Heat transfer to polymer solutions and melts flowing between parallel plates

Heat transfer to polymer solutions or melts flowing in parallel plate systems is an important aspect of polymer processing as for example in extrusion through a wide slit. The present work solves the equation of energy for pseudoplastic non-Newtonian fluids flowing between parallel plates. An exact velocity profile rather than an approximation is used. Equations are derived both for temperature profiles and mean temperatures. The results are shown to correctly represent the physical situation.     

Longitudinal growth of polymer crystals from flowing solutions. XI. The friction with the rotor surface

During the formation of ultrahigh modulus fibers by the “surface-growth process,” the takeup stress is the main limiting factor lowering the attainable takeup speeds. This paper presents an investigation into the relative importance of the various factors contributing to takeup force and stress. Equations for force and stress have been derived which appear to agree with measurements. It has been concluded that the major part of the stress stems from the friction with the rotor surface and a smaller contribution arises from the coil deformation due to the flow. The equation for the stress has been employed to compute the maximum takeup speed.     

The kinetics of fiber growth from flowing solutions

Data are presented for the longitudinal and radial growth rates of polyethylene fibers grown from high molecular weight solutions using a seeding method in Poiseuille tube flow. Results indicate growth is a two-step process with the first step the formation of very thin untapered filaments ～25 μm in diameter which grow very rapidly the full length of the capillary tube. The second step involves radial thickening of the filament into a tapered shape, the kinetics of which have been measured. The discussion includes an analysis of the rapid longitudinal growth and a critical comparison to earlier experiments in both Poiseuille and Couette flow. A possible growth mechanism is suggested to explain the high growth rates found in these experiments as well as the unusual growth observed earlier for Couette rotor growth. A discussion of some kinetic data for the radial growth process is also given along with preliminary results which indicate thickening may only occur in flow of extensional kinematics.     

Longitudinal growth of polymer crystals from flowing solutions. VIII. Mechanism of fiber formation on rotor surface

A study has been made of the mechanism of the fibrous crystallization process of high-molecular-weight polyethylene from dilute solution subjected to Couette flow. Fiber growth has been observed to take place in a gel layer adhering to the surface of the rotating inner cylinder. The fiber is both taper and ribbonlike shaped, which suggests that growth occurs primarily on the lateral surfaces. The crystal growth rate, as determined by measurements of the fiber cross section, is found to depend on the roughness and the chemical nature of the rotor surface, and is independent of the take-up speed. These observations have led to the following conclusions concerning the mechanism. Long-chain molecules adsorb onto the rotor surface. By reptation an entanglement network is formed. It has long relaxation times due to the tendency of the supercooled chains to form embryonic crystallites upon slight orientation. This network is stretched by the entanglement formation with the cilia of a seed crystal, followed by shear stresses. Stretching will lead to further crystallization. The elastically active chain parts between entanglements will lead to the extended-chain backbone crystals. Inelastic chain parts will crystallize as folded platelets of the shish kebab.     

Phase diagrams calculated for flowing polymer solutions: spinodal and three phase conditions

Spinodal lines and critical points (CPs) are calculated for flowing solutions of polystyrene in trans-decalin. Three types of CPs can be distinguished: The first consists of stable CPs (ordinary critical line) and originates from the CP of the quiescent system. The other two CPs are bound to shear. Additional stable CPs (extraordinary critical line) result for higher polymer concentrations and unstable CPs for intermediate concentrations. Ordinary and unstable critical line merge in a heterogeneous double CP. The coexistence of three phases in the flowing system (eulytic points) comes to an end as two of them merge upon an increase in shear rate at a critical end point. Received: 12 September 1997/Accepted: 24 October 1997     

Antisolvent crystallization of carbamazepine from organic solutions

Carbamazepine was crystallized from organic solutions using an antisolvent crystallization technique. Ethanol was used as a solvent for the carbamazepine and distilled water was used as an antisolvent. The carbamazepine was dissolved in the solvent, and the drug solution was injected into the antisolvent causing the particle precipitation. During the crystallization experiments, the effects of the process parameters such as solution concentration, temperature, injection rate of the solution, and the presence of ultrasound, were investigated. An analysis of the produced particles showed that external characteristics such as particle size and its distribution were a strong function of the process parameters, while the internal structures such as crystallinity and thermal stability were nearly unaffected. Smaller particles were obtained when solutions with high drug concentrations were used. Higher temperature resulted in larger crystals. Particle size was also influenced by the injection rate of the drug solutions. Carbamazepine particle size was significantly reduced when the ultrasonic wave was selectively applied.     

Longitudinal growth of polymer crystals from flowing solutions. X. Conditions for continuous growth on the rotor surface

Ultrahigh strength polyethylene fibers can be generated by stress-induced crystallization from a supercooled solution subjected to Couette flow, usually referred to as the “surface-growth” process. Under appropriate conditions, continuous fiber production can be realized for a period as long as 19 days, whereas under other circumstances a rapid interruption of the growth process is met. The present investigation deals with the origin of fiber fracture during “surface growth.” The limiting values of process variables required to maintain continuous growth have been established. Interruption of the continuous growth can occur in three different ways: (1) formation of a closed fiberloop around the rotor; (2) limited crystal growth rate; (3) rapid crystallization, leading to depletion of the gel on the rotor surface. The gel layer is being formed by adsorption of long molecules on to the rotor surface and subsequent “reptation,” resulting in a dense entanglement network of these molecules. These factors determine the boundaries of the triangularly shaped domain for continuous growth in a graph of the two main variables, namely the takeup speed and the rotor speed. Furthermore, it was noticed that the introduction of a wedge-shaped groove in the surface of the Couette rotor leads to a substantial reduction of failure. Continuous growth could be established in the temperature range from 103–125°C when p-xylene was used as a solvent. For p-xylene solutions at a crystallization temperature of 110°C and using a teflon rotor of 115 mm diameter, a maximum takeup speed and rotor speed were 16 and 180 mm/s, respectively. Basically the restrictions of the process appeared to be due to the limited rate of crystallization and rate of adsorption of polyethylene molecules on the surface of the rotor.     

Phase separation,crystallization, and structure formation in immiscible polymer solutions

Morphological and calorimetric studies of phase separation have been carried out in solutions of a crystallizable polymer in poor solvents. Hydrogenated polybutadiene with low branch content was investigated in solutions with diphenyl ether and diphenyl methane, in which the equilibrium phase diagram exhibits both liquid–liquid phase separation and crystallization of the polymer. Emphasis is placed on sample preparation protocols using thermal treatments at low concentrations where it is anticipated that both phase separation mechanisms may influence the resulting morphology. Samples prepared using either ramp cooling or isothermal crystallization exhibit porous structures such as those seen in membrane materials, that predominantly reflect liquid phase separation. However, the interplay between the different kinetics of liquid demixing and crystallization provides a mechanism to control, for instance, pore size. DSC studies during ramp cooling showed evidence of two discrete crystallization processes associated with the two liquid phases expected to be present under these circumstances. Finally, high concentration samples showed morphological evidence of liquid phase separation induced at the growth front of spherulites in otherwise single-phase polymer solutions. © 1995 John Wiley & Sons, Inc.     

Precipitation from glassy polymer solutions

Solid solutions of general-purpose polystyrene containing crystalline tetrabromoxylene, tetrachloroxylene, or tetrachlorobenzene were prepared. The effects of the low molecular weight crystalline additive concentration and the thermal history on the thermal properties of the system have been studied. The system solubility, rejection of solute, etc., were characterized by such techniques as rheology, thermal analysis (DSC), and Vicat softening point.     

Water softening using packed bed of polypyrrole from flowing solutions

Packed bed of polypyrrole/polystyrene sulfonate (PPy/PSS) electrodeposited porous carbon electrode was prepared and used for continuous water softening from flowing artificial hard water solutions. Careful preparation of the packed bed was performed in order to obtain the greatest possible degree of uniformity of the PPy/PSS-within the porous carbon matrix. The porous carbon electrode was of the type, reticulated vitreous carbon (RVC) of grades 20, 45 and 80 PPI. Cyclic voltammetry and scanning electronmicroscopy (SEM) were used to characterize the prepared electrodes. The porous electrode was used in removal of Ca²⁺ ions from flowing 0.0125 M CaCl₂ solution at different conditions. Removal efficiencies of about 10% were obtained at some conditions. This low conversion per pass calls for using multi-electrode systems or recirculation of the solution (filters) to obtain the desired Ca²⁺ and water softening levels. The energy consumption and coulombic efficiency of the overall removal process was determined at a given set of experimental conditions. Regeneration of the PPy bed was affected by the presence of dissolved oxygen in the flowing solutions.     

Molecular dynamics modeling of polymer crystallization from the melt

Molecular pathways to polymer crystallization and the structures of crystal-melt interfaces are investigated by molecular dynamics simulation. We adopt a simplified molecular model for polymethylene-like chains; the chain is made of CH₂-like beads connected by harmonic springs, and the lowest energy conformation is a linear stretched sequence of the beads with slight bending stiffness being imposed. Two molecular systems are considered, one is made of 640 chains of C100 and the other is made of 64 chains of C1000, both being placed between two parallel substrates that represent the growth surfaces of the lamellae growing toward each other. The initial melt kept at a sufficiently high temperature above the melting point is rapidly cooled down to various crystallization temperatures, and the molecular processes of crystallization that follow are investigated. In both systems, we clearly observe the growth of stacked chain-folded lamellae from the substrates. The growing lamellae have a definite tapered shape, and they show marked thickening growth along the chain axis as well as usual growth perpendicular to it. The overall crystallization rate is found to be very sensitive to the crystallization temperature, showing an apparent maximum around 320-330 K for C100. We find that the lamellae do not grow keeping pace with each other but grow in independent rates especially at higher temperatures. We also examine the structures of the lateral growth surfaces and find that the growth surfaces are locally flat and the Kossel mechanism of crystal growth seems to be operative. In addition, the fold surfaces are found to be covered with relatively short chain-folds; at least about 60-70% of the folds are connecting the nearest or the next nearest neighbor crystalline stems. No appreciable bond orientational order is found in the undercooled melt of C100 and C1000.     

Finite difference solutions of the heat equation in a molten polymer flowing in a circular tube

We present the mathematical equations that govern heat transfer in a polymer melt flowing in a circular tube with constant ambient temperature, taking into account the viscous dissipation effects. This leads to a nonlinear parabolic partial differential equation. It is shown that the exact solution of a linearized version of the governing equation can be presented in terms of the Whittaker function. A finite difference scheme is used to produce an approximate solution of the linearized problem. This numerical solution is shown to be a good approximation to the exact solution found in terms of the Whittaker function. The finite difference scheme is then modified to approximate the nonlinear parabolic partial differential equation and is compared with the results found using the finite element method. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 289–294, 2006     

Mechanisms of flow induced crystallization

This paper presents a review of the field of flow induced crystallization from solution. Experimental facts concerning the nature of fibrous nucleation and the “shishkebob” morphology which results are reviewed. The discussion of growth models emphasizes the details of the nucleation control and flow control calculations which have been presented in the literature. A major problem in the development of quantitative models for the growth mechanisms has been the lack of a reproducible growth rate data base and the reasons for this are discussed. The review emphasizes those areas of the field both experimental and theoretical, where further studies are needed before a unified theory of flow induced crystal growth can emerge.     

Quasielastic scattering from dilute polymer solutions

The initial slope $\text{Ω(q)}$ of the time-dependent scattering function and the static structure factor S(q) of macromolecules in good solvents are calculated without using the Gaussian assumption. For S(q), the scaling relation S(q)～q^?1.7 is confirmed in the intermediate q range, whereas no q dependent cross-over behaviour can be observed. The calculation of $\text{Ω(q)}$ reveals a q³ dependence in this range and no evidence is seen for an exponent apart from 3. The time-dependent scattering function S(q,t) is treated within the framework of the Gaussian assumption. Hydrodynamic as well as excluded volume interactions are incorporated. It has been found that excluded volume effects decrease the decay of the scattering function in comparison with the Gaussian chain.     

New technology of vacuum trioxane crystallization from water solutions

The paper is focused on (i) kinetics of trioxane vacuum crystallization from solution in different apparatus volumes, (ii) vapour–liquid equilibrium and (iii) crystals hardness versus process temperature. It has been found that trioxane is a well-crystallized substance with relatively high effective growth rate and, simultaneously, to some extent, crystals are resistant to attrition. Unfortunately, their elongated shape promotes breaking in the forced magma circulation type crystallizers, but still it is easy to reach well-filtrated product. To meet the objective—a profitable technology for practical application, the studies in pilot scale using industrial solutions were performed. The discussed newly developed vacuum method seems to be a promising alternative for trioxane crystals production instead of a very energy-consuming and low-efficiency cooling crystallization. The additional advantages are simplicity of operation as well as lower capital cost.     

Universal relation for polymer crystallization rates from the melt

Analysis of spherulitic growth rate data for a number of linear polymers has shown that the temperature at maximum growth rate, $\text{T}{}^1$, is related to the glass transition temperature, T_g, through the empirical equation, $\text{T}{}^1\text{= 1.26 T}{}_{\mathrm{g}}$. The universal master curve for the temperature dependence of the growth rate of crystals from the melt in reduced Gandica—Magill coordinates, $\text{ln}\text{(}\text{G}\text{G}{}^1\text{) =}\text{f(T ? T}{}_{\mathrm{\infty }}\text{)}\text{(T}{}_{\mathrm{m}}\text{? T}{}_{\mathrm{\infty }}\text{)}$, is possible only on the condition that the following empirical equation holds: $\text{0.26 =}\text{T}{}_{\mathrm{\infty }}\text{T}{}_{\mathrm{g}}\text{?}\text{T}{}_{\mathrm{\infty }}\text{T}{}_{\mathrm{m}}$. Finally, limits of variation of the ‘conformational’ contribution to the excess entropy, and of the free volume fraction at $\text{T}{}^1$ were evaluated for some polymers.     

Interpretation of dynamic scattering from polymer solutions

The theoretical results available for the interpretation of the dynamic scattering from polymer solutions have been re-examined. The scattering law S(q, t) is formulated using the eigenfunction expansion method and the linear response theory. All previously known exact expressions of S(q, t) for a single unperturbed Gaussian chain have been re-derived using the first method to demonstrate the interrelationships among the various approaches to calculation of S(q, t). The results are cast into new forms which, in many cases, are more convenient for both numerical and analytical discussions. The infinite chain results are obtained from the exact closed expression of S(q, t) for ring polymers as a special case as N → ∞. Questions like the effect of the draining parameter on the shape of S(q, t), the positive definiteness of the diffusion tensor, and the possibility of measuring the eigenvalue of the first internal mode through light scattering, have been included in the discussions.A new method has been proposed for the interpretation of the dynamic scattering experiments in terms of the initial slope, Ω, of In S(q, t). The quantity Ω can also be identified as the first cumulant of S(q, t). The advantage of this method is that $\text{Ω(q)}$ can be calculated for all q values as a function of temperature and concentration by combining the linear response theory and the blob model of chain statistics. Consequently, one is not restricted to the asymptotic small- and intermediate-q regions in order to interpret the scattering experiments. The analytical and numerical results giving $\text{Ω(q)}$ under various conditions have been presented. Using infinite chain results it is shown that Ω acts as a characteristic frequency in the sense that in both the small- and intermediate-q regions, In S(q, t) can be scaled to a q-independent shape function when time is expressed as $\text{Ωt}$. This property facilitates the measurement of Ω from S(q, t)-data using a known shape function. The feasibility of the method has been demonstrated using light scattering data on polystyrene in toluene in the transition region between small- and intermediate q-regions.     

Effect of solvent on the crystallization from dilute polyethylene solutions

The influence of the thermodynamic interaction parameter on the crystallization of very dilute solutions of polyethylene in decalin, tetralin, α-chloronaphthalene and p-xylene has been studied. Depending on the solvent, quantitative kinetics data were obtained at different temperature intervals. In comparison with the crystallization in bulk, higher crystallinity levels were obtained. The overall rate temperature coefficient has been analysed according to the nucleation theory pertinent to polymer—diluent mixtures and the results show that the basal free energy for nucleation is independent of the solvent.     

Adsorptive crystallization of benzoic acid in aerogels from supercritical solutions

In this work, adsorption and crystallization of benzoic acid in different porous carriers (silica aerogel, MCM41, Trisopor glass, zeolite) from supercritical CO₂ solutions is studied. The main purpose is to reveal the influence of the adsorptive properties of the carrier on the crystallization behavior of the solute. Therefore, both adsorption and crystallization processes are studied as a function of carrier's surface properties. Adsorption of the solute and CO₂ is measured in situ using a magnetic suspension balance, whereas crystallization is realized in a high pressure view cell. The carriers could be loaded with up to ∼35 wt.% of benzoic acid, depending on the nature and the amount of the functional groups of the carrier. The size of the benzoic acid particles obtained inside the aerogel matrix depends on the crystallization conditions and is in the range of ∼20 nm-50 μm. The crystallinity of the particles was studied and it is shown that the physical state of the loaded benzoic acid inside the pores of aerogels is influenced by benzoic acid-aerogel surface interactions: strong interactions favor the amorphous form, weak interactions favor crystalline particles. The amorphous form of benzoic acid is shown to be stable over a long time period. Thus, silica aerogels can be used for stabilizing amorphous forms of organic compounds, which can be used for instance in pharmaceutical applications for the improvement of drug bioavailability.