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A new type of model branched polymer, asymmetric H-shaped polybutadienes, consisting of central crossbars having various combinations of short and long arms attached to the ends of the crossbars, was synthesized using living anionic polymerization and chlorosilane linking chemistry. The linking agent 4-(dichloromethylsilyl)diphenylethylene provides selective reactivity to attach short or long arms on one side or both sides as desired. The samples were characterized thoroughly by size exclusion chromatography with light scattering detection (SEC-LS) and found to exhibit controlled molecular weights, as well as narrow polydispersity indices (PDIs of 1.01–1.06). Temperature gradient interaction chromatography, a method with far superior resolution as compared to SEC, also shows that these materials are well-defined, with minimal and identifiable impurities.

We report on the unusual response of a well-characterized entangled comb polymer in simple shear flow. The polymer with highly entangled backbone (about 16 entanglements) and on average 29 long branches (about 3 entanglements each) has been extensively characterized by interaction chromatography and its rheology carefully studied under controlled conditions using a special cone partitioned-plate geometry. We observe that the start-up shear stress becomes roughly rate independent above a certain critical rate, related to the relaxation time of the branches. Within the rate-independent region, the start-up shear stress displays a double overshoot. We interpret these observations in light of tube-based pompom dynamics. The key idea is that for sufficiently long branches the main stress overshoot, which reflects backbone stretching and orientation, is preceded by the withdrawal of branches into the backbone tube. The excellent quantitative comparison between the simulations and experiments supports the proposed mechanism of the double stress overshoot.

An exact polystyrene-graft-polyisoprene (PS-g-PI) synthesized by iterative anionic polymerization and graft reaction using diphenylethylene functional groups was characterized by liquid chromatography. As-prepared graft copolymer contains various byproducts other than the target PS-g-PI. After the fractionation by size exclusion chromatography (SEC), the PS-g-PI appears quite homogeneous by SEC analysis, but the temperature gradient interaction chromatography (TGIC) separation with respect to the PI branch number showed a significantly wide distribution in the number of PI grafts. The resolved TGIC peaks were fractionated, and the molecular weight of each block (backbone or branches) was estimated by liquid chromatography at critical condition (LCCC) analysis at the critical adsorption condition of the opposite block. The composition determined by LCCC analysis and 1H NMR analysis yielded a reasonably self-consistent result. Through this study, we demonstrated that SEC analysis of this type of branched co...

Size exclusion chromatography (SEC) coupled with triple detection (TD) method is widely used for branching analysis of polymers. However, there is an inherent limitation of SEC-TD method that SEC separates polymers according their hydrodynamic size. The SEC resolution of branched polymers is not high since the hydrodynamic size of branched polymers does not change as much as linear polymers with molecular weight (MW), let alone the serious band-broadening in SEC. As a solution of the problem, we propose temperature gradient interaction chromatography (TGIC)-TD method taking advantage of TGIC's characteristics of separating branched polymers according to their MW with much higher resolution than SEC. The potential of the method was demonstrated using regular star-shaped polybutadienes prepared by anionic polymerization. They were characterized by both SEC-TD and TGIC-TD methods. Detailed analysis of branch distribution was possible for narrow MW fractions in TGIC-TD while SEC-TD only provides with average branch number for SEC fractions.

We investigate the influence of the environment on the relaxation dynamics of well-defined H-polymers diluted in a matrix of linear chains. The molar mass of the linear chain matrix is systematically varied and the relaxation dynamics of the H-polymer is probed by means of linear viscoelastic measurements, with the aim to understand its altered motion in different blends, compared to its pure melt state. Our results indicate that short unentangled linear chains accelerate the relaxation of both the branches and the backbone of the H-polymers by acting as an effective solvent. On the other hand, the relaxation of the H-polymer in an entangled matrix is slowed-down, with the degree of retardation depending on the entanglement number of the linear chains. We show that this retardation can be quantified by considering that the H-polymers are moving in a dilated tube at the rhythm of the motion of the linear matrix.

We have measured the linear rheology of critically purified ring polyisoprenes, polystyrenes, and polyethyleneoxides of different molar masses. The ratio of the zero-shear viscosities of linear polymer melts η0,linear to their ring counterparts η0,ring at isofrictional conditions is discussed as a function of the number of entanglements Z. In the unentangled regime η0,linear/η0,ring is virtually constant, consistent with the earlier data, atomistic simulations, and the theoretical expectation η0,linear/η0,ring = 2. In the entanglement regime, the Z-dependence of ring viscosity is much weaker than that of linear polymers, in qualitative agreement with predictions from scaling theory and simulations. The power-law extracted from the available experimental data in the rather limited range 1 < Z < 20, η0,linear/η0,ring Z1.2±0.3, is weaker than the scaling prediction (η0,linear/η0,ring Z1.6±0.3) and the simulations (η0,linear/η0,ring Z2.0±0.3). Nevertheless, the present collection of state-of-the-art experimental data unambiguously demonstrates that rings exhibit a universal trend clearly departing from that of their linear counterparts, and hence it represents a major step toward resolving a 30-year-old problem.

HPLC elution behavior of isotopically different block copolymers was investigated. A series of three diblock copolymers of hydrogenous polystyrene and deuterated polystyrene (hPS-b-dPS), in which the length of hPS-block is fixed at 18 kg/mol and the length of dPS-block is varied from 17 kg/mol to 80 kg/mol, was synthesized and their retention behavior in liquid chromatography at critical condition (LCCC) was investigated using a C18 coated silica stationary phase and a mixed solvent of CH2Cl2 and CH3CN. At this LC separation condition, hPS is retained slightly longer than dPS. The LCCC separations were performed at both LCCC conditions of dPS and hPS established with the same stationary and mobile phases, but at different column temperatures. Since the chromatographic retention difference between dPS and hPS is very small, it was possible to elute the block copolymers at both exclusion and interaction modes at the critical condition of each individual block. We found that the block at its critical condition is not fully "invisible" in both cases. In the LCCC separation at the critical condition of dPS, hPS-b-dPS elutes after the injection solvent peak (interaction mode) due to the stronger interaction of the hPS block. Although they have the same hPS block, they do not coelute but elute in the order of decreasing total molecular weight like an elution in exclusion mode. It clearly demonstrates that the dPS block is not "invisible" at the critical condition but influences the retention of the block copolymers. Monte Carlo simulations of the partition coefficient of A-b-B into a slit pore were performed to give insight on the elution behavior of A-b-B at the critical condition of the B block. The simulation shows that a block under the critical condition influences the retention of the other "visible" block whether the "visible" block is eluted in exclusion or interaction mode. When A is eluted in the interaction mode and B is at its critical condition, the partition coefficient is found to decrease with the increase of the "invisible" B block length, conforming to the observed elution behavior in experiments.

We explored a new synthetic strategy for ultra-high molecular weight long-chain branched (LCB) polymers with equal spacing between adjacent branch points. This method can synthesize LCB polystyrene (LCB-PS) with total molecular weight of 4.9 million g/mole, 16 branches of 140 kg/mole and polydispersity index of 1.5. The introduction of multiple branch points with long side chains allows the LCB-PS to resist the elastic-driven decohesion. Even after a large step extension of stretching ratio λ = 7.4, the specimen would not undergo elastic breakup that occurs in linear PS even at λ = 2.7. These LCB-PSs are also extraordinarily more stretchable during startup uniaxial extension, with the maximum engineering stress emerging at stretching ratio λ max ≈ 4 M bb / M e , where Mbb is the molecular weight of backbone and Me is the molecular weight between entanglements.

We report on the shear flow start-up and the relaxation upon flow cessation of anionically synthesized comb polymers of different chemistries. The experimental data, obtained with a cone partitioned-plate geometry in order to avoid artifacts, showed that the start-up shear flow of combs exhibits systematic dependencies on the branching structure. They were interpreted by invoking dynamic dilution and hierarchical relaxation, which are known to control the linear viscoelastic response. For all combs studied here, the backbones remained entangled after dynamic dilution due to branch relaxation. We combined the important molecular parameters (i.e., the number and molar mass of the branches) into a single parameter, the number of entanglements of the dynamically diluted backbone, ZBBDIL., which we found to be the main scaling parameter for the observed nonlinear flow behavior. The steady viscosities as function of Weissenberg number were less shear-thinning compared to linear analogues, and the higher the amo...

We present a detailed systematic investigation of the transient uniaxial extensional response of a series of well-characterized, anionically synthesized comb polystyrenes and polyisoprenes. The comb architecture consists of a linear chain backbone with multiple branches of equal molar mass, and represents an excellent model branched polymer. The linear viscoelastic response has been studied already in great detail. Our results indicate that the strain hardening becomes more important as the Hencky strain rate is increased. In general, the larger the number of entanglements of the segments between branches and/or of the branches, the stronger the strain hardening and the smaller the characteristic rate for its onset. The key molecular parameter appears to be the number of entanglements per branch. By varying it, one can tailor the amount and onset of strain hardening. This can be rationalized by accounting for the combined effect of backbone tube dilation and extra friction, brought about by the branches. In fact, we define an effective “stretch time” of the comb as the timescale for stretch relaxation along the dilated backbone tube when accounting for the large friction that comes from the branches and suggest that extension hardening occurs at rates equal to or greater than its inverse. The good comparison of this prediction to experimental data is a promising guide toward a universal framework for understanding the effects of branches on extensional rheology, and hence providing some insight into the behavior of long-chain branched polyolefins.

We report here an easy method for the synthesis of dendrimer-like polymers with high branching functionality (1 → 8). The synthetic process involves iterative grafting reactions in a divergent way. A multi-functional core containing short segments of polyisoprene (PI), either as a star-like block copolymer of isoprene and styrene or as a linear triblock copolymer of isoprene, styrene and isoprene (coded G1), is epoxidized on the double bonds and grafted with a living block copolymer, polyisoprene-b-polystyrenyllithium (PI-b-PSLi), again with a short PI segment, through the ring-opening reaction of oxirane by polymeric anions. The resulting graft polymer, G2, possesses a definite number of PI segments at the periphery. These PI segments are further epoxidized followed by the ring-opening addition of PI-b-PSLi, affording G3. Repeating the process leads to the synthesis of a dendrimer-like polystyrene up to 5th generation with a polydispersity lower than 1.21, as measured by SEC. A feature of the process is the easily accessible high chain density in the final product, although defects exist due to steric hindrance in the reactions of high generations. The solution properties of the dendritic products are investigated using viscometry and dynamic and static laser light scattering on the molecular conformation. The results support a compact globular conformation model for the dendrimer-like products. In addition, the chain density of the products from the star-like core is higher than that of products from a linear triblock core. AFM results show that the dendritic products adopt flattened conformations and tend to form lateral sphere-like aggregates on mica substrate.

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 unpuri...

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.

It has been a long held ambition of both industry and academia to understand the relationship between the often complex molecular architecture of polymer chains and their melt flow properties, with the goal of building robust theoretical models to predict their rheology. The established key to this is the use of well-defined, model polymers, homogeneous in chain length and architecture. We describe here for the first time, the in silico design, synthesis, and characterization of an architecturally complex, branched polymer with the optimal rheological properties for such structure-property correlation studies. Moreover, we demonstrate unequivocally the need for accurate characterization using temperature gradient interaction chromatography (TGIC), which reveals the presence of heterogeneities in the molecular structure that are undetectable by size exclusion chromatography (SEC). Experimental rheology exposes the rich pattern of relaxation dynamics associated with branched polymers, but the ultimate test is, of course, did the theoretical (design) model accurately predict the rheological properties of the synthesized model branched polymer? Rarely, if ever before, has such a combination of theory, synthesis, characterization, and analysis resulted in a "yes", expressed without doubt or qualification.

We combine state-of-the-art synthetic, chromatographic, rheological, and modeling techniques in order to address the role of architectural polydispersity in the rheology of model branched polymers. This synergy is shown to be imperative in the field and leads to several important results. Even the best available synthesis is prone to “contamination” by side-products. The exact targeted macromolecular structure can be analyzed experimentally and statistically and eventually fractionated. Temperature-gradient interaction chromatography proves to be an indispensible tool in this process. All techniques are sensitive to the various macromolecular structures, but in different ways. In particular, the presence of side-products may or may not influence the linear rheology, due to competing contributions of the different relaxation processes involved, reflecting different structures at different fractions. Hence, combination of all these techniques is the key for fully decoding the architectural composition of branched polymers and its influence on rheology.

We report the synthesis and characterization by temperature gradient interaction chromatography (TGIC) and rheometry of a symmetric H-shaped polybutadiene (PBd) that we call “HA20B40”, and of a symmetric star-shaped synthetic precursor of HA20B40, and the use of these characterization data to test and validate advanced tube models (the hierarchical and, to a lesser extent, the BOB models) for long-chain branched polymers. Furthermore, by deliberately adding additional well-characterized linear and star-branched polymers into HA20B40, we mimic the effect of impurities in the sample to test the ability of the hierarchical model to account for the effect of similar such impurities, which are detected by TGIC. Our modeling predictions for HA20B40 and its blends with star and linear polymers show very good agreement with measured rheological data, indicating that the modeling validation is successful for the symmetric H-shaped polymers. We then test the hierarchical model further using literature data for symm...

The structural details of a set of highly entangled H-shaped polybutadienes (PBDs) prepared by anionic polymerization were examined in detail by three reputable laboratories using size exclusion chromatography (SEC) and temperature gradient interaction chromatography (TGIC). While SEC data indicated that samples having the desired structures (i.e., nearly monodisperse H-shaped polymer) had been produced, additional SEC data from other laboratories showed that the samples were structurally more complex than originally thought. TGIC data revealed that while the samples did not contain high molecular weight byproducts, they did contain low molecular weight byproducts. To discern these structural details of the branched PBDs, small amounts of sample were fractionated by TGIC. By combining knowledge of the polymerization process with the TGIC data of fractionated samples, it was possible to work out the detailed compositions of the samples and the branching structures of each component.

Several poly(amic diisopropyl ester-alt-imide)s have been synthesized, which are a new type of polyimide precursors. The precursors consist of amic ester and imide units alternatively on the backbone, so that they are hydrolytically stable as well as low shrinkable through thermal imidization. These precursors have an easy processability because of their good solubility in common solvents that are widely used as good solvents for most polyimide precursors. The precursors and their alternating copolyimides in films have exhibited structural orders that are estimated to have a dimension of 15–42 A (along the chain axis) and 8–16 A (along the lateral direction), depending upon the polymer backbone chemistry. However, all the precursors and resultant copolyimides were laterally packed in an irregular way. Their crystallinities were apparently low. These results might be attributed mainly to the bend or kinked units on the polymer backbone. In addition, properties of the precursors and their polyimides in films: optical and dielectric properties, glass transition, thermal imidization characteristics, thermal stability, thermal expansion and residual stress, were investigated in detail. Overall, the precursor polymers, as well as the resultant alternating copolyimides were characterized to have relatively good properties suitable for applications in the fabrication of microelectronic devices.

We show for the first time that entangled polymeric liquids containing long-chain branching can exhibit strain hardening upon startup shear. As the significant long-chain branching impedes chain disentanglement, Gaussian coils between entanglements can deform to reach the finite extensibility limit where the intrachain retraction force exceeds the value expected from the usual conformational entropy loss evaluated based on Gaussian chain statistics. The phenomenon is expected to lead to further theoretical understanding.

A phase diagram was constructed for a polystyrene-block-polyisoprene (PS-b-PI, M(W) = 32 700, f(PI) = 0.670) in thin films on Si wafer as a function of film thickness over the range of 150-2410 nm (7-107L(0) (L(0): domain spacing)). The PS-b-PI exhibits a variety of ordered phases from hexagonally perforated lamellar (HPL) via double gyroid (DG) to hexagonally packed cylinder (HEX) before going to the disordered (DIS) phase upon heating. The morphology of the PS-b-PI in thin film was investigated by grazing incidence small-angle X-ray scattering, transmission electron microscopy, and transmission electron microtomography. In thin film, the phase transition temperature is difficult to be determined unequivocally with in situ heating processes since the phase transition is slow and two phases coexist over a wide temperature range. Therefore, in an effort to find an "equilibrium" phase, we determined the long-term stable phase formed after cooling the film from the DIS phase to a target temperature and annealing for 24 h at the temperature. The temperature windows of stable ordered phases are strongly influenced by the film thickness. As the film thickness decreases, the temperature window of layer-like structures such as HPL and HEX becomes wider, whereas that of the DG stable region decreases. For the films thinner than 160 nm (8L(0)), only the HPL phase was found. In the films exhibiting DG phase, a perforated layer structure at the free surface was found, which gradually converts to the internal DG structure. The relief of interfacial tension by preferential wetting appears to play an important role in controlling the morphology in very thin films.

An emerging challenge in polymer physics is the quantitative understanding of the influence of a macromolecular architecture (i.e., branching) on the rheological response of entangled complex polymers. Recent investigations of the rheology of well-defined architecturally complex polymers have determined the composition in the molecular structure and identified the role of side-products in the measured samples. The combination of different characterization techniques, experimental and/or theoretical, represents the current state-of-the-art. Here we review this interdisciplinary approach to molecular rheology of complex polymers, and show the importance of confronting these different tools for ensuring an accurate characterization of a given polymeric sample. We use statistical tools in order to relate the information available from the synthesis protocols of a sample and its experimental molar mass distribution (typically obtained from size exclusion chromatography), and hence obtain precise information about its structural composition, i.e. enhance the existing sensitivity limit. We critically discuss the use of linear rheology as a reliable quantitative characterization tool, along with the recently developed temperature gradient interaction chromatography. The latter, which has emerged as an indispensable characterization tool for branched architectures, offers unprecedented sensitivity in detecting the presence of different molecular structures in a sample. Combining these techniques is imperative in order to quantify the molecular composition of a polymer and its consequences on the macroscopic properties. We validate this approach by means of a new model asymmetric comb polymer which was synthesized anionically. It was thoroughly characterized and its rheology was carefully analyzed. The main result is that the rheological signal reveals fine molecular details, which must be taken into account to fully elucidate the viscoelastic response of entangled branched polymers. It is important to appreciate that, even optimal model systems, i.e., those synthesized with high-vacuum anionic methods, need thorough characterization via a combination of techniques. Besides helping to improve synthetic techniques, this methodology will be significant in fine-tuning mesoscopic tube-based models and addressing outstanding issues such as the quantitative description of the constraint release mechanism.