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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.

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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

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
 TWIST        to 1, and the others determined by the ratios known from
 BEND         experiment.

 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
 DELTA        in that external field after each cycle.

 CYCLES       CYCLES is the number of cycles of 'annealing' the lattice.

              ITERATIONS is the number of times each cell is visited (on
 ITERATIONS   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.

              Number of cycles within each CYCLE (as specified by CYCLES),
 NANNEAL      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                          Output files vector00.dat and
energy20.dat :-              vector20.dat :-

    energy00     energy20               vector00                    vector20

     6.464E+00    5.620E+00      .55786   .00008   .82994     .48882  -.45931   .74168
     1.853E+00    6.349E+00      .66582   .38796   .63731     .67495  -.70895   .20454
     5.090E+00    1.764E+00      .50645   .50702   .69745    -.66842  -.51623  -.53546
     6.912E+00    1.555E+00      .78547  -.48853   .37997    -.76572  -.62948  -.13205
     5.066E+00    3.586E+00      .62835  -.74060  -.23809    -.78858  -.20860   .57847
     2.317E+00    1.012E+01      .83965   .52952  -.12078     .11488   .94499   .30625
     4.942E+00    2.822E+00     -.65531  -.34464   .67216    -.65510  -.70948   .25980
     7.401E+00    2.235E+00      .83104   .03791   .55492    -.29893  -.91350  -.27598
     8.767E-01    3.482E+00      .40006  -.22837   .88758    -.36977   .55309   .74656
     4.511E+00    4.985E+00     -.05503  -.58759  -.80729     .80935  -.27182  -.52065
     3.222E+00    8.971E+00     -.28844   .94601   .14790    -.52988   .29112  -.79654
     3.460E+00    1.225E+00     -.99753  -.02610   .06517     .51602   .07864  -.85296
     3.812E+00    2.451E+00      .73219   .19465   .65270    -.56399  -.52909   .63402
     3.154E+00    2.901E+00     -.57962  -.19747   .79060     .07972  -.76131  -.64347
     4.190E+00    5.143E+00     -.00970   .99744   .07090    -.64802  -.48385  -.58818
     9.361E+00    3.815E+00      .90731  -.38424   .17071     .43098   .52358  -.73493
     7.149E+00    1.305E+01      .18447  -.04916  -.98161    -.79945   .59428  -.08781
     1.072E+01    4.576E+00      .47213  -.87912  -.06510    -.32760   .26706   .90629
     6.686E+00    4.671E+00     -.07805  -.28375  -.95572     .14469  -.85762   .49351
     7.989E+00    6.319E+00     -.63864   .27831   .71741    -.24652  -.88551   .39383
     6.248E+00    2.459E+00     -.76545  -.62907   .13548    -.43432   .01083  -.90069
     3.998E+00    2.874E+00      .29738  -.93645  -.18609     .48483  -.78649   .38258
     6.074E+00    8.255E+00     -.17362  -.08447   .98118    -.46336  -.83029  -.30971
     9.880E+00    4.641E+00      .47497  -.05458   .87831    -.25232  -.45011   .85658
     1.388E+00    3.346E+00     -.27340   .82860   .48854    -.74216   .09869  -.66292
     1.848E+00    8.422E+00     -.49988  -.36971  -.78322    -.24277  -.44219  -.86344
     3.380E+00    3.182E+00     -.73365  -.66084  -.15828    -.36269  -.69560  -.62016
     4.770E+00    2.750E+00      .37367   .23337  -.89772    -.63772  -.34925  -.68654
     9.471E+00    7.752E+00      .07060  -.25197  -.96516    -.74537  -.32367  -.58280
     4.241E+00    5.834E+00      .85598  -.09005  -.50911     .68139   .14244   .71792
     7.863E+00    1.132E+01     -.68278  -.38792  -.61913     .60499  -.75919   .24003
     4.707E+00    2.616E+00     -.30000  -.89493   .33030    -.78529  -.61910  -.00581
     3.944E+00    6.517E+00      .26906   .95245  -.14297    -.38725   .31839  -.86526
     4.363E+00    1.122E+01      .06994   .79403  -.60384    -.74957   .64351   .15504
     7.441E+00    6.298E+00     -.03489  -.76083   .64802    -.07506   .17980   .98083
     2.088E+00    2.786E+00      .76844  -.56202  -.30600    -.12790   .60664   .78462
     1.434E+00    2.100E+00     -.82424  -.44651  -.34823     .66692   .26341  -.69702
     1.729E+00    2.535E+00     -.57501   .64527  -.50299     .26741   .86395  -.42671
     2.699E+00    2.173E+00      .94697  -.31369  -.06959     .56739  -.80267  -.18382
     3.988E+00    2.366E+00     -.59359   .49636   .63346    -.15809  -.11356  -.98087
     4.008E+00    7.904E+00     -.35893   .93289  -.02979    -.41787  -.89288   .16780
     1.554E+00    1.141E+01      .50746   .43931  -.74128    -.08567  -.49051  -.86721
     1.858E+00    2.976E+00      .13470  -.69641   .70489     .53744  -.50202  -.67760
     5.723E+00    8.736E+00      .25612   .84459  -.47017     .75390   .60612   .25348
     2.224E+00    6.057E+00     -.47979   .80938  -.33869     .13298   .22078   .96622
     2.812E+00    5.823E+00     -.58689  -.42387  -.68985     .55763   .78471   .27070
     5.610E+00    1.700E+00      .70862  -.53797   .45656    -.49886   .85782   .12362
     4.982E+00    3.459E+00      .57274   .81949  -.02011    -.76175   .14986   .63030
     6.250E+00    4.127E+00      .71043   .32686  -.62326     .21585   .66012  -.71948
     4.233E+00    6.143E+00     -.00834   .15451  -.98796     .49327   .79986   .34193
     1.997E+00    1.629E+00      .76827  -.15681   .62062    -.20879  -.59665   .77487
     1.410E+01    3.256E+00     -.06230  -.92625   .37174     .06769  -.39474   .91630
     1.012E+01    3.278E+00     -.39083  -.10202   .91479    -.31407  -.85143   .42003
     5.598E-01    6.095E+00      .34109   .14416  -.92891    -.30543  -.00984   .95216
     1.835E+00    6.301E+00      .21118   .51305  -.83198     .45272   .40015  -.79682
     8.526E+00    4.643E+00     -.83758  -.54582  -.02343     .11572   .93864   .32491
     1.291E+01    1.914E+00     -.51034   .14555   .84756     .94896   .24099  -.20345
     4.893E+00    4.145E+00      .73349   .64673  -.20914    -.64293   .76233   .07412
     7.203E+00    4.377E+00     -.23248   .09827  -.96763     .64322   .72464  -.24730
     6.716E+00    3.566E+00     -.42078   .89728  -.13357     .68227   .66418  -.30558
     5.004E+00    3.934E+00      .31335  -.22308  -.92307    -.43552   .40673   .80305
     1.390E+00    1.630E+00      .41550   .27635   .86659     .31935   .47922  -.81753
     1.854E+00    8.921E+00     -.59580   .47195  -.64983    -.67262  -.13788  -.72703
     6.540E+00    1.934E+00      .43235   .90069  -.04281    -.70507   .01628   .70896
     8.046E+00    2.779E+00     -.83755  -.25158   .48500    -.67525   .04961   .73592
     6.771E+00    6.245E+00     -.64526   .49773  -.57957    -.92762   .27825  -.24920
     1.602E+00    8.940E+00     -.67498  -.65205  -.34531    -.82318  -.27927   .49436
     6.947E+00    1.278E+01     -.69706  -.41423  -.58526    -.35066  -.43825  -.82763
     4.228E+00    2.942E+00     -.27221   .32067  -.90723    -.51240   .33949   .78880
     2.811E+00    4.261E+00      .66911  -.43345  -.60367     .29602   .35388  -.88721
     1.320E+00    4.797E+00     -.83703   .04010  -.54569    -.56792   .78623  -.24352
     5.571E+00    3.249E+00      .28539   .84133   .45904     .69166  -.67577   .25483
     8.352E+00    1.163E+01      .06469  -.91032   .40881    -.28740  -.35181  -.89086
     2.916E+00    8.988E+00      .20919   .19432  -.95837     .26737  -.94180   .20378
     2.795E+00    2.767E+00     -.27677   .87486  -.39752    -.94651  -.31155   .08405
     3.964E+00    2.628E+00     -.97464  -.09198   .20398    -.39680  -.76990   .49981
     9.934E+00    6.621E+00     -.91260   .36902   .17603    -.88185   .46428   .08233
     8.524E+00    3.452E+00     -.83942  -.27259  -.47018     .34406   .90348   .25562
     5.815E+00    4.517E+00      .17278   .97957   .10287    -.69447   .69397   .19002
     5.731E+00    2.848E+00     -.18779  -.32462   .92702     .84462   .53449  -.03052
     4.027E+00    8.431E+00      .09992  -.09789  -.99017     .02301   .97461   .22271
     6.438E+00    1.041E+01      .52382   .54943   .65095    -.71834   .66955  -.18892
     8.034E+00    4.926E+00      .44168   .80505  -.39600    -.15909  -.43210  -.88768
     8.662E+00    7.917E+00     -.33241  -.28866   .89787     .42912  -.01263  -.90316
     1.710E+01    1.798E+00      .42940   .83518   .34364     .22089   .96649  -.13077
     5.261E+00    1.071E+01      .35646   .60026  -.71597    -.83031   .03685  -.55608
     4.649E+00    1.456E+00      .48435  -.84665   .22044     .02317   .86586   .49974
     2.891E+00    3.313E+00     -.79473  -.33494  -.50619     .95902   .11852  -.25735
     4.730E+00    1.936E+00      .47977  -.80882   .34004    -.76655  -.23854   .59624
     7.785E+00    3.856E+00      .11088  -.96893  -.22110     .68786  -.52032  -.50608
     3.273E+00    8.742E+00     -.37167  -.92413  -.08855     .46964   .44595   .76195
     5.776E+00    4.836E+00     -.74237  -.64662  -.17541     .37869   .87798   .29282
     6.094E+00    2.103E+00      .53999  -.16637  -.82506    -.76079  -.42831  -.48760
     5.684E+00    8.960E+00      .42371   .09249   .90106     .42356  -.36805  -.82773
     1.131E+00    1.026E+01     -.23413   .68670   .68821     .70189  -.49800   .50927
     4.184E+00    7.010E+00      .70903   .34273   .61628    -.08637   .81514  -.57279
     7.560E+00    4.459E+00     -.46848   .35698   .80814    -.99565  -.08418   .04002
     1.062E+01    4.902E+00     -.79784  -.59084  -.11984    -.88601  -.24652   .39270
     2.988E+00    5.149E+00     -.29456   .78265   .54835     .09919   .64077  -.76130
     2.617E+00    3.929E+00      .61013  -.38096  -.69470    -.32739   .93178  -.15683
     1.534E+01    2.466E+00     -.07075   .87052  -.48702    -.76895   .46785   .43570
     4.242E+00    7.029E+00      .14690  -.09467  -.98461     .18846   .65420  -.73247
     6.420E+00    8.499E+00     -.99292   .09672   .06901    -.86818  -.38070   .31834
     5.683E+00    9.493E+00     -.69436  -.60285   .39297     .33855   .64373   .68629
     1.243E+01    2.045E+00     -.74597  -.08006  -.66115     .45652   .70930   .53711
     1.536E+01    5.829E+00     -.05350  -.35529  -.93322     .89270  -.33853   .29747
     3.208E+00    5.131E+00     -.35391   .13557   .92540     .24717   .70413   .66567
     3.365E+00    2.694E+00      .03540   .94354  -.32937     .77492   .18647   .60393
     3.182E+00    6.232E+00      .46482  -.71634   .52039     .97614  -.17864   .12345
     6.428E+00    2.057E+00     -.49593  -.84237   .21086     .27815  -.93646   .21370
     5.458E+00    5.131E+00      .75953  -.50341   .41195    -.97161   .19413   .13522
     5.247E+00    2.842E+00      .26979   .69237   .66920    -.28122  -.68106  -.67607
     5.464E+00    3.298E+00     -.32899  -.87224   .36190     .24259  -.60410  -.75909
     4.604E+00    4.071E+00     -.86596   .34219   .36472     .78422   .54537   .29593
     3.117E+00    4.257E+00      .33406  -.72109   .60699     .03553   .88273  -.46853
     9.648E+00    3.001E+00     -.48715  -.31959   .81274    -.25809  -.58411  -.76955
     2.605E+00    5.297E+00      .50838   .70815   .48997    -.41955  -.55753   .71634
     1.775E+00    7.491E+00      .16955  -.79032  -.58876     .40260   .90990   .09996
     2.650E+00    6.917E+00      .71976  -.67889  -.14508    -.33443  -.66950   .66326
     9.483E+00    2.657E+00      .01225   .99829   .05714     .89414   .43498   .10632
     6.761E+00    3.621E+00      .13667   .81664  -.56073    -.54421   .83541  -.07696
     7.241E+00    2.350E+00     -.57611  -.77319  -.26511     .54871  -.24147   .80038
     1.089E+01    1.504E+00      .57305  -.81948  -.00835    -.47342   .26306   .84064
     3.533E+00    4.672E+00      .39885  -.89769   .18726     .60501   .14733   .78247
     4.430E+00    5.307E+00     -.50369   .06757   .86124    -.49618   .77038  -.40041

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Auxiliary Routines

None.

Keywords

Liquid crystals, polymers, Monte Carlo, microstructures

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