On forced vibration of anisotropic cylinders

Summary The dynamic response of a circular cylinder with thick walls of transverse curvilinear isotropy subjected to a uniformly distributed pressure varying periodically with time is analyzed by means of the Laplace transformation, and the exact solution is obtained in closed form. The previously obtained solutions for forced vibrations with isotropy, and free vibrations with transverse curvilinear isotropy are included as special cases of the general results reported here.Nomenclature t time - r, , z cylindrical coordinates - _ii components of normal strain - _ii components of normal stress - u radial displacement - c _ij elastic constant - mass density - c ² c ₁₁/ - ² c ₂₂/c ₁₁ - a, b inner, outer radius of the cylinder - , A, B constants - forced angular frequency - function defined by (9) - p, real, complex variables - constant defined by (14) - real number - , Lamé elastic constants - J (x) Bessel function of first kind - Y (x) Bessel function of second kind - I (x) modified Bessel function of first kind - K (x) modified Bessel function of second kind     

Stability of the T ∞FT < T ∞α relation between Vogel temperatures of flow and glass transition against determination variants

Dynamic shear measurements in the frequency range from 10^–4 to 500 rad/s at the flow and main transition of a polydisperse poly(vinyl acetate) and a monodisperse polystyrene sample are presented. For both samples the Vogel temperature of the flow transition T _FT is smaller than the Vogel temperature of the main transition T , independent of the criteria used for data evaluation. The difference between the two Vogel temperatures corresponds to results for samples with other molecular weight and polydispersity from the literature. The T _FT <T relation is discussed in terms of short () and long (FT) dynamic glass transitions in entangled polymers. The relation is explained by preaveraging of the energy landscape for the long flow transition by the short glass transition.     

The relaxation of concentrated polymer solutions

The focus of this paper is on the viscoelastic properties of concentrated polymer solutions and polymer melts. Dynamic mechanical measurements were performed on various polystyrene/ethylbenzene solutions with polymer concentrations ranging from 40% up to 100% and temperatures from Tg+30°C up to 70°C (230°C for polymer melts). The basis polymers are two commerical grade polystyrenes (BASF) with M _W = 247 kg/mol and 374 kg/mol, respectively. To avoid solvent loss due to evaporating during the measurements, a special sealing technique was used.A phenomenological model which describes quantitatively the relaxation spectrum of concentrated polymer solutions from the flow regime up to the glass transition regime is developed. The relaxation data of the respective polymer melt and the glass transition temperature of the solution are the only input parameters needed. The temperature dependence is described by a universal, concentration invariant WLF-equation. The relaxation spectra are divided into two parts accounting for the entanglement and the segmental relaxation modes, respectively. The relaxation strength related to the flow and entanglement regime scale with c ^2.3, whereas the segmental relaxation strength does not alter with concentration. All relaxation times change with concentration proportional to c ^3.5. Flow curves can be calculated from these relaxation spectra and thus, our results are useful for engineering applications.Roman Symbols a _T Time temperature superposition shift - factor - a _c Time concentration superposition - shift factor in the flow regime - a _c Time concentration superposition - shift factor in the glassy regime - b _T Modulus temperature superposition - shift factor - b _c Modulus concentration shift factor - in the flow regime - b _c Modulus concentration shift factor - in the glassy regime - B Virial coefficients - c Polymer mass fraction kg/kg - c ₁ WLF-parameter - c2 WLF-parameter K - g Relaxation strength of a relaxation Pa mode - G(t) Relaxation modulus Pa - G Storage modulus Pa - G Loss modulus Pa - GN Plateau modulus of linear flexible Pa polymers - (x) Delta function: (0) = 1, - (x<>0)=0 - h() Damping function - H() Relaxation spectrum Pa - J ₀ ^N Recoverable compliance Pa^–1 - m Mass kg - M _c Critical molecular weight kg/mol - M _e Entanglement molecular weight kg/mol - M _w Weight average molecular weight kg/mol - M Number of datapoints - n Scaling exponent - N Number of discrete relaxation modes - T Temperature °C - T _g Glass transition temperature °C - V Volume 1 Greek Symbols Scaling exponent - _f Thermal expansion coefficient K^–1 - Scaling exponent - Shear deformation - Shear rate s^t–1 - Relaxation time s - _c Characteristic relaxation time of thes Cross model - _e Entanglement relaxation time s - Viscosity Pa s - ₀ Zero shear viscosity Pa s - ₀ First normal stress coefficientPa s2 - Segmental friction coefficient - Frequency rad/s Indices f Flow and entanglement regime - g Glass transition regime - i Count parameter - p Polymer - ref Reference state - s Solvent Dedicated to Prof. Dr. J. Meissner on the occasion of his retirement from the chair of Polymer Physics at the Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland     

On the viscosity-temperature behavior of polymer melts

Based on the free volume concept and the equation by Doolittle, an empirical equation is offered for the flow activation energy, E ^*, for polymer melts for the range of over 150°C above glass transition temperature, T _g. This E ^* represents the temperature coefficient of viscosity for the Newtonian region which is also equal to the value measured at constant shear stress for non-Newtonian flow. Data show that the E ^* of linear polymers approaches a constant value for a temperature range above T _g+150°C. Data on 17 polymers are correlated. The proposed equation for this region predicts the E ^* of polymer melts from the volume expansion coefficient, _l, above T _g and also from the T _g.Correlations have also been developed between E ^* and _l and between E ^* and T _g by simplifying the equation by use of the Simha-Boyer expression. A polymer having a lower _l or higher T _g generally has a higher E ^*. However, more satisfactory results are obtained by calculating E ^* from both _l and T _g. The E ^* calculated is found to agree with measurements within the experimental precision of about ±1 Kcal/mole.The effects of polymer composition, molecular weight, branching and microstructure on E ^* are also discussed. These factors influence E ^* in the way in which they effect _l and T _g.     

On the propagation of elastic waves through composite media

Summary With the aid of an ultrasonic pulse technique, the propagation of elastic waves (longitudinal as well as transverse) through polyurethane rubbers filled with different amounts of sodium chloride particles was studied. The velocity of both longitudinal and transverse waves was found to increase with filler content. From the measured wave velocities, the effective modulus for longitudinal waves,L, bulk modulus,K, and shear modulus,G, were calculated according to the relations for a homogeneous isotropic material. All three moduli appear to be monotonously increasing functions of the filler content over the whole experimentally accessible temperature range (–70 °C to + 70 °C forL andK;}-70 °C to about –20 °C forG) and they, moreover, reflect the glassrubber transition of the binder.Poisson's ratio,, was found to decrease with increasing filler content and show a rise at the high temperature side of the experimentally accessible temperature range (about –20 °C) as a result of the approach of the glass-rubber transition.In addition to the velocities, the attenuation of both longitudinal and transverse waves was measured in the temperature ranges mentioned. It was found that in the hard region tan _L as well as tan _G are independent of the filler content within the accuracy of the measurements. In the rubbery region, however, tan _L, increases with increasing filler content.Finally, the experimental data are compared with a simple macroscopic theory on the elastic properties of composite media.     

A note on the tan δ(T) peak as a glass transition indicator in biosolids

The plasticization of many biosolids can take place over a fairly broad temperature range. The resulting loss of stiffness is primarily expressed by a drastic drop of G(T) whose magnitude is usually higher than G(T) by one or two orders of magnitude. Both G(T) and G(T) have characteristic properties that can vary widely among biomaterials. Consequently, the tan (T) peak need not be a mark of the transition center and it can be observed at temperatures where different materials have undergone a very different degree of plasticization as judged by the magnitude of G(T). This is demonstrated by computer simulations using typical functions that describe G(T) and G(T) at the glass transition region and with published data on the dynamic mechanical behavior of a variety of biosolids.     

The relaxation time spectrum of nearly monodisperse polybutadiene melts

The relaxation behavior of polymers with long linear flexible chains of uniform length has been investigated by means of dynamic mechanical analysis. The relaxation time spectrum (H()) follows a scaling relationship with two self-similar regions, one for the entanglement and terminal zone, and a second one for the transition to the glass. This can be described in its most general form (termed BSW spectrum) as H() = H _e ^ne + H _g ^– n _g for < _max and H() = 0 for _max < , where H _e , H _g , n _e , n _g are material constants and _max is the molecular weight dependent cut-off of the self-similar behavior. In this study, the dynamic mechanical response has been measured and analyzed for four highly entangled, nearly monodisperse polybutadienes with molecular weights from 20000 to 200000. The data are well represented by the BSW spectrum with scaling exponents of n _e = 0.23 and n _g = 0.67. The values of the exponents obtained in this work are about the same as those found for polystyrene samples in a previous study. This suggests that the two types of polymers have a similar relaxation pattern. However, at this point further refinement of the experiments is needed before being able to draw definite conclusions about the universality of the exponents.Dedicated to Professor Arthur S. Lodge on the occasion of his 70th birthday and his retirement from the University of Wisconsin.     

About the influence of hexamethylene tetramine content on the dynamic-mechanical properties of the polymeric system: Phenolic novolac resin (PF) and nitrile rubber (NBR-29)

Summary On mixtures of phenolic novolac resin (PF) and nitrile rubber with 29% ACN-content (NBR-29) the effect of hexamethylene tetramine content was investigated by torsional pendulum measurements. The shear modulusG and the loss modulusG were registered within a temperature region from –180°C up to 200°C for different hexa-contents.The mechanical damping tests show, that with increasing hexa-content the glass transition range of the mixture is shifted to lower temperature, whereas the absorption maximum becomes smaller. This means, that the hexamethylene tetramine counteracts against the separation of the copolymer which is due to the not completely crosslinked resin and that with increasing hexa-content the mixtures become more compatible.

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Zusammenfassung Mit Hilfe des Torsionsschwingungsversuches wurde an Mischungen aus Phenolnovolakharz (PF) und Nitrilkautschuk mit 29% ACN-Gehalt (NBR-29) der Einfluß des Hexamethylentetramin-Gehalts auf den SpeichermodulG und den VerlustmodulG im Temperaturbereich von –180°C bis + 200°C in Abhängigkeit vom Hexa-Gehalt untersucht.Dabei zeigt sich, daß mit zunehmendem Hexa-Gehalt der Glasübergangsbereich der Mischung zu einer tieferen Temperaturlage hin verschoben wird, wobei der Glasübergangsbereich gleichzeitig schmaler wird. Dies bedeutet, daß das Hexamethylentetramin der Entmischung des Copolymerisats durch das nicht vollständig vernetzte Harz entgegenwirkt und mit wachsendem Hexa-Anteil die Mischung verträglicher wird.

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With 7 figures and 3 tables     

Choking of ideal-gas flow in convergent nozzles and integral nozzle characteristics

The results of a numerical and theoretical investigation of the local and integral characteristics of convergent nozzles are presented. It is shown that self-similar (choked) nozzle flow, when the gas flow rate does not depend on the external pressure, may occur at subcritical values of the pressure ratio _c . If the nozzle contour consists of the contour of the conical nozzle and the convergent part corresponds to the boundary of the emerging jet, then on a certain interval of _c this nozzle will have a higher thrust coefficient than the initial conical nozzle.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 149–157, November–December, 1994.     

Viscoelastic properties of semidilute poly(methyl methacrylate) solutions

Viscoelastic properties were examined for semidilute solutions of poly(methyl methacrylate) (PMMA) and polystyrene (PS) in chlorinated biphenyl. The number of entanglement per molecule, N, was evaluated from the plateau modulus, G _N . Two time constants, _s and ₁, respectively, characterizing the glass-to-rubber transition and terminal flow regions, were evaluated from the complex modulus and the relaxation modulus. A time constant _k supposedly characterizing the shrink of an extended chain, was evaluated from the relaxation modulus at finite strains. The ratios ₁/ _s and _k / _s were determined solely by N for each polymer species. The ratio ₁/ _s was proportional to N ^4.5 and N ^3.5 for PMMA and PS solutions, respectively. The ratio _k / _s was approximately proportional to N ^2.0 in accord with the prediction of the tube model theory, for either of the polymers. However, the values for PMMA were about four times as large as those for PS. The result is contrary to the expectation from the tube model theory that the viscoelasticity of a polymeric system, with given molecular weight and concentration, is determined if two material constants _s and G _N are known.     

Boundary layer effect on thermal NO decomposition behind incident shock waves

The thermal decomposition of nitric oxide (diluted in Argon) has been measured behind incident shock waves by means of IR diode laser absorption spectroscopy. In two independent runs the diode laser was tuned to the=0 =1² _3/2 R(18.5)-rotational vibrational transition and the=1 =2² _3/2 R(20.5)-rotational vibrational transition of nitric oxide, respectively. These two transitions originating from the vibrational ground state (=0) and the first excited vibrational state (=1) were selected in order to probe the homogeneity along the absorption path. The measured NO decomposition could satisfactorily be described by a chemical reaction mechanism after taking into account boundary layer corrections according to the theory of Mirels. The study forms a further proof of Mirels' theory including his prediction of the laminar-turbulent transition. It also shows, that the inhomogeneities from the boundary layer do not affect the IR linear absorption markedly.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

A method for measuring recompression shock unsteadiness applied to two supersonic wakes

The recompression shock system in blunt-base cylinder wakes at 0° and 10° angles-of-attack to an M=2.46 freestream is visualized by planar laser scattering, allowing the instantaneous position of the shock to be determined over a wide region of the flow. The recompression shock at =0° is highly branched and appears to be quite weak. The shock appears to be stronger at =10°, with far less branching. Correlation analysis for the =10° wake indicates that fluctuations in the shock position tend to be correlated over relatively long streamwise distances. Analysis of the shock angle for the angle-of-attack wake shows a significant variation in the local angle of the shock, with trends similar to those seen for the unsteadiness in the shock position.     

Time dependence of creep recovery in cross-linked polymers

Summary Transient creep recovery tests in simple tension were performed in a series of cross-linked high polymers in pure and plasticized states. A loading cycle was adopted according to which each specimen was loaded in creep for a time period of 16 followed by recovery for the same time period. This loading cycle was repeated for various steps of temperature from ambient temperature up to a temperature corresponding to the rubbery region of each polymer. It was shown that, while the 15 measurements of deformation after loading or unloading were approximately equal, recovery individual curves were always lagging in time the corresponding creep curves. Composite curves of creep or recovery deformation in semi-log time scale reduced to a temperature of 30 °C were plotted by applying the method of reduced variables. The creepdeformation composite curve was always advancing in time relatively to the respective recovery composite curve. This phenomenon was an accumulation of the partial difference of the corresponding individual curves.Time-shift factor versus temperature curves for creep and recovery were plotted and compared.It was established that the remaining deformation after 16 minutes of a 16 creep recovery normalized to the initial deformation at the beginning of recovery, if plotted versus temperature, presented the same shape of curves for all types of materials tested. The maxima of these curves were diminishing with addition of plasticizer according to a straight line.     

The elastic modulus of particulate composites using the concept of a mesophase

A theoretical model for the evaluation of the elastic modulus in particulate composites has been developed. The method takes into account the existence of a mesophase between main phases, which constitutes an important parameter influencing the behaviour of a composite material. This layer between the matrix and filler develops different physico-chemical properties from those of the constituent phases and variable ones along its thickness. The effect of the progressive variation of the elastic modulus of the mesophase on the modulus of the composite was estimated by applying various simple laws of variation. Convenient laws of variation were introduced, varying from a simple one, assuming a linear law, to a more refined one using a parabolic law. Experimental results with particulates, based on iron-filled epoxy composites, compared satisfactorily with other models. However, the model based on a parabolic law was superior to all others on physical grounds.List of symbols E elastic modulus - v Poisson's ratio - volume fraction - r radius - V volume - K bulk modulus - r thickness of mesophase - parameter which depends on the sudden changes of the heat capacity for the filled and unfilled polymer C _p ^f and C _p ⁰      

The development of acoustic generators and their application as a boundary layer transition control device

An experimental investigation of a controllable artificial boundary layer transition by means of electro-acoustic generators was carried out in flat-plate boundary layers. The acoustic generators were flush mounted with the model surface in order to minimize local surface roughnesses which may cause flow instabilities in the laminar boundary layer. The dependence of the input power, pulse ratio, and input frequency of the acoustic generators on the transition threshold values of the input power were determined with surface hot films. In addition, the functional application of the acoustic generators for a controllable artificial boundary layer transition was examined qualitatively by flow visualizations applying the liquid crystal technique.List of symbols A fluctuating component of the hot film anemometer output voltage - time mean hot film anemometer output voltage - ₀ time mean hot film anemometer output voltage at zero velocity - B spectral component of any measured quantity (the used dB-scale is referred to 1 Volt) - time mean hot wire anemometer output voltage - ₀ time mean hot wire anemometer output voltage at zero velocity - f frequency - I _av average input current of the acoustic generator - P mean input power of the acoustic generator - p pressure - Re Reynolds number, Re=U x t/ - t time - t _i period of pulse signal - t _p pulse width of input power - t _s time after switching off heating lamp - U freestream velocity - blowing or sucking velocity produced by the acoustic generator - x longitudinal coordinate from the leading edge (Fig. 2) - x _t distance from the flat plate to the transition location - y coordinate normal to the wall (Fig. 2) - z spanwise coordinate (Fig. 2) - angle of incidence - pulse ratio t _p /t _I - kinematic viscosity - density - ₀ wall shear stress     

The effect of rotation on conical wave beams in a stratified fluid

Experiments are conducted to test extant theory on the effect of uniform rotation on the angle of conical beam wave propagation excited by a sphere vertically oscillating at frequency in a density stratified fluid. The near-constant Brunt–Väisälä frequency stratification N produced in situ in a rotating cylindrical tank exhibits no effect of residual motion for the range of Froude numbers investigated. Good agreement between experiment and theory is found over the range of angles 15°<<65° using the synthetic schlieren visualization technique. In particular, the cut-off for wave propagation at =2, below which waves do not propagate, is clearly observed.     

Measurements of a blown zero-pressure gradient boundary layer

An experimental investigation is carried out to study the effect of a slot (t) jet injection onto the main stream parallel to a flate surface. Test runs covered a blowing ratio (M) of 1.5 to 4.2 for injection angle () of 30° and 60° to the downstream direction (x). Mean velocity (u) profiles are obtained forx/t up to 113 andy/t up to 40. Measurements are realized using a traversed fine double total head probe in a low speed wind tunnel.Results for of 30° showed that the velocity profiles have a localU _max andU _min. IncreasingM increases theU _min and eventually it disappeared from the profiles atM of 4.2 whileU _max is shifted continuously away from the surface. At this, the jet is suppressed by the main stream and is confined to the wall region which resulted in ₁ and ₂ being negative all over the surface. Changing to 60° created a separation double in the slot downstream. IncreasingM increases the bubble length while its height was abouty/t of 3. Downstream of the bubble, the jet slips under the main flow and creates a velocity peak in the wall vicinity along the test surface. For of 60°, the jet penetrates through the main stream and the flow reached the wall vicinity could not make up for the momentum deficiency in the boundary layer except at the far end of the test surface atM of 4.2.

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Messungen einer eingeblasenen Grenzschicht ohne Druckgradienten

Zusammenfassung Es wird eine experimentelle Untersuchung der Einflüsse einer Schlitzeinblasung in einen zu einer Fläche parallelen Hauptstrom durchgeführt. Die Versuche wurden mit einer Einblas-Rate (M) von 1,5 bis 4,2, einem Einblaswinkel () von 30 und 60° zur Richtung (x) stromabwärts gefahren. Hauptgeschwindigkeitsprofile (u) werden fürx/t Verhältnisse bis zu 113 undy/t Verhältnisse bis 40 erhalten. Die Messungen werden anhand einer empfindlichen Sonde in einem Windkanal durchgeführt.Ergebnisse für einen Winkel von 30° zeigen, daß die Geschwindigkeitsprofile ein lokales MaximumU _max und MinimumU _min aufweisen. Ein steigendesM läßtU _min steigen und eventuell beiM=4,2 verschwinden währendU _max sich kontinuierlich von der Oberfläche fortbewegt. Bei diesem wird der Strahl von dem Hauptstrom unterdrückt und ist auf die Wandnähe beschränkt was ein über die gesamte Oberfläche negatives ₁ und ₂ zur Folge hat. Bei Vergrößern des Winkels auf 60° erfolgt eine doppelte Separation stromabwärts. Ein Steigern vonM verursacht das Vergrößern der Blasenlänge während ihre Höhe beiy/t=3 liegt. Stromabwärts von der Blase gleitet der Strahl unter den Hauptstrom und erzeugt eine Geschwindigkeitsspitze in Wandnähe entlang der Testfläche. Für =60° dringt der Strahl in den Hauptstrom ein und die Strömung in Wandnähe kann den Impulsverlust in der Grenzschicht außer in weiter Entfernung der Testfläche, nicht wettmachen.

     

Rheology on the drawing zone in glass spinning

Summary Among investigations concerning the rheology of spinning materials from melt, or in other terms the problem of spinnability, glasses perform an example of fibre forming without crystallization along the spinning way and with surface tension playing an important role. Furthermore glasses show aNewtonian behaviour at least in the upper part of the drawing zone.As the absence of crystallization simplifies the formulation of the governing energy equation, on the other hand, the surface tension makes the applied motion equations quite complex to solve, above all in the two-dimensional analysis.The present paper shows that only a two-dimensional approach can give reliable results on the temperature, velocity and stress distribution in the drawing zone by a comparison of the theoretical and the experimental diameter profile of the forming fibre.The temperature profile has been obtained by a numerical solution of the energy equation, only after gaining experimentally the heat transfer coefficient. The results shown in the one-dimensional analysis cannot be applied in the opper part of the drawing zone.The velocity and stress distribution can be obtained by very complex numerical solutions in the very upper part of the drawing zone where the one-dimensional approach is shown unreliable. This can be thought an asymptotic solution of two-dimensional approach, reliable only after a certain distance of the spinning way from the exit of the nozzle.Furthermore, an analysis of the dimensionless numbers involved in the spinning phenomena brings up some information concerning the instability of the glass jet in comparison with that shown by materials as molten polymers or metals.As far as the rheological behaviour of glasses in the elongational shear rate is concerned, some conclusions can be drawn. F _r Froude numberU ₀ ² /gR₀ withg acceleration gravity (cm/sec²) - N _u Nusselt number 2Rh/Ka withh heat transfer coefficient (cal/cm² sec °C) andK _a air thermal conductivity (cal/cm sec °C) around the forming fibre - Q Volume rate of flow (cm³/sec) - r Radial distance from the central axis of the fibre (cm) - R Cross section radius of the fibre (cm) - R ₀ Inside diameter of the nozzle (cm) - t Quenching time (sec) - T _aT_s Temperature of fibre at the centre (°C) - T _i Initial temperature at the distancex = 0 (°C) - T ₀ Mean value of temperature of air surrounding the forming fibre (°C) - U ₀ Mean value of velocity of glass atx = 0 (cm/sec) - V Local velocity of fibre in the axial direction (cm/sec) - x Axial distance of the fibre from the nozzle exit (cm/sec) - W Weight rate of flow (g/minute) - W _e Weber numberU ₀ ² R₀/ - Glass surface tension (dynes/cm) - Angle between the fibre axis and the tangent to the fibre surface in ther, x plane (radiant). - v Air kinematic viscosity (cm²/sec) - Glass density (g/cm³) - Glass viscosity (poises) - _i Glass viscosity atT _i. - Maxwell relaxation time/G (sec) withG (dynes/cm²) elastic shear modulus of glass With 10 figures and 2 tables     

The creep behavior of ideally atactic and commercial polymethylmethacrylate

Summary The shear creep behavior of polymethylmethacrylate, PMMA, samples has been studied in the neighborhood of and above their glass temperatures. One of the materials studied was ideally atactic with equal numbers of random isotactic and syndiotactic placements, while the other was a commercial or conventional PMMA which was about 76% syndiotactic. The glass temperatures,T _g , were found to be 106 and 117 °C respectively. Evacuation above the glass temperature for several weeks was necessary before reproducible creep compliance,J (t), curves could be obtained. It is believed that absorbed water plasticized the polar materials and its removal led to the shifting of theJ (t) curves to longer times. For both materials apparently successful temperature reduction was found to be possible within the temperature range of our investigations, i.e. up to 200 °C. Retardation spectra were calculated from the reduced curves and are compared. The temperature dependences, as described by the time scale shift factors,a _T , were similar when allowance is made for the different glass temperature. Botha _T curves could not be fitted to theWilliams, Landel, andFerry, WLF, free volume expression. These are the first examples of such a deviation for amorphous high polymers. It is proposed that the primary softening dispersion has two distinctly different groups of viscoelastic mechanisms contributing to it. On this basis the primary dispersion was decomposed into the two contributions. Both of the resulting temperature dependences were satisfactorily fitted to the WLF equation. Differences in the retardation spectra are noted. The glassy compliance of the commercial PMMA appears to be about twice that of the atactic PMMA.Data on commercial PMMA is incorporated in a thesis which has been submitted in partial fulfillment of the requirements for the degree of Master of Science in Materials Engineering, University of Pittsburgh, 1970.With 12 figures and 1 table     

Application of dispersion theory to time domain reflectometry in soils

With time domain reflectometry (TDR) two dispersive parameters, the dielectric constant, , and the electrical conductivity, can be measured. Both parameters are nonlinear functions of the volume fractions in soil. Because the volume function of water ( _w) can change widely in the same soil, empirical equations have been derived to describe these relations. In this paper, a theoretical model is proposed based upon the theory of dispersive behaviour. This is compared with the empirical equations. The agreement between the empirical and theoretical aproaches was highly significant: the ( _w) relation of Topp et al. had a coefficient of determination r ² = 0.996 and the (_u) relation of Smith and Tice, for the unfrozen water content, _u, at temperatures below 0°C, had an r ² = 0.997. To obtain ( _w) relations, calibration measurements were performed on two soils: Caledon sand and Guelph silt loam. For both soils, an r ² = 0.983 was obtained between the theoretical model and the measured values. The correct relations are especially important at low water contents, where the interaction between water molecules and soil particles is strong.