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Modeling of Phase Equilibria and Surface Tension for N,N-Dimethylcyclohexylamine + Alcohol Mixtures at Different Temperatures

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Abstract

Surface tension and phase equilibria of N,N-dimethylcyclohexylamine (DMCA) mixtures with alcohol (propanol, iso-propanol, butanol, and iso-butanol) were modeled over the whole range of composition and different temperature ranging from (288.15 to 308.15) K. The predictive results of the Peng–Robinson equation of state with quadratic mixing rule indicated that the DMCA + alcohol mixtures are not azeotropic and that the bubble curve is linear, except for the DMCA + ethanol mixture. The surface tension of the binary mixtures was modeled with linear gradient theory, parachor method, Shereshefsky method, and Lamperski method. The linear gradient theory used as adjustment approach improved the results of surface tension prediction and correctly modeled this thermodynamic property for all mixtures, the flexibility of parachor method as an adjustment approach improved the predictive results for some mixtures, Shereshefsky method was able to successfully model the surface tension of the DMCA + ethanol, DMCA + propanol, and DMCA + butanol mixtures, and Lamperski method was able to successfully model the surface tension of the DMCA + propanol and DMCA + butanol mixtures, while the DMCA + ethanol and DMCA + isobutanol mixtures had an acceptable statistical deviation. Furthermore, Lamperski method was the best predicted model to model surface tension of the binary mixtures. Based on Shereshefsky model, the standard Gibbs energy of adsorption and the free energy change in the surface region were calculated. The free energy change was used to obtain the number of molecular layers in the surface region. Also, with Shereshefsky method it was obtained that alcohol is not absorbed at the surface which was also confirmed with Lamperski method. Finally, it is important to note that phase equilibria and surface tension of the DMCA + alcohol mixtures is modeled with theoretical approaches for the first time. On the other hand, for future experimental measurements of phase equilibria, our results could serve as an initial approximation of equilibrium, and the correlations obtained for the binary parameters of the linear gradient theory and parachor method can be used to predict surface tension at other temperatures outside the range 288.15 to 308.15 K.

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Abbreviations

a :

Cohesion parameter in the PR-EOS

b :

Covolume parameter in the PR-EOS

c :

Influence parameter

\(k_{ij}\) :

Interaction parameter for the quadratic mixing rule

\(n_c\) :

Number of components of the mixture

n :

Number of points in the linear gradient theory

N :

Number of experimental points

P :

Absolute pressure

R :

Universal gas constant

T :

Absolute temperature

w :

Mole fraction

x :

Liquid mole fraction

y :

Vapor mole fraction

AAD :

Statistical deviation

z :

Position in the interface

\(f_0\) :

Helmholtz energy density

A :

Adjustable parameter of the influence parameter

B :

Adjustable parameter of the influence parameter

\(\mathbb {P}\) :

Parachor parameter of the pure fluid

\(c_{ij}\) :

Cross-influence parameter

\(\overline{A}_2\) :

The molar area of the solute (2)

\(M_2\) :

Molecular weight of solute (2)

\(N_0\) :

Avogadro’s number

\(n_i\) :

Number of moles of the pure ith component

d :

Thickness of monomolecular layer

\(V_i\) :

Molar volume of the ith molecules

\(r_{12}\) :

Quotient between \(n_1\) and \(n_2\)

\(\mu\) :

Chemical potential

\(\rho\) :

Molar density

\(\gamma\) :

Surface tension

\(\Omega\) :

Grand thermodynamic potential

\(\beta _{12}\) :

Symmetric parameter of the linear gradient theory

\(\omega\) :

Acentric factor

\(\lambda _{12}\) :

Adjustable parameter of the parachor method

\(\Delta G_s\) :

Free energy change of replacing one mole of solvent with one mole of solute in the interface

\(\Delta G ^o\) :

Standard Gibbs energy of adsorption

\(\Delta \gamma _0\) :

Difference between the surface tensions of pure solvent and pure solute

\(\alpha\) :

Slope of the Shereshefsky method

\(\beta\) :

Intercept of the Shereshefsky method

\(\delta _2\) :

Number of solute molecular layers in the surface region in respect of the bulk region

\(\theta _i\) :

Surface fraction of the ith component of solution

\(\nu _i\) :

Volume fraction of the ith component of solution

c :

Critical condition

i, j :

Species

s :

Surface

b :

Bulk

ref :

Reference

0:

Equilibrium condition

exp :

Experimental

calc :

Calculated

L :

Liquid phase

V :

Vapor phase

o :

Standard

References

  1. D. Zhao, Y. Zhuang, C. Fan, F. Yang, Y. Chen, X. Zhang, J. Chem. Thermodyn. 143, 106041 (2020)

    Article  Google Scholar 

  2. X. Liang, M.L. Michelsen, G.M. Kontogeorgis, Fluid Phase Equilib. 428, 153–163 (2016)

    Article  Google Scholar 

  3. U. Brea, D. Gómez-Díaz, J.M. Navaza, A. Rumbo, J. Taiwan Inst. Chem. Eng. 102, 250–258 (2019)

    Article  Google Scholar 

  4. S. Lin, H. Lu, Y. Liu, C. Liu, B. Liang, K. Wu, J. Chem. Thermodyn. 123, 8–16 (2018)

    Article  Google Scholar 

  5. F. Tzirakis, I. Tsivintzelis, A.I. Papadopoulos, P. Seferlis, Chem. Eng. Sci. 199, 20–27 (2019)

    Article  Google Scholar 

  6. D. Papaioannou, C.G. Panayiotou, J. Chem. Eng. Data 39, 457–462 (1994)

    Article  Google Scholar 

  7. D.Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15, 59–64 (1976)

    Article  Google Scholar 

  8. T.Y. Kwak, G.A. Mansoori, Chem. Eng. Sci. 41, 1303–1309 (1986)

    Article  Google Scholar 

  9. B.S. Carey, L.E. Scriven, H.T. Davis, AIChE J. 24, 1076–1080 (1978)

    Article  Google Scholar 

  10. B.S. Carey, L.E. Scriven, H.T. Davis, AIChE J. 26, 705–711 (1980)

    Article  Google Scholar 

  11. V. Vinvs, B. Planková, J. Hruby. Int. J. Thermophys. 34, 792–812 (2013)

    Article  ADS  Google Scholar 

  12. A. Mejía, H. Segura, Int. J. Thermophys. 25, 1395–1414 (2004)

    Article  ADS  Google Scholar 

  13. A. Mejía, H. Segura, J. Wisniak, I. Polishuk, J. Phase Equilibria Diffus. 26, 215–224 (2005)

    Article  Google Scholar 

  14. A. Mejía, H. Segura, L.F. Vega, J. Wisniak, Fluid Phase Equilib. 227, 225–238 (2005)

    Article  Google Scholar 

  15. A. Hernández, M. Cartes, A. Mejía, Fuel 229, 105–115 (2018)

    Article  Google Scholar 

  16. A. Hernández, Chem. Phys. 534, 110747 (2020)

    Article  Google Scholar 

  17. A. Hernández, S. Khosharay, Int. J. Thermophys. 41, 1–22 (2020)

    Article  Google Scholar 

  18. A. Hernández, D. Zabala, Int. J. Thermophys. 42, 1–21 (2021)

    ADS  Google Scholar 

  19. Y.-X. Zuo, E.H. Stenby, J. Chem. Eng. Jpn. 29, 159–165 (1996)

    Article  Google Scholar 

  20. Y.-X. Zuo, E.H. Stenby, J. Colloid Interface Sci. 182, 126–132 (1996)

    Article  ADS  Google Scholar 

  21. Y.-X. Zuo, E.H. Stenby et al., SPE J. 3, 134–145 (1998)

    Article  Google Scholar 

  22. H. Lin, Y.Y. Duan, J.T. Zhang, Int. J. Thermophys. 29, 423–433 (2008)

    Article  ADS  Google Scholar 

  23. A. Hernández, Int. J. Thermophys. 41, 1–18 (2020)

    Article  Google Scholar 

  24. A. Hernández, Int. J. Thermophys. 42, 1–27 (2020)

    Google Scholar 

  25. J.C. Eriksson, Adv. Chem. Phys. 6, 145–174 (1964)

    Google Scholar 

  26. F.B. Sprow, J.M. Prausnitz, Trans. Faraday Soc. 62, 1105–1111 (1966)

    Article  Google Scholar 

  27. J.L. Shereshefsky, J. Colloid Interface Sci. 24, 317–322 (1967)

    Article  ADS  Google Scholar 

  28. R. Tahery, H. Modarress, J. Satherley. Chem. Eng. Sci. 60, 4935–4952 (2005)

    Article  Google Scholar 

  29. R. Tahery, J. Solut. Chem. 46, 1152–1164 (2017)

    Article  Google Scholar 

  30. R. Tahery, S. Khosharay, J. Mol. Liq. 247, 354–365 (2017)

    Article  Google Scholar 

  31. R. Tahery, J. Chem. Thermodyn. 106, 95–103 (2017)

    Article  Google Scholar 

  32. R. Tahery, J. Solut. Chem. 47, 278–292 (2018)

    Article  Google Scholar 

  33. S. Lamperski, J. Colloid Interface Sci. 144, 153–158 (1991)

    Article  ADS  Google Scholar 

  34. C. Coquelet, A. Chapoy, D. Richon, Int. J. Thermophys. 25, 133–158 (2004)

    Article  Google Scholar 

  35. X. Wu, X. Du, D. Zheng, Int. J. Thermophys. 31, 308–315 (2010)

    Article  ADS  Google Scholar 

  36. W. Su, S. Zhou, L. Zhao, N. Zhou, Int. J. Thermophys. 41, 1–24 (2020)

    Article  Google Scholar 

  37. L.A. Román-Ramírez, G.A. Leeke, Int. J. Thermophys. 41, 1–27 (2020)

    Article  Google Scholar 

  38. J.M. Prausnitz, R.N. Lichtenthaler, E.G. De Azevedo, Molecular Thermodynamics of Fluid-Phase Equilibria (Prentice Hall, Upper Saddle River, 1998).

    Google Scholar 

  39. C. Miqueu, B. Mendiboure, A. Graciaa, J. Lachaise, Fluid Phase Equilib. 207, 225–246 (2003)

    Article  Google Scholar 

  40. D.B. Macleod, Trans. Faraday Soc. 19, 38–41 (1923)

    Article  Google Scholar 

  41. J.A. Hugill, A.J. Van Welsenes, Fluid Phase Equilib. 29, 383–390 (1986)

    Article  Google Scholar 

  42. M. Caceres. Alonso, J. Nunez. Delgado, J. Chem. Eng. Data 27, 331–333 (1982)

    Article  Google Scholar 

  43. M. Caceres. Alonso, J. Nunez. Delgado, J. Chem. Eng. Data 28, 61–62 (1983)

    Article  Google Scholar 

  44. P.J. Flory, J. Chem. Phys. 10, 51–61 (1942)

    Article  ADS  Google Scholar 

  45. Aspen Plus. V10. 0; Aspen Technology Inc., Burlington (2017)

  46. T.E. Daubert, R.P. Danner, Data Compilation, Tables of Properties of Pure Compounds (DIPPR, New York, 1985)

  47. D. Zhao, Y. Zhuang, C. Fan, X. Zhang, F. Yang, Y. Chen, J. Chem. Eng. Data 65, 1547–1553 (2020)

    Article  Google Scholar 

  48. A.F.H. Ward, Trans. Faraday Soc. 42, 399–407 (1946)

  49. A. Hartkopf, B.L. Karger, Acc. Chem. Res. 6, 209–216 (1973)

    Article  Google Scholar 

Download references

Acknowledgements

A.H acknowledges the economic support given by the UCSC.

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Authors and Affiliations

  1. Departamento de Ingeniería Industrial, Facultad de Ingeniería, Universidad Católica de la Santísima Concepción, Alonso de Ribera, 2850, Concepción, Chile

    Ariel Hernández

  2. Chemical Engineering Department, Islamic Azad University, Central Tehran Branch, P.O. Box 1469669191, Tehran, Iran

    Reza Tahery

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  1. Ariel Hernández
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Hernández, A., Tahery, R. Modeling of Phase Equilibria and Surface Tension for N,N-Dimethylcyclohexylamine + Alcohol Mixtures at Different Temperatures. Int J Thermophys 42, 67 (2021). https://doi.org/10.1007/s10765-021-02815-y

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