Numerical simulations of partially‐filled rubber mixing in a 2‐wing rotor‐equipped chamber

Partially filled internal batch mixers are used for mixing of rubber compounds in the polymer industry. The use of mixing in such mixers equipped with a rotor is critical to the process itself, and hence, understanding of mixing is important in terms of evaluating how various operating parameters such as rpm, fill factor, and ram pressure affect distribution and dispersion of materials. The objective of the current study is to gain valuable insights on the influence of fill factor, which is the volume of the material relative to the volume of the chamber. Two‐dimensional (2D) computational fluid dynamics (CFD) simulations of rubber mixing in a 2‐wing rotor‐equipped chamber are presented here, for the first time, for fully‐filled/100% and partially‐filled/75% chambers. The volume‐of‐fluid (VOF) technique is employed to capture the interface between the rubber and air in partially filled isothermal simulations. Flow patterns are visualized to analyze the material movement. Massless particles are injected and various statistics are calculated from their positions in order to compare dispersive and distributive mixing characteristics between the fully‐filled and partially‐filled cases. Specifically, quantities such as mixing index and the maximum shear stress distribution history of particles are analyzed to obtain information about dispersive mixing, while length of stretch and cluster distribution index, also calculated from particles, are presented to investigate distributive mixing capabilities. All the results consistently demonstrated the superior effectiveness of partially‐filled mixing chambers in terms of their dispersive and distributive mixing characteristics in comparison to fully‐filled chambers. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44250.     

Entropy–enthalpy compensation in solution properties of solutes at infinite dilution in nonpolar polymers

The knowledge of the Flory–Huggins interaction parameter, χ, between organic liquids and polymers is very important in the study of their miscibility. From the temperature dependency of χ the enthalpy and residual entropy of solution can be determined. In this study literature data of thirty‐two solutes, ranging from alkanes to alcohols, at infinite dilution in isotatic polypropylene, poly(ethyl ethylene), and poly(dimethylsiloxane), were tested and linear entropy–enthalpy compensation was observed. The plot of residual free energy versus enthalpy of solution was also linear, with a lower correlation coefficient than the entropy–enthalpy plot. The range of enthalpy of solution was wider than those of the size corrected free energy of solution. In nonpolar solvents the enthalpy of solution reflected largely the interaction within the solute liquid state, and showed a linear trend with respect to solute cohesive energy density for n‐alcohols. The wide range of enthalpy of solution suggests the use of a two‐dimensional solubility parameter model to correlate the enthalpy of solution. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 1241–1247, 2007     

Engineering an Anti‐Graffiti System: A Study in Industrial Product Design

The objective of this work was to develop products for the anti‐graffiti market using a product design framework that takes into account the company core practices and meets customer expectations. Product development comprised several concurrent steps including market research and analysis to determine the market potential using a Quality Functional Deployment tool. From market research it was estimated that anti‐graffiti products had significant potential within Australia. A range of technical and quality parameters were tested. The Hildebrand and Hansen solubility parameters, viscosity and diffusivity estimates were mainly used for technical evaluation of products. An iterative process was used throughout in conjunction with parameter restraints to meet environmental sustainability, waste reduction and minimize resource consumption. The result was a cost effective product, tailored to customer expectations.     

Three‐dimensional solubility parameters of poly(ε‐caprolactone)

The three‐dimensional solubility parameter model was applied to analyze solution thermodynamic data of 27 solutes in poly(ε‐caprolactone) (PCL) between 70 and 110 °C. A linear regression method was compared with a nonlinear least square regression method, which searches solubility parameter components by minimization of the sum of error squares. The parameters of polymers were the same by both methods. When compared with the error in predicting χRT/V, the data showed a different slope from the simple three‐dimensional model. These deviations were reduced by a different model using a smaller weight on the polar and hydrogen bonding components. In the new model, the solubility parameter components were closer to the value of a structure analogue of PCL. The confidence intervals for the parameters were estimated from a linearized equation based on the sum of error squares. The solubility parameter components obtained were different from the average values of the five solutes with the smallest χ. The inclusion of solutes with high hydrogen bonding components contributed to the increase of the component in the nonlinear regression method. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 2002–2009, 2006     

Effect of optimization methods on Hansen solubility ellipsoids

In Hansen solubility parameters (HSPs) space, the solubility region of a solute is modeled as an axis‐aligned ellipsoid, of which Hansen sphere is a special case. The solubility ellipsoids of six materials are determined by the data fit function proposed by Hansen and a new objective function, both solved by a hybrid global‐local search algorithm. From the calculated and reported results, the validity and applicability of four types of currently used optimization methods are analyzed, the findings of and reasons for disputable problems are elucidated. The results reveal that the objective function defined for finding a smallest ellipsoid enclosing all good solvents and having the lowest number of outliers leads to reliable results, thereby has advantages over the methods based on the data fit function. The global convergence and capability of locating multiple optima are essential for a search algorithm used for determining solubility regions. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44621.     

Influences of hybrid carbon nanofillers on structures and electrical properties of sulfonated poly(1,3,4‐oxadiazole)‐based composite films

Sulfonated poly(1,3,4‐oxadiazole) (sPOD)‐based composite films, including 10 wt % hybrid carbon nanofillers composed of different weight ratios of multiwalled carbon nanotube (MWCNT) and graphene sheets, were manufactured via an efficient ultrasonication‐assisted solution mixing and casting. Fourier transform infrared (FTIR) spectra of the composite films confirmed the existence of specific interactions between sPOD backbone and MWCNT or graphene sheet. Transmission electron microscopic (TEM) images of cross sections of the composite films showed that 2‐dimensional (2D) graphene sheets formed an anisotropically oriented structure in the sPOD matrix film, but they are randomly dispersed owing to the introduction of 1‐dimensional (1D) MWCNT. Accordingly, the electrical resistivity of the composite films decreased largely from ～10³ Ω cm to ～10¹ Ω cm with the increment of the relative MWCNT content in hybrid carbon nanofillers due to the synergistic bridging effect. Thus, sPOD‐based composite films with 10 wt % hybrid carbon nanofillers exhibited high performance in electric heating by attaining rapid temperature responsiveness, high electric power efficiency, and stable maximum temperatures under given applied voltages. It was also revealed that the hybrid composite films were operationally stable over a long‐term stepwise electric heating experiment. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44499.     

Three‐dimensional simulation of multi‐material injection molding: Application to gas‐assisted and co‐injection molding

This paper presents an overview of the results obtained at the Industrial Materials Institute (IMI) on the numerical simulation of the gas‐assisted injection molding and co‐injection molding. For this work, the IMI's three‐dimensional (3D) finite element flow analysis code was used. Non‐Newtonian, non‐isothermal flow solutions are obtained by solving the momentum, mass and energy equations. Two additional transport equations are solved to track polymer/air and skin/core materials interfaces. Solutions are shown for different thin parts and then for thick three‐dimensional geometries. Different operating conditions are considered and the influence of various processing parameters is analyzed.     

Thermodynamic characterization of poly (caprolactonediol) by inverse gas chromatography

Specific retention volumes, V _g ⁰, were determined for 21 solute probes on poly (caprolactonediol) (PCLD) in the temperature range 323.15–403.15 K by inverse gas chromatography. The retention diagrams drawn between ln V _g ⁰ versus 1/T are linear for all the solutes since PCLD with ten repeating units in its chain behaving like a non polymeric material under the conditions applied. The stationary phase with melting temperature ~321 K is in the liquid state in the GC column over the temperature range studied and hence found to be suitable to determine infinite dilution partial molar thermodynamic properties of mixing for solutes on PCLD. The V _g ⁰ values have been used to calculate weight fraction activity coefficients Ω^∞ and Flory–Huggins interaction parameters, χ ₁₂^∞. The average partial molar enthalpy of solution, [`(\Updelta H)]<sub>1</sub><sup>S</sup> , \overline{\Updelta H}_{1}^{S} , and partial molar enthalpy of mixing, [`(\Updelta H)]₁^￥ , \overline{\Updelta H}_{1}^{\infty } , are calculated using V _g ⁰ and Ω^∞ respectively. The average molar enthalpy of vaporization ΔH ₁ ^V for solutes have been calculated using [`(\Updelta H)]<sub>1</sub><sup>￥</sup> \overline{\Updelta H}_{1}^{\infty } and [`(\Updelta H)]₁^S \overline{\Updelta H}_{1}^{S} values and compared with the literature values at 363.15 K which is the average column temperature. The partial molar entropy of mixing, [`(\Updelta S)]<sub>1</sub><sup>￥</sup> \overline{\Updelta S}_{1}^{\infty } calculated at 363.15 K are in good correlation with the average [`(\Updelta H)]₁^￥ \overline{\Updelta H}_{1}^{\infty } values. The total solubility parameter due to Guillet and the Hansen solubility parameters (HSP) are calculated for PCLD using χ ₁₂^∞ values. In the present work the Hansen solubility parameters have been calculated using a new method following the Hansen theory and Huang method with less weight on polar and hydrogen bonding components. The errors in the solubility HSP are lower and the correlation coefficients are better in both the methods compared to unweighted three dimensional model.     

4-羟基苯甲醛及其溴代物在氯仿中溶解度测定和关联

Solubilitees of 4-hydroxybenzaldehyde,3-bromo-4-hydroxybenzaldehyde,3,5-dibromo-4-hydroxybenzaldehyde in chloroform were messured at temperatures ranging from 283.15K to 323.15K.The measurements of temperature and enthalpy of fusion of pure solutes were used for caculation of solubility by ideal solution model,which was higher than the experimental values.The very low solubility in chloroform was due to self association of solute molecules,A λh formula was used to fit the data and had shown good correlation results.     

3D numerical investigations of the effect of fill factor on dispersive and distributive mixing of rubber under non‐isothermal conditions

Three‐dimensional, non‐isothermal, transient computational fluid dynamics simulations are conducted for rubber mixing with a set of two‐wing rotors in a partially filled chamber. The main objective is to analyze the effect of different fill factors of rubber on dispersive and distributive mixing characteristics by simulating 15 revolutions of the rotors rotating at 20 rpm. 60%, 70%, 75%, and 80% are the four different fill factors chosen for the study. An Eulerian multiphase model is employed to simulate two different phases, rubber and air, and the volume of fluid technique is used to calculate the free surface between two phases, in addition to the continuity, momentum and Energy equations. To characterize non‐Newtonian, highly viscous rubber, shear rate and temperature dependent Carreau‐Yasuda model has been used. A set of more than 3,600 massless particles are injected after a certain period of time to calculate several quantities in terms of dispersive and distributive mixing. Both the Eulerian and Lagrangian results showed that, fill factors between 70% and 80% presented the most reasonable and efficient mixing scenario, thus exhibiting the best dispersive and distributive mixing characteristics combined. POLYM. ENG. SCI., 59:535–546, 2019. © 2018 Society of Plastics Engineers     

Bimodal character of polyester–solvent interactions. I. Evaluation of the solubility parameters of the aromatic and the aliphatic ester residues of poly(ethylene terephthalate)

The Hildebrand and the Hansen solubility parameters of the aromatic and the aliphatic ester residues of poly(ethylene terephthalate), PET, are evaluated and compared to those determined experimentally. The interactions of nonaqueous solvents with the aromatic and aliphatic ester residues of PET are also described in terms of their relative basicity and acidity in the Lewis sense, where the aromatic residue may be taken as a Lewis acid and the aliphatic ester residue may be taken as a Lewis base.     

A new procedure for calculating Hansen solubility parameters of carbon nanotube/polymer composites

In this article, a new modeling and optimization procedure for Hansen solubility parameters (HSP) is developed. HSP values and the radius of interaction sphere for a solute can be determined by using this method based on experimental data at room temperature. The newly developed method could fit the experimental data better and get smaller radius of interaction sphere compared with the classical Hansen’s method. The HSP values of carbon nanotubes and polymer matrix are calculated to show the accuracy of the proposed approach. The physical affinity between the carbon nanotubes and polymer in the filler-polymer matrix system composite has been evaluated by their HSP spheres interaction.     

Hybrid modification of high‐density polyethylene with hyperbranched polyethylene‐functionalized multiwalled carbon nanotubes and few‐layered graphene

Herein, a facile method has been reported to efficiently prepare debundled multiwalled carbon nanotubes (MWCNT) and few‐layered graphene using a hyperbranched polyethylene (HBPE), and as hybrid fillers, their modification effects on high‐density polyethylene (HDPE) are well demonstrated. Stable dispersions of debundled MWCNT and graphene in chloroform were respectively obtained by sonication using the HBPE as stabilizer, and MWCNT/graphene/HDPE ternary nanocomposites were then fabricated by solution‐assisted premixing and subsequent melt mixing, at a fixed mass ratio of MWCNT/graphene of 3:1 and serially changed filler loadings. It is found that the MWCNT and graphene have good dispersibility in the composites, and as hybrid fillers, they can effectively form composite net‐like structure, which makes them show better modification effects on both the electrically and thermally conductive properties of HDPE, as compared to the single MWCNT. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44848.     

Thermodynamic interpretation of solute–polymer interactions at infinite dilution

Heats of solution at infinite dilution of solutes in poly(ethyl methacrylate) were estimated using gas–liquid chromatography over a temperature range of 417.74 K–427.55 K. The heat of solution is related to solute polarizability and dipole moment. Contributions of specific interactions such as hydrogen bonding and charge-transfer complexing to the enthalpy of solution were also determined.     

Relative solubility of tetrachlorohexafluorobisphenol-A polycarbonate in various compounds

The relative solubility of tetrachlorohexafluorobisphenol-A polycarbonate was observed in 127 organic compounds comprising 14 different chemical classes at room temperature and up to about 225°C. The polymer is soluble in numerous esters, ketones, halocarbons, heterocyclics, and amides. It is poorly soluble in alcohols and fluorocarbons. Correlation of observed solubility with Hildebrand total solubility parameters was poor; a much better correlation was observed with Hansen three-dimensional parameters. The solubility parameter of the polymer was estimated to be 9.1 (cal/cm³)^1/2 (18.7 MPa^1/2) from the averages of the Hansen parameters for 26 experimentally identified solvents. © 1993 John Wiley & Sons, Inc.     

Thermal and electrical conductivity of melt mixed polycarbonate hybrid composites co‐filled with multi‐walled carbon nanotubes and graphene nanoplatelets

In this work, we present thermoplastic nanocomposites of polycarbonate (PC) matrix with hybrid nanofillers system formed by a melt‐mixing approach. Various concentrations of multi‐walled carbon nanotubes (MWCNT) and graphene nanoplatelets (GnP) were mixed in to PC and the melt was homogenized. The nanocomposites were compression molded and characterized by different techniques. Torque dependence on the nanofiller composition increased with the presence of carbon nanotubes. The synergy of carbon nanotubes and GnP showed exponential increase of thermal conductivity, which was compared to logarithmic increase for nanocomposite with no MWCNT. Decrease of Shore A hardness at elevated loads present for all investigated nanocomposites was correlated with the expected low homogeneity caused by a low shear during melt‐mixing. Mathematical model was used to calculate elastic modulus from Shore A tests results. Vicat softening temperature (VST) showed opposite pattern for hybrid nanocomposites and for PC‐MWCNT increasing in the latter case. Electrical conductivity boost was explained by the collective effect of high nanofiller loads and synergy of MWCNT and GnP. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42536.     

Modeling thermodynamic properties of aqueous single‐solute and multi‐solute sugar solutions with PC‐SAFT

The Perturbed‐Chain Statistical Association Fluid Theory is applied to simultaneously describe various thermodynamic properties (solution density, osmotic coefficient, solubility) of aqueous solutions containing a monosaccharide or a disaccharide. The 13 sugars considered within this work are: glucose, fructose, fucose, xylose, maltose, mannitol, mannose, sorbitol, xylitol, galactose, lactose, trehalose, and sucrose. Four adjustable parameters (three pure‐sugar parameters and a k_ij between sugar and water that was allowed to depend linearly on temperature) were obtained from solution densities and osmotic coefficients of binary sugar/water solutions at 298.15 K available in literature. Using these parameters, the sugar solubility in water and in ethanol could be predicted satisfactorily. Further, osmotic coefficients and solubility in aqueous solutions containing two solutes (sugar/sugar, sugar/salt) were predicted (no additional k_ij parameters between the two solutes) reasonably. The model was also applied to predict the solubility of a sugar in a solvent mixture (e.g., water/ethanol) without additional fitting parameters. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4794–4805, 2013     

Analysis of a Two‐Layer Nozzle‐and‐Diffuser Electroosmotic Micromixer

An electroosmotic micromixer with two‐layer microchannels of a nozzle‐and‐diffuser structure was proposed. Numerical analysis of the flow and mixing was performed using the three‐dimensional Poisson‐Boltzmann and Navier‐Stokes equations with a diffusion‐convection model for the species concentration. A parametric analysis of the microchannels was performed using three geometric parameters, i.e., length of the nozzle section, length of the diffusion section, and width of the nozzle end, to investigate the impact of each parameter on the mixing performance, which was quantified by a quantitative measure based on the mass variance. The numerical results were used to improve the design of the proposed micromixer, leading to a far better mixing performance with a much shorter channel length compared to an existing electroosmotic micromixer.     

A comparison between models based on equations of state and density-based models for describing the solubility of solutes in CO2

The poor dissolution behaviour of solid drugs in biological environment leads to a low bioavailability. However, the dissolution rate of such drugs can be enhanced dramatically by reduction of the particle size. At present, supercritical fluid based particle size reduction processes are gaining in importance in pharmaceutical technology. For the design of such particle formation processes and the determination of their best operating conditions the knowledge of phase equilibrium and solute solubility in a supercritical fluid is essential. Today, models based on equations of state, together with different mixing rules, are most widely used to correlate and predict the solubility in supercritical fluids. Therefore the accurate knowledge of the required solute data, such as critical parameters, acentric factor, solid molar volume, and sublimation pressure of the solutes is essential. However, the common, non-equation of state based group-contribution methods are mostly empirical and often lead to inconsistent and unreliable results. Thus, due to the lack of information on these data, density-based models are often used for the correlation of experimental solubility data. In this investigation, the solubility of Salicylic acid, of S-Naproxen, of RS-Ibuprofen and of Phytosterol in CO₂ is correlated by different methods: two methods for the pressure-solubility correlation and two methods for the density-solubility correlation. In addition, the influence of solute data predicted by different group-contribution methods is investigated. With the exception of S-Naproxen all systems investigated can be modelled sufficient well with a non-cubic equation of state while a cubic equation of state gives less accurate results. In addition, it is shown that for the solutes investigated, the equation of state based method is very sensitive to the values of the sublimation pressure.     

Application of solubility parameters to the formulation of acrylate methacrylate film coating systems

In order to optimize the formulation of the acrylate methacrylate (AMA) coating systems, the partial solubility parameters of AMA and those of various coating solvents and plasticizers have been computed using the group contribution method of Van Krevelan and Hoftyzer. The data were analyzed in accordance with the three‐dimensional solubility parameters whereby δ_h (the hydrogen‐bonding component) was plotted against the sum of δ_d (the dipole–dipole component) and δ_p (the polar component). The data were also analyzed according to a two‐dimensional solubility parameters whereby δ_h was plotted vs δ_p to obtain the energy maps for the various compounds. With the three‐dimensional analysis, the position of the reference polymer in the energy map was centrally located and was flanked by plasticizers and solvents that were shown experimentally to be compatible with the polymer. On the other hand, the two‐dimensional analysis displaced the location of the reference polymer in the energy map leftward to the Y axis, and was not flanked by plasticizers and solvents that were compatible with it. The results show that the concept of the three‐dimensional solubility parameters was more applicable to the theoretical selection of plasticizers and solvents for the polymer studied. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 1339–1344, 2003