RELAXATION ASPECTS OF THE GLASS TRANSITION Damba S. Sanditov 1,2 , - - PowerPoint PPT Presentation

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RELAXATION ASPECTS OF THE GLASS TRANSITION Damba S. Sanditov 1,2 , - - PowerPoint PPT Presentation

Jul 20, 2023 146 likes •446 views

INVITED SCIENTIFIC REPORT 2 RELAXATION ASPECTS OF THE GLASS TRANSITION Damba S. Sanditov 1,2 , Michael I. Ojovan 3,4 1 Buryat State University, Ulan-Ude, 670000, Russia 2 Institute of Physical Material Science, Siberian Branch, Russian Academy of

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INVITED SCIENTIFIC REPORT 2

RELAXATION ASPECTS OF THE GLASS TRANSITION

Damba S. Sanditov1,2, Michael I. Ojovan3,4

1 Buryat State University, Ulan-Ude, 670000, Russia 2 Institute of Physical Material Science, Siberian Branch, Russian Academy of Sciences,

Ulan-Ude, 670047, Russia e-mail: sanditov@bsu.ru

3 Imperial College London, SW7 2AZ, United Kingdom 4Lomonosov Moscow State University, Moscow 119991, Russia

e-mail: m.ojovan@imperial.ac.uk

Joint ICTP-IAEA Workshop “Fundamentals of Vitrification and Vitreous Materials for Nuclear Waste Immobilization”. 6-10.11.2017

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Contents

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  • Background
  • Theories
  • Estimation of glass transition region δTg
  • Model of delocalised atoms
  • Sanditov equation of viscosity
  • Generalised Bartenev equation
  • Kinetic criterion of glass transition
  • Conclusions
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Buryat State University named after Dorjee Banzarov Prof Sanditov

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4 Lake Baikal is the largest freshwater lake by volume in the world, containing 22–23% of the world's fresh surface water. With 23,615.39 km3 of fresh water, it contains more water than the North American Great Lakes combined. With a maximum depth of 1,642 m, Baikal is the world's deepest lake. It is considered among the world's clearest lakes and is considered the world's oldest lake — at 25 million years, making it the most ancient lake in geological history.

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Republic of Buryatia, Ulan-Ude, Buddhist temple

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Ulan-Ude, Monument of Lenin

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Russia, Republic of Buryatia, Lake «Baikal»

  • Lake Baikal is the

largest freshwater lake by volume in the world, containing 22–23% of the world's fresh surface water.

  • With a maximum depth
  • f 1,642 m, Baikal is

the world's deepest lake.

  • The world's oldest lake

— at 25 million years is the most ancient lake in geological history.

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Background

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Bartenev proposed in 1951 the equation that is

  • ften called the main equation of glass transition:

This equation is successfully applied in relaxation spectrometry of polymers and glasses as a condition of structural relaxation transition at T = Tg. The glass transition temperature Tg depends on the cooling rate of the glass-forming melt q = dT/dt. The lower the cooling rate, the lower the glass transition temperature.

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Bartenev-Rittland equation

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Weak dependence: e.g. a changes of q by a order of magnitude (10 times) typically result in about 3% change of Tg (Tg/Tg  0.03)

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Theories

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Condition for glass transition

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A configuron is an elementary configurational excitation in an amorphous material, formed by breaking of a chemical bond and the associated strain-releasing local adjustment of centres of atomic vibration. Formation of a broken bond can be represented as a reaction when a lattice phonon is absorbed by a bond resulting in a un-relaxed broken bond which after relaxation of the surrounding environment results in formation of a quasiparticle termed a configuron ():

     

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Williams-Landel-Ferry equation for relaxation and viscosity

Estimation of Tg

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Fragility and Tg Sanditov equation

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Nemilov estimations

Overestimated data

Volkeistein-Ptitsyn estimations

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  • rganics

inorganics

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Model of delocalized atoms

Fluctuation volume Fraction of fluctuation volume

The fraction of fluctuation volume frozen at glass transition is practically a constant A double-exponent equation for viscosity

WLF constants and delocalized atoms model:

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Sanditov equation of viscosity

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Gutzov suggested the criterion: It gives unrealistic (Nemilov). It is suggested: In terms of Gutzov equation e.g.:

Kinetic criterion of glass transition

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Generalized Bartenev equation

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When lnq<<30 this reduces to

  • riginal Bartenev equation

Sanditov equation

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Conclusions

  • Glass transition of liquid has a pronounced relaxation

character and obeys kinetic laws.

  • The relation between structural relaxation time τ and

cooling rate q = dT/dt is expressed by glass transition equation: qτg = δTg.

  • Calculation of temperature interval δTg using the data on

parameters of Williams-Landel-Ferry equation and the model of delocalized atoms for inorganic oxide glasses is in an agreement with the product qτg≈ (5 – 10) K.

  • An analogous statement is true for organic glasses,

whose δTg have lower values δTg≈(1 – 3) K.

  • Bartenev equation is true at relatively low cooling rates

lnq<<30.

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  • Fraction of the fluctuation volume fg, calculated from

the data on the dependence of Tg on cooling rate of the melt coincides with calculation of fg from the data on viscosity near the glass transition region.

  • A refined version of kinetic criterion of glass transition is

proposed.

  • Excited delocalized atoms are responsible for viscous

flow of glass-forming materials, their concentration during cooling decreases and in the glass transition region reaches negligibly small values (around 3%), which is equivalent to freezing.