Relaxation Time Of Mode Research Articles

Understanding the Vibrational Structure and Ultrafast Dynamics of the Metal Carbonyl Precatalyst [Mn(ppy)(CO)4

The solution phase structure, vibrational spectroscopy, and ultrafast relaxation dynamics of the precatalyst species [Mn(ppy)(CO)4] (1) in solution have been investigated using ultrafast two-dimensional infrared (2D-IR) spectroscopy. By comparing 2D-IR data with the results of anharmonic density functional theory (DFT) calculations, we establish an excellent agreement between measured and predicted inter-mode couplings of the carbonyl stretching vibrational modes of 1 that relates to the atomic displacements of axial and equatorial ligands in the modes and the nature of the molecular orbitals involved in M-CO bonding. Measurements of IR pump-probe spectra and 2D-IR spectra as a function of waiting time reveal the presence of ultrafast (few ps) intramolecular vibrational energy redistribution between carbonyl stretching modes prior to vibrational relaxation. The vibrational relaxation times of the CO-stretching modes of 1 are found to be relatively solvent-insensitive, suggestive of limited solvent-solute interactions in the ground electronic state. Overall, these data provide a detailed picture of the complex potential energy surface, bonding and vibrational dynamics of 1, establishing a fundamental basis for the next steps in understanding and modulating precatalyst behavior.

Theory of Nonlinear Diffusion with a Physical Gapped Mode.

In a system with one conserved charge the charge diffusion is modified by nonlinear self-interactions within an effective field theory (EFT) of diffusive fluctuations. We include the slowest ultraviolet (UV) mode, constructing a UV-regulated EFT. The relaxation time of this UV mode is protected from renormalization, as supported by experimental data in a bad metal system. Furthermore, the retarded density-density Green's function acquires four branch points, eventually increasing the range of applicability. We discuss the fate of long time tails as well as implications for the quark gluon plasma.

Non-fourier phonon heat transport in graphene nanoribbon field effect transistors based on modified phonon hydrodynamic lattice Boltzmann method

Graphene, with its exceptional thermal conductivity and electron mobility, is widely recognized as a potential candidate for next-generation transistor materials. Despite the lack of pronounced phonon hydrodynamic phenomena at room temperature in graphene materials, momentum-conserving phonon normal scattering predominantly drives phonon hydrodynamic transport. Current methodologies, including the Single Mode Relaxation Time (SMRT) approximation and Fourier's law, inadequately capture phonon transport within the ballistic and hydrodynamic regimes of graphene. In light of these limitations, this study introduces a Non-gray phonon hydrodynamic lattice Boltzmann method in combination with the Temperature Jump Boundary Condition to provide a more accurate depiction of phonon heat transport in graphene nanoribbon field-effect transistors (GNRFETs) spanning these regimes. The findings reveal that our proposed model significantly mitigates heat transfer errors in GNRFETs, primarily driven by ballistic transport compared to the SMRT model. This suggests that the model's applicability extends beyond scenarios dominated by phonon hydrodynamics and is effective even in cases dominated by ballistic transport. In conclusion, our study emphasizes the impact of hydrodynamic transport on heat transfer in GNRFETs and underscores the importance of adjusting parameters related to the heating zone width and specular parameter to enhance thermal stability.

A mononuclear Fe(III) complex showing thermally induced spin crossover and slow magnetic relaxation with reciprocating thermal behaviour.

AC susceptibility measurements of [FeIII(L5)(NCSe)] reveal a field supported slow magnetic relaxation. On cooling, the relaxation time of the high-frequency fraction decreases which is a sign of reciprocating thermal behaviour. The relaxation time for the low-frequency mode at T = 2.0 K is as high as τ(LF) = 2.0 s.

Phonon non-equilibrium effects on interface thermal resistance between graphene and substrates

Accurate measurement and deep understanding of interfacial thermal transport through interfaces where two-dimensional (2D) materials are involved are crucial for efficient thermal management in nanodevices. However, there is still a large discrepancy in the measurement on the interfacial thermal resistance (ITR) at interfaces between 2D materials and substrates. In this study, two kinds of molecular dynamics techniques are utilized to investigate the ITR of graphene/silicon interfaces under steady-state and transient conditions. Our results indicate that, in both conditions, phonon non-equilibrium phenomena could lead to an overestimation of the interfacial thermal resistance. In the steady state, the overestimation of ITR arises from an exaggerated interfacial temperature difference when using specific vibrational modes as indicators of the sample temperature. In the transient regime, it is attributed to the extended thermal relaxation time of flexural acoustic modes in graphene caused by weak phonon coupling when recording the temperature evolution to extract the ITR. These findings provide a comprehensive understanding of thermal transport across the graphene/silicon interface, aiding in the optimization of graphene-based nanodevices. The study also underlines the necessity of considering the specific experimental setup and physical processes involved when interpreting ITR data obtained from measurements.

Quasi-elastic neutron scattering reveals the relationship between the dynamical behavior of phospholipid headgroups and hydration water.

The dynamics of hydration water (HW) in 1,2-dimyristoyl-sn-glycero-3-phosphoethanolamine (DMPE) was investigated by means of quasi-elastic neutron scattering (QENS) and compared with those observed in 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). The headgroup dynamics of DMPE was investigated using a mixture of tail-deuterated DMPE and D2O, and the QENS profiles were interpreted as consisting of three modes. The fast mode comprised the rotation of hydrogen atoms in -NH3+ and -CH2- groups in the headgroup of DMPE, the medium-speed mode comprised fluctuations in the entire DMPE molecule, and the slow mode comprised fluctuations in the membrane. These interpretations were confirmed using molecular dynamics (MD) simulations. The HW dynamics analysis was performed on a tail-deuterated DMPE and H2O mixture. The QENS profiles were analyzed in terms of three modes: (1) a slow mode, identified as loosely bound HW in the DMPC membrane; (2) a medium-speed mode similar to free HW in the DMPC membrane; and (3) a fast mode, identified as rotational motion. The relaxation time for the fast mode was approximately six times shorter than that of rotational water in DMPC, consistent with the results of terahertz time-domain spectroscopy. The activation energy of medium-speed HW in DMPE differed from that of free HW in DMPC, suggesting the presence of different hydration states or hydrogen-bonded networks around the phosphocholine and phosphoethanolamine headgroups.

Calculation of the damping constant and the relaxation time of the LA mode in the incommensurate phase of quartz

The damping constant (linewidth) of the LA mode is calculated as a function of temperature for the incommensurate (INC) phase of quartz by using the models of the pseudospin-phonon (PS) coupled and the energy fluctuation (EF). For this calculation, the observed linewidth () data are used at and from the literature. Close to the incommensurate phase between the and phases of quartz, the observed and the frequency shifts () are also analyzed by the power-law formula for both pressures ( and ). By using the and the inverse relaxation time () is predicted as a function of temperature ( and ) in the incommensurate phase of quartz and the values of the activation energy () are deduced. Our calculated from both models (PS and EF) explain adequately the observed behavior of the linewidth of the LA mode in the incommensurate phase of quartz. Also, our predicted can be compared with the measurements in the INC phase of this molecular crystal.

Ultrafast scattering dynamics of coherent phonons in Bi1−x Sb x in the Weyl semimetal phase

We investigate ultrafast phonon dynamics in the Bi1−x Sb x alloy system for various compositions x using a reflective femtosecond pump-probe technique. The coherent optical phonons corresponding to the A1g local vibrational modes of Bi–Bi, Bi–Sb, and Sb–Sb are generated and observed in the time domain with a few picoseconds dephasing time. The frequencies of the coherent optical phonons were found to change as the Sb composition x was varied, and more importantly, the relaxation time of those phonon modes was dramatically reduced for x values in the range 0.5–0.8. We argue that the phonon relaxation dynamics are not simply governed by alloy scattering, but are significantly modified by anharmonic phonon–phonon scattering with implied minor contributions from electron–phonon scattering in a Weyl-semimetal phase.

Diffusion Spectrum of Polymer Melt Measured by Varying Magnetic Field Gradient Pulse Width in PGSE NMR.

The translational motion of polymers is a complex process and has a big impact on polymer structure and chemical reactivity. The process can be described by the segment velocity autocorrelation function or its diffusion spectrum, which exhibit several characteristic features depending on the observational time scale—from the Brownian delta function on a large time scale, to complex details in a very short range. Several stepwise, more-complex models of translational dynamics thus exist—from the Rouse regime over reptation motion to a combination of reptation and tube-Rouse motion. Accordingly, different methods of measurement are applicable, from neutron scattering for very short times to optical methods for very long times. In the intermediate regime, nuclear magnetic resonance (NMR) is applicable—for microseconds, relaxometry, and for milliseconds, diffusometry. We used a variation of the established diffusometric method of pulsed gradient spin-echo NMR to measure the diffusion spectrum of a linear polyethylene melt by varying the gradient pulse width. We were able to determine the characteristic relaxation time of the first mode of the tube-Rouse motion. This result is a deviation from a Rouse model of polymer chain displacement at the crossover from a square-root to linear time dependence, indicating a new long-term diffusion regime in which the dynamics of the tube are also described by the Rouse model.

Combined Molecular Dynamics Simulation and Rouse Model Analysis of Static and Dynamic Properties of Unentangled Polymer Melts with Different Chain Architectures

Chain architecture effect on static and dynamic properties of unentangled polymers is explored by molecular dynamics simulation and Rouse mode analysis based on graph theory. For open chains, although they generally obey ideal scaling in chain dimensions, local structure exhibits nonideal behavior due to the incomplete excluded volume (EV) screening, the reduced mean square internal distance (MSID) can be well described by Wittmer’ theory for linear chains and the resulting chain swelling is architecture dependent, i.e., the more branches a bit stronger swelling. For rings, unlike open chains they are compact in term of global sizes. Due to EV effect and nonconcatenated constraints their local structure exhibits a quite different non-Gaussian behavior from open chains, i.e., reduced MSID curves do not collapse to a single master curve and fail to converge to a chain-length-independent constant, which makes the direct application of Wittmer’s theory to rings quite questionable. Deviation from ideality is further evidenced by limited applicability of Rouse prediction to mode amplitude and relaxation time at high modes as well as the non-constant and mode-dependent scaled Rouse mode amplitudes, while the latter is architecture-dependent and even molecular weight dependent for rings. The chain relaxation time is architecture-dependent, but the same scaling dependence on chain dimensions does hold for all studied architectures. Despite mode orthogonality at static state, the role of cross-correlation in orientation relaxation increases with time and the time-dependent coupling parameter rises faster for rings than open chains even at short time scales it is lower for rings.

The dependence of lattice thermal conductivity on phonon modes in pyrochlore‐related Ln2Sn2O7 (Ln = La, Gd)

AbstractRare‐earth pyrochlore materials are promising thermal barrier coatings materials and fundamental understanding of their thermal transport is crucial for further improving its performance. In this work, using density functional theory (DFT) method, we calculated the intrinsic lattice thermal conductivities of Ln2Sn2O7 (Ln = La, Gd) and conducted a comprehensive analysis on the mode thermal conductivity, relaxation time, Grüneisen parameters, group velocity, and specific heat, respectively. It is shown that in pyrochlore‐type materials the number of the optical phonons is much larger than that of the acoustic phonon, and the thermal conductivity of acoustic phonons are suppressed, both of which increase the contribution ratio of optical phonons. Especially, through cumulative analysis, we found that the contribution of optical phonons is significant: the ratio of optical contribution is more than 50% and 64% in La2Sn2O7 and Gd2Sn2O7. This work provides a comprehensive picture illustrating the significant role of the optical phonons in the lattice thermal conduction in rare‐earth pyrochlore materials, and points out an avenue to obtain low thermal conductivity in complex structural thermal insulation materials.

Heat transport in semiconductor crystals: Beyond the local-linear approximation

We extend the application of the nonlocal theory of Mahan and Claro [Phys. Rev. B 38, 1963 (1988)] to solve the steady-state Boltzmann–Peierls transport equation within the framework of the single mode relaxation time approximation using the modified Debye–Callaway model. We consider the case of a semi-infinite semiconductor (SC) crystal with a boundary condition at its top surface that can be considered reasonably representative of time domain thermoreflectance (TDTR) and frequency domain thermoreflectance (FDTR) techniques. The approach allows us to obtain three different contributions to the heat flux density current that shed further light on the fundamental role of nonlocality and nonlinearity in heat transport by phonons in SC crystals. Through their intrinsic and implicit shuffling effect of the crystal momentum, phonon–phonon Normal scattering processes play a key role in the onset of thermal conduction as they introduce the temperature Laplacian as a second driving potential force for the heat flux density current in addition to the conventional Fourier's temperature gradient. The developed model suits quite fairly to interpret the frequency behavior of the reduced effective thermal conductivity of SC crystals that is observed in TDTR and FDTR experiments. We obtain an expression of the effective thermal conductivity of the SC crystal that is characterized with a universal spectral suppression function that captures and describes the role, the weight, and the contribution of quasi-ballistic and non-diffusive phonons. The spectral suppression function only depends on the ratio between the phonon mean free path and the thermal penetration depth as defined based on the diffusive Fourier's law.

Non-hydrodynamic modes in viscoelastic behaviour of simple fluids

ABSTRACT We discuss the role of non-hydrodynamic processes in viscoelastic transition in pure liquids. In particular, using both analytical results and molecular dynamics simulations, we clarify the effect of the shear stress relaxation on the transverse dynamics. We use as an example the Lennard-Jones fluids. We analyse the frequency dependence of the shear modulus and its connection to the non-hydrodynamic shear relaxation mode. The analysis of the relaxation times of the non-hydrodynamic modes in longitudinal and transverse dynamics makes evidence that the emergence of the non-hydrodynamic transverse excitations outside the propagation gap is not directly connected to the onset of the positive sound dispersion.

On relaxation processes in a completely ionized plasma

Relaxation of the electron energy and momentum densities is investigated in spatially uniform states of completely ionized plasma in the presence of small constant and spatially homogeneous external electric field. The plasma is considered in a generalized Lorentz model which contrary to standard one assumes that ions form an equilibrium system. Following to Lorentz it is neglected by electron-electron and ion-ion interactions. The investigation is based on linear kinetic equation obtained by us early from the Landau kinetic equation. Therefore long-range electron-ion Coulomb interaction is consequentially described. The research of the model is based on spectral theory of the collision integral operator. This operator is symmetric and positively defined one. Its eigenvectors are chosen in the form of symmetric irreducible tensors which describe kinetic modes of the system. The corresponding eigenvalues are relaxation coefficients and define the relaxation times of the system. It is established that scalar and vector eigenfunctions describe evolution of electron energy and momentum densities (vector and scalar system modes). By this way in the present paper exact close set of equations for the densities valid for all times is obtained. Further, it is assumed that their relaxation times are much more than relaxation times of all other modes. In this case there exists a characteristic time such that at corresponding larger times the evolution of the system is reduced described by asymptotic values of the densities. At the reduced description electron distribution function depends on time only through asymptotic densities and they satisfy a closed set of equations. In our previous paper this result was proved in the absence of an external electric field and exact nonequilibrium distribution function was found. Here it is proved that this reduced description takes also place for small homogeneous external electric field. This can be considered as a justification of the Bogolyubov idea of the functional hypothesis for the relaxation processes in the plasma. The proof is done in the first approximation of the perturbation theory in the field. However, its idea is true in all orders in the field. Electron mobility in the plasma, its conductivity and phenomenon of equilibrium temperature difference of electrons and ions are discussed in exact theory and approximately analyzed. With this end in view, following our previous paper, approximate solution of the spectral problem is discussed by the method of truncated expansion of the eigenfunctions in series of the Sonine polynomials. In one-polynomial approximation it is shown that nonequilibrium electron distribution function at the end of relaxation processes can be approximated by the Maxwell distribution function. This result is a justification of Lorentz–Landau assumption in their theory of nonequilibrium processes in plasma. The temperature and velocity relaxation coefficients were calculated by us early in one- and two-polynomial approximation.

Dynamic Chelate Effect on the Li+-Ion Conduction in Solvate Ionic Liquids

Lithium–glyme solvate ionic liquids (Li–G SILs), which typically consist of a lithium-ion (Li+) solvated by glymes of oligoethers and its counter anion, are expected as promising electrolytes for lithium secondary batteries. Additionally, a specific ligand-exchange Li+ conduction mechanism was proposed at the electrode/electrolyte interface of the cell using Li–G SILs. To reveal Li+ conduction in SILs, Li–G SILs with varying ethylene oxide chain lengths were investigated using various techniques that are sensitive to solution structure and dynamics. We found good correlations between the relaxation time of the slowest dielectric mode and the ionic conductivity as well as viscosity. We propose that a dynamic chelate effect, which is closely related to solvent exchange and/or contact ion-pair formation/dissociation, is important for Li+ conduction in these Li–G SILs.

Light Scattering Study of Internal Dynamics of Hyperbranched Polymers with Controlled Branching Patterns and Low Polydispersities in Dilute Solutions

Internal dynamics of flexible polymer chains is one of the most important fundamental problems in polymer physics. Although numerous efforts have been devoted to the understanding of internal dynamics for linear polymers, little attention was paid to branched systems. This work aims to elucidate how the branching effect quantitatively influences the internal motions of long-subchain hyperbranched polymers in dilute solution. By light scattering study of four hyperbranched polystyrene samples with controlled branching patterns and low polydispersities (Mw/Mn < 1.40 and Mw ∼ 107 g/mol), we quantified and analyzed the asymptotic behavior of the reduced first cumulant [Γ* = Γ(q)/(q3kBT/η0)], the value of Γ* at high q-regime [the approximate values of Γ*(∞)], the scattering vector (q) dependence of linewidth [Γ(q)], the number of relaxation modes in Γ(q)-distribution curves, the characteristic relaxation time (τ1) of the first internal mode, and the q-dependent relative strength of internal motions. Our results reveal: (i) Γ*(∞) is not sensitive to the branching density, but more related to the fractal dimension of a given system; (ii) the asymptotic power law in the intermediate qRh regime (1.5 < qRh < 3.0), compared to Γ*(∞), is a better indicator, which could reflect the structural details of different branched systems; (iii) the branching effect could lead to the suppression of overall internal motions, but the introduction of moderate branching could enhance the contribution of some energetically favorable internal modes in linewidth distribution; (iv) by comparing the experimentally determined and theoretically calculated τ1, the result provides direct experimental evidence supporting that the classical theory is not applicable to hyperbranched polymer systems. The present work not only helps clarify some long-standing controversial issues existed in previous studies, but also provides useful experimental data for further theoretical calculations of internal dynamics for branched systems.

Incorporating surface polarization effects into large-scale coarse-grained Molecular Dynamics simulation

We implement and extend three methods for incorporating surface polarization effects into coarse-grained Molecular Dynamics (MD) simulations for LAMMPS: the boundary element method using the generalized minimum residual (GMRES) solver for solving the Poisson equation, the induced charge computation method using the successive over relaxations scheme, and the direct optimization of an energy functional of induced charge density. Our implementations are validated against the analytical results for several cases and against published results on electrolyte and polyelectrolyte adsorption on charged interfaces. We have also employed the mentioned methods to examine the effects of surface polarization due to dielectric mismatch on the conformational behavior and relaxation times of the Rouse modes of a highly charged polyelectrolyte with explicit multivalent counterions in a spherical droplet surrounded by a low dielectric medium. We have found that dielectric mismatch coupled with spatial confinement results in noticeable changes in the radius of gyration of the collapsed conformation as well as the work required to compress and stretch the chain. Dielectric confinement is therefore believed to play an important role in the packaging of polyelectrolytes, which was generally overlooked in previous studies. Finally, the parallel performance of the implemented methods for practical simulations is characterized for a model electrolyte system. For polarizable interfaces composed of more than 1000 mesh points, the induced charge computation method is found to be the most efficient.

The Influence of Carbosilane Nanosegregation on the Dynamics in 'de Vries-type' Liquid Crystals.

The mesogens QL32-6, QL33-6 and QL-34-6 contain 5-phenylpyrimidine cores and terminal nanosegregating carbosilane end groups of different lengths and are known to exhibit 'de Vries-type' properties of varying strength. We report a systematic study of the influence of the nanosegregating sublayer on the dynamics and rotational viscosities of the collective modes in the smectic A* (SmA*) and smectic C* (SmC*) phase using dielectric spectroscopy. It was found that the dynamics of the Goldstone mode corresponding to phase angle fluctuations are almost not affected while the relaxation time and rotational viscosity of the soft mode are influenced by the degree of nanosegregation. In other words, the nanosegregating sublayer does not influence the dynamics of ferroelectric switching in the SmC* phase, but is critical in inducing 'de Vries-type' properties.

Spectral concentration of thermal conductivity in GaN—A first-principles study

We find using first-principles analysis of thermal conductivity (k) in isotopically pure Gallium nitride (GaN) that almost 60% of the heat is conducted by phonons in a very narrow frequency range of 5–7 THz (spanning only 9% of the frequencies in GaN). This spectral focusing of thermal conductivity is found to be due to a combination of two effects—a large increase in lifetimes of phonons through suppression of anharmonic scattering in the 5–7 THz frequency range coupled with a large phonon density of states at the same frequencies. Understanding of the effect is provided by solving the phonon Boltzmann transport equation in the single mode relaxation time approximation along with the use of harmonic and anharmonic force constants derived from density functional theory. The results can have important implications for engineering the thermal performance of devices based on GaN.

Modal analysis of the thermal conductivity of nanowires: examining unique thermal transport features

In this study, unique thermal transport features of nanowires over bulk materials are investigated using a combined analysis based on lattice dynamics and equilibrium molecular dynamics (EMD). The evaluation of the thermal conductivity (TC) of Lenard–Jones nanowires becomes feasible due to the multi-step normal mode decomposition (NMD) procedure implemented in the study. A convergence issue of the TC of nanowires is addressed by the NMD implementation for two case studies, which employ pristine nanowires (PNW) and superlattice nanowires. Interestingly, mode relaxation times at low frequencies of acoustic branches exhibit signs of approaching constant values, thus indicating the convergence of TC. The TC evaluation procedure is further verified by implementing EMD-based Green–Kubo analysis, which is based on a fundamentally different physical perspective. Having verified the NMD procedure, the non-monotonic trend of the TC of nanowires is addressed. It is shown that the principal cause for the observed trend is due to the competing effects of long wavelength phonons and phonon–surface scatterings as the nanowire’s cross-sectional width is changed. A computational procedure is developed to decompose the different modal contribution to the TC of shell alloy nanowires (SANWs) using virtual crystal NMD and the Allen–Feldman theory. Several important conclusions can be drawn from the results. A propagons to non-propagons boundary appeared, resulting in a cut-off frequency (ωcut); moreover, as alloy atomic mass is increased, ωcut shifts to lower frequencies. The existence of non-propagons partly causes the low TC of SANWs. It can be seen that modes with low frequencies demonstrate a similar behavior to corresponding modes of PNWs. Moreover, lower group velocities associated with higher alloy atomic mass resulted in a lower TC of SANWs.