Fragility (glass physics)

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The glass transition temperature Tg-scaled Arrhenius plot of fragility of glass forming liquids indicate the distinct behavior of strong and fragile liquids. This representation of fragility is known as an "Angell Plot". Glass Fragility Schematic-en.svg
The glass transition temperature Tg-scaled Arrhenius plot of fragility of glass forming liquids indicate the distinct behavior of strong and fragile liquids. This representation of fragility is known as an "Angell Plot".

In glass sciences, fragility or "kinetic fragility" is a concept proposed by the Australian-American physical chemist C. Austen Angell. Fragility characterizes how rapidly the viscosity of a glass forming liquid approaches a very large value approximately 1012 Pa s during cooling. At this viscosity, the liquid is "frozen" into a solid and the corresponding temperature is known as the glass transition temperature Tg. Materials with a higher fragility have a more rapid increase in viscosity as approaching Tg, while those with a lower fragility have a slower increase in viscosity. Fragility is one of the most important concepts to understand viscous liquids and glasses. Fragility may be related to the presence of dynamical heterogeneity in glass forming liquids, as well as to the breakdown of the usual Stokes–Einstein relationship between viscosity and diffusion. Fragility has no direct relationship with the colloquial meaning of the word "fragility", which more closely relates to the brittleness of a material.

Contents

Definition

Formally, fragility reflects the degree to which the temperature dependence of the viscosity (or relaxation time) deviates from Arrhenius behavior. [1] This classification was originally proposed by Austen Angell. [1] [2] The most common definition of fragility is the "kinetic fragility index" m, which characterizes the slope of the viscosity (or relaxation time) of a material with temperature as it approaches the glass transition temperature from above:

where is viscosity, Tg is the glass transition temperature, m is fragility, and T is temperature. [3] Glass-formers with a high fragility are called "fragile"; those with a low fragility are called "strong". [4] For example, silica has a relatively low fragility and is called "strong", whereas some polymers have relatively high fragility [3] and are called "fragile".

Several fragility parameters have been introduced to characterise the fragility of liquids, including the Bruning–Sutton, [5] Avramov [6] and Doremus fragility parameters. [7] The Bruning–Sutton fragility parameter m relies on the curvature or slope of the viscosity curves. The Avramov fragility parameter α is based on a Kohlraush-type formula of viscosity derived for glasses: strong liquids have α ≈ 1 whereas liquids with higher α values become more fragile. Doremus indicated that practically all melts deviate from the Arrhenius behaviour, e.g. the activation energy of viscosity changes from a high QH at low temperature to a low QL at high temperature. However asymptotically both at low and high temperatures the activation energy of viscosity becomes constant, e.g. independent of temperature. Changes that occur in the activation energy are unambiguously characterised by the ratio between the two values of activation energy at low and high temperatures, which Doremus suggested could be used as a fragility criterion: RD=QH/QL. The higher RD, the more fragile are the liquids, Doremus’ fragility ratios range from 1.33 for germania to 7.26 for diopside melts.

The Doremus’ criterion of fragility can be expressed in terms of thermodynamic parameters of the defects mediating viscous flow in the oxide melts: RD=1+Hd/Hm, where Hd is the enthalpy of formation and Hm is the enthalpy of motion of such defects. Hence the fragility of oxide melts is an intrinsic thermodynamic parameter of melts which can be determined unambiguously by experiment. [8]

The fragility can also be expressed analytically in terms of physical parameters that are related to the interatomic or intermolecular interaction potential. [9] It is given as function of a parameter which measures the steepness of the interatomic or intermolecular repulsion, and as a function of the thermal expansion coefficient of the liquid, which, instead, is related to the attractive part of the interatomic or intermolecular potential. The analysis of various systems (from Lennard-Jones model liquids to metal alloys) has evidenced that a steeper interatomic repulsion leads to more fragile liquids, or, conversely, that soft atoms make strong liquids. [10]

Recent synchrotron radiation X-ray diffraction experiments showed a clear link between structure evolution of the supercooled liquid on cooling, for example, intensification of Ni-P and Cu-P peaks in the radial distribution function close to the glass-transition, and liquid fragility. [11] [12] [13]

Physical implications

The physical origin of the non-Arrhenius behavior of fragile glass formers is an area of active investigation in glass physics. Advances over the last decade have linked this phenomenon with the presence of locally heterogeneous dynamics in fragile glass formers; i.e. the presence of distinct (if transient) slow and fast regions within the material. [1] [14] This effect has also been connected to the breakdown of the Stokes–Einstein relation between diffusion and viscosity in fragile liquids. [14]

Related Research Articles

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Glass is an amorphous or non-crystalline solid. Because it is often transparent and chemically inert, glass has found widespread practical, technological, and decorative use in window panes, tableware, and optics. Some common objects made of glass like "a glass" of water, "glasses", and a "looking glass", have become named for their material.

<span class="mw-page-title-main">Melting</span> Material phase change

Melting, or fusion, is a physical process that results in the phase transition of a substance from a solid to a liquid. This occurs when the internal energy of the solid increases, typically by the application of heat or pressure, which increases the substance's temperature to the melting point. At the melting point, the ordering of ions or molecules in the solid breaks down to a less ordered state, and the solid melts to become a liquid.

<span class="mw-page-title-main">Phase transition</span> Physical process of transition between basic states of matter

In chemistry, thermodynamics, and other related fields like physics and biology, a phase transition is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure. This can be a discontinuous change; for example, a liquid may become gas upon heating to its boiling point, resulting in an abrupt change in volume. The identification of the external conditions at which a transformation occurs defines the phase transition point.

<span class="mw-page-title-main">Supercooling</span> Lowering the temperature of a liquid below its freezing point without it becoming a solid

Supercooling, also known as undercooling, is the process of lowering the temperature of a liquid below its freezing point without it becoming a solid. It is achieved in the absence of a seed crystal or nucleus around which a crystal structure can form. The supercooling of water can be achieved without any special techniques other than chemical demineralization, down to −48.3 °C (−54.9 °F). Supercooled water can occur naturally, for example in the atmosphere, animals or plants.

Vitrification is the full or partial transformation of a substance into a glass, that is to say, a non-crystalline amorphous solid. Glasses differ from liquids structurally and glasses possess a higher degree of connectivity with the same Hausdorff dimensionality of bonds as crystals: dimH = 3. In the production of ceramics, vitrification is responsible for their impermeability to water.

<span class="mw-page-title-main">Amorphous metal</span> Solid metallic material with disordered atomic-scale structure

An amorphous metal is a solid metallic material, usually an alloy, with disordered atomic-scale structure. Most metals are crystalline in their solid state, which means they have a highly ordered arrangement of atoms. Amorphous metals are non-crystalline, and have a glass-like structure. But unlike common glasses, such as window glass, which are typically electrical insulators, amorphous metals have good electrical conductivity and can show metallic luster.

In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain when stretched and immediately return to their original state once the stress is removed.

<span class="mw-page-title-main">Polyamorphism</span> Ability of a substance to exist in more than one distinct amorphous state

Polyamorphism is the ability of a substance to exist in several different amorphous modifications. It is analogous to the polymorphism of crystalline materials. Many amorphous substances can exist with different amorphous characteristics. However, polyamorphism requires two distinct amorphous states with a clear, discontinuous (first-order) phase transition between them. When such a transition occurs between two stable liquid states, a polyamorphic transition may also be referred to as a liquid–liquid phase transition.

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The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity is defined scientifically as a force multiplied by a time divided by an area. Thus its SI units are newton-seconds per square meter, or pascal-seconds.

<span class="mw-page-title-main">Glass transition</span> Reversible transition in amorphous materials

The glass–liquid transition, or glass transition, is the gradual and reversible transition in amorphous materials from a hard and relatively brittle "glassy" state into a viscous or rubbery state as the temperature is increased. An amorphous solid that exhibits a glass transition is called a glass. The reverse transition, achieved by supercooling a viscous liquid into the glass state, is called vitrification.

Johari–Goldstein relaxation, also known as the JG β-relaxation, is a universal property of glasses and certain other disordered materials. Proposed in 1969 by Martin Goldstein, JG β-relaxation were described as a secondary relaxation mechanism required to explain the viscosity behavior of liquids approaching the glass transition in the potential energy landscape picture presented in Goldstein's seminal 1969 paper. Previous experiments on glass forming liquids showed multiple relaxation times present in liquids measured by time dependent compliance measurements. Gyan Johari and Martin Goldstein measured the dielectric loss spectrum of a set of rigid glass forming molecules to further test the hypothesis of Goldstein in 1969. The relaxation, a peak in mechanical or dielectric loss at a particular frequency, had previously been attributed to a type of molecular flexibility. The fact that such a loss peak shows up in glasses of rigid molecules lacking this flexibility demonstrated its universal character.

In condensed matter physics and physical chemistry, the terms viscous liquid, supercooled liquid, and glass forming liquid are often used interchangeably to designate liquids that are at the same time highly viscous, can be or are supercooled, and able to form a glass.

Charles Austen Angell was a renowned Australian and American physical chemist known for his prolific and highly cited research on the chemistry and physics of glasses and glass-forming liquids. He was internationally recognized as a luminary in the fields of glasses, liquids, water and ionic liquids.

In polymer chemistry and polymer physics, the Flory–Fox equation is a simple empirical formula that relates molecular weight to the glass transition temperature of a polymer system. The equation was first proposed in 1950 by Paul J. Flory and Thomas G. Fox while at Cornell University. Their work on the subject overturned the previously held theory that the glass transition temperature was the temperature at which viscosity reached a maximum. Instead, they demonstrated that the glass transition temperature is the temperature at which the free space available for molecular motions achieved a minimum value. While its accuracy is usually limited to samples of narrow range molecular weight distributions, it serves as a good starting point for more complex structure-property relationships.


Dynamical heterogeneity describes the behavior of glass-forming materials when undergoing a phase transition from the liquid state to the glassy state. In dynamical heterogeneity, the dynamics of cooling to a glassy state show variation within the material.

Vitrimers are a class of plastics, which are derived from thermosetting polymers (thermosets) and are very similar to them. Vitrimers consist of molecular, covalent networks, which can change their topology by thermally activated bond-exchange reactions. At high temperatures they can flow like viscoelastic liquids, at low temperatures the bond-exchange reactions are immeasurably slow (frozen) and the Vitrimers behave like classical thermosets at this point. Vitrimers are strong glass formers. Their behavior opens new possibilities in the application of thermosets like as a self-healing material or simple processibility in a wide temperature range.

Alessio Zaccone is an Italian physicist.

The Vogel–Fulcher–Tammann equation, also known as Vogel–Fulcher–Tammann–Hesse equation or Vogel–Fulcher equation, is used to describe the viscosity of liquids as a function of temperature, and especially its strongly temperature dependent variation in the supercooled regime, upon approaching the glass transition. In this regime the viscosity of certain liquids can increase by up to 13 orders of magnitude within a relatively narrow temperature interval.

References

  1. 1 2 3 Debenedetti, P. G.; Stillinger (2001). "Supercooled liquids and the glass transition". Nature. 410 (6825): 259–267. Bibcode:2001Natur.410..259D. doi:10.1038/35065704. PMID   11258381. S2CID   4404576.
  2. ↑ Angell, C. A. (1995). "Formation of Glasses from Liquids and Biopolymers". Science. 267 (5206): 1924–1935. Bibcode:1995Sci...267.1924A. doi:10.1126/science.267.5206.1924. PMID   17770101. S2CID   927260.
  3. 1 2 Novikov, V. N.; Ding, Sokolov (2005). "Correlation of fragility of supercooled liquids with elastic properties of glasses". Physical Review E. 71 (6): 12. Bibcode:2005PhRvE..71f1501N. doi:10.1103/physreve.71.061501. PMID   16089737.
  4. ↑ Ediger, M. D.; Angell, C. A.; Nagel, S. R. (1996). "Supercooled liquids and glasses". Journal of Physical Chemistry. 100 (31): 13200–13212. doi:10.1021/jp953538d.
  5. ↑ Bruning, R.; Sutton, M. (1996). "Fragility of glass-forming systems and the width of the glass transition". J. Non-Cryst. Solids. 205–207: 480–484. Bibcode:1996JNCS..205..480B. doi:10.1016/s0022-3093(96)00264-5.
  6. ↑ Avramov, I. (2005). "Viscosity in disordered media". Journal of Non-Crystalline Solids. 351 (40–42): 3163–3173. Bibcode:2005JNCS..351.3163A. doi:10.1016/j.jnoncrysol.2005.08.021.
  7. ↑ Doremus, R.H. (2002). "Viscosity of silica". J. Appl. Phys. 92 (12): 7619–7629. Bibcode:2002JAP....92.7619D. doi:10.1063/1.1515132.
  8. ↑ Ojovan, M.I.; Travis, K.P.; Hand, R.J. (2007). "Thermodynamic parameters of bonds in glassy materials from viscosity-temperature relationships" (PDF). J. Phys.: Condens. Matter. 19 (415107): 1–12. Bibcode:2007JPCM...19O5107O. doi:10.1088/0953-8984/19/41/415107. PMID   28192319.
  9. ↑ Krausser, J.; Samwer, K.; Zaccone, A. (2015). "Interatomic repulsion softness directly controls the fragility of supercooled metallic melts". Proceedings of the National Academy of Sciences of the USA. 112 (45): 13762–7. arXiv: 1510.08117 . Bibcode:2015PNAS..11213762K. doi: 10.1073/pnas.1503741112 . PMC   4653154 . PMID   26504208.
  10. ↑ Krausser, J.; Lagogianni, A.; Samwer, K.; Zaccone, A. (2017). "Disentangling interatomic repulsion and anharmonicity in the viscosity and fragility of glasses". Physical Review B. 95 (10): 104203. arXiv: 1703.06457 . Bibcode:2017PhRvB..95j4203K. doi:10.1103/PhysRevB.95.104203. S2CID   55455714.
  11. ↑ Mattern, N. (2007). "Structure formation in liquid and amorphous metallic alloys". Journal of Non-Crystalline Solids. 353 (18–21): 1723–1731. Bibcode:2007JNCS..353.1723M. doi:10.1016/j.jnoncrysol.2007.01.042.
  12. ↑ Louzguine-Luzgin, D.V.; Belosludov, R.; Yavari, A. R.; Georgarakis, K.; Vaughan, G.; Kawazoe, Y.; Egami, T.; Inoue, A. (2011). "Structural basis for supercooled liquidfragility established by synchrotron-radiation method and computersimulation" (PDF). Journal of Applied Physics. 11 (4): 043519–043519–6. Bibcode:2011JAP...110d3519L. doi:10.1063/1.3624745.
  13. ↑ Johnson, M. L.; Bendert, J.C.; Kelton, K. F. (2013). "Structural Evolution inNi-Nb and Ni-Nb-Ta Liquids and Glasses – A Measure of Liquid Fragility?". Journal of Non-Crystalline Solids. 362: 237–245. Bibcode:2013JNCS..362..237M. doi:10.1016/j.jnoncrysol.2012.11.022.
  14. 1 2 Angell, C. A.; Ngai, K. L.; McKenna, G. B.; McMillan, P. F.; Martin, S. W. (2000). "Relaxation in glassforming liquids and amorphous solids". Appl. Phys. Rev. 88 (6): 3113–3157. Bibcode:2000JAP....88.3113A. doi:10.1063/1.1286035.
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