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Glass transition of metaphosphate glass in the viscosity‐temperature relation
Hiroshi Kobayayashi
National Metrology Institute of Japan
AIST (Retired)
Viscosity of several glasses
Viscosity of glass
h
S
∆l
G
h
S
∆l
G
Strain ε = ∆l / h
Stress σ = G / S
Definitions of shear stress and shear strain
a
ac
b
b
loading
ε (t)
ε’(t’)
t = 0 t = t0t’ = 0
Stra
in ε
(t)
Time (t)
unloading
dt
a
ac
b
b
loading
ε (t)
ε’(t’)
t = 0 t = t0t’ = 0
Stra
in ε
(t)
Time (t)
unloading
dt
ε(t) = a + b[1− exp(−t / τ)] + dt
ε’ (t’) = c + b exp(-t / τ)
Time‐dependence of strain under step‐type stress
stressσ, strainε(t)σ=ηdε(t)/dt
viscosityηη=σ/d
experimental conditions ε(t) ≤ 10‐3,t≤ 5 min.
Definition of shear viscosity
probes mobile plate
specimen fixed plate
furnace
weight
detector pulley
Schematic diagram of apparatus
Viscosity of metaphosphate glass
Viscosity of polystyrene
Viscosity of metallic glasses
By Prof. H. Numakura
of Kyoto Univ.
Viscosity of polymer glasses
Viscosity of aromatic hydrocarbon
Glass transition
・Rearrangements of groups with many molecules.
・Metals with complex molecules or with different
size compositions tend to be glasses.
Big aging effects
Effects of different compositions, and
thermal and mechanical treatments on viscosity
1.00 1.04 1.08 1.12 1.16 1.20 1.248
9
10
11
12
13
14
Tg/T
Log
η (
Pa・
s)
(AgI)0.5(AgPO3)0.5
AgPO3
Viscosity of metaphosphate glass with different compositions
1.00 1.04 1.08 1.12 1.16 1.20 1.248
9
10
11
12
13
14
as received
Polystyrene
annealed
loaded
Tg/T
Log
η (
Pa・
s)
Viscosity of polystyrene
with different treatments
Temperature‐rate dependence of Tg
Two transition temperatures were discovered.
In glass
Disorders Properties different from crystals
Intermediate Range Orders
Particular properties of glasses
including the glass transition
Intermediate Range Order (IRO)
Cooperative Rearranging Region (CRR)
Spatial Heterogeneity (SH)
Cluster
Short range orders in liquidsSize of them is about 2 A.This situation is the same as that in glasses and crystals.
Medium range structures in supercooled liquids
Icosahedron in metallic glassesSize of them is about 5 A.
They are precursors of IROs.
Intermediate range orders Intermediate range orders in glassesin glassesCrystalline nanoclusters or compound nanoclusters Size of them is about 2 nm.They yield their small interfacial energy to form glasses.
Long range orders in glassesNo
Theories for glass transition
• Free volume theory: phenomenal theory• Adam‐Gibbs theory : phenomenal theory• Mode coupling theory: basic theory• Molecular dynamic theory: simulation• Energy landscape theory: simulation• Renormalization group theory: basic theory
No theory can explain the glass transition phenomena.
IROs, which increase in size and number decreasingto Tg, suppress the crystallization of the super liquidsand generate the glass states below Tg.
Activation process with double well potential
Potential barrier height U Activation energy E
Constant E in Arrhenius state Freezing of IROs in glasses
Adam‐Gibbs theory (1965) showsτ = τ0exp(C/TSc)τ: relaxation timeτ0, C: constantsT: temperatureSc: configurational entropy
When Sc is proportional to (T‐T0)/T0,η =η0exp(DT0/(T‐T0) (VTF equation)
η: viscosityη0, D. T0: constants
When Sc is constant,η =η0exp(E/RT) (Arrhenius equation)
E: activation energyR: gas constant
Conclusions• Viscosities do not diverge at any temperature.• Process is a phase transition from the VTF state to the Arrhenius state at Tg with no latent heat.
• Viscosity is more sensitive to the composition, thermal and mechanical treatments in the glass state than in the supercooled liquids.
• New (viscous) transition temperature was discovered at lower than Tg by the DSC.
• Idea of IROs for the glass transition is proposed to explain our data.
The glass transition is due toa self‐organization of the IROsof nanometer orders in size
in the glass state.