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Program MAP_POLY_LIQUID

  1. Provenance of code.
  2. Purpose of code.
  3. Specification.
  4. Description of subroutine's operation.
  5. References.
  6. Parameter descriptions.
  7. Error indicators.
  8. Accuracy estimate.
  9. Any additional information.
  10. Example of code
  11. Auxiliary subroutines required.
  12. Keywords.
  13. Download source code.
  14. Links.

Provenance of Source Code

John Hobdell, Dr Gerhard Goldbeck-Wood and Professor Alan Windle
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.

Contacts:
Dr Gerhard Goldbeck-Wood (gg212@cam.ac.uk) or
Mr John Hobdell (jrh18@cam.ac.uk)

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Purpose

MAP_POLY_LIQUID simulates liquid crystal microstructure using the Monte Carlo method in two or three dimensions as a function of the elastic constants of the liquid crystals and of temperature - it is essentially an annealing program which predicts the microstructure as it evolves. The simulated microstructure includes the field of "directors" representing the average local molecular orientation.

Typical examples of liquid crystals and liquid crystal polymers include small anisotropic molecules such as those used in digital displays, MBBA, Kevlar® (polyaride) and Vectra® (polyester).

IMPORTANT

Note that this program has been written using the IRIX Fortran complier, and therefore uses extensions which are not part of the ANSI F77 standard. In particular, the malloc and getargs intrinsics are used.

Note also that the executable is constructed using the Unix MAKE utility, for which a Makefile is provided.

The distribution also includes files containing sample input and output data.

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Specification

Language:FORTRAN - see Important note above.
Product form:Source code

The program reads inputs from a file named by the user: this name will be an argument of the execution command. The input file is keyword driven (which means that the inputs can be in any order within the file).

The keywords are :-

XSIZE x dimension of Monte Carlo lattice.
YSIZE y dimension of Monte Carlo lattice.
ZSIZE z dimension of Monte Carlo lattice.
GEOMETRY The initial director configuration and boundary conditions. There is a choice between a number of options including :-
  • PERIODIC for a random configuration with periodic boundary conditions and
  • FILE for reading the configuration from a data file.
see GEOMFILE for more information.
DIMENSIONS Lattice dimension, 2 or 3.
SPLAY The SPLAY, TWIST and BEND elastic constants are given in dimensionless units in the program. Usually BEND will be set to 1, and the others determined by the ratios known from experiment.
TWIST
BEND
K24 The saddle-splay elastic constant, which is usually set to zero.
FIELD FIELD is the strength of an external field which couples to the z-component of the directors. DELTA specifies a change in that external field after each cycle.
DELTA
CYCLES CYCLES is the number of cycles of 'annealing' the lattice.
ITERATIONS ITERATIONS is the number of times each cell is visited (on average, since the visits are determined randomly) in each cycle.
GEOMFILE Director array input file.
MOVEFILE Array of moveable directors. Needs to be specified only if the director array is read from file (see GEOMETRY).
SEED Random number generator seed.
BETAINIT Initial value of 1/kT.
BETAFACTOR Factor by which the initial BETAINIT (1/kT) is multiplied in each ANNEAL cycle; allows gradual reduction in temperature.
NANNEAL Number of cycles within each CYCLE (as specified by CYCLES), during which the temperature programme defined by the BETAFACTOR is applied.

Each point on the Monte Carlo lattice represents one director.

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Description

The particular method implemented here focusses on predicting the characteristic director structures. It will distinguish between different classes of liquid crystal materials; in particular, small molecule versus polymer liquid crystals. This code helps in the interpretation of micrographs taken using polarised light microscopy and scanning electron microscopy. It is useful therefore in the molecular design of engineering polymers.

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References

  1. J.R. Hobdell and A.H. Windle, Liquid Crystals 19, 401-407 (1995).
  2. J.R. Hobdell and A.H. Windle, J.Chem.Soc.Faraday Trans. 91, 2497-2505 (1995).
  3. S.E. Bedford and A.H.Windle, J.Chem.Soc.Faraday Trans.Liq.Cryst. 15, (1993), p31.

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Parameters

Input parameters

XSIZE - double precision
x dimension of Monte Carlo lattice.

YSIZE - double precision
y dimension of Monte Carlo lattice.

ZSIZE - double precision
z dimension of Monte Carlo lattice.

GEOMETRY - character
The initial director configuration and boundary conditions. See Specification for options.

DIMENSIONS - integer
Lattice dimension, 2 or 3.

SPLAY - double precision
The splay elastic constant (dimensionless).

TWIST - double precision
The twist elastic constant (dimensionless).

BEND - double precision
The bend elastic constant (dimensionless).

K24 - double precision
The saddle-splay elastic constant (usually set to zero).

FIELD - double precision
The strength of an external field which couples to the z-component of the directors.

DELTA - double precision
Specifies a change in an external field after each cycle.

CYCLES - integer
The number of cycles of 'annealing' the lattice.

ITERATIONS - integer
Average number of times each cell is visited.

GEOMFILE - character
Director array input file.

MOVEFILE - character
Array of moveable directors.

SEED - double precision
Random number generator seed.

BETAINIT - double precision
Initial value of 1/kT.

BETAFACTOR - double precision
Factor by which the initial BETAINIT (1/kT) is multipled in each ANNEAL cycle.

NANNEAL - integer
Number of cycles within each CYCLE (as specified by CYCLES).

Output parameters

All output is to data files.

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Error Indicators

There are a number of error indicators which point to the subroutine in which the error arises.

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Accuracy

The reference list contains comparisons between the calculations and experimental micrographs. The energies of certain configurations have been measured to be in very good agreement with analytical calculations. The code reproduces accurately the so-called Fredricks transitions.

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Further Comments

We are currently working on extending the theory to situations in which the material is sheared. Further information is available on the Polymer Group Homepage <http://www.msm.cam.ac.uk/polymer/index.html>.

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Example

1. Program text

       See full program

2. Program data

Input file :-

XSIZE  5
YSIZE  5
ZSIZE  5
DIMENSIONS 3
GEOMETRY PERIODIC
SPLAY 10.0d0
TWIST 0.1d0
BEND  1.0d0
K_24 0.0d0
FIELD 0.00d0
DELTA 0.00d0
CYCLES 20
ITERATIONS 1000
NANNEAL 1
BETAINIT 30d0
BETAFACTOR 10d0
ANGLEFACTOR 0.10d0
DIRECTORY

3. Program results

Output files energy00.dat and
energy20.dat :-

energy00 energy20
   6.464E+00
   1.853E+00
   5.090E+00
   6.912E+00
   5.066E+00
   2.317E+00
   4.942E+00
   7.401E+00
   8.767E-01
   4.511E+00
   3.222E+00
   3.460E+00
   3.812E+00
   3.154E+00
   4.190E+00
   9.361E+00
   7.149E+00
   1.072E+01
   6.686E+00
   7.989E+00
   6.248E+00
   3.998E+00
   6.074E+00
   9.880E+00
   1.388E+00
   1.848E+00
   3.380E+00
   4.770E+00
   9.471E+00
   4.241E+00
   7.863E+00
   4.707E+00
   3.944E+00
   4.363E+00
   7.441E+00
   2.088E+00
   1.434E+00
   1.729E+00
   2.699E+00
   3.988E+00
   4.008E+00
   1.554E+00
   1.858E+00
   5.723E+00
   2.224E+00
   2.812E+00
   5.610E+00
   4.982E+00
   6.250E+00
   4.233E+00
   1.997E+00
   1.410E+01
   1.012E+01
   5.598E-01
   1.835E+00
   8.526E+00
   1.291E+01
   4.893E+00
   7.203E+00
   6.716E+00
   5.004E+00
   1.390E+00
   1.854E+00
   6.540E+00
   8.046E+00
   6.771E+00
   1.602E+00
   6.947E+00
   4.228E+00
   2.811E+00
   1.320E+00
   5.571E+00
   8.352E+00
   2.916E+00
   2.795E+00
   3.964E+00
   9.934E+00
   8.524E+00
   5.815E+00
   5.731E+00
   4.027E+00
   6.438E+00
   8.034E+00
   8.662E+00
   1.710E+01
   5.261E+00
   4.649E+00
   2.891E+00
   4.730E+00
   7.785E+00
   3.273E+00
   5.776E+00
   6.094E+00
   5.684E+00
   1.131E+00
   4.184E+00
   7.560E+00
   1.062E+01
   2.988E+00
   2.617E+00
   1.534E+01
   4.242E+00
   6.420E+00
   5.683E+00
   1.243E+01
   1.536E+01
   3.208E+00
   3.365E+00
   3.182E+00
   6.428E+00
   5.458E+00
   5.247E+00
   5.464E+00
   4.604E+00
   3.117E+00
   9.648E+00
   2.605E+00
   1.775E+00
   2.650E+00
   9.483E+00
   6.761E+00
   7.241E+00
   1.089E+01
   3.533E+00
   4.430E+00
   5.620E+00
   6.349E+00
   1.764E+00
   1.555E+00
   3.586E+00
   1.012E+01
   2.822E+00
   2.235E+00
   3.482E+00
   4.985E+00
   8.971E+00
   1.225E+00
   2.451E+00
   2.901E+00
   5.143E+00
   3.815E+00
   1.305E+01
   4.576E+00
   4.671E+00
   6.319E+00
   2.459E+00
   2.874E+00
   8.255E+00
   4.641E+00
   3.346E+00
   8.422E+00
   3.182E+00
   2.750E+00
   7.752E+00
   5.834E+00
   1.132E+01
   2.616E+00
   6.517E+00
   1.122E+01
   6.298E+00
   2.786E+00
   2.100E+00
   2.535E+00
   2.173E+00
   2.366E+00
   7.904E+00
   1.141E+01
   2.976E+00
   8.736E+00
   6.057E+00
   5.823E+00
   1.700E+00
   3.459E+00
   4.127E+00
   6.143E+00
   1.629E+00
   3.256E+00
   3.278E+00
   6.095E+00
   6.301E+00
   4.643E+00
   1.914E+00
   4.145E+00
   4.377E+00
   3.566E+00
   3.934E+00
   1.630E+00
   8.921E+00
   1.934E+00
   2.779E+00
   6.245E+00
   8.940E+00
   1.278E+01
   2.942E+00
   4.261E+00
   4.797E+00
   3.249E+00
   1.163E+01
   8.988E+00
   2.767E+00
   2.628E+00
   6.621E+00
   3.452E+00
   4.517E+00
   2.848E+00
   8.431E+00
   1.041E+01
   4.926E+00
   7.917E+00
   1.798E+00
   1.071E+01
   1.456E+00
   3.313E+00
   1.936E+00
   3.856E+00
   8.742E+00
   4.836E+00
   2.103E+00
   8.960E+00
   1.026E+01
   7.010E+00
   4.459E+00
   4.902E+00
   5.149E+00
   3.929E+00
   2.466E+00
   7.029E+00
   8.499E+00
   9.493E+00
   2.045E+00
   5.829E+00
   5.131E+00
   2.694E+00
   6.232E+00
   2.057E+00
   5.131E+00
   2.842E+00
   3.298E+00
   4.071E+00
   4.257E+00
   3.001E+00
   5.297E+00
   7.491E+00
   6.917E+00
   2.657E+00
   3.621E+00
   2.350E+00
   1.504E+00
   4.672E+00
   5.307E+00

Output files vector00.dat and
vector20.dat :-

vector00 vector20
   .55786   .00008   .82994
   .66582   .38796   .63731
   .50645   .50702   .69745
   .78547  -.48853   .37997
   .62835  -.74060  -.23809
   .83965   .52952  -.12078
  -.65531  -.34464   .67216
   .83104   .03791   .55492
   .40006  -.22837   .88758
  -.05503  -.58759  -.80729
  -.28844   .94601   .14790
  -.99753  -.02610   .06517
   .73219   .19465   .65270
  -.57962  -.19747   .79060
  -.00970   .99744   .07090
   .90731  -.38424   .17071
   .18447  -.04916  -.98161
   .47213  -.87912  -.06510
  -.07805  -.28375  -.95572
  -.63864   .27831   .71741
  -.76545  -.62907   .13548
   .29738  -.93645  -.18609
  -.17362  -.08447   .98118
   .47497  -.05458   .87831
  -.27340   .82860   .48854
  -.49988  -.36971  -.78322
  -.73365  -.66084  -.15828
   .37367   .23337  -.89772
   .07060  -.25197  -.96516
   .85598  -.09005  -.50911
  -.68278  -.38792  -.61913
  -.30000  -.89493   .33030
   .26906   .95245  -.14297
   .06994   .79403  -.60384
  -.03489  -.76083   .64802
   .76844  -.56202  -.30600
  -.82424  -.44651  -.34823
  -.57501   .64527  -.50299
   .94697  -.31369  -.06959
  -.59359   .49636   .63346
  -.35893   .93289  -.02979
   .50746   .43931  -.74128
   .13470  -.69641   .70489
   .25612   .84459  -.47017
  -.47979   .80938  -.33869
  -.58689  -.42387  -.68985
   .70862  -.53797   .45656
   .57274   .81949  -.02011
   .71043   .32686  -.62326
  -.00834   .15451  -.98796
   .76827  -.15681   .62062
  -.06230  -.92625   .37174
  -.39083  -.10202   .91479
   .34109   .14416  -.92891
   .21118   .51305  -.83198
  -.83758  -.54582  -.02343
  -.51034   .14555   .84756
   .73349   .64673  -.20914
  -.23248   .09827  -.96763
  -.42078   .89728  -.13357
   .31335  -.22308  -.92307
   .41550   .27635   .86659
  -.59580   .47195  -.64983
   .43235   .90069  -.04281
  -.83755  -.25158   .48500
  -.64526   .49773  -.57957
  -.67498  -.65205  -.34531
  -.69706  -.41423  -.58526
  -.27221   .32067  -.90723
   .66911  -.43345  -.60367
  -.83703   .04010  -.54569
   .28539   .84133   .45904
   .06469  -.91032   .40881
   .20919   .19432  -.95837
  -.27677   .87486  -.39752
  -.97464  -.09198   .20398
  -.91260   .36902   .17603
  -.83942  -.27259  -.47018
   .17278   .97957   .10287
  -.18779  -.32462   .92702
   .09992  -.09789  -.99017
   .52382   .54943   .65095
   .44168   .80505  -.39600
  -.33241  -.28866   .89787
   .42940   .83518   .34364
   .35646   .60026  -.71597
   .48435  -.84665   .22044
  -.79473  -.33494  -.50619
   .47977  -.80882   .34004
   .11088  -.96893  -.22110
  -.37167  -.92413  -.08855
  -.74237  -.64662  -.17541
   .53999  -.16637  -.82506
   .42371   .09249   .90106
  -.23413   .68670   .68821
   .70903   .34273   .61628
  -.46848   .35698   .80814
  -.79784  -.59084  -.11984
  -.29456   .78265   .54835
   .61013  -.38096  -.69470
  -.07075   .87052  -.48702
   .14690  -.09467  -.98461
  -.99292   .09672   .06901
  -.69436  -.60285   .39297
  -.74597  -.08006  -.66115
  -.05350  -.35529  -.93322
  -.35391   .13557   .92540
   .03540   .94354  -.32937
   .46482  -.71634   .52039
  -.49593  -.84237   .21086
   .75953  -.50341   .41195
   .26979   .69237   .66920
  -.32899  -.87224   .36190
  -.86596   .34219   .36472
   .33406  -.72109   .60699
  -.48715  -.31959   .81274
   .50838   .70815   .48997
   .16955  -.79032  -.58876
   .71976  -.67889  -.14508
   .01225   .99829   .05714
   .13667   .81664  -.56073
  -.57611  -.77319  -.26511
   .57305  -.81948  -.00835
   .39885  -.89769   .18726
  -.50369   .06757   .86124
   .48882  -.45931   .74168
   .67495  -.70895   .20454
  -.66842  -.51623  -.53546
  -.76572  -.62948  -.13205
  -.78858  -.20860   .57847
   .11488   .94499   .30625
  -.65510  -.70948   .25980
  -.29893  -.91350  -.27598
  -.36977   .55309   .74656
   .80935  -.27182  -.52065
  -.52988   .29112  -.79654
   .51602   .07864  -.85296
  -.56399  -.52909   .63402
   .07972  -.76131  -.64347
  -.64802  -.48385  -.58818
   .43098   .52358  -.73493
  -.79945   .59428  -.08781
  -.32760   .26706   .90629
   .14469  -.85762   .49351
  -.24652  -.88551   .39383
  -.43432   .01083  -.90069
   .48483  -.78649   .38258
  -.46336  -.83029  -.30971
  -.25232  -.45011   .85658
  -.74216   .09869  -.66292
  -.24277  -.44219  -.86344
  -.36269  -.69560  -.62016
  -.63772  -.34925  -.68654
  -.74537  -.32367  -.58280
   .68139   .14244   .71792
   .60499  -.75919   .24003
  -.78529  -.61910  -.00581
  -.38725   .31839  -.86526
  -.74957   .64351   .15504
  -.07506   .17980   .98083
  -.12790   .60664   .78462
   .66692   .26341  -.69702
   .26741   .86395  -.42671
   .56739  -.80267  -.18382
  -.15809  -.11356  -.98087
  -.41787  -.89288   .16780
  -.08567  -.49051  -.86721
   .53744  -.50202  -.67760
   .75390   .60612   .25348
   .13298   .22078   .96622
   .55763   .78471   .27070
  -.49886   .85782   .12362
  -.76175   .14986   .63030
   .21585   .66012  -.71948
   .49327   .79986   .34193
  -.20879  -.59665   .77487
   .06769  -.39474   .91630
  -.31407  -.85143   .42003
  -.30543  -.00984   .95216
   .45272   .40015  -.79682
   .11572   .93864   .32491
   .94896   .24099  -.20345
  -.64293   .76233   .07412
   .64322   .72464  -.24730
   .68227   .66418  -.30558
  -.43552   .40673   .80305
   .31935   .47922  -.81753
  -.67262  -.13788  -.72703
  -.70507   .01628   .70896
  -.67525   .04961   .73592
  -.92762   .27825  -.24920
  -.82318  -.27927   .49436
  -.35066  -.43825  -.82763
  -.51240   .33949   .78880
   .29602   .35388  -.88721
  -.56792   .78623  -.24352
   .69166  -.67577   .25483
  -.28740  -.35181  -.89086
   .26737  -.94180   .20378
  -.94651  -.31155   .08405
  -.39680  -.76990   .49981
  -.88185   .46428   .08233
   .34406   .90348   .25562
  -.69447   .69397   .19002
   .84462   .53449  -.03052
   .02301   .97461   .22271
  -.71834   .66955  -.18892
  -.15909  -.43210  -.88768
   .42912  -.01263  -.90316
   .22089   .96649  -.13077
  -.83031   .03685  -.55608
   .02317   .86586   .49974
   .95902   .11852  -.25735
  -.76655  -.23854   .59624
   .68786  -.52032  -.50608
   .46964   .44595   .76195
   .37869   .87798   .29282
  -.76079  -.42831  -.48760
   .42356  -.36805  -.82773
   .70189  -.49800   .50927
  -.08637   .81514  -.57279
  -.99565  -.08418   .04002
  -.88601  -.24652   .39270
   .09919   .64077  -.76130
  -.32739   .93178  -.15683
  -.76895   .46785   .43570
   .18846   .65420  -.73247
  -.86818  -.38070   .31834
   .33855   .64373   .68629
   .45652   .70930   .53711
   .89270  -.33853   .29747
   .24717   .70413   .66567
   .77492   .18647   .60393
   .97614  -.17864   .12345
   .27815  -.93646   .21370
  -.97161   .19413   .13522
  -.28122  -.68106  -.67607
   .24259  -.60410  -.75909
   .78422   .54537   .29593
   .03553   .88273  -.46853
  -.25809  -.58411  -.76955
  -.41955  -.55753   .71634
   .40260   .90990   .09996
  -.33443  -.66950   .66326
   .89414   .43498   .10632
  -.54421   .83541  -.07696
   .54871  -.24147   .80038
  -.47342   .26306   .84064
   .60501   .14733   .78247
  -.49618   .77038  -.40041

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Auxiliary Routines

None.

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Keywords

liquid crystals, polymers, monte carlo, microstructures

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Download

Download source code

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MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.

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