Challenges and opportunities:a hopeful future of polymer rheology in China

Polymer rheology has a long research tradition and holds an important position in the scientific community.It is supposed to be a valuable subject to the vast polymer industry.This article points out the exciting developments that are transforming our understanding of the world of polymer rheology.We discuss not only the emerging challenges in the area but also how China might wish to seize the moment,pick up the trend and take advantage of the potential economic benefits to the huge petro-chemical industry...     

Viscoelasticity and self-diffusion in melts of entangled asymmetric star polymers

The crossover from linear to branched polymer dynamics in highly entangled melts was investigated with a series of asymmetric three-arm stars of poly(ethylene-alt-propylene). Two arms of equal length formed a linear backbone, kept constant through the series, while branches of various length were appended as the third arm. The materials were made by carbanionic polymerization of isoprene and the judicious application of chlorosilane linking chemistry. Subsequent saturation of the polymeric double bonds with deuterium and hydrogen, followed by fractionation, led to a set of structurally matched, nearly monodisperse pairs of deuterium-labeled and fully hydrogenous samples. Dynamic moduli were measured over wide ranges of frequency and temperature. With increasing branch length, the resulting master curves evolve smoothly, but with surprising rapidity, from the relatively narrow terminal spectrum of linear polymers to the much broader spectrum of symmetric stars. The viscosity η_o increases rapidly with branch length, and the diffusion coefficient D, obtained by forward recoil spectrometry, decreases even more rapidly. The product η_oD, however, distinguishes the transition from linear to branched polymer dynamics most clearly: for a backbone with about 38 entanglements, the crossover is already approaching completion for a single mid-backbone branch with only about three entanglements. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1943–1954, 1997     

Short‐time stretch relaxation of entangled polymer solutions investigated using full Rouse model predictions

We conduct a systematical investigation into the short‐time stretch relaxation behavior (i.e., shorter than the Rouse time but sufficiently longer than the glassy time) of entangled polymer liquid in single‐step strain flows, on the basis of theory/data comparisons for a broad series of type‐A entangled polymer solutions. First, within existing normal‐mode formulations, the Rouse model predictions on a full‐chain stretch relaxation in single‐step strain flows are derived for a popular 1‐D model proposed within the Doi–Edwards tube model, as well as for the original 3‐D model for nonentangled systems. In addition, an existing formula for the aforementioned 1‐D model that, however, rested upon a consistent‐averaging or the so‐called uniform‐chain‐stretch approximation is simultaneously examined. Subsequently, the previously derived formulas on chain stretch relaxation are directly incorporated into a reliable mean‐field tube model that utilizes the linear relaxation spectrum and the Rouse time constant consistently determined from linear viscoelastic data. It is found that the predictions of the 1‐D model differ substantially from that of the original 3‐D model at short times. Theory/data comparisons further indicate that the 1‐D model without approximations seems able to describe fairly well the nonlinear relaxation data under investigation. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1199–1211, 2006     

Atomistic hybrid particle‐field molecular dynamics combined with slip‐springs: Restoring entangled dynamics to simulations of polymer melts

In hybrid particle‐field (hPF) simulations (J. Chem. Phys., 2009 130, 214106), the entangled dynamics of polymer melts is lost due to chain crossability. Chains cross, because the field‐treatment of the nonbonded interactions makes them effectively soft‐core. We introduce a multi‐chain slip‐spring model (J. Chem. Phys., 2013 138, 104907) into the hPF scheme to mimic the topological constraints of entanglements. The structure of the polymer chains is consistent with that of regular molecular dynamics simulations and is not affected by the introduction of slip‐springs. Although slight deviations are seen at short times, dynamical properties such as mean‐square displacements and reorientational relaxation times are in good agreement with traditional molecular dynamics simulations and theoretical predictions at long times.     

挑战与机遇: 聚合物流变学在中国的前途

聚合物流变学有很久的科研传统并在高分子科学与工程中具有重要的地位,是一个对聚合物产业有相当价值的领域. 本文指出近来出现的令人兴奋的研究成果. 这些发现正在改变着我们对于聚合物流变学的认识. 我们不仅讨论众多新的挑战, 也谈到中国应如何抓住时机, 认定走向, 挖掘潜在的巨大经济效益.     

Pinch-off dynamics and extensional relaxation times of intrinsically semi-dilute polymer solutions characterized by dripping-onto-substrate rheometry

Stream-wise velocity-gradients associated with extensional flows arise in thinning liquid necks spontaneously formed during jetting, printing, coating, spraying, atomization, and microfluidic-based drop formation. In this contribution, we employ Dripping-onto-Substrate (DoS) rheometry protocols to measure the extensional rheology response of intrinsically semi-dilute polymer solutions by visualizing and analyzing capillary-driven thinning of a columnar neck formed between a nozzle and a sessile drop. We show that extensional viscosity that quantifies the resistance to stream-wise velocity gradients is orders of magnitude higher than the shear viscosity. Although shear flows only weakly perturb the chain dimensions, extensional flows can strongly stretch and orient the chains, thus influencing both intra- and inter-chain interactions. We find that the extensional relaxation times for intrinsically semi-dilute PEO solutions in a good solvent for five different molecular weights increase linearly with concentration, exhibiting a stronger concentration dependence than observed for dilute solutions, or anticipated by blob models, developed for relaxation of weakly perturbed chains in a good solvent. The observed distinction between the concentration-dependent relaxation dynamics of intrinsically dilute and semi-dilute solutions arises due the complex influence of stretching, conformational anisotropy, and polymer concentration on excluded volume and hydrodynamic interactions of flexible, highly extensible polymers. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1692–1704     

Study on the relationship between the mechanical properties and processing for self-reinforced polymers. Part 1: A theory of stress-induced crystallization for entangled polymer networks

A new theory of stress-induced crystallization for entangled polymer networks is presented. It is based on the theory of viscoelasticity with constraints of trapped entanglements and crystallites using a model of fibrillar and lamellar morphology engendered by the extended and folded-chain crystallization. The probability distribution function of the end-to-end vector for two kinds of constituent chains and the viscoelastic free energy of deformation for two kinds of networks have been calculated. The relationships of stress to strain for four types of deformation were derived. The theory is successful in relating the equilibrium degree of crystallinity and the melting temperature to the extension ratio for networks with stress-induced crystallization. Furthermore, the theory provides a theoretical foundation for studying the dependences of tensile modulus and strength on the processing and testing conditions for self-reinforced polymers.Nomenclature A initial cross-section - a _j radius ofjth spheres - a _k radius ofkth spheres - a _kj radius of different spheres - B _cr structure factor for the folded-chains in the crystallite aggregate-polymer chain networks - B _ef structure factor for the folded-chains in the trapped entanglement networks - C ₁ material constant for the folded-chains in entanglement or/and crosslink networks - C _1c material constant for the folded-chains in entanglement or/and crosslink networks with stress-induced crystallization - C _100cr material parameter for the folded-chains in the crystallite aggregate-polymer chain networks - C _100ef material parameter for the folded-chains in the trapped entanglement networks - C ₂ material constant for the entanglement chains in the entanglement or/and crosslink networks - C _2c material constant for the entanglement chains in the entanglement or/and crosslink networks with stress-induced crystallization - C ₃ material constant for the extended-chains in the entanglement or/and crosslink networks - C _3c material constant for the extended-chains in the entanglement or/and crosslink networks with stress-induced crystallization - C _200cr material parameter for the extended-chains in the crystallite aggregate-polymer chain networks - C _200ef material parameter for the entanglement chains in the trapped entanglement networks - C _cr structure factor for the extended-chains in the crystallite aggregate-polymer chain networks - C _ef structure factor for the extended-chains in the trapped entanglement networks - C _020ef material parameter for the entanglement chains in the trapped entanglement networks - C _000cr material parameter for the crystal-lite aggregate-polymer chains in connection with changing volume - D _cr structure factor for the crystallite aggregate-polymer chains in connection with changing volume - D _ef structure factor for the entanglement chains in the trapped entanglement networks - dv volume element - F elastic free energy of deformation - F _crT elastic free energy of deformation for the crystallite aggregate-polymer chain networks - F _cT free energy of crystallization for the crystallite region - F _eT elastic free energy of deformation for the trapped entanglement networks - F _TT total free energy for the crystallizable entangled or/and crosslinked networks with stress-induced crystallization - F _TT ⁰ change in free energy of deformation from a deformed state to a free state for entangled networks with a given crystallinity - F ⁰ net change in free energy of deformation at a free state - f force - f _cr number of chains emanating from a crystallite aggregate in the crystallite aggregate-polymer chain networks - (1–f) fraction of trans-isomers on the extended and folded-chains in the constituent chains by crystallite aggregates - G _c total number of the extended and folded-chains in the crystalline region - G _c number of the folded-chains in the crystalline region - G _c number of the extended-chains in the crystalline region - G _c ⁰ total number of the crystallizable extended and folded-chains in the crystallite aggregate-polymer chain networks - H _u heat of fusion per link of polymer - H _u heat of fusion per gram of polymer - k Boltzmann constant - k _h rate constant for the change of constituent chain by crystallite aggregates - k _g rate constant for the change of constituent chains by entanglement - number average molecular weight - r the end-to-end vector length of the chain in a conjected state - r ⁰ coordination number - r _i the end-to-end vector length ofith chains in conjected state - r _j vector length from the center of crystallite aggregate to thejth chain end in the conjected state - r _k vector length from the center of crystallite aggregate to thekth chain end in the conjected state - t time of drawing - T incipient melting temperature of the deformed materials - T _m ⁰ melting temperature of the undeformed materials - t _x stress alongx direction - t _y stress alongy direction - t _z stress alongz direction - u change in energy of the rotational isomers - W(r) probability that the center of the constituent chains with different dimensions lies in the spherical shellr andr+dr - W degree of crystallinity - W ₀ Nagai function of the end-to-end vector for a chain - draw ratio - _g coefficient of relaxation time for the constituent chains by entanglement - _g interface factor for the constituent chains by crystallite aggregate - _x y _z components of alongx, y andz directions - ₀ ² parameter for a chain in free state - _0j ² parameter for thejth chains of the trapped entanglement networks in free state - _0k ² parameter for thekth chains of the crystallite aggregate-polymer chain networks in free state - _rj ² parameter for therj-th chain of the trapped entanglement networks in conjected state - _rk ² parameter for therk-th chains of the crystallite aggregate-polymer chain networks in conjected state - _rj ² parameter forrj-th chains of the trapped entanglement networks in conjected state - _k ² parameter for k-th chains of the crystallite aggregae-polymer chain networks in conjected state - _crk dimension of thekth constituent chains by crystallite aggregate in the crystallite aggregate-polymer networks - _edk dimension of thekth constituent chains by the extended-chain crystallite aggregate in the extended-chain crystallite aggregate-polymer chain networks - _ef dimension of thejth constituent chains by entanglement in the trapped entanglement networks - _fc j dimension of thejth constituent chains by folded-chain crystallite aggregate in the folded-chain crystallite aggregate-polymer chain networks - _{crkx crky crkz} components of _crk alongx, y, z directions - _crk number of the constituent chains with dimension _crk - _crT total number of the constituent chains by crystallite aggregate in the crystallite aggregate-polymer chain networks - _efi number of the constituent chains with dimension _efi - _efT total number of the constituent chains by entanglement in the trapped entanglement networks - _crT total number of chains in the crystallite aggregate-polymer chain networks - _efT total number of chains in trapped entanglement networks - _cr total number of elastic chains in the crystallite aggregate-polymer chain networks - stress - _n normal stress - _s shear stress - degree of constrained severity by crystallite aggregate in the crystal-lite aggregate-polymer chain networks - degree of constrained severity by entanglement in trapped entanglement networks - _r front factor in the crystallite aggregate-polymer chain networks - _r front factor in the entanglement networks - number of conformations     

Nonlinear rheology of highly entangled polymer solutions in start‐up and steady shear flow

Orientation angle and stress‐relaxation dynamics of entangled polystyrene (PS)/diethyl phthalate solutions were investigated in steady and step shear flows. Concentrated (19 vol %) solutions of 0.995, 1.81, and 3.84 million molecular weight (MW) PS and a semidilute (6.4 vol %) solution of 20.6 million MW PS were used to study the effects of entanglement loss on dynamics. A phase‐modulated flow birefringence apparatus was developed to facilitate measurements of time‐dependent changes in optical equivalents of shear stress (n₁₂ ≈ Cσ) and first normal stress differences (n₁ = n₁₁ ? n₂₂ ≈ CN₁) in a planar‐Couette shear‐flow geometry. Flow birefringence results were supplemented with cone‐and‐plate mechanical rheometry measurements to extend the range of shear rates over which entangled polymer dynamics are studied. In slow (τ > ) steady shear‐flow experiments using the ultrahigh MW polymer sample (20.6 × 10⁶ MW PS), steady‐state n₁₂ and n₁ results manifest unusual power‐law dependencies on shear rate [n_12,ss ～ ^0.4 and n_1,ss ～ ^0.8]. At shear rates in the range τ < < τ, steady‐state orientation angles χ_SS are found to be nearly independent of shear rate for all but the most weakly entangled materials investigated. For solutions containing the highest MW PS, an approximate plateau orientation angle χ_p in the range 20–24° is observed; χ_p values ranging from 14 to 16° are found for the other materials. In the start‐up of fast steady shear flow (γ˙ ≥ τ), transient undershoots in orientation angle are also reported. The molecular origins of these observations were examined with the help of a tube model theory that accommodates changes in polymer entanglement density during flow. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2275–2289, 2001     

Drawing of microshear deformation zones in glassy polymers: Poly(phenylene oxide) (PPO)

The topography of the microscopic shear deformation zones (SDZ) in the glassy polymer PPO was studied by using atomic force microscopy (AFM) and was used to analyze the growth and breakdown of the SDZ. It was found that the local stress and strain are almost constant within the deformation zones but higher than those in the elastic regions. The maximum strain rate during stretching was found to always locate near the SDZ boundaries, indicating that most drawing took place there. With both the local stress and strain obtained for every point within the SDZ, it is possible to construct a full stress-strain curve for the drawing of the tiny local deformation zones. The stress-strain curve clearly demonstrates a yield point in the beginning of microyielding where the tensile modulus was found to be much lower than that in the elastic regime. Some strain hardening, however, took place at larger deformation. Moreover, we found that for each microscopic region participated in the microdrawing the local strain rate increased with local strain until a critical strain around 0.65 was reached, after which the strain rate decreased with strain. This critical strain may be related to the chain entanglement network structure because it shifted to 0.75 when PS diluents were blended into PPO, indicating that strain hardening was delayed by the increase of chain entanglement mesh size. © 1996 John Wiley & Sons, Inc.     

Bead-spring models of entangled polymer melts: Comparison of hard-core and soft-core potentials

Two bead-spring models of flexible chains for generic coarse graining of entangled polymer melts, the excluded volume Kremer–Grest (KG) model and the modified segmental repulsive potential (mSRP) combined with a weakly repulsive potential, are compared. For chains containing an equivalent number of entanglements, we compare the chain characteristics of the KG and mSRP polymer models by determining the ratios of the entanglement lengths , the required total number of particles to capture comparable entanglement phenomena , and the time scaling ratios τ^mSRP/τ^KG. Our findings show that systems using the mSRP polymer model require half the number of particles and relax four times faster compared to the KG polymer model. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Molecular dimensions and melt rheology of an all‐aromatic liquid crystalline polymer

The molecular dimensions and melt rheology of a thermotropic all‐aromatic liquid crystalline polyester (TLCP) composed of p‐hydroxy benzoic acid, hydroquinone, terephthalic acid, and 2,4‐naphthalenedicarboxylic acid is examined. The Mark–Houwink exponent (α) of 0.95 is estimated for the TLCP. The persistence length estimated from molecular weight (M) and intrinsic viscosity ([η]) data using the Bohdanecky–Bushin equation is about 95 Å, whereas that estimated from light scattering data is 117 Å. These persistence lengths and the observed α value, both higher than those for flexible polymers, suggest that the present TLCP is a semirigid polymer. The zero shear melt viscosity (η₀) varies with approximately M⁶ for molecular weight M > 3 × 10⁴ g/mol; below this molecular weight, η₀ varies almost linearly with M. Widely different entanglement molecular weights (M_e) are predicted, depending on the method used; the plateau modulus estimates M_e of about 8 × 10⁵ g/mol, whereas the ratio of mean square end‐to‐end distance and molecular weight (〈R²〉₀/M) predicts M_e's either too small (0.33 g/mol) or too large (2.5 × 10⁶ g/mol), depending on the theory used. Although the change in the molecular weight dependency of melt viscosity appears to be associated with the onset of entanglement coupling of the semirigid molecules, its origin needs further investigation. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2378–2389, 2001     

Frequency and molecular-mass-dependent nonexponential proton NMR relaxation in polymer melts

A theoretical treatment of the nonexponential relaxation behavior of the different proton nuclear magnetic resonance (NMR) relaxation processes in polymer melts is presented. Formulas are derived for a three-component model given by two versions and a homogeneous distribution of correlation times. The theoretical results were tested with measurements of T₁, T_2e, and T₂ as functions of frequency and molecular mass in linear fractionated polyethylene samples. While the T₁ relaxation always yields exponential magnetization decays, the T_2e and T₂ measurements show biexponential relaxation behavior. From the calculations it was found that the correlation time of the local motion is independent of the molecular mass, whereas the correlation time of the slowest motional process increases with M^2.8_w for the three-component model and with M^2.2_w for the distribution of correlation times, respectively. © 1992 John Wiley & Sons, Inc.     

Strain hardening of polycarbonate in the glassy state: Influence of temperature and molecular weight

This study is concerned with the temperature and molecular weight dependence of the strain-hardening behavior of polycarbonate. It is shown that the strain-hardening modulus reduces with increasing temperature and decreasing molecular weight. This result is interpreted in terms of temperature accelerated relaxation of the entanglement network. Moreover, it is shown that frozen-in orientations, induced by homogeneous deformations above the glass transition temperature, lead to anisotropic yield behavior that can be fully rationalized (and modelled) in terms of a superimposed stress contribution of the prestrained network. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2041–2049, 2004     

Inclusion of the effects of polydispersity and volatility on the random chain scission statistical analysis for polymer degradation

The statistical product distribution for a linear polydisperse polymer of finite molecular weight was included into the statistical analysis for a system undergoing random chain scission showing the effect of volatilization of species other than monomer. Two sets of equations were derived. One set is for the nonvolatile fraction; the other is for the volatile fraction. Within each set there are three equations, one for the number of polymer molecules, the second for the molar (or number) fraction, and the third for the weight fraction of polymer molecules containing a specific number of repeat units. As degradation proceeds the polydispersity index should converge to a value of 1 rather than 2, which has been reported previously. The expected effects of polydispersity, number‐average degree of polymerization, and volatility were treated individually, and we determined that the molecular weight of a polymer has no theoretical influence on the product distribution. As for the effect of volatility, we determined that only the volatile product distribution would change. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3690–3696, 2000     

Wear and friction in glassy polymers: Microscratch on blends of polystyrene and poly (2,6-dimethyl-1,4-phenylene oxide)

The microscopic process of abrasive wear and friction in glassy polymers was studied by using a special microscratch technique. A miscible blend of polystyrene (PS) and poly(phenylene oxide) (PPO) was used. It was found that as the composition varies there seems to exist two wear regimes in the blends controlled by different breakdown mechanisms corresponding to the brittle—ductile transition. Detailed study of the contact loads and SEM micrographs indicate that abrasive wear in the glassy polymers is controlled by microcracking under the asperity contacts. The critical load τ_c for initiating microscopic cracks can be linked to the macroscopic wear via a statistical Weibull model where τ_c is taken to be the mean of a strength distribution function. On the other hand, the friction coefficient was found to be independent of the composition but to vary strongly with the contact load. It approaches zero at the extrapolated zero load, but increases rapidly and eventually levels off with contact load. This behavior can be understood by a simple frictional adhesion model in which the polymer deformation during a frictional contact is analyzed by considering the compressive plastic ploughing and shearing yielding around the asperity contact. The shear strength S_o of the polymer/asperity contacts was found to vary with the normal load. The vertical scratch hardness H_v, which characterizes the spontaneous indentation yielding on the polymer surface, was found to be independent of scratch length and depth, and indeed can be regarded as a material constant. Although both S_o and H_v can accurately describe the frictional behavior of the glassy polymers, they bear no correlation to abrasive wear in the same materials. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1295–1309, 1997     

Effects of flexibility on liquid crystalline polymer behavior: The nematic broken rod

A new theory for liquid crystalline polymers is developed, and its behavior in simple shear flow is analyzed. The theory accounts for molecular flexibility by employing a microstructure consisting of two rigid rods linked by a joint with a tunable stiffness. The probability distribution function equation for the orientation of the arms of the broken rod is derived. The adaptation of the smoothed particle hydrodynamics (SPH) technique for obtaining numerical solutions to this theory is detailed. The behavior of the theory at equilibrium is derived analytically and compared with numerical results; the SPH technique is then used to obtain results in flow. It is found that in the limit of a nearly stiff joint, the model gives behavior that is very similar to that of rigid rod polymers, the only difference being a lesser tendency to tumble due to greater variation in the order parameter. For nearly free joints, the shear flow induces interesting dynamics for the transition between states with the arms outstretched and those where they are folded up (so‐called “hairpins” of main‐chain LCPs). © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 281–300, 1999     

Rheological measurements and light-scattering experiments of dilute solutions of high molecular polystyrene. Light-scattering of flowing polymer solutions

We describe the behavior of dilute polymer solutions by means of light-scattering under shear flow. Solution properties of polystyrene in benzene over a wide range of molecular weight has been studied to determine the coefficientsa andK of the Mark-Houwink relationship and to estimate the rheological conditions with regard to light-scattering experiments of flowing polymer solutions. The investigations were carried out to measure the shear-rate dependence of macromolecules in solution, e.g., to observe an orientation and changing of the mean-square radius of gyration.