Bond Strength Coordination Number Fluctuation Research Articles

Estimations and implications of the mean binding energy and the fluctuation between the structural units in chalcogenide glasses

The mean binding energy and the fluctuation between the structural units in chalcogenide glassy systems are estimated by using the Bond Strength-Coordination Number Fluctuation (BSCNF) model. Chalcogenide glasses can be considered to be formed by an agglomeration of structural units. For this kind of glasses, the structural units are connected to each other by weak intermolecular forces. From the results obtained in the present study, it is suggested that the binding energy estimated by the BSCNF model corresponds to the intermolecular forces between the structural units. The analysis by the BSCNF model also suggests that the viscous flow or the structural relaxation results by breaking the weaker parts of the bonds in the intermolecular connections. This picture of the viscous flow is in agreement with the structural model of covalent glasses and the photo-induced properties in chalcogenide glasses proposed by other authors.

Bond Strength-Coordination Number Fluctuation Model of Viscosity: An Alternative Model for the Vogel-Fulcher-Tammann Equation and an Application to Bulk Metallic Glass Forming Liquids.

The Vogel-Fulcher-Tammann (VFT) equation has been used extensively in the analysis of the experimental data of temperature dependence of the viscosity or of the relaxation time in various types of supercooled liquids including metallic glass forming materials. In this article, it is shown that our model of viscosity, the Bond Strength—Coordination Number Fluctuation (BSCNF) model, can be used as an alternative model for the VFT equation. Using the BSCNF model, it was found that when the normalized bond strength and coordination number fluctuations of the structural units are equal, the viscosity behaviors described by both become identical. From this finding, an analytical expression that connects the parameters of the BSCNF model to the ideal glass transition temperature T0 of the VFT equation is obtained. The physical picture of the Kohlrausch-Williams-Watts relaxation function in the glass forming liquids is also discussed in terms of the cooperativity of the structural units that form the melt. An example of the application of the model is shown for metallic glass forming liquids.

Fractional Exponent of the Modified Stokes-Einstein Relation in the Metallic Glass-Forming Melt Pd<sub>43</sub>Cu<sub>27</sub>Ni<sub>10</sub>P<sub>20</sub>

The diffusion coefficient in the metallic glass-forming systems such as Pd-Cu-Ni-P exhibits a marked deviation from the Stokes-Einstein (SE) relation in the proximity of the glass transition temperature. Such a deviation is characterized by the fractional exponent p of the modified SE expression. For the material Pd43Cu27Ni10P20, it has been reported that it takes the value p = 0.75. In this work, it is shown that the value of p is highly correlated with the ratio ED / ENB, where ED and ENB are the activation energies for diffusion coefficient D and cooperativity NB defined by the Bond Strength-Coordination Number Fluctuation (BSCNF) model. The present paper reports that for the metallic glass-forming melt Pd43Cu27Ni10P20, the fractional exponent p can be calculated accurately within the framework of the BSCNF model.

Theoretical analysis of the temperature and pressure dependences of the viscosity in supercooled liquids

In this paper, a method to analyze the temperature and pressure dependences of the viscosity or of the structural relaxation time in supercooled liquids is shown from the point of view of chemical bonding. The model used in this analysis is the Bond Strength–Coordination Number Fluctuation (BSCNF) model originally proposed by one of the authors. A theoretical relationship between the Vogel temperature T0 of the well-known Vogel-Flucher-Tammann (VFT) equation and our model parameters which contain some microscopic information on bonding connectivity among the structural units that form the melt has been obtained. Using the theoretical relationship, we analyzed the dynamics of two kinds of molecular glass forming liquids under pressure, (a) 4,4'-methylenebis(N,N-diglycidylaniline), and (b) BMPC: 1,1'-di(p-methoxyphenyl)cyclohexane. The result obtained suggests that by applying pressure in these materials, the intermolecular cooperativity is suppressed due to increases in the mean total bond strength and the fluctuations of the structural units.

Pressure dependence of the fragility in metallic glass forming liquids: Predictions from a theoretical model and materials properties correlations

By studying the pressure dependence of the fragility, it is expected that new horizons will open to understand the relaxation behaviour of supercooled liquids. However, as far as the authors are informed, no study has been performed on pressure dependence of the fragility in bulk metallic glass forming systems. In the present study, such dependence is investigated based on materials properties correlations. It is suggested that the effect of pressure on the fragility of bulk metallic glasses is very small. Our analysis indicates also that the fragility of metallic glasses will increase with the application of pressure. This behaviour contrasts with the behaviour observed in molecular systems, where the fragility remains almost constant or decreases slightly with the application of pressure. The result found is discussed in terms of the bond strength-coordination number fluctuation model of the viscosity.

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.

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.

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.