Proton Glass Research Articles

Replica Symmetric Solutions of Random Field Tunneling Model for Proton Glasses

We investigate for the replica-symmetric solutions of the tunneling model proton glass with longitudinal random field of Gaussian distribution. From the replica-symmetric solutions we obtain phase diagrams for each random field distribution, especially the de Almeida-Thouless stability lines in the temperature ( T ) - average interaction strength ( J 0 ) plane and also in the temperature ( T ) - external longitudinal field ( H ) plane.

Nonlinear Susceptibility in Random Field Tunneling Model for Proton Glass

Replica-symmetric solution of the transverse tunneling model for proton glass with longitudinal Gaussian random field is employed to obtain an analytic solution of the nonlinear susceptibility h nl . The results show smearing of the nonlinear susceptibility near the glass transition by the Gaussian random field. Both the cusp anomaly of linear susceptibility and the divergence of nonlinear susceptibility are thus suppressed by random fields of Gaussian distribution.

Nonlinear Susceptibility in Random Field Tunneling Model for Proton Glass

Replica-symmetric solution of the transverse tunneling model for proton glass with longitudinal Gaussian random field is employed to obtain an analytic solution of the nonlinear susceptibility h nl . The results show smearing of the nonlinear susceptibility near the glass transition by the Gaussian random field. Both the cusp anomaly of linear susceptibility and the divergence of nonlinear susceptibility are thus suppressed by random fields of Gaussian distribution.

1/f noise and dynamical heterogeneity in glasses.

We investigate the relationship between two experimental sets of data related to dynamical heterogeneity, the coefficient alpha of 1/f(alpha) dipolar noise derived from the nonexponentiality of the dielectric or magnetic response near and above the mean relaxation time, and the range Delta(z) of the relaxation times. We find that in different classes of glasses, including spin and proton glasses, relaxor materials, and glass-forming liquids, this relationship exhibits the same trend.

Dynamical effects in quantum droplet model of Ising spin glass in a transverse field

The equilibrium behaviour of linear dynamical susceptibility is investigated in terms of quantum Ising spin glass droplet model. The imaginary part of linear ac susceptibility χ″( ω, T) as function of temperature T and frequency of external ac field ω is analytically calculated on the basis of the linear dynamical response theory. It is found that such dependence of χ″( ω, T) shows a glassy behaviour. A qualitative agreement with experimental data, for example, in quantum dipole magnet LiHo x Y 1− x F 4 and proton glass is found.

Acoustic anomalies in quasi-2D Cs5H3(SO4)4×x H2O crystal

The paper describes Brillouin light scattering studies of longitudinal acoustic (LA)phonons in Cs5H3(SO4)4×x H2O (PCHS) crystals attemperatures from 100 K to 360 K.The acoustic response of the crystal at different frequencies is analysed in detail.It is shown that boththe velocity and damping of sound exhibit a strong dispersion caused by relaxationprocesses in the region of transformation into the glass-like phase (Tg≈260 K).A strong anisotropy in theacoustic response, attributable to the quasi-two dimensional (quasi-2D) structure of PCHS,is revealed.The LA phonon damping is calculated in the framework of a number of relaxationmodels.It is shown that, in the vicinity of Tg, anomalies in ultrasonic damping ofthe LA phononspropagating in the basal plane reflect the cooperative effect of freezing of acid protons.At thesame time, the anomaly in damping of the LA phonon propagating perpendicular to the basal planeis described in terms of the Debye model and is due to the interaction between protonson hydrogen bonds and LA phonons.This suggests that the proton glass state realized at T<Tg is ofquasi-2D nature.

Evidence for a quasi-two-dimensional proton glass state in Cs5H3(SO4)(4); xH(2)O Crystals.

We describe damping of hypersonic and ultrasonic longitudinal acoustic (LA) phonons in crystals of Cs 5H (3)(SO (4))(4);xH 2O (PCHS) between 100 and 360 K. The damping of LA phonons exhibits strong dispersion caused by relaxation processes in the region of transformation into the glasslike phase (T(g) approximately 260 K). Near T(g) the damping of ultrasonic phonons propagating in the basal plane reflects the cooperative freezing of acid protons. The damping of LA phonons propagating perpendicular to the basal plane can be fit by the Debye model and is due to the interaction between protons and LA phonons. This suggests that the proton glass state that is realized at T<T(g) has a quasi-two-dimensional nature.

Phase coexistence of hyderogen-bonded mixed crystals

The complex dielectric constants and polarization of the hydrogen-bonded mixed crystals, K1−x(NH4)xH2PO4 and Rb1−x(NH4)xH2AsO4, near the ferroelectric-proton glass phase boundary have been investigated as a function of temperature. Coexistence of both phases was discovered from a glassy dispersion at low temperature and a ferroelectric anomaly. The dielectric dispersion due to the coexisting proton glass state occurred at lower temperatures than for pure proton glass composition. The detection of polarization after field-cooling or zero field-cooling the sample showed that the ferroelectric domain and polarization were retained in the glass freezing process. These results are qualitatively consistent with the expectation of the infinite ranged random-bond random-field model in the presence of macroscopic polarization.

Hydration water, charge transport and protein dynamics.

The hydration water of proteins is essential to biological activity but its properties are not yet fully understood. A recent study of dielectric relaxation of hydrated proteins [A. Levstik et al., Phys. Rev E.60 7604 (1999)] has found a behavior typical of a proton glass, with a glass transition of about 268 K. In order to analyze these results, we investigate the statistical mechanics and dynamics of a model of `two-dimensional water' which describes the hydrogen bonding scheme of bounded water molecules. We discuss the connection between the dynamics of bound water and charge transport on the protein surface as observed in the dielectric measurements.

Dielectric1/fnoise of proton glass on a hydrated protein surface

From nonexponentiality of dielectric relaxation detected in hydrated lysozyme powder we evaluate the power spectrum x(2)(omega) of the fluctuating dipole moment X(2) of one macromolecule, due to the glass of protons migrating on the protein surface. Near room temperature, the contribution to the total dipole moment by the integrated strength of the 1/f(alpha) noise in the frequency range from 10(4) to 10(6) Hz, is well consistent with early Kirkwood's predictions in solution and more recent computations. The biochemical significance of the nonequilibrium region near the Vogel-Fulcher temperature T0 approximately 268 K calls for further investigations.

LOW TEMPERATURE LINEAR DYNAMICAL SUSCEPTIBILITY OF THE ISING SPIN GLASS IN A TRANSVERSE FIELD

Low-temperature equilibrium dynamical behavior of the linear ac susceptibility in d-dimensional Ising spin glass with short-range interactions between spins in transverse field is investigated in terms of droplet model. The real part of linear ac susceptibility [Formula: see text] as functions of temperature T and frequency of external ac field ω is calculated. Frequency and temperature dependence of [Formula: see text] shows a glassy behavior. For instance, we find a broad maximum for [Formula: see text] which shifts towards higher temperatures with increasing frequency of ac-field. The temperature of maximum Tf(ω) depends on frequency and increases with frequency up to the magnitude where [Formula: see text] starts to decrease. A qualitative agreement of our calculations with experimental data, for example, in quantum dipole magnet LiHoxY1-xF4 and proton glasses, is found.

Study of the anisotropic dielectric behavior ofRb1−x(NH4)xH2PO4(x=0.15and 0.17) mixed crystals

The complex dielectric constants and polarization of the mixed crystals of ${\mathrm{Rb}}_{1\ensuremath{-}x}({\mathrm{NH}}_{4}{)}_{x}{\mathrm{H}}_{2}{\mathrm{PO}}_{4}$ (RADP) with $x=0.15$ and 0.17 have been measured along the tetragonal a and c axes as a function of temperature. Phase coexistence of ferroelectric order and proton glass in RADP can be confirmed from a dielectric dispersion distinguished from the ferroelectric domain wall freezing at low temperature. The dielectric dispersion, which was ascribed to the proton glass state, occurred at much lower temperatures compared to pure proton glass composition. The detection of depolarization after field-cooling or zero-field cooling the sample, showed that the ferroelectric domain and polarization were retained in the glass freezing process. The result is qualitatively consistent with the expectation of the mean-field model in the presence of macroscopic polarization. The phase coexistence may be a common feature of ${\mathrm{KH}}_{2}{\mathrm{PO}}_{4}$ family mixed crystals.

Dipolar glass phase and non ergodic behavior in (BP)0.15(BPI)0.85

The dipolar freezing in the proton glass (BP)0.15(BPI)0.85. investigated through thermal cycles involving pyroelectric effect measurements, with zero bias and 1.8 kV/cm, evidenced the ergodic to non ergodic phase transition, confirming the quasi-static freezing of the dipoles in the proton glass phase.

Proton freezing in hydrated lysozyme powders

The dielectric relaxation of hydrated powder of the protein lysozyme has suggested a behavior typical of proton glasses. An analysis by a temperature-frequency plot presented here revealed that ergodicity would be broken due to the divergence of the longest relaxation time at 266 K, thus indicating that this hydrated protein belongs indeed to a proton glass family. However, the temperature behavior of the static dielectric constant and the average relaxation frequency indicates a transition near 273 K which precedes the glassy freezing transition. This transition deserves further study, since it seems that its origin cannot be trivially connected to the formation of bulk ice.

Pressure effect on the proton glass Rb1minus;x(NH4)xH2PO4: A neutron study

The effect of a hydrostatic pressure on RADP compound is studied by means of elastic and inelastic neutron scattering. From the diffuse incommensurate scattering, a phase diagram for freezing is established. At a given pressure, freezing temperatures are always higher than those derived from dielectric measurements. Transverse acoustic phonons are also studied under a pressure of 5kbar. They exhibit a strong damping at low temperature in contrast to their behaviour at atmospheric pressure. The piezoelectric coupling model accounts for these results.

Proton glass freezing in hydrated lysozyme powders.

At room temperature, the dielectric relaxation of hydrated powder of the protein lysozyme is known to be due to protons migrating between ionized side chains. A recent study of this relaxation at lower temperatures suggested a behavior typical of proton glasses. An analysis of the complex dielectric susceptibility by a temperature-frequency plot presented here has revealed that ergodicity is broken due to the divergence of the longest relaxation time at 266 K, indicating specifically that this hydrated protein is a proton glass. A change in the temperature behavior of the static dielectric constant and the average relaxation frequency at 273 K indicates a further transition occurring at this temperature, whose nature remains to be investigated.

Protonic conductivity in KH2PO4 family studied by NMR

Protonic conductivity in the KH2PO4 family of hydrogen-bonded insulators has been studied via the proton NMR lineshape and the decay of the NMR transverse nuclear spin magnetization of 87Rb nuclei in a spatially inhomogeneous electric field gradient. A large difference in the time scales of the decays of Hahn spin echo and Carr–Purcell echo train was observed. The Hahn echo decay curves show an exponential decay with the exponent proportional to the cube of time that is characteristic for diffusive motions. The proton NMR spectrum demonstrates the presence of mobile protons which produce a motionally narrowed absorption line above 220 K. The same effects were observed in several pure ferroelectric and antiferroelectric members of the KH2PO4 family as well as in their mixtures – the proton glasses.

Dielectric relaxation of a proton glass in hydrated protein powders

Dielectric relaxation in the kHz to MHz range displayed by hydrated powders of the protein lysozyme at room temperature is mainly due to protons migrating between ionized side chains. Quite recently we have measured the frequency and temperature dependence of this relaxation, and we have detected the freezing to a broad distribution of relaxation times, typical of proton glasses. Below the freezing temperature of about 270 K the system is not ergodic, in analogy with the behavior of proton glass crystals made up by random mixtures of ferro- and antiferroelectric compounds.

Protonic inter-H-bond motion and ionic conductivity in hydrogen-bonded proton glasses

Low-frequency dynamics of the hydrogen-bonded proton glass ${\mathrm{Rb}}_{1\ensuremath{-}x}{(\mathrm{N}\mathrm{H}}_{4}{)}_{x}{\mathrm{H}}_{2}{\mathrm{AsO}}_{4}$ and its deuterated form has been investigated by measuring the decay of the NMR transverse nuclear-spin magnetization of ${}^{87}\mathrm{Rb}$ nuclei in a spatially inhomogeneous electric-field gradient, ${}^{1}\mathrm{H}$ line shape and ${}^{2}\mathrm{H}$ two-dimensional exchange NMR techniques. A large difference in the time scales of the decay of Hahn echo and Carr-Purcell echo train was observed between room temperature and 10 K. The Hahn echo decay curves showed an exponential decay with the exponent proportional to the cube of time that is characteristic for random stochastic atomic motions. The proton NMR spectrum demonstrates the presence of mobile protons which produce a motionally narrowed absorption line above 220 K. Two-dimensional exchange NMR experiment on the deuterated glass demonstrated the existence of slow thermally activated deuteron hopping between different hydrogen bonds, the process that represents the ionic conductivity. The same effects were observed also in several pure compounds of the ${\mathrm{KH}}_{2}{\mathrm{PO}}_{4}$ family. The observed low-frequency dynamics is not a peculiarity of the proton glass phase but represents the protonic inter-H-bond motion and ionic conductivity that is a common feature of the ${\mathrm{KH}}_{2}{\mathrm{PO}}_{4}$ family.

Phase coexistence in proton glass

Proton glasses are crystals of composition M1−x(NW4)xW2A04, where M = K,Rb,Cs, W = H,D, A = P, As. For x = 0 there is a ferroelectric (FE) transition, while for x-1 there is an antiferroelectric (AFE) transition. In both cases, the transition is from a paraelectric (PE) state of tetragonal structure with dynamically disordered hydrogen bonds to an ordered state of orthorhombic structure. For an intermediate x range there is no transition, but the hydrogen rearrangements slow down, and eventually display nonergodic behavior characteristic of glasses. We and others have shown from spontaneous polarization, dielectric permittivity, nuclear magnetic resonance, and neutron diffraction experiments that for smaller x there is coexistence of ferroelectric and paraelectric phases, and for larger × there is coexistence of antiferroelectric and paraelectric phases. We present a method for analytically describing this coexistence, and the degree to which this coexistence is spatial and/or temporal. We discuss also the experimental determination of these coexistence parameters.