Coordination Number Fluctuation Research Articles

Correlation between fragility and cooperativity in bulk metallic glass-forming liquids

It is known that the structural relaxation in supercooled liquid and glassy metals exhibit a non-Debye type relaxation behavior and a VFT-like temperature dependence. Such behaviors are often characterized by the exponent of the Kohlrausch–Williams–Watts (KWW) function and by the value of the fragility. In the present work, a quantity N B which gives the number of structural units involved in the thermally activated viscous flow is introduced to characterize the bulk metallic glass-forming liquids. N B is defined from the Bond Strength – Coordination Number Fluctuation (BSCNF) model of the viscosity. It is shown that N B can be a new indicator that quantifies the degree of cooperativity within the bulk metallic glass-forming liquids. For several bulk metallic glass-forming liquids, it is shown that the characteristic temperature ratio T 0/ T g, N B, and the stretched exponent β KWW are mutually correlated through the fragility index m derived from the BSCNF model.

Viscosity of Metallic Glass Forming Liquids: Analysis Based on Bond Strength-Coordination Number Fluctuations

A model that describes the viscous behavior in terms of the mean values of the bond strength, the coordination number, and their fluctuations of the structural units that form the melt has been proposed by one of the authors. In the present study, the viscous behavior of several metallic glass forming systems are analyzed by using the model. From the analysis, microscopic information such as the number of bonds that must be broken to observe the viscous flow is obtained. It is also shown that when the magnitudes of energy and coordination number fluctuations are equal, the behavior of the viscosity described by our model corresponds perfectly to the behavior described by the Vogel-Fulcher-Tammann (VFT) equation.

Correlation between Ionic Diffusion and Cooperativity in Ionic Liquids

A new physical quantity N B is proposed to analyze the transport properties of ionic liquids. The quantity, which is defined from our model of viscosity, the bond strength – coordination number fluctuation (BSCNF) model, quantifies the degree of cooperativity among the constituent elements in viscous liquids. It is shown that the new quantity N B provides additional information to the conventional transport coefficients such as viscosity, diffusion coefficient, and ionic conductivity. In the present work, the temperature dependence of the activation energies for the diffusion coefficient and the cooperativity described by N B are discussed for several kinds of ionic liquids. The result obtained suggests that the activation energies for the diffusion coefficient and N B are strongly correlated.

Thermodynamic Principles of Metal Binding to Biological Systems

We study the selective binding of the softer K+ ion over the harder Na+ and Mg++ ions to the 58 nucleotide ribosomal RNA fragment and the S2 site of the KcsA K+ channel using all atom MD simulations. The ribosomal RNA is interesting in that it binds the K+ over the harder Mg++ ion. We calculate the free energy of exchanging K+ with Mg++ in the binding site relative to the change in the aqueous solution. In order to explain the selectivity, we find that it is necessary to consider the change in the internal energy of the ion binding site. Interestingly, similar physics is observed in the KcsA S2 site. There we elucidate the role of coordination number fluctuations, ion-site binding energetics, and site-site interaction energetics in determining the selectivity of the S2 site for K+: once again, the reduced strain in the site in the presence of K+ (relative to Na+) explains selectivity. Thus, despite the uncommon origin and completely different chemical composition of the binding site, in both the cases the binding site is constricted in the presence of the harder ion and causes an increase in the unfavorable electrostatic strain. This strain is what leads to the observed selectivity for the softer K+ ion.

Correlation between the temperature range of cooperativity and the fragility index in ion conducting polymers

Abstract The effect of the plasticizer in the ion transport properties of a neat poly-(ethylene oxide), PEO-based ionomer, is investigated by the use of the bond strength–coordination number fluctuation (BSCNF) model of the viscosity. The plasticized forms of PEO-based ionomer considered contain 6 wt.% of six miscible solvents with a wide range of dielectric constants. Recently, based on a relationship derived from the BSCNF that reproduces accurately the Vogel–Fulcher–Tammann (VFT) equation, we have proposed an expression for the fragility index dependence of the normalized temperature range of cooperativity (Tc − Tk) / Tg, where Tk is the Kauzmann temperature and Tc is a crossover temperature that demarcates two distinct dynamical regimes (low-T and high-T) above the glass transition temperature Tg. In the present work, the scope of such an expression is extended to the study of some ion conducting polymers. The values of the fragility index of the materials in consideration here are calculated from the VFT equation. These values of the fragility index enable us to evaluate the characteristic parameters B* and C* of the BSCNF for each material sample. The excellent agreement of the theoretical expression with the experimental data implies that by contrasting the PEO-based ionomer with plasticized forms, the normalized temperature range of cooperativity remains VFT-like. This result reinforces the idea that although the ionic conductivity increases dramatically with plasticization, the mechanism of ion transport remains unchanged.

A model for the temperature dependence of the viscosity in Cu–As–Se system

The microscopic bonding behavior of amorphous Cu x (As 2Se 3) 1− x ( x = 0.00, 0.01, 0.05, 0.10 and 0.20) is studied from the point of view of the viscosity. The model used in this analysis describes the temperature dependence of the viscosity in terms of the mean bond strength E 0, the mean coordination number Z 0, and their fluctuations Δ E, Δ Z of the structural units that form the melt. The model reproduces quite well the temperature dependence of the viscosity of Cu x (As 2Se 3) 1− x observed experimentally. According to the theory, the fragility of the system increases as the fluctuation of the total bond strength increases. It is shown that the viscous flow is accompanied by the cooperative movements of the structural units and occurs by breaking selectively the weaker parts of the bonds between the structural units. This notion is related to the concept of Cooperatively Rearranging Region (CRR) in the theory of Adam–Gibbs. By analyzing the model, the fluctuation of the total bond strength in Cu–As–Se system is evaluated quantitatively, and the composition dependence of the fragility is discussed in terms of bond strength and the coordination number between the structural units. The analysis suggests that in the Cu x (As 2Se 3) 1− x system, there must be a strong composition dependence in the bond strength and a weak composition dependence in the fragility and coordination number fluctuation.

Ab Initio Molecular Dynamics Simulation of the Structure and Proton Transport Dynamics of Methanol−Water Solutions

Ab initio molecular dynamics simulations are employed to study the structural and proton transport properties of methanol-water mixtures. Structural characteristics analyzed at two different methanol mole fractions (X(M) = 0.25 and X(M) = 0.5) reveal enhanced structuring of water as the methanol mole fraction increases in agreement with recent neutron diffraction experiments. The simulations reveal the existence of separate hydrogen-bonded water and methanol networks, also in agreement with the neutron diffraction data. The addition of a single proton to the X(M) = 0.5 mixture leads to an anomalous structural or Grotthuss-type diffusion mechanism of the charge defect in which water-to-water, methanol-to-water, and water-to-methanol proton transfer reactions play the dominant role with methanol-to-methanol transfers being much less significant. Unlike in bulk water, where coordination number fluctuations drive the proton transport process, suppression of the coordination number of waters in the first solvation shell of the defect diminish the importance of coordination number fluctuations as a driving force in the structural diffusion process. The charge defect is found to reside preferentially at the interface between water and methanol networks. The length of the ab initio molecular dynamics run (approximately 120 ps), allowed the diffusion constant of the charge defect to be computed, yielding a value of D = 4.2 x 10(-5) cm2/s when deuterium masses are assigned to all protons in the system. The relation of this value to excess proton diffusion in bulk water is discussed. Finally, a kinetic theory is introduced to identify the relevant time scales in the proton transfer/transport process.

The coordination number fluctuations in liquid metals

The coordination number fluctuations in liquid metals

Cavity distribution in liquid water and hydrophobic hydration

Cavity distributions are examined in liquid water, a Lennard-Jones fluid and an artificial liquid having the same molecular arrangement as water at 25 °C and 1 g/cm −3. It is found that the chemical potential of cavity formation is much reduced in liquid water compared with that of the artificial liquid. This arises from a difference in fluctuation of coordination number around a central molecule. A structural enhancement in water is observed near a large cavity.

Vibrational line broadening in molten nitrate mixtures: A static model for the coordination number and concentration fluctuations

The isotropic Raman spectra of the ν1(A′1) mode of NO−3 are measured in molten NaNO3–TlNO3 mixtures at various concentrations (the mole fraction of NaNO3, 1≥CA≥0) at 600 K. Vibrational correlation functions in mixtures at CA≂0.8–0.5 show a considerable contribution of inhomogeneous vibrational dephasing. A model is presented which accounts simultaneously for the coordination number fluctuation and the concentration fluctuation at the reference anion. Concentration dependence of the isotropic Raman band shape (peak frequency, bandwidth, and asymmetry) is fully explained by the static model for the molten NaNO3–TlNO3 and LiNO3–RbNO3 mixtures. The bandwidths at mole fractions of about 0.5, slightly smaller than those calculated with the static model, suggest a motional narrowing due to diffusion dynamics. The model also makes predictions on the concentration dependence of the spectral line profile in terms of the interaction with the nearest neighbors and diffusion dynamics in liquid mixtures.

Raman spectral studies of the dynamics of ions in molten LiNO3–RbNO3 mixtures. II. Vibrational dephasing: Roles of fluctuations of coordination number and concentration

The isotropic Raman spectra of the ν1 (A′1) mode of NO−3 ions are measured in molten LiNO3–RbNO3 mixtures at various concentrations and at temperatures from 478 to 750 K. The isotropic Raman bandwidth Γiso is found to increase almost linearly with the mole fraction c(Li+) of LiNO3, from 9–13 cm−1 for molten RbNO3 to 26–27 cm−1 for molten LiNO3. Vibrational correlation functions are analyzed on the basis of a model of simultaneous homogeneous and inhomogeneous vibrational dephasing. The contribution of inhomogeneous dephasing was found to be negligibly small in mixtures of c(Li+)≲0.33. While in mixtures of concentrations c(Li+)≳0.5, homogeneous and inhomogeneous processes are found to give comparable contributions to the total vibrational widths, where the latter contribution increases as the temperature decreases. The observed isotropic Raman bands are asymmetric. The asymmetry parameter α=Γ1/Γh , where Γ1 and Γh are the half-widths at half-maximum height of the low and high frequency sides of the band, is larger than one in molten LiNO3 and RbNO3, while α is smaller than one in molten mixtures of concentrations c(Li+)=0.33–0.67. This concentration dependent asymmetry is found to arise predominantly from coordination number fluctuation, i.e., fluctuation of the environmental cation number of a reference NO−3 ion, while concentration fluctuation in the coordination sphere plays a minor role. A model of local environmental states in a molten mixture, which assumes a linear change of vibrational frequency with neighboring cation numbers, is presented. The observed spectral asymmetry can be interpreted by assuming that the equilibrium distribution has a peak at the small coordination number side in pure molten LiNO3 and RbNO3, while the distribution peak shifts to the high coordination number side in molten mixtures.