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Thermal probe of vapor–liquid thermodynamic equilibrium

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Abstract

Vapor pressure data and evaporation/sublimation rate of liquid and solid samples are key parameters for designing new process units in terms of design, operability, and safety. In addition, for the case of hazardous materials, health and environmental aspects become essential. Conventional methods for obtaining these data mostly require significant material, time, and energy. Thermal analysis methods including differential scanning calorimetry (DSC) and thermogravimetry (TG) can both offer a platform for studying transition behavior of liquids/solids to the vapor phase. Yet, there are limitations, operational considerations, and analysis precautions to be accounted for in order to obtain highly valuable data. In particular, specific cautions should be taken for the case of liquid mixtures. Therefore, it is essential that the fundamentals and underlying principles of using DSC and TG methods for vapor pressure data generation are comprehensively understood so that one can effectively tune the methods according to the specific nature of the study. The dynamic nature of these methods develops a quasi-equilibrium state, where one should attempt to optimize the conditions as such that the temperature program effect becomes negligible on the initial condition of the sample. In this work, an integrative approach is followed to discuss the fundamentals and operational aspects of using DSC and TG for generating accurate vaporization and vapor pressure data of liquid samples. Specific attention is dedicated to elaborate on optimizing not only the experimental conditions to achieve isothermal boiling, but also data analysis step. Therefore, different considerations regarding post-run analysis are discussed. Moreover, due to the high importance of hydrocarbons, specific attention is also given to the application of these two methods to obtain vapor pressure data of hydrocarbons. The constructive discussions in this work develop an overview of the fundamentals of the method, provide the most significant contributions to the topic in a unifying manner, and suggest inputs and highlight the limitations of the techniques for future studies.

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References

  1. Akisawa Silva LY, Matricarde Falleiro RM, Meirelles AJA, Krähenbühl MA. Vapor–liquid equilibrium of fatty acid ethyl esters determined using DSC. Thermochim Acta. 2011;512:178–82. https://doi.org/10.1016/j.tca.2010.10.002.

    Article  CAS  Google Scholar 

  2. Khoshooei MA, Sharp D, Maham Y, Afacan A, Dechaine GP. A new analysis method for improving collection of vapor-liquid equilibrium (VLE) data of binary mixtures using differential scanning calorimetry (DSC). Thermochim Acta. 2018;659:232–41. https://doi.org/10.1016/j.tca.2017.12.010.

    Article  CAS  Google Scholar 

  3. Harvey J-P, Saadatkhah N, Dumont-Vandewinkel G, Ackermann SLG, Patience GS. Experimental methods in chemical engineering: Differential scanning calorimetry-DSC. Can J Chem Eng. 2018;96:2518–25. https://doi.org/10.1002/cjce.23346.

    Article  CAS  Google Scholar 

  4. Saadatkhah N, Carillo Garcia A, Ackermann S, Leclerc P, Latifi M, Samih S, et al. Experimental methods in chemical engineering: Thermogravimetric analysis-TGA. Can J Chem Eng. 2020;98:34–43. https://doi.org/10.1002/cjce.23673.

    Article  CAS  Google Scholar 

  5. Ipser H. Vapor pressure methods: a source of experimental thermodynamic data. Berichte der Bunsengesellschaft für Phys Chemie. 1998;102:1217–24. https://doi.org/10.1002/bbpc.19981020926.

    Article  CAS  Google Scholar 

  6. Wisniak J. Historical development of the vapor pressure equation from dalton to antoine. J Phase Equilibria. 2001;22:622. https://doi.org/10.1007/s11669-001-0026-x.

    Article  CAS  Google Scholar 

  7. Östmark H, Wallin S, Ang HG. Vapor pressure of explosives: a critical review. Propellants Explos Pyrotech. 2012;37:12–23. https://doi.org/10.1002/prep.201100083.

    Article  CAS  Google Scholar 

  8. Malanowski S. Experimental methods for vapour-liquid equilibria. Part I. Circulation methods. Fluid Phase Equilib. 1982. https://doi.org/10.1016/0378-3812(82)80035-6.

    Article  Google Scholar 

  9. Malanowski S. Experimental methods for vapour-liquid equilibria. II. Dew- and bubble-point method. Fluid Phase Equilib. 1982. https://doi.org/10.1016/0378-3812(82)80026-5.

    Article  Google Scholar 

  10. Sayegh SG, Vera JH. Model-free methods for vapor-liquid equilibria calculations Binary systems. Chem Eng Sci. 1980;35:2247–56. https://doi.org/10.1016/0009-2509(80)87002-3.

    Article  CAS  Google Scholar 

  11. Hu Y, Liu H, Prausnitz JM. A model-free method for calculating vapor-liquid equilibria for multicomponent systems from total-pressure or boiling-point data. Fluid Phase Equilib. 1994;95:73–92. https://doi.org/10.1016/0378-3812(94)80062-6.

    Article  CAS  Google Scholar 

  12. Sage BH, Schaafsma JG, Lacey WN. Phase equilibria in hydrocarbon systems V. Pressure-Volume-Temperature relations and thermal properties of propane. Ind Eng Chem. 1934. https://doi.org/10.1021/ie50299a021.

    Article  Google Scholar 

  13. Casserino M, Blevins DR, Sanders RN. An improved method for measuring vapor pressure by DSC with automated pressure control. Thermochim Acta. 1996;284:145–52. https://doi.org/10.1016/0040-6031(96)02923-1.

    Article  CAS  Google Scholar 

  14. Stross FH, Abrams ST. Thermal analysis of the system sodium stearate-cetane. J Am Chem Soc. 1951;73:2825–8. https://doi.org/10.1021/ja01150a116.

    Article  CAS  Google Scholar 

  15. Vassallo DA, Harden JC. Precise phase transition measurements of organic materials by differential thermal analysis. Anal Chem. 1962;34:132–5. https://doi.org/10.1021/ac60181a040.

    Article  CAS  Google Scholar 

  16. Morita H, Rice HM. Characterization of organic substances by differential thermal analysis: general experimental technique. Anal Chem. 1955;27:336–9. https://doi.org/10.1021/ac60099a002.

    Article  CAS  Google Scholar 

  17. Varma MCP. Differential thermal analysis of organic solids. J Appl Chem. 1958;8:117–21. https://doi.org/10.1002/jctb.5010080206.

    Article  CAS  Google Scholar 

  18. Krawetz AA, Tovrog T. Determination of vapor pressure by differential thermal analysis. Rev Sci Instrum. 1962;33:1465–6. https://doi.org/10.1063/1.1717805.

    Article  CAS  Google Scholar 

  19. Barrall EM, Porter RS, Johnson JF. Microboiling point determination at 30–760 Torr by differential thermal analysis. Anal Chem. 1965;37:1053–4. https://doi.org/10.1021/ac60227a030.

    Article  CAS  Google Scholar 

  20. Wisnewski AM, Calhoun RJ, Witnauer LP. Pressure chamber for use during differential thermal analyses. J Appl Polym Sci. 2018;9:3935–8. https://doi.org/10.1002/app.1965.070091215.

    Article  Google Scholar 

  21. Staub H, Schnyder M. A new method for the determination of heat of vaporization by quantitative differential thermal analysis. Thermochim Acta. 1974;10:237–43. https://doi.org/10.1016/0040-6031(74)80019-5.

    Article  CAS  Google Scholar 

  22. Morie GP, Powers TA, Glover CA. Evaluation of thermal analysis equipment for the determination of vapor pressure and heat of vaporization. Thermochim Acta. 1972;3:259–69. https://doi.org/10.1016/0040-6031(72)80002-9.

    Article  CAS  Google Scholar 

  23. Charles RG. Vapor pressures by differential thermal analysis: application to some nickel chelates. Thermochim Acta. 1980;38:315–27. https://doi.org/10.1016/0040-6031(80)85039-8.

    Article  CAS  Google Scholar 

  24. Khoshooei MA. Vapour-Liquid Equilibrium of by-Products n-Alcohols and 1, 3-Propanediol from Polyol Production. University of Alberta (Canada); 2013.

  25. Seyler RJ. Parameters affecting the determination of vapor pressure by differential thermal methods. Thermochim Acta. 1976;17:129–36. https://doi.org/10.1016/0040-6031(76)85019-8.

    Article  CAS  Google Scholar 

  26. Kemme HR, Kreps SI. Vapor pressure determination by differential thermal analysis. Anal Chem. 1969;41:1869–72. https://doi.org/10.1021/ac60282a004.

    Article  CAS  Google Scholar 

  27. Kemme HR, Kreps SI. Vapor pressure of primary n-alkyl chlorides and alcohols. J Chem Eng Data. 1969;14:98–102. https://doi.org/10.1021/je60040a011.

    Article  CAS  Google Scholar 

  28. Siitsman C, Kamenev I, Oja V. Vapor pressure data of nicotine, anabasine and cotinine using differential scanning calorimetry. Thermochim Acta. 2014;595:35–42. https://doi.org/10.1016/j.tca.2014.08.033.

    Article  CAS  Google Scholar 

  29. Brozena A, Fielder D. Subambient applications of differential thermal analysis for the determination of vapor pressure. Thermochim Acta. 1992;212:63–8. https://doi.org/10.1016/0040-6031(92)80220-Q.

    Article  CAS  Google Scholar 

  30. Barrall EM. Precise determination of melting and boiling points by differential thermal analysis and differential scanning calorimetry. Thermochim Acta. 1973;5:377–89. https://doi.org/10.1016/0040-6031(73)80016-4.

    Article  CAS  Google Scholar 

  31. Contreras MD, Girela F, Parera A. The perfection of a method for the determination of the temperature/vapour-pressure function of liquids by differential scanning calorimetry. Thermochim Acta. 1993;219:167–72. https://doi.org/10.1016/0040-6031(93)80494-U.

    Article  CAS  Google Scholar 

  32. Tilinski D, Puderbach H. Experiences with the use of DSC in the determination of vapor pressure of organic compounds. J Therm Anal Calorim. 1989;35:503–13. https://doi.org/10.1007/BF01904452.

    Article  CAS  Google Scholar 

  33. Butrow AB, Seyler RJ. Vapor pressure by DSC: extending ASTM E 1782 below 5 kPa. Thermochim Acta. 2003;402:145–52. https://doi.org/10.1016/S0040-6031(02)00604-4.

    Article  CAS  Google Scholar 

  34. Brozena A. Vapor pressure of 1-octanol below 5kPa using DSC. Thermochim Acta. 2013;561:72–6. https://doi.org/10.1016/j.tca.2013.03.018.

    Article  CAS  Google Scholar 

  35. Barrall EM, Porter RS, Johnson JF. Heats of transition for nematic mesophases. J Phys Chem. 1964;68:2810–3. https://doi.org/10.1021/j100792a011.

    Article  CAS  Google Scholar 

  36. Khoshooei MA, Sharp D, Afacan A, Dechaine GP. Vapor-liquid equilibrium data of binary mixtures of 1-hexanol, 1-heptanol, 1-nonanol and 1,3-propanediol at P = 101.3 kPa using differential scanning calorimetry (DSC). J Chem Thermodyn. 2019;132:105–12. https://doi.org/10.1016/j.jct.2018.12.030.

    Article  CAS  Google Scholar 

  37. Silva LYA, Falleiro RMM, Meirelles AJA, Krähenbühl MA. Determination of the vapor pressure of ethyl esters by Differential Scanning Calorimetry. J Chem Thermodyn. 2011;43:943–7. https://doi.org/10.1016/j.jct.2011.01.017.

    Article  CAS  Google Scholar 

  38. Troni KL, Damaceno DS, Ceriani R. Improving a variation of the DSC technique for measuring the boiling points of pure compounds at low pressures. J Chem Thermodyn. 2016;100:191–7. https://doi.org/10.1016/j.jct.2016.04.023.

    Article  CAS  Google Scholar 

  39. Butrow AB, Buchanan JH, Tevault DE. Vapor pressure of organophosphorus nerve agent simulant compounds. J Chem Eng Data. 2009;54:1876–83. https://doi.org/10.1021/je8010024.

    Article  CAS  Google Scholar 

  40. Matricarde Falleiro RM, Akisawa Silva LY, Meirelles AJA, Krähenbühl MA. Vapor pressure data for fatty acids obtained using an adaptation of the DSC technique. Thermochim Acta. 2012;547:6–12. https://doi.org/10.1016/j.tca.2012.07.034.

    Article  CAS  Google Scholar 

  41. Falleiro RMM, Meirelles AJA, Krähenbühl MA. Experimental determination of the (vapor + liquid) equilibrium data of binary mixtures of fatty acids by differential scanning calorimetry. J Chem Thermodyn. 2010;42:70–7. https://doi.org/10.1016/j.jct.2009.07.008.

    Article  CAS  Google Scholar 

  42. Perrenot B, de Vallière P, Widmann G. New pressure DSC cell and some applications. J Therm Anal. 1992;38:381–90. https://doi.org/10.1007/BF01915502.

    Article  CAS  Google Scholar 

  43. Astra H-L, Oja V. Vapour pressure data for 2-n-propylresorcinol, 4-ethylresorcinol and 4-hexylresorcinol near their normal boiling points measured by differential scanning calorimetry. J Chem Thermodyn. 2019;134:119–26. https://doi.org/10.1016/j.jct.2019.03.008.

    Article  CAS  Google Scholar 

  44. Wisnewski AM, Calhoun RJ Jr, Witnauer LP. Pressure chamber for use during differential thermal analyses. J Appl Polym Sci. 1965;9:3935–8. https://doi.org/10.1002/app.1965.070091215.

    Article  CAS  Google Scholar 

  45. Farritor RE, Tao LC. An improved method of measurement of vaporization heat of volatile liquids with a differential scanning calorimeter. Thermochim Acta. 1970;1:297–304. https://doi.org/10.1016/0040-6031(70)80034-X.

    Article  CAS  Google Scholar 

  46. Damaceno DS, Matricarde Falleiro RM, Krähenbühl MA, Meirelles AJA, Ceriani R. Boiling points of short-chain partial acylglycerols and tocopherols at low pressures by the differential scanning calorimetry technique. J Chem Eng Data. 2014;59:1515–20. https://doi.org/10.1021/je401080p.

    Article  CAS  Google Scholar 

  47. Siitsman C, Oja V. Extension of the DSC method to measuring vapor pressures of narrow boiling range oil cuts. Thermochim Acta. 2015;622:31–7. https://doi.org/10.1016/j.tca.2015.04.011.

    Article  CAS  Google Scholar 

  48. Eubank PT, Lamonte BG, Javier Alvarado JF. Consistency tests for binary VLE data. J Chem Eng Data. 2000;45:1040–8. https://doi.org/10.1021/je9902692.

    Article  CAS  Google Scholar 

  49. Van Ness HC. Thermodynamics in the treatment of vapor/liquid equilibrium (VLE) data. Pure Appl Chem. 1995;67:859–72. https://doi.org/10.1351/pac199567060859.

    Article  Google Scholar 

  50. Kang JW, Diky V, Chirico RD, Magee JW, Muzny CD, Abdulagatov I, et al. Quality assessment algorithm for vapor−liquid equilibrium data. J Chem Eng Data. 2010;55:3631–40. https://doi.org/10.1021/je1002169.

    Article  CAS  Google Scholar 

  51. Cunico LP, Damaceno DS, Matricarde Falleiro RM, Sarup B, Abildskov J, Ceriani R, et al. Vapour liquid equilibria of monocaprylin plus palmitic acid or methyl stearate at P=(1.20 and 2.50) kPa by using DSC technique. J Chem Thermodyn. 2015. https://doi.org/10.1016/j.jct.2015.07.033.

    Article  Google Scholar 

  52. Damaceno DS, Ceriani R. Vapor-liquid equilibria of monoacylglicerol + monoacylglicerol or alcohol or fatty acid at subatmospheric pressures. Fluid Phase Equilib. 2017;452:135–42. https://doi.org/10.1016/j.fluid.2017.08.013.

    Article  CAS  Google Scholar 

  53. Damaceno DS, Ceriani R. Vapor–liquid equilibria of binary systems with long-chain organic compounds (fatty alcohol, fatty ester, acylglycerol, and n-paraffin) at subatmospheric pressures. J Chem Eng Data. 2018;63:2840–7. https://doi.org/10.1021/acs.jced.8b00168.

    Article  CAS  Google Scholar 

  54. Troni KL, Damaceno DS, Ceriani R. Evaluation of a variation of the differential scanning calorimetry technique for measuring boiling points of binary mixtures at subatmospheric pressures. J Chem Eng Data. 2020;65:3334–43. https://doi.org/10.1021/acs.jced.0c00111.

    Article  CAS  Google Scholar 

  55. Hacura A, Kaczorowska B. Raman microscopic characterization of phase separation in binary n-alkane mixtures. J Mol Struct. 2005;744–747:581–4. https://doi.org/10.1016/j.molstruc.2004.12.010.

    Article  CAS  Google Scholar 

  56. Cousty J, Pham VL. Formation of partially demixed two-dimensional solid solutions from binary mixtures of n-alkanes with very different lengths. Phys Chem Chem Phys. 2003;5:599–603. https://doi.org/10.1039/B206529K.

    Article  CAS  Google Scholar 

  57. Ferreira M, Schwarz CE. Low-pressure VLE measurements and thermodynamic modeling, with PSRK and NRTL, of binary 1-alcohol + n-alkane systems. J Chem Eng Data. 2018;63:4614–25. https://doi.org/10.1021/acs.jced.8b00680.

    Article  CAS  Google Scholar 

  58. Qiu X, Tan SP, Dejam M, Adidharma H. Novel isochoric measurement of the onset of vapor–liquid phase transition using differential scanning calorimetry. Phys Chem Chem Phys. 2018;20:26241–8. https://doi.org/10.1039/C8CP05613G.

    Article  CAS  PubMed  Google Scholar 

  59. Qiu X, Tan SP, Dejam M, Adidharma H. Isochoric measurement of the evaporation point of pure fluids in bulk and nanoporous media using differential scanning calorimetry. Phys Chem Chem Phys. 2020;22:7048–57. https://doi.org/10.1039/D0CP00900H.

    Article  CAS  PubMed  Google Scholar 

  60. Chatterjee K, Hazra A, Dollimore D, Alexander KS. Estimating vapor pressure curves by thermogravimetry: a rapid and convenient method for characterization of pharmaceuticals. Eur J Pharm Biopharm. 2002;54:171–80. https://doi.org/10.1016/S0939-6411(02)00079-6.

    Article  CAS  PubMed  Google Scholar 

  61. Hikal WM, Paden JT, Weeks BL. Rapid estimation of thermodynamic parameters and vapor pressures of volatile materials at nanoscale. ChemPhysChem. 2012;13:2729–33. https://doi.org/10.1002/cphc.201200355.

    Article  CAS  PubMed  Google Scholar 

  62. Price DM. A fit of the vapours. Thermochim Acta. 2015;622:44–50. https://doi.org/10.1016/j.tca.2015.04.030.

    Article  CAS  Google Scholar 

  63. García Santander CM, Gómez Rueda SM, de Lima da Silva N, de Camargo CL, Kieckbusch TG, Wolf Maciel MR. Measurements of normal boiling points of fatty acid ethyl esters and triacylglycerols by thermogravimetric analysis. Fuel. 2012; 92:158–61. https://doi.org/10.1016/j.fuel.2011.08.011.

  64. Zhou G, Roby S, Wei T, Yee N. Fuel heat of vaporization values measured with vacuum thermogravimetric analysis method. Energy Fuels. 2014;28:3138–42. https://doi.org/10.1021/ef402491p.

    Article  CAS  Google Scholar 

  65. Goodrum JW, Geller DP, Lee SA. Rapid measurement of boiling points and vapor pressure of binary mixtures of short-chain triglycerides by TGA method. Thermochim Acta. 1998;311:71–9. https://doi.org/10.1016/S0040-6031(97)00377-8.

    Article  CAS  Google Scholar 

  66. Goodrum JW, Geller DP. Rapid thermogravimetric measurements of boiling points and vapor pressure of saturated medium- and long-chain triglycerides. Bioresour Technol. 2002;84:75–80. https://doi.org/10.1016/S0960-8524(02)00006-8.

    Article  CAS  PubMed  Google Scholar 

  67. Goodrum JW. Rapid measurements of boiling point and vapor pressure of short-chain triglycerides by thermogravimetric analysis. J Am Oil Chem Soc. 1997;74:947–50. https://doi.org/10.1007/s11746-997-0009-0.

    Article  CAS  Google Scholar 

  68. Damaceno DS, Jesus EP, Ceriani R. Experimental data and prediction of normal boiling points of partial acylglycerols. Fuel. 2018;232:470–5. https://doi.org/10.1016/j.fuel.2018.05.160.

    Article  CAS  Google Scholar 

  69. Goodrum JW. Volatility and boiling points of biodiesel from vegetable oils and tallow. Biomass Bioenerg. 2002;22:205–11. https://doi.org/10.1016/S0961-9534(01)00074-5.

    Article  CAS  Google Scholar 

  70. Goodrum JW, Siesel EM. Thermogravimetric analysis for boiling points and vapour pressure. J Therm Anal. 1996;46:1251–8. https://doi.org/10.1007/BF01979239.

    Article  CAS  Google Scholar 

  71. Langmuir I. The vapor pressure of metallic tungsten. Phys Rev. 1913;2:329–42. https://doi.org/10.1103/PhysRev.2.329.

    Article  Google Scholar 

  72. Rong Y, Gregson CM, Parker A. Thermogravimetric measurements of liquid vapor pressure. J Chem Thermodyn. 2012;51:25–30. https://doi.org/10.1016/j.jct.2012.02.021.

    Article  CAS  Google Scholar 

  73. Chatterjee K, Dollimore D, Alexander K. A new application for the Antoine equation in formulation development. Int J Pharm. 2001;213:31–44. https://doi.org/10.1016/S0378-5173(00)00644-X.

    Article  CAS  PubMed  Google Scholar 

  74. Wright SF, Dollimore D, Dunn JG, Alexander K. Determination of the vapor pressure curves of adipic acid and triethanolamine using thermogravimetric analysis. Thermochim Acta. 2004;421:25–30. https://doi.org/10.1016/j.tca.2004.02.021.

    Article  CAS  Google Scholar 

  75. Chatterjee K, Dollimore D, Alexander K. Calculation of vapor pressure curves for ethyl, propyl, and butyl parabens using thermogravimetry. Instrum Sci Technol. 2001;29:133–44. https://doi.org/10.1081/CI-100103461.

    Article  CAS  Google Scholar 

  76. Phang P, Dollimore D, Evans SJ. A comparative method for developing vapor pressure curves based on evaporation data obtained from a simultaneous TG-DTA unit. Thermochim Acta. 2002;392–393:119–25. https://doi.org/10.1016/S0040-6031(02)00092-8.

    Article  Google Scholar 

  77. Price DM, Hawkins M. Calorimetry of two disperse dyes using thermogravimetry. Thermochim Acta. 1998;315:19–24. https://doi.org/10.1016/S0040-6031(98)00272-X.

    Article  CAS  Google Scholar 

  78. Phang P, Dollimore D. The calculation of the vapor pressures of antioxidants over a range of temperatures using thermogravimetry. Thermochim Acta. 2001;367–368:263–71. https://doi.org/10.1016/S0040-6031(00)00651-1.

    Article  Google Scholar 

  79. de Oliveira CEL, Cremasco MA. Determination of the vapor pressure of Lippia gracilis Schum essential oil by thermogravimetric analysis. Thermochim Acta. 2014;577:1–4. https://doi.org/10.1016/j.tca.2013.11.023.

    Article  CAS  Google Scholar 

  80. Kunte GV, Ail U, Ajikumar PK, Tyagi AK, Shivashankar SA, Umarji AM. Estimation of vapour pressure and partial pressure of subliming compounds by low-pressure thermogravimetry. Bull Mater Sci. 2011;34:1633–7. https://doi.org/10.1007/s12034-011-0369-9.

    Article  CAS  Google Scholar 

  81. Surov OV. Thermogravimetric method used to determine the saturated vapor pressure in a wide range of values. Russ J Appl Chem. 2009;82:42–6. https://doi.org/10.1134/S1070427209010091.

    Article  CAS  Google Scholar 

  82. Szczotok AM, Kjøniksen A-L, Rodriguez JF, Carmona M. The accurate diffusive model for predicting the vapor pressure of phase change materials by thermogravimetric analysis. Thermochim Acta. 2019;676:64–70. https://doi.org/10.1016/j.tca.2019.04.001.

    Article  CAS  Google Scholar 

  83. Price DM, Bashir S, Derrick PR. Sublimation properties of x, y-dihydroxybenzoic acid isomers as model matrix assisted laser desorption ionisation (MALDI) matrices. Thermochim Acta. 1999;327:167–71. https://doi.org/10.1016/S0040-6031(98)00606-6.

    Article  CAS  Google Scholar 

  84. Rojas A, Vieyra-Eusebio MT. Enthalpies of sublimation of ferrocene and nickelocene measured by calorimetry and the method of Langmuir. J Chem Thermodyn. 2011;43:1738–47. https://doi.org/10.1016/j.jct.2011.06.001.

    Article  CAS  Google Scholar 

  85. Ramos F, Ledo JM, Flores H, Camarillo EA, Carvente J, Amador MP. Evaluation of sublimation enthalpy by thermogravimetry: analysis of the diffusion effects in the case of methyl and phenyl substituted hydantoins. Thermochim Acta. 2017;655:181–93. https://doi.org/10.1016/j.tca.2017.06.024.

    Article  CAS  Google Scholar 

  86. Vecchio S, Brunetti B. Vapor pressures and standard molar sublimation enthalpies of three 6-methylthio-2,4-di(alkylamino)-1,3,5-triazine derivatives: simetryn, ametryn, and terbutryn. J Chem Eng Data. 2007;52:1585–94. https://doi.org/10.1021/je600580r.

    Article  CAS  Google Scholar 

  87. Sućeska M, Mušanić SM, Houra IF. Kinetics and enthalpy of nitroglycerin evaporation from double base propellants by isothermal thermogravimetry. Thermochim Acta. 2010;510:9–16. https://doi.org/10.1016/j.tca.2010.06.014.

    Article  CAS  Google Scholar 

  88. Vecchio S, Catalani A, Rossi V, Tomassetti M. Thermal analysis study on vaporization of some analgesics. Acetanilide and derivatives Thermochim Acta. 2004;420:99–104. https://doi.org/10.1016/j.tca.2003.09.039.

    Article  CAS  Google Scholar 

  89. Vecchio S. Standard molar enthalpies and entropies of vaporization for two low-melting trichlorophenoxy herbicides. J Therm Anal Calorim. 2006;84:271–8. https://doi.org/10.1007/s10973-005-7261-z.

    Article  CAS  Google Scholar 

  90. Vecchio S, Brunetti B. Standard sublimation enthalpies of some dichlorophenoxy acids and their methyl esters. J Chem Eng Data. 2005;50:666–72. https://doi.org/10.1021/je049626l.

    Article  CAS  Google Scholar 

  91. Lerdkanchanaporn S, Dollimore D. An investigation of the evaporation of stearic acid using a simultaneous TG-DTA unit. Thermochim Acta. 1998;324:15–23. https://doi.org/10.1016/S0040-6031(98)00519-X.

    Article  CAS  Google Scholar 

  92. Burnham L, Dollimore D, Alexander K. Calculation of the vapor pressure-temperature relationship using thermogravimetry for the drug allopurinol. Thermochim Acta. 2001;367–368:15–22. https://doi.org/10.1016/S0040-6031(00)00652-3.

    Article  Google Scholar 

  93. Aggarwal P, Dollimore D, Alexander K. The use of thermogravimetry to follow the rate of evaporation of an ingredient used in perfumes. J Therm Anal. 1997;49:595–9. https://doi.org/10.1007/BF01996741.

    Article  CAS  Google Scholar 

  94. Shen L, Alexander KS. A thermal analysis study of long chain fatty acids. Thermochim Acta. 1999;340–341:271–8. https://doi.org/10.1016/S0040-6031(99)00272-5.

    Article  Google Scholar 

  95. Félix-Rivera H, Ramírez-Cedeño ML, Sánchez-Cuprill RA, Hernández-Rivera SP. Triacetone triperoxide thermogravimetric study of vapor pressure and enthalpy of sublimation in 303–338 K temperature range. Thermochim Acta. 2011;514:37–43. https://doi.org/10.1016/j.tca.2010.11.034.

    Article  CAS  Google Scholar 

  96. Verevkin SP, Ralys RV, Zaitsau DH, Emelyanenko VN, Schick C. Express thermo-gravimetric method for the vaporization enthalpies appraisal for very low volatile molecular and ionic compounds. Thermochim Acta. 2012. https://doi.org/10.1016/j.tca.2012.03.018.

    Article  Google Scholar 

  97. Lewczyk DC, Cohan JW, Goetz ML, Trafford BL, Fuller RL, Sparks JR. Kinetic treatment of evaporation via thermogravimetric analysis: The case of d-Limonene. Ind Eng Chem Res. 2020;59:15069–74. https://doi.org/10.1021/acs.iecr.0c02864.

    Article  CAS  Google Scholar 

  98. Ralys RV, Uspenskiy AA, Slobodov AA. Deriving properties of low-volatile substances from isothermal evaporation curves. J Non-Equilibrium Thermodyn. 2016. https://doi.org/10.1515/jnet-2015-0030.

    Article  Google Scholar 

  99. Vecchio S, Brunetti B. Vapor pressures and standard molar enthalpies, entropies, and Gibbs free energies of sublimation of 2,4- and 3,4-dinitrobenzoic acids. J Chem Thermodyn. 2009;41:880–7. https://doi.org/10.1016/j.jct.2009.02.008.

    Article  CAS  Google Scholar 

  100. Vecchio S. Vapor pressures and standard molar enthalpies, entropies and Gibbs energies of sublimation of two hexachloro herbicides using a TG unit. Thermochim Acta. 2010;499:27–33. https://doi.org/10.1016/j.tca.2009.10.017.

    Article  CAS  Google Scholar 

  101. Vecchio S, Tomassetti M. Vapor pressures and standard molar enthalpies, entropies and Gibbs energies of sublimation of three 4-substituted acetanilide derivatives. Fluid Phase Equilib. 2009;279:64–72. https://doi.org/10.1016/j.fluid.2009.02.001.

    Article  CAS  Google Scholar 

  102. Vecchio S. Thermogravimetric method for a rapid estimation of vapor pressure and vaporization enthalpies of disubstituted benzoic acids: an attempt to correlate vapor pressures and vaporization enthalpies with structure. Struct Chem. 2013;24:1821–7. https://doi.org/10.1007/s11224-013-0232-2.

    Article  CAS  Google Scholar 

  103. Vecchio S, Brunetti B. Thermochemical study of 2,4-, 2,6- and 3,4-dihydroxybenzoic acids in the liquid phase using a TG apparatus. Thermochim Acta. 2011;515:84–90. https://doi.org/10.1016/j.tca.2011.01.001.

    Article  CAS  Google Scholar 

  104. Price DM. Vapor pressure determination by thermogravimetry. Thermochim Acta. 2001;367–368:253–62. https://doi.org/10.1016/S0040-6031(00)00676-6.

    Article  Google Scholar 

  105. Flynn JH, Dickens B. Steady-state parameter-jump methods and relaxation methods in thermogravimetry. Thermochim Acta. 1976;15:1–16. https://doi.org/10.1016/0040-6031(76)80087-1.

    Article  CAS  Google Scholar 

  106. Dollimore D. A breath of fresh air. Thermochim Acta. 1999;340–341:19–29. https://doi.org/10.1016/S0040-6031(99)00250-6.

    Article  Google Scholar 

  107. Pena R, Ribet JP, Maurel JL, Valat L, Lacoulonche F, Chauvet A. Sublimation and vaporisation processes of S(−) efaroxan hydrochloride. Thermochim Acta. 2003;408:85–96. https://doi.org/10.1016/S0040-6031(03)00321-6.

    Article  CAS  Google Scholar 

  108. Menon D, Dollimore D, Alexander KS. A TG–DTA study of the sublimation of nicotinic acid. Thermochim Acta. 2002;392–393:237–41. https://doi.org/10.1016/S0040-6031(02)00106-5.

    Article  Google Scholar 

  109. Price DM. Volatilisation, Evaporation and vapour pressure studies using a thermobalance. J Therm Anal Calorim. 2001;64:315–22. https://doi.org/10.1023/A:1011522020908.

    Article  CAS  Google Scholar 

  110. Blaine RL, Hahn BK. Obtaining kinetic parameters by modulated thermogravimetry. J Therm Anal Calorim. 1998;54:695–704. https://doi.org/10.1023/A:1010171315715.

    Article  CAS  Google Scholar 

  111. Phang P. The analysis of perfume fixatives by simultaneous TG-DTA studies. Thermochim Acta. 1999;340–341:139–45. https://doi.org/10.1016/S0040-6031(99)00260-9.

    Article  Google Scholar 

  112. Marsanich K, Zanelli S, Barontini F, Cozzani V. Evaporation and thermal degradation of tetrabromobisphenol A above the melting point. Thermochim Acta. 2004;421:95–103. https://doi.org/10.1016/j.tca.2004.03.013.

    Article  CAS  Google Scholar 

  113. Barontini F, Cozzani V. Assessment of systematic errors in measurement of vapor pressures by thermogravimetric analysis. Thermochim Acta. 2007;460:15–21. https://doi.org/10.1016/j.tca.2007.05.005.

    Article  CAS  Google Scholar 

  114. Pieterse N, Focke WW. Diffusion-controlled evaporation through a stagnant gas: estimating low vapour pressures from thermogravimetric data. Thermochim Acta. 2003;406:191–8. https://doi.org/10.1016/S0040-6031(03)00256-9.

    Article  CAS  Google Scholar 

  115. Focke WW. A revised equation for estimating the vapour pressure of low-volatility substances from isothermal TG data. J Therm Anal Calorim. 2003;74:97–107. https://doi.org/10.1023/A:1026325719190.

    Article  CAS  Google Scholar 

  116. Beverley KJ, Clint JH, Fletcher PDI. Evaporation rates of pure liquids measured using a gravimetric technique. Phys Chem Chem Phys. 1999. https://doi.org/10.1039/A805344H.

    Article  Google Scholar 

  117. Bassi M. Estimation of the vapor pressure of PFPEs by TGA. Thermochim Acta. 2011;521:197–201. https://doi.org/10.1016/j.tca.2011.04.024.

    Article  CAS  Google Scholar 

  118. Parker A, Babas R. Thermogravimetric measurement of evaporation: Data analysis based on the Stefan tube. Thermochim Acta. 2014;595:67–73. https://doi.org/10.1016/j.tca.2014.09.011.

    Article  CAS  Google Scholar 

  119. Kendler R, Dreisbach F, Seif R, Pollak S, Petermann M. Method for estimating vapour pressures based on thermogravimetric measurements with a magnetic suspension balance. Thermochim Acta. 2018;664:128–35. https://doi.org/10.1016/j.tca.2018.05.001.

    Article  CAS  Google Scholar 

  120. Zghal I, Farjas J, Camps J, Dammak M, Roura P. Thermogravimetric measurement of the equilibrium vapour pressure: Application to water and triethanolamine. Thermochim Acta. 2018;665:92–101. https://doi.org/10.1016/j.tca.2018.05.007.

    Article  CAS  Google Scholar 

  121. Barontini F, Cozzani V. Thermogravimetry as a screening tool for the estimation of the vapor pressures of pure compounds. J Therm Anal Calorim. 2007;89:309–14. https://doi.org/10.1007/s10973-006-7915-5.

    Article  CAS  Google Scholar 

  122. Vlasov VA. Diffusion-kinetic model of liquid evaporation from a Stefan tube: A solution to the Stefan diffusion problem. Int J Heat Mass Transf. 2020;163: 120379. https://doi.org/10.1016/j.ijheatmasstransfer.2020.120379.

    Article  CAS  Google Scholar 

  123. Li D. Vaporization kinetics and vapor pressures for petroleum fractions using thermogravimetry analysis. Adv Mater Res. 2011;236–238:534–7. https://doi.org/10.4028/www.scientific.net/AMR.236-238.534.

  124. Ahmadi Khoshooei M, Fazlollahi F, Maham Y. A review on the application of differential scanning calorimetry (DSC) to petroleum products: Characterization and kinetic study. J Therm Anal Calorim. 2019;138:3455–84. https://doi.org/10.1007/s10973-019-08244-2.

    Article  CAS  Google Scholar 

  125. Ahmadi Khoshooei M, Fazlollahi F, Maham Y, Hassan A, Pereira-Almao P. A review on the application of differential scanning calorimetry (DSC) to petroleum products: wax crystallization study and structural analysis. J Therm Anal Calorim. 2019;138:3485–510. https://doi.org/10.1007/s10973-019-08022-0.

    Article  CAS  Google Scholar 

  126. Ahmadi KM. Investigating deposition of nanocatalysts in porous media for catalytic downhole upgrading processes. SPE Annu Tech Conf Exhib. 2020. https://doi.org/10.2118/204260-STU.

    Article  Google Scholar 

  127. Castellanos-Díaz O, Schoeggl FF, Yarranton HW, Satyro MA. Measurement of heavy oil and bitumen vapor pressure for fluid characterization. Ind Eng Chem Res. 2013;52:3027–35. https://doi.org/10.1021/ie303397y.

    Article  CAS  Google Scholar 

  128. Schwarz BJ, Wilhelm JA, Prausnitz JM. Vapor pressures and saturated-liquid densities of heavy fossil fuel fractions. Ind Eng Chem Res. 1987;26:2353–60. https://doi.org/10.1021/ie00071a030.

    Article  CAS  Google Scholar 

  129. Rannaveski R, Oja V. A new thermogravimetric application for determination of vapour pressure curve corresponding to average boiling points of oil fractions with narrow boiling ranges. Thermochim Acta. 2020;683: 178468. https://doi.org/10.1016/j.tca.2019.178468.

    Article  CAS  Google Scholar 

  130. Rannaveski R, Järvik O, Oja V. A new method for determining average boiling points of oils using a thermogravimetric analyzer. J Therm Anal Calorim. 2016;126:1679–88. https://doi.org/10.1007/s10973-016-5612-6.

    Article  CAS  Google Scholar 

  131. Siitsman C, Oja V. Application of a DSC based vapor pressure method for examining the extent of ideality in associating binary mixtures with narrow boiling range oil cuts as a mixture component. Thermochim Acta. 2016;637:24–30. https://doi.org/10.1016/j.tca.2016.05.011.

    Article  CAS  Google Scholar 

  132. Gustavsson B. Volatility determination of oils by TG. Thermochim Acta. 1991;175:73–7. https://doi.org/10.1016/0040-6031(91)80248-H.

    Article  CAS  Google Scholar 

  133. Carbognani Ortega LA, Carbognani J, Almao PP. Correlation of thermogravimetry and high temperature simulated distillation for oil analysis: Thermal cracking influence over both methodologies. In: Ovalles C, Moir ME, editors. The Boduszynski Continuum: Contributions to the Understanding of the Molecular Composition of Petroleum. Washington: Academic; 2018. pp. 10–223. https://doi.org/10.1021/bk-2018-1282.ch010.

  134. Wen Fan Li Peng, Ke-Chang Xie L-PC. Simulated distillation of coal tar. Energy Sources. 2001. https://doi.org/10.1080/00908310151092416.

    Article  Google Scholar 

  135. Mondragon F, Ouchi K. New method for obtaining the distillation curves of petroleum products and coal-derived liquids using a small amount of sample. Fuel. 1984;63:61–5. https://doi.org/10.1016/0016-2361(84)90256-4.

    Article  CAS  Google Scholar 

  136. Dyszel SM. A thermogravimetric method for distinguishing Alaskan crude oil from that of other world sources. Thermochim Acta. 1980;38:299–310. https://doi.org/10.1016/0040-6031(80)85037-4.

    Article  Google Scholar 

  137. Barbooti MM, El-Sharifi TH. Chemical evaluation of crude oils by programmed thermogravimetric analysis. Thermochim Acta. 1989;153:1–10. https://doi.org/10.1016/0040-6031(89)85417-6.

    Article  CAS  Google Scholar 

  138. Cardillo P, Giavarini C, Vecchi C. Characteristics of bitumens extracted from Italian bituminous rocks and shales. Fuel. 1984;63:1518–22. https://doi.org/10.1016/0016-2361(84)90218-7.

    Article  CAS  Google Scholar 

  139. Yusupova TN, Ganeeva YM, Okhotnikova ES, Romanov GV. The use of thermal analysis methods for monitoring the development of bitumen reservoirs using thermal recovery technologies. J Therm Anal Calorim. 2017. https://doi.org/10.1007/s10973-017-6712-7.

    Article  Google Scholar 

  140. Salmerón Sánchez M, Monleón Pradas M, Gómez Ribelles JL. Thermal transitions of benzene in a poly(ethyl acrylate) network. J Non Cryst Solids. 2002;307–310:750–7. https://doi.org/10.1016/S0022-3093(02)01557-0.

    Article  Google Scholar 

  141. Jessie Lue S, Wei Yang S. Sorption of organic solvents in poly(dimethyl siloxane) membrane. I. Permeant states quantification using differential scanning calorimetry. J Macromol Sci Part B. 2005. https://doi.org/10.1080/00222340500251162.

    Article  Google Scholar 

  142. Suzuki M, Norinaga K, Iino M. Macroscopic observation of thermal behavior of concentrated solution of coal extracts. Fuel. 2004;83:2177–82. https://doi.org/10.1016/j.fuel.2004.06.006.

    Article  CAS  Google Scholar 

  143. Hruljova J, Järvik O, Oja V. Application of differential scanning calorimetry to study solvent swelling of Kukersite oil shale macromolecular organic matter: a comparison with the fine-grained sample volumetric swelling method. Energy Fuels. 2014;28:840–7. https://doi.org/10.1021/ef401895u.

    Article  CAS  Google Scholar 

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Acknowledgements

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. The author greatly appreciates helpful discussions and constructive insights from Prof. Dr. Yadollah Maham that enabled significant enrichment of the article.

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    Milad Ahmadi Khoshooei

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Ahmadi Khoshooei, M. Thermal probe of vapor–liquid thermodynamic equilibrium. J Therm Anal Calorim 147, 6015–6034 (2022). https://doi.org/10.1007/s10973-021-10972-3

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