Inverse Relaxation Research Articles

Characterizing protein-protein-interaction in high-concentration monoclonal antibody systems with the quartz crystal microbalance.

Making use of a quartz crystal microbalance (QCM), concentrated solutions of therapeutic antibodies were studied with respect to their behavior under shear excitation with frequencies in the MHz range. At high protein concentration and neutral pH, viscoelastic behavior was found in the sense that the storage modulus, G', was nonzero. Fits of the frequency dependence of G'(ω) and G''(ω) (G'' being the loss modulus) using the Maxwell-model produced good agreement with the experimental data. The fit parameters were the relaxation time, τ, and the shear modulus at the inverse relaxation time, G* (at the "cross-over frequency" ωC = 1/τ). The influence of two different pharmaceutical excipients (histidine and citrate) was studied at variable concentrations of the antibody and variable pH. In cases, where viscoelasticity was observed, G* was in the range of a few kPa, consistent with entropy-driven interactions. τ was small at low pH, where the antibody carries a positive charge. τ increased with increasing pH. The relaxation time τ was found to be correlated with other parameters quantifying protein-protein interactions, namely the steady shear viscosity (η), the second osmotic virial coefficient as determined with both self-interaction chromatography (B22,SIC) and static light scattering (B22,SLS), and the diffusion interaction parameter as determined with dynamic light scattering (kD). While B22 and kD describe protein-protein interactions in diluted samples, the QCM can be applied to concentrated solutions, thereby being sensitive to higher-order protein-protein interactions.

Calculation of the frequency shifts and damping constant for the Raman modes (A$_{1g}$, B$_{1})$ near the tetragonal-cubic transition in SrTiO$_{3}$

Raman shifts of the soft mode A$_{1g}$ and the B$_{1}$ mode are calculated at various pressures at room temperature for the cubic-tetragonal transition (P$_{C}$ = 9.5 GPa) in SrTiO$_{3}$. This calculation is performed using the observed volume data through the mode Grüneisen parameters of A$_{1g}$ and B$_{1}$, which vary with pressure, by fitting to the experimental wavenumbers in this crystalline system. Calculated Raman shifts are then used as order parameters to predict the pressure dependence of the damping constant and the inverse relaxation time for the cubic-tetragonal transition in SrTiO$_{3}$. Our predictions from the pseudospin-phonon coupling and the energy fluctuation models can be compared with the experimental measurements when available in the literature.

Dielectric relaxation study of sulfolane-water mixtures

Abstract In the present work broadband dielectric spectra are reported for sulfolane-water mixtures in the complete composition range. The complex dielectric permittivity was measured at frequencies between 100 MHz and 50 GHz and at three temperatures 298.15 K, 308.15 K and 318.15 K. The permittivity spectra in these mixtures reveal a single relaxation process, which can be described by the Cole-Davidson relaxation function. The dielectric parameters, static dielectric constant (e S ), relaxation time (τ) and relaxation strength (Δe) have been determined by the least squares fit method. The concentration and temperature dependent excess dielectric constant and excess inverse relaxation time of the binary mixtures have been calculated. The obtained results confirm that strong interactions take place between sulfolane and water molecules.

Temperature dependence of the polarization, dielectric constant, damping constant and the relaxation time close to the ferroelectric-paraelectric phase transition in LiNbO3

We calculate the order parameter (spontaneous polarization) and the inverse dielectric susceptibility at various temperatures in the ferroelectric phase of LiNbO3 for its ferroelectric-paraelectric phase transition (TC=1260K) using the Landau phenomenological model. For this calculation, the Raman frequencies of the soft optic mode (TO1) are used as the order parameter and the fitting procedure is employed for both the order parameter and the inverse dielectric susceptibility by means of the observed data from the literature. The temperature dependences of the damping constant and the inverse relaxation time are also computed using the pseudospin-phonon coupled model and the energy fluctuation model for the ferroelectric phase of LiNbO3. The activation energy is deduced from the damping constant for both models studied and compared with the kBTC value of LiNbO3.We find that the order parameter (Raman frequency of the TO1 mode) and the inverse dielectric susceptibility decrease with increasing temperature, as expected from the mean field model. We also find that the damping constant and the inverse relaxation time of this soft mode increases and decreases, respectively, with increasing temperature on the basis of the two models studied in the ferroelectric phase of LiNbO3. This indicates that our method of calculation is satisfactory to describe the observed behaviour of the ferroelectric-paraelectric phase transition in LiNbO3.

Crossover of large to small radius polaron in ionic crystals

The crossover of large to small radius polaron is studied in terms of the inverse-relaxation time and temperature. It is found that the small radius polaron exists at higher temperature than the large radius polaron. A formula which relates the inverse-relaxation time to the ratio of arbitrary temperature and Debye temperature of the crystal is derived. The polaron crossover temperatures in NaCl and KBr are found from plotted graphs. The straight line emerging at the Debye temperature TD of a graph reflects the increase of the inverse relaxation time for increasing temperature up to the collapse of the small radius polaron. The relationship between the small and large radius polarons is found and known ratios of the effective and the bare masses of the electrons for the two substances are used to validate our results. The small radius polaron’s mass is later compared with the mass obtained from the hopping formula and is found to be approximately equal. Finally, we point out that the crossover temperature is material-specific since it depends on the Debye and the effective dielectric function.

Electrical and optical conductivities of hole gas in p-doped bulk III–V semiconductors

We study electrical and optical conductivities of hole gas in p-doped bulk III-V semiconductors described by the Luttinger Hamiltonian. We provide exact analytical expressions of the Drude conductivity, inverse relaxation time for various impurity potentials, Drude weight, and optical conductivity in terms of the Luttinger parameters γ1 and γ2. The back scattering is completely suppressed as a result of the helicity conservation of the heavy and light hole states. The energy dependence of the relaxation time for the hole states is different from the Brooks-Herring formula for electron gas in n-doped semiconductors. We find that the inverse relaxation time of heavy holes is much less than that of the light holes for Coulomb-type and Gaussian-type impurity potentials and vice-versa for a short-range impurity potential. The Drude conductivity increases non-linearly with the increase in the hole density. The exponent of the density dependence of the conductivity is obtained in the Thomas-Fermi limit. The Drude weight varies linearly with the density even in the presence of the spin-orbit coupling. The finite-frequency optical conductivity goes as ω, and its amplitude strongly depends on the Luttinger parameters. The Luttinger parameters can be extracted from the optical conductivity measurement.

Damping constant and the relaxation time calculated for the lowest-frequency soft mode in the ferroelectric phase of Cd2Nb2O7

The temperature dependence of the phonon frequency ωph and of the damping constant Γsp due to pseudospin-phonon coupling of the lowest-frequency soft mode is calculated in the ferroelectric phase near the transition temperature (TC=196K) in Cd2Nb2O7. Raman frequency of the soft mode is used as an order parameter which is calculated from the molecular field theory. On that basis, the damping constant is calculated by fitting the expressions from the pseudospin-phonon coupled model and the energy fluctuation model to the observed linewidth from the literature below TC in Cd2Nb2O7. From our analysis, we find that the molecular field theory is adequate for the soft mode behaviour and that both models are also satisfactory for the divergence behaviour of the damping constant as TC is approached from the ferroelectric phase in Cd2Nb2O7.Values of the activation energy U are extracted from the temperature dependence of the damping constant (HWHM) of the soft mode in the ferroelectric phase of this crystal. Also, the inverse relaxation time is predicted using the Raman frequency and damping constant close to the TC in the ferroelectric phase of Cd2Nb2O7, which increases considerably as TC is approached from the ferroelectric phase, as observed experimentally.

Dielectric relaxation studies of binary mixture of β-picoline and methanol using time domain reflectometry at different temperatures

Complex permittivity spectra of binary mixtures of varying concentrations of [Formula: see text]-picoline and Methanol (MeOH) have been obtained using time domain reflectometry (TDR) technique over frequency range 10 MHz to 25 GHz at 283.15, 288.15, 293.15 and 298.15 K temperatures. The dielectric relaxation parameters namely static permittivity ([Formula: see text]), high frequency limit permittivity ([Formula: see text]) and the relaxation time ([Formula: see text]) were determined by fitting complex permittivity data to the single Debye/Cole-Davidson model. Complex nonlinear least square (CNLS) fitting procedure was carried out using LEVMW software. The excess permittivity ([Formula: see text]) and the excess inverse relaxation time (1/[Formula: see text] which contain information regarding molecular structure and interaction between polar–polar liquids were also determined. From the experimental data, parameters such as effective Kirkwood correlation factor (geff), Bruggeman factor (fB) and some thermo dynamical parameters have been calculated. Excess parameters were fitted to the Redlich–Kister polynomial equation. The values of static permittivity and relaxation time increase nonlinearly with increase in the mol–fraction of MeOH at all temperatures. The values of excess static permittivity ([Formula: see text]E) and the excess inverse relaxation time (1/[Formula: see text] are negative for the studied [Formula: see text]-picoline — MeOH system at all temperatures.

Temperature dependence of the damping constant and the relaxation time close to the tetragonal-cubic phase transition in SrZrO3

The damping constant Γsp due to the pseudospin-phonon coupling is calculated as a function of temperature using the pseudospin-phonon coupled model and the energy fluctuation model close to the tetragonal-cubic transition (TC = 1443 K) in SrZrO3. Using the observed Raman frequencies and the linewidth (FWHM) of the soft modes (Eg and A1g) from the literature, predictions of both models studied, are examined for the tetragonal-cubic transition in this crystalline system. Values of the activation energy U are extracted and also the inverse relaxation time is predicted as a function of temperature close to the phase transition studied in SrZrO3.Divergence behaviour of the damping constant (FWHM) of the soft modes is predicted from both models as also observed experimentally when TC is approached from the tetragonal to the cubic phase in SrZrO3. The relaxation time also diverges close to the TC in this crystal. It is indicated that the tetragonal-cubic transition is of a second order as predicted from both models studied here, as also observed experimentally in SrZrO3.

Influence of temperature on viscoelastic–viscoplastic behavior of poly(lactic acid) under loading–unloading

Experimental data are reported on poly(lactic acid) (PLA) in tensile loading–unloading tests and relaxation tests under stretching and retraction at temperatures ranging from room temperature up to 50°C. Two characteristic features of the time‐dependent response of PLA are revealed: (i) with a decrease in minimum stress under retraction at a fixed temperature, relaxation curves change their shape from monotonically decaying with time (simple relaxation), to non‐monotonic (mixed relaxation) to monotonically increasing (inverse relaxation) and (ii) with an increase in temperature, inverse relaxation after unloading down to the zero stress evolves into mixed relaxation with a pronounced shift of the peak position to smaller relaxation times. Constitutive equations are derived for the mechanical behavior of PLA, and adjustable parameters in the stress–strain relations are found by fitting the observations. Ability of the model to predict the time‐dependent response under cyclic deformation is confirmed by numerical simulation. POLYM. ENG. SCI., 57:239–247, 2017. © 2016 Society of Plastics Engineers

Microwave dielectric relaxation spectroscopy studies on associative polar binary mixtures of nitrobenzene with primary alcohols

The microwave dielectric relaxation behavior of binary mixtures of nitrobenzene with primary alcohols namely ethanol, 1-propanol and 1-butanol has been studied at different temperatures using Time Domain Reflectometry method. The measured complex dielectric spectra of pure and mixture solutions have been fitted with Debye model using least square method. The obtained static dielectric and relaxation time constant values are plotted against mole fraction of solute. The important dielectric parameters such as excess dielectric constant, excess inverse relaxation time and effective Kirkwood correlation factors are computed and the same has been used to interpret the intermolecular interaction and dynamic change in the solution. Furthermore, the mixing effect of nitrobenzene in different chain length alcohols has been explored by concentration dependent excess dielectric constant values. The positive molar enthalpy values of mixtures indicate that the heat energy is absorbed owing to the process of dipole reorientation. Moreover, the heterogeneous interaction between solute and solvent molecular functional groups has been confirmed by equi-molar FT-IR spectra analysis.

Damping Constant (Linewidth) and the Relaxation Time of the Brillouin LA Mode for the Ferroelectric-Paraelectric Transition in PbZr1-xTixO3.

The damping constant (linewidth) of the longitudinal acoustic (LA) mode is calculated as a function of temperature using the observed Brillouin frequencies of this mode from the literature for the ferroelectric-paraelectric transition ( TC = 657 K) in PbZr1-xTixO3 ( x = 0.45 ). For this calculation of the damping constant, the pseudospin-phonon coupled model and the energy fluctuation model are used by fitting to the observed data for the Brillouin frequencies of the LA mode in the ferroelectric ( ) and paraelectric ( T > TC) phases of this compound ( x = 0.45 ). Values of the activation energy are deduced for both ferroelectric and paraelectric phases. The relaxation time is also obtained by means of fitting to the observed data from the literature for the inverse relaxation time at various temperatures in the paraelectric phase of PbZr1-xTixO3. The temperature dependences of the damping constant and of the relaxation time with the values of the activation energy that we have calculated indicate that the pseudospin-phonon coupled model and the energy fluctuation model are capable of describing the ferroelectric-paraelectric transition ( TC = 657 K) in PbZr1-xTixO3 ( x = 0.45 ) adequately.

Thermodynamic and Molecular Dielectric Relaxation Studies of Polar–Polar Binary Mixtures Using Time Domain Reflectometry Technique

The complex dielectric spectra of nitrobenzene, 2-butanol and their binary mixtures were measured in the frequency range of 10 MHz–20 GHz at different temperatures using Time Domain Reflectometry. The static permittivities and relaxation times were extracted from the complex dielectric spectra of the pure compounds and binary mixtures by fitting to the Debye model using the least-squares fitting method. The derived static permittivity (e 0) and dielectric relaxation time (τ 0) values were used to calculate various dielectric parameters including the excess dielectric constant, effective Kirkwood correlation factor, excess inverse relaxation time and thermodynamic parameters. Excess dielectric parameters were fitted with the Redlich–Kister type polynomial equation. The result from dielectric analyses confirms the formation of a heterogeneous complex structure by association of unlike molecules. This hetero-molecule interactions produce a electric field in the mixtures and, as a result, the effective dipoles rotate faster. Molecular rotation and dipole reorientation motions in these complex system are discussed in terms of the molar activation entropy and enthalpy. Additionally, the hydrogen bond interaction between solute and solvent were confirmed by FT–IR spectral analysis.

Brittle fracture in associative polymers: the case of ionomer melts.

Ionomers are interesting due to their applications in coatings, adhesives, films and packaging materials. A study of the underlying mechanisms for fracture in ionomers is consequently of both practical as well as theoretical interest. In this study, we employ high speed imaging coupled with uniaxial extensional rheometry to delineate the mechanics leading to the brittle fracture of ionomer melts. When these ionomers are elongated at a rate higher than the inverse relaxation time of physical crosslinks, an edge fracture occurs at a critical stress. Parabolic fracture profiles provide evidence that the phenomenon is purely elastic and bulk dissipation has little impact on the crack profile. Experimental results are interpreted within the Griffiths theory for linear elastic materials and the de Gennes theory for viscoelastic materials.

Dielectric Relaxation Studies of Binary Mixture of α‐Picoline and Methanol Using Time Domain Reflectometry at Different Temperatures

AbstractComplex permittivity spectra of binary mixtures of varying concentrations of α‐picoline and methanol (MeOH) were obtained using time domain reflectometry (TDR) technique over frequency range 10 MHz to 25 GHz at 283.15 K, 288.15 K, 293.15 K and 298.15 K temperatures. The dielectric relaxation parame‐ ters namely static permittivity (σ0), high frequency limit permittivity (σoo1) and the relaxation time (ρ) were determined by fitting complex permittivity data to the single Debye/Cole‐Davidson model. Complex non linear least square (CNLS) fitting procedure was carried out using LEVMW software. The excess static permittivity (σ0E) and the excess inverse relaxation time (1/ρ)E which contains information regarding mo‐ lecular structure and interaction between polar — polar liquids, were also determined. From the experimental data, effective Kirkwood correlation factor (geff) and Bruggeman factor (fB) were calculated. Excess parameters were fitted to the Redlich‐Kister polynomial equation. The values of static permittivity and relaxation time increase non‐linearly with increase in the mol fraction of MeOH at all temperatures. The values of excess static permittivity (σ0E) and the excess inverse relaxation time (1/ρ)E are negative for the studied α‐picoline — MeOH system at all temperatures.

Convective Cage Release in Model Colloidal Glasses.

The mechanism of flow in glassy materials is interrogated using mechanical spectroscopy applied to model nearly hard sphere colloidal glasses during flow. Superimposing a small amplitude oscillatory motion orthogonal onto steady shear flow makes it possible to directly evaluate the effect of a steady state flow on the out-of-cage (α) relaxation as well as the in-cage motions. To this end, the crossover frequency deduced from the viscoelastic spectra is used as a direct measure of the inverse microstructural relaxation time, during flow. The latter is found to scale linearly with the rate of deformation. The microscopic mechanism of flow can then be identified as a convective cage release. Further insights are provided when the viscoelastic spectra at different shear rates are shifted to scale the alpha relaxation and produce a strain rate-orthogonal frequency superposition, the colloidal analogue of time temperature superposition in polymers with the flow strength playing the role of temperature. Whereas the scaling works well for the α relaxation, deviations are observed both at low and high frequencies. Brownian dynamics simulations point to the origins of these deviations; at high frequencies these are due to the deformation of the cages which slows down the short-time diffusion, while at low frequency, deviations are most probably caused by some mild hydroclustering.

Optically Monitored Electrical Switching in VO2

We demonstrate a hybrid silicon–vanadium dioxide (Si-VO2) electro-optic modulator that enables direct probing of both the electrically triggered semiconductor-to-metal phase transition in VO2 and the reverse transition from metal to semiconductor. By using a two-terminal in-plane VO2 electrical switch atop a single-mode silicon waveguide, the phase change can be initiated electrically and probed optically, separating the excitation and measurement processes and simplifying the analysis of the metal-to-semiconductor dynamics. We demonstrate a record switch-on time for high-speed electrical semiconductor-to-metal transition, with switching times less than 2 ns, and quantify the slower inverse transition, which is dominated by thermal dissipation and relaxation of the metallic rutile lattice to the monoclinic semiconducting phase. By limiting the current through the VO2 to reduce Joule heating, we enable inverse relaxation times as fast as 3 ns.

Dielectric relaxation studies of binary mixture of diethylene glycol mono phenyl ether and methanol by Time Domain Reflectometry

The complex permittivity spectra of binary liquid mixtures of diethylene glycol mono phenyl ether (DEGMPE) with methanol (MeOH) were determined in a frequency range of 10MHz to 25GHz using Time Domain Reflectometry (TDR) at four different temperatures 283.15, 288.15 293.15 and 298.15K, through entire concentration range. The dielectric parameters viz. static permittivity (ε), high frequency limit dielectric permittivity (ε∞1) and relaxation time (τ) have been obtained by CNLS fit method. From the experimental data, parameters such as excess static permittivity (εE), excess permittivity at optical frequency (ε∞E), excess inverse relaxation time (1/τ)E, effective Kirkwood correlation factor (geff), corrective Kirkwood correlation factor (gf) and some thermo-dynamical parameters have been calculated. Excess parameters were fitted to the Redlich–Kister type polynomial equation.

Nonlinear energy dissipation of magnetic nanoparticles in oscillating magnetic fields

The heating of magnetic nanoparticle suspensions subjected to alternating magnetic fields enables a variety of emerging applications such as magnetic fluid hyperthermia and triggered drug release. Rosensweig (2002) [25] obtained a model for the heat dissipation rate of a collection of non-interacting particles. However, the assumptions made in this analysis make it rigorously valid only in the limit of small applied magnetic field amplitude and frequency (i.e., values of the Langevin parameter that are much less than unity and frequencies below the inverse relaxation time). In this contribution we approach the problem from an alternative point of view by solving the phenomenological magnetization relaxation equation exactly for the case of arbitrary magnetic field amplitude and frequency and by solving a more accurate magnetization relaxation equation numerically. We also use rotational Brownian dynamics simulations of non-interacting magnetic nanoparticles subjected to an alternating magnetic field to estimate the rate of energy dissipation and compare the results of the phenomenological theories to the particle-scale simulations. The results are summarized in terms of a normalized energy dissipation rate and show that Rosensweig's expression provides an upper bound on the energy dissipation rate achieved at high field frequency and amplitude. Estimates of the predicted dependence of energy dissipation rate, quantified as specific absorption rate (SAR), on magnetic field amplitude and frequency, and particle core and hydrodynamic diameter, are also given.

Spectral Decomposition of a Fokker–Planck Equation at Criticality

The mean field for a complex network consisting of a large but finite number of random two-state elements, \(M\), has been shown to satisfy a nonlinear Langevin equation. The noise intensity is inversely proportional to \(\sqrt{M} \). In the limiting case \(M = \infty \), the solution to the Langevin equation exhibits a transition from exponential to inverse power law relaxation as criticality is approached from above or below the critical point. When \(M < \infty \), the inverse power law is truncated by an exponential decay with rate \(\varGamma \), the evaluation of which is the main purpose of this article. An analytic/numeric approach is used to obtain the lowest-order eigenvalues in the spectral decomposition of the solution to the corresponding Fokker–Planck equation and its equivalent Schrodinger equation representation.