Liquid Crystal/Flexible Polymer Mixture

We investigate the effects phase ordering has on phase separation by modelling a mixture of short liquid-crystals (N_lc=10) and long, flexible polymers (N_polymer=100). The following pictures show the system's behavior over time.

N=linear system size
phi0 = average volume fraction of liquid-crystals
(Note: phi = phi_lcvolume fraction of liquid crystals; 1-phi = phi_polymer volume fraction of polymer coils.)
T=temperature in arbitrary units to which we quench the mixture (Note: We always begin with a mixed, homogeneous, isotropic system.)

Information provided beneath the pictures:

time - an unscaled, dimensionless quantity.
(Times in parentheses are also dimensionless but are scaled wrt tau.)
deltaphi - degree of phase separation (phi pictures only)
deltaphi = (phi in LC-rich domain) - (phi in polymer-rich domain)
[Note: in elsie - deltaphi = phi_max - phi_min]
S_o - degree of ordering (S_o pictures only)
S_o = S_o in LC-rich domain
[Note: in elsie - S_o = S_max]

Scroll down to particular runs . . . .

System initially unstable to phase separation only.
System initially unstable to phase ordering only.
System initially unstable to phase separation and phase ordering, but more strongly unstable to phase separation.
System initially unstable to phase separation and phase ordering, but more strongly unstable to phase ordering.
Finite size effects?!?!?

Check-out our complete list of elsie runs.

System initially unstable to phase separation only.

N=100, phi0=0.68, T=0.95 (A4, A4p2)

phi profile -- without phase ordering

time=1.708253e+07
(11.4688)
deltaphi=3.62560e-01

time=3.416505e+07
(22.9376)
deltaphi=3.73910e-01

time=6.833010e+07
(45.8752)
deltaphi=3.72220e-01

time=1.366602e+08
(91.7504)
deltaphi=3.73340e-01

phi_short-isotropic-molecules
0.2 --> 1.0
polymer-rich --> pure solvent

phi profile -- with phase ordering

time=1.708253e+07
(11.4688)
deltaphi=3.64440e-01

time=3.416505e+07
(22.9376)
deltaphi=4.41080e-01

time=6.833010e+07
(45.8752)
deltaphi=4.55340e-01

time=1.366602e+08
(91.7504)
deltaphi=4.58590e-01

phi_lc
0.2 --> 1.0
polymer-rich --> pure LCs

S_o profile

time=1.708253e+07
(11.4688)
S_o=1.78805e-02

time=3.416505e+07
(22.9376)
S_o=1.18812e-01

time=6.833010e+07
(45.8752)
S_o=1.25884e-01

time=1.366602e+08
(91.7504)
S_o=1.26047e-01

S_o^lc-rich
0 --> 0.3
isotropic --> nematic

More snapshots of this quench at later times.

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System initially unstable to phase ordering only.

N=100, phi0=0.95, T=0.95 (e6)

phi profile -- without phase ordering

No phase separation.

phi profile -- with phase ordering

time=2.041707e+06
(22.9376)
deltaphi=8.1540e-02

time=4.083414e+06
(45.8752)
deltaphi=1.3416e-01

time=8.166829e+06
(91.7504)
deltaphi=2.4975e-01

time=1.633366e+07
(183.5008)
deltaphi=3.3984e-01

time=1.727826e+07
(194.1130)
deltaphi=3.4043e-01

phi_lc
0.2 --> 1.0
polymer-rich --> pure LCs

S_o profile

time=2.041707e+06
(22.9376)
S_o=1.12282e-01

time=4.083414e+06
(45.8752)
S_o=1.14860e-01

time=8.166829e+06
(91.7504)
S_o=1.20003e-01

time=1.633366e+07
(183.5008)
S_o=1.22387e-01

time=1.727826e+07
(194.1130)
S_o=1.22407e-01

S_o^lc-rich
0 --> 0.3
isotropic --> nematic

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System initially unstable to phase separation and phase ordering, but more strongly unstable to phase separation.

N=100, phi0=0.85, T=0.50 (C4, C4p)

phi profile -- without phase ordering

time=2.966115e+04
(0.7168)
deltaphi=3.20000e-04

time=5.932230e+04
(1.4336)
deltaphi=5.90000e-04

time=1.186446e+05
(2.8672)
deltaphi=2.49000e-03

time=2.372892e+05
(5.7344)
deltaphi=5.77000e-02

time=3.722775e+05
(8.9966)
deltaphi=7.09920e-01

phi_short-isotropic-molecules
0.2 --> 1.0
polymer-rich --> pure solvent

phi profile -- with phase ordering

time=2.966115e+04
(0.7168)
deltaphi=1.40100e-02

time=5.932230e+04
(1.4336)
deltaphi=3.00900e-02

time=1.186446e+05
(2.8672)
deltaphi=1.34620e-01

time=1.975160e+05
(4.7732)
deltaphi=6.86060e-01

phi_lc
0.2 --> 1.0
polymer-rich --> pure LCs

S_o profile

time=2.966115e+04
(0.7168)
S_o=5.25358e-03

time=5.932230e+04
(1.4336)
S_o=7.48449e-03

time=1.186446e+05
(2.8672)
S_o=2.91848e-02

time=1.975160e+05
(4.7732)
S_o=2.33579e-01

S_o^lc-rich
0 --> 0.3
isotropic --> nematic

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System initially unstable to phase separation and phase ordering, but more strongly unstable to phase ordering.

N=100, phi0=0.91, T=0.50 (B6r2, B6p)

phi profile -- without phase ordering

time=4.752467e+06
(11.4688)
deltaphi=7.53970e-01

time=9.504933e+06
(22.9376)
deltaphi=7.60930e-01

time=1.900987e+07
(45.8752)
deltaphi=7.62050e-01

time=2.319886e+07
(55.9842)
deltaphi=7.62160e-01

phi_short-isotropic-molecules
0.2 --> 1.0
polymer-rich --> pure solvent

phi profile -- with phase ordering

time=3.712865e+04
(0.0896)
deltaphi=9.69000e-03

time=7.425729e+04
(0.1792)
deltaphi=1.93200e-02

time=1.485146e+05
(0.3584)
deltaphi=3.19560e-01

time=1.628230e+05
(0.3929)
deltaphi=4.55610e-01

phi_lc
0.2 --> 1.0
polymer-rich --> pure LCs

S_o profile

time=3.712865e+04
(0.0896)
S_o=1.52894e-02

time=7.425729e+04
(0.1792)
S_o=4.41358e-02

time=1.485146e+05
(0.3584)
S_o=2.68615e-01

time=1.628230e+05
(0.3929)
S_o=2.80462e-01

S_o^lc-rich
0 --> 0.3
isotropic --> nematic

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Finite size effects?!?!?

There seems to be finite size effects when we conduct shallow critical quenches (phi_crit=0.76).

N=100, phi0=0.76, T=0.95 (A2, A2p3)

phi profile -- without phase ordering

time=7.941550e+06
(11.4688)
deltaphi=3.53620e-01

time=1.589072e+07
(22.9376)
deltaphi=3.70470e-01

time=3.178144e+07
(45.8752)
deltaphi=3.76680e-01

time=6.356288e+07
(91.7504)
deltaphi=3.80620e-01

time=1.271258e+08
(183.5008)
deltaphi=3.75630e-01

phi_short-isotropic-molecules
0.2 --> 1.0
polymer-rich --> pure solvent

phi profile -- with phase ordering

time=7.941550e+06
(11.4688)
deltaphi=3.51330e-01

time=1.589072e+07
(22.9376)
deltaphi=3.74740e-01

time=3.178144e+07
(45.8752)
deltaphi=4.71180e-01

time=6.356288e+07
(91.7504)
deltaphi=4.66370e-01

time=1.271258e+08
(183.5008)
deltaphi=4.65680e-01

phi_lc
0.2 --> 1.0
polymer-rich --> pure LCs

S_o profile

time=7.941550e+06
(11.4688)
S_o=1.31802e-02

time=1.589072e+07
(22.9376)
S_o=2.27370e-02

time=3.178144e+07
(45.8752)
S_o=1.24874e-01

time=6.356288e+07
(91.7504)
S_o=1.24125e-01

time=1.271258e+08
(183.5008)
S_o=1.23663e-01

S_o^lc-rich
0 --> 0.3
isotropic --> nematic

N=200, phi0=0.76, T=0.95 (A2r4, A2r4p)

phi profile -- without phase ordering

time=7.941550e+06
(11.4688)
deltaphi=3.5398e-01

time=1.589072e+07
(22.9376)
deltaphi=3.8273e-01

time=3.178144e+07
(45.8752)
deltaphi=3.8475e-01

time=4.941182e+07
(71.3239)
deltaphi=3.8333e-01

phi_short-isotropic-molecules
0.2 --> 1.0
polymer-rich --> pure solvent

phi profile -- with phase ordering

time=7.941550e+06
(11.4688)
deltaphi=3.6048e-01

time=1.589072e+07
(22.9376)
deltaphi=3.9201e-01

time=3.178144e+07
(45.8752)
deltaphi=4.7216e-01

time=3.484637e+07
(50.2993)
deltaphi=4.7478e-01

phi_lc
0.2 --> 1.0
polymer-rich --> pure LCs

S_o profile

time=7.941550e+06
(11.4688)
S_o=1.45608e-02

time=1.589072e+07
(22.9376)
S_o=3.23227e-02

time=3.178144e+07
(45.8752)
S_o=1.24937e-01

time=3.484637e+07
(50.2993)
S_o=1.25163e-01

S_o^lc-rich
0 --> 0.3
isotropic --> nematic

Last updated April 16, 1998.

Any comments? Contact aml@chem.ucla.edu.

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