Schneider Equation Research Articles

Evaluation and statistical description for the soil characteristics in Nasiriyah based on Eurocode 7

The reliability-based geotechnical design emerged with Eurocode 7 standards and is still popular. This paper studies the engineering properties of a model of Nasiriyah soil. It aims to calculate the distinctive value of Nasiriyah soil and describe the different identification methods for laboratory tests. Knowledge of the properties of engineering parameters is essential for accurate design, measurement methods, and geotechnical investigation, and the Eurocode 7 approach of the soil is essential for geotechnical design. Therefore data were collected, and the characteristic values were determined using statistical methods. Three project sites in Nasiriyah city were studied to determine the correlation of soil strength parameters and calculate the characteristic value based on Eurocode 7. The study results showed that the Marquez method and Schneider's equations give characteristic values with a 95% reliable and economical design within the measured data range, taking into account the average, coefficient of variation of the site, and the number of measured data. It is found that the most appropriate characteristic values of the soil of the studied sites are less than the mean by half a standard deviation.

Modeling and simulation of morphology variation during the solidification of polymer melts with amorphous and semi-crystalline phases

The solidification of polymer melts in practical processing such as extrusion, injection molding and blow molding can significantly influence the inner structure and performance of final products. The investigation of its mechanism has both scientific and industrial interests. In the study, the three-dimensional mathematical model is developed for the simulation of morphology variation in the solidification of polymer melts with amorphous and semi-crystalline phases. The amorphous phase is simulated as the finite extensible nonlinear elastic dumbbell with a peterlin closure approximation (FENE-P) fluid and the semi-crystalline phase is approximated as rigid rods that grow and oriented in the flow field. The model of amorphous phase and semi-crystalline phase are coupled through the stress and momentum balance and the feedback of crystallinity to the system relaxation time. The evolution of crystallization kinetics process are described by using a set of Schneider equation that discriminating the relative roles of the thermal and the flow effect on the crystallization behavior. With the standard Galerkin formulation adopted as basic computational framework, the discrete elastic viscous stress splitting algorithm in cooperating with the streamline upwinding approach serves as a relatively robust numerical scheme by using penalty finite element–finite difference simulation with a decoupled solving algorithm. The proposed mathematical model and numerical method have been successfully applied to the investigation of solidification of polymer melts in the extrusion process. The variations of orientation and crystallization morphology during the solidification process are further discussed. Copyright © 2014 John Wiley & Sons, Ltd.

Numerical investigation of the crystallization and orientation behavior in polymer processing with a two-phase model

The crystallization and orientation behavior of a polymeric material can significantly influence the performance of products in practical processing. In this study, the variations in morphology that occur during solidification in polymer processing are mathematically modeled using a two-phase model. The amorphous phase is approximated as a finite extensible nonlinear elastic dumbbell with a Peterlin closure approximation (FENE-P) fluid, and the semi-crystalline phase is modeled as rigid rods oriented within the flow field. The crystallization and orientation behavior are numerically investigated using the penalty finite element–finite difference method with a decoupled algorithm. The evolution of the crystallization process is described by Schneider's equation, which differentiates between the effects of thermal and flow states. The hybrid closure approximation is adopted for the calculation of the three-dimensional orientation tensor. The discrete elastic viscous split stress (DEVSS) algorithm, which incorporates the streamline upwind scheme, is introduced to improve calculation stability. The variations in morphology during polymer processing are successfully predicted using the proposed mathematical model and numerical method. The influence of processing conditions on the crystallization and orientation behavior is further discussed.

Modeling and Simulation of the Crystallization Behavior of Polymer Melts in the Hollow-Profile Extrusion Process Using the Coexistence Model of Spherulite and Shish-Kebab

The thermally and flow induced crystallization behavior of polymer melts has been investigated by using penalty finite element-finite difference simulation with a decoupled solving algorithm. The coexistence model of spherulite and shish-kebab is proposed to describe the evolution of crystallization kinetics process. The Schneider equation and Eder equation are adopted to discriminate the relative roles of the thermal and the flow effect on the crystallization behavior. The proposed mathematical model and numerical method have been successfully applied to the investigation of crystallization behavior in the hollow-profile extrusion process. Both the evolution of crystalline size within the extrusion die and the effects of processing conditions on the crystallization kinetics process are discussed.

Interactions in a blend of two polymers greatly differing in glass transition temperature

Blends of poly(N-methyldodecano-12-lactam) PMDL with poly(4-vinyphenol) PVPh have been studied by the DSC and ATR FTIR methods. The difference in glass transition temperature Tg between the components is 206 °C. A single composition-dependent Tg suggests miscibility of the system, that is, homogeneity on the scale of about 10 nm. Fitting of the equation of Brostow et al. to the Tg data indicates relatively strong specific interactions and high complexity of the system. The Schneider's equation applied separately to low- and high-PVPh regions provides good agreement with experiment; the calculated curves cross at the point of PVPh weight fraction 0.27. In the low-PVPh region, the analysis indicates weak interactions with predominance of segment homocontacts and strong involvement of conformational entropy. In the high-PVPh region, strong specific interactions predominate and entropic effects are suppressed. Composition dependences of the heat capacity difference at Tg and the width of glass transition indicate strong interactions in the system and existence of certain heterogeneities on segmental level, respectively. According to ATR FTIR, hydrogen bonds between PVPh as proton donor and PMDL as proton acceptor induce miscibility in blends of higher PVPh content (above about 0.28 weight fraction). In low-PVPh blends, it is conformational entropy that enables intimate intermolecular mixing. Hydrogen bonds adopt several (distorted) geometries and are on average stronger than average hydrogen bonds formed in self-associating PVPh. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011

Mechanical and thermal properties of perfluoroalkyl ethyl methacrylate–methyl methacrylate statistical copolymers synthesized in supercritical carbon dioxide

Poly(methyl methacrylate-ran-perfluoroalkyl ethyl methacrylate) copolymers having varying perfluoroalkyl ethyl methacrylate ester (Zonyl-TM) contents were synthesized in supercritical CO 2. Complete amorphous structures of the copolymers were verified by XRD. Young's modulus ( Y mod ) of the copolymers was decreased linearly from 1.57 to 1.08 GPa and T g values from 102 to 77 °C with the increase of Zonyl-TM content. A linear relationship between the Y mod and the T g values of the copolymer was also found. The increase of the large branched pendant groups resulted in the increase of the free volume and a corresponding decrease in Y mod and T g of the copolymers. A good fit was found when the Schneider equation was used. Negative deviation from the Gordon–Taylor equation was observed when Zonyl-TM content was lower than 14% due to rapid increase in free volume and then a positive deviation was found due to the dipole–dipole interactions between the methyl ester and fluoroalkyl ester groups.

Numerical modeling of nonisothermal polymer crystallization kinetics: Flow and thermal effects

AbstractA numerical model able to simulate polymer crystallization under nonisothermal flows is developed. It is based on the assumption that the trace of the extra‐stress tensor, calculated according to a viscoelastic multimode Upper Convected Maxwell (UCM) model, is the driving force of the flow‐induced extra nucleation. Two distinct sets of Schneider equations are used to describe the growth of thermally and flow induced nuclei. The model is then coupled with the momentum equations and the energy equation. As an application, a shear flow configuration between two plates (Couette flow) is simulated. The relative influence of the mechanical and thermal phenomena on the crystallization development as well as the final morphology distribution is then analyzed as a function of the shearing intensity and the cooling kinetics, in terms of nucleation density and crystallite mean sizes. POLYM. ENG. SCI., 50:2044–2059, 2010. © 2010 Society of Plastics Engineers

Copolymers of methyl methacrylate and fluoroalkyl methacrylates: Effects of fluoroalkyl groups on the thermal and optical properties of the copolymers

Fluoroalkyl methacrylates, 2,2,2-trifluoroethyl methacrylate (1), hexafluoroisopropyl methacrylate (2), 1,1,1,3,3,3-hexafluoro-2-methyl-2-propyl methacrylate (3), and perfluoro t-butyl methacrylate (4) were synthesized. Homopolymers and copolymers of these fluoroalkyl methacrylates with methyl methacrylate (MMA) were prepared and characterized. With the exception of the copolymers of MMA and 2,2,2-trifluoroethyl methacrylate (1), the glass transition temperatures (Tgs) of the copolymers were found to deviate positively from the Gordon-Taylor equation. The positive deviation from the Gordon-Taylor equation could be accounted for by the dipole–dipole intrachain interaction between the methyl ester group and the fluoroalkyl ester group of the monomer units. These Tg values of the copolymers were found to fit with the Schneider equation. The fitting parameters in the Schneider equation were calculated, and R2 values, the coefficients of determination, were almost 1.0. The refractive indices of the copolymers, measured at 532, 633, and 839 nm wavelengths, were lower than that of PMMA and showed a linear relationship with monomer composition in the copolymers. 2 and MMA have a tendency to polymerize in an alternating uniform monomer composition, resulting in less light scattering. This result suggests that the copolymer prepared with an equal molar ratio of 2 and MMA may have useful properties with applications in optical devices. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 4748–4755, 2008

Mechanistic investigations of phase behavior in Eudragit ®E blends

Blends of Eudragit ®E (EE) and polymeric excipients using thermal analysis and FTIR spectroscopy were examined. The interactions amongst the blend components were quantified in terms of parameters K 1 and K 2 in Schneider equation and were explained on the basis of interactions between the functional groups of the blend constituents investigated by FTIR spectroscopy. EE formed miscible blends with EC and polyelectrolyte complexes increasing in strength in the order: ES < HPMCP < CAP < EL. From the T g data the weight fraction of EE in the polyelectrolyte complex was determined. The importance of formulating polyelectrolyte complexes in stoichiometric ratios has been highlighted. The duration over which the release can be sustained by polyelectrolyte complexes has been correlated with equilibrium swelling of the polyelectrolyte complex and parameter K 1 for the first time. This would help in the choice of blend constituents and composition to tailor drug release.

Blends of Reverse Enteric Polymer with Enteric and pH-Independent Polymers: Mechanistic Investigations for Tailoring Drug Release

Blends of conventional reverse enteric polymer with enteric polymers result in insoluble polyelectrolyte complexes and hence cannot be used in film coatings. We report a new set of miscible blends of a new reverse enteric polymer (NREP) synthesized by us with enteric and pH-independent polymers. The nature of interactions between polymers in the blends has been established by analyzing Fourier transform infrared (FTIR) spectra. The extent of interaction has been investigated by thermal analysis and quantified in terms of parameters K1 and K2 in the Schneider equation. Based on these values, the interactions between NREP and these polymers have been ranked in the order EC (ethylcellulose) < ES (Eudragit S) < HPMCP (hydroxypropyl methylcellulose phthalate). The quantification of interactions in blends helps explain the release pattern of cefuroxime axetil (CA) at gastric pH and tailor the release of other drugs according to their pharmacokinetic characteristics. The understanding also provides a more rational approach for selection of polymers and their content in the coating compositions, rather than an empirical approach.

Poisson Involutions, Spin Calogero-Moser Systems Associated with Symmetric Lie Subalgebras and the Symmetric Space Spin Ruijsenaars-Schneider Models

We develop a general scheme to construct integrable systems starting from realizations in symmetric coboundary dynamical Lie algebroids and symmetric coboundary Poisson groupoids. The method is based on the successive use of Dirac reduction and Poisson reduction. Then we show that certain spin Calogero-Moser systems associated with symmetric Lie subalgebras can be studied in this fashion. We also consider some spin-generalized Ruisjenaars- Schneider equations which correspond to the $N$-soliton solutions of $A^{(1)}_n$ affine Toda field theory. In this case, we show how the equations are obtained from the Dirac reduction of some Hamiltonian system on a symmetric coboundary dynamical Poisson groupoid.

Physicochemical evaluation of PVP–thiazide diuretic interactions in co-spray-dried composites—analysis of glass transition composition relationships

The aim of this study was to evaluate the possible interactions in the solid state between the thiazide diuretics: bendroflumethiazide (BFMT), hydroflumethiazide (HFMT) and hydrochlorothiazide (HCT) and polyvinylpyrrolidone (PVP) following processing. The glass transition temperatures ( T g s) of a range of binary co-spray-dried PVP–thiazide composites were determined and compared to the predictions of the Gordon–Taylor, Fox, Couchman–Karasz, Kwei and Schneider equations. The solid composites of the thiazide diuretics and PVP were prepared by a spray drying technique. Properties of composites were determined with the use of helium pycnometry and FTIR spectroscopy. For many systems studied the experimentally detected T g s exhibited large positive deviations when compared with the values predicted by the Gordon–Taylor, Fox and Couchman–Karasz equations. The data was better fitted by the Schneider equation consistent with a drug–polymer interaction. FTIR analysis revealed that strong hydrogen bonding between the sulphonamide groups of the thiazide diuretics and the PVP molecule was responsible for the increase in the T g s. Additionally, in the case of BFMT–PVP composites, an interaction between the phenyl group and polymer ring was apparent. Glass transition–composition behaviour for amorphous drug–PVP composites deviated from the predictions of the commonly used Gordon–Taylor equation. Deviations were consistent with interactions between the components in the amorphous mixtures. The Schneider equation may be successfully applied to fit the T g-composition profiles obtained, where other models fail to give good predictions.

Crystal shapes and crystallization in continuum modeling

A crystallization model appropriate for application in continuum modeling of complex processes is presented. As an extension to the previously developed Schneider equations [W. Schneider, A. Köppel, and J. Berger, “Non-isothermal crystallization of polymers,” Int. Polym. Proc. 2, 151 (1988)], the model presented here allows one to account for the growth of crystals of various shapes and to distinguish between one-, two-, and three-dimensional growth, e.g., between rod-like, plate-like, and sphere-like growth. It is explained how a priori knowledge of the shape and growth processes is to be built into the model in a compact form and how experimental data can be used in conjunction with the dynamic model to determine its growth parameters. The model is capable of treating transient processing conditions and permits their straightforward implementation. By using thermodynamic methods, the intimate relation between the crystal shape and the driving forces for phase change is highlighted. All these capabilities and the versatility of the method are made possible by the consistent use of four structural variables to describe the crystal shape and number density, irrespective of the growth dimensionality.

POLYURETHANE-EPOXY MALEATE OF BISPHENOL A BLENDS

Blends of polyurethane with epoxy maleate of Bisphenol A were synthesized and their miscibility, the physico-mechanical properties, as well as the thermal behavior were studied. Differential scanning calorimetry (DSC) measurements showed a single composition-dependent glass transition temperature (Tg), and is evidence for a good miscibility of the studied systems. The variation of Tg's of the blends versus composition (Fox, Gordon-Taylor, and Schneider equations) showed the presence of some physical interactions between polyurethane and epoxy maleate polymers. Generally, the physico-mechanical properties of the blends are lower as than those of polyurethane. This suggests that epoxy maleate of Bisphenol A operates in a mixture with polyurethane only as a plasticizer. The thermal behavior of the studied blends showed no large differences to that of polyurethane.

Glass transition behaviour and interactions in [formula omitted] blends

The glass transition temperatures ( T gs) of binary blends of poly( p-vinyl phenol) with poly(methyl methacrylate), poly(ethyl methacrylate) and poly(ethyl methacrylate- co-methyl methacrylate) have been determined. The experimental T g-composition data do not obey the Couchman-Karasz equation. However, the Gordon-Taylor, the Kwei and the Schneider equations fit the experimental data quite well. The values of the Gordon-Taylor k parameters, as well as the measurements of the glass transition widths, suggest a similar average intensity of the specific intermolecular interactions in the systems studied here, which is in agreement with the Fourier transform infra-red results. The Kwei and the Schneider equations are able to reflect the additional stabilization due to the dilution of copolymer repulsive interactions in the poly(p- vinyl phenol) poly(ethyl methacrylate-co- methyl methacrylate) blends.

Intermolecular interactions in binary multiblock copolymer blends

The glass transition temperature of the soft phase has been studied in blends of multiblock polyetherester (PEE) with multiblock polyesterurethane (PUA) and poly(ether carbonate)urethane (PUC) copolymer. The K 1 and K 2 coefficients from the Schneider equation and the q parameter from the modified Kwei equation have been used to monitor the strength of intermolecular interaction. A suggestion for the partial miscibility of the PEE/PUC blends in the soft phase is proposed.