Mode Coupling Theory Approach to the Liquid‐State Dynamics

Bagchi, Biman; Bhattacharyya, S. K.

doi:10.1002/9780470141762.ch2

Cited by 66 publications

(42 citation statements)

References 225 publications

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“…The generalized hydrodynamic matrix T (5T ) (k) generated for transverse five-variable dynamic model (13) was used in the analysis of dynamic eigenvalues and eigenvectors contributing to corresponding time correlation functions (11).…”

Section: 66mentioning

confidence: 99%

“…Upon the success of the hydrodynamic theory in explanation of the three-peak shape of the scattered intensity of light in liquids, 5,6 several generalized schemes were proposed to describe the dynamic structure factors of pure liquids on the boundary and outside the hydrodynamic regime obtained from the inelastic neutron scattering (INS) and Xray scattering (IXS) experiments as well as by molecular dynamics (MD) simulations. [7][8][9] Local and non-local mode coupling approaches [10][11][12][13] were applied to explanation of a deviation of the dispersion of the longitudinal collective modes with increasing wave numbers from the hydrodynamic linear dispersion ω hyd (k) = c s k, where c s is the adiabatic speed of sound. Intensive theoretical studies based on extended kinetic theory [14][15][16] and viscoelastic memory function approach [17][18][19] revealed features of the short-wavelength longitudinal collec- tive excitations, which can even exist outside the first pseudoBrillouin zone in liquids and were also obtained from the analysis of the inelastic neutron scattering experiments.…”

Section: Introductionmentioning

confidence: 99%

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Pressure-induced emergence of unusually high-frequency transverse excitations in a liquid alkali metal: Evidence of two types of collective excitations contributing to the transverse dynamics at high pressures

Bryk

Ruocco

Scopigno

et al. 2015

The Journal of Chemical Physics

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Unlike phonons in crystals, the collective excitations in liquids cannot be treated as propagation of harmonic displacements of atoms around stable local energy minima. The viscoelasticity of liquids, reflected in transition from the adiabatic to elastic high-frequency speed of sound and in absence of the long-wavelength transverse excitations, results in dispersions of longitudinal (L) and transverse (T) collective excitations essentially different from the typical phonon ones. Practically, nothing is known about the effect of high pressure on the dispersion of collective excitations in liquids, which causes strong changes in liquid structure. Here dispersions of L and T collective excitations in liquid Li in the range of pressures up to 186 GPa were studied by ab initio simulations. Two methodologies for dispersion calculations were used: direct estimation from the peak positions of the L/T current spectral functions and simulation-based calculations of wavenumber-dependent collective eigenmodes. It is found that at ambient pressure, the longitudinal and transverse dynamics are well separated, while at high pressures, the transverse current spectral functions, density of vibrational states, and dispersions of collective excitations yield evidence of two types of propagating modes that contribute strongly to transverse dynamics. Emergence of the unusually high-frequency transverse modes gives evidence of the breakdown of a regular viscoelastic theory of transverse dynamics, which is based on coupling of a single transverse propagating mode with shear relaxation. The explanation of the observed high-frequency shift above the viscoelastic value is given by the presence of another branch of collective excitations. With the pressure increasing, coupling between the two types of collective excitations is rationalized within a proposed extended viscoelastic model of transverse dynamics. Unlike phonons in crystals, the collective excitations in liquids cannot be treated as propagation of harmonic displacements of atoms around stable local energy minima. The viscoelasticity of liquids, reflected in transition from the adiabatic to elastic high-frequency speed of sound and in absence of the long-wavelength transverse excitations, results in dispersions of longitudinal (L) and transverse (T) collective excitations essentially different from the typical phonon ones. Practically, nothing is known about the effect of high pressure on the dispersion of collective excitations in liquids, which causes strong changes in liquid structure. Here dispersions of L and T collective excitations in liquid Li in the range of pressures up to 186 GPa were studied by ab initio simulations. Two methodologies for dispersion calculations were used: direct estimation from the peak positions of the L/T current spectral functions and simulation-based calculations of wavenumber-dependent collective eigenmodes. It is found that at ambient pressure, the longitudinal and transverse dynamics are well separated, while at high pressures, the...

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Section: 66mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Pressure-induced emergence of unusually high-frequency transverse excitations in a liquid alkali metal: Evidence of two types of collective excitations contributing to the transverse dynamics at high pressures

Bryk

Ruocco

Scopigno

et al. 2015

The Journal of Chemical Physics

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“…where the longitudinal component of the vertex function, γ l d (k), and the Einstein frequency of the solvent, ω 0 , can be calculated from the solvent-solvent interaction potential, v(r), and the radial distribution factor, g(r), from the following expressions: [37][38][39] γ l d (q) = −m −1 ρ d r exp(−ik · r)g(r)…”

Section: Theory and Calculation Detailsmentioning

confidence: 99%

“…36 The total dynamics is predicted in terms of solute-solvent binary collision and collective structural relaxation through a mode-coupling approach. [37][38][39] Evidently, the binary collision part describes the initial ultrafast response where solvent distribution around a solute at extremely short time is approxi- mated by the equilibrium radial distribution function. 36 This amounts to stating that the solute is trapped inside a solvent cage at short time where collision against the solvent cage carries out the initial phase of the solvation energy relaxation.…”

Section: Introductionmentioning

confidence: 99%

Ultrafast solvation response in room temperature ionic liquids: Possible origin and importance of the collective and the nearest neighbour solvent modes

Daschakraborty

Biswas

2012

The Journal of Chemical Physics

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Recent three-pulse photon echo peak shift (3PEPS) measurements [M. Muramatsu, Y. Nagasawa, and H. Miyasaka, J. Phys. Chem. A 115, 3886 (2011)] with several room temperature ionic liquids (RTILs) have revealed multi-exponential dynamics with ultrafast solvation timescale in the range, 20 < τ(1)∕fs < 250, for both imidazolium and phosphonium RTILs. This is striking for two reasons: (i) the timescale is much faster than those reported by the dynamic Stokes shift (DSS) experiments [S. Arzhantsev, H. Jin, G. A. Baker, and M. Maroncelli, J. Phys. Chem. B 111, 4978 (2007)] and (ii) sub-hundered femtosecond solvation response in phosphonium ionic liquids is reported for the first time. Here, we present a mode coupling theory based calculation where such ultrafast solvation in 3PEPS measurements has been visualized to originate from the nearest neighbour solute-solvent interaction. Consideration of Lennard-Jones interaction for the nearest neighbour solute-solvent non-dipolar interaction leads to biphasic dynamics with a predicted ultrafast time constant in the ∼100-250 fs range, followed by a slower one similar to that reported by the 3PEPS measurements. In addition, the calculated fast time constants and amplitudes are found to be in general agreement with those from computer simulations. Different microscopic mechanisms for ultrafast solvation response measured by the 3PEPS and DSS experiments have been proposed and relative contributions of the collective and nearest neighbour solvent modes investigated. Relation between the single particle rotation and ultrafast polar solvation in these RTILs has been explored. Our analyses suggest 3PEPS and DSS experiments are probably sensitive to different components of the total solvation energy relaxation of a laser-excited dye in a given ionic liquid. Several predictions have also been made, which may be re-examined via suitable experiments.

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“…If A(q) is positive so that the system is stable to fluctuations, then, in equilibrium, the structure factor intensity is I(q) ∼ φ * (q, t)φ(q, t) ∼ η 2 /A(q). The intensity autocorrelation function g 2 (q, ∆t) exhibits an exponential decay with time constant 1/2A(q) [6] so that τ (q) ∼ I (q) . Thus, the classic de Gennes relationship…”

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confidence: 99%

de Gennes Narrowing and the Relationship Between Structure and Dynamics in Self-Organized Ion Beam Nanopatterning

Myint,

Ludwig,,

Wiegart

et al. 2020

Preprint

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Investigating the relationship between structure and dynamical processes is a central goal in condensed matter physics. Perhaps the most noted relationship between the two is the phenomenon of de Gennes narrowing, in which relaxation times in liquids are proportional to the scattering structure factor. Here a similar relationship is discovered during the self-organized ion beam nanopatterning of silicon using coherent x-ray scattering. However, in contrast to the exponential relaxation of fluctuations in classic de Gennes narrowing, the dynamic surface exhibits a wide range of behavior as a function of length scale, with a compressed exponential relaxation at lengths corresponding to the dominant structural motif -self-organized nanoscale ripples. These behaviors are reproduced in simulations of a nonlinear model describing the surface evolution. We suggest that the compressed exponential behavior observed here is due to the morphological persistence of the self-organized surface ripple patterns which form and evolve during ion beam nanopatterning.

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Mode Coupling Theory Approach to the Liquid‐State Dynamics

Cited by 66 publications

References 225 publications

Pressure-induced emergence of unusually high-frequency transverse excitations in a liquid alkali metal: Evidence of two types of collective excitations contributing to the transverse dynamics at high pressures

Pressure-induced emergence of unusually high-frequency transverse excitations in a liquid alkali metal: Evidence of two types of collective excitations contributing to the transverse dynamics at high pressures

Ultrafast solvation response in room temperature ionic liquids: Possible origin and importance of the collective and the nearest neighbour solvent modes

de Gennes Narrowing and the Relationship Between Structure and Dynamics in Self-Organized Ion Beam Nanopatterning

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