Melt Viscosity, Non-Equilibrium Viscosity, & Glass Transition

Practice flashcards for reviewing concepts related to melt viscosity, glass transitions, non-equilibrium states, and thermal history modeling based on Material Kinetics lecture notes.

Viscosity

A measure of the resistance of a melt to shear deformation over time, or the ratio of applied shear stress to the resulting shear strain rate.

Newton's Law of Viscosity

The relationship where the shear viscosity coefficient $\eta$ is defined as $\eta = \frac{\sigma_{xy}}{\dot{\epsilon}_{xy}}$ where $\sigma_{xy}$ is shear stress and $\dot{\epsilon}_{xy}$ is the shear strain rate.

Poise (P)

An older unit of viscosity where the conversion to the standard unit is $1\,\text{Pa}\cdot\text{s} = 10\,\text{Poise}$.

Isocom Temperature

A temperature at which a material reaches a specific, constant viscosity value, used to define reference points on a viscosity-temperature curve.

Melting Point (Glass Industry)

The temperature at which the viscosity is exactly $10^1\,\text{Pa}\cdot\text{s}$ ($10\,\text{Pa}\cdot\text{s}$), allowing sufficient convection for melt homogeneity.

Working Point

The temperature where the melt viscosity is $10^{3}\,\text{Pa}\cdot\text{s}$, typically the stage where the melt is moved to a forming machine.

Softening Point

The temperature at which viscosity is $10^{6.6}\,\text{Pa}\cdot\text{s}$, representing the minimum viscosity required to avoid deformation under the material's own weight.

Annealing Point

The temperature where internal stress is relaxed within minutes, defined at a viscosity of $10^{12}\,\text{Pa}\cdot\text{s}$ or $10^{12.2}\,\text{Pa}\cdot\text{s}$.

Strain Point

The temperature where viscosity is $10^{13.5}\,\text{Pa}\cdot\text{s}$, regarded as the maximum usage temperature for glass and polymer products.

Rotating Cylinder Viscometer

A technique for measuring high-temperature viscosity ($\eta < 10^6\,\text{Pa}\cdot\text{s}$) by measuring the torque required to rotate a cylindrical spindle at a constant speed.

Beam Bending Viscometer

The most accurate method for measuring viscosity ($\eta \sim 10^7 - 10^{12}\,\text{Pa}\cdot\text{s}$) near the annealing and strain points by measuring the deflection rate of a rectangular beam specimen.

Angell Diagram

A plot showing $\log_{10}(\eta)$ as a function of the glass transition temperature scaled by temperature ($T_g/T$) to identify strong and fragile liquids.

Fragility Index ($m$)

A measure of the rate of change of liquid kinetics during cooling through the glass transition, defined as the slope of the $\log_{10}(\eta)$ vs $T_g/T$ plot at $T_g$, where $T_g/T = 1$.

Strong Liquids

Liquids that show Arrhenius-like viscosity scaling with temperature, such as silica ($SiO_2$) and germania ($GeO_2$), and have low indices of fragility.

Fragile Liquids

Liquids that show non-Arrhenius viscosity scaling with temperature, resulting in drastic changes in activation barriers for viscous flow as they cool towards $T_g$.

Vogel-Fulcher-Tammann (VFT) Equation

An empirical equation for the viscosity-temperature relationship: $\log(\eta) = \log(\eta_\infty) + \frac{b}{T - T_0}$ where $\eta_\infty$, $b$, and $T_0$ are fitting parameters.

Avramov-Milchev (AM) Equation

A viscosity model based on atomic jumping and activation energy distributions: $\eta = \eta_\infty \exp\left(\left(\frac{\tau}{T}\right)^\alpha\right)$ where $\eta_\infty$, $\tau$, and $\alpha$ are parameters.

Mauro-Yue-Ellison-Gupta-Allan (MYEGA) Equation

A 3-parameter viscosity model based on entropy that provides physically realistic scaling at both high and low temperature limits.

Adam-Gibbs (AG) Model

A model proposing that atoms in a melt are grouped into Cooperatively Rearranging Regions (CRR), where viscosity is inversely proportional to configuration entropy ($S_{c}$).

Universal Limit of $\eta_\infty$

The universal lower limit for melt viscosity across different chemical compositions, found to be approximately $10^{-2.93}\,\text{Pa}\cdot\text{s}$.

Kauzmann Paradox

The phenomenon where the entropy of a supercooled liquid, if extrapolated linearly to low temperatures, appears to intersect the entropy of the corresponding crystal at a finite temperature ($T_K$).

Bingham Plastic

A non-Newtonian fluid that does not deform until the applied shear stress exceeds a yield point, such as toothpaste or clay suspensions.

Thixotropy

A reversible decrease in viscosity over time due to applied stress, where the change is time-dependent rather than just stress-magnitude dependent (e.g., sweet soy sauce).

Volume Viscosity ($\eta_V$)

A viscous response where the fluid volume changes as a result of hydrostatic pressure, described by $\eta_V = \frac{P-P_0}{\dot{\epsilon}_V}$.

Supercooled Liquid

A liquid state that is cooled below its normal freezing/melting point ($T_m$) while remaining in a metastable equilibrium state without crystallizing.

Glass

A non-equilibrium, kinetically constrained state of matter that possesses a liquid-like (amorphous) structure but solid-like physical properties.

Fictive Temperature ($T_f$)

An order parameter in glass science used to describe the non-equilibrium state, representing the temperature at which the liquid structure was 'frozen' into the glass.

Mauro-Allan-Potuzak (MAP) Model

A modern model that describes non-equilibrium viscosity as a function of temperature ($T$), composition, and fictive temperature ($T_f$).

Isostructural Viscosity

The viscosity regime below the glass transition where the material's atomic configuration is frozen, resulting in Arrhenius-like temperature dependence.

Topology Constraint Theory

A theory that classifies glass networks into flexible ($n < 3$), isostatic ($n = 3$), or stressed rigid ($n > 3$) based on the number of rigid constraints per atom ($n$).

Ergodicity Parameter ($x$)

A parameter defined in the context of the glass transition to describe the transition from an ergodic (liquid) to non-ergodic (glass) state.