Simple Landau Model of the Liquid-RII-RI Rotator Phases of Alkanes
Prabir K. Mukherjee, Santanu Dey
.
DOI: 10.4236/jmp.2012.31012   PDF    HTML     4,944 Downloads   8,087 Views   Citations

Abstract

Simple Landau free energy function is presented to describe the Liquid-RII-RI phase sequence of alkanes and transitions between them. The order parameters necessary to describe these rotator phase transitions are identified. We present a mean-field description of the Liquid-RII and Liquid-RI transitions. General arguments are presented for the topology of the phase diagram in the vicinity of the Liquid-RII-RI triple point. Within this model the Liquid-RII and Liquid-RI transitions are found to be always strongly first order. Calculations based on this model agree qualitatively with experiments.

Share and Cite:

P. Mukherjee and S. Dey, "Simple Landau Model of the Liquid-RII-RI Rotator Phases of Alkanes," Journal of Modern Physics, Vol. 3 No. 1, 2012, pp. 80-84. doi: 10.4236/jmp.2012.31012.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] J. Doucet, I. Denicolo and A. Craievich, “X-Ray Study of the Rotator Phase of the Odd-Numbered Paraffins C17H36, C19H40, and C21H44,” Journal of Chemical Physics, Vol. 75, No. 3, 1981, pp. 1523-1529. doi:10.1063/1.442185
[2] U. Ungar and N. Masic, “Order in the Rotator Phase of n-Alkanes,” The Journal of Physical Chemistry, Vol. 89, No. 6, 1985, pp. 1036-1042. doi:10.1021/j100252a030
[3] E. B. Sirota, H. E. King Jr., D. M. Singer and H. H. Shao, “Rotator Phases of the Normal Alkanes: An X-Ray Scattering Study,” Journal of Chemical Physics, Vol. 98, No. 7, 1993, pp. 5809-5824. doi:10.1063/1.464874
[4] E. B. Sirota and D. M. Singer, “Phase Transitions among the Rotator Phases of the Normal Alkanes,” Journal of Chemical Physics, Vol. 101, No. 12, 1994, pp. 10873- 10882. doi:10.1063/1.467837
[5] E. B. Sirota, “Remarks Concerning the Relation between Rotator Phases of Bulk n-Alkanes and Those of Langmuir Monolayers of Alkyl-Chain Surfactant on Water,” Langmuir, Vol. 13, No. 14, 1997, pp. 3849-3859. doi:10.1021/la9702291
[6] M. V. Kumar, S. K. Prasad and D. S. S. Rao, “Confinement Driven Weakening of the Rotator Phase Transitions in an Alkane through a Possible Tricritical Point,” Langmuir, Vol. 26, No. 23, 2010, pp. 18362-18368. doi:10.1021/la1037266
[7] U. Zammit, M. Marinelli and F. Mercuri, “Analysis of the Order Character of the RIIRI and the RIRV Rotator Phase Transitions in Alkanes by Photopyroelectric Calorimetry,” The Journal of Physical Chemistry B, Vol. 114, No. 24, 2010, pp. 8134-8139. doi:10.1021/jp102609y
[8] U. Zammit, M. Marinelli, F. Mercuri and F. Scudieri, “Effect of Quenched Disorder on the RI-RV, RII-RI and Liquid-RII Rotator Phase Transition in Alkanes,” The Journal of Physical Chemistry B, Vol. 115, No. 10, 2011, pp. 2331-2337. doi:10.1021/jp111067z
[9] H. Rensmo, A. Ongaro, D. Ryam and D. Fitzmaurice, “Self-assembly of alkane capped silver and silica nanoparticles,” Journal of Materials Chemistry, Vol. 12, No. 9, 2002, pp. 2762-2768. doi:10.1039/b204057c
[10] K. Jiang, B. Xia, D. Fu, F. Luo, G. Liu, Y. Su and D. Wang, “Solid-Solid Phase Transition of n-Alkanes in Multiple Nanoscale Confinement,” The Journal of Physical Chemistry B, Vol. 114, No. 3, 2010, pp. 1388-1392. doi:10.1021/jp9111475
[11] I. Denicolo, A. F. Craievich and J. Doucet, “X-Ray Diffraction and Calorimetric Phase Study of a Binary Paraffin: C23-C48-C24H50,” Journal of Chemical Physics, Vol. 80, No. 12, 1984, pp. 6200-6203. doi:10.1063/1.446722
[12] R. G. Snyder, G. Conti, H. L. Strauss and D. L. Dorset, “Termally-Induced Mixing in Partially Microphase Segregated Binary n-Alkane Crystals,” The Journal of Physical Chemistry, Vol. 97, No. 28, 1993, pp. 7342-7350. doi:10.1021/j100130a037
[13] E. B. Sirota, H. E. King Jr., G. J. Hughes and W. K. Wan, “Novel Phase Behavior in Normal Alkanes,” Physical Review Letters, Vol. 68, No. 4, 1992, pp. 492-495. doi:10.1103/PhysRevLett.68.492
[14] E. B. Sirota, H. E. King Jr., H. H. Shao and D. M. Singer, “Rotator Phases in Mixtures of n-Alkanes,” The Journal of Physical Chemistry, Vol. 99, No. 2, 1995, pp. 798-804. doi:10.1021/j100002a050
[15] E. B. Sirota, D. M. Singer and H. E. King Jr., “Structural Effects of High Pressure Gas on the Rotator Phases of Normal Alkanes,” Journal of Chemical Physics, Vol. 100, No. 2, 1994, pp. 1542-1551. doi:10.1063/1.466633
[16] J.-P. Ryckaert, I. R. McDonald and M. L. Klein, “Disorder in the Pseudohexagonal Rotator Phase of n-Alkanes: Molecular-Dynamics Calculations for Tricosane,” Molecular Physics, Vol. 67, No. 5, 1989, pp. 957-979. doi:10.1080/00268978900101561
[17] N. Wentzel and S. T. Milner, “Crystal and Rotator Phases of n-Alkanes: A Molecular Study,” Journal of Chemical Physics, Vol. 132, 2010, pp. 044901-(1-10).
[18] N. Wentzel and S. T. Milner, “Simulation of Multiple Ordered Phases in C23 N-Alkane,” Journal of Chemical Physics, Vol. 134,2011, pp. 224504-(1-11).
[19] S. T. Milner and N. Wentzel, “Twist Solitons in Ordered Phases of n-Alkanes,” Soft Matter, Vol. 7, No. 16, 2011, pp. 7477-7492. doi:10.1039/c1sm05326d
[20] A. Marbeuf and R. J. Brown, “Molecular Dynamics in n-Alkanes: Premelting Phenomena and Rotator Phases,” Journal of Chemical Physics, Vol. 124, 2006, pp. 054901- (1-9).
[21] M. Cao and P. A. Monson, “Solid-Fluid and Solid-Solid Phase Equilibrium in a Model of n-Alkane Mixtures,” Journal of Chemical Physics, Vol. 120, No. 6, 2004, pp. 2980-2988. doi:10.1063/1.1637332
[22] M. Cao and P. H. Monson, “Solid-Fluid and Solid-Solid Equilibrium in Hard Sphere United Atom Models of n-Alkanes: Rotator Phase Stability,” The Journal of Physical Chemistry B, Vol. 113, No. 42, 2009, pp. 13866- 13873. doi:10.1021/jp902887w
[23] A. Würger, “Rotator Phases and Herringbone Order in Langmuir Monolayers and Alkanes,” Journal of Chemical Physics, Vol. 112, No. 8, 2000, pp. 3897-3908. doi:10.1063/1.480537
[24] P. K. Mukherjee and M. Deutsch, “Landau Theory of the RII-RI-RV Rotator Phases,” Physical Review B, Vol. 60, No. 5, 1999, pp. 3154-3162. doi:10.1103/PhysRevB.60.3154
[25] P. K. Mukherjee, “Rotator-I to Rotator-I Phase Transition in Alkanes,” Journal of Chemical Physics, Vol. 113, No. 10, 2000, pp. 4472-4475. doi:10.1063/1.1287422
[26] P. K. Mukherjee, “Elastic Properties of the Rotator Phases of Pentacosane C25H52,” Journal of Chemical Physics, Vol. 116, No. 24, 2002, pp. 10787-10793. doi:10.1063/1.1479711
[27] P. K. Mukherjee, “Structural Phase Transition in Pentacosane C25H52,” Journal of Chemical Physics, Vol. 126, 2007, pp. 114501-(1-7).
[28] P. K. Mukherjee, “Landau Model of the RII-RI-RV Rotator Phases in Mixtures of Alkanes,” Journal of Chemical Physics, Vol. 127, 2007, pp. 074901-(1-6).
[29] P. K. Mukherjee, “Simple Landau Model of the RIV- RIII-RV Rotator Phases of Alkanes,” Journal of Chemical Physics, Vol. 129, 2008, pp. 021101-(1-3).
[30] P. K. Mukherjee, “Pressure Effect on the Rotator-II to Rotator-I Transition of Alkanes,” Journal of Chemical Physics, Vol. 130, 2009, pp. 214906-(1-4).
[31] P. K. Mukherjee, “Tricritical Behavior of the Rotator Phases of Normal Alkanes,” The Journal of Physical Chemistry B, Vol. 114, No. 17, 2010, pp. 5700-5703. doi:10.1021/jp1000495
[32] P. K. Mukherjee, “Renormalization-Group Analysis of the RI-RV Rotator Phase Transition,” Journal of Chemical Physics, Vol. 134, 2011, pp. 224502-(1-6).
[33] P. K. Mukherjee, “Elastic Properties of the RIV-RIII Rotator Phases of Alkanes,” Journal of Physics and Chemistry of Solids, Vol. 102, 2011, pp. 1166-1169.
[34] P. K. Mukherjee, “Tricritical Behavior of the R -R Rotator Phase Transition in a Mixture of Alkanes with Nanoparticles,” Journal of Chemical Physics, Vol. 135, 2011, pp. 134505-(1-6).
[35] V. M. Kaganer, H. M?hwald and P. Dutta, “Structure and Phase Transitions in Langmuir Monolayers,” Reviews of Modern Physics, Vol. 71, No. 3, 1999, pp. 779-819. doi:10.1103/RevModPhys.71.779

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.