Multimodal Relaxation Research Articles

Polymer architecture dictates multiple relaxation processes in soft networks with two orthogonal dynamic bonds

Materials with tunable modulus, viscosity, and complex viscoelastic spectra are crucial in applications such as self-healing, additive manufacturing, and energy damping. It is still challenging to predictively design polymer networks with hierarchical relaxation processes, as many competing factors affect dynamics. Here, networks with both pendant and telechelic architecture are synthesized with mixed orthogonal dynamic bonds to understand how the network connectivity and bond exchange mechanisms govern the overall relaxation spectrum. A hydrogen-bonding group and a vitrimeric dynamic crosslinker are combined into the same network, and multimodal relaxation is observed in both pendant and telechelic networks. This is in stark contrast to similar networks where two dynamic bonds share the same exchange mechanism. With the incorporation of orthogonal dynamic bonds, the mixed network also demonstrates excellent damping and improved mechanical properties. In addition, two relaxation processes arise when only hydrogen-bond exchange is present, and both modes are retained in the mixed dynamic networks. This work provides molecular insights for the predictive design of hierarchical dynamics in soft materials.

Low-Power Low-Complexity FM-UWB Hybrid Transceiver for Communication and Ranging

A frequency-modulated ultrawideband (FM-UWB) hybrid transceiver, with a high system reuse ratio up to 90%, is fabricated in the 65-nm CMOS process for both short-range wireless communication and high-resolution radar ranging. The radio frequency (RF) front-ends (RFFEs) based on module stacking and current reuse achieve significant RF power savings of about 30% and 50% for the transmitter and the receiver (RX), respectively. The presented IF zero-crossing delay discrimination benefits a high radar resolution less than 1 cm. A multimode relaxation oscillator (OSC) for the reconfigured triangular subcarrier generation and a dual-path ring voltage-controlled oscillator (VCO) for the linear FM, stacked by a wideband push–pull power amplifier (PA), generate an FCC-compliant UWB signal. An active balun embedded low-noise amplifier (LNA) and two symmetric-detuning band-passed filters (BPFs) are stacked with the bandwidth extension to linearly demodulate the UWB FM signal. Experimental results show that the 3.75–4.25-GHz hybrid transceiver has an energy efficiency of 1.9 nJ/bit with an active area of 0.7 mm2 and a power dissipation of 1.9 mW and achieves the RX sensitivity of −71 dBm and the transmitted power of −14.1 dBm, with a bit error rate (BER) of 10−4 at a distance of 4 m under the data rate (DR) of 0.1–1.0 Mbps. The transceiver also achieves the noise figure (NF) of 4.8 dB and the phase noise of −78.6 dBc/Hz at 1-MHz offset frequency.

The nonlinear stress relaxation behavior after a step shear of star‐shaped styrene‐butadiene rubber filled with precipitated silica: Experiment and simulation

AbstractThe nonlinear stress relaxation behavior after a step shear strain of star‐shaped SSBR/silica compounds containing 21 vol% filler of various surface areas was measured and simulated using constitutive equations. A styrene‐butadiene rubber (SBR) gum and SBR filled with silica having BET surface areas of 55, 135, 160, and 195 m2/g were used. Relaxation modulus behavior of the filled compounds was found to be dependent on surface area. Specifically, stress relaxation tests indicated that an increase in surface area led to increase in values of relaxation moduli in both the linear and nonlinear regimes. The time‐dependent relaxation modulus exhibited a plateau at long times of relaxation in compounds containing silica of high surface area. Additionally, good time‐strain superpositions were achieved for all samples at intermediate times of relaxation, and the strain‐dependent damping function decreased with filler surface area. The constitutive equations proposed by Leonov and Simhambhatla and Leonov, modified to include multimodal relaxation of the particle network, were used to predict the time evolution of the relaxation modulus in the nonlinear regime for all samples. The simulations provided good results for the SBR gum for all tested strain levels. Also, in the compounds filled with silica, both models satisfactorily described the experimental observation in the nonlinear regime at low strain levels. However, at higher strain levels, due to a possible slip effect, the simulations overpredicted measured values of the relaxation moduli, thus leading to only qualitative predictions of the observed behavior. It is also possible that neither model accurately captured the floc rupture kinetics of these complex rubber compounds.

Bulk viscosity of liquid noble gases.

An equation of state for the bulk viscosity of liquid noble gases is proposed. On the basis of dedicated equilibrium molecular dynamics simulations, a multi-mode relaxation ansatz is used to obtain precise bulk viscosity data over a wide range of liquid states. From this dataset, the equation of state emerges as a two-parametric power function with both parameters showing a conspicuous saturation behavior over temperature. After passing a temperature threshold, the bulk viscosity is found to vary significantly over density, a behavior that resembles the frequency response of a one pole low-pass filter. The proposed equation of state is in good agreement with available experimental sound attenuation data.

A simple measurement method of molecular relaxation in a gas by reconstructing acoustic velocity dispersion

Recently, a decomposition method of acoustic relaxation absorption spectra was used to capture the entire molecular multimode relaxation process of gas. In this method, the acoustic attenuation and phase velocity were measured jointly based on the relaxation absorption spectra. However, fast and accurate measurements of the acoustic attenuation remain challenging. In this paper, we present a method of capturing the molecular relaxation process by only measuring acoustic velocity, without the necessity of obtaining acoustic absorption. The method is based on the fact that the frequency-dependent velocity dispersion of a multi-relaxation process in a gas is the serial connection of the dispersions of interior single-relaxation processes. Thus, one can capture the relaxation times and relaxation strengths of N decomposed single-relaxation dispersions to reconstruct the entire multi-relaxation dispersion using the measurements of acoustic velocity at 2N + 1 frequencies. The reconstructed dispersion spectra are in good agreement with experimental data for various gases and mixtures. The simulations also demonstrate the robustness of our reconstructive method.

Capturing molecular multimode relaxation processes in excitable gases based on decomposition of acoustic relaxation spectra

Existing two-frequency reconstructive methods can only capture primary (single) molecular relaxation processes in excitable gases. In this paper, we present a reconstructive method based on the novel decomposition of frequency-dependent acoustic relaxation spectra to capture the entire molecular multimode relaxation process. This decomposition of acoustic relaxation spectra is developed from the frequency-dependent effective specific heat, indicating that a multi-relaxation process is the sum of the interior single-relaxation processes. Based on this decomposition, we can reconstruct the entire multi-relaxation process by capturing the relaxation times and relaxation strengths of N interior single-relaxation processes, using the measurements of acoustic absorption and sound speed at 2N frequencies. Experimental data for the gas mixtures CO2–N2 and CO2–O2 validate our decomposition and reconstruction approach.

Kinetics of Chain Exchange between Diblock Copolymer Micelles

Dissipative particle dynamics simulation is employed to study the chain exchange kinetics between micelles of diblock copolymer in aqueous solution via in silico hybridization method. One focus is placed on the effect of chain flexibility on the dynamic behavior by varying the spring constant in the bead‐spring model. The length ratio of hydrophilic to hydrophobic block is also varied. It is found that chain expulsion/insertion is the dominant mechanism in the chain exchange process. The most interesting finding is the multimodal relaxation behavior for the chain exchange and expulsion when the spring constant is small or the length ratio of hydrophilic to hydrophobic block is large. This phenomenon is due to an increase in size polydispersity of micelles with rising population of small aggregates/micelles, for which the exchange kinetics is faster. Micelles with larger aggregation numbers (>10) are found to follow single exponential relaxation kinetics. image

Direct simulation Monte Carlo modeling of relaxation processes in polyatomic gases

Relaxation processes of polyatomic molecules are modeled and implemented in an in-house Direct Simulation Monte Carlo code in order to enable the simulation of atmospheric entry maneuvers at Mars and Saturn’s Titan. The description of rotational and vibrational relaxation processes is derived from basic quantum-mechanics using a rigid rotator and a simple harmonic oscillator, respectively. Strategies regarding the vibrational relaxation process are investigated, where good agreement for the relaxation time according to the Landau-Teller expression is found for both methods, the established prohibiting double relaxation method and the new proposed multi-mode relaxation. Differences and applications areas of these two methods are discussed. Consequently, two numerical methods used for sampling of energy values from multi-dimensional distribution functions are compared. The proposed random-walk Metropolis algorithm enables the efficient treatment of multiple vibrational modes within a time step with reasonable computational effort. The implemented model is verified and validated by means of simple reservoir simulations and the comparison to experimental measurements of a hypersonic, carbon-dioxide flow around a flat-faced cylinder.

Multidimensional dynamic piezoresponse measurements: Unraveling local relaxation behavior in relaxor-ferroelectrics via big data

Compositional and charge disorder in ferroelectric relaxors lies at the heart of the unusual properties of these systems, such as aging and non-ergodicity, polarization rotations, and a host of temperature and field-driven phase transitions. However, much information about the field-dynamics of the polarization in the prototypical ferroelectric relaxor (1−x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-xPT) remains unprobed at the mesoscopic level. Here, we use a piezoresponse force microscopy-based dynamic multimodal relaxation spectroscopy technique, enabling the study of ferroelectric switching and polarization relaxation at mesoscopic length scales, and carry out measurements on a PMN-0.28PT sample with minimal polishing. Results indicate that beyond a threshold DC bias the average relaxation increases as the system attempts to relax to the previous state. Phenomenological fitting reveals the presence of mesoscale heterogeneity in relaxation amplitudes and clearly suggests the presence of two distinct amplitudes. Independent component analysis reveals the presence of a disorder component of the relaxation, which is found to be strongly anti-correlated with the maximum piezoresponse at that location, suggesting smaller disorder effects where the polarization reversal is large and vice versa. The disorder in the relaxation amplitudes is postulated to arise from rhombohedral and field-induced tetragonal phase in the crystal, with each phase associated with its own relaxation amplitude. These studies highlight the crucial importance of the mixture of ferroelectric phases in the compositions in proximity of the morphotropic phase boundary in governing the local response and further highlight the ability of PFM voltage and time spectroscopies, in conjunction with big-data multivariate analyses, to locally map disorder and correlate it with parameters governing the dynamic behavior.

Decoupling multimode vibrational relaxations in multi-component gas mixtures: Analysis of sound relaxational absorption spectra

Decoupling the complicated vibrational—vibrational (V—V) coupling of a multimode vibrational relaxation remains a challenge for analyzing the sound relaxational absorption in multi-component gas mixtures. In our previous work [Acta Phys. Sin. 61 174301 (2012)], an analytical model to predict the sound absorption from vibrational relaxation in a gas medium is proposed. In this paper, we develop the model to decouple the V—V coupled energy to each vibrational—translational deexcitation path, and analyze how the multimode relaxations form the peaks of sound absorption spectra in gas mixtures. We prove that a multimode relaxation is the sum of its decoupled single-relaxation processes, and only the decoupled process with a significant isochoric-molar-heat can be observed as an absorption peak. The decoupling model clarifies the essential processes behind the peaks in spectra arising from the multimode relaxations in multi-component gas mixtures. The simulation validates the proposed decoupling model.

Combined THz and Microwave Dielectric Spectroscopy of Intermolecular Interactions in Homologous Protic Ionic Liquids

We report on a detailed and systematic study of the inter molecular dynamics of a homologous series of protic alkylammonium-formate ionic liquids in a broad spectral window, combining THz time-domain and microwave dielectric methods. The joint experiments yield the complex dielectric function over more than four orders of magnitude in frequency. The dielectric absorption data smoothly join with data from Fourier transform far-infrared (FT-FIR) spectroscopy. All dielectric spectra were fitted to a multimodal relaxation model. The observed processes are assigned to low-frequency re-orientational relaxation of the dipolar ions and to intermolecular vibrations between the cations and anions. The dielectric spectra show a dependence on the length and OH-functionalization of the alkyl residues of the cation.

Characterizing the dynamic behavior of nano-TiO2 agglomerates in suspensions by photocorrelation spectroscopy

Metal oxide nanoparticles are small but easily form agglomerates in suspension, depending on the strength of particle–particle and particle–media interactions. To understand the agglomeration behavior of nanoparticles in media and relate to it to product performance testing, measurement methods are desired to characterize highly scattering metal oxide nanoparticle suspensions without dilution. In this article, we describe the advantages of using photocorrelation spectroscopy (PCS) in a backscattering detection configuration to carry out a realistic agglomerate size measurement in multiple scattering media found in most metal oxide nanoparticle suspensions. The dynamic behavior of nano-titanium dioxide (TiO2) particles in buffer solutions of different chemical composition and pH values was investigated as a sample system using PCS. The resulting autocorrelation functions (AFs) at different time intervals, particle concentrations, and pH values were measured at several detection angles. The AF exhibits a multi-mode relaxation time feature and the calculated hydrodynamic diameters strongly depended on media composition and detection angle. This result indicates that the size and dispersion of nano-TiO2 agglomerates are significantly affected by solution media. A measurement protocol for determining size and dispersion of metal oxide particles in media is proposed and related to a performance test found in industry.

Multimodal Relaxation Method

This paper describes the Multimodal Relaxation Method (MRM) which can be used in life, executive, business, sports or health coaching to enhance performance and reduce or manage stress. Within sports and health coaching it can be used to reduce physical tension and enhance physiological control, e.g. lower heart rate and reduce blood pressure.

Negative thixotropy of polymer solutions. 2. A systematic study of the time-dependent viscosity of partially hydrolyzed polyacrylamide

Systematic measurements are presented on the negative thixotropy of partially hydrolyzed polyacrylamide solutions in a water/glycerine mixture. The time dependence of the viscosity is obtained as a function of the shear stress for a large range of polymer concentrations. The results are analyzed in terms of our model for negative thixotropy in polymer solutions described in a preceeding paper [10]. The experimental results are shown to be in agreement with the model calculations to a large extent. It is demonstrated that improvements could most probably be made by including a multimodal relaxation time spectrum into the model.

On the master equation approach of vibrational relaxation in condensed media

The purpose of this paper has been to examine the validity and limitations of the Pauli master equation and to demonstrate the use of the master equation approach in describing the vibrational relaxation in the condensed phase. The master equations for vibrational relaxation of a number of model systems have been derived. The calculation of rate constants of vibrational relaxation has been discussed. The solution of the master equations of multimode relaxation at low temperatures has been presented. The Brownian motion of an oscillator linearly coupled with the medium has been investigated and a model of the coupling between the vibrational relaxation and other unimolecular processes (like electronic relaxation, etc.) has been developed.