Isothermal crystallization kinetics in a limited volume. A geometrical approach based on Evans' theory

A new theoretical approach of the isothermal crystallization of a thin polymer film is proposed. This model, derived from Evans' theory, is in very good agreement with a previous one, but is much more interesting because it makes it possible to calculate the transformed volume fraction anywhere in the film. The main effects of decreasing thickness are a slower average crystallization of the film and a decrease in the Avrami exponent caused by a slower crystallization of the polymer close to the surfaces.A slight modification of the model allows us to calculate the isothermal crystallization kinetics at any point of the film when it contains two identical transcrystalline regions on its surfaces.All the models are well verified by computer simulations.     

A generalization of the Rouse-Zimm model

The idea of consistently averaging the hydrodynamic interaction and its various consequences for Hookean dumbbells are reviewed. For long chains this idea can be used to generalize the Rouse-Zimm model for polymer solutions. Unlike the usual Rouse-Zimm model, the new model for steady shear flow predicts a nonzero second normal stress coefficient and shear rate dependent material functions. In the limit of long chains, the viscosity and the normal stress coefficients are universal functions of the reduced shear rate.This paper was presented at the Frühjahrstagung des Fachausschusses Polymerphysik der Deutschen Physikalischen Gesellschaft at Kaiserslautern (West Germany), March 12–14, 1986.     

Gaussian approximation for Hookean dumbbells with hydrodynamic interaction: Translational diffusivity

The recently developed Gaussian approximation for the hydrodynamic interaction is used to discuss the translational diffusivity of polymers in dilute solutions undergoing homogeneous flows. For the Hookean dumbbell model, we derive the diffusion tensors associated with (i) the average polymer velocity caused by external forces; (ii) the mean-square displacement of a single polymer caused by the Brownian forces; and (iii) the polymer mass flux caused by concentration gradients. We discuss the model predictions for these diffusion tensors for steady shear flow in detail.This paper was presented at the Frühjahrstagung des Fachausschusses Polymerphysik der Deutschen Physikalischen Gesellschaft in Hamburg (West Germany), March 14–16,1988.     

X-ray investigations of the formation of core-fibrils crystallized out of the oriented melt

Crystallization models for the formation of core-fibrils crystallized from the oriented melt are discussed by comparing results from X-ray experiments with theoretical predictions. Two sets of polymer blends, the systems iPP/PB-1 and iPP/aPP have been measured. From wide angle X-ray scattering, the thicknesses of the core-fibrils, lattice distortions, and unit-cell parameters have been determined. Interface distribution functions have been used to evaluate the axial morphology of the fibers from meridional small angle X-ray scattering curves. It appears that the morphological predictions made by the crystallization models of Pennings and of Hoffman cannot be confirmed by the experimental findings. The diffusion model proposed by Petermann partially describes the morphological properties of the core-fibrils.     

Overall crystallization kinetics of thin polymer films. General theoretical approach. I. Volume nucleation

A general theoretical approach of the overall crystallization kinetics of thin polymer films is developed. This new model makes it possible to calculate the evolution of the transformed volume fraction anywhere in the film, whatever the cooling conditions are. In its isothermal limit this model is equivalent to previous approaches which have been well verified by a computer simulation. In conclusion, it is pointed out that both isothermal and anisothermal determinations of crystallization kinetic parameters are greatly dependent on the sample thickness.     

Some novel crystallization kinetic peculiarities in finely dispersing polymer blends

The morphology and the crystallization of blends of poly(vinylidene fluoride) (PVDF) with polyamide-6 (PA-6), and with poly(butylene terephthalate) (PBTP), were investigated in detail by electron microscopy and by DSC. In some of the blends, the dispersed component exhibits rather small particle sizes and, followingly, a high number density of the dispersed particles which is in the order of magnitude of, or exceeds the number density of the usually nucleating heterogeneities. In these blends, the crystallization of the dispersed component proceeded in two steps, induced by different nucleating species (fractionated crystallization). The nuclei concentrations in the components and the specific interfacial energies of the PVDF nucleation steps were estimated. An unusual type of fractionated crystallization occurs in some cases: matrix and disperse phases crystallize completely coincident due to a specific mutual nucleating efficiency of both components. An estimation of the interfacial energies involved suggests a nucleating activity of PVDF crystals for PA-6. Moreover, a rise of the crystallization temperatures of the PA-6 and PBTP matrix phases is observed that may indicate a migration of nucleating impurities during melt processing from PVDF towards the second component.     

Temperature dependence of the non-Newtonian viscosity of elongated micellar solutions

We report in this work new results of the study on the non-Newtonian viscosity of aqueous micellar solutions of cetyltrimethylammonium bromide (CTAB) in the presence of potassium bromide (KBr), in the concentration range where the elongated micelles overlap. The experiments have been performed as a function of the surfactant concentration, temperature and shear rate by use of a Couette-viscosimeter.In the non-Newtonian range, at relatively low surfactant concentration (0.25 M/l), our results show that the flow curves obtained at different temperatures converge to a single liner curve with a characteristic slope varying with the surfactant concentration. These same data can be superposed on a master curve when appropriate reduced variables are used. The shape of the flow curves obtained at different temperatures for a sufficiently high surfactant concentration is similar to that obtained for monodisperse polymer solutions at different molecular weights. The slope obtained of about –1 is also predicted by Graessley's model in the theory of microviscoelasticity based on the concept of entanglement for polymer solutions. However, at surfactant concentration higher than 0.25 M/l our results show an unusual behavior. Above some critical shear rate it is possible to obtain an increase of the apparent viscosity with temperature. One possible explanation of this effect can be found in the increase of the entanglement with concentration coupled with the temperature and direct now effects on scission and recombination rate of the micelles.     

Melt drawing as a route to high performance polyethylene

Well established routes for obtaining stiff and strong polyethylene (PE) involve solid state drawing either of solution crystallized gel films or melt crystallized spherulitic PE. The aim of this work is to show the potential of melt deformation as an alternative route for obtaining highly oriented products. Our previous work on the melt deformation route showed that oriented PE fibers could be directly extruded under appropriately controlled conditions [8,9]. Here, we show that PE films (or filaments) can also be melt drawn in the temperature window 130–160 °C, thus yielding oriented products. The advantage of melt drawing over direct melt extrusion is that it allows a wider operational latitude and thus does not require such carefully controlled conditions.The morphology produced by melt deformation is different from solid state deformation and consists of extended chain fibrils with platelet overgrowths. The relative amount of fibrils and platelets depends on operating parameters. The temperature window of PE melt drawing is identified with the regime where some flow induced crystallization takes place. The conditions for melt drawability are of wider generality for crystallizable flexible chain polymers. They are: (i) adequate strain rate to overcome entropie resistance to chain extension, (ii) but not high enough to activate the elastic response of the transient networks in the entangled system, (iii) sufficient strain to fully extend the chain, (iv) appropriate temperature for flow-induced crystallization and strain hardening, and (v) cooling to freeze the oriented structure.Ultra high molecular weight PEs were not the most suitable for melt drawing due to their high recoverable elongation in the melt (melt elasticity) in addition to added limitations imposed by their nascent grain systeme. Our work suggests that an optimum molecular weight for melt drawing is¯M _w(400–900)×10³ with further possibilities for improvement through multimodal distributions.     

Thermomechanical degradation of macromolecules

Extensional flow techniques are used to investigate thermomechanical scission of polymer solutions from ambient temperatures up to 150°C. We report precise central scission of chains beyond a critical fracture strain-rate. These results can be well accounted for by a Thermally Activated Barrier to Scission (TABS) model. We speculate upon the origin of degradation in simple shear flows and report novel results on degradation in porous media and ultrasonic sound fields, which contain dominant extensional components. Finally, we show how the nature and degree of degradation is affected by concentration and polydispersity. In semi-dilute entangled solutions, the degradation rates increase, are much higher for polydisperse solutions and the scission becomes progressively more random along the chain.Dedicated to Professor H. H. Kausch on the occasion of his 60th birthday     

Dielectric relaxation in polymeric solids Part 1. A new model for the interpretation of the shape of the dielectric relaxation function

A model is proposed which explains the shape of the dielectric relaxation function at the glass transition of polymers. The model is based on the idea that the molecular mobility at the glass transition is controlled by intra- and intermolecular interaction. In addition, a specific model for the local chain dynamics in amorphous polymer systems is used. According to the scaling hypothesis of molecular dynamics the model relates the high frequency dependence of the dielectric loss curve to the local chain dynamics and the low frequency dependence to the intermolecular correlation.     

Further electron microscope observations on polyethylene III. Smectic intermediate state during melting and crystallization

While it was possible to demonstrate in the first part of this paper [1] that the granular structure in an LPE melt created by short-time staining with chlorosulfonic acid is an artifact, it was demonstrated in the second part [2] that an artifact can actually be useful. It makes it possible to differentiate between the mobile melt and a very thin layer of fixed melt on the crystalline lamellae which corresponds to the switchboard model.This third part reports the discovery of a smectic type of liquid crystal intermediate state both in the melting and in the crystallization processes, which many authors regarded as impossible because of the flexibility of the molecules in polyethylene.Extracts presented at the 32nd Hauptversammlung der Kolloid-Gesellschaft und Berliner Polymeren Tage 1985, 2–4 October 1985 in Berlin     

Effects of thermal history on the rigid amorphous phase in poly(phenylene sulfide)

The rigid amorphous phase of semicrystalline poly(phenylene sulfide) (PPS) has been studied as a function of thermal history using scanning calorimetry, dielectric relaxation, density, and small-angle x-ray scattering (SAXS). Based on the new heat of fusion of perfect crystalline PPS, which is 26.7±0.8 cal/gram, the weight fraction of rigid amorphous phase is shown to be nearly twice as large as previously reported [1]. The mass fraction of the rigid amorphous phase ranges from 0.24 to 0.42 and is dependent upon thermal treatment. We have taken the approach of assuming a three-phase model for the morphology of semicrystalline PPS consisting of crystalline lamellae, mobile amorphous, and rigid amorphous components. Using this three-phase model, we determine that the average density of the rigid amorphous fraction is 1.325 g/cc, which is slightly larger than the density of the mobile amorphous phase fraction and was insensitive to thermal history. From the SAXS long period, the layer thicknesses of the mobile amorphous phase, rigid amorphous phase, and crystal lamellae were estimated. Only the lamellar thickness shows a systematic variation with thermal history, increasing with melt or cold crystallization temperature, or with decreasing cooling rate.     

Shear field modification of strongly flocculated suspensions — Aggregate morphology

Rheological and microscopical studies have been made to elucidate the effects of shear fields on the morphology of concentrated, aggregated model colloids. The models employed are well-characterised, predominantly chargestabilised polymer latices, coagulated by the addition of excess electrolyte. Continuous shear rheological and viscoelastic measurements indicate a very significant decrease in shear yield stress, apparent viscosity and shear modulus following prolonged shearing.Electron microscopy reveals the source of these changes. Freshly coagulated suspensions form networks that are porous, strong and qualitatively similar to simulated structures for diffusion limited aggregation. Following protracted shearing, the network structure is rearranged to yield discrete, tightly packed aggregates with a characteristic size, which is principally a function of the primary particle size.     

Characteristics and flow behavior of molten tin-polypropylene blend systems

An experimental study of tin-polypropylene compounds involving melt mixing and melt extrusion and molding over a range of temperatures is described. Problems of coalescence which make continuous mixing impossible above the melting temperature are described. Significant coalescence of the tin also results in extrusion and injection-molding problems. The influence of tin content and melt temperature on shear viscosity and extrusion character is discussed and interpreted. The electrical properties of the compounds are investigated.     

Crystallization of microphase-separated block copolymers with two crystallizing blocks

Statistical poly block copolymers of polyamide with polyethyleneoxide are investigated. The regularities governing the formation of their phase structure depending on the composition, temperature, and prehistory of the system are established. The character of crystallization of both blocks is shown to be due to their mutual solubility in the melt. Some peculiarities of microphase crystallization in PA/PEO block copolymers are revealed. It is found that, depending on the character of phase separation in the system, a PEO block may be crystallized either unimodally or in two well-separated temperature ranges.Dedicated to Prof. W. Pechhold on the occasion of his 60th birthday.     

Discussion of craze formation and growth in amorphous polymers in terms of the multiplicity of glass transition at low temperatures

A craze, the typical deformation zone in an amorphous polymer, can be divided into a precraze and a proper craze. A better understanding of the two corresponding formation processes is possible in terms of glass transition multiplicity.The precraze is associated with the molecular mobility in the confined flow zone, which is part of the main transition. The proper craze corresponds to the mobility in the flow transition zone (terminal zone for shear). A negative pressure generated by nonuniaxial stress is considered to be important for the maintainance of the molecular mobility in these zones belowT _g . The behavior of the zones at negative pressure and low temperatures Tg is considered using a pressure-temperature diagram. The fibril structure of crazes is discussed by a defect diffusion model for the proper glass transition; it is correlated with the sequential physical aging of the corresponding frozen structural defects. Typical mode lengths of the molecular mobilities in the different zones are compared with typical craze parameters. The structure of the craze material is considered to result from confined flow processes which cannot percolate because in the main transition the flow is confined by entanglements, and in the flow transition zone the flow is stopped by releasing the negative pressure due to crack propagation.     

X-ray scattering study of molecular order in a liquid crystal-side group polysiloxane

The molecular structure of a polysiloxane with phenyl benzoate mesogenic side groups was investigated in an x-ray scattering study in the partially crystalline, smectic and nematic phase, and in the melt. In the crystalline phase polymer molecules have the form of straight ribbons with a double-comb-conformation. A bilayer structure is built up by regular stacking. Layers are the dominating structure element not only in the crystalline and smectic phase, but also in the nematic phase, and even in the isotropic melt. Layers are planar in the smectic phase and curved in the nematic phase, with an asymmetric distribution of the normal vectors about the director. In the isotropic melt there is evidence for the occurrence of clusters with layer-like short-range order.     

A light scattering study of the influence of poly(ethylene glycol) on the droplet size and the interdroplet interaction in a water-in-oil-microemulsion

Dynamic and static light scattering techniques were used to study the droplet size and the interdroplet interaction of w/o microemulsions consisting of cetyltrimethyl-ammonium bromide (CTAB), hexyl carbitol, toluene, water and poly(ethylene glycol). The results were analyzed in terms of a hard-sphere model with a perturbation. For the microemulsions without polymer, their droplet sizes increased only slightly (R=10.1 to 11.0 nm) and the perturbation became more attractive as the molar ratio of H₂O/CTAB was raised from 50 to 82. In contrast, an increase in polymer concentration or polymer molecular weight not only increased the droplet sizes but also changed the perturbation to become more repulsive. In addition, it is envisaged that the interactions between the cationic groups of CTAB and the ether linkages of the poly(ethylene glycol) may also enhance the rigidity of the interfaces, hence the stability of the microemulsions.     

Shear-induced deformation of polystyrene coils in dilute solution from small angle neutron scattering 2. Variation of shear gradient,molecular mass and solvent viscosity

The technique of small angle neutron scattering (SANS) has been used to study the conformation of polystyrene chains in dilute solution under a constant shear gradient. The experiments reveal a distinct anisotropy of the molecular dimensions with regard to the directions parallel and perpendicular to the flow direction on the 2D-multidetector. The deformation ratio of the single polymer chain (R ²/R _iso ² )–1 as a function of the reduced shear gradient=([] · · M _w G)/RT shows a transition from the ideal ²-behaviour for dynamic infinitely flexible coils found at small gradients, to a behaviour with smaller increase at larger. These results are qualitatively consistent with the theory of Cerf for a polymer with finite internal viscosity in a shear gradient. At low(<1), a better agreement with the model of a free-draining coil (Rouse behaviour) than with the Zimm model is observed.     

Role of ionic species and valency on the steady shear behavior of partially hydrolyzed polyacrylamide solutions

Polyacrylamides are anionic polymers with a large number of charges along the polymer chains. The rheological properties of aqueous polyacrylamide solutions can be significantly modified by varying the solvent environment with the addition of salt. The presence of cations substantially reduces the inter- and intra-molecular interactions of the macroions. It was found that the valency of the cation has a strong effect on the rheological behavior of polyacrylamide solutions, but the size and type of salt have a negligible effect.The reduction in the solution viscosity with di-valent salts (e.g., CaCl₂, MgCl₂, BaCl₂, and MgSO₄) can be as high as an order of magnitude compared with mono-valent salt (KI, KC1, NaCl, and NaBr), depending on the salt concentration and shear rate. An identical viscosity function can be obtained for different types of polyacrylamide solutions by varying the salt content in solution. This interesting feature provides a useful means in the development and preparation of certain ideal fluids for simulation studies of complex flow problems.