A theoretical model for the prediction of thermal expansion behaviour of particulate composites

The thermal expansion coefficient of particle-reinforced polymers was evaluated using a theoretical model which takes into account the adhesion efficiency between the inclusions and the matrix — an important factor affecting the thermomechanical properties of a composite. To measure the adhesion efficiency a boundary interphase, i.e. a layer between the matrix and the fillers having a structure and properties different from those of the constituent phases, was considered. This layer is assumed to have varying properties.To obtain information concerning the properties and extent of the interphase, an experimental study of the thermal behaviour of aluminium-epoxy composites was undertaken. Differential Scanning Calorimetry (DSC) measurements were performed to evaluate heat capacity with respect to temperature. In addition, the effects of different factors, such as heating rate and filler concentration on the glass transition temperature of the composite, were examined. The sudden changes in heat capacity values in the glass transition region were used to estimate the extent of the boundary interphase according to an existing theory.Finally, the values of the thermal expansion coefficient, predicted by this model, were compared with theoretical results obtained by other authors and with experimental results.     

Interfacial effects on the melt state behavior of polyethylene-EPDM-calcium carbonate composites

Dynamic mechanical spectra of various composites of high density polyethylene (PE), ethylene propylene diene rubber (EPDM), and calcium carbonate were obtained at 190°C with a parallel plate instrument. Interfacial effects were found to have a significant influence on the dynamic mechanical behavior of these composites.Composites of calcium carbonate in PE displayed prominent particle—particle interaction effects. This resulted in a greatly enhanced dynamic shear modulusG _d due to the filler addition. Treatment of the calcium carbonate with gamma-aminopropyltriethoxysilane (-APS) or gamma-methacryloxypropyltrimethoxysilane (-MPS) significantly reduced the particle—particle interactions. Solution deposition of EPDM or EPDM grafted with maleic anhydride (EPDM-MA) on the calcium carbonate, before incorporation into a PE composite, also had a significant effect on the composite properties. Comparison of data from composites treated with EPDM vs. EPDM-MA suggested the presence of an interaction between the calcium carbonate surface and the maleic anhydride modification. This conclusion was further supported by solid state proton NMR relaxation model experiments which showed significant immobilization of the EPDM-MA chains on the filler surface. The treatment of calcium carbonate with-APS or-MPS before incorporation into multicomponent polyethylene-rubber-filler composites also had a significant influence on the dynamic mechanical properties of the resultant composites. There is evidence for a reaction between-APS and EPDM-MA during processing on the roll mill.     

The effect of molecular weight distribution on the elongational properties of linear polymers

The elongational properties of a series of six polypropylene and two polystyrene samples have been studied at constant rate of strain. A Wagner-type constitutive equation has been used to fit the experimental data, and the shape of the damping function has been correlated with the polydispersity index of the samples. As the memory function or relaxation function of linear viscoelasticity may be derived from the molecular-weight distribution using either molecular or phenomenological models, it is therefore possible to calculate the stress growth function of a linear polymer in elongation from its molecular-weight distribution.     

Rheological material functions of polymer solutions using a generalized Maxwell model with slip functions Part I: Theory

A generalization of the Maxwell model for polymer systems is derived that replaces the velocity gradient in the Eulerian expression for the upper convected derivative by a tensorial kinematic function. Applying the principle of objectivity this tensorial function is reduced to two scalar slip functions. In shear flows, only one of the two occurs. Material functions are calculated in closed form, and asymptotic conditions are formulated that guarantee isotropic behaviour of the material in sudden strains.Presented at the second conference Recent Developments in Structured Continua, May 23–25, 1990, in Sherbrooke, Québec, Canada.     

Dynamic-mechanical properties of interfacially modified glass sphere filled polyethylene

Model composites of spherical glass particles dispersed in a matrix of high density polyethylene were prepared both with and without interfacial modification by an azidofunctional trialkoxysilane. Dynamic mechanical measurements of the composites in the melt state were recorded. The unmodified composites behave as theoretically predicted and the effect of particle—particle interaction at high volume fractions can be measured. The composites with a modified interfacial region have greater shear moduli due to the effect of a region surrounding the particle modified by the silane. The material in this region is largely bound to the glass surface and was examined by Fourier transform infrared spectroscopy after extraction of the bulk matrix. Theoretical calculations are shown to be useful in calculating the mechanical properties and volume fraction of the interfacial region.     

The non-isothermal elastic dumbbell: A model for the thermal conductivity of a polymer solution

In a flowing polymeric liquid, molecular orientation will give rise to anisotropic conduction of heat. In this paper, a theory is presented relating the thermal conductivity tensor to the deformation history of the fluid. The basis of this theory is formed by the Hookean dumbbell. It is shown that the anisotropy of the thermal conductivity is proportional to the polymer contribution to the extra-stress tensor. This stress-thermal law makes it relatively simple to incorporate anisotropic heat conduction into the numerical simulation of a flowing polymeric liquid.     

Untersuchung der verdickung von latex-dispersionen durch ethylacrylat-methacrylsäure-copolymere

Zusammenfassung Es wurden dynamische and stationdre Scherversuche durchgeführt, um den Verdickungseinfluß von Copolymeren aus Ethylacrylat and 15, 40 bzw. 65 Gew. % Methacrylsdure auf Latex-Dispersionen aus Ethylacrylat mit 0 bzw. 1 Gew. % Acrylsaure zu untersuchen. Nach Überschreiten eines Schwellwertes der Verdickungsmittelkonzentration, welche mit dem Sauregehalt im Verdickungsmittel und im Latex abnahm, wurde ein starker Anstieg des Speicher-und Verlust-Moduls (G and G) sowie der Fließgrenze und der Thixotropie beobachtet. Gleichzeitig wurde ein Überwiegen der viskosen Eigenschaften sowie eine zunehmende Flockulationsfähigkeit des Verdickungsmittels festgestellt. Bei größerem Säuregehalt im Latex überwogen die elastischen Eigenschaften, gleichzeitig erhöhte sich die Bestandigkeit gegen Flockulation. Die Verdickungswirkung der unterschiedlich zusammengesetzen Systeme wird durch die Ausbildung einer Raumnetzstruktur erklärt. Das Flockulationsverhalten wird auf Änderungen der Ladung und des freien Volumens zurückgeführt.

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The thickening effect of latices of ethylacrylate-methacrylic acid copolymers (15, 40, and 65 wt. % of the acid) on latices of ethylacrylate-acrylic acid copolymers (0 and 1 wt. % of the acid) was studied by using dynamic and steady shear flow measurement. It was found that beyond a certain concentration of the thickener the storage modulus G, the loss modulus G, the yield stress values, and thixotropic behavior rapidly increased. At the same time, viscous properties and the flocculation ability of the thickeners prevailed. On the contrary, an increase in acid content in the latex made the elastic properties and flocculation resistance of the system more pronounced. The thickening effect is explained by the formation of an ordered structure. The flocculation behavior is explained by changes of the electrical charge and the free volume.

Teilweise vorgetragen an der Jahrestagung der Deutschen Rheologischen Gesellschaft, 13.–15. Mai 1991, Berlin.     

Comparison between uniaxial and biaxial elongational flow behavior of viscoelastic fluids as predicted by differential constitutive equations

Behavior of polymer melts in biaxial as well as uniaxial elongational flow is studied based on the predictions of three constitutive models (Leonov, Giesekus, and Larson) with single relaxation mode. Transient elongational viscosities in both flows are calculated for three constitutive models, and steady-state elongational viscosities are obtained as functions of strain rates for the Giesekus and the Larson models.Change of elongational flow behavior with adjustable parameter is investigated in each model. Steady-state viscosities _E and _B are obtained for the Leonov model only when the strain-hardening parameter is smaller than the critical value _cr determined in each flow. In this model, uniaxial elongational viscosity _E increases with increasing strain rate , while biaxial elongational viscosity _B decreases with increasing biaxial strain rate _B . The Giesekus model predictions depend on the anisotropy parameter . _E and _B increase with strain rates for small _B while they decrease for large . When is 0.5, _E in increasing, but _B is decreasing. The Larson model predicts strain-softening behavior for both flows when the chain-contraction parameter > 0.5. On the other hand, when is small, the steady-state viscosities of this model show distinct maximum around = _B = 1.0 with relaxation time . The maximum is more prominent in _E than in _B .     

On the cone and plate deformation of a rubber-like material: Instability

In this report it is shown that the place boundary-value problem, for a small deformation superimposed on the large cone-and-plate deformation of a Mooney-Rivlin material, has no unique solution at some displacement angles of the cone. The kinematics of the small deformation are chosen such that the problem is reduced to a set of ordinary differential equations. With respect to this restricted class of kinematics the cone-and-plate deformation is unstable.     

The evolution of linear viscoelasticity during the vulcanization of polyethylene

The evolution of linear viscoelasticity during the vulcanization of polyethylene is studied through the gel point. The material in the vicinity of the gel point is described by two scaling laws: one characterizes the viscoelasticity at the critical point and a second characterizes the evolution of viscoelasticity near the gel point. Time Resolved Mechanical Spectroscopy is used to observe both scaling phenomena. The material at the gel point displays power law relaxation over five decades of time with a power-law relaxation exponent equal to 0.32. This study conforms with previous findings that this exponent is composition-dependent. The longest relaxation time diverges in the vicinity of the gel point as _max |p _c - p| ^–1/, and we find = 0.2. This result conforms with previous reports that this exponent may be independent of composition. The Arrhenius flow activation energy for this material undergoes three-fold changes during crosslinking up to the gel point. A single-adjustable-parameter stretched-exponential-power law relaxation function is an inadequate representation of crosslinked materials over any significant range of extent of the reaction up to the gel point.     

Finite shear strain behavior of a crosslinking polydimethylsiloxane near its gel point

A power law distribution of relaxation times, large normal stress differences, and physical rupture of molecular network strands dominate the shear behavior of polymers at the gel point (critical gels). This is shown in a series of well-defined experiments with increasing magnitude of shear on a model-network polymer system consisting of a linear, telechelic, vinyl-terminated poly-dimethylsiloxane (PDMS) and a four-functional siloxane crosslinker. Stable samples were prepared by stopping the crosslinking reaction at different extents of reaction in the vicinity of the gel point (GP). The Gel Equation has been shown to be valid up to strains of about 2 when using a finite strain tensor. Larger strains have been found to disrupt the network structure of the crosslinking polymer, and introduce a mechanical delay to the gel point. A sample that was crosslinked beyond the gel point (p>p _c ) can be reduced from the solid state to a critical gel, or even to a viscoelastic liquid, depending on the magnitude of shear strain. As a consequence, the relaxation exponent of a critical gel created under the influence of shear is less than that of a quiescently crosslinked critical gel.     

Prediction of the non-linear rheological properties of polymer solutions by means of the Rouse-Zimm model with slippage

The non-affine deformation of macromolecules and the slippage function are discussed. In case of polymer solutions with moderate concentration the slippage function is determined by means of the Cox-Merz rule. The non-linear viscoelasticity of these solutions is described with the aid of the Rouse-Zimm model with slippage function. The theoretical predictions show good agreement with published experimental data.     

Effect of solids concentration in dense suspensions of silica-iron(III) oxide and water

The rheological properties of dense suspensions, of silica, iron (III) oxide and water, were studied over a range of solids concentrations using a viscometer, which was modified so as to prevent settling of the solid components. Over the conditions studied, the material behaved according to power—law flow relationships. As the concentrations of silica and iron(III) oxide were increased, an entropy term in the flow equation was identified which had a silica dependent and an iron (III) oxide dependent component. This was attributed to a tendency to order into some form of structural regularity. A, A, B, C pre-exponential functions (K Pa^–n s^–1) - C _ox volume fraction iron (III) oxide - Q activation energy (kJ mol^–1) - R gas constant (kJ mol^–1 K^–1) - R _v silica/water volume ratio - T temperature (K) - n power-law index - H enthalpy (kJ mol^–1) - S entropy change (kJ mol^–1 K^–1) - shear strain rate (s^–1) - shear stress (Pa)     

The unraveling of a polymer chain in a strong extensional flow

By assuming that in a strong extensional flow a polymer molecule in dilute solution is quickly driven into a folded or kinked state in which drag and entropic elastic forces dominate over the Brownian force, we derive kink dynamics equations that describe the unraveling of the molecule in the extensional flow. Solving these equations numerically, we find that although the ends of the chain move, on average, affinely in the flow field until the chain is unfolded to about 1/3 of its fully extended length, large viscous stresses are produced because the solvent must flow around nonextending strands of polymer that lie between neighboring kinks. These predictions are compared with available experimental data and with other theoretical models.     

The time-dependent stress-optical behavior of polycarbonate in the glass transition region

The mechanical and stress-optical behavior of Bisphenol-A polycarbonate was investigated in the glass-transition region. For this purpose, optical creep experiments were carried out in shear and elongation on a tensile tester specially designed for use on a microscope state. A Kohlrausch Williams Watts equation (KWW) with a temperature-independent parameter could successfully be applied to the curves describing the time-dependent values of the stress-optical coefficient for several temperatures. The temperature dependence of the corresponding retardation time could be established and described by the WLF equation. For variable stresses the time-dependent birefringence is obtained from a generalized linear stress-optical rule as modeled according to linear superposition. The time-temperature superposition principle was applied to all measurements. With the dynamic moduli some deviations were observed at the transition from the rubbery plateau to the relaxation. The strain-optical coefficient was found to decrease with increasing time and strain. The strain dependence was found to be independent of temperature at constant stress.     

On some nearly viscometric flows of viscoelastic liquids

Superposition of oscillatory shear imposed from the boundary and through pressure gradient oscillations and simple shear is investigated. The integral fluid with fading memory shows flow enhancement effects due to the nonlinear structure. Closed-form expressions for the change in the mass transport rate are given at the lowest significant order in the perturbation algorithm. The elasticity of the liquid plays as important a role in determining the enhancement as does the shear dependent viscosity. Coupling of shear thinning and elasticity may produce sharp increases in the flow rate. The interaction of oscillatory shear components may generate a steady flow, either longitudinal or orthogonal, resulting in increases in flow rates akin to resonance, and due to frequency cancellation, even in the absence of a mean gradient. An algorithm to determine the constitutive functions of the integral fluid of order three is outlined.Nomenclature A _n Rivlin-Ericksen tensor of order . - A _k Non-oscillatory component of the first order linear viscoelastic oscillatory velocity field induced by the kth wave in the pressure gradient - d Half the gap between the plates - e _x, e _z Unit vectors in the longitudinal and orthogonal directions, respectively - G(s) Relaxation modulus - G History of the deformation - Stress response functional - I() Enhancement defined as the ratio of the frequency dependent part of the discharge to the frequencyindependent part of it at the third order - I ^*() Enhancement defined as the ratio of the increase in discharge due to oscillations to the total discharge without the oscillations - k Power index in the relaxation modulus G(s) - k _i ^–1 Relaxation times in the Maxwell representation of the quadratic shear relaxation modulus (s ₁, s ₂) - m _i ^–1, n _i ^–1 Relaxation times in the Maxwell representations of the constitutive functions ₁(s ₁,s ₂,s ₃) and ₄ (s ₁, s ₂,s ₃), respectively - P Constant longitudinal pressure gradient - p Pressure field - _mx ,⁽³⁾ _nz ,⁽³⁾ Mean volume transport rates at the third order in the longitudinal and orthogonal directions, respectively - ₀,⁽³⁾, ₁,⁽³⁾ Frequency independent and dependent volume transport rates, respectively, at the third order - s = t- Difference between present and past times t and      

Rheological behavior of water-creosote and creosote-water emulsions

The effect of temperature on the steady-shear viscosity of two base emulsions (water-in-creosote (w/o) and creosote-in-water (o/w)) and a pigment emulsified creosote (PEC) was investigated. The PEC is a water-in-creosote emulsion which contains also a solid, micronised pigment, and is used industrially as a wood preservative. All three emulsions exhibited shear thinning characteristics at different temperatures. The viscosity-shear rate relationships follow a modified Quemada model. A temperature-superposition method using the reduced variables / and t _c was applied to yield a master plot for each of these emulsions at different temperatures. The effect of creosote concentration on the viscosity of four other o/w emulsions at different temperatures was also studied. The same reduced variables were able to produce a temperature-concentration superposition plot for all of the o/w emulsion results.The effective (average) radius of the globules (dispersed phase) was found to increase with increasing temperature for the base w/o and the PEC emulsion. The collision theory could be used to explain the increase in the droplet size. However, while little overall variation in globule size was observed for the o/w emulsions, microscopic observation indicated an increase in the proportion of large diameter droplets with temperature at the highest creosote concentration (60%). A creaming effect (phase concentration) was observed with these emulsions at higher temperatures, precluding an accurate estimate of droplet size based on collision theory.Seconded from Koppers Coal Tar Products, Newcastle, N.S.W., Australia.     

Electrical noise generated by the capillary flow of alkalized latex dispersions carrying carboxyl groups

It has been demonstrated that strong electrical noise is generated during capillary flow of an alkalized latex dispersion of copolymer carrying carboxylic groups where the dispersion particles are swollen. On the other hand, if the content of dissociated carboxylic groups in the alkalized dispersion is higher and swelling turns into decomposition of the particles to macromolecules or their aggregates, the thermal (Nyquist) noise at rest remains unaffected by flow, even if the flow curves are similar to corresponding ones when strong noise is generated. Viscosities and first normal stress differences measured at lower shear stresses suggest that the occurrence of noise generation during flow is affected, not only by pseudoplasticity and elasticity of the liquid, but also by its microstructure.     

Consistency tests for start-up and cessation deformations of viscoelastic fluids

The time-dependent shear stress and first normal stress difference were measured for a polystyrene solution for start-up and cessation-flow experiments over a relatively wide range of shear rate. Consistency tests for the K-BKZ model were applied to the data, and it was concluded that the K-BKZ equation generally does not satisfactorily describe the start-up and cessation data. Modified consistency tests were developed using a strain-coupling constitutive equation, and the evidence suggests that most of the differences between the predictions of the K-BKZ theory and experiment can be explained by including a strain-coupling effect in the rheological constitutive equation.     

Linear rheology of viscoelastic emulsions with interfacial tension

Emulsions of incompressible viscoelastic materials are considered, in which the addition of an interfacial agent causes the interfacial tension to depend on shear deformation and variation of area. The average complex shear modulus of the medium accounts for the mechanical interactions between inclusions by a self consistent treatment similar to the Lorentz sphere method in electricity. The resulting expression of the average modulus includes as special cases the Kerner formula for incompressible elastic materials and the Oldroyd expression of the complex viscosity of emulsions of Newtonian liquids in time-dependent flow.