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'''Editor-In-Chief:''' Henry A. Hoff | |||
==Overview== | |||
Some of the internal kinetic energy of amorphous substances can be in the form of interparticle bonds. A broken interparticle [[chemical bond]] and associated strain-releasing local adjustment in centers of [[vibration]] form a '''configuron''', an elementary configurational excitation in an [[amorphous]] material.<ref name=Angell>{{cite journal|author=Angell CA, Rao KJ |year=1972|month= |title= Configurational excitations in condensed matter, and "bond lattice" model for the liquid-glass transition|journal=J Chem Physics. |volume=57 |issue=1 |pages=470–81|doi= 10.1063/1.1677987 }}</ref> Configurons help to understand the transition from a [[solid]] to a [[fluid]] with viscous flow. | |||
==Introduction== | |||
An amorphous [[substance]] is any in which there is no long-range order over the positions of its constituent particles; i.e., no [http://en.wikipedia.org/wiki/Translational_symmetry translational periodicity]. Some of the internal [[kinetic energy]] of these substances can be in the form of interparticle bonds. The particles making up an amorphous substance can range in size from an [[electron]] to [http://en.wikipedia.org/wiki/Star stars] in a [http://en.wikipedia.org/wiki/Galaxy galaxy] or galaxies in a [http://en.wikipedia.org/wiki/Galaxy_groups_and_clusters galactic cluster]. [[Water]] is an amorphous substance that also can be [[Crystal|crystalline]]. Amorphous substances undergo transitions from solid to liquid, solid to gas, or liquid to gas, or gas to plasma, for example. | |||
The chemical bonding within many amorphous substances can produce short-range order while there is long-range disorder. The short-range order is often a symmetrical arrangement of polyhedra. The long-range disorder can be approached with the disordered arrangement of space-filling polyhedra. These polyhedra are bonded together in a solid and undergo bond breaking through the transitions from solid to fluid. A model based on the configuron or configurational microstate<ref name=Angell1>{{ cite book |author=Angell CA |title=Chapter 1. Glass formation and the nature of the glass transitions, ''in'' Insulating and semiconducting glasses, Volume 17 of Series on directions in condensed matter physics |publisher=World Scientific |year=2000 |editor=Boolchand P |pages=1-54 |isbn=9810236735, 9789810236731 }}</ref> is an approach to understanding the [[viscosity]] changes that occur with changes in temperature. | |||
==Amorphous substances== | ==Amorphous substances== | ||
The particles in an amorphous substance can be [[Subatomic particle|subatoms]], [[atom]]s, [[ion]]s, [[molecules]], [[dust]], [http://en.wikipedia.org/wiki/Crystallite crystallites], or [http://en.wikipedia.org/wiki/Particle_size_(grain_size) grains], stones, [http://en.wikipedia.org/wiki/Boulders boulders], or larger [[debris]]. | The particles in an amorphous substance can be [[Subatomic particle|subatoms]], [[atom]]s, [[ion]]s, [[molecules]], [[dust]], [http://en.wikipedia.org/wiki/Crystallite crystallites], or [http://en.wikipedia.org/wiki/Particle_size_(grain_size) grains], stones, [http://en.wikipedia.org/wiki/Boulders boulders], or larger [[debris]]. From the point of view of bonding by [[Gravitation|gravity]] the [http://en.wikipedia.org/wiki/Universe universe] is an amorphous substance. | ||
{{wiktionarypar|stone}} | {{wiktionarypar|stone}} | ||
Amorphous substances can fall into the usual categories of [[Amorphous solid|solid]], [[liquid]], [[gas]], or [[Plasma (physics)|plasma]]. But some substances which are amorphous, such as [http://en.wikipedia.org/wiki/Sand| sand] are [[fluid]]s. | Amorphous substances can fall into the usual categories of [[Amorphous solid|solid]], [[liquid]], [[gas]], or [[Plasma (physics)|plasma]]. But some substances which are amorphous, such as [http://en.wikipedia.org/wiki/Sand| sand], are [[fluid]]s. | ||
Water as a liquid has much of the available kinetic energy expressed through additional [http://en.wikipedia.org/wiki/Degrees_of_freedom_(physics_and_chemistry) degrees of freedom] than [[water vapor]]. Some of this energy is in the form of intermolecular bonds. These bonds are a resistance to flow. [[Water]] has a resistance to flow that is considered relatively "thin", having a lower [[Viscosity#Viscosity of water|viscosity]] than other liquids such as [[vegetable oil]]. At 25°C, water has a nominal viscosity of 1.0 × 10<sup>-3</sup> Pa∙s and motor oil has a nominal apparent viscosity of 250 × 10<sup>-3</sup> [[pascal (unit)|Pa]]∙[[second|s]].<ref name=Raymond>{{cite book|author=Raymond A. Serway| title=Physics for Scientists & Engineers|edition=4th Edition| publisher=Saunders College Publishing| year=1996|isbn=0-03-005932-1 }}</ref> | Water as a liquid has much of the available kinetic energy expressed through additional [http://en.wikipedia.org/wiki/Degrees_of_freedom_(physics_and_chemistry) degrees of freedom] than [[water vapor]]. Some of this energy is in the form of intermolecular bonds. These bonds are a resistance to flow. [[Water]] has a resistance to flow that is considered relatively "thin", having a lower [[Viscosity#Viscosity of water|viscosity]] (µ<sub>L</sub>) than other liquids such as [[vegetable oil]]. At 25°C, water has a nominal viscosity of 1.0 × 10<sup>-3</sup> Pa∙s and motor oil has a nominal apparent viscosity of 250 × 10<sup>-3</sup> [[pascal (unit)|Pa]]∙[[second|s]].<ref name=Raymond>{{cite book|author=Raymond A. Serway| title=Physics for Scientists & Engineers|edition=4th Edition| publisher=Saunders College Publishing| year=1996|isbn=0-03-005932-1 }}</ref> | ||
[[Viscosity#Viscosity of amorphous materials|Viscous flow]] in [[Amorphous solid|amorphous materials]] such as water is a thermally activated process:<ref name=Ojovon>{{cite journal|author=Ojovan MI, Lee WE|year=2004 |title=Viscosity of network liquids within Doremus approach |journal=J Appl Phys.|volume=95|issue=7|pages=3803–10 | doi = 10.1063/1.1647260|unused_data=|month}}</ref> | [[Viscosity#Viscosity of amorphous materials|Viscous flow]], which results from viscosity, in [[Amorphous solid|amorphous materials]] such as water is a thermally activated process as is viscosity:<ref name=Ojovon>{{cite journal|author=Ojovan MI, Lee WE|year=2004 |title=Viscosity of network liquids within Doremus approach |journal=J Appl Phys.|volume=95|issue=7|pages=3803–10 | doi = 10.1063/1.1647260|unused_data=|month}}</ref> | ||
:<math>{\ | :<math>{\mu_L} = A_L \cdot e^{Q_L/RT},</math> | ||
where ''Q<sub>L</sub>'' is the activation energy in the liquid state, ''T'' is temperature, ''R'' is the molar gas constant and ''A'' is approximately a constant. | where ''Q<sub>L</sub>'' is the activation energy in the liquid state, ''T'' is temperature (K), ''R'' is the molar gas constant and ''A<sub>L</sub>'' is approximately a constant. | ||
With | With | ||
:< | : Q<sub>L</sub> ≥ H<sub>m</sub>, | ||
where H<sub>m</sub> is the enthalpy of motion of the broken hydrogen bonds. | where H<sub>m</sub> is the enthalpy of motion of the broken hydrogen bonds. | ||
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==Solid-liquid transition in amorphous substances== | ==Solid-liquid transition in amorphous substances== | ||
In principle, given a sufficiently high cooling rate, any liquid can be made into an [[amorphous solid]]. Cooling reduces molecular mobility. If the cooling rate is faster than the rate at which molecules can organize into a more thermodynamically favorable [[Crystal|crystalline]] state, then an amorphous solid will be formed. Because of [[entropy]] considerations, many polymers can be made into amorphous solids by cooling even at slow rates. In contrast, if molecules have sufficient time to organize into a structure with two- or three-dimensional order, then a crystalline (or [http://en.wikipedia.org/wiki/Crystallinity semi-crystalline]) solid is formed. Water is one example. Because of its small molecular size and ability to quickly rearrange, it cannot be made amorphous without resorting to specialized hyperquenching techniques. These produce [[amorphous ice]], which has a quenching rate in the range of metallic glasses.<ref name=Ojovan>{{cite journal |author=Ojovan MI |year=2008|month=Sep |title= Configurons: thermodynamic parameters and symmetry changes at glass transition |journal=Entropy. |volume=10 |pages=334–64 |doi= 10.3390/e10030334 |http://www.mdpi.org/entropy/papers/e10030334.pdf }}</ref> | In principle, given a sufficiently high cooling rate, any liquid can be made into an [[amorphous solid]]. Cooling reduces molecular mobility. If the cooling rate is faster than the rate at which molecules can organize into a more thermodynamically favorable [[Crystal|crystalline]] state, then an amorphous solid will be formed. Because of [[entropy]] considerations, many [[polymers]] can be made into amorphous solids by cooling even at slow rates. In contrast, if molecules have sufficient time to organize into a structure with two- or three-dimensional order, then a crystalline (or [http://en.wikipedia.org/wiki/Crystallinity semi-crystalline]) solid is formed. Water is one example. Because of its small molecular size and ability to quickly rearrange, it cannot be made amorphous without resorting to specialized hyperquenching techniques. These produce [[amorphous ice]], which has a quenching rate in the range of metallic glasses.<ref name=Ojovan>{{cite journal |author=Ojovan MI |year=2008|month=Sep |title= Configurons: thermodynamic parameters and symmetry changes at glass transition |journal=Entropy. |volume=10 |pages=334–64 |doi= 10.3390/e10030334 |http://www.mdpi.org/entropy/papers/e10030334.pdf }}</ref> | ||
The higher the temperature of an amorphous material the higher the configuron concentration. The higher the configuron concentration the lower the viscosity. As configurons form percolating clusters, an amorphous solid can transition to a liquid. This clustering facilitates viscous flow. Thermodynamic parameters of configurons can be found from viscosity-temperature relationships.<ref name=Ojovan/> | The higher the temperature of an amorphous material the higher the configuron concentration. The higher the configuron concentration the lower the viscosity. As configurons form [http://en.wikipedia.org/wiki/Percolation percolating] [http://en.wikipedia.org/wiki/Cluster clusters], an amorphous solid can transition to a liquid. This clustering facilitates viscous flow. Thermodynamic parameters of configurons can be found from viscosity-temperature relationships.<ref name=Ojovan/> | ||
==Short-range order== | ==Short-range order== | ||
Like a liquid an amorphous solid has a topologically disordered distribution of particles but elastic properties of an isotropic solid. The symmetry similarity of both liquid and solid phases cannot explain the qualitative differences in their behavior. | Like a liquid an amorphous solid has a [http://en.wikipedia.org/wiki/Topology topologically] disordered distribution of particles but [[Elasticity (physics)|elastic]] properties of an [[Isotropy|isotropic]] solid. The [[symmetry]] similarity of both liquid and solid phases cannot explain the qualitative differences in their behavior. | ||
Due to [[chemical bonding]] characteristics amorphous solids such as [[Glass|glasses]] do possess a high degree of short-range order with respect to local atomic [[Polyhedron|polyhedra]].<ref name=Salmon>{{ cite journal |author=Salmon PS |title=Amorphous materials: Order within disorder |url=http://www.nature.com/nmat/journal/v1/n2/abs/nmat737.html |journal=Nature Materials. |volume=1 |issue=2 |year=2002 |pages=87-8 |doi=10.1038/nmat737 }}</ref> The amorphous structure of glassy silica has no long range order but shows [http://en.wikipedia.org/wiki/Glass local ordering] with respect to the [[tetrahedral]] arrangement of oxygen atoms around silicon atoms. | Due to [[chemical bonding]] characteristics amorphous solids such as [[Glass|glasses]] do possess a high degree of short-range order with respect to local atomic [[Polyhedron|polyhedra]].<ref name=Salmon>{{ cite journal |author=Salmon PS |title=Amorphous materials: Order within disorder |url=http://www.nature.com/nmat/journal/v1/n2/abs/nmat737.html |journal=Nature Materials. |volume=1 |issue=2 |year=2002 |pages=87-8 |doi=10.1038/nmat737 }}</ref> The amorphous structure of glassy silica has no long range order but shows [http://en.wikipedia.org/wiki/Glass local ordering] with respect to the [[tetrahedral]] arrangement of oxygen atoms around silicon atoms. | ||
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==Bond structure== | ==Bond structure== | ||
One useful approach is to consider the bond system instead of considering the set of particles that form the substance.<ref name=Ojovan/> For each state of matter we can define the set of bonds by a bond lattice model.<ref name=Ojovan/> The congruent bond lattice for amorphous | One useful approach is to consider the bond system instead of considering the set of particles that form the substance.<ref name=Ojovan/> For each state of matter we can define the set of bonds by a bond [http://en.wikipedia.org/wiki/Lattice_model_(physics) lattice model].<ref name=Ojovan/> The [http://en.wikipedia.org/wiki/Congruence congruent] bond lattice for amorphous [[Materials science|material]]s is a disordered structure. Moreover the bond lattices of amorphous solids and liquids may have different symmetries in contrast to the [[symmetry]] similarity of particles in a liquid or fluid and solid phases. | ||
For an amorphous material a given unit can be delimited by its nearest neighbors so that its structure may be characterized by a distribution of [http://en.wikipedia.org/wiki/Voronoi_diagram Voronoi polyhedra] filling the space of the disordered material. Molecular dynamics simulations have revealed that the difference between a liquid and glass of an amorphous material results from the formation of percolation clusters of broken bonds in the Voronoi network.<ref name=Medvedev>{{ cite journal |author=Medvedev NN, Geider A, Brostow W |title=Distinguishing liquids from amorphous solids: Percolation analysis on the Voronoi network |journal=J Chem Phys. |year=1990 |month= |volume=93 |issue= |pages=8337-42 }}</ref> | For an amorphous material a given unit can be delimited by its nearest neighbors so that its structure may be characterized by a distribution of [http://en.wikipedia.org/wiki/Voronoi_diagram Voronoi polyhedra] filling the space of the disordered material. [[Molecular dynamics|Molecular dynamics simulations]] have revealed that the difference between a liquid and glass of an amorphous material results from the formation of percolation clusters of broken bonds in the [http://en.wikipedia.org/wiki/Voronoi_diagram Voronoi network].<ref name=Medvedev>{{ cite journal |author=Medvedev NN, Geider A, Brostow W |title=Distinguishing liquids from amorphous solids: Percolation analysis on the Voronoi network |journal=J Chem Phys. |year=1990 |month= |volume=93 |issue= |pages=8337-42 }}</ref> | ||
==[http://en.wikipedia.org/wiki/Hausdorff_dimension Hausdorff dimension]== | ==[http://en.wikipedia.org/wiki/Hausdorff_dimension Hausdorff dimension]== | ||
The Hausdorff dimension (d) generalizes the notion of the dimension of a real [[Vector (spatial)|vector space]]. In particular, the Hausdorff dimension of a single point is zero, | The Hausdorff dimension (d) generalizes the notion of the dimension of a real [[Vector (spatial)|vector space]]. In particular, the Hausdorff dimension of a single point is zero, a line is one, a plane is two, a solid is three, etc. The Hausdorff dimension can be thought of as the power of radii for a set of space filling balls formally expressed by | ||
:<math>C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i>0\Bigr\}.</math> | :<math>C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i>0\Bigr\}.</math> | ||
where C is the space (S)-filling Content of a countable number (the index number - i) of balls whose radii are dimensioned to produce the space-filling balls. | where C is the space (S)-filling Content of a countable number (the index number - i) of balls whose radii (r<sub>i</sub>) are dimensioned (volumed) to produce the space-filling balls. | ||
In three dimensions, the balls can be spheres of many different radii and the volume of each ball is proportional to its r<sup>3</sup>. Hence the Hausdorff dimension, d = 3. In four dimensions, the balls can be [[Multivariate normal distribution#Geometric interpretation|hyperspheres]] of many different radii and the volume of each ball is proportional to its r<sup>4</sup>. Consider a sphere that changes its radius with time. At each time the sphere has a finite radius r<sub> | In three dimensions, the balls can be spheres of many different radii and the volume of each ball is proportional to its r<sup>3</sup>. Hence the Hausdorff dimension, d = 3. In four dimensions, the balls can be [[Multivariate normal distribution#Geometric interpretation|hyperspheres]] of many different radii and the volume of each ball is proportional to its r<sup>4</sup>. Consider a sphere that changes its radius with time. At each time the sphere has a finite radius r<sub>ti</sub> that differs from each t-1(i-1) before and after t+1(i+1). The volume calculated is proportional to r<sub>space-filling</sub><sup>4</sup> that equals the space occupied for all time. | ||
[http://en.wikipedia.org/wiki/Fractals Fractals] often are spaces whose Hausdorff dimension strictly exceeds the [[Dimension#Lebesgue covering dimension|topological dimension]]. A 2-dimensional fractal has a Hausdorff dimension, d as 2<d<3. | [http://en.wikipedia.org/wiki/Fractals Fractals] often are spaces whose Hausdorff dimension strictly exceeds the [[Dimension#Lebesgue covering dimension|topological dimension]]. A 2-dimensional fractal has a Hausdorff dimension, d as 2<d<3. | ||
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Amorphous ice is used in some scientific experiments, especially in [[electron cryomicroscopy]] of biomolecules.<ref name=Dubochet>{{ cite journal |author=Dubochet J, Adrian M, Chang JJ, Homo JC, Lepault J, McDowell AW, Schultz P |title=Cryo-electron microscopy of vitrified specimens |journal=Q Rev Biophys. |volume=21 |pages=129-228 |year=1988 }}</ref> The individual molecules can be preserved for imaging in a state close to what they are in liquid water. | Amorphous ice is used in some scientific experiments, especially in [[electron cryomicroscopy]] of biomolecules.<ref name=Dubochet>{{ cite journal |author=Dubochet J, Adrian M, Chang JJ, Homo JC, Lepault J, McDowell AW, Schultz P |title=Cryo-electron microscopy of vitrified specimens |journal=Q Rev Biophys. |volume=21 |pages=129-228 |year=1988 }}</ref> The individual molecules can be preserved for imaging in a state close to what they are in liquid water. | ||
Hydrated proteins may also be classed among glass-forming systems, but they show great departures from thermorheological simplicity.<ref name=Green>{{ cite journal |author=Green JL, Fan J, Angell CA |title=The protein-glass analogy: some insights from homopeptide comparisons |journal=J Phys Chem. |month=Dec |year=1994 |volume=98 |issue=51 |pages=13780-90 |doi=10.1021/j100102a052 }}</ref> | |||
==Enthalpy of motion for water configurons== | ==Enthalpy of motion for water configurons== | ||
A simple estimate of | A simple estimate of Q<sub>L</sub> can be obtained by using the two temperatures 0°C and 100°C, where µ=1.79 x 10<sup>-3</sup> Pa·s at 0°C and 0.28 x 10<sup>-3</sup> Pa·s at 100°C, and solving for A<sub>L</sub> and Q<sub>L</sub>. A<sub>L</sub> = 7.7 x 10<sup>-7</sup> Pa·s and Q<sub>L</sub> = 18 kJmol<sup>-1</sup>. R=8.314472 JK<sup>-1</sup>mol<sup>-1</sup>. Temperature is in K (273.15 + °C). Q<sub>L</sub> includes the energy to break the hydrogen bond and move the configuron, as such H<sub>M</sub> ≤ Q<sub>L</sub>. Using | ||
A<sub>L</sub> and Q<sub>L</sub> to calculate the viscosity of water and comparing the calculated values to the experimentally determined ones for a [http://en.wikipedia.org/wiki/Viscosity#Viscosity_of_water range of temperature values] shows that there is a systematic deviation at the higher temperatures. As the data for the viscosity of water vapor is [http://en.wikipedia.org/wiki/Viscosity#Viscosity_of_water available], A<sub>V</sub> and Q<sub>V</sub> can be estimated: A<sub>V</sub> ~ 1.2 x 10<sup>-4</sup> Pa·s and Q<sub>V</sub> ~ - 6.0 kJmol<sup>-1</sup>. This added to the calculated configuron contribution | |||
:<math>{\mu_L} = A_L \cdot e^{Q_L/RT} + A_V \cdot e^{Q_V/RT},</math> | |||
improves the fit to the liquid water viscosity data remarkably well, suggesting that like other gas molecules mixed into water, water vapor can also be.<ref name=Hyatt>{{ cite journal |author=Hyatt MT, Levinson HS |title=Water Vapor, Aqueous Ethyl Alcohol, and Heat Activation of Bacillus megaterium | |||
Spore Germination |journal=J Bacteriol. |month=Jun |year=1968 |volume=95 |issue=6 |pages=2090-101 |pmid=4970224 }}</ref> | |||
== Acknowledgements == | == Acknowledgements == | ||
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==References== | ==References== | ||
{{reflist}} | {{reflist|2}} | ||
==See also== | ==See also== | ||
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*[[Amorphous ice]] | *[[Amorphous ice]] | ||
*[[Glass]] | *[[Glass]] | ||
*[http://en.wikipedia.org/wiki/Slump Slump] | |||
*[http://geology.about.com/library/bl/images/blslump.htm Slump Landslide] | |||
==External links== | ==External links== | ||
*[http://www.lsbu.ac.uk/water/amorph.html Discussion of amorphous ice] at [[London South Bank University|LSBU]]'s website. | *[http://www.lsbu.ac.uk/water/amorph.html Discussion of amorphous ice] at [[London South Bank University|LSBU]]'s website. | ||
*[http://www.sciencemag.org/cgi/content/summary/294/5550/2305?rbfvrToken=765f39b90461f7428be6054763df6aa5a115d711 Glassy Water] from [[Science (journal)|Science]], on [[phase diagram]]s of water (requires registration) | *[http://www.sciencemag.org/cgi/content/summary/294/5550/2305?rbfvrToken=765f39b90461f7428be6054763df6aa5a115d711 Glassy Water] from [[Science (journal)|Science]], on [[phase diagram]]s of water (requires registration) | ||
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[[Category:Homogeneous chemical mixtures]] | [[Category:Homogeneous chemical mixtures]] | ||
{{WH}} | {{WH}} | ||
{{WS}} | {{WS}} | ||
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Editor-In-Chief: Henry A. Hoff
Overview
Some of the internal kinetic energy of amorphous substances can be in the form of interparticle bonds. A broken interparticle chemical bond and associated strain-releasing local adjustment in centers of vibration form a configuron, an elementary configurational excitation in an amorphous material.[1] Configurons help to understand the transition from a solid to a fluid with viscous flow.
Introduction
An amorphous substance is any in which there is no long-range order over the positions of its constituent particles; i.e., no translational periodicity. Some of the internal kinetic energy of these substances can be in the form of interparticle bonds. The particles making up an amorphous substance can range in size from an electron to stars in a galaxy or galaxies in a galactic cluster. Water is an amorphous substance that also can be crystalline. Amorphous substances undergo transitions from solid to liquid, solid to gas, or liquid to gas, or gas to plasma, for example.
The chemical bonding within many amorphous substances can produce short-range order while there is long-range disorder. The short-range order is often a symmetrical arrangement of polyhedra. The long-range disorder can be approached with the disordered arrangement of space-filling polyhedra. These polyhedra are bonded together in a solid and undergo bond breaking through the transitions from solid to fluid. A model based on the configuron or configurational microstate[2] is an approach to understanding the viscosity changes that occur with changes in temperature.
Amorphous substances
The particles in an amorphous substance can be subatoms, atoms, ions, molecules, dust, crystallites, or grains, stones, boulders, or larger debris. From the point of view of bonding by gravity the universe is an amorphous substance.
Amorphous substances can fall into the usual categories of solid, liquid, gas, or plasma. But some substances which are amorphous, such as sand, are fluids.
Water as a liquid has much of the available kinetic energy expressed through additional degrees of freedom than water vapor. Some of this energy is in the form of intermolecular bonds. These bonds are a resistance to flow. Water has a resistance to flow that is considered relatively "thin", having a lower viscosity (µL) than other liquids such as vegetable oil. At 25°C, water has a nominal viscosity of 1.0 × 10-3 Pa∙s and motor oil has a nominal apparent viscosity of 250 × 10-3 Pa∙s.[3]
Viscous flow, which results from viscosity, in amorphous materials such as water is a thermally activated process as is viscosity:[4]
- <math>{\mu_L} = A_L \cdot e^{Q_L/RT},</math>
where QL is the activation energy in the liquid state, T is temperature (K), R is the molar gas constant and AL is approximately a constant.
With
- QL ≥ Hm,
where Hm is the enthalpy of motion of the broken hydrogen bonds.
Solid-liquid transition in amorphous substances
In principle, given a sufficiently high cooling rate, any liquid can be made into an amorphous solid. Cooling reduces molecular mobility. If the cooling rate is faster than the rate at which molecules can organize into a more thermodynamically favorable crystalline state, then an amorphous solid will be formed. Because of entropy considerations, many polymers can be made into amorphous solids by cooling even at slow rates. In contrast, if molecules have sufficient time to organize into a structure with two- or three-dimensional order, then a crystalline (or semi-crystalline) solid is formed. Water is one example. Because of its small molecular size and ability to quickly rearrange, it cannot be made amorphous without resorting to specialized hyperquenching techniques. These produce amorphous ice, which has a quenching rate in the range of metallic glasses.[5]
The higher the temperature of an amorphous material the higher the configuron concentration. The higher the configuron concentration the lower the viscosity. As configurons form percolating clusters, an amorphous solid can transition to a liquid. This clustering facilitates viscous flow. Thermodynamic parameters of configurons can be found from viscosity-temperature relationships.[5]
Short-range order
Like a liquid an amorphous solid has a topologically disordered distribution of particles but elastic properties of an isotropic solid. The symmetry similarity of both liquid and solid phases cannot explain the qualitative differences in their behavior.
Due to chemical bonding characteristics amorphous solids such as glasses do possess a high degree of short-range order with respect to local atomic polyhedra.[6] The amorphous structure of glassy silica has no long range order but shows local ordering with respect to the tetrahedral arrangement of oxygen atoms around silicon atoms.
Bond structure
One useful approach is to consider the bond system instead of considering the set of particles that form the substance.[5] For each state of matter we can define the set of bonds by a bond lattice model.[5] The congruent bond lattice for amorphous materials is a disordered structure. Moreover the bond lattices of amorphous solids and liquids may have different symmetries in contrast to the symmetry similarity of particles in a liquid or fluid and solid phases.
For an amorphous material a given unit can be delimited by its nearest neighbors so that its structure may be characterized by a distribution of Voronoi polyhedra filling the space of the disordered material. Molecular dynamics simulations have revealed that the difference between a liquid and glass of an amorphous material results from the formation of percolation clusters of broken bonds in the Voronoi network.[7]
Hausdorff dimension
The Hausdorff dimension (d) generalizes the notion of the dimension of a real vector space. In particular, the Hausdorff dimension of a single point is zero, a line is one, a plane is two, a solid is three, etc. The Hausdorff dimension can be thought of as the power of radii for a set of space filling balls formally expressed by
- <math>C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i>0\Bigr\}.</math>
where C is the space (S)-filling Content of a countable number (the index number - i) of balls whose radii (ri) are dimensioned (volumed) to produce the space-filling balls.
In three dimensions, the balls can be spheres of many different radii and the volume of each ball is proportional to its r3. Hence the Hausdorff dimension, d = 3. In four dimensions, the balls can be hyperspheres of many different radii and the volume of each ball is proportional to its r4. Consider a sphere that changes its radius with time. At each time the sphere has a finite radius rti that differs from each t-1(i-1) before and after t+1(i+1). The volume calculated is proportional to rspace-filling4 that equals the space occupied for all time.
Fractals often are spaces whose Hausdorff dimension strictly exceeds the topological dimension. A 2-dimensional fractal has a Hausdorff dimension, d as 2<d<3.
There is a symmetry change expressed by step-wise variation in the Hausdorff dimension (d) for bonds at the solid-liquid transition.[5] In the solid state d=3 but for the liquid state d=df (the fractal d) = 2.55 ± 0.05.[8] df occurs at each broken bond.
Glass transition temperature of water
The glass transition temperature for water is about 136 K or -137°C. Factors in the formation of amorphous ice include ingredients that form a heterogenous mixture with water (such as is used in the production of ice cream), pressure (which may convert one form into another), and cryoprotectants that lower its freezing point and increase viscosity. Melting low-density amorphous ice (LDA) between 140 and 210 K through its transition temperature shows that it is more viscous than normal water.[9] LDA has a density of 0.94 g/cm³, less dense than the densest water (1.00 g/cm³ at 277 K), but denser than ordinary ice.
Amorphous ice is used in some scientific experiments, especially in electron cryomicroscopy of biomolecules.[10] The individual molecules can be preserved for imaging in a state close to what they are in liquid water.
Hydrated proteins may also be classed among glass-forming systems, but they show great departures from thermorheological simplicity.[11]
Enthalpy of motion for water configurons
A simple estimate of QL can be obtained by using the two temperatures 0°C and 100°C, where µ=1.79 x 10-3 Pa·s at 0°C and 0.28 x 10-3 Pa·s at 100°C, and solving for AL and QL. AL = 7.7 x 10-7 Pa·s and QL = 18 kJmol-1. R=8.314472 JK-1mol-1. Temperature is in K (273.15 + °C). QL includes the energy to break the hydrogen bond and move the configuron, as such HM ≤ QL. Using AL and QL to calculate the viscosity of water and comparing the calculated values to the experimentally determined ones for a range of temperature values shows that there is a systematic deviation at the higher temperatures. As the data for the viscosity of water vapor is available, AV and QV can be estimated: AV ~ 1.2 x 10-4 Pa·s and QV ~ - 6.0 kJmol-1. This added to the calculated configuron contribution
- <math>{\mu_L} = A_L \cdot e^{Q_L/RT} + A_V \cdot e^{Q_V/RT},</math>
improves the fit to the liquid water viscosity data remarkably well, suggesting that like other gas molecules mixed into water, water vapor can also be.[12]
Acknowledgements
The content on this page was first contributed by: Henry A. Hoff.
Initial content for this page in some instances came from Wikipedia.
References
- ↑ Angell CA, Rao KJ (1972). "Configurational excitations in condensed matter, and "bond lattice" model for the liquid-glass transition". J Chem Physics. 57 (1): 470–81. doi:10.1063/1.1677987.
- ↑ Angell CA (2000). Boolchand P, ed. Chapter 1. Glass formation and the nature of the glass transitions, in Insulating and semiconducting glasses, Volume 17 of Series on directions in condensed matter physics. World Scientific. pp. 1–54. ISBN 9810236735, 9789810236731 Check
|isbn=value: invalid character (help). - ↑ Raymond A. Serway (1996). Physics for Scientists & Engineers (4th Edition ed.). Saunders College Publishing. ISBN 0-03-005932-1.
- ↑ Ojovan MI, Lee WE (2004). "Viscosity of network liquids within Doremus approach". J Appl Phys. 95 (7): 3803–10. doi:10.1063/1.1647260. Text "month" ignored (help)
- ↑ 5.0 5.1 5.2 5.3 5.4 Ojovan MI (2008). "Configurons: thermodynamic parameters and symmetry changes at glass transition". Entropy. 10: 334–64. doi:10.3390/e10030334. Text "http://www.mdpi.org/entropy/papers/e10030334.pdf " ignored (help); Unknown parameter
|month=ignored (help) - ↑ Salmon PS (2002). "Amorphous materials: Order within disorder". Nature Materials. 1 (2): 87–8. doi:10.1038/nmat737.
- ↑ Medvedev NN, Geider A, Brostow W (1990). "Distinguishing liquids from amorphous solids: Percolation analysis on the Voronoi network". J Chem Phys. 93: 8337–42.
- ↑ Ojovan MI, Lee WE (2006). "Topologically disordered systems at the glass transition". J Phys: Condens Matter. 18 (50): 11507–20. doi:10.1088/0953-8984/18/50/007. Unknown parameter
|month=ignored (help) - ↑ "Liquid water in the domain of cubic crystalline ice Ic".
- ↑ Dubochet J, Adrian M, Chang JJ, Homo JC, Lepault J, McDowell AW, Schultz P (1988). "Cryo-electron microscopy of vitrified specimens". Q Rev Biophys. 21: 129–228.
- ↑ Green JL, Fan J, Angell CA (1994). "The protein-glass analogy: some insights from homopeptide comparisons". J Phys Chem. 98 (51): 13780–90. doi:10.1021/j100102a052. Unknown parameter
|month=ignored (help) - ↑ Hyatt MT, Levinson HS (1968). "Water Vapor, Aqueous Ethyl Alcohol, and Heat Activation of Bacillus megaterium
Spore Germination". J Bacteriol. 95 (6): 2090–101. PMID 4970224. Unknown parameter
|month=ignored (help); line feed character in|title=at position 80 (help)
See also
External links
- Discussion of amorphous ice at LSBU's website.
- Glassy Water from Science, on phase diagrams of water (requires registration)
- Structure of amorphous ice