Low-frequency Mechanical Spectroscopy Research Articles

Frozen-to-jamming-to-fluid Transition of Weakly Sheared Granular Systems by Low-frequency Mechanical Spectroscopy

Granular matter usually displays frozen, jamming and fluidized states when submitted to an external vibration with increasing intensity. The dissipation properties of granular systems with three different millimeter-size glass grains (0.1, 0.5 and 1.9 mm) have been investigated by a modified low-frequency inverted torsion pendulum under a shear strain and an external pressure. With increasing the immersed depth of the oscillating probe, all the systems show the frozen, jamming and fluidized behaviors. Furthermore, the critical depth at which the transition occurs increases with increasing grain size, but decreases with the application of pressure. A qualitative explanation is tentatively proposed to understand the underlying mechanism of complex viscoelastic properties of the glass particle systems.

Relaxation dynamics in pyrrolidinium based ionic liquids: The role of the anion conformers

We report density functional theory (DFT) calculations and low-frequency mechanical spectroscopy results on two ionic liquids having the same N-butyl-N-methyl-pyrrolidinium cation (PYR14), but different anions, (nonafluorobutanesulfonyl)(toluenesulfonyl)imide (IMT4) and 1,3 hexafluoropropane-disulfonylimide (IM3), belonging to the per(fluoroalkylsulfonyl)imide family. For both samples, a relaxation process is observed in their supercooled liquid phase, which can be described by a hopping model between non-equivalent configurations. In agreement with previous results, the relaxation is attributed to the ions motion. The comparison among calculations of the anion conformers population and the analysis of the experimental data points out that the non-equivalent configurations between which the ion motion occurs involve a different configuration for the anion.

Low-Frequency Mechanical Spectroscopy of Lanthanum Cobaltite Based Mixed Conducting Oxides

Abstract The low-frequency mechanical spectra of lanthanum cobaltite based mixed conducting oxides have been measured using a computer-controlled inverted torsion pendulum. The results indicate that the internal friction spectra and shear modulus depend on the Sr doping contents (x). For undoped samples, no internal friction peak is observed. However, for La0.8Sr0.2CoO3‒δ, three internal friction peaks (P2, P3 and P4) are observed. In addition to these peaks, two more peaks (P0 and P1) are observed in La0.6Sr0.4CoO3‒δ. The P0 and P1 peaks show characteristics of a phase transition, while the P2, P3 and P4 peaks are of relaxation-type. Our analysis suggests that the P0 peak is due to a phase separation and the P1 peak is related to the ferromagnetic–paramagnetic phase transition. The P2, P3 and P4 peaks are associated with the motion of domain walls. The formation of this kind of domain structure is a consequence of a transformation from the paraelastic cubic phase to the ferroelastic rhombohedral phase. With partial substitution of Fe for Co, only one peak is observed, which is discussed as a result of different microstructure.

Relaxation Dynamics and Phase Transitions in Ionic Liquids: Viscoelastic Properties from the Liquid to the Solid State

In the present work we performed low-frequency mechanical spectroscopy experiments to measure the mechanical modulus of two ionic liquids and its variation during the main phase transitions occurring by varying the temperature, in the both liquid and the solid states. The liquids share the same anion, the bis(trifluoromethanesulfonyl)imide, and present different cations, 1-butyl-1-methylpyrrolidinium and 1-allyl-3-H-imidazolium. A thermally activated relaxation process is found in the liquid phase and is analyzed in terms of a modified Debye model. The obtained parameters provide indications about the nature and the mechanism giving rise to the peak, which is attributed to the ions motion by means of hopping processes. Moreover, density functional calculations were performed, and the comparison with the analysis of the experimental data suggests that the anion conformers are likely to be involved in the different configurations among which the ions can rearrange.

Development Of High-Resolution Mechanical Spectroscopy, HRMS: Status And Perspectives. HRMS Coupled With A Laser Dilatometer

Abstract Recent achievements in the development of low-frequency high-resolution mechanical spectroscopy (HRMS) are briefly reported. It is demonstrated that extremely low values of the loss angle, ϕ, (tanϕb = 1×10−5) can be measured as a function of frequency, and the precision in estimation of the dynamic modulus is better than 1×10−5 in arbitrary units. Three conditions must be fulfilled to obtain high resolution in subresonant and resonant mechanical loss measurements: (1) noise in stress and elastic strain signals must be lower than 70 dB, (2) high quality of stress and strain signals must be tested both in the frequency- and time-domains, and (3) the estimation of the mechanical loss and modulus must be verified by at least two different computing methods operating in the frequency- and time-domains. It is concluded that phase measurements in the subresonant domain are no longer determined by precision in estimation of the loss angle. Recent developments in high-resolution resonant mechanical loss measurements stem from the application of advanced nonparametric and parametric computing methods and algorithms to estimate the logarithmic decrement and the elastic modulus from exponentially damped free decaying oscillations embedded in experimental noise. It is emphasized that HRMS takes into account the presence of noise in the stress and strain signals, which has not yet been addressed in the literature. The coupling of a low-frequency mechanical spectrometer with an in-situ laser dilatometer is suggested as a new perspective research area in Materials Science.

Mechanical Spectroscopy: Some Applications On Structural Changes And Relaxation Dynamics In Soft Matter

Abstract The general trend in soft matter is to study systems of increasing complexity covering a wide range in time and frequency. Mechanical spectroscopy is a powerful tool for understanding the structure and relaxation dynamics of these materials over a large temperature range and frequency scale. In this work, we collect a few recent applications using low-frequency mechanical spectroscopy for elucidating the structural changes and relaxation dynamics in soft matter, largely based on the author’s group. We illustrate the potential of mechanical spectroscopy with three kinds of soft materials: colloids, polymers and granular systems. Examples include structural changes in colloids, segmental relaxations in amorphous polymers, and resonant dissipation of grain chains in three-dimensional media. The present work shows that mechanical spectroscopy has been applied as a necessary and complementary tool to study the dynamics of such complex systems.

Dynamics in N-Isopropylacrylamide-acrylic Acid Copolymer Aqueous Solution from Mechanical Spectroscopy

Gaining control over precise and predictable structures of colloidal systems and understanding the abundant dynamic behaviors remains a formidable challenge. In this study, low-frequency mechanical spectroscopy was applied to investigate the dynamics of aqueous solutions of N-isopropylacrylamide-acrylic acid (NIPAM-AA) copolymers with three different AA contents. A mechanical loss valley was found for the solution with low molar fraction of AA (f(AA)), f(AA) = 25 and 50 mol %, and a loss peak was shown for the solution with f(AA) = 75 mol %. The former is suggested to be due to the particle glass phase of repulsive micelles above the low critical solution temperature, whereas the latter is associated with the α relaxation behavior of NIPAM-AA/water mixture at high concentrations. The relaxation time of the α relaxation seems to follow a simple Arrhenius temperature dependence. The activation energy H is ∼53 kJ/mol, and the larger H value is suggested to be due to multiple strong hydrogen bonds in the copolymer solution. The present work demonstrates that by controlling the proportion of ingredients in the colloidal systems the systems can exhibit distinct dynamic behaviors, which is helpful in the design and fabrication of colloids.

Synthesis, Thermodynamics, and Dynamics of Poly(4-tert-butylstyrene-b-methyl methacrylate)

A series of symmetric poly(4-tert-butylstyrene-block-methyl methacrylate) (PtBS-b-PMMA) diblock copolymers with varying molar masses and narrow molar mass distributions were prepared using sequential anionic polymerization. Order-to-disorder transition (ODT) temperatures were determined as a function of the overall degree of polymerization, N, using a combination of low-frequency dynamic mechanical spectroscopy (DMS) and variable temperature small-angle X-ray scattering (SAXS), leading to a mean-field expression for the segment–segment interaction parameter, χ = (41.2 ± 0.9)/T – (0.044 ± 0.002). This material is characterized by a larger value of χ, and much greater temperature sensitivity, than polystyrene-b-PMMA, providing access to tunable lamellar periods (pitch) down to 14 nm at technologically relevant temperatures. Nucleation and growth of lamellae, following cooling from the disordered state, was characterized by SAXS well above the glass transition temperature (Tg ≈ 130 °C) and extrapolated to lower processing temperatures based on polymer chain relaxation times extracted from time–temperature superposed DMS data. These results qualify PtBS-b-PMMA as an attractive candidate for development as a new lithographic material.

DFT-based Estimation of Damped Oscillation Parameters in Low-Frequency Mechanical Spectroscopy

In this paper, we analyze and compare the properties of different well-known and also new nonparametric discrete Fourier transform (DFT)-based methods for resonant frequency and logarithmic decrement estimation in application to mechanical spectroscopy. We derive a new DFT interpolation algorithm for a signal analyzed with Rife-Vincent class-I windows and also propose new formulas that extend Bertocco and Yoshida methods. We study errors of the resonant frequency and logarithmic decrement estimation in realistic conditions that include measurement noise and a zero-point drift. We also investigate the systematic errors of the estimation methods of interest. A nonlinear least squares time-domain parametric signal fitting is used to determine the boundaries of statistical efficiency in all tests.

Mechanical relaxation studies of α and slow β processes in Nd65Fe15Co10Al10 bulk metallic glass

The relaxation dynamics of the primary α and secondary β processes in Nd65Fe15Co10Al10 bulk metallic glass has been investigated by using low-frequency mechanical spectroscopy, differential scanning calorimetry (DSC) and x-ray diffraction. From the shift of internal friction peaks by the frequency change, the activation energy of β relaxation (Eβ) is found to be about 1.01 eV, and a correlation between Eβ and glass transition temperature (Tg) is found Eβ ≈ 24 RTg, indicating that the β relaxation is intrinsic in metallic glasses. According to the coupling model, the uncoupled activation energy of α relaxation (Eα*) is found to be about 1.38 eV, still larger than the value of Eβ corresponding to a simple Debye relaxation process. The possible mechanism and the connection between α and β relaxations are discussed.

Phase diagram of the Pluronic L64–H2O micellar system from mechanical spectroscopy

The linear viscoelastic properties of aqueous Pluronic L64 solutions have been investigated at high copolymer concentrations (25-62 wt%) using our modified low-frequency mechanical spectroscopy. The concentration-temperature phase diagram of the L64/H(2)O system was constructed by studying the evolution of the loss modulus and loss tangent as temperature is increased at a fixed frequency. A particular attention was focused on the dynamics approaching the beginning and ending points (39% and 60%) of the fusiform gel region in the phase diagram. The dynamics is found to have a similar viscoelastic behavior at the low and high concentrations, where a frequency scaling expected for a static percolated network is exhibited. Moreover, with increasing temperature, the system above the critical gel concentration undergoes a transition from a viscoelastic liquid to a solid gel through a percolated particle network. Therefore, our results suggest that the formation of the gel is dominated by the percolation of the particle clusters.

Low Frequency Mechanical Spectroscopy of High Damping Mg-3wt.%Ni Alloy

The Dynamic Mechanical Analysis (DMA) was applied to investigate the low frequency mechanical spectroscopy response of as-cast high damping Mg-3wt.%Ni hypoeutectic alloys. There are two peaks appearing on the temperature dependent damping spectrum (-100 - 420 °C). The broad peak P1 is overlapped by some small peaks due to the thermally activated dislocation movement, while the P2 peak is a solute grain boundary relaxation peak.

Mechanical damping in nanostructured Nd 60Fe 30Al 10 magnetic alloys

Nanostructured Nd 60Fe 30Al 10 magnetic alloys were obtained by melt spinning at a tangential wheel speed of 5 m/s. Magnetic and stress relaxation processes were investigated in the as cast condition. Low frequency mechanical spectroscopy studies (dynamic elastic torsion modulus and internal damping measurements) were conducted at fixed frequencies between 0.1 and 1 Hz, in the range [150–480 K]. The low temperature internal damping and dynamic elastic modulus exhibited a large heating–cooling hysteresis and two damping peaks: one due to a stress induced relaxation mechanism operating near 200 K [1 Hz] and another one, at about 260–270 K, which could not be correlated with any step in the modulus, indicating that it is not anelastic in origin. The high temperature damping was described by an exponential background and a broad peak contribution centered at about 400 K (1 Hz). The resulting maximum is frequency dependent, but it is little sensitive to applied fields up to 30 mT. On contrary, the elastic modulus behavior associated to this maximum resulted largely affected by frequency, the external fields and the magnetic state of the sample.

Characterization of poly(ethylene terephthalate) used in commercial bottled water

The aim of this study is to determine which compounds are present into drinking water packaged in poly(ethylene terephtalate) bottles and to know the origin of these substances in relationship with the material.A screening procedure was established for the detection of unknown compounds into bottled water. A panel of water bottles has been tested after exposure to extreme conditions of temperature and UV radiation to accelerate the possible migration of substances.At the same time, physico-chemical characterization of polymeric material has been performed namely calorimetric analysis, IRTF and low-frequency mechanical spectroscopy. The results thus obtained allow understanding in a better way the migration kinetics of molecules inside the polymer, it means the pollution of the bottled water.

Slow dynamics of the α and α′ relaxation processes in poly(methyl methacrylate) through the glass transition studied by mechanical spectroscopy

In this paper, low-frequency mechanical spectroscopy has been used to study poly(methyl methacrylate) (PMMA) melt around the glass transition temperature Tg for shedding light on its unique relaxation behaviors. The mechanical spectra show an asymmetrical broad structure with a maximum peak on the high-temperature side and a shoulder peak on the low-temperature side. The shoulder peak corresponds to the α relaxation due to the local segmental motion; while the maximum peak is assigned to the α′ relaxation due to the slow motion of longer chain segments or chains. The α relaxation mode has a stronger temperature dependence of relaxation time than the α′ mode, causing the α′ mode to merge with the α mode with decreasing temperature toward Tg. Time-temperature superposition (TTS) breaks down in the entire temperature range due to the different friction coefficients of the α and α′ relaxations. For only the α′ process, TTS is found to hold for PMMA melt, where the high-frequency decay of the mechanical loss decreases like a power law of the frequency with an exponent of −1/3. Moreover, compared with the dielectric results, the relaxation times of β and α relaxations from mechanical measurements are about one order of magnitude slower than those from dielectric experiments.

Morphology and dynamical behaviour of grafted copolymers

The interactions between the main chain and lateral chains in grafted polymers play an important role on their dynamics. This is a complex issue, since several length scales are to be taken into account, from the local intramacromolecular interactions between linked moieties up to intermolecular interactions in phase separated systems. Such phenomena are investigated on the basis of new copolymers obtained by controlled radical polymerization. The effect of two parameters are studied separately, namely (i) the number of grafted chains on the main chain (cellulose acetate) and (ii) the length of grafted moieties (poly(methyl(diethylene glycol)methacrylate)). The dynamics of molecular motions was assessed by Low Frequency Mechanical Spectroscopy and Broad Band Dielectric Spectroscopy. The complex shear and dielectric moduli were measured on thin films (60 μm thickness) as a function of frequency and temperature. The sensitivity of these relaxation spectroscopy techniques, as compared to calorimetry measurements, allowed to study the effects of (i) the chemical structure of the copolymers and (ii) the microstructure at the nanoscale, as investigated by Small Angle X-ray Scattering. It is shown that the main parameter is the soft grafted moities content: as expected the molecular mobility increases as the content of soft grafted chains increases. In addition, it is shown that this molecular mobility is drastically depressed by thermal treatment.

Hydrogen related peaks in Cu–LaNi 4.7Al 0.3

In this work, the effect of Ni substitution by Cu in the LaNi 4.7Al 0.3 hydride-forming alloy was studied in order to apply it to the negative electrodes of Ni–MH batteries. SEM, EDS and X-ray diffraction techniques were used to analyze the microstructure, composition and crystalline structure of the samples. A maximum electrochemical discharge capacity of 130 mAh/g was obtained. Internal friction (IF) and shear modulus ( G) were measured by means of low frequency mechanical spectroscopy, between 100 and 450 K. In the electrochemical activated sample, two main IF peaks and typical relaxation steps in G showed up at 200 and 280 K. The first is ascribed to interactions between hydrides and H atoms in solid solution and dislocations, while the last one is attributed to the β ↔ α hydride phase transformation.

Low-frequency mechanical spectroscopy study of conformational transition of polymer chains in concentrated solutions

A low-frequency mechanical spectroscopy approach for liquids was proposed for studying conformational transition of polymer chains in concentrated solutions. The technique is applied to aqueous solutions of a poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO) triblock copolymer in order to determine if chain conformation is altered in response to temperature. Two transitions are revealed by mechanical spectra and verified by differential thermal analysis with increasing temperature, which may be related to the unimer-to-micelle transition and the phase separation, respectively. The transitions are also found to be much dependent on the concentration of the solution and the addition of NaCl. Moreover, it reveals that the PEO blocks play a more important role in the micellar crystallization process. This study may be helpful in understanding the dynamics of polymer chains in concentrated solutions.

Recent Advances in Determination of the Logarithmic Decrement and the Resonant Frequency in Low-Frequency Mechanical Spectroscopy

The advantages of the OMI algorithm to compute the logarithmic decrement and the resonant frequency from free decaying oscillations is reported. The OMI algorithm is proved to be the best solution in the computation of the logarithmic decrement and the resonant frequency for high damping levels.

Long-term physical ageing of amorphous polymers

The dynamic properties of amorphous polymers were investigated during long-term ageing by means of high resolution low-frequency mechanical spectroscopy. Two polymers are considered in this work, namely atactic polystyrene and quenched amorphous poly(ethylene naphthalate). It is shown that during ageing at temperatures higher than that of secondary relaxation, but lower than that of the primary one (if tested at 1 Hz), the strength of the secondary relaxation first increases and then decreases for long ageing times. This phenomenon is explained on the basis of the concepts of the heterogeneous cohesion of the amorphous network at the nanometric scale and the cooperation of molecular motions responsible for the secondary relaxations.