Dielectric and Viscoelastic Study of Entanglement Dynamics: A Review of Recent Findings

This article gives a review of the results of recent dielectric and viscoelastic studies for entangled binary blends of linear cis-polyisoprenes to explain the current understanding of the equilibrium entanglement dynamics on the basis of the molecular picture of dynamic tube dilation (DTD). Comparison of dielectric and viscoelastic properties reveals that the full-DTD picture regarding the relaxed portions of the chains as a solvent fails for the high molecular weight component chain in the blends at intermediate times. This failure is related to insufficient constraint release (CR) equilibration of the entanglement segments of this chain. A partial-DTD picture properly considering this CR equilibration successfully describes the linear relaxation behavior of the blends. The dielectric and viscoelastic properties of PI under fast flow, being affected by the flow-activated CR/DTD mechanism, are also presented in order to demonstrate the usefulness of the comparison of these properties in both equilibrium and non-equilibrium states.     

Effects of chain length distribution on viscoelastic properties of entangled linear polymers: Blending laws for binary blends

The reptation idea of de Gennes and the tube model theory of Doi and Edwards are extended to explain the terminal viscoelastic properties of binary blends in the highly entangled state of two linear monodisperse polymers with different molecular weights M₁ and M₂. A modified tube model is proposed that considers the significance of the constraint release by local tube renewal in accounting for the relaxation process of the higher molecular weight chain. Its relaxation by both reptation and the constraint release is remodeled as the disengagement by pure reptation of an equivalent primitive chain. From knowledge of the longest relaxation times of the blend components, the stress equation is formulated from which blending laws of viscoelastic properties for the binary blends are derived. To force better agreement between theory and experiment at the pure monodisperse limits of the blends, a crude treatment to include the effect of contour-length fluctuation in the equivalent-chain model is also discussed. Theoretical predictions of the zero-shear viscosity and steady-state shear compliance are shown to be in good agreement with literature data on undiluted polystyrenes and polybutadienes over a wide range of the blend composition and M₂/M₁ ratio. The asymptotic of the laws for blends with M₂/M₁ → 1 and 0 are comparable to those from the relaxation spectrum proposed by others earlier on the basis of the tube model.     

The formation of “inverted” core-shell latexes

It has been found that when hydrophobic monomers are polymerized in the presence of highly hydrophilic polymer seed particles, the second-stage hydrophobic polymers form cores surrounded by the first-stage hydrophilic polymers, resulting in “inverted” core-shell latexes. The formation of core-shell morphology by this inversion process has been found to be dependent on the hydrophilicity and molecular weight of the first-stage hydrophilic polymers and the extent of phase separation between the two polymers involved. Particle morphology has been examined by electron microscopy, surface acid titration, alkali swelling of particles, and surface reactivity.     

Processability of a metallocene‐catalyzed linear PE improved by blending with a small amount of UHMWPE

The processability of a metallocene‐catalyzed polyethylene blended in the melt with low amounts of ultra‐high molecular weight polyethylene was evaluated. Our morphological and thermal studies revealed that the blends were structurally heterogeneous, formed by a matrix of metallocene polyethylene and homogeneously distributed particles of ultra‐high molecular weight material. The visible particles were smaller than those of the reactor powder. Also observed was some degree of interaction between both phases. Rheological data indicated an intense effect of morphology on viscoelastic functions, beyond that expected for a system composed of noninteractive phases. Collectively, our findings suggest the existence, to some extent, of a homogeneous phase at the molecular level composed of a fraction of ultra‐high molecular weight species and metallocene polyethylene. This gives rise to a striking behavior during processing in that the blends show improved extrusion performance the higher their ultra‐high molecular weight polyethylene content. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2963–2971, 2005     

Extent of branching from linear viscoelasticity of long‐chain‐branched polymers

We present new results and examine literature data concerning the linear viscoelastic behavior of polyethylene with sparse to intermediate levels of long‐chain branching (LCB). These branched polymers displayed a common rheological signature, namely, a region of frequency‐independent loss tangent along with the corequisite scaling of the storage and loss moduli to the same frequency exponent. This apparent power‐law response occurred within a finite frequency window and bore resemblance to the behavior of physical gels. The appearance of this region, however, was the consequence of the presence of two distinct, yet partially overlapping, terminal relaxation processes. After considering the analogous relaxation behavior of wholly linear polymers with bimodal molecular weight distributions, we considered the polymers with LCB as blends of linear and branched species to develop a simple method of quantifying the extent of LCB. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1671–1684, 2004     

Supramolecular Porphyrin Copolymer Assembled through Host–Guest Interactions and Metal–Ligand Coordination

Bisporphyrin cleft molecule 1 Zn possessing a guest moiety assembled to form supramolecular polymers through host–guest interactions. Bispyridine cross‐linkers created interchain connections among the supramolecular polymers to form networked polymers in solution. Solution viscometry confirmed that the cross‐linked supramolecular polymers were highly entangled. Frequency‐dependent linear viscoelastic spectroscopy revealed that the supramolecular polymers generated well‐entangled solutions with associating and networking polymers, whereas the solid‐like aggregates moved individually without breaking and reforming structures below the transition temperature of 9.6 °C. Morphological transition of the supramolecular polymers was evidenced by AFM images; the non‐cross‐linked polymer resulted in wide‐spread thin networks, while the cross‐linked networks produced thicker worm‐like nanostructures. The supramolecular networks gelled in 1,1,2,2‐tetrachloroethane, and an elastic free‐standing film was fabricated with a Young’s modulus of 1 GPa.     

“Living radical” polymerization of styrene in the presence of a nitroxide compound

The influence of parameters such as styrene dilution and active site concentration on the polymerization of styrene in the presence of a di-tert-butyl nitroxide adduct (A-T) was examined. It is confirmed that the rate of styrene polymerization is independent of A-T concentration, with no monomer dilution effect. An increase in radical concentration generated in the medium leads to faster propagation, but the molecular weight of the polymers formed is alway controlled by the A-T concentration.     

Stereocomplex formation between enantiomeric poly(α‐methyl‐α‐ethyl‐β‐propiolactones): Effect of molecular weight

Optically pure S(?) and R(+)‐poly(α‐methyl‐α‐ethyl‐β‐propiolactones) (PMEPLs) of controlled low molecular weights were synthesized by anionic polymerization of the corresponding optically active monomers, and characterized using gel permeation chromatography, Maldi‐TOF mass spectrometry, and NMR spectroscopy. Blends of PMEPLs of opposite configurations and different molecular weights were investigated. All blends lead to the formation of a stereocomplex and its crystallization prevails over a wide range of mixing ratios. The stereocomplex melts 30–40 °C above that of the corresponding pure polymers, depending on the molecular weight; pairs of polymers having similar molecular weights exhibit the highest melting temperatures and enthalpies of fusion. Finally, when the stereocomplex is dispersed in a PMEPL matrix, it acts as a very effective nucleation agent for the crystallization of the polymer in excess. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2380–2389, 2007     

Rheological properties of poly(2,6-dimethylphenylene oxide)—polystyrene blends

The viscoelastic (VE) response of freeze-dried blends of polystyrene (PS) and poly-(2,6-dimethyl phenylene oxide) (PPO) has been studied as a function of composition, frequency, and temperature to examine the degree of rheological compatibility. When blended together, the relaxation processes of both molecular species exhibit the same temperature dependence. However, the temperature dependence of the VE response is a function of composition. It is shown that this behavior can be predicted from the measured glass transition temperatures by assuming the additivity of the free volumes of the components. The properties of the blends are compared at equal free volumes. The effective segmental friction factor is found to be independent of composition while the modulus of the rubbery plateau increases with PPO concentration. This result is interpreted as a change in the entanglement molecular weight M_e of the blends. When the changes in M_e are considered, the relationship between the zero-shear viscosity η0 and the 3.4 power of the weight-average molecular weight, commonly found for high molecular weight homopolymers, predicts the compositional dependence of η0 for the PPO–PS blends. It is concluded that the PPO–PS system forms a rheologically compatible blend.     

Abiotic and biotic degradation of aliphatic polyesters from “petro” versus “green” resources

Aliphatic polyesters are degradable by abiotic and/or biotic hydrolysis. The accessibility of a polymer to degradative attack by living organisms is not dependent on its origin, but on its molecular composition and architecture. Synthetic polymers with intermittent ester linkage (e.g. polyesters, polyurethanes etc.) are accessible to biodegradative attack of esterase. On the other hand aliphatic polyesters are also quickly degraded by a pure abiotic hydrolysis. The results from abiotic and biotic hydrolyses of polycaprolactone (PCL) (from “petro” resource), poly(L-lactide) (PLLA) and polyhydroxyalkanoates (PHA) (from “green” resources) are presented and discussed with the respect to rate of degradation, molecular weight changes and degradation product pattern. For the environmental consequences, the type of formed degradation products are of importance and not the origin of the polymer.     

Relation between Polymer Conformational Structure and Dynamics in Linear and Ring Polyethylene Blends

Atomistic molecular dynamics simulations of ring‐linear polyethylene blends are employed to understand the relationship between chain conformational structure and the melt dynamics of these blends. As observed in previous studies, this study confirms that ring polymers in pure melts do not exhibit screened excluded volume interactions, contrary to linear polymers. Moreover, the average molecular shapes of the rings are quite distinct from both swollen and ideal ring polymers under theta conditions, and instead rather resemble branched polymers with screened binary excluded volume interactions, e.g., percolation clusters. Upon adding linear chains to a melt of pure rings, we find significant swelling of the rings and a corresponding shape change that is qualitatively similar to dissolving rings in a small molecule good solvent. This swelling, arising from altered self‐excluded volume interactions, translates into a large decrease in ring diffusivity, an effect that becomes more amplified when the polymer melt is entangled.     

Investigation of the rheological and mechanical behavior of Polypropylene/ultra-high molecular weight polyethylene compounds related to new online process control

Ultra-high molecular weight polyethylene (UHMWPE) is a high performance material that has excellent wear and impact strength compared to other polymers. Due to its chemical structure and molecular mass, UHMWPE is difficult to handle on standard extrusion systems. In this paper, the compounding, rheological, and mechanical behavior of different Polypropylene (PP)/UHMWPE blends were investigated. Raw materials were blended on a co-rotating twin screw extruder. The shear and extensional viscosity of polymer blends were investigated using an inline rheometer. Mechanical and rheological properties were presented for various UHMWPE loadings, and correlations between mechanical and rheological data were examined.     

Pre-Averaged Sampling On the Entanglement Kinetics for Polymer Dynamics

A new model for entangled polymer dynamics based on pre-averaged sampling of the entanglement structure is proposed. Although it has been reported that sliplink simulations are powerful and promising to predict entangled polymer dynamics, it is still unpractical to calculate polymers with many entanglements. In the present study, a possible approach to achieve fast calculation is proposed by pre-averaged sampling of entanglement structure with skipping detail kinetics of entanglements dominated by chain ends in conventional sliplink models. To achieve time development of the chain conformation and entanglement structure, i) number of entanglement per chain and number of monomers for each segment are randomly obtained from the equilibrium distribution proposed by Schieber [J. Chem. Phys. 2003 , 118, 5162] and ii) the renewed entanglement structure is mechanically equilibrated. The established power-laws on molecular weight dependence of chain dimension, the longest relaxation time and self-diffusion coefficient were reasonably reproduced. Comparison on linear viscoelastic response is also discussed.     

Flow,high-elastic (recoverable) deformation,and rupture of uncured high molecular weight linear polymers in uniaxial extension

The behavior of narrow molecular weight distribution polymers has been investigated under uniaxial extension at constant deformation rate and at constant stress. It has been established that up to rupture these polymers behave as linear viscoelastic bodies. A detailed investigation of the rupture phenomenon has shown that the rupture of fluid polymers is due to their transition to the rubbery state at critical deformation rates, with the result that they disintegrate like quasi-cured rubbers. The effect of the temperature and the molecular weight on the critical conditions of rupture has been described in terms of viscoelastic relaxation.     

Steady flow and dynamic viscosity of branched butadiene–styrene block copolymers

Steady flow and dynamic viscosities were determined for symmetrical linear and starbranched block copolymers of butadiene and styrene above their upper (polystyrene) glass transition. Block structures examined were B-S-B, (B-S-)₃, S-B-S, (S-B-)₃ and (S-B-)₄. At constant molecular weight and total styrene content viscosities were greater for polymers terminating in styrene blocks, irrespective of branching. Branching decreased the viscosity of either polybutadiene-terminated or polystyrene-terminated block polymers, compared at equal M _w. However, comparisons at equal block lengths showed that the length of the terminal blocks, not the total molecular weight, governs the viscoelastic behavior of these polymers to a surprisingly good approximation. This unusual result is rationalized in terms of the two-phase domain structure of these polymers, which persists to a significant degree in the melt. Below the glass transition of the polystyrene blocks the effects of branching were masked by differences in the morphology of the domain structure unrelated to branching.     

Bulk and surface properties of blends with semifluorinated polymers and block copolymers

The goal of the investigation presented here is the development of extremely hydrophobic materials based on polysulfone that can be applied, for instance, as fouling-resistant membrane materials. The concept used is the addition of semifluorinated polymers to polysulfone in suitable blend compositions. The influence of molecular parameters like chain structure of the semifluorinated polymer (segmented block copolymers, random copolymers) and segment molecular weight on the state of phase separation in the bulk and its influence on the surface properties have been systematically examined. It could be shown that segmented block copolymers with semifluorinated polyester segments with intermediate segment molecular weight are more suitable in blends with polysulfone than random polysulfone copolymers having semifluorinated side chains with respect to form homogeneous thin films (coatings) with highly non-wetting properties.     

MISCIBILITY IN COPOLYMER/HOMOPOLYMER BLENDS

In order to study the miscibility of a copolymer with its corresponding homopolymers, varieties of multicomponent polymers including simple graft, muhibranch, diblock, triblock and four-arm block copolymers and so-called ABCPs were synthesized and characterized. The morphologies of the blends comprising the copolymers and the corresponding homopolymers were examined by electron microscopy. It is concluded that besides molecular weight, architecture of a copolypaers has apparent effect on the miscibility, i.e. the more complex is molecular architecture, the greater is conformation restriction in microdomain formation and the less is solubility of homopolymer in corresponding domains. In addition, a density gradient model is suggested for describing the segment distribution of the bound and free chains in block-homopolymer systems. Using this model, Helfand's theory is extended to the blends of copolymer and homopolymer predicting the miscibility which is in good agreement with the experimental results.     

Effects of ultrasonic oscillations on linear viscoelastic behaviors of metallocene‐catalyzed linear low density polyethylene and its blends with low density polyethylene

The effects of ultrasonic oscillations on linear viscoelastic behaviors of metallocene‐catalyzed linear low density polyethylene (mLLDPE) and its blends with low density polyethylene (LDPE) were investigated in this article. The experimental results showed that ultrasonic oscillations can increase the cross modulus, characteristic time, plateau modulus, complex viscosity, zero shear viscosity, and flow activation energy of mLLDPE. Molecular weight of mLLDPE increases but molecular polydispersity index decreases in the presence of ultrasonic oscillations. It has been found for mLLDPE/LDPE blends that the addition of LDPE as well as ultrasonic oscillations can decrease the cross modulus but increase the characteristic time of the blends. The complex viscosity, zero shear viscosity, and flow activation energy of the blends increase by the addition of LDPE, but decrease in the presence of ultrasonic oscillations. Shear thinning effect of the blends is improved because of the addition of LDPE. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3030–3043, 2005     

Linear and non-linear dynamics of entangled linear polymer melts by modified tunable coarse-grained level dissipative particle dynamics

Dissipative particle dynamics (DPD) is a well-known simulation method for soft materials and has been applied to a variety of systems. However, doubts have been cast recently on its adequacy because of upper coarse-graining limitations, which could prevent the method from being applicable to the whole mesoscopic range. This paper proposes a modified coarse-grained level tunable DPD method and demonstrates its performance for linear polymeric systems. The method can reproduce both static and dynamic properties of entangled linear polymer systems well. Linear and non-linear viscoelastic properties were predicted and despite being a mesoscale technique, the code is able to capture the transition from the plateau regime to the terminal zone with decreasing angular frequency, the transition from the Rouse to the entangled regime with increasing molecular weight and the overshoots in both shear stress and normal-stress differences upon start-up of steady shear.     

Universality of linear viscoelasticity of monodisperse linear polymers

We suggest a universal plot that superposes linear viscoelastic data of nearly monodisperse polymers on a single curve, regardless of the molecular weight, temperature, and species of polymers. The plotting method is based on the time–temperature superposition and rescaling of viscoelastic functions with terminal behavior. Without any information from molecular theories, the plot supports the fact that the molecular theories of the linear viscoelasticity of monodisperse polymers are independent of the species of polymers. Although an appropriate scaling may show universality by separately extracting the reptational mode and the Rouse mode from the whole set of viscoelastic data, our plotting method shows universality in a unified manner that scales the viscoelastic functions measured over the whole frequency range. We explain the origin of the universality of the plot in terms of molecular theory, the phenomenological spectra of the relaxation time (the BSW and CW spectra), and the principle of time–temperature superposition. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2730–2737, 2004