Pressure Effect on Thermodynamic Quantities for the Solid-Liquid Phase Transition in n-tridecane, n-hexadecane and n-octadecane

Abstract

The pressure effect is investigated regarding the solid – liquid equilibria (SLE) in n-alkanes. Using the Landau phenomenological model, the pressure dependences of the thermodynamic functions are predicted and the phase diagrams are constructed for the solid – liquid transitions in the binary mixtures of n-alkanes. The experimental data from the literature are used for the phase diagrams in the mixtures. Our fits for the phase diagrams are reasonably good. Regarding the cubic dependence of the concentration (T-X, P-X) and the linear dependence of the pressure (P-T) on the temperature, our results show that the n-tridecane is distinguished from the other mixtures due to its lowest freezing temperature (T_1=291.08 K) and correspondingly higher concentration (x_1=0.1982). It is found that the divergence behaviour of the heat capacity (C) with the critical exponent 1⁄2 from the extended mean field model is in particular more apparent at the room temperature (293.15 K) at various pressures for the solid – liquid transition. This is accompanied with the pressure dependences of the order parameter, susceptibility, entropy and enthalpy for those mixtures as studied here.

Keywords

• Phase diagrams
• Thermodynamic quantities
• Landau model
• n-tridecane
• . n-hexadecane
• n-octadecane

References

1. D.S. Fu, Y.L. Su, B.Q. Xie, H.J. Zhu, G.M. Liu and D.J. Wang, “Phase change materials of n-alkane-containing microcapsules: observation of coexistence of ordered and rotator phases”, Phys. Chem. Chem. Phys., 13, 2021-2026, 2011.
2. D.S. Fu, Y.F. Liu, X. Gao, Y.L. Su, G.M. Liu, D.J. Wang, “Binary n-Alkane Mixtures from Total Miscibility to Phase Separation in Microcapsules: Enrichment of Shorter Component in Surface Freezing and Enhanced Stability of Rotator Phases”, J. Phys. Chem. B, 116, 3099-3105, 2012.
3. P.K. Mukherjee, “Pressure effect on the rotator-II to rotator I transition of alkanes”, J. Chem. Phys., 130, 214906, 2009.
4. A. Craievich, J. Doucet and I. Denicolo, “Molecular disorder in even-numbered paraffins”, Phys. Rev. B, 32, 4164-4168, 1985.
5. G. Ungar, N. Masic, “Order in the rotator phase of normal alkanes”, J. Phys. Chem., 89, 1036-1042, 1985.
6. E. B. Sirota, “Rotator phases of the normal alkanes: An x-ray scattering study”, J. Chem. Phys., 98, 5809-5824, 1993.
7. E. B. Sirota, “Remarks concerning the relation between rotator phases of bulk n-alkanes and those of langmuir monolayers of alkyl-chain surfactants on water”, Langmuir, 13, 3849-3859, 1997.
8. I. Koljanin, M. Pozar, B. Lovrincevic, “Structure and Dynamics of liquid linear and cyclic alkanes: A molecular Dynamics study”, Fluid Phase Equilibria, 550, 113237, 2021.

9. D.S. Fu, Y.F. Liu, G.M. Liu, Y.L. Su, D.J. Wang, “Confined crystallization of binary n-alkane mixtures: stabilization of a new rotator phase by enhanced surface freezing and weakened intermolecular interactions”, Phys. Chem. Chem. Phys., 13, 15031-15036, 2011.
10. R.R. Nelson, W. Webb and J.A. Dixon, “First-order phase transitions of six normal paraffins at elevated pressures”, J. Chem. Phys., 33, 1756-1764, 1960.
11. B. Koppitz and A. Würflinger, “Differential thermal analysis at elevated pressure”, Colloid Polym. Sci., 252, 999-1000, 1974.
12. C. Josefiak, A. Würflinger and G.M. Schneider, “Differential thermal analysis under high pressure”, Colloid Polym. Sci., 255, 170-171, 1977.
13. S.N. Gunasekara, S. Kumova, J.N. Chiu, V. Martin, “Experimental phase diagram of the dodecane-tridecane system as phase change material in cold storage”, Int. J. Ref., 82, 130-140, 2017.
14. J.L. Daridon, J. Pauly and M. Milhet, “High pressure solid-liquid phase equilibria in synthetic waxes”, Phys. Chem. Chem. Phys., 4, 4458-4461, 2002.
15. T. Shen, H. Peng, X. Ling, “Experimental Measurements and Thermodynamic Modeling of Melting Temperature of the Binary Systems n-C11H24-n-C14H30, n-C12H26-n-C13H28, n-C12H26-n-C14H30, and n-C13H28-n-C-15 H-32 for Cryogenic Thermal Energy Storage”, Ind. Eng. Chem. Res., 58, 15026-15035, 2019.
16. P.K. Mukherjee and M. Deutsch, “Landau theory of the R-II-R-I-R-V rotator phases of alkanes”, Phys. Rev. B, 60, 3154-3162, 1999.
17. C. Ma, Q. Zhou, F. Li, J. Hao, J. Wang, L. Huang, F. Huang, Q. Cui, “Rotator phases of n-heptane under high pressure: Raman scattering and X-ray diffraction studies”, J. Phys. Chem. C, 115, 18310-18345, 2011.
18. M. Krishnan, S. Balasubramanian, “n-heptane under pressure: Structure and dynamics from molecular simulations”, J. Phys. Chem. B, 109, 1936-1946, 2005.
19. D. Cholakova and N. Denkov, “Rotator phases in alkane systems: In bulk, surface layers and micro/nano-confinements”, Adv. Colloid Interface Sci., 269, 7-42, 2019.
20. B. He, V. Martin, F. Setterwall, “Liquid-solid phase equilibrium study of tetradecane and hexadecane binary mixtures as phase change materials (PCMs) for comfort cooling storage”, Fluid Phase Equilibria, 212, 97-109, 2003.
21. M. Milhet, J. Pauly, J.A.P. Coutinho, M. Dirand, J.L. Daridon, “Liquid-solid equilibria under high pressure of tetradecane plus pentadecane and tetradecane plus hexadecane binary systems”, Fluid Phase Equilibria, 235, 173-181, 2005. S. Corsetti, T. Rabl, D. McGloin and J. Kiefer, “Intermediate phases during solid to liquid transitions in long-chain n-alkanes”, Phys. Chem. Chem. Phys., 19, 13941-13950, 2017.
22. H. Yurtseven, T. Emirosmanoglu, O. Tari, “Calculation of the Liquid-Solid Phase Diagram and the Thermodynamic Quantities of the Binary System of Tetradecane and Hexadecane Using the Mean Field Theory”, J. Sol. Chem., 50, 1335-1362, 2021.
23. H. Yurtseven, E. Kilit Dogan, “Calculation of the phase diagram of n-alkanes (CnH2n+2) by the Landau mean field theory”, Fluid Phase Equilibria, 556, 113377, 2022.
24. O. Tari, H. Yurtseven, “Calculation of the T-X phase diagram of tetradecane+hexadecane and tetradecane+pentadecane under high pressure by the landau mean field theory”, Fluid Phase Equilibria, 559, 113499, 2022.
25. H. Yurtseven and O. Tari, “Calculation of the T-X phase diagram and the thermodynamic quantities for the binary mixtures of tetradecane + hexadecane using the Landau mean field model”, Phys. Chem. Liq., 61, 340-364, 2023.
26. O. Tari and H. Yurtseven, “Calculation of the phase diagrams (T - X and T - P) and the thermodynamic quantities for the solid – liquid equilibria in n-tridecane”, Int. J. Thermodynamics, 26, 37-45, 2023.
27. H. Yan, H. Yang, J. Luo, N. Yin, Z. Tan and Q. Shi, “Thermodynamic insights into n-alkanes phase change materials for thermal energy storage”, Chin. Chem. Lett., 32, 3825-3832, 2021.
28. S. A. Burrows, I. Korotkin, S.K. Smoukov, E. Boek and S. Karabasov, “Benchmarking of Molecular Dynamics Force Fields for Solid–Liquid and Solid–Solid Phase Transitions in Alkanes”, J. Phys. Chem. B, 125, 5145-5159, 2021.
29. P.K. Mukherjee, “Effect of silica nanoparticles on the heat capacity of the rotator phase transitions of alkanes”, Phase Transit., 95, 322-330, 2022.
30. D. Cholakova, D. Glushkova, Z. Valkova, S. Tsibranska-Gyoreva, K. Tsvetkova, S. Tcholakova and N. Denkov, “Rotator phases in hexadecane emulsion drops revealed by X-ray synchrotron techniques”, J. Colloid Interface Sci., 604, 260-271, 2021.
31. P. Morawski, J. A. P. Coutinho, U. Domanska, “High pressure (solid + liquid) equilibria of n-alkane mixtures: experimental results, correlation and prediction”, Fluid Phase Equilibria, 230, 72-80, 2005.
32. G. Fritsch, “A Landau-type model for the melting transition”, Phys. Stat. Sol. (a), 31, 107-118, 1975.
33. C.C. Huang and J.M. Viner, “Nature of the Smectic-A-Smectic-C phase transition in liquid crystals”, Phys. Rev. A, 25, 3385-3388, 1982.
34. S. Dumrongrattana, G. Nounesis and C.C. Huang, “Measurement of tilt angle and heat capacity in the vicinity of one smectic-A chirl smectic-C transtion”, Phys. Rev. A, 33, 2181-2183, 1986.
35. P.K. Mukherjee, “Simple Landau model of the RIV-RIII-RV rotator phases of alkanes”, J. Chem. Phys., 129, 021101, 2008.
36. P.K. Mukherjee, “Tricritical behavior of the RI–RV rotator phase transition in a mixture of alkanes with nanoparticles”, J. Chem. Phys., 135, 134505, 2011.
37. P.K. Mukherjee and S. Dey, “Simple Landau Model of the Liquid-RII-RI Rotator Phases of Alkanes”. J. Mod. Phys., 3, 80-84, 2012.
38. J.C. Toledano and P. Toledano, “The Landau theory of Phase Transition”, World Scientific, Singapore, 1987.
39. D. Machon, “Phenomenological theory of the phase diagrams of binary eutectic systems”, Phys. Rev. B, 71, 024110, 2005.
40. A. Hammami and M. Raines, “Paraffin deposition from crude oils: comparison of laboratory results to field data”, SPE-38776, 273-287, 1997.
41. H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena, Clarendon, Oxford, 1971.
42. J.J. Binner, N. J. Dowrick, A. J. Fisher, M.E.J. Newman, The Theory of Critical Phenomena, An Introduction to the Renormalization Group, Oxford University Press, New York, Chapter 3, 1992.