8 and regular combs (having uniform MW branches).10 Also, a number of experimental works have been carried out to verify the theoretical prediction and to establish a reliable experimental methodology for branching analysis of polymers.7,11−14 Combining SEC separation and multiple detection, it is possible to separate polydisperse polymers into narrow (in elution volume) fractions and to measure MW, Rg2, and [η] for each eluting fraction online. If we assume that each fraction of SEC effluent contains polymers homogeneous in both MW and chain architecture, and if we have an appropriate g′ function for the polymer system, one can map the bivariate distribution in MW and branch number of a branched polymer by SEC/TD method. The results in the literature cannot be said to be very successful and the deviations have been attributed to the following reasons. (1) All theories dealing with g factor were developed for random-walk chain (Gaussian distribution of the chain segments) model while most of the experimental works carried out in good solvent condition including all the SEC/TD experiments. (2) Because of the difficulty to measure Rg2 precisely, in particular for the polymers with small Rg2, the intrinsic viscosity was more frequently measured. But the relationship between g and g′ is not well-established.
(R g 2)B (R g 2)L
(1)
where the subscripts B and L denote branched and linear polymers, respectively. Later, Zimm and Kilb reported that the ratio of intrinsic viscosity, [η], would give equivalent information on the chain size contraction upon branching.9 g′ ≡
[η]B [η]L
(2)
Since [η] can be measured with a higher precision than Rg2, particularly for low-MW polymers, g′ is more frequently measured experimentally. However, an appropriate relationship © 2012 American Chemical Society
Received: September 30, 2011 Revised: March 20, 2012 Published: April 10, 2012 3550
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mechanism, the PS sample contains regular star-shaped polymers of varying number of branches while each branch has a very narrow MW distribution. The linear PS was synthesized by anionic polymerization using n-butyl Li as an initiator, which is known to yield a broader MW distribution due to a relatively slow initiation rate of n-butyl Li.33 To prepare a linear PS sample whose SEC elution volume fully overlaps with the star-shaped PS, three different MW linear PS were prepared and then mixed to obtain such a MW distribution. The characterization data of the polymer samples are given in Table 1.
In this paper, we would like to focus on another problem in the SEC/TD branching analysis. Although it is not frequently addressed in branching analyses by the SEC/TD method, an SEC fraction would not contain homogeneous polymer species.15−17 Let alone the serious band broadening in SEC, SEC does not separate polymers according to MW but chain size. Polymers with different MW and different chain architecture can have the same chain size. If an SEC fraction does not contain polymers of homogeneous MW (local polydispersity), the basic assumption in the SEC/TD branching analysis based on the chain contraction factor of Zimm and Stockmayer is no longer valid. This problem may not be serious when the chain size has a monotonous dependence on MW such as regular star-shaped polymers, but it can be a source of error for branched polymers in general. As a solution of the problem described above, we propose two-dimensional liquid chromatography (2D-LC) analysis. 2D-LC is a powerful tool for the analysis of complex polymers which have distributions in more than one molecular characteristic.18−23 In most 2D-LC separations of synthetic polymers carried out so far, interaction chromatography (IC) has been used for the first-D LC separating the polymers by chemical heterogeneity while the second-D separation has been done by SEC separating the polymer chains with respect to the molecular size.20,24−27 But IC can separate polymers according to MW as well with much higher resolution than SEC.28,29 In particular, temperature gradient interaction chromatography (TGIC) has become a well-established technique to separate branched polymers according to MW nearly independent of long chain branching.30−36 Taking advantage of the sensitivity on MW of IC separation, a branched polymer system can be separated according to MW first and then SEC/TD analysis can be applied to the homogeneous MW fractions, which conforms to the analysis scheme based on chain contraction concept. In this study, we report online TGIC × SEC mode 2D-LC characterization of branched polymers by fractionating the samples into homogeneous MW fractions before the SEC/TD analysis. To demonstrate the problem in conventional SEC/TD analysis of branched polymer systems, we employed a model system: an artificial mixture of linear and star-shaped PS. The star-shaped PS was prepared by linking polystyryl anions with divinylbenzene to yield a series of star-shaped PS with different number of branches of equal length. Therefore, the mixture of star-shaped PS and linear PS has a bivariate distribution in both MW and branch number. Such an IC × SEC mode 2D-LC separation of branched polymers has been done earlier by Gerber et al. They demonstrated a mixture of star-shaped and linear polymers by off-line32 as well as online37 by IC x SEC mode 2D-LC. Gorbunov et al. reported a simulation result on the 2D-LC separation for the same mixture system.38 However, they only demonstrated the separation itself, not on the branching analysis by multiple detection method. In this study, we successfully demonstrated that such a 2D-LC separation can be combined with triple detection to correctly characterize the complex branched polymer.
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Table 1. Molecular Weight Characteristics of Linear PS, Star-Shaped PS, and PS Mixturea linear PS
a
star-shaped PS
PS mixture
Mw
Mw/Mn
Mw,arm
Mw
Mw/Mn
Mw
Mw/Mn
127 000
1.46
30 000
152 000
2.01
144 000
1.89
Determined by SEC/light scattering detection.
SEC Analysis. Two mixed bed columns (Polymer Lab. Mixed C, 300 × 7.8 mm i.d.) were used at a column temperature of 40 °C. Eluent was THF (Samchun, HPLC grade) at a flow rate of 0.8 mL/min. SEC chromatograms were recorded with a light scattering (LS)/ refractive index (RI)/viscometer (DP) (Viscotek TDA 302) and a UV absorption detector (TSP, UV100 at 260 nm wavelength). The dn/dc value for PS in THF is 0.185 mL/g. Polymer samples were dissolved in THF at a concentration of ca. 1 mg/mL, and the injection volume was 100 μL. RP-TGIC Analysis. For the reversed phase (RP)-TGIC analysis, a C18 bonded silica column (Nueleosil C18, 5 μm, 300 Å pore, 150 × 4.6 mm i.d.) was used. Mobile phase was a CH2Cl2/CH3CN mixture (57/43, v/v, Samchun, HPLC grade) at a flow rate of 0.5 mL/min. Temperature of the column was controlled by circulating fluid from a programmable bath/circulator (ThermoHaake, C25P) through a homemade column jacket. The chromatograms were recorded with an LS (Wyatt, MiniDawn), RI (Shodex, RI-101), and a UV absorption (TSP, UV 2000 at 260 nm wavelength) detectors for online determination of absolute MW of polymers. RP-TGIC × SEC 2D-LC Analysis. For the first-D RP-TGIC separation, the same experimental conditions as in the one-dimensional RP-TGIC analysis were used except for the flow rate. The flow rate of the first-D RP-TGIC was set low at 0.01 mL/min to synchronize with the second-D SEC separation. For the second-D SEC separation, one mixed bed column (Polymer Lab. Mixed C, 300 × 7.8 mm i.d.) was employed. Temperature of the SEC column was controlled at 60 °C by a column oven (Futecs, AT-4000). Eluent was THF (Samchun, HPLC grade) at a flow rate of 1.2 mL/min. The chromatograms were recorded with a triple detector (Viscotek TDA 302) for online determination of the absolute MW and intrinsic viscosity of polymers.
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RESULTS AND DISCUSSION To demonstrate the problem associated with “local polydispersity” in the conventional SEC/TD branching analysis, we selected a PS mixture as a model system consisting of equal amount of the linear PS and the star-shaped PS. Figure 1a displays SEC chromatograms of the three samples; the linear, the star-shaped, and the 1:1 mixture of the two. In the SEC chromatogram of the star-shaped PS, which has a distribution in branch number, is partially resolved as separate peaks. The lowest MW peak is the single arm and the two arm star (a linear PS with MW = 2 × MWarm) appears as a shoulder of the main peak containing more highly branched species which are not resolved. It is a natural result of size-based SEC separation since the chain size of regular star-shaped polymers does not change much as the number of arm increases, and SEC resolution is not high due to the band broadening. The linear PS is a mixture of three PS samples prepared by anionic
EXPERIMENTAL SECTION
Materials. The star-shaped polystyrene (PS) sample was synthesized by linking anionic-polymerized polystyryl anions with divinylbenzene (DVB). The polymerization of styrene was carried out in cyclohexane using sec-butyl Li as an initiator. Details of the synthetic procedure were reported previously.39 Because of the synthetic 3551
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been reported to fall in a range of 0.5−1.5. For regular starshaped polymers, it was found experimentally as 0.7−0.8 in good solvent conditions.11 Intrinsic viscosity vs MW plots of the three polymer samples are shown in Figure 2. Linear PS exhibits a linear dependence
Figure 2. Intrinsic viscosity vs MW plots of linear PS (black square), star-shaped PS (red circle), and PS mixture (blue triangle).
of log [η] on log MW conforming to the Mark−Houwink relationship with a slope of 0.72, which is consistent with the literature values for linear random coils in the range of 0.7− 0.74.41 The intrinsic viscosity of star-shaped PS (red circle) is lower than linear PS (black square), indicating that chain branching leads to contraction of the chain size relative to the linear polymers at the same MW. The deviation increases as MW (thus branch number) increases. Since linear and starshaped PS having the same hydrodynamic volume coelute in the SEC separation, the intrinsic viscosity of the PS mixture (blue triangle) falls in between the linear and star-shaped PS. The g′ values calculated from the intrinsic viscosities of the three samples are plotted as a function of MW in Figure 3a.
Figure 1. (a) SEC chromatograms of the linear PS, star-shaped PS, and PS mixture. (b) Molecular weight vs elution time plots of linear PS (solid line) and star-shaped PS (dashed line). Separation condition: two mixed bed columns (Polymer Laboratories, PL mixed C), THF eluent at the column temperature of 40 °C. Flow rate was 0.8 mL/min.
polymerization with n-butyl Li initiation. The three PS samples were mixed to give the overall peak shape similar to that of the star-shaped PS and at the same time to cover the entire elution volume range of the star-shaped PS. Therefore, the 1:1 mixture of the linear and star-shaped PS yields an SEC chromatogram showing the same general feature of the star-shaped polymer. Since the SEC separation is based on hydrodynamic volume, polymers with different MW can coelute due to the differences in their chain architectures. Figure 1b displays the plots of MW vs SEC elution time for the star-shaped PS (dashed red line) and the linear PS (solid black line) determined by light scattering detection. Star-shaped PS elutes later than linear PS of the same MW. In other words, a star-shaped PS coelutes with a lower MW linear PS since a star-shaped polymer has a chain size smaller than the linear polymer of the same MW. Therefore, an SEC fraction of the PS mixture contains coeluting two different MW species: a linear PS of lower MW and a star PS of higher MW. Such local polydispersity may lead to an erroneous result in SEC/TD branching analysis.15−17,40 As the branch number of regular star-shaped polymers increases, the contraction factor decreases from 1. For regular star-shaped polymers, the following equation was derived to relate the branch number, f, to the chain contraction factor, g.8
g=
3f − 2 f2
(3)
The relationship between g and g′ is often given by g′ ≅ g ε
(4) Figure 3. Plots of g′ (a) and branching number f (b) vs molecular weight for linear PS (black square), star-shaped PS (red circle), and PS mixture (blue triangle).
The exponent ε depends on a number of factors including solvent, temperature, and chain architecture. The ε value has 3552
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The g′ value of star-shaped PS decreases rapidly upon increase of MW. The g′ values for the mixture fall in between the linear and star-shaped PS. In Figure 3b, the branch number, f, calculated according to eqs 3 and 4 is plotted against MW. The value of ε in eq 4 was determined with a priori information that MWstar = f × MWarm for the regular star-shaped PS. The best fit of branch number vs MWstar was obtained when ε = 0.7 was used. The direct comparison of g and g′ was not attempted, but this should be a good enough confirmation of the ε value for this study. Even though the resolution of SEC for the starshaped PS is not so good and an SEC fraction contains a mixture of differently branched species to some extent, the elution sequence was maintained well and the analysis based on the chain contraction concept seems to work reasonably well. For the linear PS, the g′ value (in Figure 3a) and the branch number (in Figure 3b) of linear PS were calculated relative to the best-fit Mark−Houwink equation displayed in Figure 2 (solid line), and it follows f = 2 closely over the entire MW range as expected. The PS mixture shows an intermediate branch number between the star-shaped PS and the linear PS. It is an expected result considering the coelution of linear and star-shaped PS. This result does not reflect the correct picture of the polymer system. The correct picture should be two separate lines of star-shaped PS and linear PS, indicating that the sample is a mixture of the two polymer species. Furthermore, the MW axis does not represent homogeneous polymer species but a weight-average MW of linear and star-shaped PS having the same chain size. The problem displayed in Figure 3 arises from the fact that a SEC fraction contains polymer species polydisperse in both MW and chain architecture. To carry out the branching analysis based on the chain contraction concept, it is necessary to separate polymers according to MW first. IC is an adequate technique for the purpose.42,43 TGIC is known to separate branched polymers according to MW nearly independent of chain architecture.3,4,30−36 Figure 4 displays RP-TGIC
chromatograms of the three polymer samples. A sharp peak appearing at tE ≈ 5 min in all three chromatograms is the injection solvent peak. In the star-shaped PS chromatogram, a series of the peaks corresponds to star-shaped PS with increasing branch number since MWstar is “quantized” by MWarm with a narrow MW distribution. These peaks were not well resolved in the SEC separation (Figure 1a) due to its sizesensitive separation as well as band broadening. By virtue of its high resolution and sensitivity to MW, IC can resolve the branched polymer far better than SEC according to the branch number. Nonetheless, as the number of arms increases, the elution peaks start to overlap. This is mainly due to the overlap of the finite MW distribution of the branched species even though each star-shaped PS species has a very narrow MW distribution close to the Poisson distribution.44 The elution peak of linear PS is multimodal in contrast to the unimodal shape in SEC. The linear PS sample is a mixture of three different linear PS samples prepared by anionic polymerization using n-butyl Li initiator to cover the elution volume range of the star-shaped PS in SEC. The three linear PS components are partially resolved in the TGIC separation by virtue of the low band broadening in TGIC while they are hardly discernible in the SEC separation (Figure 1a). Plots of MW vs TGIC elution time of the three samples are also shown in Figure 4. The three PS samples show identical MW vs elution time plots, indicating the sensitivity of TGIC retention on MW not on chain architecture in contrast to SEC (Figure 1b). If RP-TGIC/TD analysis is carried out based on the chain contraction factor concept, the problem of inhomogeneous MW fraction in SEC/TD analysis can be resolved. Nonetheless, it is not avoidable that an RP-TGIC fraction of the PS mixture is still a mixture of linear and star-shaped PS at the same MW. Therefore, it will provide a correct average branch number as a function of MW, but a full mapping of the branched structure of the polymer system is still not possible. If the linear and branched species in a homogeneous MW fraction obtained from RP-TGIC separation can be further separated according to the chain size, a full mapping of the branched structure could be achieved. To pursue the idea, a 2D-LC separation was carried out by combining RP-TGIC and SEC as the first-D and the second-D LC separation, respectively. For the fast repetition of the second-D SEC separation, one GPC column and a fast flow rate had to be used at the cost of resolution to some extent. A triple detection system (light scattering, differential refractive index, viscosity detectors) was employed as the second-D LC detectors. The results of the online 2D-LC separation for the PS mixture are displayed in Figure 5 in which three 2D-LC chromatograms obtained by LS, RI, and viscosity detectors are shown in the form of contour map. They have similar shapes but with distinct intensity distribution. The characteristic intensity profile represent the different response of the three detectors: RI detector shows the concentration distribution while the LS detector signal is approximately proportional to MW × concentration, and the viscosity detector (differential pressure, DP) signal is approximately proportional to MWα × concentration where α is the Mark−Houwink exponent. In the 2D-LC chromatograms, unreacted arms and stars with a small number of arms show up as resolved peaks at RP-TGIC tE ≈ 350−450 min. Projections of a 2D-LC chromatogram to each axis corresponds to the 1D-LC chromatogram of the corresponding axis, and the general features of SEC and RP-TGIC chromatograms shown in Figures 1a and 4 can be observed.
Figure 4. RP-TGIC chromatogram of three samples recorded by a UV detector. The molecular weights obtained by light scattering detection are also shown in the plot. The temperature program is shown in the top abscissa. Separation condition: Nucleosil C18, 500 Å pore, 7 μm particle, 150 × 4.6 mm i.d. Eluent: CH2Cl2/CH3CN (57/43, v/v) at a flow rate of 0.5 mL/min. 3553
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column was used to speed up the analysis), only a trace of peak splitting at the completion of the linear PS elution is observed. We further examined the 2D-LC chromatogram as to whether the first-D TGIC separation indeed yielded the fractions with homogeneous MW. The three second-D SEC chromatograms of the TGIC fractions at tE = 500, 550, and 600 min are displayed in Figure 6. In addition to the chromatograms (LS, RI, and DP
Figure 5. Contour plots of RP-TGIC × SEC 2D-LC chromatograms of the mixture of star-shaped PS and linear PS: first-D RP-TGIC: column (Nucleosil C18, 500 Å, 7 μm particle, 150 × 4.6 mm), eluent: CH2Cl2/CH3CN (57/43, v/v) at a flow rate of 0.01 mL/min second-D SEC: PL mixed-C (Polymer Lab, 300 × 8 mm i.d.), THF eluent at a flow rate of 1.2 mL/min; column temperature: 60 °C.
Figure 6. Second-D SEC chromatograms of the first-D TGIC fractions eluting at tE = 500, 550, and 600 min. Normalized signal intensity from light scattering (red), refractive index (black), and viscosity (blue) detectors are plotted together. Log intrinsic viscosity of the sample (blue circle), log intrinsic viscosity of linear polymer of the same molecular weight as the sample (red triangle), and calculated branch number (black square) are also shown. Mw, Mn, and Mw/Mn are obtained by light scattering detection.
But the 2D-LC chromatogram contains more information than two 1D-LC chromatograms. One feature we can see easily before the detailed analysis is the splitting of the chromatogram toward high-MW marked with arrows. If the resolution of the SEC separation is good, peak splitting between the linear PS and starshaped PS would be like Figure 1b since RP-TGIC separates polymer according to MW. Because of the relatively poor resolution of SEC (to make the situation worse, only one SEC
detection), intrinsic viscosity of the sample ([η]), MW (plotted as the equivalent intrinsic viscosity of linear PS of the same MW, [η]lin, to compare with [η] in the same scale), and branch 3554
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SEC/TD analysis assuming homogeneous SEC fraction yields an incorrect picture in both MW and branch number. To improve the accuracy in the SEC/TD branching analysis, we propose 2D-LC, RP-TGIC × SEC separation as a potential solution in which branched polymers are first separated into homogeneous MW fractions by RP-TGIC and then the homogeneous MW fractions are subjected to SEC/TD analysis. We demonstrated that such a 2D-LC/TD method combined with Zimm−Stockmayer contraction factor concept could yield a far more accurate picture of the chain branching in complex polymer systems.
number calculated by eq 3 are also plotted. The deviation of [η] from [η]lin reflects the extent of branching of the eluting polymer species. First of all, the Mw/Mn values measured by LS detection are very close to 1 (1.004 or 1.005) for all cases, indicating that the first-D TGIC separation successfully separated the mixture sample according to MW as expected. At tE = 500 min, polymer species of MW ∼ 120 000 is eluted which contains 4-arm star-shaped PS. But they were not well separated from the linear PS because of the low resolution of SEC. As a result, the branch number of the whole polymer was obtained as ∼2.5. As the number of branches increases, the SEC separation of the star-shaped PS from the linear PS of the same MW is getting better since the size difference increases as the number of branches increases. At tE = 550 (MW ∼ 160 000) and 600 min (MW ∼ 220 000), the SEC chromatograms showed a clear drop of [η] as the elution time increases, indicating that the branched polymers (∼5-arm and ∼7-arm star-shaped polymers, respectively) elutes at the late part of the peak while linear polymers of the same MW elutes at the early part. Nonetheless, the calculated branch number is still lower than the true value. The same type of SEC/TD analysis based on chain contraction factor can be done for every set of the second-D SEC/ TD chromatograms, and the result is displayed in Figure 7.
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AUTHOR INFORMATION
Corresponding Author
*Tel: +82-54-279-2109; Fax: +82-54-279-3399; e-mail tc@ postech.ac.kr. Author Contributions †
Equal contributions.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We acknowledge the support from NRF via NRL (R0A-2007000-20125-0), SRC (R11-2008-052-03002), and WCU (R312008-000-10059-0) programs and from LGchem.
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REFERENCES
(1) McLeish, T. C. B. Adv. Phys. 2002, 51, 1379−1527. (2) Graessley, W. W. Polymeric Liquids and Networks: Dynamics and Rheology; Taylor & Francis Group: New York, 2008; p 550. (3) Snijkers, F.; van Ruymbeke, E.; Kim, P.; Lee, H.; Nikopoulou, A.; Chang, T.; Hadjichristidis, N.; Pathak, J.; Vlassopoulos, D. Macromolecules 2011, 44, 8631−8643. (4) Chen, X.; Rahman, M. S.; Lee, H.; Mays, J.; Chang, T.; Larson, R. Macromolecules 2011, 44, 7799−7809. (5) Mori, S.; Barth, H. G. Size Exclusion Chromatography; SpringerVerlag: New York, 1999; p 208. (6) Striegel, A. M. Anal. Chem. 2005, 77, 104A−113A. (7) Striegel, A. M. Encycl. Chromatogr., 3rd ed. 2010, 2, 1417−1420. (8) Zimm, B. H.; Stockmayer, W. H. J. Chem. Phys. 1949, 17, 1301− 1314. (9) Zimm, B. H.; Kilb, R. W. J. Polym. Sci. 1959, 37, 19−42. (10) Casassa, E. F.; Berry, G. C. J. Polym. Sci., Polym. Phys. Ed. 1966, 4, 881−897. (11) Burchard, W. Adv. Polym. Sci. 1999, 143, 113−194. (12) Farmer, B. S.; Terao, K.; Mays, J. W. Int. J. Polym. Anal. Charact. 2006, 11, 3−19. (13) Radke, W.; Müller, A. H. E. Macromolecules 2005, 38, 3949− 3960. (14) Roovers, J. Polymer 1979, 20, 843−849. (15) Gaborieau, M.; Gilbert, R. G.; Gray-Weale, A.; Hernandez, J. M.; Castignolles, P. Macromol. Theory Simul. 2007, 16, 13−28. (16) Castignolles, P.; Graf, R.; Parkinson, M.; Wilhelm, M.; Gaborieau, M. Polymer 2009, 50, 2373−2383. (17) Gaborieau, M.; Castignolles, P. Anal. Bioanal. Chem. 2011, 399, 1413−1423. (18) Berek, D. Anal. Bioanal. Chem. 2010, 396, 421−441. (19) Im, K.; Park, H.-W.; Kim, Y.; Chung, B.; Ree, M.; Chang, T. Anal. Chem. 2007, 79, 1067−1072. (20) Im, K.; Park, H.-W.; Lee, S.; Chang, T. J. Chromatogr., A 2009, 1216, 4606−4610. (21) Pasch, H.; Adler, M.; Rittig, F.; Becker, S. Macromol. Rapid Commun. 2005, 26, 438−444. (22) van der Horst, A.; Schoenmakers, P. J. J. Chromatogr., A 2003, 1000, 693−709.
Figure 7. Plot of branch number vs MW for PS mixture. Solid lines are for star-shaped PS (red line) and linear PS (blue line). Black dotted line is the 1D-SEC analysis result (Figure 3b).
If everything was done perfectly, only two lines corresponding to linear and star-shaped polymers should be seen. However, the limited resolution in the fast second-D SEC separation leaves artifacts between the two lines. In addition, branch numbers of star-shaped PS were somewhat underestimated at low branch number region where SEC cannot resolve the starshaped PS from the linear PS with the same MW very well. Nonetheless, by virtue of the first-D TGIC separation according to MW and the subsequent SEC/TD measurements, the distributions of both linear and star-shaped PS are clearly visible. As the number of branches increases, the branch analysis becomes more precise in contrast to the 1D-SEC/TD analysis shown in Figure 3b. In summary, we investigated a problem in branching analysis by the SEC/TD method associated with “local polydispersity”, coelution of polymer species of the same size but polydisperse in both chain architecture and MW. We demonstrated the problem by using a model system: a mixture of linear and starshaped PS. To apply the chain contraction factor concept for the branching analysis, it is necessary to compare the chain size of polymers at the same MW. Therefore, the simple-minded 3555
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(23) Edam, R.; Meunier, D. M.; Mes, E. P. C; Van Damme, F. A.; Schoenmakers, P. J. J. Chromatogr., A 2008, 1201, 208−214. (24) Jiang, X.; Van der Horst, A.; Lima, V.; Schoenmakers, P. J. J. Chromatogr., A 2005, 1076, 51−61. (25) Raust, J. A.; Brull, A.; Moire, C.; Farcet, C.; Pasch, H. J. Chromatogr., A 2008, 1203, 207−216. (26) Ginzburg, A.; Macko, T.; Dolle, V.; Bruell, R. J. Chromatogr., A 2010, 1217, 6867−6874. (27) Roy, A.; Miller, M. D.; Meunier, D. M.; de Groot, A. W.; Winniford, W. L.; Van Damme, F. A.; Pell, R. J.; Lyons, J. W. Macromolecules 2010, 43, 3710−3720. (28) Lee, W.; Lee, H.; Cha, J.; Chang, T.; Hanley, K. J.; Lodge, T. P. Macromolecules 2000, 33, 5111−5115. (29) Al Samman, M.; Radke, W.; Khalyavina, A.; Lederer, A. Macromolecules 2010, 43, 3215−3220. (30) Lee, H.; Chang, T.; Harville, S.; Mays, J. W. Macromolecules 1998, 31, 690−694. (31) Perny, S.; Allgaier, J.; Cho, D.; Lee, W.; Chang, T. Macromolecules 2001, 34, 5408−5415. (32) Gerber, J.; Radke, W. Polymer 2005, 46, 9224−9229. (33) Im, K.; Kim, Y.; Chang, T.; Lee, K.; Choi, N. J. Chromatogr., A 2006, 1103, 235−242. (34) Ahn, S.; Im, K.; Chang, T.; Chambon, P.; Fernyhough, C. M. Anal. Chem. 2011, 83, 4237−4242. (35) Chambon, P.; Fernyhough, C. M.; Im, K.; Chang, T.; Das, C.; Embery, J.; McLeish, T. C. B.; Read, D. J. Macromolecules 2008, 41, 5869−5875. (36) Li, S. W.; Park, H. E.; Dealy, J. M.; Maric, M.; Lee, H.; Im, K.; Choi, H.; Chang, T.; Rahman, M. S.; Mays, J. Macromolecules 2011, 44, 208−214. (37) Gerber, J.; Radke, W. e-Polym. 2005, 45. (38) Gorbunov, A. A.; Vakhrushev, A. V. Polymer 2009, 50, 2727− 2735. (39) Lee, H.-J.; Lee, K.; Choi, N. J. Polym. Sci., Part A: Polym. Chem. 2005, 43, 870−878. (40) Tobita, H.; Saito, S. Macromol. Theory Simul. 1999, 8, 513−519. (41) Brandrup, J., Immergut, E. H., Eds.; Polymer Handbook, 4th ed.; Wiley-Interscience: New York, 1998; p 1920. (42) Chang, T. Adv. Polym. Sci. 2003, 163, 1−60. (43) Chang, T. J. Polym. Sci., Polym. Phys. 2005, 43, 1591−1607. (44) Ryu, J.; Im, K.; Yu, W.; Park, J.; Chang, T.; Lee, K.; Choi, N. Macromolecules 2004, 37, 8805−8807.
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