Measurements of the complex shear modulus of polymers under hydrostatic pressure usina the quartz resonator method

Abstract

The quartz resonator method measures the complex shear modulus or compliance of viscoelastic materials in the frequency range from 50 kHz to 140 MHz at temperatures between ?150°C and 300°C and pressures up to 1 GPa. This method can be applied to viscous fluids or polymer melts -even in their glassy or seminystalline regime.

The phase diagram of poly(diethylsiloxane) PDES (a mesophase polymer) was determined for two samples with different molecular weight at pressures up to 400 MPa and temperatures between 20°C and 100°C. Phase transitions are indicated by a sharp bend in the shear compliance although the volume effect of the mesophase-isotropic transition vanishes around 80 MPa.

The pressure dependence of the glass relaxation process (in PVAc), was studied by measuring the change of the complex shear modulus with pressure at constant temperatures between 95°C and 145°C and pressures up to 600 MPa. Additionally to the relaxation process, also the pressure dependence of the real part of the shear modulus in the glassy region can be determined for testing the dislocation concept in the meandermodell by W. Pechhold.     

Rubber friction: Comparison of theory with experiment

We have measured the friction force acting on a rubber block slid on a concrete surface. We used both unfilled and filled (with carbon black) styrene butadiene (SB) rubber and have varied the temperature from −10 °C to 100 °C and the sliding velocity from 1 μm/s to 1000 μm/s. We find that the experimental data at different temperatures can be shifted into a smooth master-curve, using the temperature-frequency shifting factors obtained from measurements of the bulk viscoelastic modulus. The experimental data has been analyzed using a theory which takes into account the contributions to the friction from both the substrate asperity-induced viscoelastic deformations of the rubber, and from shearing the area of real contact. For filled SB rubber the frictional shear stress σ_f in the area of real contact results mainly from the energy dissipation at the opening crack on the exit side of the rubber-asperity contact regions. For unfilled rubber we instead attribute σ_f to shearing of a thin rubber smear film, which is deposited on the concrete surface during run in. We observe very different rubber wear processes for filled and unfilled SB rubber, which is consistent with the different frictional processes. Thus, the wear of filled SB rubber results in micrometer-sized rubber particles which accumulate as dry dust, which is easily removed by blowing air on the concrete surface. This wear process seams to occur at a steady rate. For unfilled rubber a smear film forms on the concrete surface, which cannot be removed even using a high-pressure air stream. In this case the wear rate appears to slow down after some run in time period.     

Study of the formation kinetics of Metastable phases in quenched Al-Mg-Si Alloys

The results of the experimental study of the formation kinetics of metastable phases during decomposition of supersaturated solid solutions of quenched Al-Mg-Si alloys are presented. The process has been studied by measuring the electrical conductivity at low temperatures (18–85°C) and by measuring the Young’s modulus using the acoustic method in the temperature range 120–220°C. The method of measuring the Young’s modulus is characterized by a high precision and has made it possible to distinguish between the successive stages of the decomposition due to the formation of Guinier-Preston zones, particles of the pre-β″/β″ and β′-phases. The effective activation energies have been calculated using the obtained data on the characteristic durations of the stages of the process at different temperatures. It has been shown that the activation energy of the formation and evolution of particles in the β″-phase is considerably lower than the activation energy of diffusion of alloying element atoms at equilibrium conditions, which is caused by the effect of long-lived quenching vacancies. This energy is close to the activation energy of migration of the ν + Mg complex and, according to the obtained results, is equal to 0.58 eV.     

Measurements of vocal fold tissue viscoelasticity: approaching the male phonatory frequency range

Viscoelastic shear properties of human vocal fold tissues have been reported previously. However, data have only been obtained at very low frequencies (< or = 15 Hz). This necessitates data extrapolation to the frequency range of phonation based on constitutive modeling and time-temperature superposition. This study attempted to obtain empirical measurements at higher frequencies with the use of a controlled strain torsional rheometer, with a design of directly controlling input strain that introduced significantly smaller system inertial errors compared to controlled stress rheometry. Linear viscoelastic shear properties of the vocal fold mucosa (cover) from 17 canine larynges were quantified at frequencies of up to 50 Hz. Consistent with previous data, results showed that the elastic shear modulus (G'), viscous shear modulus (G"), and damping ratio (zeta) of the vocal fold mucosa were relatively constant across 0.016-50 Hz, whereas the dynamic viscosity (eta') decreased monotonically with frequency. Constitutive characterization of the empirical data by a quasilinear viscoelastic model and a statistical network model demonstrated trends of viscoelastic behavior at higher frequencies generally following those observed at lower frequencies. These findings supported the use of controlled strain rheometry for future investigations of the viscoelasticity of vocal fold tissues and phonosurgical biomaterials at phonatory frequencies.     

Oscillations of polymeric microbubbles: effect of the encapsulating shell

A model for the oscillation of gas bubbles encapsulated in a thin shell has been developed. The model depends on viscous and elastic properties of the shell, described by thickness, shear modulus, and shear viscosity. This theory was used to describe an experimental ultrasound contrast agent from Nycomed, composed of air bubbles encapsulated in a polymer shell. Theoretical calculations were compared with measurements of acoustic attenuation at amplitudes where bubble oscillations are linear. A good fit between measured and calculated results was obtained. The results were used to estimate the viscoelastic properties of the shell material. The shell shear modulus was estimated to between 10.6 and 12.9 MPa, the shell viscosity was estimated to between 0.39 and 0.49 Pas. The shell thickness was 5% of the particle radius. These results imply that the particles are around 20 times more rigid than free air bubbles, and that the oscillations are heavily damped, corresponding to Q-values around 1. We conclude that the shell strongly alters the acoustic behavior of the bubbles: The stiffness and viscosity of the particles are mainly determined by the encapsulating shell, not by the air inside.     

Ocean surface films measured by interferential microwave probe

Summary Measurements on sea surface films were conducted during five separate experimental periods in the following marine areas: the Sicilian Channel, the Gulf of Maine (spring and fall periods), Bermuda, and the Pacific Ocean West of Southern California. The measurements consisted in surface elevation sampling using an interferential microwave probe with frequency spectra evaluation. Wave spectra were performed for both clean and film-covered sea surface conditions to determine the wave attenuation ratio within the 2–20 Hz spectral range. The method is able to detect, chart and characterize sea surface films. Theoretical analyses of the results yield several viscoelastic film parameters: the modulus of elasticity, the relaxation frequency and the maximum of the damping ratio as a function of wave frequency. The analysed data are interpreted to infer film weathering effects, surface concentration of film-forming constituents, and compactness of the organic sea surface film.     

The plastic properties of carbon tetrabromide

The shear strength of polycrystalline carbon tetrabromide was measured over the temperature range from 275–375°K which includes the well-known polymorphic transition near 320°K. A large discontinuity in strength was observed at the transformation. The results are compared with earlier measurements on carbon tetrachloride and other soft solids.     

Response of thin polymer layers confined between solid surfaces and submitted to normal oscillatory deformations

Summary The viscoelastic properties of liquids close to solid surfaces differ from the bulk. Nanorheology has been performed by using a surface force apparatus adapted to operate as a rheometer in a sphere-plane geometry. Axial oscillatory measurements have been carried out with high polymer solutions filling the gap. The deformations were kept sufficiently small not to perturb the film structure and were applied in a large range of frequency (10⁻³ to 10² s⁻¹). It is shown that the complex modulus characterizing the confined medium can be split into two components: a shear modulus (it accounts for the viscous dissipation due to the flow of solvent molecules through the mesh created by the long polymer chains which connect the two solid surfaces) and a compression modulus which is related to the normal stress response of the chains confined between the solid surfaces. The hydrodynamic screening lengthξ _h and the correlation length ξ deduced from the two moduli are compared and are found to scale in the same way as a function of the distance between the two surfaces. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Influence of bubbly clusters on the characteristics of the two-phase gas-liquid flow in a flat channel

Results of experimental investigation of a bubbly gas-liquid flow in horizontal and weakly inclined (from −20° to +20°) flat channel are presented. These measurements were carried out within the 0.2–1 m/s range of superficial velocities and volumetric gas flow rate ratio of up to 0.2. The hydrodynamic structure was measured by the electrochemical method with application of wall shear stress and conductivity microprobes. During the experiments signals of shear stress on the upper channel wall and local gas flow rate ratio were recorded completely. After numerical treatment of recorded signals the profiles of local gas flow rate ratio were obtained, average shear stress and its relative mean square pulsations on the upper channel wall were determined. It is shown that under the studied regimes the bubbles are grouped into clusters, and the bubbly flow is presented by alternation of bubbly clusters and single-phase liquid with separate bubbles and without them. Average wall shear stress and absolute shear stress pulsations in the range of bubbly clusters and beyond them were determined. Histograms of probability density distribution were obtained for the wall shear stress on the upper wall. It is shown that average shear stress and absolute pulsations in clusters are significantly higher than those in the flow zone free from bubbles. The work was financially supported by the Russian Foundation for Basic Research (No. 07-08-00405a).     

Broad bandwidth optical and mechanical rheometry of wormlike micelle solutions

We characterize the linear viscoelastic shear properties of an aqueous wormlike micellar solution using diffusing wave spectroscopy (DWS) based tracer microrheology as well as various mechanical techniques such as rotational rheometry, oscillatory squeeze flow, and torsional resonance oscillation covering the frequency range from 10(-1) to 10(6) rad/s. Since DWS as well as mechanical oscillatory squeeze flow and torsional resonance oscillation cover a sufficiently high frequency range, the persistence length of wormlike micelles could be determined directly from rheological measurements for the first time.     

Rheological Investigations of Copolymers of N-(Substituted Maleimide)s with Styrene in Dimethylsulfoxide

The viscoelastic behavior of poly(N-(4-formylphenoxy-4′-carbonylphenyl)maleimide-co-styrene) and poly(N-(4-carboxyphenyl)maleimide-co-styrene) in dimethylsulfoxide is investigated. The rheological parameters (elastic modulus, viscous modulus, loss tangent) were determined at different temperatures in the range 20°C–80°C. Poly(N-(4-carboxyphenyl)maleimide-co-styrene) exhibits a Newtonian behavior in the frequency range from 0.05 to 700 rad/s at all temperatures. For poly(N-(4-formylphenoxy-4′-carbonylphenyl)maleimide-co-styrene), a shear thinning behavior was observed at temperatures below 40°C (pseudoplastic behavior), whereas at higher temperatures the sample exhibits Newtonian flow throughout the studied frequencies range. The activation energies of the flow (calculated by using the zero shear viscosity values) give indications about the intensity of polymer-polymer interactions as a function of the maleimide monomer structure.     

Measurement of dynamic properties of viscoelastic materials

A new method for measurement of viscoelastic properties of materials, based on the exact solution of the problem of the forced oscillations of a flat sample loaded by inertial mass, is proposed. The device for these measurements is described. The elasticity modulus and loss tangent are measured within the frequency range from 100 Hz to 10 kHz at relative deformation of a sample below 1%. The approximate formulas for calculation of viscoelastic properties are derived, and the conditions of their applicability are determined. The methods for expansion of the frequency range and measurement of materials with extremely high loss tangent are proposed. The proposed method is compared with the current Standard. It is shown that the new method has the higher accuracy and expanded range of parameter measurements, and the construction of device is easy and reliable, since it does not require the knowledge on the oscillation properties of vibration source. The work was financially supported by the Russian Foundation for Basic Research (Grant No. 06-08-00193-a).     

An unique method of determining the excitation energy migration coefficient in organic liquid scintillators

An experimental method is described to determine the excitation energy migration coefficient Λ in an organic liquid scintillator by measuring the energy transfer rate parameterk ₃ and the quenching rate parameterk _7b as a function of temperature in the range of 20°C–70°C. In this experiment we have used toluene as donor, ethyl-1-n-butyl-2-methyl-5-hydroxyindole-3-carboxylate (EBMHC) as acceptor and bromobenzene as quencher. The values of Λ are found to be in good agreement with literature values. Hence this method can be used to determine the migration coefficient in organic liquid scintillators.     

Development of conductive transparent indium tin oxide (ITO) thin films deposited by direct current (DC) magnetron sputtering for photon-STM applications

Highly conductive and transparent indium tin oxide (ITO) thin films, each with a thickness of 100 nm, were deposited on glass and Si(100) by direct current (DC) magnetron sputtering under an argon (Ar) atmosphere using an ITO target composed of 95% indium oxide and 5% tin oxide for photon-STM use. X-ray diffraction, STM observations, resistivity and transmission measurements were carried out to study the formation of the films at substrate temperatures between 40 and 400 °C and the effects of thermal annealing in air between 200 and 400 °C for between1 and 5 h. The film properties were highly dependent on deposition conditions and on post-deposition film treatment. The films deposited under an Ar atmosphere pressure of ∼1.7×10^-3 Torr by DC power sputtering (100 W) at substrate temperatures between 40 and 400 °C exhibited resistivities in the range 3.0–5.7×10^-5 Ω m and transmissions in the range 71–79%. After deposition and annealing in air at 300 °C for 1 h, the films showed resistivities in the range 2.9–4.0×10^-5 Ω m and transmissions in the range 78–81%. Resistivity and transmission measurements showed that in order to improve conductive and transparent properties, 2 h annealing in air at 300 °C was necessary. X-ray diffraction data supported the experimental measurements of resistivity and transmission on the studies of annealing time. The surface roughness and film uniformity improve with increasing substrate temperature. STM observations found the ITO films deposited at a substrate temperature of 325 °C, and up to 400 °C, had domains with crystalline structures. After deposition and annealing in air at 300 °C for 1 h the films still exhibited similar domains. However, after deposition at substrate temperatures from 40 °C to 300 °C, and annealing in air at 300 °C for 1 h, the films were shown to be amorphous. More importantly, the STM studies found that the ITO film surfaces were most likely to break after deposition at a substrate temperature of 325 °C and annealing in air at 300 °C for 2 or 3 h. Such findings give some inspiration to us in interpreting the effects of annealing on the improvement of conductive and transparent properties and on the transition of phases. In addition, correlations between the conductive/transparent properties and the phase transition, the annealing time and the phase transition, and the conductive/transparent properties and the annealing time have been investigated. Received: 10 July 2000 / Accepted: 27 October 2000 / Published online: 9 February 2001     

Ultrasonic interferometry for the measurement of shear velocity and attenuation in viscoelastic solids

A method for the measurement of the shear properties of solid viscoelastic materials is presented. The viscoelastic material is cut into a cylindrical sample which is clamped between two rods. The transmission and reflection coefficient spectra of the fundamental torsional mode through the sample are measured by means of two pairs of piezoelectric transducers placed at the free ends of the rod-sample-rod system. Such spectra exhibit maxima and minima which occur approximately at the resonance frequencies of the free viscoelastic cylinder. Therefore, the shear velocity can be obtained by measuring the frequency interval between two consecutive maxima or minima. The shear attenuation is derived by best fitting the analytical expression of the reflection and transmission coefficients to the experimental spectra. The test is very quick to set up as the sample is simply clamped between the two rods.     

Extraction of cross-sections of inelastic scattering from energy spectra of reflected atomic particles

REELS spectra of the electrons reflected off niobium are measured with energy resolution <0.5 eV within the 5–40 eV energy range of the probing beam. The measurements were performed for the scattering angles θ = 45° and θ = 120° by means of two electron guns. The process of energy losses is described within the framework of a model with three different energy loss laws: surface, intermediate, and bulk layers are considered. Differential cross-sections of inelastic scattering are represented in the form of simple equations.     

The structural, elastic and thermodynamic properties of intermetallic compound CeGa2

The structural, elastic and thermodynamic characteristics of CeGa₂ compound in the AlB₂ (space group: P6/mmm) and the omega trigonal (space group: P-3m1) type structures are investigated using the methods of density functional theory within the generalized gradient approximation (GGA). The thermodynamic properties of the considered structures are obtained through the quasi-harmonic Debye model. The results on the basic physical parameters, such as the lattice constant, the bulk modulus, the pressure derivative of bulk modulus, the phase-transition pressure (P _t ) from P6/mmm to P-3m1 structure, the second-order elastic constants, Zener anisotropy factor, Poisson’s ratio, Young’s modulus, and the isotropic shear modulus are presented. In order to gain further information, the pressure and temperature-dependent behavior of the volume, the bulk modulus, the thermal expansion coefficient, the heat capacity, the entropy, Debye temperature and Grüneisen parameter are also evaluated over a pressure range of 0–6 GPa and a wide temperature range of 0–1800 K. The obtained results are in agreement with the available experimental and the other theoretical values.     

Viscoelastic properties of tri(O.tolyl) phosphate from light scattering and ultrasonic techniques

From our light scattering and the literature ultrasonic experiments, the shear and longitudinal moduli of the tri(O-tolyl)phosphate are calculated in a temperature range of nearly 70°C above Tg. From ?2°C to + 10°C the retardational compliance J_R/J∞ is found to be equal to 8.0 ± 0.1 and the retardational time C_R calculated. The relaxational modulus is obtained from ?55 to +10°C.     

Radiation impedance of a finite circular piston on a viscoelastic half-space with application to medical diagnosis

In a recent study a new analytical solution was developed and validated experimentally for the problem of surface wave generation on a linear viscoelastic half-space by a rigid circular disk located on the surface and oscillating normal to it. The results of that study suggested that, for the low audible frequency range, some previously reported values of shear viscosity for soft biological tissues may be inaccurate. Those values were determined by matching radiation impedance measurements with theoretical calculations reported previously. In the current study, the sensitivity to shear viscoelastic material constants of theoretical solutions for radiation impedance and surface wave motion are compared. Theoretical solutions are also compared to experimental measurements and numerical results from finite-element analysis. It is found that, while prior theoretical solutions for radiation impedance are accurate, use of such measurements to estimate shear viscoelastic constants is not as precise as the use of surface wave measurements.     

Mechanical relaxation of single crystal mats of polyethylene in a crystalline dispersion region

Stress-relaxation measurements have been conducted over the temperature range 15°–105°C on mats of single crystals of two linear polyethylene fractions. The single crystals were grown isothermally at several different temperatures. The relaxation modulus was observed to be strain dependent, indicating that the single crystal mats exhibited nonlinearity.

In spite of this appearance of nonlinearity, it was found possible, when the relaxation modulus was extrapolated to zero strain by an appropriate method, to obtain correct relaxation spectra for the mats of single crystals prepared by isothermal crystallization. This spectrum was then used to calculate the dynamic viscoelastic functions and, for the unannealed sample crystallized at 80°C, good agreement was found between experimental results and calculated ones. Two annealed samples showed multiple absorptions and, under these circumstances, strict application of the method of reduced variables for time and temperature was impractical.

The effect of molecular weight on the intensity of the relaxation spectrum was investigated. It was found that the single crystal with the higher molecular weight showed an increased spectrum intensity.

Observations were also made of the effect of increased lamellar thickness on both the relaxation spectra and the dynamic complex moduli and the results obtained on the fractions studied were compared with prior studies in whole polymer.