Acoustic properties of Kel F-800 copolymer up to 85 GPa

Acoustic properties of the fluorinated copolymer Kel F-800 were determined with Brillouin spectroscopy up to pressures of 85 GPa at 300 K. This research addresses outstanding issues in high-pressure polymer behavior, as to date the acoustic properties and equation of state of any polymer have not been determined above 20 GPa. We observed both longitudinal and transverse modes in all pressure domains, allowing us to calculate the C(11) and C(12) moduli, bulk, shear, and Young's moduli, and the density of Kel F-800 as a function of pressure. We found the behavior of the polymer with respect to all parameters to change drastically with pressure. As a result, we find that the data are best understood when split into two pressure regimes. At low pressures (less than ～5 GPa), analysis of the room temperature isotherm with a semi-empirical equation of state yielded a zero-pressure bulk modulus K(o) and its derivative K(0) (') of 12.8 ± 0.8 GPa and 9.6 ± 0.7, respectively. The same analysis for the higher pressure data yielded values for K(o) and K(0) (') of 34.9 ± 1.7 GPa and 5.1 ± 0.1, respectively. We discuss this significant difference in behavior with reference to the concept of effective free volume collapse.     

Ultraviolet and visible Brillouin scattering study of viscous relaxation in 3-methylpentane down to the glass transition

Brillouin light scattering spectra from transverse and longitudinal acoustic waves in liquid and supercooled 3-methylpentane have been collected from room temperature down to 80 K, just above the glass transition. Spectra at different wave vectors have been obtained using 532 nm and 266 nm excitation. We found evidence of a shear relaxation with a characteristic time of 100 s at the glass transition which only partly accounts for the relaxation observed in the propagation and attenuation of the longitudinal modes. The inclusion of a relaxing bulk viscosity contribution with a relaxation time of the order of 10(2) ns at the glass transition is found to adequately reproduce the experimental data including transient grating data at a much lower frequency. A consistent picture of relaxed shear and bulk moduli as a function of temperature is derived. These two quantities are found to be related by a linear relation suggesting that a Cauchy-like relation holds also above the glass transition.     

Brillouin scattering of H2O ice to megabar pressures

The sound velocity in polycrystalline ice was measured as a function of pressure at room temperature to 100 GPa, through the phase field of ice VII and crossing the ice X transition, by Brillouin scattering in order to examine the elasticity, compression mechanism, and structural transitions in this pressure range. In particular, we focused on previously proposed phase transitions below 60 GPa. Throughout this pressure range, we find no evidence for anomalous changes in compressibility, and the sound velocities and elastic moduli do not exhibit measurable discontinuous shifts with pressure. Subtle changes in the pressure dependence of the bulk modulus at intermediate pressures can be attributed to high shear stresses at these compressions. The C(11) and C(12) moduli are consistent with previously reported results to 40 GPa and increase monotonically at higher pressures.     

The effect of intramolecular relaxations on the damping of longitudinal and transverse phonons in polysiloxanes studied by Brillouin spectroscopy

The effect of intramolecular relaxations on the damping of longitudinal and transverse phonons was studied in poly(methylphenylsiloxane) (PMPS) and poly(ethylmethylsiloxane) (PEMS) polymers by means of Brillouin spectroscopy. It is shown that studies of the polarized and depolarized Brillouin spectra as functions of temperature and pressure allow for the separation of the contributions of the internal and structural relaxations to the damping of longitudinal and transverse phonons, respectively. In polymers with intramolecular relaxations these processes contribute not only to the damping of longitudinal phonons, according to theoretical predictions, but also transverse phonons, in contradiction to the theory.     

Mechanical strength of amorphous CaCO3 colloidal spheres

Amorphous glassy CaCO3 colloidal spheres of monomodal size distribution were studied by high-resolution Brillouin light scattering. The Young modulus of 37 GPa and shear modulus of 14 GPa of glassy CaCO3 at a density of 1.9 g/cm3 were extracted from the particle vibration frequencies by employing acoustic wave scattering cross-section calculations. The line shape of the low-frequency modes is a sensitive index of the particle polydispersity.     

A study of the acoustic mode structure of oriented poly(ethylene)

The low-frequency acoustic vibrational modes of solid poly(ethylene) (PE) oriented by stretching and hydrostatic extrusion are studied with Brillouin spectroscopy. The experimental results evidence a damping of the longitudinal acoustic mode propagating in the direction parallel to the orientation axis of the samples. The results are discussed in terms of the theoretically derived acoustic dispersion relations for the PE crystal.     

Equation of state of water under negative pressure

We report on the simultaneous measurements of the speed of sound and the density in liquid water under negative pressure. Application of a focused acoustic wave to the bulk liquid is able to generate negative pressures before nucleation of the vapor phase occurs. A method for time-resolved Brillouin scattering is developed to measure the speed of sound during the passage of a 1 MHz ultrasonic wave. This is coupled with a fiber optic probe hydrophone which allows the determination of the density. Together, these methods give an ambient temperature equation of state of metastable liquid water down to the acoustic cavitation threshold. Empirical equations of state of water are based on experimental data at positive pressure; the validity of their extrapolation to negative pressures had been tested only indirectly or with very weakly metastable liquid. We provide thermodynamic data that prove the fidelity of recent equations of state down to -26 MPa. However, this raises questions regarding the nature of the cavitation threshold observed in acoustic experiments, which is far less negative than expected.     

Elastic excitations in polycarbonate membranes

Brillouin light scattering was used to probe acoustic waves propagating with both longitudinal and transverse polarizations in the surface and the bulk of self‐supported particle track‐etched polycarbonate membranes with 15‐ and 80‐nm nanopores. The recorded scattering line shape at gigahertz frequencies reveals changes in the surface waves of the membranes which are more pronounced for the 80‐nm nanopores despite the low porosity (0.7 and 0.05%). Because the measured elastic constants (1.2 and 6.2 GPa) were found to compare very well with the values for thick polycarbonate film, modifications of the elasto‐optical coefficients and/or the transparency might be the reason for the different scattering line shapes. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3311–3317, 2004     

Swelling of physically cross-linked copolymers in water vapour

A general thermodynamic equation for the swelling of a cross-linked polymer system in the vapour of a swelling agent has been derived under isothermal and isobaric conditions. The equation is used to describe the equilibrium uptake of water by elastomers Arnitel^® (DSM), which are hard-soft-segment block copolymers in which the hard segments poly(butylene terephthalate) crystallise and are responsible for a physical cross-linking. The gravimetrically determined degrees of swelling of different elastomers in water vapour of various partial pressures are analysed and discussed by the application of an extended semi-empirical swelling equation of Flory-Huggins-Staverman-van Santen.     

Hydrogel characteristics of electron-beam-immobilized poly(vinylpyrrolidone) films on poly(ethylene terephthalate) supports

A novel strategy for the preparation of thin hydrogel coatings on top of polymer bulk materials was elaborated for the example of poly(ethylene terephthalate) (PET) surfaces layered with poly(vinylpyrrolidone) (PVP). PVP layers were deposited on PET foils or SiO2 surfaces (silicon wafer or glass coverslips) precoated with PET and subsequently cross-linked by electron beam treatment. The obtained films were characterized by ellipsometry, X-ray photoelectron spectroscopy, infrared spectroscopy in attenuated total reflection, atomic force microscopy (AFM), and electrokinetic measurements. Ellipsometric experiments and AFM force-distance measurements showed that the cross-linked layers swell in aqueous solutions by a factor of about 7. Electrokinetic experiments indicated a strong hydrodynamic shielding of the charge of the underlying PET layer by the hydrogel coatings and further proved that the swollen films were stable against shear stress and variation of pH. In conclusion, electron beam cross-linking ofpreadsorbed hydrophilic polymers permits a durable fixation of swellable polymer networks on polymer supports which can be adapted to materials in a wide variety of shapes.     

A novel method for static equation-of state-development: equation of state of a cross-linked poly(dimethylsiloxane) (PDMS) network to 10 GPa

Pressure-volume-temperature (PVT) equation-of-state (EOS) information for polymers and polymeric composites is valuable for predicting their response to extreme conditions. An obstacle in determining equations of state for polymeric materials is the lack of a simple, static experimental method for acquiring PVT data for solid networks and liquids at pressures greater than several kilobars. Here, we report a novel approach in determining static EOS for polymers using high-pressure diamond-anvil cells coupled with optical microscopy and image analysis. Results are presented for a cross-linked poly(dimethylsiloxane) polymer, Sylgard 184. Static isothermal results were fitted to empirical and semiempirical equations of state, including the Tait, Birch-Murnaghan, and Vinet forms. Static PV data were also converted to pseudoshock velocity-pseudoparticle velocity (U(s)-u(p)) for comparison to dynamic Hugoniot data. A linear Rankine-Hugoniot fit U(s)=s(T)u(p)+c(T) gives c(T)=1.572 km/s and s(T)=1.703. s(T) is related to the pressure derivative of the bulk modulus B(0) (') by s(T)=(B(0) (')+1)/4 and B(0) (')=5.8. A comparison of the static and shock data is given, along with an estimate of the Grüneisen parameter, and a discussion of the free volume content in the polymer network, and limitations of this novel method.     

Heat capacity, Raman, and Brillouin scattering studies of M2O-MgO-WO3-P2O5 glasses (M=K,Rb)

The authors report the results of temperature-dependent Brillouin scattering from both transverse and longitudinal acoustic waves, heat capacity studies as well as room temperature Raman scattering studies on M2O-MgO-WO3-P2O5 glasses (M=K,Rb). These results were used to obtain information about structure and various properties of the studied glasses such as fragility, elastic moduli, ratio of photoelastic constants, and elastic anharmonicity. They have found that both glasses have similar properties but replacement of K+ ions by Rb+ ions in the glass network leads to decrease of elastic parameters and P44 photoelastic constant due to increase of fragility. Based on Brillouin spectroscopy they show that a linear correlation between longitudinal and shear elastic moduli holds over a large temperature range. This result supports the literature data that the Cauchy-type relation represents a general rule for amorphous solids. An analysis of the Boson peak revealed that the form of the frequency distribution of the excess density of states is in agreement with the Euclidean random matrix theory. The reason of the observed shift of the maximum frequency of the Boson peak when K+ ions are substituted for Rb+ ions is also briefly discussed.     

Effect of pressure on thermal conductivity and pressure collapse of ice in a polymer-hydrogel and kinetic unfreezing at 1 GPa

We report a study of aqueous solutions of poly(vinylalcohol) and its hydrogel by thermal conductivity, κ, and specific heat measurements. In particular, we investigate (i) the changes in the solution and the hydrogel at 0.1 MPa observed in the 350-90 K range and of the frozen hydrogel at 130 K observed in the range from 0.1 MPa to 1.3 GPa, and (ii) the nature of the pressure collapse of ice in the frozen hydrogel and kinetic unfreezing on heating of its high density water at 1 GPa. The water component of the polymer solution on cooling either first phase separates and then freezes to hexagonal ice or freezes without phase separation and the dispersed polymer chains freeze-concentrate in nanoscopic and microscopic regions of the grain boundaries and grain junctions of the ice crystals in the frozen state of water in the hydrogel. The change in κ with temperature at 1 bar is reversible with some hysteresis, but not reversible with pressure after compression to 0.8 GPa at 130 K. At high pressures the crystallized state collapses showing features of κ and specific heat characteristic of formation of high density amorphous solid water. The pressure of structural collapse is 0.08 GPa higher than that of ice at 130 K. The slowly formed collapsed state shows kinetic unfreezing or glass-liquid transition temperature at 140 K for a time scale of 1 s. Comparison with the change in the properties observed for ice shows that κ decreases when the polymer is added.     

The elastic constants and related properties of beta-HMX determined by Brillouin scattering

By scattering from a variety of acoustic phonons, a complete stiffness tensor has been determined for crystalline beta-HMX. The results are compared with recent experimental and theoretical determinations of the elastic constants and bulk modulus. Reasons for disagreement are discussed in terms of experimental limitations and anharmonic effects. The observed ordering of stiffness constants, C(11) (18.4 GPa), C(22) (14.4 GPa), and C(33) (12.4 GPa), is qualitatively associated with physical phenomena including cleavage planes, patterns in crystal growth, and molecular packing. This interpretation is further corroborated by the linear compressibilities plotted in three crystallographic planes. The Voigt-Reuss-Hill bulk and shear moduli were found to be 9.9 and 3.7 GPa, respectively. The elasticity of beta-HMX is also discussed in relation to proposed mechanisms for the initiation of detonation.     

Contribution of surface rayleigh waves to the heat capacity of poly(vinyl chloride)

The method of surface acoustic waves is employed to determine the frequency and temperature dependences of the molar heat capacity of poly(vinyl chloride) on the contribution of Rayleigh local components of the longitudinal and transverse vibrations of structural units of the polymer. The calculated and experimental data are compared in terms of their dependence on the relaxation state of the system.     

Structural, electronic, bonding, and elastic properties of NH3BH3: a density functional study

The structural, electronic, bonding, and elastic properties of the low-temperature orthorhombic phase of NH(3)BH(3) are studied by means of first-principles total energy calculations based on the pseudopotential method. The calculated structural parameters of NH(3)BH(3) are found to be in good agreement with the experimental values. From the band structure calculations, the compound is found to be an indirect bandgap insulator with the bandgap of 5.65 eV (5.90 eV) with LDA(GGA) along the Γ-Z direction. The Mulliken bond population and the charge density distributions are used to analyze the chemical bonding in NH(3)BH(3) . The study reveals that B-H bonds are more covalent than N-H bonds. The elastic constants are predicted for ambient as well as pressures up to 6 GPa, from which theoretical values of all the related mechanical properties such as bulk modulus, shear modulus, Young's modulus, Poisson's ratio, and anisotropy factors are calculated. It is found that NH(3)BH(3) is mechanically stable at ambient and also external pressures up to 6 GPa. As pressure increases all the calculated elastic moduli of NH(3)BH(3) increase, indicating that the compound becomes more stiffer and hard under pressure. From the ratio of shear modulus to bulk modulus (G/B), we conclude NH(3)BH(3) to be ductile in nature, and the ductility increases with pressure. The present results confirm the experimentally observed less plastic nature of the low-temperature phase of NH(3)BH(3) .     

Surface Dynamic Elasticity of Poly(ethylene oxide) Monolayers on a Water Surface

The methods of transverse and longitudinal surface waves and of oscillating barrier were used to measure a surface dynamic elasticity of poly(ethylene oxide) films spread on aqueous substrate within the frequency range of 0.001–520 Hz. Unlike the adsorption films, the main relaxation processes in the spread poly(ethylene oxide) films are observed at higher frequencies. A comparison of static and dynamic values of the surface elasticity shows that the surface film at surface polymer concentrations higher than 0.4 mg/m² cannot be considered already as purely two-dimensional film. It was found that the surface tension (surface pressure) can be insufficiently sensitive to conformational transformations in the surface polymer films.     

Lattice dynamics of InAs under hydrostatic pressures

The lattice dynamics of InAs under variable hydrostatic pressures is investigated on the basis of an ‘11-parameter’ rigid-ion model (RIM). The calculated phonon dispersion curves are in satisfactory agreement with the neutron scattering data (available for the TA modes only) measured at room temperature and atmospheric pressure. The one- and two-phonon densities of states functions and mode Gruneisen parameters have been computed at two arbitrary hydrostatic pressures. The effect of high pressure on the phonon dispersion curves is shown to lead to a typical ‘softening’ in the transverse acoustic modes and eventually to a phase trnasformation of the compound.     

Flow characteristics of poly(ethylene terephthalate) deduced from pressure drop measurements

A unique capillary die was designed which made possible the measurement of extrusion pressure at various locations along the capillary length. Entrance pressure drops, exit pressures, and other rheological characteristics were determined for the flow of poly(ethylene terephthalate) through this extrusion apparatus. The effect of die entrance angle, extrusion temperature, throughput rate and polymer molecular weight were considered. Two samples differing in molecular weight exhibited power-law behavior at shear rates below 1000s^?1. The entrance pressure drops and exit pressures were observed to increase with increasing molecular weight; furthermore, at a specific temperature, both-increased with increasing shear rate. The values for entrance pressure drop obtained using Bagley analysis were consistently higher than those obtained from direct measurements.