Prediction of average droplet size in flowing immiscible polymer blends

The paper is focused on calculation of the average droplet size in immiscible blends during their steady flow. Available theoretical and experimental results of studies of the droplet breakup and coalescence are utilized to derive the equations describing dynamic equilibrium between the droplet breakup and coalescence. New expression for the coalescence efficiency, reliably reflecting recent theoretical results, is proposed. The equation for the average steady droplet size, controlled by the stepwise breakup mechanism and coalescence of droplets with not very different sizes, is derived for blends containing up to 10–20 vol % of the droplets. For blends with above approximate 20 vol % of the droplets, the breakup by the Tomotika mechanism and coalescence in highly polydisperse system is modeled. Results of the derived equations are compared with experimental data; qualitative agreement is found for the dependence of the droplet size on the amount of the dispersed phase. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 45250.     

Relationship between interfacial tension and dispersed‐phase particle size in polymer blends. I. PP/EPDM

Simple blends with different viscosity ratios of the components as well as compatibilized blends varying both in type and content of compatibilizers were used to study the relation between interfacial tension and dispersed‐phase particle size for PP/EPDM (80/20 wt %) blends in this work. Four compatibilizing systems, poly(ethylene‐co‐methacrylic acid) ionomers (EMA–I), dicumyl peroxide (DCP), DCP combined with EMA–I, and DCP in combination with trimethylol propane triacrylate (TMPTMA), were used. For blends prepared in an internal mixer, a power law relation was found between capillary number and torque ratio of the blends' components. This relation was used to estimate the interfacial tension for the compatibilized blends. The relation between steady‐state torque of the blends as a measure of viscosity and the estimated values of interfacial tension were also investigated. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 3148–3159, 2002     

Relationship between interfacial tension and dispersed‐phase particle size in polymer blends. II. PP/PA6

Simple blends with different viscosity ratios of the components as well as compatibilized blends varying both in type and content of the compatibilizers were used to study the relation between the interfacial tension and the dispersed‐phase particle size for PP/PA6 (80/20 wt %) blends in this work. Four compatibilizing systems including poly(ethylene‐co‐methacrylic acid) ionomers, a maleic anhydride‐grafted propylene copolymer, maleic anhydride‐grafted polypropylene, and a maleic anhydride‐grafted styrene ethylene butylene copolymer were used. For blends prepared in an internal mixer, a power‐law relation was found between the capillary number and the torque ratio of the blends' components. This relation was used to estimate the interfacial tension for the compatibilized blends. The relation between the steady‐state torque of the blends as a measure of viscosity and the estimated values of interfacial tension were also investigated. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 54–63, 2003     

Nonuniformity of phase structure in immiscible polymer blends

This article is focused on the phase structure development in immiscible polymer blends during melt mixing. Nonuniformity of the phase structure, i.e., the coexistence of areas containing particles with markedly different size distribution, was detected in quenched and compression molded samples of a number of various blends prepared by long and intensive mixing in the chamber of a Plasticorder. The same effect was found also for polystyrene/polyamide blends prepared in a twin‐screw extruder. It was shown that neglecting nonuniformity of the phase structure can lead to considerable error in evaluation of the effect of system parameters on the blend morphology. The reasons for the effect were discussed and it was found that inhomogeneous flow field in mixers is a plausible explanation of the nonuniform phase structure. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers     

Morphology development in immiscible polymer blends during crystallization of the dispersed phase under shear flow

Crystallization under shear of dispersed polybutylene terephthalate (PBT) fibers in copolymer polyethylene-methyl acrylate matrix (EMA) was investigated using a hot optical shear device. Crystallization during isotherm and cooling process was studied. Static crystallization experiments were carried out for comprehension purpose. Differential scanning calorimetry (DSC) analysis was performed in order to predict the crystallization behavior of PBT. Shear enhancement of its crystallization was thus demonstrated from rheological experiments. Interfacial tension of EMA/PBT blend was experimentally measured using the hot optical shear device. Theoretical break-up times of PBT fibers were also calculated. Control of the morphology through shear rate and crystallization time balance was demonstrated. Static crystallization experiments show that decreasing crystallization time favor fibrillar morphology. Breaking up of fibers was brought to the fore during dynamic crystallization experiments due to heterogeneous development of the crystallization along the fiber. During the dynamic crystallization, rapid quenching enables fibrillar morphology. Long crystallization times associated with low shear rates allow nodular morphology.     

Polymer blend de‐mixing and morphology development of immiscible polymer blends during tube flow

This work is an investigation of morphology and de‐mixing of polymer blends during melt flow through a tube. Morphology is the relative size, shape and location of each distinguishable phase present in a polymer blend. De‐mixing is the shear‐induced migration of different types of polymers away from each other during the flow. The ability to tailor de‐mixing during extrusion can potentially result in a new family of plastics waste recycling processes with mixed waste entering an extruder and separate streams of different polymer types leaving it. Also, control of morphology development can lead to the formation of layered structures without the need for two or more extruders and co‐extrusion. This work is directed at elucidating morphology development and de‐mixing of polymer blends in the most simple process design: melt flow through a tube. Shear‐induced migration was quantitatively shown in various polyethylene‐polypropylene, polypropylene‐nylon 6 and polyethylene‐nylon 6 blends. The migration observed was in accord with the hypothesis that the system tends to minimize its rate of energy dissipation for a fixed flow rate. The ratio of the viscosity of the dispersed phased to that of the continuous phase greatly influenced the morphology of polypropylene‐nylon 6 and polyethylenenylon 6 blends: a droplet‐dispersed phase structure occurred at a high viscosity ratio, whereas a multi‐layer structure resulted at viscosity ratios near unity. Shear‐induced deformation and coalescence contributed to formation of the multi‐layer structure.     

Chemical sensing materials based on electrically‐conductive immiscible polymer blends

Two families of electrically‐conductive immiscible polymer blends were studied as liquid sensing materials for an homologous series of alcohols. The systems studied include: multiphase matrices [containing carbon black (CB)] consisting of either polypropylene or high‐impact polystyrene as the major phase and thermoplastic polyurethane as the minor dispersed phase; and polyaniline (PANI) dispersed within a polystyrene matrix. Extruded filaments, produced by a capillary rheometer at various shear‐rate levels were used in the sensing experiments. The electrical resistance of these filaments was selectively sensitive to the various alcohols. Moreover, the responses displayed by these filaments are reproducible and reversible. The sensing behaviour of these blends is determined by the nature of the blend components, the blend composition and the processing conditions. An attempt is made to identify the dominant mechanisms controlling the sensing process in CB‐containing immiscible polymer blends and PANI‐containing blends. In addition, the sensing performances of these blends are compared in the light of their sensing mechanisms. Copyright © 2005 Society of Chemical Industry     

Theory of coalescence in immiscible polymer blends

The theory of coalescence in melts of polymer blends was derived on the basis of the Smoluchowski theory for colloid systems. An approximation for a flux of particles used for solutions of colloids in water was analyzed. It is shown that this approximation cannot be used for polymer blends, and an approximation is suggested that could be justifiably used for them. A system of equations was derived for the time dependence of the number of individual i-mers, using the relation suggested for the diffusion flux of particles. In an approximation of the uniform increase in particle size, equations were found for the time dependence of the number of particles, the average radius of the particle, and the interface area in the volume unit of the blend. The suggested theory predicts measurable coalescence in considerably more viscous systems than mechanically applied relations of the Smoluchowski theory for aqueous colloid solutions.     

In line study of droplet deformation in polymer blends in channel flow

We present in situ measurements of a dilute polymer blend in channel flow using an optical flow cell placed at the exit of a twin screw extruder. At weak shear stress, we find mildly deformed ellipsoidal droplets whereas at moderate sher rtes we find coexistence between large aspect ratio strings and ellipsoidal droplets. In the regime of low to moderate stress, depth resolved optical microscopy reveals that the deformation is a function of local shear stress. At large shear stress, the droplet breakup is suppressed; mildly deformed droplets at high capillary number are observed, in contrast to the Taylor model. Optical light scattering provides complementary morphological information that is averaged over the channel depth and confirms the optical microscopy. We discuss these results in terms of Taylor theory and normal forces.     

Stress prediction for polymer blends with various shapes of droplet phase

The excess shear stress after application of large step strains in polymer blend is calculated from observed shapes of deformed droplets in immiscible matrix, based on the Doi-Ohta expression for the interface contribution to the stress. The calculation is made for droplet shapes of flat ellipsoid, rod with end caps, dumbbell and ellipsoid of revolution. The predicted excess relaxation modulus agrees very well with experimental data normalized per one droplet with the volume-averaged radius for a poly(isobutylene)/poly(dimethyl siloxane) blend with narrow distribution of droplet size. Especially, slow stress relaxation in the intermediate stage and faster relaxation thereafter predicted from the rod like and dumbbell shapes are consistent with the experimental data. For a blend of hydroxypropylcellulose solution/poly(dimethyl siloxane) with broad distribution of droplet size, the predicted excess relaxation modulus agrees reasonably well with experimental data by taking account of the size distribution.     

Influence of oil phase concentration on droplet size distribution and stability of oil‐in‐water emulsions

The objective of this study was to investigate the effect of oil phase concentration, at different emulsification conditions concerning homogenization time and emulsifier content, on droplet size distribution and stability of corn oil‐in‐water emulsions. Emulsions were prepared with 3, 5, 10, and 20% w/w triethanolamine oleate (calculated on oil amount), 0.53% w/w carboxymethylcellulose (calculated on water amount), and 5, 10, 20, 30, or 40% w/w oil, and homogenized 5, 10, 20, and 60 min. It was found that increase in oil phase concentration led to decrease in specific surface area and increase in polydispersity of emulsion at lower emulsifier concentration and less intense homogenization. At emulsifier concentrations ≤10% and homogenization time ranges of 20–60 min the non‐monotonous variation in droplet size parameters with oil concentration was observed, as a result of the interaction between triethanolamine oleate and carboxymethylcellulose, which were confirmed by viscosity measurements. However, at emulsifier concentration of 20% an increase in specific surface area and decrease in polydispersity with the increase in oil concentration occurred due to an increase in equilibrium concentration of emulsifier in the continuous phase. Further, influence of oil concentration on emulsion creaming stability was found to be independent on emulsifier concentration and homogenization time. Therefore, a decrease in creaming with increase in oil concentration was observed in all the examined triethanolamine oleate (TEAO) concentration and homogenization time ranges. Practical applications: Emulsions are colloidal systems which can be encountered in different industrial sectors, such as food, pharmaceutical, cosmetics, oil industry, etc. Determination of the droplet size of emulsion is probably the most important way of their characterization, since it influences the properties of emulsion such as rheology, texture, shelf life stability, appearance, taste, etc. The size of the droplets depends on a wide range of parameters. One of them is certainly the concentration of the oil phase. However, since the impact of one parameter is often influenced with the intensity of the other variable involved in the emulsion generation, the aim of the present work was to examine the effect of corn oil concentration on droplet size parameters and stability of oil‐in‐water emulsions at different emulsification conditions. Therefore a step toward creation of emulsions with desired final properties was made.     

Rheo-Optical behavior of binary polymer blends: The effect of simple shear flow on phase behavior

The phase behavior of polymer blends under simple shear flow has been studied using a custom-designed rheo-optical system consisting of a two-dimensional small-angle light scattering (SALS) device incorporated into a conventional rheometer. Two-dimensional SALS images were gathered for model polymer blend systems with different quiescent phase behavior: polystyrene/polyisobutylene (PS/PIB) that exhibits upper critical solution temperature phase behavior and polystyrene/poly(vinyl methyl ether) (PS/PVME) that shows lower critical solution temperature phase behavior. For the PS/PIB blend, shear-induced phase mixing occurred at a critical shear rate. Below that critical shear rate, the dispersed phase was highly elongated parallel to the flow direction. For PS/PVME blends, a streak scattering pattern was observed even though the sample became optically clear after shearing. We observed, apparently for the first time, the development of a bright-streak pattern from a transient dark-streak pattern for a polymer blend system under shear. Rheo-microscopy studies revealed an intriguing wave pattern that developed coincident with the observation of a streak pattern by SALS. The relationship between the two phenomena has not yet been established.     

Investigation of interfacial slip in immiscible polymer blends

In this study, we investigated an interfacial slip phenomenon occurring in immiscible polymer blends. We chose a binary polymer blend in which the interaction parameter, χ, between the component polymers is high, and thus the interface is thin and entanglement is weak. It was observed that the negative viscosity deviation (NVD) of the blends is large, which might be attributable to interfacial slippage between the interfaces. It was also observed that incorporation of a compatibilizer in the blends significantly reduced the NVD, via suppression of interfacial slip due to increased interfacial strength. We carried out a specially designed experiment to verify that interfacial slip is indeed responsible for the NVD. We prepared several blend samples having different phase sizes ranging from 50 ∼ 5 μm, and evaluated the shear stress vs. shear rate relationships of the samples using a capillary rheometer. We observed that the viscosities of the samples decreased as the phase sizes decreased, which is strong evidence of the occurrence of interfacial slip.     

Effects of periodic and non‐periodic chaotic mixing on morphology development of immiscible polymer blends

The effects of periodic and non‐periodic chaotic mixing on the morphology development in the blending of polypropylene as dispersed phase and polyamide 6 as continuous phase in a 2D batch chaotic mixer were investigated with experimental and computational fluid dynamic (CFD) methods. The rotor motions were delivered in steady, periodic (sine waveform and square waveform), and non‐periodic (recursive protocol (RP) and restricted random sequence (RRS)) manners. The mixing efficiency was evaluated with flow number, Poincare map, morphology, droplet size and its distribution. Compared with the sine waveform, RP waveform could eliminate the island structures which existed in the flow domains and its corresponding spatial stretching distribution was more uniform. The recursively generated flow using RP lead to higher mixing efficiency and smaller droplet size with narrow distribution. However, the performance of RRS was ordinary even worse due to its random sequence.© 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

Prediction of dispersed phase drop diameter in polymer blends: The effect of elasticity

This paper discusses the prediction of the dispersed phase drop diameter in polymer blends considering the viscoelastic properties of polymers. The prediction is based on a simple force proportionality. Polymers are viscoelastic, and thus the elasticity of the matrix and the elasticity of the dispersed phase affect the drop size. The forces that deform a polymer droplet in a polymer matrix are the shear forces, η_mγ, and the matrix first normal stress, T_11,m. This deformation is resisted by the interfacial forces, 2 Γ/D and the drop's first normal stress, T_11,d. As a first approximation, the forces were balanced to predict the particle size in polymer blends. The diameter of the dispersed phase was predicted reasonably well for several systems at different operating conditions. It was observed for some systems (PS/PP, PS/EPMA, PS/PA330) that, as the shear rate increased, the diameter of the dispersed phase initially decreased. At a critical shear rate, the diameter reached a minimum value, and beyond it, the diameter increased with shear. This critical value was found to be between 100 to 162.5 s⁻¹ for a PS/PP system. The force balance predicts this minimum drop diameter at a similar critical shear rate. The specific energy input (the amount of energy input into the blend) could not explain the phenomenon of a minimum drop diameter with increase in shear. This minimum is not observed for the high concentration systems, such as the 20% PP dispersed in PS, since the effects of coalescence become significant. In reactive blends, the predicted drop diameter was closer to the experimentally determined diameter, and there was less variation in diameter with changes in shear rate.     

Morphology study of immiscible polymer blends in a vane extruder

This study reports the morphology development of polymer blends in a novel vane extruder in which polymer mainly suffers from elongational deformation field. Rapidly cooled samples of polypropylene/polystyrene (PP/PS) are collected in the vane extruder after stable extrusion. Furthermore, the shape and size of the dispersed phase from initial to final stages are analyzed. In addition, in order to compare the final size of the dispersed phase, different immiscible blends, including polypropylene/polyamide and PP/PS, are prepared by vane extruder and twin‐screw extruder, respectively. The results show that the dispersed phase is made to change rapidly from stretched striations to droplets under the strong elongational deformation field in the vane extruder. Furthermore, the droplet size of dispersed phase of blends prepared by vane extruder is much smaller than that prepared by twin‐screw extruder, indicating that the vane extruder is more efficient in mixing for immiscible polymer blends. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

Effect of addition protocol on mixing in miscible and immiscible polymer blends

The effects of the addition protocol are investigated for very‐low‐viscosity‐ratio model miscible and immiscible blends consisting of two polyethylenes (PE) and polystyrene (PS)/polyethylene (PE), respectively, are investigated. Miscible and immiscible blends with a matched viscosity ratio of 0.003 are compounded using three different addition protocols: simultaneous solids addition; sequential solids addition; and sequential liquids addition. These protocols correspond to addition of a solid additive to the feed hopper of an extruder; addition of a solid additive into the melting zone in an extruder; and addition of a liquid additive into the melting zone of an extruder. Both of these blends are shown to exhibit phase‐inversion‐like behaviors using a simultaneous solids addition protocol, regardless of concentration. Using either of the sequential addition protocols results in macroscopic segregation of the minor‐phase material to high‐shear‐rate regions of the mixer, delaying mixing. At long mixing times, however, all three protocols achieve a similar dispersed droplet morphology. Furthermore, the simultaneous solids addition protocol is shown to be the least energetically intensive, and the simultaneous solids requires the least amount of time of the three protocols to achieve maximum mixing torque for blends consisting of 20 wt% minor phase.     

Effects of emulsion parameters on relaxation behaviors for immiscible polymer blends

The relaxation behaviors of the binary immiscible blends reflected on the plots of the storage modulus and the imaginary part of complex viscosity were investigated using the Maxwell and the Palierne models. It was revealed that the peaks in the high‐ and low‐frequency regions on the complex viscosity imaginary part plot are owing to the relaxations of the blend and deformed dispersed droplets, respectively. Based on these two models, six emulsion parameters (interfacial tension, relaxation times and viscosities of two components, and dispersed phase volume fraction) were investigated in terms of their effects on the shape features of the plots of the imaginary part of complex viscosity and the Cole–Cole. The results showed that the viscosities of two components and dispersed phase volume fraction play key roles in the radii of the two circular arcs on the Cole–Cole plot. Furthermore, the two circular arcs are well separated in the case of lower interfacial tensions and dispersed phase viscosities, shorter matrix relaxation times, and higher matrix viscosities and dispersed phase volume fractions. The total relaxation time of the deformed dispersed droplets increases with increasing the viscosities of two components, especially with decreasing the interfacial tension. Three types of polymer blends were prepared and their dynamic frequency sweep testing results demonstrated the effectiveness of the corresponding predicted results. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 39690.     

Modeling droplet deformation in melt spinning of polymer blends

We report the results of a study of droplet deformation in uniaxial elongational flow under nonisothermal conditions. A mathematical model is developed that simulates deformation conditions in fiber spinning. To test our model, a blend of polypropylene and polystyrene was spun into fibers. The blend morphology of the fibers is accurately predicted by the proposed model. Morphological studies have shown that immiscible additives remain dispersed in the matrix as suspended droplets and that the droplets are elongated into fibrils under the action of shear or extensional forces during processing.