Logarithmic Frequency Research Articles

Fine structure of the glass transition in amorphous polymers. Part 1. Interpretation of shear curves with the aid of the fluctuation dissipation theorem

AbstractThe phenomenological interpretation of shear curves is refined by application of the fluctuation dissipation theorem and the WIENER‐KHINTCHIN theorem. The loss peaks of shear modulus and compliance near the glass transition of amorphous polymers can be attributed to two different molecular motions. An interpretation of the two peaks by one kind of molecular motion (uniform model) would imply that its flanks two logarithmic frequency decads away from the center were significantly more intensive than other molecular motions at these frequencies.

Transient electrical response of K 0.30MoO 3: Effects of isoelectronic dopants

In this paper, we examine the variation of threshold fields and the transient response of tungsten- and rubidium- substituted K 0.30MoO 3. We find that the dc threshold electric field for the onset of nonlinear behavior scales linearly with tungsten concentration, but varies as the square of the rubidium concentration, indicating strong and weak pinning effects, respectively. In tungsten- substituted samples, the threshold field becomes a strong function of frequency in the range 0.01– 1000 Hz. Above a critical frequency which depends on the doping level, the threshold field is proportional to -log (frequency). We interpret these results as a further example of the spin glass- like response of the CDW. Nonlinear conductivity is observed only after the voltage has exceeded the threshold for a finite time interval.

Interrelations between relaxation distribution functions and apparent activation energy of flow

Starting from both the three-dimensional diagram of viscoelastic properties in the reciprocal temperature — log frequency — space and the time-temperature interrelation via apparent activation energy of flow, the possibility of theoretical interpretation of the isochronal behaviour is demonstrated, in analogy to the isothermal one. The determinative apparent activation energy of local flow is related with the relaxation spectra over the entire range of validity of the time-temperature superposition principle. Thus a theoretical background is offered for the method recommended before for the evaluation of the apparent activation energy of flow, which is applicable to calculate both isotherm and isochrone shift factors.

Morphological and Viscoelastic Properties of Ultradrawn Polyethylene with Such a High Young's Modulus as Super-Strength-Steel

Solution viscosity measurements have been used to define the optimum concentration for the ultradrawn films of high molecular weight polyethylene produced by gelation/crystallization from solution. For a molecular weight of 4×106 the optimum concentration was 0.5g/100ml. Dry gel films prepared from the solution of this concentration could be elongated at 135°C to a remarkably high draw ratio λ=300. The Young's modulus and the tensile strength, 202 and 6.2 GPa respectively, of the drawn film are among the highest reported for polyethylene ; the observed Young's modulus is consistent with the modulus of polyethylene in the chain axis direction. The origin of the high drawability was discussed in terms of the morphology of the dry gel film as studied by wide-angle X-ray diffraction, small angle X-ray scattering, and scanning electron microscopy. The facile drawability is interpreted as due to the transformation from a folded to a fibrous crystal. A suitable number of entanglements in the chains connecting crystal lamellas is necessary to induce the transformation.Temperature-dependence of complex dynamic modulus functions was measured in the range of frequency from 0.1 to 100 Hz in order to study crystal dispersions of polyethylene. At temperatures lower than 70°C, master curves of loss modulus are obtained through only horizontal shift of the modulus function along the logarithmic frequency axis. By contrast, the temperature-frequency superposition above 70°C requires the vertical shift as well as the horizontal shift of the function. The Arrhenius plots indicate that there exist two mechanical dispersions, one at higher and the other at lower temperature sides of the reference temperature of 70°C. The activation energies of these dispersions range from 98.3 to 104.2 kJ/mol (from 23.5 to 24.9 kcal/mol) and from 78.2 to 80.8 kJ/mol (from 18.7 to 19.3 kcal/mol), respectively. These results indicate that the dispersions belong to α1 and α2 mechanisms, respectively, which have been reported by a number of authors.

Programmable digital sine-wave generator

0where ~0 is the initial phase and T is the integration parameter. The main problem of PSG design is control of the instantaneous signal frequency f(t) over a wide range. Analog generators that realize frequency modulation (sweep) use a mechanical sweep drive, whilemore modern generators use electronic sweep. In these generators, the accuracy of reproduction of f(t) is low, due to nonlinearity of the characteristics of the controlling and controlled elements. For example, in the 1047 instrument (Brul and Kier, Denmark), the sweep rate is set electronically with an error of 3-5% for a linear and i020% for a logarithmic frequency variation. This is a common shortcoming of analog devices. The use of modern digital techniques [i] allows automatic control of the signal frequency. Other prohlems arise here, however, that are characteristic of digital devices, the most important of which is selection of a method of solving problem (2) in real time. We shall examine the principal methods for designing digital measuring generators of modulated signals of the form of (i), describe a PSG based on KRI804VSi LSI microprocessors, and present its technical specifications. We shall use the proposed approach to design programmable digital generators of signals of any form (which is determined by a function generator) with any (with known limitations) given laws of frequency f(t) and amplitude U(t) modulation. In digital devices, integration is performed by one of the numerical methods. In the

Dielectric and dynamic mechanical measurements of poly(4‐methyl pentene‐1)

AbstractThe α‐relaxation process of poly(4‐methyl pentene‐1) was studied by dielectric and dynamic mechanical means. The complex dielectric constant was determined at nine discrete frequencies from 100 to 10,000 Hz and over a temperature range of −50–90°C. The complex dynamic mechanical Young's modulus was determined over the audiofrequency range of 10–22,000 Hz and a temperature range of 21–76°C, from which a master curve was constructed. The relaxation process was studied by comparing the activation energies and width of the dispersion curves. The results of a logarithmic frequency vs. reciprocal temperature plot of the loss peak maxima show that both the dielectric and mechanical curves are roughly linear but have different slopes. From the slopes the activation energies were determined. For the dielectric data an activation energy of 39 kcal/mol was obtained, whereas for the mechanical data a value of 106 kcal/mol was found. The width of the dispersion curves was determined by using a Cole–Cole empirical fit. The width of the dielectric dispersion curve is narrower by as much as a factor of 3 than the mechanical dispersion curve. It is concluded that the energy to cause the large scale molecular motion involved in the α‐relaxation is lower when excited by an alternating electric field than by an alternating stress field. Also the number of repeat units involved is smaller in the dielectric case than in the mechanical case.

Continuous measurement of dynamic tensile mechanical properties in polymer solids over a wide range of frequencies. III. Effect of absorbed water on nylon 6 at 23°c

AbstractThe dynamic tensile mechanical properties (E′, E″, and tanδ) of nylon 6 have been studied over the frequency range 10−25−102 Hz and water content up to 12.6 wt % at a constant temperature of 23°C. From the dispersion maps in the coordinates of frequency and water content, the relaxation behavior can be classified into three regions of water content: (A) dry to 2 wt %, (B) 2‐5 wt % and (C) 5 wt % to wet. For region B, it is found that the logarithmic frequency shift Δ logfα/Δx of the α dispersion per 1 wt % change of water content is 1.7. Taking into consideration that the change of glass transition temperature per 1 wt % change of water content Δ Tg/Δx is 3.7°C (according to Kettle), we find Δ logfα/ΔTg = 0.5. For regions A and C, such an evaluation cannot be made. The effect of absorbed water on the dynamic mechanical properties at 23°C is discussed in terms of two kinds of processes: (a) formation of water‐amide hydrogen bonds with free amide groups and (b) scission of amide‐amide hydrogen bonds.

Log amplitude is a linear function of log frequency in NREM sleep EEG of young and elderly normal subjects

The log of the amplitude of EEG waves during NREM sleep is a linear function of the log of their frequency. The slope of this function is reliable within individuals, is significantly less steep in elderly than in young subjects and, in both groups, becomes flatter across successive NREM periods. We interpret these results as consistent with the hypothesis that the function of NREM sleep is to reverse the effects of waking on the brain. According to this model the decreased steepness of slope in the elderly and in later NREM periods reflects the diminishing intensity of these processes. Whatever the correct interpretation, the within-subject consistency of slope values permits their empirical study as a function of experimental manipulations. In addition, the quantitative F-A function established here (A =c/F b) sets constraints that may prove useful for physiologic models of EEG waves during sleep.

Measurement and theory of wheezing breath sounds.

We measured the time and frequency domain characteristics of breath sounds in seven asthmatic and three nonasthmatic wheezing patients. The power spectra of the wheezes were evaluated for frequency, amplitude, and timing of peaks of power and for the presence of an exponential decay of power with increasing frequency. Such decay is typical of normal vesicular breath sounds. Two patients who had the most severe asthma had no exponential decay pattern in their spectra. Other asthmatic patients had exponential patterns in some of their analyzed sound segments, with a range of slopes of the log power vs. log frequency curves from 5.7 to 17.3 dB/oct (normal range, 9.8-15.7 dB/oct). The nonasthmatic wheezing patients had normal exponential patterns in most of their analyzed sound segments. All patients had sharp peaks of power in many of the spectra of their expiratory and inspiratory lung sounds. The frequency range of the spectral peaks was 80-1,600 Hz, with some presenting constant frequency peaks throughout numerous inspiratory or expiratory sound segments recorded from one or more pickup locations. We compared the spectral shape, mode of appearance, and frequency range of wheezes with specific predictions of five theories of wheeze production: 1) turbulence-induced wall resonator, 2) turbulence-induced Helmholtz resonator, 3) acoustically stimulated vortex sound (whistle), 4) vortex-induced wall resonator, and 5) fluid dynamic flutter. We conclude that the predictions by 4 and 5 match the experimental observations better than the previously suggested mechanisms. Alterations in the exponential pattern are discussed in view of the mechanisms proposed as underlying the generation and transmission of normal lung sounds. The observed changes may reflect modified sound production in the airways or alterations in their attenuation when transmitted to the chest wall through the hyperinflated lung.

The Approximation of Prescribed Magnitude and Phase Characteristics

A method is presented to determine simple transfer functions describing the input-output properties of continuous linear time-invariant systems. These transfer functions belong to a certain class of models including rational fractions and the transcendental function concerning time-lags. The evaluation of such models is based on the graphical representation of the logarithmic frequency plots (Bode-plots) of the given system in a fixed frequency range. The problem is then treated as an approximation problem in that sense that one fits the magnitude plot as well as the phase plot of the unknown model to the given plots in an interactive graphics dialog.

Dielectric properties of metastable solid MBBA under pressure

Dielectric measurements on metastable solid MBBA were performed in the frequency range from 0.5 to 100 kHz under pressures up to 6 kbar. The application of pressure shifts the dielectric relaxation curves towards higher temperatures. With increasing pressure, the dielectric relaxation strength increases in the low pressure region up to about 3.5 kbar and after that tends to saturate in the high pressure region. The activation parameters, such as the activation enthalpy, entropy and free energy obtained from the linear relation between the logarithmic relaxation frequency and the reciprocal absolute temperature, increase with increasing pressure. The inflection point pt was found to be at about 3.5 kbar on the curves of activation parameters versus pressure. These facts suggest that different relaxation mechanisms should be applied to the low pressure region below pt and the high pressure region above pt. The pressure dependence of the glass transition temperature was inferred from the pressure dependence of the loss maximum temperature.

Logarithmic frequency dependence of the dynamical conductivity of one-dimensional disordered systems at low frequencies: a computer simulation for a very long chain

The low-frequency behaviour of the dynamical conductivity sigma ( omega ) for electrons on very long (106 sites) one-dimensional disordered chains is investigated by computer simulation. Berezinskii's result (1974) which is asymptotically exact in the limit of weak disorder and shows the behaviour sigma ( omega )/ sigma 0 to 32( omega tau )2(ln2(4 omega tau )- pi 2/4+(2C-3)ln(4 omega tau )+ ...) at low frequencies ( sigma 0, tau and C denote the Drude value of the conductivity, the relaxation time of the electrons and Euler's constant, respectively), is established for the first time by a direct numerical method. A discussion is given of a simple derivation of the coefficient 32. It is also found that this low-frequency behaviour remains almost when disorder is introduced, unchanged even when the disorder is strong.

Relaxation phenomena and induced polarization

We deal with the general subject of the linear system behavior of material media that have dispersive electrical properties. In this review we deal with phenomenological theory which begins with a general statement of Ohm's law that relates the macroscopic electric field and the current density at a point in the medium. The complex constant of proportionality is the complex resistivity that forms the basis of the discussion. Various ways to represent the frequency dependence of the complex resistivity are described. The corresponding time domain or transient response characteristics are also considered in the context of the induced polarization properties of the medium. We point out that it is often fruitful to represent the dispersion as a superposition of basic relaxation processes. In fact, if such distributions are sufficiently broad, the effective complex resistivity varies in magnitude in almost a linear manner with the logarithm of frequency. The corresponding phase is approximately a constant that is proportional to the slope of the amplitude curve on log frequency basis. This same slope parameter is also descriptive of the transient decay of the system when the linear response is plotted on a log time base. This general behavior seems to be a general property of such composite media as textured rock, mineralized material and biological suspensions where we can expect that the scale of the dispersive mechanisms is quite broad.

Theory of amorphous-silicon charge-coupled devices

The theory of operation of amorphous-silicon charge-coupled devices has been studied numerically and analytically under the assumption that the localized states in amorphous-silicon are distributed exponentially with respect to energy. The transfer inefficiency ε is found to depend not only on the localized state density but also on the transit time and initial density of signal electrons. The approximate analysis shows that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\ln(\epsilon)</tex> is a linear function of logarithmic clock frequency, and that its coefficient is given by the characteristic temperature which represents the steepness of the localized state density distribution in amorphous-silicon.

Analysis of voice fundamental frequency contours for declarative sentences of Japanese.

A model for the generation of fundamental frequency contours (F0 contours) of spoken, sentences is presented for the purpose of elucidating the relationship between the sentence F0 contour and the linguistic and non-linguistic information. It is based on a quantitative formulation of the process whereby the logarithmic fundamental frequency is controlled in proportion to the sum of two components corresponding respectively to the effects of phrase and accent. The model's parameters were determined to give the best approximation to an observed F0 contour on the basis of the mean squared error. Analysis of natural utterances of various declarative sentences of Japanese revealedthat the model can generate close approximations to observed F0 contours from a set of discrete commands and a small number of parameters. The extracted parameters were found to be closely related to linguistic factors and factors constituting thenaturalness of speech. These results provide a means for generating natural F0 contours from a small set of parameters and rules for synthesis.

Interrelations between shift factors of viscoelastic functions and apparent activation energy of flow

The applicability of an approach is tested experimentally, which interrelates the frequency as well as the temperature shift of isotherm and isochrone viscoelastic data with the apparent activation energy of the viscous flow. The procedure is based on the evaluation of the slopes of isotherms in the log viscoelastic function — log frequency plot and of isochrones in the log function — reciprocal temperature plot. Experimental data demonstrate that the approach applies over the entire temperature range from the high-temperature melt to the glass transition, where the WLF equation fails oftenly. The temperature range of variable activation energy turns out to be substantially smaller than supposed. Above Tg + 40 K constant activation energy suffices, suggesting that the range of validity of the EYRING model is quite larger than usually admitted.

Phase effects and profile analysis

Randomizing the phase of the components of a tonal complex on each presentation has little effect on detection of an intensity increment of the central component. The complex consisted of eleven equal amplitude tones ranging from 200 to 5000 Hz. The spacing between adjacent components was equal on a logarithmic frequency scale. The signal was a sinusoid added in‐phase to the central, 1000‐Hz component. The overall sound pressure level of the sound was varied on each presentation according to a rectangular distribution with a range of 40 dB and a median sound pressure level per component of 45 dB. Over 50 complexes with different waveforms were generated by randomly selecting different starting phases for each component. Eight of these waveforms were selected, and each was presented as the complex for more than 500 trials in a 2AFC experiment. Thresholds for a signal added to each of these different complexes had a total range of only 2.4 dB. In a final test, we selected a different waveform on each presen...

Effects of cigarette smoking and oral nicotine on hand tremor.

The effect of nicotine on hand tremor was assessed by measuring the current induced in a coil by a magnet attached to the finger. Experiment 1 assessed the amplitude of tremor induced by smoking two cigarettes in a group of 33 subjects drawn from two age groups. Smoking increased tremor significantly. Age, sex, and anxiety levels had no effect. Experiment 2 assessed the effect of smoking on tremor frequency. Analog recordings of tremor in 10 subjects were processed to yield the total power in 20 1-Hz bands from 1 to 20 Hz. The log amplitude showed a strong linear relationship to the log frequency, but this relationship was not affected by smoking. Smoking also had no effect on peak frequency in the frequency spectrum. Experiment 3 confirmed that the effects of smoking on tremor were attributable to nicotine. Twelve subjects were tested before and after smoking a cigarette and before and after chewing gum containing 4 mg nicotine. The two conditions induced comparable increases in tremor. A 2-mg nicotine preparation tested in eight subjects had no effect on tremor. Tremor may be a useful index of the central activity of nicotine and may help illuminate its mechanism of action.

Dielectric logging with downhole invasion effects

The transfer impedance between conducting coils is evaluated to estimate the downhole dielectric properties that can contribute to more effective exploration and production of gas/oil reservoirs. The earth formation with a borehole-mud filtrate invasion is simulated by concentric zones of variable dielectric properties to account for rocks saturated by different fluids. We have imposed analytical restrictions to allow only magnetic-dipole coupling between logging coils and to limit logging source frequencies from 10 to 30 MHz for typical coil spacings. Depending on the depth of invasion front, guided waves may exist in the invaded formation. When guided waves do not exist, rapidly converging branchcut integrations are used to evaluate the transfer impedance. When the invasion front begins to support guided waves the numerical convergence becomes somewhat slower using spatial-band-limited integrations. Both types of integration are used to produce inversion charts from which dielectric properties and invasion-front radii can be estimated from downhole-measurable transfer impedances. Ambiguity in parameter inversion is also demonstrated to provide insight for developing a future inverse process based on array processing of adequately sampled data.

Temperature-Frequency Equivalence of the Viscoelastic Properties of Anhydrous Lanolin USP

□ Methods of data analysis novel to pharmaceutical semisolids have been applied to the dynamic mechanical data obtained for anhydrous lanolin USP. It was found that the viscoelastic parameters determined over a wide range of temperatures and shear frequencies could be superposed. Elastic moduli (G′) and viscous moduli (G″) obtained at low temperatures (T) and frequencies (v), were equivalent to moduli obtained at high T and v. Empirical shifts of modulus versus shear frequency data obtained at different temperatures were used to produce G′ and G″ versus v master curves (complete log modulus versus log frequency behavior at a constant temperature). A method of reduced variables, in conjunction with an Arrhenius-type relation, proved useful in calculating the energy of activation for the structural processes involved in a major mechanical transition.