Coordination Number Fluctuation Research Articles

Rigid Cations Induce Enhancement of Microheterogeneity and Exhibit Anomalous Ion Diffusion in Water-Ethanol Mixtures.

Because of the amphiphilic nature of ethanol in the aqueous solution, ions cause an interesting microheterogeneity where the water molecules and the hydroxy groups of ethanol preferentially solvate the ions, while the ethyl groups tend to occupy the intervening space. Using computer simulations, we study the dynamics of rigid monovalent cations (Li+, Na+, K+, and Cs+) in aqueous ethanol solutions with chloride as the counterion. We vary both the size of the ions and the composition of the mixture to explore size- and composition-dependent ion diffusion. The relative stability of enhanced microheterogeneous configurations makes ion diffusion slower than what would be surmised by using the bulk properties of the mixture, using the Stokes-Einstein relation. We study the structure through partial radial distribution functions and the stability through coordination number fluctuations. The ion diffusion coefficient exhibits sharp re-entrant behavior when plotted against viscosity varied by composition. Our studies reveal multiple anomalous features of ion motion in this mixture. We formulate a mode-coupling theory (MCT) that takes into account the interaction between different dynamical components; MCT can incorporate the effects of heterogeneous dynamics and nonlinearity in composition dependence that arise from the feedback between mutually dependent ion-solvent dynamics.

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.

Violation of the Harris-Barghathi-Vojta Criterion.

In 1974, Harris proposed his celebrated criterion: Continuous phase transitions in d-dimensional systems are stable against quenched spatial randomness whenever dν>2, where ν is the clean critical exponent of the correlation length. Forty years later, motivated by violations of the Harris criterion for certain lattices such as Voronoi-Delaunay triangulations of random point clouds, Barghathi and Vojta put forth a modified criterion for topologically disordered systems: aν>1, where a is the disorder decay exponent, which measures how fast coordination number fluctuations decay with increasing length scale. Here we present a topologically disordered lattice with coordination number fluctuations that decay as slowly as those of conventional uncorrelated randomness, but for which the clean universal behavior is preserved, hence violating even the modified criterion.

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.

Dynamic Fluctuation of U3+ Coordination Structure in the Molten LiCl-KCl Eutectic via First Principles Molecular Dynamics Simulations.

The dynamic fluctuation of the U3+ coordination structure in a molten LiCl-KCl mixture was studied using first principles molecular dynamics (FPMD) simulations. The radial distribution function, probability distribution of coordination numbers, fluctuation of coordination number and cage volume, self-diffusion coefficient and solvodynamic mean radius of U3+, dynamics of the nearest U-Cl distances, and van Hove function were evaluated. It was revealed that fast exchange of Cl- occurred between the first and second coordination shells of U3+ accompanied with fast fluctuation of coordination number and rearrangement of coordination structure. It was concluded that 6-fold coordination structure dominated the coordination structure of U3+ in the molten LiCl-KCl-UCl3 mixture and a high temperature was conducive to the formation of low coordinated structure.

A Comparative Study of Molecular Motion Cooperativity in Polymeric and Metallic Glass-Forming Liquids

In order to investigate the relationship between the bonding nature and the cooperative relaxation, a comparative study of the relaxation behavior in polymeric and metallic glass forming systems has been performed based on the Bond Strength–Coordination Number Fluctuation (BSCNF) model developed by the authors. In the present work, we studied the correlations between the fragility m, the Vogel temperature T0, the degree of molecular cooperativity NB, and the Kohlrausch exponent βKWW. The results show that T0 and NB increase, whereas βKWW decreases systematically with the increase of m. Reflecting the difference of the interatomic interactions of the materials considered, the analysis by the present study reveals that the value of NB in ion-conducing polymers is about 5 times larger than that in metallic systems, and for each system, the material dependence of βKWW is clearly seen in the fragility index m and the cooperativity NB.

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.

Non-Arrhenius ionic conductivity in solid electrolytes: A theoretical model and its relation with the bonding nature

Some solid electrolytes exhibit the non-Arrhenius type ionic conductivity whose origin is still not well understood. In the present study, a model for the non-Arrhenius ionic conductivity is proposed by exploiting the formulation of the bond strength–coordination number fluctuation (BSCNF) model developed originally to describe the transport properties of supercooled liquids. According to the present model, the origin of the non-Arrhenius ionic conductivity as described by the VFT equation traces back to the bonding energy fluctuations of the diffusing ions within the solid. The model suggests that good ionic conductors exhibit a non-Arrhenius behavior in the ionic conductivity. The present study reveals also that the degree of the non-Arrhenius behavior of different materials is separated roughly into two groups depending on the nature of the chemical bonds. One of these groups consists mainly of compounds such as Ag ion conductors, and the other group contains materials such as Li ion conductors.

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.

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 relationship between diffusivity and cooperativity of supercooled liquids in the proximity of glass transition

In structurally disordered glass-forming liquids, the Stokes–Einstein (SE) law for translational diffusivity is violated, in particular, in the proximity of the glass transition temperature. Usually, the violation of the SE law is explained as due to the decoupling of the diffusivity from the viscous flow. Meanwhile, one of the prominent features observed in the supercooled liquids is the drastic increase of the viscosity with the decrease of temperature. The origin of the increase of the viscosity is attributed to the increase of the molecular motion cooperativity. In the present study, it is shown that the translational diffusivity of glass-forming liquids can be correlated with the cooperativity involved in the thermally activated viscous flow. In the present analysis, the cooperativity is defined in the framework of the bond strength–coordination number fluctuation (BSCNF) model of the viscosity. The result of the analysis suggests that the translational diffusivity is driven by the bond-breaking and bond-switching between the structural units that compose the network structure.

Bond energy and coordination number model for relaxor ferroelectrics

Based on the gaussian-type distributions of bond energy and coordination number for barium titanate systematic ferroelectrics doping with a certain quantity of dopants, the bond energy and coordination number fluctuation model is used to derive the relationship between peak of dielectric constant and testing frequency. The universal Vogel-Fulcher function of the relationship is demonstrated, when the fluctuations of bond energy and coordination number approach to each other. The frozen temperature of the Vogel-Fulcher function is related only to actuation energy and relative fluctuation of bond energy. The mechanisms of dispersion due to homogenous distribution of dopants in low doping concentration and relaxor due to gaussian-type distribution of dopants over a critical concentration are investigated. It is suggested that strong inhibitory effect of substituted ions on formation and growth of ferroelectric domain is the main source of bond energy fluctuation and coordination number fluctuation.

A Study on the Correlation between Fragility and Cooperativity in Wide Class of Glass-forming Substances

The understanding of the cooperativity and heterogeneity in various kinds of glass forming liquids is a hot topic. In the present paper, the relationship between the cooperativity and the fragility has been studied based on the bond strength- coordination number fluctuation model. The model describes the temperature dependence of the viscosity of many kinds of glass forming liquids 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 indicates that the length scale of the cooperativity region in typical fragile systems is about 1 to 3 nm.

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.

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.