The entanglement concept in polymer rheology

In this paper, we examine the melt rheology of well-defined, model polymers where the long chain branching (LCB) is precisely known from the synthesis. All of these are made by the hydrogenation of polybutadiene, but they vary greatly in the level and type of LCB present. We find that all polymers that have LCB show a greater degree of shear thinning than linear chains. This applies both to those with a single branch (stars) and also to those with multiple branches per chain (such as combs). However, only molecules with multiple branches induce extensional thickening in a sample. Only a small amount of these comblike molecules, on the order of 5%, are needed to show this effect. We also show here how a new method of treating the shear data, the so-called Van Gurp−Palmen analysis, can give a more easily interpreted form of the results that can reveal the length and amount of branches in a sample. The insights generated from this work show the importance of access to well-defined polymers with several kinds...

Well-Defined, Model Long Chain Branched Polyethylene. 2. Melt Rheological Behavior

The scope of this Perspective is to highlight innovative contributions in the synthesis of well-defined complex macromolecular architectures and to emphasize the importance of these materials to polymer physical chemistry, physics, theory, and applications. In addition, this Perspective tries to enlighten the past and show possible pathways for the future. Among the plethora of polymerization methods, we briefly report the impact of the truly living and controlled/living polymerization techniques focusing mainly on anionic polymerization, the mother of all living and controlled/living polymerizations. Through anionic polymerization well-defined model polymers with complex macromolecular architectures having the highest molecular weight, structural and compositional homogeneity can be achieved. The synthesized structures include star, comb/graft, cyclic, branched and hyberbranched, dendritic, and multiblock multicomponent polymers. In our opinion, in addition to the work needed on the synthesis, properties...

50th Anniversary Perspective: Polymers with Complex Architectures

The present invention relates to thermoplastic moulding compositions of (A) thermoplastic polycarbonates, if appropriate mixed with (B) thermoplastic polyalkylene terephthalates and, if appropriate, additionally with (C) elastomeric graft polymers, characterized in that they contain (D) a terpolymer of acrylates, vinyl esters and unsaturated nitriles.

Thermoplastic moulding compositions

Some time ago, one of us'.' introduced a model of relaxation in complex systems in which the relaxation rate conventionally considered as time independent in simpler systems may become time dependent. Relaxations are manifested by the decay (or saturating growth) of some macroscopic variable such as polarization, stress, electric field, volume, or enthalpy, in appropriate complex systems such as glasses, amorphous polymers, polymer melts, viscous liquids, ionic conductors, and amorphous semicond u c t o r ~ . ~ The mechanism for the macroscopic relaxation can often be traced on the microscopic level, however, to a fundamental relaxation mode with simple relaxation rate W, = 7;' of the primitive species (PS) that is isolated except for its interaction with the heat bath. The PS can be a molecular moiety or a structural unit in structural relaxations; a dipolar group or a mobile charged entity (ionic or electronic) in dielectric relaxations; a polymer chain in polymer melt terminal viscoelastic relaxation; etc. In many complex systems, the fundamental relaxation mode often occurs within the domain of short-range order so that all PSs have essentially the same W,. For example, most glasses, metallic glasses, and viscous liquids have some short-range order. Even in a linear polymer melt, monodispersive samples can be prepared such that all chains have almost the same length (or molecular weight, M ) . Here the PS can be identified as the individual polymer chains. An example of a fundamental mode is the terminal ( p = 1) Rouse mode4 which describes the longest wavelength relaxation of the chain. The simple relaxation rate W, is the same for all chains. It is the nature of complex systems, however, that an individual PS cannot be considered to be completely isolated from other PSs or other neighboring species. Rather, a PS is coupled via molecular, ionic, electronic, or other interactions with its complex environment, an environment that may include other PSs. Relaxation of a PS then involves sequential cooperative adjustments by both its complex environment and the PS itself. For the example of entangled monodisperse linear polymer melts, the terminal Rouse mode of any chain cannot relax without coupling via entanglements with other chains. Such cooperative adjustments act to slow the simple relaxation rate W, at times longer than a time t , = w;' that is characteristic of the cooperative adjustments. The time t , is determined by the complex environment, which has a

Three Coupled Relations for Relaxations in Complex Systemsa

Effect of molecular structure on polyethylene melt rheology. I. Low-shear behavior

The effect of long-and short-chain branching in polymer molecules on gel-permeation chromatographic (GPC) separation is discussed. The calculation of calibration curves for branched polymers is developed from the universal calibration technique based on the hydrodynamic volume concept and previously established relationships for the effect of branching on molecular dimensions. Typical calibration curves are shown for different branching models and degrees of branching. As branching increases, the curves are shown to converge. Methods of characterizing branching and molecular weight distributions of franctions and whole polymers from GPC and intrinsic viscosity data are presented.

Determination of polymer branching with gel‐permeation chromatography. I. Theory

The dependence of the melt flow of polymers on temperature is of both theoretical and commercial importance. A useful representation of the temperature dependence of the shear-dependent viscosity, based on superposition of flow curves at various temperatures, has previously been presented by the author for several olefin polymers. This method is extended in the current work to styrene and styrene-acrylonitrile based polymers. The melt viscosity-temperature dependence of a broad range of styrenic polymers and copolymers, ranging from polystyrene to 82 percent AN styrene-acrylonitrile copolymer, with and without rubber inclusions, was investigated. Flow curves at the various temperatures were found to be superimposable, as had earlier been found to be the case for olefin polymers, and a unique quantitative relationship between the superposition shift factors and temperature was found applicable to the entire family of polymers. The resultant energy of activation for viscous flow is in excellent agreement with previously published results for polystyrene Newtonian viscosities, and the magnitude of the shift factors is consistent with a limited set reported for ABS polymers. Independent tests of the derived relationships provided excellent prediction of measured viscosities. Thus, it is considered that a general viscosity-temperature relationship has been defined for this family of polymers, independent of molecular structural detail.

A generalized melt viscosity-temperature dependence for styrene and styrene-acrylonitrile based polymers

A knowledge of the variation of melt viscosity of thermoplastic polymers with both shear rate and temperature is of considerable importance to plastics engineers as well as to polymer rheologists. The actual measurement of melt viscosity at a large number of temperatures and shear rates is frequently a tedious and time-consuming task. A technique has been developed, based upon the applicability of shear rate-temperature superposition, for predicting the flow curves of a number of olefin polymers and copolymers at various temperatures from experimental data obtained at one temperature for the material in question. The experimental validity for superimposing log shear stress—log shear rate curves at different temperatures along the log shear rate axis has been established for both high and low density polyethylenes, polypropylene, polybutene-1, and poly (ethylene vinyl acetate) copolymers. The temperature dependence of the resultant shift factors has been determined for each system, and the method of utilizing this information to predict viscosities as a function of temperature and shear rate is discussed.

Prediction of melt viscosity flow curves at various temperatures for some olefin polymers and copolymers

Miscibility in blends of poly(styrene-co-acrylonitrile) (PSAN) with several other polymeric components has been investigated over a range of compositions by means of thermal analysis and transmission electron microscopy. Systems in vestigated were (i) PSAN/polycarbonate (PC), (ii) PSAN/styrene-maleic anhydride-methyl methacrylate terpolymer (S/MA/MM), (iii) PSAN/polynorbornene nitrile (PNN), and (iv) PSAN//S/MA/MM//PC. PSAN/PC was demonstrated to be partially miscible in all proportions over the PSAN copolymer composition range 23–70 wt % AN, while the miscibility or lack thereof of PSAN//S/MA/MM depended on the relative AN and MA contents of the PSAN and S/MA/MM, respectively. In contrast, PSAN/PNN was found to be immiscible in all proporations, while the system PSAN//S/MA/MM//PC was shown to be partially miscible. Deformation studies performed on rubber-modified versions of these blends defined deformation mode and microstructural deformation behavior. Dual extensometer tensile testing yielded relative contributions of crazing and of plastic flow, which correlated both with blend composition and with toughness. TEM observations of deformed specimens indicated a deformation process in the multiphase matrix blends consisting of craze initiation and propagation in the rubber-containing phase, craze arresting in the ductile second matrix phase, and coordinated extensive deformation of the matrix phases and of the rubber particles, where the ability to support the latter coordinated forms of deformation were observed to increase with increasing proportion of plastically deforming phase.

R. A. Mendelson

Papers

Effect of molecular structure on polyethylene melt rheology. I. Low-shear behavior

Determination of polymer branching with gel‐permeation chromatography. I. Theory

A generalized melt viscosity-temperature dependence for styrene and styrene-acrylonitrile based polymers

Prediction of melt viscosity flow curves at various temperatures for some olefin polymers and copolymers

Miscibility and deformation behavior in some thermoplastic polymer blends containing poly(styrene-co-acrylonitrile)