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Sublimation (phase transition)

Sublimation is the transition of a substance directly from the solid to the gas state,[1] without passing through the liquid state.[2] 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 or desublimation, in which a substance passes directly from a gas to a solid phase.[3] 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).[4] While vaporization from liquid to gas occurs as evaporation from the surface if it occurs below the boiling point of the liquid, and as boiling with formation of bubbles in the interior of the liquid if it occurs at the boiling point, there is no such distinction for the solid-to-gas transition which always occurs as sublimation from the surface.

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

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 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. Thus, any solid can sublimate if its vapour pressure is higher than the surrounding partial pressure of the same substance, and in some cases sublimates at an appreciable rate (e.g. water ice just below 0 °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.

The term sublimation refers 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.

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, 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.

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.

Examples

Carbon dioxide

 
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 °C (194.65 K, −109.30 °F) at atmospheric pressure, whereas its melting into liquid CO2 can occur along the solid-liquid line at pressures and temperatures above the triple point (i.e., 5.1 atm, −56.6 °C).

Water

Snow and ice sublime, although more slowly, at temperatures below the freezing/melting point temperature line at 0 °C for partial pressures below the triple point pressure of 612 Pa (0.00604 atm).[5] 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.[citation needed]

Naphthalene

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 at standard atmospheric temperature[6] with the sublimation point at around 80 °C or 176 °F.[7] At low temperature, its vapour pressure is high enough, 1 mmHg at 53 °C,[8] to make the solid form of naphthalene evaporate into gas. On cool surfaces, the naphthalene vapours will solidify to form needle-like crystals.

 
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.

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.

Iodine produces fumes on gentle heating, although this is above the triple point and therefore not true sublimation. 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 fingerprints on paper.[9]Arsenic can also sublime at high temperatures.

Cadmium and zinc are not suitable materials for use in vacuum because they sublime much more than other common materials.[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.[10][11] 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.[12] 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.[13] He writes:[14]

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.[15] This leads to the following approximate sublimation enthalpy. A similar approximation can be found for the entropy term if rigid bodies are assumed.[16][17] 

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

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

References

  1. ^ "Sublimate". Merriam-Webster Dictionary.
  2. ^ Whitten, Kenneth W.; Gailey, Kenneth D.; Davis, Raymond E. (1992). General chemistry (4th ed.). Saunders College Publishing. p. 475. ISBN 0-03-072373-6.
  3. ^ 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.
  4. ^ "Sublime". Dictionary.com Unabridged (Online). n.d.
  5. ^ 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.
  6. ^ Caroll, J. (2014). Natural Gas Hydrates. p. 16. ISBN 9780128005750.
  7. ^ Staff writer(s) (2015). "what solid go through sublimation?". National Science Foundation and UCSB School-University partnership. Retrieved 13 November 2015.
  8. ^ Pavia, D. (2005). Introduction to organic laboratory technique. pp. 781–782. ISBN 978-0534408336.
  9. ^ Girard, James (2011). Criminalistics: Forensic Science, Crime and Terrorism. Jones & Bartlett Learning. pp. 143–144. ISBN 978-0-7637-7731-9.
  10. ^ R. B. King Organometallic Syntheses. Volume 1 Transition-Metal Compounds; Academic Press: New York, 1965. ISBN 0-444-42607-8.
  11. ^ 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.
  12. ^ 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.
  13. ^ DiBernard, Barbara (1980). Alchemy and Finnegans wake. SUNY Press. p. 57. ISBN 978-0873953887.
  14. ^ Ripley, George (1591). Compound of Alchemy.
  15. ^ Gavezzotti, A. (1997). Theoretical Aspects and Computer Modeling of the Molecular Solid State. Chichester: Wiley and Sons.
  16. ^ 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.
  17. ^ 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.

External links

  •   Media related to Sublimation at Wikimedia Commons

sublimation, phase, transition, sublimates, redirects, here, other, uses, sublimation, sublimation, transition, substance, directly, from, solid, state, without, passing, through, liquid, state, sublimation, endothermic, process, that, occurs, temperatures, pr. Sublimates redirects here For other uses see Sublimation Sublimation is the transition of a substance directly from the solid to the gas state 1 without passing through the liquid state 2 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 or desublimation in which a substance passes directly from a gas to a solid phase 3 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 4 While vaporization from liquid to gas occurs as evaporation from the surface if it occurs below the boiling point of the liquid and as boiling with formation of bubbles in the interior of the liquid if it occurs at the boiling point there is no such distinction for the solid to gas transition which always occurs as sublimation from the surface Dark green crystals of nickelocene sublimed and freshly deposited on a cold finger 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 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 Thus any solid can sublimate if its vapour pressure is higher than the surrounding partial pressure of the same substance and in some cases sublimates at an appreciable rate e g water ice just below 0 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 The term sublimation refers 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 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 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 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 Contents 1 Examples 1 1 Carbon dioxide 1 2 Water 1 3 Naphthalene 1 4 Other substances 2 Purification by sublimation 3 Historical usage 4 Sublimation predictions 5 Dye sublimation printing 6 See also 7 Table 8 References 9 External linksExamplesCarbon dioxide 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 C 194 65 K 109 30 F at atmospheric pressure whereas its melting into liquid CO2 can occur along the solid liquid line at pressures and temperatures above the triple point i e 5 1 atm 56 6 C Water Snow and ice sublime although more slowly at temperatures below the freezing melting point temperature line at 0 C for partial pressures below the triple point pressure of 612 Pa 0 00604 atm 5 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 citation needed Naphthalene 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 at standard atmospheric temperature 6 with the sublimation point at around 80 C or 176 F 7 At low temperature its vapour pressure is high enough 1 mmHg at 53 C 8 to make the solid form of naphthalene evaporate into gas On cool surfaces the naphthalene vapours will solidify to form needle like crystals 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 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 Iodine produces fumes on gentle heating although this is above the triple point and therefore not true sublimation 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 fingerprints on paper 9 Arsenic can also sublime at high temperatures Cadmium and zinc are not suitable materials for use in vacuum because they sublime much more than other common materials 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 10 11 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 gt 99 99 are needed to satisfy the standards for consumer electronics and other applications citation needed Historical usageIn 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 12 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 13 He writes 14 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 predictionsThe 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 15 This leads to the following approximate sublimation enthalpy A similar approximation can be found for the entropy term if rigid bodies are assumed 16 17 D H sublimation U lattice energy 2 R T displaystyle Delta H text sublimation U text lattice energy 2RT Dye sublimation printingMain article 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 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 alsoAblation Enthalpy of sublimation Freeze drying Freezer burn common process involving sublimation Phase diagramTablePhase transitions of matter vte ToFrom Solid Liquid Gas PlasmaSolid Melting SublimationLiquid Freezing VaporizationGas Deposition Condensation IonizationPlasma RecombinationReferences Sublimate Merriam Webster Dictionary Whitten Kenneth W Gailey Kenneth D Davis Raymond E 1992 General chemistry 4th ed Saunders College Publishing p 475 ISBN 0 03 072373 6 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 Sublime Dictionary com Unabridged Online n d 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 Caroll J 2014 Natural Gas Hydrates p 16 ISBN 9780128005750 Staff writer s 2015 what solid go through sublimation National Science Foundation and UCSB School University partnership Retrieved 13 November 2015 Pavia D 2005 Introduction to organic laboratory technique pp 781 782 ISBN 978 0534408336 Girard James 2011 Criminalistics Forensic Science Crime and Terrorism Jones amp Bartlett Learning pp 143 144 ISBN 978 0 7637 7731 9 R B King Organometallic Syntheses Volume 1 Transition Metal Compounds Academic Press New York 1965 ISBN 0 444 42607 8 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 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 amp Co p 233 DiBernard Barbara 1980 Alchemy and Finnegans wake SUNY Press p 57 ISBN 978 0873953887 Ripley George 1591 Compound of Alchemy Gavezzotti A 1997 Theoretical Aspects and Computer Modeling of the Molecular Solid State Chichester Wiley and Sons 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 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 External links Media related to Sublimation at Wikimedia Commons Retrieved from https en wikipedia org w index php title Sublimation phase transition amp oldid 1138074382, wikipedia, wiki, book, books, library,

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