Analytical Rheology of Asymmetric H-Shaped ... - ACS Publications

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Analytical Rheology of Asymmetric H-Shaped Model Polybutadiene Melts Xue Chen,†,∥,⊥ Hyojoon Lee,‡,⊥ M. Shahinur Rahman,§ Taihyun Chang,‡ Jimmy Mays,§ and Ronald Larson*,† †

Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States Department of Chemistry and Division of Advanced Materials Science, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Korea § Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37966, United States ‡

ABSTRACT: An asymmetric H-shaped model polybutadiene (PBd) melt, H(SS13LL20)B58, with a backbone of molar mass 58 kg/mol and with two short arms of molar mass 13 kg/ mol and two long arms with molar masses around 20 kg/mol, was designed and synthesized by anionic polymerization and purified by fractional precipitation. To obtain this novel structure, two short arms were synthesized and linked together using 4-(dichloromethylsilyl)diphenylethylene (DCMSDPE). The backbone was then grown from this linkage point to produce an asymmetric star intermediate terminating in a reactive anion at the end of the backbone. The two long arms were similarly grown in a separate reaction vessel and then linked by DCMSDPE, and these linked long arms were then attached to the backbone of the asymmetric star. The multiple steps of this reaction scheme led to multiple possible byproducts. The most likely of these were identified and quantified by temperature gradient interaction chromatography (TGIC) performed on both purified and unpurified H(SS13LL20)B58 product and its asymmetric star-shaped synthetic precursor. We then performed linear rheological studies on purified and unpurified H(SS13LL20)B58, its star precursor, and blends of the purified H polymer with its star precursor and found that their rheological behaviors can be predicted reasonably accurately by the “hierarchical model” [Wang et al. (2010)], if the impurities identified by TGIC are accounted for in the rheological modeling. These results show that TGIC characterization of product and intermediate reaction products, supplemented by rheological studies of controlled blends, are important steps in determining the accuracy of rheological models of polymers with complex branching architectures. hyperbranched (or branch-on-branch) topologies.14 The rheology of such long-chain branched polymers is extremely sensitive to branch length and branch polydispersity as well as to topology. In fact, failure to predict accurately the rheology of such materials might sometimes be the result of imperfections in the synthesis of these polymers, which are never completely monodisperse nor completely free of contaminating polymers, such as unreacted branches, or complex multiply branched side products. Often conventional analytical techniques are unable to detect such impurities at the small levels that can strongly influence rheological properties as discussed in this paper. For this reason, rheological data themselves are looked to as a means of assessing sample purity and quality. However, one confronts the problem of ill-posedness or even circular reasoning, since one is looking to such data as a means of confirming or improving rheological models. If deviations between model predictions and measured rheology could either indicate imperfections in synthesis that are difficult to pick up

1. INTRODUCTION Long-chain branching has pronounced effects on rheological and processing properties of polyolefins, and the control of long-chain branching for optimal processing has long been a goal of polymer synthetic chemists. Measuring and modeling the rheology of such polymers could be of great assistance in designing and synthesizing such polymers in two important ways: (1) it would allow one to infer the likely processing characteristics of the polymer (for example, the “melt strength”) and (2) it might confirm or even determine which branching structures are actually present in the melt, since these might differ from what the synthetic chemist intended to make.1 This latter use of rheology is sometimes referred to as “analytical rheology”, i.e., the use of rheology as an analytical characterization tool that can augment the information gleaned from size exclusion chromatography and other analytical methods.2 To pursue either of these goals, the ability must be developed to predict the rheology of branched polymers with different levels and types of branching. To this end, various researchers have studied a “zoo” of various lowpolydispersity model long-chain branched polymers, with topologies ranging from star3−8 to “H”9 to “comb”10−13 and © 2012 American Chemical Society

Received: February 21, 2012 Revised: May 31, 2012 Published: June 29, 2012 5744

dx.doi.org/10.1021/ma300337x | Macromolecules 2012, 45, 5744−5756

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confidence, both in the quality of our rheological data and in the predictive power of our rheological model, than would be possible in the absence of these added steps. Our study describes the following tasks: (1) synthesis of a model asymmetric H-shaped 1,4-PBd (polybutadiene) polymer that is carefully designed to test physical theories; (2) careful characterization of the molar mass and branching properties of the asymmetric H polymer; (3) purification of the H polymer by fractionation; (4) blending of the asymmetric H polymer with its precursor star-shaped 1,4-PBd; (5) measurement of the linear rheological properties of the asymmetric H polymer and its blends; (6) comparison of the measured viscoelastic properties with predictions derived from the proposed theory. This paper is organized as follows. Section 2 describes the synthesis techniques and sample characterization. In section 3, we describe the hierarchical tube theory and modeling details. In section 4, we introduce our synthesized product H(SS13LL20)B58 and its asymmetric star-shaped synthetic precursor S(SS13B58) and describe molecular characterization and rheological measurements and compare the rheology to the predictions of the “hierarchical model”. In particular, we show that the “hierarchical model” yields quantitative predictions for our asymmetric H polymers and its blend with its precursor. Conclusions are drawn in section 5.

using the standard characterization methods or indicate failings of the rheological model, how is one to obtain reliable inferences from the rheological data? Here we seek to address this conundrum through both improved sample characterization using temperature gradient interaction chromatography (TGIC)15,16 and through “combinatorial rheology”. By “combinatorial rheology” we mean the measurement of the rheology of both the sample itself and of blends of the sample with simpler linear and star-branched polymers.17 These measurements are then modeled theoretically and used to help confirm or determine more precisely the composition of the original sample. Combinatorial rheology seeks to overcome the ambiguity inherent in modeling rheological data for a polymer sample of uncertain or questionable compositional purity. It does this by supplementing data for the polymer itself with multiple other sets of data obtained by blending the test polymer with polymers of known, simple, structure and by seeking to predict the rheology of all such blends using a single rheological model with fixed input parameters. By challenging both the rheological model and the presumed sample structure with multiple sets of data, one enhances the probability of correctly inferring both the compositional purity of the original sample and the reliability of the rheological model. In a previous paper,18 we followed this approach for anionically synthesized symmetric H polybutadienes, where all four side-branches were of the same length. Symmetric H polymers composed of polystyrene, polyisoprene, or polybutadiene have also been previously studied by multiple groups.9,19−23 Here we study in great detail a model “asymmetric H” polybutadiene melt, with two long arms and two short arms, specially synthesized for this purpose. Our work thus represents the first study of a well-characterized, anionically synthesized, asymmetric H molecule. Asymmetric H molecules are representative of H-shaped polymers in commercial melts, which contain branches of differing length. Because of the novel synthesis method, the reactions that actually occur in synthesizing the asymmetric H are explored in detail here through advanced characterization methods. We model the rheology of the H polymer and its synthetic precursor using a generalized advanced “tube” model (the “hierarchical model”) that allows inclusion of multiple branching architectures and of arbitrary polydispersity in both backbone and branch molecular weights. This model is therefore able, in principle, to predict the rheology of not only ideal monodisperse symmetric H polymers but also the effect of arm and backbone polydispersity and the effect of impurities that might be present in the polymer due to the imperfection of the reaction and of the fractionation or that we deliberately mix into the polymer as a means of assessing the sensitivity of the rheology to such impurities. We characterize both the H polymer and its synthetic precursor, which is an asymmetric three-armed star-shaped polymer, by temperature gradient interaction chromatography (TGIC) and rheology. The characterization is carried out both before and after purification to increase our confidence in their composition structures and to help identify the reactions that have occurred. We also combine the characterization information with that obtained from the rheology of samples deliberately contaminated with known impurities of known concentration, to estimate whether the purified sample is pure enough to show little influence of the remaining impurities on the rheology. The end result is a much higher level of

Figure 1. Polybudienes studied in this work: (1) asymmetric threearmed star S(SS13B58) and (2) asymmetric H-shaped PBd, H(SS13LL20)B58.

2. EXPERIMENTS 2.1. Materials and Synthesis. The asymmetric H-shaped polymer H(SS13LL20)B58 is illustrated in Figure 1 (2), and its asymmetric three-armed star-shaped synthetic precursor, “S(SS13B58)”, is depicted in Figure 1 (1). Both 1,4-PBds with targeted molar masses were designed and synthesized as described below. As shown in Figure 1 (1), the three-armed asymmetric star has two identical short arms with targeted molar mass of 13 kg/mol and one long arm with targeted molar mass of 58 kg/mol. The asymmetric Hshaped PBd illustrated in Figure 1 (2) has two identical short arms attached to one end of the backbone and two identical long arms attached to another end. The molar masses of the targeted short arms, long arms, and the backbone of this asymmetric H PBd are 13, 20, and 58 kg/mol, respectively. Thus, the asymmetric H PBd is named H(SS13LL20)B58. To obtain high-quality branched polymers, the Hshaped 1,4-PBd was purified by using toluene/methanol as the solvent/nonsolvent pair. Because of our interest in developing rheological methods of identifying and characterizing the composition of complex mixtures of branched polymer species, we here study both the unpurified and purified H-shaped polymers, designating them respectively using the suffices “-UP” or “-P”. For example, H(SS13LL20)B58-UP designates the unpurified asymmetric H-shaped PBd with the targeted molar masses of 13, 20, and 58 kg/mol, respectively, for the short arm, long arm, and backbone. The samples 5745


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Figure 2. Reaction scheme for H(SSLL)B synthesis. we use here are believed to have very similar vinyl content, about 6%, since their synthesis conditions are the same. Figure 2 shows the synthetic route to produce asymmetric H(SS13LL20)B58.24 A living short arm of molar mass 13 kg/mol was synthesized using s-BuLi initiator in benzene at room temperature. An excess amount of living PBdLi was then added to 4(dichloromethylsilyl)diphenylethylene (DCMSDPE) to replace two chlorines. The result is an in-chain diphenylethylene (DPE) with two short arms. The third arm or a cross-bar of molar mass 58 kg/mol was synthesized by subsequent addition of s-BuLi and butadiene monomer. A solution of long arms with molar mass 20 kg/mol was synthesized separately, and then pairs of long arms were coupled, as was done for the short arms, by addition of DCMSDPE. Again, an excess of long arms was added to in-chain DPE having two long arms connected to it, so that all DCMSDPE would be consumed, if all long arms remained as living anions until linked together by DCMSDPE. (We will show evidence below, however, that some free DCMSDPE in fact survived this process, despite the use of excess long arms.) An asymmetric living star was then added to DPE with two long arms in the presence of tetrahydrofuran (THF); a dark red color formed immediately, indicating the activation of DPE. The reaction was terminated with degassed methanol to obtain the desired asymmetric H(SS13LL20)B58. 2.2. TGIC Characterization. The TGIC separations were carried out using a standard high performance liquid chromatography (HPLC) system equipped with a C18 bonded silica column (AkzoNobel, Kromasil, 300 Å pore, 150 mm × 4.6 mm, 5 μm particle size); the mobile phase was 1,4-dioxane at a flow rate of 0.4 mL/min. The sample solutions were prepared at ∼5 mg/mL in 1,4dioxane, and the injection volume was 100 μL.TGIC chromatograms were recorded with a light scattering detector (Wyatt miniDAWN), a

UV absorption detector (Younglin), and a refractive index detector (Shodex RI-101). The column temperature was programmed as a linear ramp from18 °C to up to 30 °C to have the PBd samples elute completely. A more detailed description of the principles and practice of TGIC can be found elsewhere.15,16 2.3. Preparation of Blends. The method of preparing the PBd blends was presented in our previous publication.18 In brief, targeted weight fractions of star or H polymers were dissolved in toluene that had been filtered through 0.2 μm pore sterile filters, allowing about a week in a fume hood for evaporation of the solvent. The samples were then dried under vacuum at room temperature for another 2 weeks to ensure removal of the excess toluene. Two methods were used to determine that excess toluene had been completely removed: (1) no toluene smell after drying under vacuum; (2) the weight of the sample become constant. The blends after drying were stored in a refrigerator for later use. 2.4. Rheological Measurements. Samples were compression molded into circular disks of 25 mm diameter and around 1.2 mm in height on a hot press. For each sample, linear viscoelastic measurements were performed in oscillatory shear mode with an ARES strain-controlled rheometer with a 25 mm parallel plate geometry and around 1 mm gap. Before starting the measurements, we left the sample in the parallel plate fixture to allow it relax for at least 12 h. Small-strain oscillatory shear tests were conducted at a constant temperature of 25 °C with frequency sweeps from 100 to 0.0001 rad/s. All strains were confirmed to be in the range of linear response. To make sure the samples are chemically stable and at equilibrium during the measurements, after making measurements from 100 to 0.0001 rad/s, we repeated the measurements from 100 to 0.001 rad/s on the same sample. The data were found to be repeatable to within 1% error, indicating that the sample had equilibrated sufficiently prior to the first 5746


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run. Carrying out the rheology under a nitrogen atmosphere and in the presence of added antioxidant helped to ensure sample stability.

relaxed long arms of the original H molecule, and one long arm, which is the backbone of the original H (see Figure 3b). As the two “short arms” of Figure 3b completely relax, the molecule finally becomes a “linear” chain with two branch points at the two ends, illustrated in Figure 3c. The final relaxation then occurs by arm retractions and reptation of an effectively “linear” chain. The beads incorporate the friction added to the chain backbone by the side branches. To predict the rheological behaviors of the samples, the dilution exponent α and the coefficient of branch-point drag p2 are set to be α = 4/3 and p2 = 1/12, as was done in our previous work.18 In addition to the material-independent parameters α and p2, the three material-dependent tube model parameters, namely the plateau modulus G0N, the entanglement molecular weight Me, and the frictional equilibration time τe, are set to be the same as those used previously,18 i.e., G0N = 1.095 MPa, Me = 1620, and τe = 5 × 10 −7 s. Furthermore, the “arm-frozen” option of the “hierarchical model” is used for all our predictions (see the definition of “arm-frozen” in Wang et al.25). We note here that while most available rheological models contain the same basic mechanisms of relaxation that are included in the version of the “hierarchical model” used here, there are other options, including models by Das et al.31 and van Ruymbeke et al.32 In addition, the “dilution” exponent α is sometimes taken to be unity, rather than the value α = 4/3 chosen here. It has also recently been suggested that α should be unity at short times and 4/3 at longer times.33 While it is beyond the scope of the present work to discuss these issues, we do note that refinements of these models are still underway and could lead to improved models in the future.

3. THEORY AND MODELING Here we validate the theory and pursue “combinatorial rheology” using the “hierarchical model” (v3.0).25 The “hierarchical model” has been successfully validated for linear, symmetric star, “T”- and “Y”-shaped asymmetric stars, symmetric H-shaped polymers, linear−linear blends, and commercial metallocene polyethylene copolymers.25−30 In particular, we found that the hierarchical model works well for the symmetric H-shaped polymers when the molecular characteristics, i.e., polydispersity of molecular weights and molecular structures, of the samples are well characterized by TGIC.18 Here we will validate this “hierarchical model” (v3.0) on the asymmetric H-shaped PBd and its blends with a star polymer and infer the compositional purity of the asymmetric H PBd. The relaxation processes described by the “hierarchical model” are illustrated for the case of an asymmetric H in Figure 3. A short time after a small step strain, only the arms can relax inward from their tips. When the two identical short arms are fully relaxed, they are replaced by a frictional bead at the branch point. The partially relaxed molecule becomes a “Y”-shaped star molecule with two identical “short arms”, which are the partially

4. RESULTS AND DISCUSSION 4.1. Synthesis of H(SS13LL20)B58. Perny et al.23 prepared a symmetric H PBd with high 1,4 addition by attaching the living linear chains to the functionalized backbone to generate the H polymer. This synthesized material was characterized by temperature gradient interaction chromatography (TGIC), which indicated that the H PBd sample is a mixture of 70% H polymer, 25% low molar mass byproduct, and 5% high molar mass byproduct. This synthetic strategy employed by Perny et al.23 is not able to produce regular asymmetric H-shaped polymers because the short and long arms will randomly attach to the two ends of the backbone, thereby introducing many different products. However, a novel strategy to prepare symmetric H-PBd by anionic polymerization was developed recently.34 It is based on the idea that coupling two “half H” (i.e., star-shaped) molecules will generate an H molecule. In our new work, we use another novel strategy to synthesize asymmetric H-shaped polymers by coupling two living long arms with the end of one arm of an asymmetric star-shaped molecule as illustrated in Figure 2.24 Based on this reaction mechanism, described in detail elsewhere,24 the stoichiometry of the reactant, and the molar mass of star, the most likely products and byproducts of the H molecule and its precursor are shown in Figure 4. During step 3 of Figure 2 (the step to generate asymmetric star-shaped precursor), the s-BuLi functions as an activator of DPE as well as removing any excess DCMSDPE in the system. At the end of step 3, no free and reactive DCMSDPE should be in the system, especially after the treatment with s-BuLi. During the long-arm coupling process (step 4), a 2:1 ratio of living arms to DCMSDPE was

Figure 3. Conceptualization of algorithm for computing hierarchical relaxation of an asymmetric H-shaped H(SSLL)B polymer. 5747


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Figure 4. The most probable products and byproducts formed during the synthesis of asymmetric star and H(SSLL)B. The lengths of all segments are shown in parentheses with s, l, and b equal to the length of short arm, long arm, and backbone, respectively. The products listed in step 5 include only the products produced by reaction of compound 8 from step 4 with all of the products of step 3. Additional possible byproducts in the final H product are listed in Figure 7b,c.

used. Living long arms was added dropwise to DCMSDPE, and when the coupling is thought to be 80−90% complete, the reaction was stopped to avoid 3-arm byproducts. In our case we

used a large excess of living anions to eliminate free DCMSDPE. Therefore, if there are any byproducts produced by step 4, in most cases, the most likely byproduct should be a 5748


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single long arm coupled to DPE arising from incomplete coupling of the two long arms, and this single long arm with DPE is available to react with two products of step 3. But another scenario is also possible: if the long arms are quenched before they couple, this will leave unreacted DCMSDPE free to link products of step 3 together. In principle, the products of step 2 should be similar to those of step 4; however, no free and reactive DCMSDPE can survive after treatment by s-BuLi at step 3. In summary, the possible products at step 3 are all living anions, while the possible products at step 4 are either a long arm with DPE moiety (product 10a in Figure 4) or a long-arm living anion (product 10b in Figure 4) or both, in addition to the desired coupled pair of long arms (product 8 in Figure 4) and a three-arm star (product 9 in Figure 4). TGIC characterization of the intermediates of step 4 is needed to determine whether the single long arm is a long-arm living anion or a long arm with DPE moiety and to quantify the amounts of these possible byproducts. We will discuss the products of reaction step 5 after discussion of the TGIC results below. 4.2. H(SS13B20)B58 and Its Precursors. 4.2.1. TGIC Characterization of H(SS13B20)B58 and Its Precursors. It has been shown that TGIC is an interaction chromatography technique that has much superior resolution to SEC.23,35−38 We thus employ TGIC for all molecular characterization here. TGIC chromatograms of the short and long arms of H(SS13B20)B58 are displayed in Figures 5a and 5b, respectively. The absolute molar masses of the short and long arms were determined as 13.2 and 19.5 kg/mol, respectively, by light scattering detection. The measured molar mass values were well matched with target molar masses of 13 and 20 kg/ mol, respectively. The nicely overlapped polymer peaks recorded by refractive index detector (Δn, black curve) representing the concentration of the polymer and by light scattering detector at 90° scattering angle (R90, red curve) approximately representing molar mass × concentration reflect that the polymers eluting in the unimodal peak are quite homogeneous in molar mass. This is a characteristic signal of narrowly dispersed polymers prepared by anionic polymerization. The TGIC chromatogram of the intermediates of the coupled L-arm (the intermediate B in Figure 2) is presented in Figure 5c. This shows three peaks at elution times of 7.5, 11.2, and 16.3 min, corresponding to one long arm (24K), two coupled long arms (42K), and a tiny peak corresponding to star of three long arms, respectively. Because of its small size, peak 3 can be ignored. The refractive index detection curve representing the amount of polymer shows that peak 2, the desired product (8 in Figure 4), accounts for about 77 wt % of the total, while peak 1, the single long arm, accounts for about 22 wt %. One interesting thing is that according to UV absorption curve at 260 nm (A260, green curve), the first peak does not seem to contain much DPE. The A260 signal represents the concentration of DPE moiety since PBd does not absorb light at 260 nm. The strong A260 double peak over 4−6 min is due to the elution of the injection solvent. A small A260 peak eluting at 6−8 min accounting for about 3% of the whole A260 peaks does not match with the elution time of the peak for one long arm at 7.5 min. Therefore, we can conclude that the single arm in the intermediates of the coupled L-arm does not contain a DPE moiety. Unfortunately, we were not able to elucidate the nature of the small UV peak. We speculate that it may represent free DCMSDPE. In any event, it is clear

Figure 5. TGIC characterization of (a) short, (b) long arms, and (c) coupled long arms of H(SS13LL20)B58.

that the one long arm is mostly either a free living long arm anion or a prematurely terminated long arm, which is one possibility mentioned in section 4.1. We will discuss the implications of this in more detail later. For the stars (A in Figure 2), however, the TGIC curve (Figure 6) shows multiple elution peaks indicating that the synthesis generated the expected additional byproducts shown in Figure 4. The TGIC of S(SS13B58)-UP (unpurified star) shows five distinct peaks in Figure 6a. From the absolute peak molar masses determined by LS detection and the synthetic scheme, the structures of the polymers in each peak are illustrated on the right side of Figure 6a: coupled short arms (29K), free backbone (57K), backbone with one short arm (75K), target star (90K), and star with one additional short arm (101K). There are two other small peaks around elution times 6 and 11 min, which might correspond to the molecules 3 and 2 in Figure 4. Because of their small amounts and the limited signal-to-noise ratio in TGIC to identify their weight fractions, these two small peaks will be ignored in what follows. After the fractionation, in S(SS13B58)-P (purified star) (Figure 6b) low 5749


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Figure 6. (a) TGIC characterization of S(SS13B58)-UP(left) and probable structures corresponding to each peak (right). The dashed lines are backbone segments, and the short solid lines are short arms. (b) TGIC characterization of S(SS13B58)-P(left) and probable structures of each peak (right).

DCMSDPE was consumed. The very small amount of star containing three long arms in the coupled L arm (peak 3 in Figure 5c), the significant amount of single arm without the DPE moiety (peak 1 in Figure 5c), and the small UV absorption of the single arm peak, which we suspect represents surviving DCMSDPE, are all in support of this scenario. In this scenario, the surviving DCMSDPE could link together any two living anions at steps 3 and 4 of Figure 4. However, free living anions at step 3 of Figure 4 that are present only in small amounts, when coupled to other anions of similarly small amount, should produce negligible quantity of products. Thus, the most likely byproducts under this scenario, listed in Figure 7b, are produced by the coupling of relatively abundant (2s+b) (product 4 in Figure 4) with itself and with other products 5, 6, and 7 in Figure 4. Thus, other self-coupling of anions such as (3s+b)+(3s+b) are not listed due to their expected tiny concentrations in unpurified H. Among the byproducts listed in Figure 7b, (2s+b)+(b+2s) is the most likely one due to the large concentration of (2s+b) in the unpurified star, which is about 68 wt % (see Table 1). As the reaction goes further, due to the reactivity of the double bond, albeit much lower than chlorosilyl group, in DCMSDPE, it is also possible for any three living anions to react with DCMSDPE, which is similar to the reaction mechanism of generating product 2 or 9 in Figure 4. This would produce many high molar mass peaks. In Figure 7c, as an example, we only list three possible products under this mechanism, and many other possible products are not listed here. We will include these three, at very low concentration, in

molar mass byproducts are partially removed, but there are still significant amounts of the byproducts left. After the further reaction of A and B in Figure 2, the H polymer H(SS13B20)B58-UP contains many side products, such as the possibilities depicted in Figure 7, for which the corresponding TGIC curve is shown in Figure 8a. The mechanisms of synthesis of some of these products and byproducts are shown in Figure 4. According to the reaction scheme shown in Figure 2, the H(SS13B20)B58 is generated by adding the coupled long arms to unpurified star. During this process, the desired product and three other byproducts, as listed in Figure 7a, could be generated. Note that only the product 8 at step 4 in Figure 4 (i.e., two coupled long arms) can react with the four components at step 3 of Figure 4. This is because that product 9 has no reactive double bond to react with anion chains, and most of the single long arm 10b does not seem to contain the DPE moiety as discussed previously and so cannot react further. Our scenario to explain the other byproducts with molar mass between around 100K and 200K, observed by TGIC of the unpurified H polymer in Figure 8a, is that for some reason, such as long arms becoming quenched before they couple, there remains a small amount of free DCMSDPE in the reaction vessel at the end of step 4, although excess L-arm was used in the titration with DCMSDPE. If the reaction had gone according to plan, it would be difficult for free DCMSDPE to survive. But if some inadvertent termination of L-arm occurred in the reaction, the reaction might have stopped before all 5750


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structures similar to those in Figure 7c. The small peak 2 likely corresponds to the linked short arms, s+s, even though the light-scattering molecular weight is rather high, 39K. The assignment of this peak to s+s is reasonable because the elution time for peak 2 is slightly higher than peak 1 for the single long arm, which is consistent with the slightly high molecular weight of s+s (around 26.4K), relatively to l (19.5K), and because the size of peak 2 is considerably smaller than for peak 1, which is consistent with the fact that TGIC shows more single long arm l in Figure 5c and double short arm s+s in Figure 6a. Peak 2 is small in any event, containing only 1.6% of the products. Other minor peaks have light scattering molar masses reasonably close to what is expected, based on the assigned structures. In any event, the small sizes of these peaks makes assignment errors less consequential than for the major peaks 1, 3, 7, 10, and 12. The Gaussian fitting of the TGIC data provides us with the molar masses, weight fractions, and polydispersity indices of each component in the sample, and on the basis of the discussion above, we can infer the probable structures of some of the peaks and make reasonable guesses for the others. Such information is needed for the “hierarchical model” predictions. The TGIC data shown in Figures 5, 6, and 8 allow us to estimate the concentrations and PDI’s of the main products as well as byproducts in S(SS13B58)-P, S(SS13B58)-UP, H(SS13LL20)B58-P, and H(SS13LL20)B58-UP PBds. The detailed method of analysis of TGIC data was described previously.18 Based on that method,18 the characteristics of each peak in the TGIC spectrum for S(SS13B58)-UP, S(SS13B58)-P, H(SS13LL20)B58-P, and H(SS13LL20)B58-UP samples are summarized in Tables 1, 2, 3, and 4. The assigned structures corresponding to each peak are shown in Figures 6, and 7 and summarized in Tables 1−4. The PDI’s of each component (or peak) for these samples are nearly unity; i.e., each component is nearly monodisperse. For the unpurified asymmetric star S(A213B58)-UP, which is used to prepare the asymmetric H(SS13LL20)B58, the main product takes up about 68% by mass of the sample. For the asymmetric H PBds, peaks from 1 to 6 of H(SS13LL20)B58-P correspond closely to the peaks from 7 to 15 of H(SS13LL20)B58-UP, respectively. Peaks from 1 to 9 of H(SS13LL20)B58-UP almost completely disappear after purification since fractionation removed the low molar mass polymers. However, the byproducts having similar molar mass (namely peaks from 7 to 15 in H(SS13LL20)B58-UP and peaks from 1 to 9 in H(SS13LL20)B58−P) could not be removed well. Meanwhile, after purification, the relative amount of the main product of H(SS13LL20)B58-P has increased from weight fraction of about 30% to about 40%. Please also note here that the molar masses of short arm and long arm assigned in the structure are somewhat different from those measured from the TGIC analysis of precursor arms as shown in Figure 5. This deviation likely results from the measurement uncertainty in Figures 6 and 8 due to the low intensity of light scattering and RI detector signals of low molar mass polymers. Based on the molar masses of arms and final products, the calculated molar masses of the backbone of the H range from 56 to 62 kg/mol. We believe that the molar masses from Figure 5, i.e., TGIC characterizations of the simple short arms and long arms, are more reliable since no other impurities are present in Figure 5, and we will use these values in our modeling below. We will also check the effect of this assumption on the predicted rheology.

Figure 7. Probable products in the final H(SS13LL20)B58 polymer. The dashed lines are backbone segments, the short solid lines are short arms, and the long solid lines are long arms. (a) Probable products produced by the expected coupling reactions of the coupled pair of long arms (product 8 from Figure 4) from reaction step 4 with the products (4, 5, 6, and 7 of Figure 4) of step 3. These are the same products that appear at step 5 in Figure 4. (b) Probable products produced as a result of excess DCMSDPE from step 4 leading to the coupling together of products from step 3, namely product 4 from step 3 with each of the products (4, 5, 6, and 7) from step 3. (Only the products containing 4 have high enough concentrations to be listed here.) Note that the dashed lines for products 5 through 8 are double length, corresponding to two backbone segments coupled together. (c) Examples of possible products generated due to unstable DCMSDPE, which could couple together three products of step 3. The labeled molecular weights are calculated using values for the molar masses of the short arm, long arm, and backbones of 13.2, 19.5, and 59 kg/mol, respectively.

our characterization, since such products with these molar masses help fit the measured TGIC spectrum. But because of the high uncertainty in our choice of the byproducts selected in Figure 7c, we include these only as examples of possible very high molecular weight species, and we will test the sensitivity of our rheological predictions to the presence of these byproducts. Thus, TGIC characterization helps us to settle on reasonable choices for the components in H(SS13LL20)B58-UP and their concentrations. As shown in Figure 8a, there are five distinct major peaks with multiple peak shoulders and multiple small peaks. Using a Gaussian fitting method presented somewhere else,18,38 we identify and quantify a total of 15 components in H(SS13LL20)B58-UP, as shown in Figure. 8b, of which peaks 1, 3, 7, 10, and 12 have relative large weight fractions. The likely corresponding structures are summarized in Table 3. Based on the discussion above regarding the byproducts, peak 1 very likely corresponds to the single long arm without DPE moiety (23K). Peak 3 with a molar mass of about 44 kg/mol might correspond to the unreacted coupled long arms. Peak 7 is likely the unreacted symmetric star (2s+b) (90K), and the main peak 10 is our desired product H with the molecular weight of 128K. For peak 12 with high molecular weight around 165K, the most likely structure is (2s+b)+(b+2s) as discussed above, considering the large amount of 2s+b in the unpurified star. The three peaks with elution times ranging between 20 and 30 min are not completely separated. This might be due to the presence of the other byproducts listed in Figure 7, whose molecular weights are in the range of 90K to 165K. The long tail with elution time larger than 30 min might be produced by 5751


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Figure 8. (a) TGIC characterization of H(SS13LL20)B58-UP and (b) its Gaussian fitting of the RI curve; (c) TGIC characterization of H(SS13LL20)B58-P and (d) its Guassian fitting of the RI curve.

As described in section 3, the “hierarchical model” (v3.0) is employed here to calculate the rheological behaviors of these materials. The three tube model parameters G0N = 1.095 MPa, Me = 1620, and τe = 5 × 10−7 s, taken from previous work, are used for all predictions without adjustment. Each component of S(SS13B58)-P, S(SS13B58)-UP, H(SS13LL20)B58-P, and H(SS13LL20)B58-UP is taken to be monodisperse, based on their PDIs of nearly unity. The TGIC characterization was conducted independently to determine the molecular characteristics. However, as discussed above, due to the somewhat inconsistent molar masses of the short arms, long arms, and backbone characterized by TGIC (Figures 5, 6, and 8), there are multiple options for choosing values of these molar masses in the modeling calculations. Taking the molar masses of the short arm and long arm to be 13.2 and 19.5 kg/mol, respectively, which are the values obtained by TGIC characterizations on the arms directly, yields the modeling predictions shown in Figure 9. In this calculation, the backbone is considered to be 59 kg/mol, which is an average value from the star TGIC characterization information. As shown in Figure 9, the predictions for both the precursors and final asymmetric H products match the experimental data well, suggesting that our determinations of the polymer structures and molar masses are close to the correct ones. As another option, the molar masses of short arm, long arm, and backbone are all taken from the TGIC characterization of components of the asymmetric star and asymmetric H, in which the molar masses of short arm, long arm, and backbone are 14.5, 23, and 57 kg/mol, which are obtained from the simplest components in asymmetric star or asymmetric H, respectively. The corresponding hierarchical model predictions are shown in Figure 10. As shown in Figure 10, the “hierarchical model” works well for the unpurified star and H but does not

Table 1. Molecular Characteristics of S(SS13B58)-UP

a

Mpa

peak no. in Figure 6a

weight fraction (%)

(kg/mol)

PDI

probable structure

1 2 3 4 5

2.8 8.9 10.7 68.3 9.3

29 57 75 90 101

1.01 1.00 1.00 1.00 1.00

s+s b s+b 2s+b 3s+b

Mp is from light scattering detection during TGIC characterization.

Table 2. Molecular Characteristics of S(SS13B58)-P

a

peak no. in Figure 6b

weight fraction (%)

Mpa (kg/mol)

PDI

probable structure

1 2 3 4

5.0 11.8 75.5 7.7

56 75 90 101

1.00 1.00 1.00 1.00

b s+b 2s+b 3s+b


4.2.2. Linear Viscoelastic Properties and “Hierarchical Model” Predictions. By applying the methods described above, the rheological experiment data of both the unpurified and purified asymmetric star and asymmetric H polymers are shown in Figure 9. As can be seen, both the purified star, i.e., S(SS13B58)-P, and purified H, i.e., H(SS13LL20)B58-P, relax slower than their unpurified counterparts, which is consistent with the presence of greater amounts of large molar mass components in the purified samples, according to the TGIC characterization in Figures 6 and 8. The difference in relaxation between purified and unpurified H polymers is particularly large, showing the large effect that impurities can have on the rheology of branched polymers. 5752


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Table 3. Molecular Characteristics of H(SS13LL20)B58-UP peak no. in Figure 8b

structure no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 a

Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure

4 4 4 4 4 4 4 4 4 4 4 7 7 7 7

(10) (1) (8) (5) (9) (7) (4) (6) (14) (11) (13) (5) (12) (11) (10)

weight fraction (%)

Mpa (kg/mol)

PDI

assumed structure

7.6 1.6 6.0 1.5 1.0 2.8 16.0 3.1 4.8 29.1 7.9 9.8 4.9 2.5 1.4

23 39 45 62 73 77 89 98 118 128 139 165 176 219 263

1.00 1.00 1.00 1.00 1.01 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.01

l s+s l+l b l+l+l (star) s+b 2s+b (star) 3s+b (star) s+b+2l 2s+b+2l 3s+b+2l 2s+b+b+2s b+b+b 2s+b+b+b+s (2s+b)×3


modeling predictions. Furthermore, to confirm the molar masses of arms and backbone, the rheology of a 50/50 blend of H(SS13LL20)B58-UP and its precursor S(SS13B58)-UP is also predicted here using the molar masses of the short arm, long arm, and backbone of 13.2, 19.5, and 59 kg/mol. As shown in Figure 11, the good prediction of the “hierarchical model” for this 50/50 blend also indicates that these are the right choices of the molar masses. Combining the knowledge from TGIC characterization and the modeling predictions on the rheological data of S(SS13B58)-UP, H(SS13LL20)B58-UP, and a 50/50 blend of the two, we can thus increase the likelihood of obtaining the most accurate characterization. This finding that an average 8% difference in molar masses of arms and backbones can generate significant difference in rheology challenges the traditional characterization technique SEC, which has a standard deviation in molar mass characterization ranging from 0.7% to 34%.39 The long tail between t = 30 min and t = 33 min in the chromatograms in Figure 8 is represented in the rheological modeling by the three components presented in Figure 7c. The effect of this long tail is checked by ignoring these three components and comparing with the predictions of Figure 9. As shown in Figure 12, for H(SS13LL20)B58-P, no significant difference is observed except the bump between frequency 10−5 and 10−4, which is outside of the range of the experimental data. As we discussed above, the bump is due to the long tail effects. For H(SS13LL20)B58-UP, the prediction without the long tail lies below the experimental data, although not greatly so. In our previous paper,18 we guessed that this high molecular tail might represent an H polymer with extra arms, and so there we checked the effect of this by rerunning our rheological predictions with inclusion of a “pom-pom” molecule at a volume fraction (i.e., a few percent) consistent with the size of the high molecular weight tail in the chromatogram. We found that inclusion of this extra component had negligible effect on the rheology, probably because the extra arms relax as quickly as the other arms, and so only act to produce a somewhat more sluggish terminal relaxation of the molecule containing them. Since these larger molecules with extra arms relax at the very end, the entanglement network by then has already been highly diluted by constraint release, and so the somewhat more sluggish reptation of these dilute species may not have much effect on the rheological predictions. We will show in Figure 13

Table 4. Molecular Characteristics of H(SS13LL20)B58-P peak no. in Figure 8d 1 2 3 4 5 6 7 8 9 a

structure no. Figure Figure Figure Figure Figure Figure Figure Figure Figure

4 4 4 4 4 7 7 7 7

(4) (6) (14) (11) (13) (5) (12) (11) (10)

weight fraction (%)

Mpa kg/mol

PDI

assumed structure

4.7 3.2 2.3 41 12.4 25.9 6.8 2.5 0.8

90 108 120 130 137 166 181 221 272

1.01 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

2s+b (star) 3s+b (star) s+b+2l 2s+b+2l 3s+b+2l 2s+b+b+2s b+b+b 2s+b+b+b+s (2s+b)×3


Figure 9. Experimental storage modulus G′ and loss modulus G″ data and “hierarchical model” calculations for purified star S(SS13B58)-P, unpurified star S(SS13B58)-UP, purified H H(SS13LL20)B58-P, and unpurified H H(SS13LL20)B58-UP, using values for the molar masses of the short arm, long arm, and backbones of 13.2, 19.5, and 59 kg/ mol, respectively. Solid symbols (solid lines) and open symbols (dashed lines) are experimental data (theoretical predictions) for G′ and G″, respectively.

work well for the purified star and H. Comparing Figures 9 and 10 shows that a small difference in the molar mass of arms and backbone (i.e., 13.2K, 19.5K, and 59K vs 14.5K, 23K, and 57K, respectively) can result in significant differences in the 5753


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Figure 10. The same as Figure 9, except the molar masses of the short arm, long arm, and backbone are 14.5, 23, and 57 kg/mol, respectively.

Figure 13. Determination of the effect of impurities on the rheology of the synthesized precursor S(SS13B58)-P and H(SS13LL20)B58-P materials obtained by comparing the predictions of 100% pure materials with the predictions for the actual materials containing the measured concentrations of impurities.

Figure 11. Experimental storage modulus G′ and loss modulus G″ and “hierarchical model” calculations for H(SS13LL20)B58-UP, S(SS13B58)-UP, and a 50/50 blend of the two. The molar masses of the short arm, long arm, and backbones are taken to be 13.2, 19.5, and 59 kg/mol, respectively. Solid symbols (solid lines) and open symbols (dashed lines) are experimental data (theoretical predictions) for G′ and G″.

smaller amount of the high molecular weight tail probably does not greatly affect the rheology of this polymer. From previous analysis and discussion, S(SS13B58)-P and H(SS13LL20)B58-P contain respectively about 75.5% and 41% of the targeted asymmetric star and asymmetric H polymer as the main product. To determine the effect of the contaminants on the rheology, we calculate the rheology of the theoretically pure monodisperse star and pure monodisperse H polymer without any contaminants, i.e., the rheology that the samples would have if the weight fractions of the star or H component were 100%, instead of 75.5% and 41%, respectively. In Figure 13, we compare this predicted rheology with that predicted for the mixture of components inferred to be present in S(SS13B58)-P and H(SS13LL20)B58-P and with the experimental data, respectively. As shown in Figure 13, there is no significant difference between the theoretically pure monodisperse H(our targeted H PBd) and H(SS13LL20)B58-P over the frequency range of about 10−4−100 rad/s, although there is a predicted bump below the frequency of 10−4 in the H polymer rheology, which results from the long tail of high molecular weight components. For S(SS13B58)-P, there is a small, but distinct, difference between the pure monodisperse star (our targeted asymmetric star) and S(SS13B58)-P, and this difference is probably due to the low molar mass components in the sample. This example shows how rheological modeling can help determine the level of purification required to produce

that even the 10% high molecule weight impurity present in the purified H polymer H(SS13LL20)B58-P has only a modest effect on its relaxation behavior. Thus, we expect that the much

Figure 12. Effects of the high molecular tail on the rheology predictions. The symbols are experimental data, and the solid lines are same as the predictions in Figure 9, using all the products in Table 3, while the dashed lines omit the last three entries in Table 3, which are the byproducts given in Figure 7c. 5754


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the support from NRF via SRC (R11-2008-052-03002) and WCU (R31-2008-000-10059-0) programs

data that are insensitive to remaining impurities. It also shows how the sensitivity to impurities depends not only on the amount of the impurities but even more so on the identity of the impurities. Since no synthetic sample can be completely pure, modeling of this kind, along with measurement of the rheology of unpurified samples, and of deliberately blended samples offers the prospect of determining when sufficient purification of a given sample has been attained.

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(1) Dealy, J. M.; Larson, R. G. Structure and Rheology of Molten Polymers: From Structure To Flow Behavior and Back Again; Hanser Gardner Publications, Inc.: Cincinnati, OH, 2006. (2) Janzen, J.; Colby, R. H. J. Mol. Struct. 1999, 485, 569. (3) Graessley, W. W.; Roovers, J. Macromolecules 1979, 12, 959. (4) Raju, V. R.; Rachapudy, H.; Graessley, W. W. J. Polym. Sci., Polym. Phys. Ed. 1979, 17, 1223. (5) Pearson, D. S.; Mueller, S. J.; Fetters, L. J.; Hadjichristidis, N. J. Polym. Sci., Polym. Phys. Ed. 1983, 21, 2287. (6) Fetters, L. J.; Kiss, A. D.; Pearson, D. S.; Quack, G. F.; Vitus, F. J. Macromolecules 1993, 26, 647. (7) Adams, C. H.; Hutchings, L. R.; Klein, P. G.; McLeish, T. C. B.; Richards, R. W. Macromolecules 1996, 29, 5717. (8) Frischknecht, A. L.; Milner, S. T.; Pryke, A. R.; Young, N.; Hawkins, R.; McLeish, T. C. B. Macromolecules 2002, 35, 4801. (9) Daniels, D. R.; McLeish, T. C. B.; Kant, R.; Crosby, B. J.; Young, R. N.; Pryke, A.; Allgaier, J.; Groves, D. J.; Hawkins, R. J. Rheol. Acta 2001, 40, 403. (10) Roovers, J.; Graessley, W. W. Macromolecules 1981, 14, 766. (11) Roovers, J. Macromolecules 1984, 17, 1196. (12) Chambon, P.; Fernyhough, C. M.; Im, K.; Chang, T.; Das, C.; Embery, J.; McLeish, T. C. B.; Read, D. J. Macromolecules 2008, 41, 5869. (13) Snijkers, F.; van Ruymbeke, E.; Kim, P.; Lee, H.; Nikopoulou, A.; Chang, T.; Hadjichristidis, N.; Pathak, J.; Vlassopoulos, D. Macromolecules 2011, 44, 8631. (14) Lee, A. T.; McHugh, A. J. Macromolecules 2001, 34, 9080. (15) Chang, T. J. Polym. Sci., Polym. Phys. Ed. 2005, 43, 1591. (16) Ryu, J.; Chang, T. Anal. Chem. 2005, 77, 6347. (17) Larson, R. G. Macromolecules 2001, 34, 4556. (18) Chen, X.; Rahman, M.; Lee, H.; Mays, J.; Chang, T.; Larson, R. Macromolecules 2011, 44, 7799. (19) Roovers, J.; Toporowski, P. M. Macromolecules 1981, 14, 1174. (20) McLeish, T. C. B. Macromolecules 1988, 21, 1062. (21) Hakiki, A.; Young, R. N.; Mcleish, T. C. B. Macromolecules 1996, 29, 3639. (22) McLeish, T. C. B.; Allgaier, J.; Bick, D. K.; Bishko, G.; Biswas, P.; Blackwell, R.; Blottiere, B.; Clarke, N.; Gibbs, B.; Groves, D. J.; Hakiki, A.; Heenan, R. K.; Johnson, J. M.; Kant, R.; Read, D. J.; Young, R. N. Macromolecules 1999, 32, 6734. (23) Perny, S.; Allgaier, J.; Cho, D.; Lee, W.; Chang, T. Macromolecules 2001, 34, 5408. (24) Rahman, M.; Lee, H.; Chen, X.; Chang, T.; Larson, R.; Mays, J. ACS Macro Lett. 2012, 1, 537. (25) Wang, Z. W.; Chen, X.; Larson, R. G. J. Rheol. 2010, 54, 223. (26) Park, S. J.; Larson, R. G. J. Rheol. 2005, 50, 21. (27) Park, S. J.; Shanbhag, S.; Larson, R. G. Rheol. Acta 2005, 44, 319−330. (28) Chen, X.; Larson, R. G. Macromolecules 2008, 41, 6871. (29) Chen, X.; Costeux, C.; Larson, R. G. J. Rheol. 2010, 54, 1185. (30) Chen, X.; Stadler, F. J.; Munstedt, H.; Larson, R. G. J. Rheol. 2010, 54, 393. (31) Das, C.; Inkson, N. J.; Read, D. J.; Kelmanson, M. A.; McLeish, T. C. B. J. Rheol. 2006, 50, 207. (32) van Ruymbeke, E.; Bailly, C.; Keunings, R.; Vlassopoulos, D. Macromolecules 2006, 39, 6248. (33) van Ruymbeke, E.; Masubuchi, Y.; Watanabe, H. Macromolecules 2012, 45, 2085. (34) Rahman, M. S.; Aggarwal, R.; Larson, R. G.; Dealy, J. M.; Mays, J. Macromolecules 2008, 41, 8225. (35) Lee, W.; Lee, H.; Cha, J.; Chang, T.; Hanley, K. J.; Lodge, T.P. Macromolecules 2000, 33, 5111. (36) Park, S.; Cho, D.; Ryu, J.; Kwon, K.; Lee, W.; Chang, T. Macromolecules 2002, 35, 5974.

5. CONCLUSIONS An asymmetric H-shaped model polybudtadiene melt has been designed and synthesized using a novel strategy. Both the purified and unpurified asymmetric star precursor S(SS13B58) and the final products have been characterized thoroughly by TGIC. From the TGIC and likely reaction mechanisms, we have proposed likely impurities arising in the intermediates and final product. The large number of likely impurities suggests that improvement in the synthesis method would be desirable. We found that the measured rheology of the purified and unpurified precursor star, of the purified and unpurified H, and of a 50/50 blend of the unpurified H, H(SS13LL20)B58-UP, with its precursor star S(SS13B58)-UP, agreed reasonably well with the predictions of the “hierarchical model” (v3.0) for entangled polymer blends. The results indicate the reliability of this model, which can therefore aid in detecting compositional purity of the original materials. The methods employed here(1) synthesis of novel model branched structures, (2) fractionation, (3) characterization of melt composition by TGIC, (4) rheological measurements on the purified and unpurified model polymer and on blends of the model polymer with well-characterized linear or star diluents, and (5) rheological prediction using a generalized rheological modelwhen combined, provide a way to both identify impurities and their influence on rheology and to test and validate models of complex branched polymers. Taken together, they represent a way of implementing the strategy of “combinatorial rheology”, whereby inevitable limitations in synthetic purity and sample characterization can be overcome by producing multiple rheological data sets on the same polymer blended with well-characterized simpler polymers and predicting these data with advanced rheological models. This approach also builds the expertise needed to accomplish the ultimate aim, which is the development of models to predict the rheology of complex commercial melts, and to infer molecular characterization from such measurements.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address ∥

REFERENCES

The Dow Chemical Company, Midland, MI 48640.

Author Contributions ⊥

Equal contributions.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge support from NSF under Grants DMR 0906587 and DMR 0906893. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation (NSF). T.C. acknowledges 5755


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(37) Ryu, J.; Im, K.; Yu, W.; Park, J.; Chang, T.; Lee, K.; Choi, N. Macromolecules 2004, 37, 8805. (38) 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. (39) Podzimek, S. Light Scattering, Size Exclusion Chromatography and Asymmetric Flow Field Flow Fractionation: Powerful Tools for the Characterization of Polymers, Proteins and Nanoparticles; Wiley: New York, 2011.

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