Decades In Amplitude Research Articles

Vibration Measurements by Self-Mixing Interferometry: An Overview of Configurations and Benchmark Performances

Self-mixing interferometry (SMI) is suitable to sense and measure vibrations of amplitudes ranging from picometers to millimeters at frequencies from sub-Hz to MHz’s. As an optical probe, SMI has the advantage of being non-invasive with the ability to measure without any treatment of the target surface and operate from a substantial standoff distance from the target. As an additional advantage, the SMI configuration is much simpler than that of conventional interferometers as it does not require any optical part external to the laser source. After a short introduction to the basics of SMI, we review the development of configurations of SMI instruments for vibration measurements, based on both analog and digital processing, with record performance to cover the range of vibration amplitudes from 0.1 nm to 1 mm, frequencies up to MHz, and stand-off distances up to 100 m. These performances set a benchmark that is unequaled by other approaches reported so far in the literature. The configurations we describe are (i) a simple MEMS-response testing instrument based on fringe counting, (ii) a half-fringe locking vibrometer for mechanical mode analysis and transfer function measurements, with a wide linear response on six decades of amplitude, (iii) a vibrometer with analog switching cancellation for μm-to-mm amplitude of vibrations, and (iv) a long standoff distance vibrometer for testing large structures at distances up to 100 m and with nm sensitivity. Lastly, as the vibrometer will almost invariably operate on untreated, diffusing surfaces, we provide an evaluation of phase-induced speckle pattern errors affecting the SMI measurement.

Dynamics of a Paradigmatic Linear Polymer: A Proton Field-Cycling NMR Relaxometry Study on Poly(ethylene–propylene)

The dynamics of melts of linear poly(ethylene-alt-propylene) (PEP) of different molar masses (M) is investigated by 1H field-cycling (FC) NMR relaxometry. Employing a commercial and a home-built relaxometer the spin-lattice relaxation rate R1(ω) is measured in the frequency range of 200 Hz to 30 MHz and the temperature range of 200–400 K. Transforming the FC NMR relaxation data to the susceptibility representation and applying frequency–temperature superposition, master curves for the dipolar correlation function CDD(t/τα) (containing intra- and intermolecular contributions) are constructed which extend up to six decades in amplitude and eight in time. Here, τα is the time scale of the structural (α-) relaxation, which is obtained over several decades. Comparison with previously reported FC data for polybutadiene (PB) discloses very similar CDD(t). Depending on M, all the five relaxation regimes of a polymer melt are covered: in addition to the α-process (0) and the terminal relaxation (IV), which are imm...

Intermolecular Spin Relaxation and Translation Diffusion in Liquids and Polymer Melts: Insight from Field‐Cycling1H NMR Relaxometry

With the advent of commercial field-cycling (FC) spectrometers, NMR relaxometry has gained new momentum as a method of investigating dynamics in liquids and polymers. The outcome of FC NMR experiments is spin-lattice relaxation time versus frequency (relaxation dispersion). In the case of protons, due to the intra- and intermolecular origin of dipolar interactions, the relaxation dispersion reflects rotational as well as translational dynamics. The latter shows a universal dispersion law at low frequencies, which allows determination of the diffusion coefficient D(T) in addition to the rotational correlation time τ(rot)(T), that is, FC (1)H NMR becomes an alternative to field-gradient NMR spectroscopy. Subdiffusive translation found in polymers can be accessed by singling out the intermolecular relaxation through isotope dilution experiments, and the mean square displacement can then be revealed as a function of time, thus complementing neutron scattering experiments. Likewise, information on reorientational dynamics is provided by the intramolecular relaxation. Assuming frequency-temperature superposition the corresponding correlation functions can be monitored up to eight decades in amplitude and time, which allows thorough testing of current polymer theories.

Protracted Crossover to Reptation Dynamics: A Field Cycling1H NMR Study Including Extremely Low Frequencies

The segmental dynamics of 1,4-polybutadiene is investigated by means of electronic field cycling 1H NMR. The frequency dependence (dispersion) of the spin–lattice relaxation time is probed over a broad range of temperature (223–408 K), molecular mass (355 ≤ M (g/mol) ≤ 441 000), and frequency (200 Hz–30 MHz). The extremely low frequencies are accessed by employing a home-built compensation for earth and stray fields extending prior reports about 2 decades to lower frequencies. Applying frequency–temperature superposition yields master curves over 10 decades in frequency (or time), and after Fourier transform the full dipolar correlation function is traced over up to 8 decades in amplitude. Several relaxation regimes can be identified, and their power-law exponents are compared to the predictions of the Doi–Edwards tube-reptation model, namely the free Rouse (I) and the constrained Rouse regime (II). Whereas the predicted value of the power-law exponent of regime II is 0.25, we find that it depends on M an...

Dipolar and Bond Vector Correlation Function of Linear Polymers Revealed by Field Cycling 1H NMR: Crossover from Rouse to Entanglement Regime

We apply field cycling NMR to study segmental reorientation dynamics in melts of linear 1,4-polybutadiene (PB) in the entanglement regime (M ≥ Me). Dispersion data of the spin−lattice relaxation time T1(ω) are transformed to the susceptibility representation χ′′(ω) = ω/T1(ω), and using frequency temperature superposition master curves χ′′(ωτs) are constructed which reflect spectral contributions from glassy as well as polymer specific dynamics. The correlation time τs is determined by glassy dynamics. Transforming χ′′(ωτs) into the time domain and studying the crossover from Rouse to entanglement regime, the full dipolar or segmental reorientational correlation function F2(t/τs) is presented covering six decades in amplitude and 8 decades in time. Assuming F2(t) ≅ ⟨ub(t)ub(0)⟩2 the bond vector correlation function ϕb(t) = ⟨ub(t)ub(0)⟩ is obtained. Reaching Z = M/Me ≤ 9, comparison with theoretical predictions by the tube-reptation model as well as renormalized Rouse theory reveals significant discrepancie...

A detailed test of mode-coupling theory on all time scales: Time domain studies of structural relaxation in a supercooled liquid

The dynamics of supercooled salol (phenyl salicylate) was measured in the time domain using optical Kerr effect techniques. By combining several experimental setups, data spanning more than six decades in amplitude and time (∼100 fs to ∼1 μs) were observed. The data have a complex shape, ranging from high-frequency intramolecular oscillations at short times, to nearly exponential relaxation at long times. As predicted by mode-coupling theory (MCT), the data for some ranges of time appear as power laws. The slowest power law, the von Schweidler power law, has an almost constant exponent of ∼0.59 over the entire temperature range studied (247–340 K). Above the MCT Tc (T>∼1.17 Tg, where Tg is the laboratory glass transition temperature) for t>∼1 ps, the decays are shown to be in excellent agreement with the master curve predicted by ideal MCT when higher order terms are included. However, the data do not display the plateau predicted by ideal MCT. To discuss the data at all temperatures, the intermediate time scale portion of the data, 2<t<10 to 500 ps (depending on the temperature), is modeled as a power law that falls between the critical decay and the von Schweidler power law. This intermediate power law shows significant temperature dependence with an exponent that decreases to a value of ∼−1 below Tc. Calculations using extended MCT, for a full range of hopping times, demonstrate that the temperature dependence of the intermediate time scale data near and below Tc cannot be explained by extended MCT.

Application of GaAs and CdTe photoconductor detectors to X-ray flash radiography

Abstract Some insulating GaAs and CdTe:Cl photoconductor probes were qualified on high energy X-ray single-shot flash generators. The estimated minimum detected dose per flash corresponding to a 230 mrad direct beam attenuated by 200 mm lead was 20 μ rad. The dynamic range was about 4 decades in amplitude or charge, with a good linearity. Such detectors, by locating the origin of the parasitic scattered beam, could be used to eliminate this parasitic beam in X-ray flash radiography in detonics experiments. Imaging possibilities are mentioned, as well as X-ray generator monitoring with such detectors or with neutron preirradiated photoconductors.