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{{Short description|Transition from solid to gas}}
{{redirect|Sublimates||Sublimation (disambiguation){{!}}Sublimation}}
{{Redirect|Sublimates||Sublimation (disambiguation)}}
{{distinguish|subliminal stimuli}}
{{pp|small=yes}}
<!--
READ BEFORE EDIT, sublimation refers to ALL THREE CASES:
1. Sublime gradually: below triple point and left of solid-gas boundary
(similar to evaporation)
(bottom left of solid in phase diagram)
2. Sublime rapidly: below triple point and at solid-gas boundary
(similar to boiling)
3. Sublime gradually: above triple point and left of solid-liquid boundary (yes, solid sublimes above triple point)
(also similar to evaporation, just higher pressure)
(top left of solid in phase diagram)
These three cases jointly exhaust the solid space in the phrase diagram. This makes sense, after all, technically, all solids sublime (depending mostly on vapour pressure, which is very situational).
One may notice there is a fourth case in the solid space, that is, at the solid-liquid boundary. It is uncertain if the solid is still defined as subliming WHILE melting, and in case it is, it would be subliming gradually.
-->
<!--
checking some online English dictionaries:
1. sublime and sublimate are both valid, and both have some other meanings
https://www.merriam-webster.com/dictionary/sublime#did-you-know
(also almost every dictionary)
2. sublimate may mean the product
https://www.merriam-webster.com/dictionary/sublimate#dictionary-entry-2
https://www.collinsdictionary.com/dictionary/english/sublimate
https://www.dictionary.com/browse/sublimate
https://chambers.co.uk/search/?query=sublimate&title=21st
https://www.wordreference.com/definition/sublimate
3. sublimation may also mean itself followed by deposition
https://www.collinsdictionary.com/dictionary/english/sublime
https://www.dictionary.com/browse/sublime
4. sublimation seems used to mean deposition alone but this meaning is now completely obsolete, few if any online dictionary has such meaning as of 2023, the archaic use is likely phased out
-->

[[File:Nickelocen an einem Kühlfinger.jpg|thumb|right|Dark green [[crystals]] of [[nickelocene]], sublimed and freshly deposited on a [[cold finger]]]]
[[File:Nickelocen an einem Kühlfinger.jpg|thumb|right|Dark green [[crystals]] of [[nickelocene]], sublimed and freshly deposited on a [[cold finger]]]]
[[File:Sublimation of iodine.webm|thumb|Sublimation of iodine]]


'''Sublimation''' is the [[Phase transition|transition of a substance]] directly from the [[solid]] to the [[gas]] state, without passing through the [[liquid]] state.<ref>{{cite book |last1=Whitten |first1=Kenneth W. |last2=Gailey |first2=Kenneth D. |last3=Davis |first3=Raymond E. |title=General chemistry |url=https://archive.org/details/generalchemistry00whit_0 |url-access=registration |date=1992 |publisher=Saunders College Publishing |isbn=0-03-072373-6 |page=[https://archive.org/details/generalchemistry00whit_0/page/475 475] |edition=4th}}</ref> The verb form of sublimation is ''sublime'', or less preferably, ''sublimate''.<ref name=":0">{{cite Merriam-Webster|Sublimate}}</ref> ''Sublimate'' also refers to the product obtained by sublimation.<ref name=":0" /><ref>[https://www.collinsdictionary.com/dictionary/english/sublimate "Sublimate"]. [[Collins English Dictionary#CollinsDictionary.com|CollinsDictionary.com Dictionary]].</ref> The point at which sublimation occurs rapidly (for further details, see [[#False correspondence with vaporization|below]]) is called critical sublimation point, or simply sublimation point. Notable examples include sublimation of [[dry ice]] at room temperature and atmospheric pressure, and that of solid [[iodine]] with heating.
'''Sublimation''' is the transition of a substance directly from the [[solid]] to the [[gas]] phase, without passing through the intermediate [[liquid]] phase.<ref>{{cite Merriam-Webster|Sublimate}}</ref> Sublimation is an [[endothermic process]] that occurs at temperatures and pressures below a substance's [[triple point]] in its [[phase diagram]], which corresponds to the lowest pressure at which the substance can exist as a liquid. The reverse process of sublimation is [[deposition (phase transition)|deposition]] or desublimation, in which a substance passes directly from a gas to a solid phase.<ref name="DepositionDef">{{cite journal |title=Controlling condensation and frost growth with chemical micropatterns |first=Jonathan B. |last=Boreyko |first2=Ryan R. |last2=Hansen |first3=Kevin R. |last3=Murphy |first4=Saurabh |last4=Nath |first5=Scott T. |last5=Retterer |first6=C. Patrick |last6=Collier |journal=Scientific Reports |year=2016 |volume=6 |pages=19131 |doi=10.1038/srep19131 |pmid=26796663 |pmc=4726256 |bibcode=2016NatSR...619131B}}</ref> Sublimation has also been used as a generic term to describe a solid-to-gas transition (sublimation) followed by a gas-to-solid transition ([[deposition (phase transition)|deposition]]).<ref>{{Dictionary.com|Sublime}}</ref> While a transition from liquid to gas is described as [[evaporation]] if it occurs below the boiling point of the liquid, and as [[boiling]] if it occurs at the boiling point, there is no such distinction within the solid-to-gas transition, which is always described as sublimation.


The reverse process of sublimation is [[deposition (phase transition)|''deposition'']] (also called ''desublimation''), in which a substance passes directly from a gas to a solid phase, without passing through the liquid state.<ref name="DepositionDef">{{cite journal |title=Controlling condensation and frost growth with chemical micropatterns |first1=Jonathan B. |last1=Boreyko |first2=Ryan R. |last2=Hansen |first3=Kevin R. |last3=Murphy |first4=Saurabh |last4=Nath |first5=Scott T. |last5=Retterer |first6=C. Patrick |last6=Collier |journal=Scientific Reports |year=2016 |volume=6 |pages=19131 |doi=10.1038/srep19131 |pmid=26796663 |pmc=4726256 |bibcode=2016NatSR...619131B}}</ref>
At [[standard conditions for temperature and pressure|normal pressures]], most [[chemical compound]]s and [[chemical element|elements]] possess three different states at different [[temperature]]s. In these cases, the transition from the solid to the [[gaseous state]] requires an intermediate liquid state. The pressure referred to is the ''[[partial pressure]]'' of the substance, not the ''total'' (e.g. atmospheric) pressure of the entire system. So, all solids that possess an appreciable [[vapour pressure]] at a certain temperature usually can sublime in air (e.g. water ice just below 0&nbsp;°C). For some substances, such as [[carbon]] and [[arsenic]], sublimation is much easier than [[evaporation]] from the melt, because the pressure of their [[triple point]] is very high, and it is difficult to obtain them as liquids.


All solids sublime, though most sublime at extremely low rates that are hardly detectable. At [[standard conditions for temperature and pressure|normal pressures]], most [[chemical compound]]s and [[chemical element|elements]] possess three different states at different [[temperature]]s. In these cases, the transition from the [[solid]] to the [[gas]] state requires an intermediate liquid state. The pressure referred to is the ''[[partial pressure]]'' of the substance, not the ''total'' (e.g. atmospheric) pressure of the entire system. Thus, any solid can sublime if its [[vapour pressure]] is higher than the surrounding partial pressure of the same substance, and in some cases, sublimes at an appreciable rate (e.g. water ice just below 0&nbsp;°C).
The term ''sublimation'' refers to a [[physical change]] of [[state of matter|state]] and is not used to describe the transformation of a solid to a gas in a chemical reaction. For example, the dissociation on heating of solid [[ammonium chloride]] into hydrogen chloride and ammonia is ''not'' sublimation but a chemical reaction. Similarly the combustion of candles, containing [[paraffin wax]], to [[carbon dioxide]] and [[water vapor]] is ''not'' sublimation but a chemical reaction with oxygen.


For some substances, such as [[carbon]] and [[arsenic]], sublimation from solid state is much more achievable than [[evaporation]] from liquid state and it is difficult to obtain them as liquids. This is because the pressure of their [[triple point]] in its [[phase diagram]] (which corresponds to the lowest pressure at which the substance can exist as a liquid) is very high.
Sublimation is caused by the absorption of heat which provides enough energy for some molecules to overcome the [[intermolecular force|attractive forces]] of their neighbors and escape into the vapor phase. Since the process requires additional energy, it is an [[endothermic]] change. The [[enthalpy of sublimation]] (also called heat of sublimation) can be calculated by adding the [[enthalpy of fusion]] and the [[enthalpy of vaporization]].


Sublimation is caused by the absorption of heat which provides enough energy for some molecules to overcome the [[intermolecular force|attractive forces]] of their neighbors and escape into the vapor phase. Since the process requires additional energy, sublimation is an [[endothermic]] change. The [[enthalpy of sublimation]] (also called heat of sublimation) can be calculated by adding the [[enthalpy of fusion]] and the [[enthalpy of vaporization]].
[[File:Comparison carbon dioxide water phase diagrams.svg|thumb|upright=2|Comparison of phase diagrams of carbon dioxide (red) and water (blue) showing the carbon dioxide sublimation point (middle-left) at 1 atmosphere. As dry ice is heated, it crosses this point along the bold horizontal line from the solid phase directly into the gaseous phase. Water, on the other hand, passes through a liquid phase at 1 atmosphere.]]

== Confusions ==
While the definition of sublimation is simple, there is often confusion as to what counts as a sublimation.

=== False correspondence with vaporization ===
[[Vaporization]] (from liquid to gas) is divided into two types: vaporization on the surface of the liquid is called [[evaporation]], and vaporization at the boiling point with formation of bubbles in the interior of the liquid is called [[boiling]]. However there is ''no'' such distinction for the solid-to-gas transition, which is always called sublimation in both corresponding cases.

==== Potential distinction ====
For clarification, a distinction between the two corresponding cases is needed. With reference to a [[phase diagram]], the sublimation that occurs left of the solid-gas boundary, the triple point or the solid-liquid boundary (corresponding to evaporation in vaporization) may be called ''gradual sublimation''; and the substance ''sublimes gradually'', regardless of rate. The sublimation that occurs at the solid-gas boundary (critical sublimation point) (corresponding to boiling in vaporization) may be called ''rapid sublimation'', and the substance ''sublimes rapidly''. The words "gradual" and "rapid" have acquired special meanings in this context and no longer describe the rate of sublimation.{{cn|date=April 2024}}<!-- This distinction is used only on this page and nowhere else, to minimize confusion. If there is a better distinction, change it along with the examples. If this violates the policy of Wikipedia, please delete this paragraph, and if possible, also provide a better solution. -->

=== Misuse for chemical reaction ===
The term ''sublimation'' refers specifically to a [[physical change]] of [[state of matter|state]] and is not used to describe the transformation of a solid to a gas in a chemical reaction. For example, the dissociation on heating of solid [[ammonium chloride]] into hydrogen chloride and ammonia is ''not'' sublimation but a chemical reaction. Similarly the combustion of candles, containing [[paraffin wax]], to [[carbon dioxide]] and [[water vapor]] is ''not'' sublimation but a chemical reaction with oxygen.

=== Historical definition ===
Sublimation is historically used as a generic term to describe a two-step phase transition ― a solid-to-gas transition (sublimation in a more precise definition) followed by a gas-to-solid transition ([[deposition (phase transition)|deposition]]).<ref>{{Dictionary.com|Sublime}}</ref><ref>[https://www.collinsdictionary.com/dictionary/english/sublime "Sublime"]. [[Collins English Dictionary#CollinsDictionary.com|CollinsDictionary.com Dictionary]].</ref> (See [[#Historical usage|below]])


==Examples==
==Examples==
[[File:Comparison carbon dioxide water phase diagrams.svg|thumb|upright=2|Comparison of phase diagrams of carbon dioxide (red) and water (blue) showing the carbon dioxide sublimation point (middle-left) at 1 atmosphere. As dry ice is heated, it crosses this point along the bold horizontal line from the solid phase directly into the gaseous phase. Water, on the other hand, passes through a liquid phase at 1 atmosphere.]]
The examples shown are substances that noticeably sublime under certain conditions.

===Carbon dioxide===
===Carbon dioxide===
[[File:Dry Ice Vapor (17490553041).jpg|thumb|[[Dry ice]] subliming in air]]
[[File:Dry Ice Vapor (17490553041).jpg|thumb|[[Dry ice]] subliming in air]]
Solid [[carbon dioxide]] ([[dry ice]]) sublimes everywhere along the line below the triple point (e.g., at the temperature of −78.5&nbsp;°C (194.65 K, {{convert|194.65|K|F|disp=output only}}) at [[atmospheric pressure]], whereas its melting into liquid CO<sub>2</sub> can occur only along the line at pressures and temperatures above the triple point (i.e., 5.2 atm, −56.4&nbsp;°C).
Solid [[carbon dioxide]] ([[dry ice]]) sublimes rapidly along the solid-gas boundary (sublimation point) below the triple point (e.g., at the temperature of −78.5&nbsp;°C, at [[atmospheric pressure]]), whereas its melting into liquid CO<sub>2</sub> can occur along the solid-liquid boundary ([[melting point]]) at pressures and temperatures above the triple point (i.e., 5.1 atm, −56.6&nbsp;°C).


===Water===
===Water===
[[Snow]] and [[ice]] sublime, although more slowly, at temperatures below the freezing/[[melting point]] temperature line at 0&nbsp;°C for most pressures; see line below triple point.<ref>{{cite journal |last=Fassnacht |first=S. R. |year=2004 |title=Estimating Alter-shielded gauge snowfall undercatch, snowpack sublimation, and blowing snow transport at six sites in the coterminous USA |journal=Hydrol. Process |doi=10.1002/hyp.5806 |bibcode=2004HyPr...18.3481F |volume=18 |issue=18 |pages=3481–3492}}</ref> In [[freeze-drying]], the material to be dehydrated is frozen and its water is allowed to sublime under reduced pressure or vacuum. The loss of snow from a [[snowfield]] during a cold spell is often caused by sunshine acting directly on the upper layers of the snow. [[Ablation]] is a process that includes sublimation and erosive wear of [[glacier ice]].
[[Snow]] and [[ice]] sublime gradually at temperatures below the solid-liquid boundary (melting point) (generally 0&nbsp;°C), and at partial pressures below the triple point pressure of {{convert|612|Pa|atm|abbr=on}}, at a low rate.<ref>{{cite journal |last=Fassnacht |first=S. R. |year=2004 |title=Estimating Alter-shielded gauge snowfall undercatch, snowpack sublimation, and blowing snow transport at six sites in the coterminous USA |journal=Hydrol. Process. |doi=10.1002/hyp.5806 |bibcode=2004HyPr...18.3481F |volume=18 |issue=18 |pages=3481–3492|s2cid=129927018 }}</ref> In [[freeze-drying]], the material to be dehydrated is frozen and its water is allowed to sublime under reduced pressure or vacuum. The loss of snow from a [[snowfield]] during a cold spell is often caused by sunshine acting directly on the upper layers of the snow. Sublimation of ice is a factor to the erosive wear of [[glacier ice]], also called [[ablation]] in [[glaciology]].{{citation needed|date=October 2021}}


===Naphthalene===
===Naphthalene===
[[File:Sublimation reaction of naphthalene.jpg|thumb|Experimental set up for the sublimation reaction of [[naphthalene]], solid naphthalene sublimes and form the crystal-like structure at the bottom of the [[watch glass]]]]
[[File:Crystal-like sublimated naphthalene.jpg|thumb|Solid compound of [[naphthalene]] sublimed to form a crystal-like structure on the cool surface.]]


[[Naphthalene]], an organic compound commonly found in pesticides such as [[mothball]]s, sublimes easily because it is made of non-polar molecules that are held together only by [[Van der Waals force|van der Waals]] intermolecular forces. Naphthalene is a solid that sublimes at [[standard conditions for temperature and pressure|standard atmospheric temperature]]<ref>
[[Naphthalene]], an organic compound commonly found in pesticides such as [[mothball]]s, sublimes easily because it is made of non-polar molecules that are held together only by [[Van der Waals force|van der Waals]] intermolecular forces. Naphthalene is a solid that sublimes gradually at [[standard temperature and pressure]],<ref>
{{cite book
{{cite book
|last=Caroll |first=J.
|last=Caroll |first=J.
Line 29: Line 83:
|isbn=9780128005750
|isbn=9780128005750
|page=16
|page=16
|publisher=Gulf Professional
}}</ref> with the sublimation point at around 80{{nbsp}}°C or 176{{nbsp}}°F.<ref>
}}</ref> at a high rate, with the critical sublimation point at around {{convert|80|C|F}}.<ref>
{{cite web
{{cite web
|author=Staff writer(s)
|author=Staff writer(s)
|date=2015
|date=2015
|title=what solid go through sublimation?
|title=what solids go through sublimation?
|publisher=National Science Foundation and UCSB School-University partnership
|publisher=National Science Foundation and UCSB School-University partnership
|url=http://scienceline.ucsb.edu/getkey.php?key=4306
|url=http://scienceline.ucsb.edu/getkey.php?key=4306
Line 44: Line 99:
|isbn=978-0534408336
|isbn=978-0534408336
|pages=781–782
|pages=781–782
|publisher=Thomson Brooks/Cole
}}</ref> to make the solid form of naphthalene evaporate into gas. On cool surfaces, the naphthalene vapours will solidify to form needle-like crystals.
}}</ref> to make the solid form of naphthalene evaporate into gas. On cool surfaces, the naphthalene vapours will solidify to form needle-like crystals.


===Iodine===
[[File:Sublimation reaction of naphthalene.jpg|thumb|Experimental set up for the sublimation reaction of [[naphthalene]] Solid naphthalene sublimes and form the crystal-like structure at the bottom of the [[watch glass]]]]
[[Iodine]] sublimes gradually and produces visible fumes on gentle heating at [[standard conditions for temperature and pressure|standard atmospheric temperature]]. It is possible to obtain liquid iodine at atmospheric pressure by controlling the temperature at just between the melting point and the boiling point of iodine. In [[forensic science]], iodine vapor can reveal latent [[fingerprint]]s on paper.<ref>{{cite book
[[File:Crystal-like sublimated naphthalene.jpg|thumb|Solid compound of [[naphthalene]] sublimed to form a crystal-like structure on the cool surface.]]

===Other substances===
[[File:Camphor sublimation 1.jpg|thumb|upright|[[Camphor]] subliming in a [[cold finger]]. The crude product in the bottom is dark brown; the white purified product on the bottom of the cold finger above is hard to see against the light background.]]

[[Iodine]] produces fumes on gentle heating. It is possible to obtain liquid iodine at atmospheric pressure by controlling the temperature at just above the melting point of iodine. In [[forensic science]], iodine vapor can reveal latent [[fingerprint]]s on paper.<ref>{{cite book
|last=Girard |first=James
|last=Girard |first=James
|year= 2011
|year= 2011
Line 60: Line 111:
|pages= 143–144
|pages= 143–144
}}</ref>
}}</ref>
[[Arsenic]] can also sublime at high temperatures.


=== Other substances ===
[[Cadmium]] and [[zinc]] are not suitable [[materials for use in vacuum]] because they sublime much more than other common materials.{{cn|date=May 2019}}
[[File:Camphor sublimation 1.jpg|thumb|upright|[[Camphor]] subliming in a [[cold finger]]. The crude product in the bottom is dark brown; the white purified product on the bottom of the cold finger above is hard to see against the light background.]]

[[Arsenic]] sublimes gradually upon heating at [[atmospheric pressure]], and sublimes rapidly at {{convert|887|K|C}}.<ref name="Holl3">{{cite book |last=Holleman |first=Arnold F. |title=Lehrbuch der Anorganischen Chemie |author2=Wiberg, Egon |author3=Wiberg, Nils |date=1985 |publisher=Walter de Gruyter |isbn=978-3-11-007511-3 |edition=91–100 |pages=675–681 |language=de |chapter=Arsen}}</ref>

[[Cadmium]] and [[zinc]] sublime much more than other common materials, so they are not suitable [[materials for use in vacuum]].{{citation needed|date=May 2019}}


==Purification by sublimation==
==Purification by sublimation==
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Sublimation is a technique used by [[chemist]]s to purify [[chemical compound|compounds]]. A solid is typically placed in a [[sublimation apparatus]] and heated under [[vacuum]]. Under this reduced [[pressure]], the solid [[volatility (chemistry)|volatilizes]] and condenses as a purified compound on a cooled surface ([[cold finger]]), leaving a non-volatile residue of [[impurities]] behind. Once heating ceases and the vacuum is removed, the purified compound may be collected from the cooling surface.<ref>R. B. King ''Organometallic Syntheses''. Volume 1 Transition-Metal Compounds; Academic Press: New York, 1965. {{ISBN|0-444-42607-8}}.</ref><ref name=HarwoodMoodyEOCPAP>{{cite book
Sublimation is a technique used by [[chemist]]s to purify [[chemical compound|compounds]]. A solid is typically placed in a [[sublimation apparatus]] and heated under [[vacuum]]. Under this reduced [[pressure]], the solid [[volatility (chemistry)|volatilizes]] and condenses as a purified compound on a cooled surface ([[cold finger]]), leaving a non-volatile residue of [[impurities]] behind. Once heating ceases and the vacuum is removed, the purified compound may be collected from the cooling surface.<ref>R. B. King ''Organometallic Syntheses''. Volume 1 Transition-Metal Compounds; Academic Press: New York, 1965. {{ISBN|0-444-42607-8}}.</ref><ref name=HarwoodMoodyEOCPAP>{{cite book
|last1=Harwood |first1=Laurence M. |last2=Moody |first2=Christopher J.
|last1= Harwood
|first1= Laurence M.
|last2= Moody
|first2= Christopher J.
|year= 1989
|year= 1989
|title= Experimental organic chemistry: Principles and Practice
|title= Experimental organic chemistry: Principles and Practice
Line 74: Line 132:
|publisher= WileyBlackwell
|publisher= WileyBlackwell
|isbn= 978-0-632-02017-1
|isbn= 978-0-632-02017-1
|pages= 154–155
|pages= [https://archive.org/details/experimentalorga00harw/page/154 154–155]
|url= https://archive.org/details/experimentalorga00harw/page/154
}}</ref>
}}</ref>
For even higher purification efficiencies, a [[temperature gradient]] is applied, which also allows for the separation of different fractions. Typical setups use an evacuated glass tube that is heated gradually in a controlled manner. The material flow is from the hot end, where the initial material is placed, to the cold end that is connected to a pump stand. By controlling temperatures along the length of the tube, the operator can control the zones of re-condensation, with very volatile compounds being pumped out of the system completely (or caught by a separate [[cold trap]]), moderately volatile compounds re-condensing along the tube according to their different volatilities, and non-volatile compounds remaining in the hot end.
For even higher purification efficiencies, a [[temperature gradient]] is applied, which also allows for the separation of different fractions. Typical setups use an evacuated glass tube that is heated gradually in a controlled manner. The material flow is from the hot end, where the initial material is placed, to the cold end that is connected to a pump stand. By controlling temperatures along the length of the tube, the operator can control the zones of re-condensation, with very volatile compounds being pumped out of the system completely (or caught by a separate [[cold trap]]), moderately volatile compounds re-condensing along the tube according to their different volatilities, and non-volatile compounds remaining in the hot end.
Vacuum sublimation of this type is also the method of choice for purification of organic compounds for use in the [[organic electronics|organic electronics industry]], where very high purities (often > 99.99%) are needed to satisfy the standards for consumer electronics and other applications.
Vacuum sublimation of this type is also the method of choice for purification of organic compounds for use in the [[organic electronics|organic electronics industry]], where very high purities (often > 99.99%) are needed to satisfy the standards for consumer electronics and other applications.{{citation needed|date=October 2021}}


==Historical usage==
==Historical usage==
In ancient [[alchemy]], a protoscience that contributed to the development of modern chemistry and medicine, alchemists developed a structure of basic laboratory techniques, theory, terminology, and experimental methods. ''Sublimation'' was used to refer to the process in which a substance is heated to a vapor, then immediately collects as sediment on the upper portion and neck of the heating medium (typically a [[retort]] or [[alembic]]), but can also be used to describe other similar non-laboratory transitions. It is mentioned by alchemical authors such as [[Basil Valentine]] and [[George Ripley (alchemist)|George Ripley]], and in the [[Rosarium philosophorum]], as a process necessary for the completion of the [[magnum opus (alchemy)|magnum opus]]. Here, the word ''sublimation'' is used to describe an exchange of "bodies" and "spirits" similar to laboratory phase transition between solids and gases. Valentine, in his ''Triumphal Chariot of Antimony'' (published 1678) makes a comparison to [[spagyrics]] in which a vegetable sublimation can be used to separate the spirits in wine and beer.<ref>{{cite book |last=Barrett |first=Francis |date=1815 |title=The lives of alchemystical philosophers: with a critical catalogue of books in occult chemistry, and a selection of the most celebrated treatises on the theory and practice of the hermetic art |publisher=Macdonald and Son for Lackington, Allen, & Co. |page=233}}</ref> Ripley uses language more indicative of the mystical implications of sublimation, indicating that the process has a double aspect in the spiritualization of the body and the corporalizing of the spirit.<ref>{{cite book |last=DiBernard |first=Barbara |year=1980 |title=Alchemy and Finnegans wake. |publisher=SUNY Press |isbn=978-0873953887 |page=57}}</ref> He writes:<ref>Ripley, George (1591). [http://www.levity.com/alchemy/ripgat8.html ''Compound of Alchemy''].</ref>
In ancient [[alchemy]], a [[protoscience]] that contributed to the development of modern chemistry and medicine, alchemists developed a structure of basic laboratory techniques, theory, terminology, and experimental methods. ''Sublimation'' was used to refer to the process in which a substance is heated to a vapor, then immediately collects as sediment on the upper portion and neck of the heating medium (typically a [[retort]] or [[alembic]]), but can also be used to describe other similar non-laboratory transitions. It was mentioned by alchemical authors such as [[Basil Valentine]] and [[George Ripley (alchemist)|George Ripley]], and in the ''[[Rosarium philosophorum]]'', as a process necessary for the completion of the [[magnum opus (alchemy)|magnum opus]]. Here, the word ''sublimation'' was used to describe an exchange of "bodies" and "spirits" similar to laboratory phase transition between solids and gases. Valentine, in his ''[[Basil Valentine#Selected publications|Le char triomphal de l'antimoine]]'' (Triumphal Chariot of Antimony, published 1646) made a comparison to [[spagyrics]] in which a vegetable sublimation can be used to separate the spirits in wine and beer.<ref>{{cite book |last=Barrett |first=Francis |date=1815 |title=The lives of alchemystical philosophers: with a critical catalogue of books in occult chemistry, and a selection of the most celebrated treatises on the theory and practice of the hermetic art |url=https://archive.org/details/livesofalchemyst00barr |publisher=Macdonald and Son for Lackington, Allen, & Co. |page=[https://archive.org/details/livesofalchemyst00barr/page/233 233]}}</ref> Ripley used language more indicative of the mystical implications of sublimation, indicating that the process has a double aspect in the spiritualization of the body and the corporalizing of the spirit.<ref>{{cite book |last=DiBernard |first=Barbara |year=1980 |title=Alchemy and Finnegans wake. |publisher=SUNY Press |isbn=978-0873953887 |page=[https://archive.org/details/alchemyfinnegans0000dibe/page/57 57] |url=https://archive.org/details/alchemyfinnegans0000dibe/page/57 }}</ref> He writes:<ref>Ripley, George (1591). [http://www.levity.com/alchemy/ripgat8.html ''Compound of Alchemy''].</ref>


<blockquote><poem>
<blockquote><poem>
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==Sublimation predictions==
==Sublimation predictions==


The [[enthalpy]] of sublimation has commonly been predicted using the [[equipartition theorem]]. If the [[lattice energy]] is assumed to be approximately half the packing energy, then the following thermodynamic corrections can be applied to predict the enthalpy of sublimation. Assuming a 1 [[molar concentration|molar]] [[ideal gas]] gives a correction for the thermodynamic environment (pressure and volume) in which pV = RT, hence a correction of 1RT. Additional corrections for the [[molecular vibration|vibrations]], [[rigid rotor|rotations]] and translation then need to be applied. From the [[equipartition theorem]] gaseous rotation and translation contribute 1.5RT each to the final state, therefore a +3RT correction. Crystalline vibrations and rotations contribute 3RT each to the initial state, hence −6RT. Summing the RT corrections; −6RT + 3RT + RT = −2RT.<ref name=Gavezzotti>{{cite book |last=Gavezzotti |first=A. |date=1997 |title=Theoretical Aspects and Computer Modeling of the Molecular Solid State |publisher=Wiley and Sons |location=Chichester}}</ref> This leads to the following approximate sublimation enthalpy. A similar approximation can be found for the [[entropy]] term if rigid bodies are assumed.<ref>{{cite journal |last1=McDonagh |first1=J. L. |author2=Nath |last3=De Ferrari |first3=Luna |last4=Van Mourik |first4=Tanja |last5=Mitchell |first5=John B. O. |year=2014 |title=Uniting Cheminformatics and Chemical Theory To Predict the Intrinsic Aqueous Solubility of Crystalline Druglike Molecules |journal=Journal of Chemical Information and Modeling |doi=10.1021/ci4005805 |pmid=24564264 |pmc=3965570 |volume=54 |issue=3 |pages=844–56}}</ref><ref>{{cite journal|last1=McDonagh|first1=James|last2=Palmer|first2=David S.|last3=Van Mourik|first3=Tanja|last4=Mitchell|first4=John B. O.|title=Are The Sublimation Thermodynamics of organic molecules predictable?|journal=Journal of Chemical Information and Modeling|volume=56|issue=11|pages=2162–2179|date=17 October 2016|doi=10.1021/acs.jcim.6b00033|pmid=27749062|issn=1549-9596|hdl=10023/11874|url=https://strathprints.strath.ac.uk/58416/1/McDonagh_etal_JCIM_2016_Are_the_sublimation_thermodynamics_of_organic.pdf}}</ref>
The [[enthalpy]] of sublimation has commonly been predicted using the [[equipartition theorem]]. If the [[lattice energy]] is assumed to be approximately half the packing energy,{{clarify|date=June 2020 |reason=Define packing energy and explain why it is different from lattice energy}} then the following thermodynamic corrections can be applied to predict the enthalpy of sublimation. Assuming a 1 [[molar concentration|molar]] [[ideal gas]] gives a correction for the thermodynamic environment (pressure and volume) in which pV = RT, hence a correction of 1RT. Additional corrections for the [[molecular vibration|vibrations]], [[rigid rotor|rotations]] and translation then need to be applied. From the [[equipartition theorem]] gaseous rotation and translation contribute 1.5RT each to the final state, therefore a +3RT correction. Crystalline vibrations and rotations contribute 3RT each to the initial state, hence −6RT. Summing the RT corrections; −6RT + 3RT + RT = −2RT.<ref name=Gavezzotti>{{cite book |last=Gavezzotti |first=A. |date=1997 |title=Theoretical Aspects and Computer Modeling of the Molecular Solid State |publisher=Wiley and Sons |location=Chichester}}</ref> This leads to the following approximate sublimation enthalpy. A similar approximation can be found for the [[entropy]] term if rigid bodies are assumed.<ref>{{cite journal |last1=McDonagh |first1=J. L. |author2=Nath |last3=De Ferrari |first3=Luna |last4=Van Mourik |first4=Tanja |last5=Mitchell |first5=John B. O. |year=2014 |title=Uniting Cheminformatics and Chemical Theory To Predict the Intrinsic Aqueous Solubility of Crystalline Druglike Molecules |journal=Journal of Chemical Information and Modeling |doi=10.1021/ci4005805 |pmid=24564264 |pmc=3965570 |volume=54 |issue=3 |pages=844–56}}</ref><ref>{{cite journal|last1=McDonagh|first1=James|last2=Palmer|first2=David S.|last3=Van Mourik|first3=Tanja|last4=Mitchell|first4=John B. O.|title=Are The Sublimation Thermodynamics of organic molecules predictable?|journal=Journal of Chemical Information and Modeling|volume=56|issue=11|pages=2162–2179|date=17 October 2016|doi=10.1021/acs.jcim.6b00033|pmid=27749062|issn=1549-9596|hdl=10023/11874|url=https://strathprints.strath.ac.uk/58416/1/McDonagh_etal_JCIM_2016_Are_the_sublimation_thermodynamics_of_organic.pdf|hdl-access=free}}</ref>
<math> \Delta H_{\text{sublimation}} = -U_{\text{lattice energy}} - 2RT</math>
<math> \Delta H_{\text{sublimation}} = -U_{\text{lattice energy}} - 2RT</math>

==Dye-sublimation printing==
{{Main|Dye-sublimation printer}}

Dye-sub printing is a digital printing technology using full color artwork that works with polyester and polymer-coated substrates. Also referred to as digital sublimation, the process is commonly used for decorating apparel, signs and banners, as well as novelty items such as cell phone covers, plaques, coffee mugs, and other items with sublimation-friendly surfaces. The process uses the science of sublimation, in which heat and pressure are applied to a solid, turning it into a gas through an endothermic reaction without passing through the liquid phase.{{citation needed|date=October 2021}}

In sublimation printing, unique sublimation dyes are transferred to sheets of “transfer” paper via liquid gel ink through a piezoelectric print head. The ink is deposited on these high-release inkjet papers, which are used for the next step of the sublimation printing process. After the digital design is printed onto sublimation transfer sheets, it is placed on a heat press along with the substrate to be sublimated.{{citation needed|date=October 2021}}

In order to transfer the image from the paper to the substrate, it requires a heat press process that is a combination of time, temperature and pressure. The heat press applies this special combination, which can change depending on the substrate, to “transfer” the sublimation dyes at the molecular level into the substrate. The most common dyes used for sublimation activate at 350 degrees Fahrenheit. However, a range of 380 to 420 degrees Fahrenheit is normally recommended for optimal color.{{citation needed|date=October 2021}}

The result of the sublimation process is a nearly permanent, high resolution, full color print. Because the dyes are infused into the substrate at the molecular level, rather than applied at a topical level (such as with screen printing and direct to garment printing), the prints will not crack, fade or peel from the substrate under normal conditions.{{citation needed|date=October 2021}}


==See also==
==See also==
*[[Ablation]]
*[[Ablation]]
*[[Dye-sublimation printer]]
*[[Freezer burn]] – common process involving sublimation
*[[Enthalpy of sublimation]]
*[[Enthalpy of sublimation]]
*[[Freeze-drying]]
*[[Freeze-drying]]
*[[Freezer burn]] – common process involving sublimation
*[[Phase diagram]]
*[[Phase diagram]]
*[[Phase transition|Phase transitions]]


==Table of phase transitions of matter==
{{Table of phase transitions}}
{{Table of phase transitions}}
{{Clear}}
{{Clear}}
Line 111: Line 182:
{{Reflist|30em}}
{{Reflist|30em}}


==External links==
== External links ==
*{{Commonscat-inline|Sublimation}}
* {{Commons category-inline|Sublimation}}

{{Clear}}
{{Separation processes}}
{{Separation processes}}
{{States of matter}}
{{States of matter}}
{{Authority control}}


[[Category:Alchemical processes]]
[[Category:Alchemical processes]]

Latest revision as of 16:31, 26 September 2024

Dark green crystals of nickelocene, sublimed and freshly deposited on a cold finger
Sublimation of iodine

Sublimation is the transition of a substance directly from the solid to the gas state, without passing through the liquid state.[1] The verb form of sublimation is sublime, or less preferably, sublimate.[2] Sublimate also refers to the product obtained by sublimation.[2][3] The point at which sublimation occurs rapidly (for further details, see below) is called critical sublimation point, or simply sublimation point. Notable examples include sublimation of dry ice at room temperature and atmospheric pressure, and that of solid iodine with heating.

The reverse process of sublimation is deposition (also called desublimation), in which a substance passes directly from a gas to a solid phase, without passing through the liquid state.[4]

All solids sublime, though most sublime at extremely low rates that are hardly detectable. At normal pressures, most chemical compounds and elements possess three different states at different temperatures. In these cases, the transition from the solid to the gas state requires an intermediate liquid state. The pressure referred to is the partial pressure of the substance, not the total (e.g. atmospheric) pressure of the entire system. Thus, any solid can sublime if its vapour pressure is higher than the surrounding partial pressure of the same substance, and in some cases, sublimes at an appreciable rate (e.g. water ice just below 0 °C).

For some substances, such as carbon and arsenic, sublimation from solid state is much more achievable than evaporation from liquid state and it is difficult to obtain them as liquids. This is because the pressure of their triple point in its phase diagram (which corresponds to the lowest pressure at which the substance can exist as a liquid) is very high.

Sublimation is caused by the absorption of heat which provides enough energy for some molecules to overcome the attractive forces of their neighbors and escape into the vapor phase. Since the process requires additional energy, sublimation is an endothermic change. The enthalpy of sublimation (also called heat of sublimation) can be calculated by adding the enthalpy of fusion and the enthalpy of vaporization.

Confusions

While the definition of sublimation is simple, there is often confusion as to what counts as a sublimation.

False correspondence with vaporization

Vaporization (from liquid to gas) is divided into two types: vaporization on the surface of the liquid is called evaporation, and vaporization at the boiling point with formation of bubbles in the interior of the liquid is called boiling. However there is no such distinction for the solid-to-gas transition, which is always called sublimation in both corresponding cases.

Potential distinction

For clarification, a distinction between the two corresponding cases is needed. With reference to a phase diagram, the sublimation that occurs left of the solid-gas boundary, the triple point or the solid-liquid boundary (corresponding to evaporation in vaporization) may be called gradual sublimation; and the substance sublimes gradually, regardless of rate. The sublimation that occurs at the solid-gas boundary (critical sublimation point) (corresponding to boiling in vaporization) may be called rapid sublimation, and the substance sublimes rapidly. The words "gradual" and "rapid" have acquired special meanings in this context and no longer describe the rate of sublimation.[citation needed]

Misuse for chemical reaction

The term sublimation refers specifically to a physical change of state and is not used to describe the transformation of a solid to a gas in a chemical reaction. For example, the dissociation on heating of solid ammonium chloride into hydrogen chloride and ammonia is not sublimation but a chemical reaction. Similarly the combustion of candles, containing paraffin wax, to carbon dioxide and water vapor is not sublimation but a chemical reaction with oxygen.

Historical definition

Sublimation is historically used as a generic term to describe a two-step phase transition ― a solid-to-gas transition (sublimation in a more precise definition) followed by a gas-to-solid transition (deposition).[5][6] (See below)

Examples

Comparison of phase diagrams of carbon dioxide (red) and water (blue) showing the carbon dioxide sublimation point (middle-left) at 1 atmosphere. As dry ice is heated, it crosses this point along the bold horizontal line from the solid phase directly into the gaseous phase. Water, on the other hand, passes through a liquid phase at 1 atmosphere.

The examples shown are substances that noticeably sublime under certain conditions.

Carbon dioxide

Dry ice subliming in air

Solid carbon dioxide (dry ice) sublimes rapidly along the solid-gas boundary (sublimation point) below the triple point (e.g., at the temperature of −78.5 °C, at atmospheric pressure), whereas its melting into liquid CO2 can occur along the solid-liquid boundary (melting point) at pressures and temperatures above the triple point (i.e., 5.1 atm, −56.6 °C).

Water

Snow and ice sublime gradually at temperatures below the solid-liquid boundary (melting point) (generally 0 °C), and at partial pressures below the triple point pressure of 612 Pa (0.00604 atm), at a low rate.[7] In freeze-drying, the material to be dehydrated is frozen and its water is allowed to sublime under reduced pressure or vacuum. The loss of snow from a snowfield during a cold spell is often caused by sunshine acting directly on the upper layers of the snow. Sublimation of ice is a factor to the erosive wear of glacier ice, also called ablation in glaciology.[citation needed]

Naphthalene

Experimental set up for the sublimation reaction of naphthalene, solid naphthalene sublimes and form the crystal-like structure at the bottom of the watch glass
Solid compound of naphthalene sublimed to form a crystal-like structure on the cool surface.

Naphthalene, an organic compound commonly found in pesticides such as mothballs, sublimes easily because it is made of non-polar molecules that are held together only by van der Waals intermolecular forces. Naphthalene is a solid that sublimes gradually at standard temperature and pressure,[8] at a high rate, with the critical sublimation point at around 80 °C (176 °F).[9] At low temperature, its vapour pressure is high enough, 1 mmHg at 53 °C,[10] to make the solid form of naphthalene evaporate into gas. On cool surfaces, the naphthalene vapours will solidify to form needle-like crystals.

Iodine

Iodine sublimes gradually and produces visible fumes on gentle heating at standard atmospheric temperature. It is possible to obtain liquid iodine at atmospheric pressure by controlling the temperature at just between the melting point and the boiling point of iodine. In forensic science, iodine vapor can reveal latent fingerprints on paper.[11]

Other substances

Camphor subliming in a cold finger. The crude product in the bottom is dark brown; the white purified product on the bottom of the cold finger above is hard to see against the light background.

Arsenic sublimes gradually upon heating at atmospheric pressure, and sublimes rapidly at 887 K (614 °C).[12]

Cadmium and zinc sublime much more than other common materials, so they are not suitable materials for use in vacuum.[citation needed]

Purification by sublimation

Crystals of ferrocene after purification by vacuum sublimation

Sublimation is a technique used by chemists to purify compounds. A solid is typically placed in a sublimation apparatus and heated under vacuum. Under this reduced pressure, the solid volatilizes and condenses as a purified compound on a cooled surface (cold finger), leaving a non-volatile residue of impurities behind. Once heating ceases and the vacuum is removed, the purified compound may be collected from the cooling surface.[13][14] For even higher purification efficiencies, a temperature gradient is applied, which also allows for the separation of different fractions. Typical setups use an evacuated glass tube that is heated gradually in a controlled manner. The material flow is from the hot end, where the initial material is placed, to the cold end that is connected to a pump stand. By controlling temperatures along the length of the tube, the operator can control the zones of re-condensation, with very volatile compounds being pumped out of the system completely (or caught by a separate cold trap), moderately volatile compounds re-condensing along the tube according to their different volatilities, and non-volatile compounds remaining in the hot end. Vacuum sublimation of this type is also the method of choice for purification of organic compounds for use in the organic electronics industry, where very high purities (often > 99.99%) are needed to satisfy the standards for consumer electronics and other applications.[citation needed]

Historical usage

In ancient alchemy, a protoscience that contributed to the development of modern chemistry and medicine, alchemists developed a structure of basic laboratory techniques, theory, terminology, and experimental methods. Sublimation was used to refer to the process in which a substance is heated to a vapor, then immediately collects as sediment on the upper portion and neck of the heating medium (typically a retort or alembic), but can also be used to describe other similar non-laboratory transitions. It was mentioned by alchemical authors such as Basil Valentine and George Ripley, and in the Rosarium philosophorum, as a process necessary for the completion of the magnum opus. Here, the word sublimation was used to describe an exchange of "bodies" and "spirits" similar to laboratory phase transition between solids and gases. Valentine, in his Le char triomphal de l'antimoine (Triumphal Chariot of Antimony, published 1646) made a comparison to spagyrics in which a vegetable sublimation can be used to separate the spirits in wine and beer.[15] Ripley used language more indicative of the mystical implications of sublimation, indicating that the process has a double aspect in the spiritualization of the body and the corporalizing of the spirit.[16] He writes:[17]

And Sublimations we make for three causes,
The first cause is to make the body spiritual.
The second is that the spirit may be corporeal,
And become fixed with it and consubstantial.
The third cause is that from its filthy original.
It may be cleansed, and its saltiness sulphurious
May be diminished in it, which is infectious.

Sublimation predictions

The enthalpy of sublimation has commonly been predicted using the equipartition theorem. If the lattice energy is assumed to be approximately half the packing energy,[clarification needed] then the following thermodynamic corrections can be applied to predict the enthalpy of sublimation. Assuming a 1 molar ideal gas gives a correction for the thermodynamic environment (pressure and volume) in which pV = RT, hence a correction of 1RT. Additional corrections for the vibrations, rotations and translation then need to be applied. From the equipartition theorem gaseous rotation and translation contribute 1.5RT each to the final state, therefore a +3RT correction. Crystalline vibrations and rotations contribute 3RT each to the initial state, hence −6RT. Summing the RT corrections; −6RT + 3RT + RT = −2RT.[18] This leads to the following approximate sublimation enthalpy. A similar approximation can be found for the entropy term if rigid bodies are assumed.[19][20]

Dye-sublimation printing

Dye-sub printing is a digital printing technology using full color artwork that works with polyester and polymer-coated substrates. Also referred to as digital sublimation, the process is commonly used for decorating apparel, signs and banners, as well as novelty items such as cell phone covers, plaques, coffee mugs, and other items with sublimation-friendly surfaces. The process uses the science of sublimation, in which heat and pressure are applied to a solid, turning it into a gas through an endothermic reaction without passing through the liquid phase.[citation needed]

In sublimation printing, unique sublimation dyes are transferred to sheets of “transfer” paper via liquid gel ink through a piezoelectric print head. The ink is deposited on these high-release inkjet papers, which are used for the next step of the sublimation printing process. After the digital design is printed onto sublimation transfer sheets, it is placed on a heat press along with the substrate to be sublimated.[citation needed]

In order to transfer the image from the paper to the substrate, it requires a heat press process that is a combination of time, temperature and pressure. The heat press applies this special combination, which can change depending on the substrate, to “transfer” the sublimation dyes at the molecular level into the substrate. The most common dyes used for sublimation activate at 350 degrees Fahrenheit. However, a range of 380 to 420 degrees Fahrenheit is normally recommended for optimal color.[citation needed]

The result of the sublimation process is a nearly permanent, high resolution, full color print. Because the dyes are infused into the substrate at the molecular level, rather than applied at a topical level (such as with screen printing and direct to garment printing), the prints will not crack, fade or peel from the substrate under normal conditions.[citation needed]

See also

Table of phase transitions of matter

Phase transitions of matter ()
To
From
Solid Liquid Gas Plasma
Solid
Melting Sublimation
Liquid Freezing
Vaporization
Gas Deposition Condensation
Ionization
Plasma Recombination

References

  1. ^ Whitten, Kenneth W.; Gailey, Kenneth D.; Davis, Raymond E. (1992). General chemistry (4th ed.). Saunders College Publishing. p. 475. ISBN 0-03-072373-6.
  2. ^ a b "Sublimate". Merriam-Webster.com Dictionary. Merriam-Webster.
  3. ^ "Sublimate". CollinsDictionary.com Dictionary.
  4. ^ Boreyko, Jonathan B.; Hansen, Ryan R.; Murphy, Kevin R.; Nath, Saurabh; Retterer, Scott T.; Collier, C. Patrick (2016). "Controlling condensation and frost growth with chemical micropatterns". Scientific Reports. 6: 19131. Bibcode:2016NatSR...619131B. doi:10.1038/srep19131. PMC 4726256. PMID 26796663.
  5. ^ "Sublime". Dictionary.com Unabridged (Online). n.d.
  6. ^ "Sublime". CollinsDictionary.com Dictionary.
  7. ^ Fassnacht, S. R. (2004). "Estimating Alter-shielded gauge snowfall undercatch, snowpack sublimation, and blowing snow transport at six sites in the coterminous USA". Hydrol. Process. 18 (18): 3481–3492. Bibcode:2004HyPr...18.3481F. doi:10.1002/hyp.5806. S2CID 129927018.
  8. ^ Caroll, J. (2014). Natural Gas Hydrates. Gulf Professional. p. 16. ISBN 9780128005750.
  9. ^ Staff writer(s) (2015). "what solids go through sublimation?". National Science Foundation and UCSB School-University partnership. Retrieved 13 November 2015.
  10. ^ Pavia, D. (2005). Introduction to organic laboratory technique. Thomson Brooks/Cole. pp. 781–782. ISBN 978-0534408336.
  11. ^ Girard, James (2011). Criminalistics: Forensic Science, Crime and Terrorism. Jones & Bartlett Learning. pp. 143–144. ISBN 978-0-7637-7731-9.
  12. ^ Holleman, Arnold F.; Wiberg, Egon; Wiberg, Nils (1985). "Arsen". Lehrbuch der Anorganischen Chemie (in German) (91–100 ed.). Walter de Gruyter. pp. 675–681. ISBN 978-3-11-007511-3.
  13. ^ R. B. King Organometallic Syntheses. Volume 1 Transition-Metal Compounds; Academic Press: New York, 1965. ISBN 0-444-42607-8.
  14. ^ Harwood, Laurence M.; Moody, Christopher J. (1989). Experimental organic chemistry: Principles and Practice (Illustrated ed.). WileyBlackwell. pp. 154–155. ISBN 978-0-632-02017-1.
  15. ^ Barrett, Francis (1815). The lives of alchemystical philosophers: with a critical catalogue of books in occult chemistry, and a selection of the most celebrated treatises on the theory and practice of the hermetic art. Macdonald and Son for Lackington, Allen, & Co. p. 233.
  16. ^ DiBernard, Barbara (1980). Alchemy and Finnegans wake. SUNY Press. p. 57. ISBN 978-0873953887.
  17. ^ Ripley, George (1591). Compound of Alchemy.
  18. ^ Gavezzotti, A. (1997). Theoretical Aspects and Computer Modeling of the Molecular Solid State. Chichester: Wiley and Sons.
  19. ^ McDonagh, J. L.; Nath; De Ferrari, Luna; Van Mourik, Tanja; Mitchell, John B. O. (2014). "Uniting Cheminformatics and Chemical Theory To Predict the Intrinsic Aqueous Solubility of Crystalline Druglike Molecules". Journal of Chemical Information and Modeling. 54 (3): 844–56. doi:10.1021/ci4005805. PMC 3965570. PMID 24564264.
  20. ^ McDonagh, James; Palmer, David S.; Van Mourik, Tanja; Mitchell, John B. O. (17 October 2016). "Are The Sublimation Thermodynamics of organic molecules predictable?" (PDF). Journal of Chemical Information and Modeling. 56 (11): 2162–2179. doi:10.1021/acs.jcim.6b00033. hdl:10023/11874. ISSN 1549-9596. PMID 27749062.