Boltzmann distribution as a basic universal expression of activation energy for viscous flow, chemical reactions and mechanical failures

Malyshev, V. P.; Makasheva, A. M.

doi:10.17580/tsm.2018.10.01

Cited by 4 publications

(7 citation statements)

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“…Similar results were obtained by the authors of [28] on the dynamic viscosity of Cu -Sn melt at temperatures of 1100, 1200 and 1300 °C. The viscosity peak area is at the concentration at 15-30 at.% Sn.…”

Section: Methodology and Calculationsupporting

confidence: 90%

“…When comparing the dependence of the enthalpy of mixing on the composition and temperature dependences of viscosity, there is a correlation in the region of maximum formation according to the authors [26][27][28]. In [12] and [26] it is suggested that there is a quantitative relationship between these characteristics (K Т and Т ' mix H…”

Section: Methodology and Calculationmentioning

confidence: 99%

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Relationship between temperature dependence of viscosity of Cu – Sn alloys and phase diagram of state

Makasheva¹,

Malyshev²,

BEKBAYEVA³

2023

nfm

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The relationship between the liquidus line and viscosity isotherms was established for the copper-tin system based on the partial-cluster model within the concept of chaotic particles. The equations of temperature dependences of dynamic viscosity for copper and tin melts, as well as for the partial-cluster model of Cu -Sn alloy at different temperatures are derived. The shapes of the liquidus line curves duplicate the viscosity isotherms from the calculated data, which use smoothed temperature dependences for pure metals Cu and Sn, as well as different thermal chaotization barriers during the transformation of the alloy to the liquid state. The cause of deviation from the regularity of the general features of the liquidus line and viscosity isotherms was found. It consists in the formation of associated complexes of the CuxSny type, which are statistically stable chemical groupings without separation into a separate phase. These complexes (clusters) are in dynamic equilibrium with the solution matrix, characterized by a disorderly distribution of atoms. The formation of such groups is accompanied by the release of heat. This is accounted for in the partial-cluster viscosity model as an additional thermal barrier to chaotization during cluster fracture with further heating of the melt. Consideration of the new component made it possible to obtain an adequate dependence of the viscosity of Cu -Sn alloy on its composition and the thermal barrier on the liquidus line at 1100 °С. Directions for further determination of the model with the purpose of its refinement and wide use in adapting it to experimental data on viscosity at high temperatures of melts from their state diagrams are outlined and verified.

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Section: Methodology and Calculationsupporting

confidence: 90%

Section: Methodology and Calculationmentioning

confidence: 99%

Relationship between temperature dependence of viscosity of Cu – Sn alloys and phase diagram of state

Makasheva¹,

Malyshev²,

BEKBAYEVA³

2023

nfm

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“…This value should be determined on a wide variety of materials in order to identify any regularities in its change or constancy. Previously, in works [19] [20] [21] [22], it was analyzed on contrast data relating to the viscosity of simple substances and complex slag systems, and in all cases the specific activation energy of a viscous flow, E/ā, did not go beyond the energy of the van der Waals forces [23]. Being the weakest and most unsaturated intermolecular bonds, they are overcome in the first place, which makes it possible to argue about the nature of the viscous flow, which consists in breaking the associates without destroying the clusters that retain the binding energy of the particles in a solid state even with their virtual existence [19] [20] [21].…”

Section: Methodical Partmentioning

confidence: 99%

“…Table 4. Reference [24] and calculated by (21) and (22) values of the dynamic viscosity and the degree of association of clusters of liquid potassium chloride. Points-reference data [24], line-by (21).…”

Section: Calculations Of Viscosity Using the Cluster-associate Model mentioning

confidence: 99%

“…to the opposite expression of the exponent of the fraction sign. As shown in[22], only the identity transformation of theFrenkel's equation by taking inverse values in the left and right sides of the equation the original meaning of the probability of overcoming the thermal barrier based on the fundamental Boltzmann's distribution. In this case, inverse dimensional values, by definition, relate to fluidity, and the value of E-to the activation energy of fluidity, and not viscosity, as it formally follows from the Frenkel's equation.…”

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Clusters: Viscosity Cause?

Malyshev¹,

Makasheva²

2019

OJPC

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The significance of the work is determined by the need to develop a cluster theory of the liquid state of a substance in order to more deeply substantiate the viscosity, which is still expressed by empirical parameters within the framework of ideal ideas about the stratified flow of a liquid. According to the reference data on the dynamic viscosity of the melts for chlorides of the first group of the Periodic System, the approximating dependences in the form of cluster-associate and Frenkel's models were constructed at various temperatures. The first model is based on taking into account the share of particles that cannot overcome the thermal melting barrier and thus serve to form virtual clusters and associates while preserving the structural motifs of the solid phase. In the framework of the cluster-associate viscosity model developed by the authors, these formations determine the melt viscosity and serve as flow units to which the energy of fluid motion is applied. The Frenkel's model allows us to estimate the activation energy of fluidity. Calculations show that by comparing this energy with the degree of cluster association obtained in the framework of the cluster-associate model, a fairly close linear correlation is obtained, and the proportionality coefficient has the meaning of the activation energy per cluster. This energy does not go beyond the van der Waals energy of the unsaturated intermolecular bond characteristic of the interaction of particles in a liquid. This confirms the earlier established by the authors a similar pattern for melts of simple substances, based on the understanding of fluidity as a consequence of the destruction of cluster associates while preserving the clusters themselves.

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Relationship between the cluster theory of liquids and the Frenkel—Andrade viscosity model

Malyshev

Makasheva

2020

Russ Chem Bull

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Boltzmann distribution as a basic universal expression of activation energy for viscous flow, chemical reactions and mechanical failures

Cited by 4 publications

References 0 publications

Relationship between temperature dependence of viscosity of Cu – Sn alloys and phase diagram of state

Relationship between temperature dependence of viscosity of Cu – Sn alloys and phase diagram of state

Clusters: Viscosity Cause?

Relationship between the cluster theory of liquids and the Frenkel—Andrade viscosity model

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