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Phase diagram of the uniaxial and biaxial soft–core Gay–Berne model
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10.1063/1.3646310
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Affiliations:
1 Dipartimento di Chimica Fisica e Inorganica, Università di Bologna, viale Risorgimento 4, 40136 Bologna, Italy
2 Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom
a) Author to whom correspondence should be addressed. Electronic mail: roberto.berardi@unibo.it.
b) Present address: School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom.
J. Chem. Phys. 135, 134119 (2011)
/content/aip/journal/jcp/135/13/10.1063/1.3646310
http://aip.metastore.ingenta.com/content/aip/journal/jcp/135/13/10.1063/1.3646310
View: Figures

## Figures

FIG. 1.

Representative profiles for the uniaxial GBSC potential with σ x = σ y = σ c = 1 σ0, σ z = 3 σ0, and ε x = ε y = 1 ε0, ε z = 0.2 ε0, μ = 1, ν = 3, and slopes , −80, −60, −40, −30, and −20. (See text for additional details.) The steepness for the logistic seaming function was , and a threshold cut–off value ‖1 − f‖ = 10−6 was used (see Ref. 29). The energy curves are relative to the side–by–side interaction of two parallel ellipsoids. A plot for the standard GB side–by–side interaction energy is also provided for comparison.

FIG. 2.

The average dimensionless potential energy ⟨U⟩/ε0 (plate A), pressure (plate B), compressibility factor ⟨P⟩/(ρk B T) (plate C), and the second virial coefficient B 2 (plate D) plotted against the reduced temperature T/T IN for uniaxial ellipsoids modelled either with the standard GB potential (see Ref. 34) or the GBSC parametrisation described in the text. The soft–core energy slopes were , −80, −60, −40, and −30, while the logistic function steepness was . The results from the NVT MD simulation of the standard uniaxial GB model (see Ref. 34) are also plotted. The rms errors computed, as described in the text, from a block average analysis of the simulation results (see supplementary material of Ref. 46) are also plotted as error bars, however, their size smaller than that of the symbols makes them hardly visible. For every SC parametrisation studied T IN is the specific nematic–isotropic transition temperature, respectively, , 5.05, 4.55, 3.85, and 3.45. The thick grey lines join the I–N and N–Sm transition temperatures for the GBSC models. The standard GB model has instead . The state points have been computed from MD simulations in the NVT ensemble for N = 1024 particles samples at dimensionless density .

FIG. 3.

The orientational order parameter plotted against dimensionless temperature (plate A), and reduced temperature T/T IN (plate B), for the GBSC uniaxial ellipsoids of various softness , −80, −60, −40, −30, and −20 as described in the text. (See the legend of Figure 2 for additional details.)

FIG. 4.

The radial correlation function g(r) for nematic phases with similar orientational order parameter formed by standard and GBSC uniaxial ellipsoids of various softness , −80, −60, −40, −30, and −20 at dimensionless temperatures , 3.5, 3.3, 3.1, 2.8, 2.6, and 2.3 as described in the text. The radial distribution functions parallel (g(r )), and perpendicular (g(r )) to the director are shown in the insets. (See the legend of Figure 2 for additional details.)

FIG. 5.

The phase diagrams plotted against dimensionless temperature for the uniaxial GBSC ellipsoids of various softness , −80, −60, −40, −30, and −20 as described in the text. Samples in the isotropic (I), nematic (N), and smectic (Sm) phases are represented as crosses, circles, and triangles. The I–N and N–Sm transition temperatures for the standard uniaxial GB model (see Ref. 34) are plotted as vertical grey bars. (See the legend of Figure 2 for additional details.)

FIG. 6.

Snapshot of an N sample for the uniaxial GBSC ellipsoids of softness at , and .

FIG. 7.

The average dimensionless potential energy ⟨U⟩/ε0 (plate A), pressure (plate B), compressibility factor ⟨P⟩/(ρk B T) (plate C), and second virial coefficient B 2 (plate D) plotted as a functions of reduced temperature T/T IN for biaxial ellipsoids modelled either with the standard GB potential (see Ref. 35) or the GBSC parametrisation described in the text. The soft–core energy slopes were , −80, −60, −40, and −30, while the logistic function steepness was . The biaxial system with does not form a nematic phase upon cooling. The points from the NVT MD simulation of the standard biaxial GB model (see Ref. 35) are also plotted. The rms errors computed, as described in the text, from a block average analysis of the simulation results (see supplementary material of Ref. 46) are also plotted as error bars, however their size smaller than that of the symbols makes them hardly visible. For every SC parametrisation studied T IN is the specific nematic–isotropic transition temperature, respectively , 5.25, 4.45, 3.65, and 3.15. The thick grey lines join the I–N, N–Nb, and Nb–Sb transition temperatures for the GBSC models. The standard biaxial GB model has instead . The state points have been computed from MD simulations in the NVT ensemble for N = 1024 particles samples at dimensionless number density .

FIG. 8.

The orientational order parameters and plotted against dimensionless temperature (plate A, uniaxial; plate C, biaxial), and reduced temperature T/T IN (plate B, uniaxial; plate D, biaxial), for the biaxial GBSC ellipsoids of various softness , −80, −60, −40, and −30 as described in the text. (See the legend of Figure 7 for additional details.)

FIG. 9.

The phase diagrams plotted against dimensionless temperature for the biaxial GBSC ellipsoids of various softness , −80, −60, −40, and −30 as described in the text, and in the legend of Figure 7. Samples in the isotropic (I), nematic (N), biaxial nematic (Nb), and biaxial smectic (Sb) phases are represented as crosses, circles, squares, and triangles. The I–N, N–Nb, and Nb–Sb transition temperatures for the standard biaxial GB model (see Ref. 35) are plotted as vertical grey bars.

FIG. 10.

Snapshot of a Nb sample for the biaxial GBSC ellipsoids of softness at , , and .

/content/aip/journal/jcp/135/13/10.1063/1.3646310
2011-10-07
2014-04-24

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