Melt solidification in polymer processing

This paper treats two cases of polymer melt solidification in rectangular geometry. The cases treated are the one of static solidification and that of solidification during flow in a narrow gap channel. Both cases are solved using the method of Dussinberre, which reduces the two-phase moving boundary case to a single phase problem, simplifying the mathematics considerably. The numerical solutions are based on a combination of the concept of flow analysis network (FAN), a finite element method developed for solving polymer flow problems, with a Crank-Nicolson implicit finite difference scheme. The methods may be used in computing the cooling down period and preventing “short” conditions in injection molding dies. Examples of solidification of high density polyethylene illustrate the applicability of the method.     

Morphological changes during oriented polymer crystallization

A theory of the stress-induced crystallization of polymeric networks is presented which takes into account 1) the free energy of fusion, 2) crystal surface energies and 3) entropic changes in the amorphous sections of crystallizing chains. It is assumed that the vector running from one end to the other of the crystallite is oriented in the direction of network extension, irrespective of crystal morphology, thus minimizing the free energy of crystallization. Assuming that the network assumes the crystal morphology which minimizes the free energy of the network at a given degree of crystallinity and that the crystallization proceeds along this lowest free energy path, it is predicted for simple network extension that growth of a perfectly oriented extended-chain crystal occurs initially, changing to a one-fold crystal oriented perpendicular to extension at low extension and to a two-fold crystal having nearly perfect orientation at High extension. The stress is predicted to decay initially and then to rise as the network chains switch from an extended-to a folded-chain morphology. Spatial factors which may trap chains in the ex tended-chain morphology or prematurely stopping the crystallization process can result in a mixed crystal morphology. At high extension, the structure is similar to that of the shish kebab.     

Shear-rate-dependence modeling of polymer melt viscosity

Steady-shear-viscosity data sets for commercial-grade acrylonitrile-butadiene-styrene terpolymer, nylon, polycarbonate, poly(methylmethacrylate), and polystyrence are fitted in terms of a generalized Cross/Carreau modeling for the shear-rate dependence. Based upon extensive data sets from the open literature as well as in-house measurements, it is shown that the shear-rate dependence can be more accurately described in terms of the Cross rather than Carreau model. Although the resulting viscosity fits based upon these two models might differ by 20% or more for the same well-characterized data set, the resulting effect upon simulating the injection-molding process is found to be much smaller since such predictions reflect a range of shear stresses (varying linearly from centerline to wall of cavity) over which the two models alternate in relative magnitude. This is demonstrated by detailed representative numerical predictions which are presented for both the filling and post-filling stages.     

Heat transfer and solidification of polymer melt flow in a channel

A numerical study is carried out on the conjugate thermal transport and solidification in polymer melts flowing through channels. A continuum model with the enthalpy formulation is used for a laminar, two-dimensional, axisymmetric, incompressible, and steady flow. The influences of axial diffusion, viscous dissipation, and temperature-dependent viscosity are included. A fully elliptic, control volume, finite difference method is employed to solve the governing equations. Numerical results are analyzed by examining the effects of outer wall temperature, Biot number, and mass flow rate. Isotherms and other results are also presented.     

Experimental modeling of solvent-casting thin polymer films

An apparatus was designed and assembled to study the solvent removal from solution-cast thin polymer films. The computer interfacing of a thermogravimetric analyzer, spectrophotometer, electronic flowmeters, and control valves for the apparatus enabled the preprogramming of the carrier gas velocity, carrier gas solvent content, and temperature profiles to simulate the environment experienced in large parallel flow industrial driers. The apparatus has also been designed and operated to enable the visual observation of the drying film with an optical microscope. Initial experimental studies conducted with the apparatus involved the effect of temperature on solvent removal. The results indicate that high dryer gas temperatures can apparently cause skinning of the film surface resulting in slower solvent removal rates. The skin formation can be suppressed by higher solvent concentration in the carrier gas. The visual observations revealed the formation of standing waves in the film surface during drying at high gas velocities (>2OO cm/min). The wave formation at least partially overcomes the effect of skinning by increasing the surface area of the film, and may be the manifestation of flow instabilities involving circulation within the film.     

Numerical simulation of semicrystalline polymer flowing in an empty tube with solidification

A methodology is set forth for the numerical solution of the transient freezing problem of a viscous power-law fluid flowing in a cold empty tube with a frozen layer forming on the inside tube surface. The fluid considered is the melt of a semicrystalline polymer with temperature dependent viscosity. The solution domain encompasses both the liquid and solid phases. Coordinate transformations are employed to immobilize and to straighten the moving, curved interface. An implicit finite difference method is employed to solve the governing equations. Numerical results are analyzed by examining the effects of the Peclet number, Nahme number, Stefen number, and the power law index on the profiles of the frozen layer. Variations of the thickness of the frozen layer as a function of time and axial coordinate are also presented.     

Morphological characterization of simulated polymer blends by light scattering

The morphology and the properties of polymer blends are closely related to processing conditions. A skin/core morphology, with a minor phase undergoing variations in orientation and aspect ratio from the surface to the core of the material is observed in processes such as the injection molding of blends. The use of optical inspection to control the stability and the quality of the product on-line is an interesting tool. In this paper, polymer composites made from glass fibers and glass microspheres embedded in a matrix of PS are used to simulate two-phase polymer blend morphology with a skin/core configuration. The relationships between the morphology of two-phase systems and the diffuse pattern scattered from an incident light beam are investigated through an analysis of the iso-intensity plots. Information can be obtained from the ratio of the axes of the ellipsoidal iso-intensity domains for depth-invariant blend morphology, and from the variation of this ratio as a function of the distance from the center of the pattern for depth-varying morphology samples. It is shown that one can differentiate the skin morphology and thickness effects.     

Mathematical modeling of weather-induced degradation of polymer properties

Weather-induced degradation of polymer properties is caused by all the factors of weather, which include solar radiation, temperature, humidity, wind, rain, environmental pollutants, thermal cycling (cold night and hot days), and sand abrasion. Linear low-density polyethylene (LLDPE) is exposed to natural weather, and degradation is monitored by the mechanical properties testing system, Fourier transform infrared (FTIR) spectroscopy, and differential scanning calorimetry (DSC). Three mathematical models were developed with weather parameters as independent parameters and mechanical property (tensile strength), chemical change (carbonyl growth), and thermal property (percent crystallinity) as dependent parameters. The mechanical property was found to be more dependent on the ultraviolet (UV) portion of the total solar radiation, chemical change was found to be synergestically effected by UV and total solar radiation, and change in thermal property was because of UV, total solar radiation, and temperature. Humidity and other weather parameters were found to play a less significant role in the weather-induced degradation of LLDPE properties.     

Characterization and modeling of sintering of polymer particles

An experimental study of simultaneous sintering of several particles has been carried out using spherical polymer grains. Considering rotational molding condition, coalescence of several grains in contact, happens simultaneously on internal surface of the mould. Theoretical model based on the effect of surface tension and viscosity can accurately predict the coalescence of a pairs of grains. However, it was observed in this study that coalescence rate changes with presence of neighboring grains and their position and the theoretical model proposed for two grains, is not able to predict the coalescence rate of mutli‐grains. Based on this finding, we have modified this model with taking into account the effect of neighboring particles in the sintering rate of multi‐grains. Obtained modified model is capable of predicting the multi‐grains sintering rate observed in this study. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Methods of testing the solidification point of fibres spun from a polymer melt

A mathematical model correlating the position of the solidification point with the change in the thickness of a spun fibre along its length. The calculated data were confirmed experimentally. The spectral range of changes in the fibre thickness as a function of migration of the solidification point caused by pulsation of cooling air expands as the number of filaments increases. For this reason, it is preferable to use the nonuniformity factor for assessing the effect of migration of the solidification point on the properties of a complex fibre. For monofilaments, evaluation of the correlation between migration of the solidification point and the properties of the fibre using the reciprocal correlation coefficient is acceptable and accurate. Methods of monitoring the solidification point of a fibre from a melt are examined, their errors are estimated, and recommendations for use are given. Altai State Technical University, Barnaul. Translated fromKhimicheskie Volokna, No. 3, pp. 54–59, May–June, 2000.     

Quality modeling and analysis of polymer composite products

The present article gives a new direction for quality modeling and analysis of polymer matrix composite products. Quality of composite products depends upon conformance of requirements of the customer. These requirements are translated into design specifications of all the contributing factors and subsystems up to component level of composite system. Quality of interaction amongst different subsystems, sub‐subsystems, and other factors affects quality of products are also to be considered. Therefore, the present article considers quality of subsystems as well as quality of all interactions together and modeled using graph theory, matrix algebra as quality graph, quality matrix, and quality permanent function of the composite product. These models are useful to design quality of every subsystem and factors in such a manner that can lead to achieve six‐sigma limits (almost zero error) i.e. 3.34 defects per million products produced. A number of analytical tests derived from these models help to carry out optimum selection of qualities of subsystems and interactions for designing competitive composite products. SWOT (strength–weakness–opportunities–threats) analysis integrated with these models becomes very powerful tool to convert an unsuccessful product into successful competitive product. Evaluation, ranking, and comparison procedures can be developed with the help of these proposed models. Coefficients of similarity and dissimilarity are developed for comparison among feasible products. Step‐by‐Step procedure based on systems approach is useful to designer, manufacturer at conceptual stage of design, and during manufacturing stages of composite products. This is basically a virtual prototyping methodology of complete system, leading to high quality competitive composite products. POLYM. COMPOS. 27:329–340, 2006. © 2006 Society of Plastics Engineers     

Monte-Carlo modeling of dense polymer melts near nanoparticles

Using Monte-Carlo techniques, we study polymer chain conformations near nanoparticles for dense melts of high molecular weight. Our results indicate the presence of a thin interfacial region (1-2 nm in thickness) within which polymer segments orient tangentially to the particle surface causing a stretching and widening of the chain ellipsoid. That region is also characterized by an accumulation of chain ends and a decrease in polymer density. Nanoparticles also affect polymer properties far away into the bulk. Thus, at small particle radius, we observe an overall swelling of the polymer chains when the distance between the centers of mass of nearest-neighbor particles becomes smaller than the radius of gyration of the chains.     

Multiscale modeling for polymer systems of industrial interest

Atomistic-based simulations such as molecular mechanics (MM), molecular dynamics (MD), and Monte Carlo-based methods (MC) have come into wide use for materials design. Using these atomistic simulation tools, one can analyze molecular structure on the scale of 0.1–10 nm. Although molecular structures can be studied easily and extensively by these atom-based simulations, it is less realistic to predict structures defined on the scale of 100–1000 nm with these methods. For the morphology on these scales, mesoscopic modeling techniques such as the dynamic mean field density functional theory (Mesodyn) and dissipative particle dynamics (DPD) are now available as effective simulation tools. Furthermore, it is possible to transfer the simulated mesoscopic structure to finite element modeling tools (FEM) for calculating macroscopic properties for a given system of interest. In this paper, we present a hierarchical procedure for bridging the gap between atomistic and macroscopic modeling passing through mesoscopic simulations. In particular, we will discuss the concept of multiscale modeling, and present examples of applications of multiscale procedures to polymer–organoclay nanocomposites. Examples of application of multiscale modeling to immiscible polymer blends and polymer–carbon nanotubes systems will also be presented.     

Mathematical modeling of squashing flows of heated polymer particles

A combination of shear and extension is encountered in the squashing flows of heated polymer particles. Extensional rate affects the non-Newtonian viscosity in determining the flow field in the squashing of cylindrical particles, but both the extensional and shear rates are equally important for disc-like particles. A viscous-type constitutive equation is used for simplicity. The solution of the momentum equations satisfying no-slip boundary conditions leads to a particle flattening equation that can predict flattening ratios of nonisothermal particles in terms of rheological parameters and dimensionless groups of process variables. Application of this analysis to roll fusing of toner particles in copiers is described in a companion article in this issue.     

On the modeling of quiescent crystallization of polymer melts

In this paper we present a way of modeling crystallization in polymers within the confines of a new general framework that has been developed to describe materials undergoing dissipative processes. Crystallization in polymers is in general an irreversible process, and a characteristic of all such processes is the production of entropy. In addition to postulating constitutive forms for the internal energy and entropy, we prescribe a constitutive relation for the entropy production. This in turn aids in deriving the crystallization rate equation from the second law, under the constraint that all real processes tend to maximize the rate of entropy production. After developing the general framework we derive specific models and compare the predictions of the model against experimental data available for quiescent crystallization in the literature. The predictions of the theory compare very well with the available experimental data for Nylon‐6 obtained by Patel and Spruiell (1).     

An approach in modeling the tubular polymer reactor

An analytical solution for diffusion with a homogeneous first-order reaction in the bulk and a heterogeneous reaction at the reactor wall in a non-Newtonian laminar flow tubular reactor is presented by using the Galerkin technique. The effect of reaction rate constants on dispersion is studied under isothermal conditions. It is found that, for the same mean velocity of the flow, the effective dispersion coefficient decreases with increase in the chemical reaction rate constants.     

Morphological states for a ternary polymer blend demonstrating complete wetting

For the most part, ternary polymer blends demonstrate complete wetting behavior. Conceptually, this is the state where one of the components will always tend to completely separate the other two and from a thermodynamic viewpoint is described as the case where two of the three possible binary spreading coefficients are negative and the other is positive, as defined by Harkins spreading theory. This work examines the complete range of morphological states possible for such a system over the entire ternary composition diagram as prepared by melt mixing. A ternary polymer blend comprised of high-density polyethylene (HDPE), polystyrene (PS), and poly(methyl methacrylate) (PMMA) is selected as a model system demonstrating complete wetting and four sub-categories of morphologies can be identified including: a) matrix/core-shell dispersed phase; b) tri-continuous; c) matrix/two separate dispersed phases, and d) bi-continuous/dispersed phase morphologies. Electron microscopy as well as a technique based on the combination of focused ion beam irradiation and atomic force microscopy are used to clearly illustrate and identify the various phases. Solvent extraction/gravimetry is used to examine the extent of continuity of the systems so as to effectively identify regions of high continuity. Triangular compositional diagrams are used to distinguish these various morphological regions and the results are interpreted in light of the interfacial tension of the various binary combinations and their subsequent spreading coefficients. The effect of the molecular weight and of viscosity ratio on the phase size of the various structures is also considered.