Bond Strength-Coordination Number Fluctuation Model Research Articles

Network Relaxation and Cooperativity in Ion Conducting Polymers PEO-Li: An Analysis Based on the BSCNF Model

The understanding of fundamental materials properties is indispensable for the development of functional materials. Some years ago, it has been reported that the fragility in poly (ethylene oxide)-based Li+ ion conductors decreases with the Li+ ion content. The behavior was considered as unexpected and the origin unclear. In the present study, it is shown that the Bond Strength-Coordination Number Fluctuation (BSCNF) model of structural relaxation developed by the present authors provides an explanation to the observed behavior. The analysis based on the BSCNF model indicates that the cooperativity, or the number of correlated structural units involved in the network relaxation decreases with the Li+ ion content.

Model Description of the Unusual Temperature Dependence of the Viscosity of Metallic Glass-Forming Liquids

The temperature dependence of the viscosity of some metallic glass forming liquids (MGFLs) exhibits an unusual behavior. At high temperature, the temperature dependence is quite weak, whereas at low temperature, the viscosity varies exponentially. Recently, this type of behavior are attracting much attention, because it can be considered as a manifestation of the fragile-to-strong transition. Well known classic viscosity models do not describe such kind of behavior over a wide temperature range. In the present report, it is shown that a modified version of the Bond Strength-Coordination Number Fluctuation (BSCNF) model describes the behavior observed in MGFLs. For the convenience of the readers, a brief review of the BSCNF model is also given.

Linking the glass-forming ability to the Arrhenius crossover of structural relaxation

We studied on a link between the Arrhenius crossover (AC) of structural relaxation and the glass-forming ability (GFA) in fragile liquids based on the bond strength–coordination number fluctuation (BSCNF) model proposed by the authors. According to the BSCNF model, an Arrhenius-like relaxation behavior appears at high temperature due to the presence of large fluctuations with strong mean binding energy, which could lead to an enhancement of GFA. We show that this behavior is consistent with the experimental observation in fragile glass-formers and with the thermodynamic liquid model which enables to assess the free energy barrier between amorphous and crystalline phases. In the present study, the implication of the AC-like behavior of fragile systems is discussed in terms of the GFA.

Ionic Diffusion and Dissociation in Room-Temperature Ionic Liquids

The clarification of the degree of ionic dissociation occurring in liquid-electrolyte systems such as those used in current lithium-ion batteries is important from both, fundamental and application points of views. In the present study, based on the bond strength–coordination number fluctuation (BSCNF) model proposed by the authors, we consider the relation between the ionic diffusion and dissociation in room-temperature ionic liquids. Specifically, we show firstly, that the molar conductivity Λ is well correlated with the degree of molecular cooperativity NB defined by the BSCNF model. This correlation enables to connect the cooperativity with the degree of ionic dissociation in ionic liquids. Through the comparison between the ionic diffusion coefficients and the molar conductivity, we discuss on a possible relation between these quantities.

Arrhenius Crossover Phenomena and Ionic Conductivity in Ionic Glass‐Forming Liquids

Herein, the relation between the Arrhenius crossover (AC) behaviors in the structural relaxation and the electrical conductivity relaxation is explored in terms of the Bond Strength–Coordination Number Fluctuation (BSCNF) model developed by the authors. For the ionic glass‐forming liquids and solution examined, Ca2K3(NO3)7, Ca2Rb3(NO3)7, ZBLAN20 and (LiCl)0.16(H2O)0.84, the electric conductivity at high temperature resembles the behavior of the high‐temperature structural relaxation. This mutual relationship suggests a similar origin of the AC behaviors for both, structural and electrical relaxation. The difference between them is reflected in the different temperatures that demarcate the AC behaviors. The implication of this difference to the occurrence of the high ionic conduction via the decoupling mechanism is discussed in terms of the BSCNF model and the fractional Stokes–Einstein law.

The bond strength–coordination number fluctuation model of viscosity: Concept and applications

The viscous flow of materials above the glass-transition temperature is a dissipative process which occurs accompanied by the internal friction and thus involves many-body interactions among the constituent elements. To understand the structural relaxation of supercooled liquids, we have proposed the Bond Strength–Coordination Number Fluctuation (BSCNF) model that describes the temperature dependence of the viscosity in terms of the mean values of the bond strength E0 and the coordination number Z0, and their fluctuations ΔE and ΔZ of the structural units that form the melt. In this work, firstly, after reviewing the concept and formulations of the BSCNF model, we show some applications of the model to polymers and ionic liquids. We also discuss on a theoretical foundation of the VFT law in terms of the BSCNF model, and its relation with the WLF equation is presented. A directionality in the study of structural relaxation is pointed out based on the statistical aspect of the BSCNF model. Finally, in connection with the decoupling mechanism which is crucial to understand the properties of superionic polymer conductors, we mention on the Arrhenius crossover phenomenon in the ionic conduction.

A Model for Non-Arrhenius Ionic Conductivity.

Non-Arrhenius ionic conductivity is observed in various solid electrolytes. The behavior is intriguing, because it limits the magnitude of ionic conductivity at high temperatures. Understanding the nature of this behavior is of fundamental interest and deserves attention. In the present study, the temperature dependence of the ionic conductivity in solids and liquids is analyzed using the Bond Strength–Coordination Number Fluctuation (BSCNF) model developed by ourselves. It is shown that our model describes well the temperature dependence of ionic conductivity that varies from Arrhenius to non-Arrhenius-type behavior. According to our model, the non-Arrhenius behavior is controlled by the degree of binding energy fluctuation between the mobile species and the surroundings. A brief discussion on a possible size effect in non-Arrhenius behavior is also given. Within the available data, the BSCNF model suggests that the size effect in the degree of the non-Arrhenius mass transport behavior in a poly (methyl ethyl ether)/polystyrene (PVME/PS) blend is different from that in a-polystyrene and polyamide copolymer PA66/6I.

Evaluation of a Characteristic Temperature in the Relaxation of Metallic Glass Forming Liquids

The high-temperature viscosity of metallic glass-forming liquids is investigated by using the Bond Strength-Coordination Number Fluctuation (BSCNF) model developed by the authors. For many glass-forming liquids, a salient change in the structural relaxation is observed above the melting point. The temperature dependence of the structural relaxation exhibits a deviation from an Arrhenius-like behavior, and upon cooling it transforms to a non-Arrhenius-like one. In the present study, we show that the BSCNF model describes well the high-temperature viscosity behaviors of metallic liquids. The analysis based on the BSCNF model also enables to extract a characteristic temperature at high temperature. The results of the present study show that such characteristic temperature can be a good indicator for the evaluation of the range of the transition from the Arrhenius-like to the non-Arrhenius-like relaxation behavior.

Analysis and characterization of the transition from the Arrhenius to non-Arrhenius structural relaxation in fragile glass-forming liquids

We have studied the transition from an Arrhenius-like to a non-Arrhenius-like structural relaxation behavior in fragile glass-forming liquids. This transition is denoted by the temperature TA that usually occurs above the melting point Tm and the dynamic crossover temperature TB. Recent studies reveal that TA is a characteristic temperature related with the dynamical properties of the system. However, its unambiguous determination is not easy. In this work, a method to obtain the temperature TA from the experimental data of α-relaxation time is presented. The obtained TA is compared with the cooperativity onset temperature Tx extracted from the bond strength–coordination number fluctuation model. The result reveals that TA is close to Tx for fragile liquids. From the result of the present analyses combined with the linear relation Tx $$\propto$$ T0, where T0 is the Vogel temperature, the Arrhenius crossover phenomenon in fragile liquids is linked to the low-temperature structural relaxation dynamics.

A measure of cooperativity in non-Arrhenius structural relaxation in terms of the bond strength–coordination number fluctuation model

In order to understand the non-Arrhenius structural relaxation in a systematic way, a measure of cooperativity is employed, which is based on the bond strength–coordination number fluctuation model developed by the authors. In our model, the cooperativity is described by the temperature-dependent number of structural units NB involved in the structural relaxation, which increases from unity at the high temperature limit up to of the order of 100 near the glass transition temperature Tg. This is comparable to that estimated by the Donth formula, but is much larger than that obtained from the Adam–Gibbs model. At higher temperature region a characteristic temperature Tx is extracted from the cooperativity analysis, which could be associated with the transition temperature TA across which the relaxation behavior changes from Arrhenius-like to non-Arrhenius-like. In the polymer melts and molecular liquids investigated, the characteristic temperature ratio Tx/Tg is found to be 1.67–1.81, which agrees with the typical TA/Tg values reported. The extracted temperature Tx enables the characterization of the high-temperature relaxation behavior in a new way that differs from other methods. A possible interpretation of TA is given in terms of the cooperativity onset.

Elastic properties and activation energy profiles of viscosity in Ge–Se system across the glass-transition range

The relation between the temperature dependence of shear modulus G(T) and viscosity η(T) of GexSe1−x (0≤x≤0.30) system across the glass-transition range is investigated using several ideas: the Wachtman equation for G, the shoving model and the bond strength–coordination number fluctuation (BSCNF) model of viscosity. Firstly, the present study shows that the empirical Wachtman equation reproduces reasonably well the shear modulus data. Next, it is shown that the shoving model implemented with the analysis of G describes quite well the high viscosity data in the glass state. Besides, the viscosity in the supercooled liquid side, especially for Ge3Se7, exhibits a clear change from Arrhenius-like to VFT-like temperature dependence upon heating. From the viscosity analysis for the composition GeSe4, GeSe3 and Ge3Se7, we obtain a maximum value for the activation energy across the glass-transition range. This result implies that there is an energetic barrier that the structural units need to surmount collectively before the occurrence of the viscous flow. The temperature variation of the activation energy also suggests that in terms of the BSCNF model, the decomposition of network structure upon heating is linked with the collective excitations of the structural units, which gives a viewpoint relevant to the softening of glass.

Development of a Model for Analyzing the Temperature Dependence of the Viscosity of Ion Conducting Polymers and Ionic Liquids

The bond strength-coordination number fluctuation (BSCNF) model of the viscosity developed by the authors considers that the viscous flow occurs by breaking and twisting the connections between the structural units that form the melt. The analytical expression of the viscosity that results from such processes is written in terms of the average bond strength, the average coordination number, and their fluctuations of the structural units. In the present study, we use the BSCNF model to investigate the temperature dependence of the viscosity of ion conducting polymers LiClO4-PPG and NaCF3SO3-PPG, and ionic liquids[bmim][PF6], [bpy] [BF4], [bmpro][(CF3SO2)2N], [bpy] [(CF3SO2)2N] and [bmim][(CF3SO2)2N]. For ion conducting polymers, the analysis of the α-relaxation process is also presented. A case study done for ionic liquids indicates that the cooperativity for molecular motion which is evaluated from the viscosity analysis can be correlated with the diffusion coefficients and the ionic conductivities. The results of this study indicate that the BSCNF model is an effective model that could be used to analyze and interpret the measured temperature dependence of the viscosity.

Analysis of Cooperativity in Metallic Glass Forming Liquids

The relation between fragility and cooperativity of atomic motion in bulk metallic glass forming liquids is studied based on the bond strength-coordination number fluctuation model. The model describes the temperature dependence of the viscosity in terms of the mean values of the bond strength, coordination number and their fluctuations of the structural units that form the melt. According to the model, the cooperativity increases with the increase of fragility. The model estimates that the magnitude of the cooperativity NB extends approximately from 7 to 60 structural units, depending on the material. The temperature dependence of NB for different metallic glass forming systems reveals that NB increases with the decrease of temperature. The relation between NB and diffusivity of atoms is discussed briefly.

Analysis of the ionic conductivity in lithium salt-containing ionic liquids based on the bond strength–coordination number fluctuation model

The temperature dependence of the ionic conductivity of ionic liquids (ILs) and lithium salt mixtures (Li-ILs) that consist of N-methyl-N-propyl-pyrrolidinium (P13+) and 1-ethyl-3-methylimidazolium (emim+) as cations, and bis(trifluoromethanesulfonyl)amide (TFSA−) and bis(fluorosulfonyl)amide (FSA−) as anions has been analyzed in terms of the fractional Stokes–Einstein (FSE) law and the bond strength–coordination number fluctuation (BSCNF) model of viscosity. In the present paper a new expression for the ionic conductivity is introduced to describe the temperature dependence of the ionic conductivity. It is shown that the derived relation of the ionic conductivity is in good agreement with the experimental values for the TFSA−-based ILs and Li-ILs. Meanwhile, a noticeable change in the FSE behavior is confirmed for the case of FSA−-based system. The relation between the molar conductivity Λ and the viscosity η is also discussed based on the fractional form of these quantities, ΛT ∝ (T/η)p, which is in turn, in good agreement with the experimental value for both systems. The present analysis also shows that according to the strong/fragile classification of liquids, the FSA−-based ILs and Li-ILs are stronger than the TFSA−-based ones, implying that the component anions influence qualitatively the difference in electrical and structural relaxations.

Understanding the Vogel–Fulcher–Tammann law in terms of the bond strength–coordination number fluctuation model

It is shown that an expression similar to the Vogel–Fulcher–Tammann (VFT) equation of viscosity can be derived from the bond strength–coordination number fluctuation (BSCNF) model. The parameters BVFT and T0 of the VFT equation, η=η0exp[BVFT/(T−T0)], are related directly to the parameters of the BSCNF model; BVFT≅E0Z0/R and T0≅|ΔE||ΔZ|/R, where E0 and Z0 are the mean values of the bond strength and the coordination number of the structural units, and ΔE and ΔZ are their fluctuations and R is the gas constant. According to the BSCNF model, the viscous flow occurs by breaking or twisting the bonds that connect the structural units of the melt. From the analytical expression obtained in the present study, an expression for the strength parameter D can be also derived. Namely, D is written as D=BVFT/T0≅(E0Z0)/(|ΔE||ΔZ|). This relation indicates that D includes information of the fluctuations that characterize the disorder of glass-forming materials.

A comparative study of the viscosity of ion conducting polymers based on the bond strength-coordination number fluctuation model and other models

According to the bond strength-coordination number fluctuation (BSCNF) model of viscosity proposed some years ago by one of the authors, viscosity is controlled by the relaxation of structural units that form the melt, and is described in terms of the average bond strength, coordination number, and their fluctuations of the structural units. In the present paper, a comparative study of the viscosity of ion conducting polymeric system is presented. The analysis has been done though the BSCNF model and other models widely used in the literature such as Vogel–Fulcher–Tamman and Williams–Landel–Ferry equations. The result reveals that the three models describe well the temperature dependence of the viscosity reported experimentally. As a gross trend, the fragility of the polymeric system in consideration increases with the increase in the concentration of salts. Based on the analysis with the BSCNF model, such a behavior has been interpreted to arise from the disruption of the network that results by the addition of salts. The comparative study also reveals that the BSCNF model could provide a physical interpretation to the empirical parameters used in other models.

Correlation between the nonlinear optical constants and the structural relaxation parameters in chalcogenide glasses

It is well known that chalcogenide glasses exhibit high values of nonlinear optical constants in addition to the widely studied photostructural changes. However, the relations between these properties are not sufficiently understood. On the other hand, according to the bond strength-coordination number fluctuation (BSCNF) model proposed by one of the authors, the viscous behavior is described in terms of the average bond strength, coordination number, and their fluctuations of the structural units that form the system. In the present study, the interrelation between the nonlinear optical constants and the structural relaxation parameters defined from the BSCNF model has been investigated for the case of chalcogenide systems. It is found that the third order nonlinear optical susceptibility increases with the fluctuations of the structural relaxation parameters. The correlation found is discussed based on the BSCNF model and the average electronegativity.

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.