Materials Algorithms Project
Program Library
- Provenance of code.
- Purpose of code.
- Specification.
- Description of subroutine's operation.
- References.
- Parameter descriptions.
- Error indicators.
- Accuracy estimate.
- Any additional information.
- Example of code
- Auxiliary subroutines required.
- Keywords.
- Download source code.
- Links.
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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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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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
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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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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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- J.R. Hobdell and A.H. Windle, Liquid Crystals 19, 401-407 (1995).
- J.R. Hobdell and A.H. Windle, J.Chem.Soc.Faraday Trans. 91, 2497-2505 (1995).
- S.E. Bedford and A.H.Windle, J.Chem.Soc.Faraday Trans.Liq.Cryst. 15, (1993), p31.
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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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There are a number of error indicators which point to the subroutine in which the error
arises.
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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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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 <https://www.msm.cam.ac.uk/polymer/index.html>.
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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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None.
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liquid crystals, polymers, monte carlo, microstructures
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Download source code
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