Relation between the grafting density of liquid crystal macromolecule and the symmetry of self-assembled bulk phase: coarse-grained molecular dynamics study

I consider a generic coarse-grained model suitable for the study of bulk self-assembly of liquid crystal (LC) macromolecules. The cases include LC dendrimers, gold nanoparticles modified by polymer chains with terminating LC groups and oth. The study is focused on the relation between a number of gr...

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Published in:	Condensed Matter Physics
Date:	2013
Main Author:	Ilnytskyi, J.M.
Format:	Article
Language:	English
Published:	Інститут фізики конденсованих систем НАН України 2013
Online Access:	https://nasplib.isofts.kiev.ua/handle/123456789/120848
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Journal Title:	Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:	Relation between the grafting density of liquid crystal macromolecule and the symmetry of self-assembled bulk phase: coarse-grained molecular dynamics study / J.M. Ilnytskyi // Condensed Matter Physics. — 2013. — Т. 16, № 4. — С. 43004:1-12. — Бібліогр.: 35 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine

_version_	1860233772118573056
author	Ilnytskyi, J.M.
author_facet	Ilnytskyi, J.M.
citation_txt	Relation between the grafting density of liquid crystal macromolecule and the symmetry of self-assembled bulk phase: coarse-grained molecular dynamics study / J.M. Ilnytskyi // Condensed Matter Physics. — 2013. — Т. 16, № 4. — С. 43004:1-12. — Бібліогр.: 35 назв. — англ.
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container_title	Condensed Matter Physics
description	I consider a generic coarse-grained model suitable for the study of bulk self-assembly of liquid crystal (LC) macromolecules. The cases include LC dendrimers, gold nanoparticles modified by polymer chains with terminating LC groups and oth. The study is focused on the relation between a number of grafted chains, Nch, and the symmetry of the self-assembled bulk phases. Simple space-filling arguments are used first to estimate stability intervals for a rod-like, disc-like and spherulitic conformations in terms of Nch. These are followed by coarse-grained molecular dynamics simulations for both spontaneous and aided self-assembly of LC macromolecules into bulk phases. In spontaneous self-assembly runs, essential coexistence of rod-like and disc-like conformations is observed (via analysis of the histograms for the molecular asphericity) in a broad interval of Nch, which prevents formation of defect-free structures. The use of uniaxial and planar aiding fields is found to improve self-assembly into monodomain phases by promoting conformations of respective symmetry. Strong shape-phase relation, observed experimentally, is indicated also by the simulations by the coincidence of the stability intervals for the respective conformations with those for the bulk phases. Розглянуто узагальнену модель, придатну для опису об’ємного впорядкування рiдкокристалiчних (РК) макромолекул (наприклад, РК дендримерiв; наночастинок золота, модифiкованих полiмерними ланцюжками iз кiнцевими РК групами тощо). Дослiдження концентрується на взаємозв’язку мiж кiлькiстю приєднаних ланцюжкiв N ch та симетрiєю впорядкованої фази. Використовуючи простi геометричнi обчислення спочатку оцiнено iнтервали стабiльностi для стержне-, диско- та сферо-подiбних молекулярних конформацiй залежно вiд N ch . Далi виконано моделювання за допомогою молекулярної динамiки для спонтанного та керованого самовпорядкування РК макромолекул в об’ємнi фази. Пiд час спонтанного самовпорядкування шляхом аналiзу гiстограм для молекулярної асферичностi виявлено спiвiснування стержне-та дископодiбних конформацiй в широкому iнтервалi N ch , що перешкоджає формуванню бездефектних структур. Використання одновiсного або планарного керуючих полiв суттєво покращує самовпорядкування вiдповiдних монодоменних фаз шляхом селекцiї конформацiй з вiдповiдною симетрiєю. Сильна залежнiсть мiж формою молекули та симетрiєю фази, яка спостерiгається експериментально, також виявляється i при моделюваннi – через спiвпадiння iнтервалiв стабiльностi вiдповiдних конформацiй та об’ємних фаз.
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fulltext	#ONDENSED -ATTER 0HYSICS� �� 6OL� �� .O �� ÿ�� $/)� ��#-0�� HTTP��WWW�ICMP�LVIV�UA�JOURNAL 2ELATION BETWEEN THE GRAFTING DENSITY OF LIQUID CRYSTAL MACROMOLECULE AND THE SYMMETRY OF SELF ASSEMBLED BULK PHASE� COARSE GRAINED MOLECULAR DYNAMICS STUDY �-� )LNYTSKYI )NSTITUTE FOR #ONDENSED -ATTER 0HYSICS OF THE .ATIONAL !CADEMY OF 3CIENCES OF 5KRAINE� � 3VIENTSITSKII 3T�� ,VIV� 5KRAINE 2ECEIVED !UGUST �� ) CONSIDER A GENERIC COARSE GRAINED MODEL SUITABLE FOR THE STUDY OF BULK SELF ASSEMBLY OF LIQUID CRYSTAL �,# MACROMOLECULES� 4HE CASES INCLUDE ,# DENDRIMERS� GOLD NANOPARTICLES MODI1ED BY POLYMER CHAINS WITH TERMI NATING ,# GROUPS AND OTHERS� 4HE STUDY IS FOCUSED ON THE RELATION BETWEEN A NUMBER OF GRAFTED CHAINS�N ch � AND THE SYMMETRY OF THE SELF ASSEMBLED BULK PHASES� 3IMPLE SPACE 1LLING ARGUMENTS ARE USED 1RST TO ESTIMATE STABILITY INTERVALS FOR A ROD LIKE� DISC LIKE AND SPHERULITIC CONFORMATIONS IN TERMS OFN ch � 4HESE ARE FOLLOWED BY COARSE GRAINED MOLECULAR DYNAMICS SIMULATIONS FOR BOTH SPONTANEOUS AND AIDED SELF ASSEMBLY OF ,# MACRO MOLECULES INTO BULK PHASES� )N SPONTANEOUS SELF ASSEMBLY RUNS� ESSENTIAL COEXISTENCE OF ROD LIKE AND DISC LIKE CONFORMATIONS IS OBSERVED �VIA ANALYSIS OF THE HISTOGRAMS FOR THE MOLECULAR ASPHERICITY IN A BROAD INTERVAL OFN ch � WHICH PREVENTS THE FORMATION OF DEFECT FREE STRUCTURES� 4HE USE OF UNIAXIAL AND PLANAR AIDING 1ELDS IS FOUND TO IMPROVE SELF ASSEMBLY INTO MONODOMAIN PHASES BY PROMOTING CONFORMATIONS OF RESPECTIVE SYMMETRY� 3TRONG SHAPE PHASE RELATION� OBSERVED EXPERIMENTALLY� ISALSO INDICATED BY THE SIMULATIONS BY THE COINCIDENCE OF THE STABILITY INTERVALS FOR THE RESPECTIVE CONFORMATIONS WITH THOSE FOR THE BULK PHASES� +EY WORDS�MACROMOLECULES� LIQUID CRYSTALS� SELF ASSEMBLING� MOLECULAR DYNAMICS STRUCTURE EFFECTS ON THE ORDER 0!#3� ��.S� ��6X� ��#Z� ��'D �� )NTRODUCTION 7HEN DIFFERENT �IN SIZE� SHAPE OR INTERACTION POTENTIAL MOLECULAR FRAGMENTS ARE COMBINED INTO A SINGLE MOLECULE� THEN ONE OBTAINS THE SO CALLED POLYPHILICMATERIAL ;�� = �THE SIMPLEST EXAMPLE BEING WELL KNOWN AMPHIPHILES � )F SUCH A MOLECULE IS BIG ENOUGH� THEN IT REPRESENTS A SUPERMOLECULAR OBJECT� ALTHOUGH THE SUPRAMOLECULAR EFFECTS ARE ALSO POSSIBLE VIA SELF ASSEMBLY OF POLYPHILIC MACROMOLECULES INTO BULK ORDERED PHASES ;�ÿ�=� 4HE SELF ASSEMBLY IS PREDOMINANTLY DRIVEN BY A MICROPHASE SEPARATION� WHICH� IN TURN� DEPENDS ON BOTH THE DETAILS OF MOLECULAR ARCHITECTURE AND ON THE LEVEL OF CHEMICAL COMPATIBILITY BETWEEN THE CONSTITUENT PARTS OF A MOLECULE� ,# POLYPHILIC MACROMOLECULES INCORPORATE MESOGENIC GROUPS IN ADDITION TO BRANCHED POLYMER CHAINS� NANOPARTICLES� ETC� 6ARIATION OF A MOLECULAR ARCHITECTUREGIVES RISE TO MAIN OR SIDE CHAIN ,# POLYMERS� ,# DENDRIMERS AND ELASTOMERS� ,# GOLD METAMATERIALS ;�ÿ��=� 4HE MICROPHASE SEPARATION IN SUCH SYSTEMS ORIGINATES FROM POOR MISCIBILITY OF AROMATIC AND ALIPHATICFRAGMENTS� AND�OR SIZE DIFFERENCES BETWEEN THEM �E�G�� LARGER NANOPARTICLE AND SMALLER POLYMER BEAD ORMESOGEN AS WELL AS ON THE OTHER DETAILS OF INTERPARTICLE INTERACTIONS� $ESPITE A BROAD VARIETY OF POSSIBLE MOLECULAR ARCHITECTURES� CERTAIN CASES BEAR PROMINENT SIMILARITIES� 'OOD EXAMPLE IS PROVIDED BY THE EXISTENCE OF MANY COMMON FEATURES IN SELF ASSEMBLY OF ,# DENDRIMERS AND ,# GOLD METAMATERIALS ;�� ÿ��=� AND ) WILL CONCENTRATEON THESE PARTICULAR CASES IN THIS STUDY� "OTH h �-� )LNYTSKYI� �� http://dx.doi.org/10.5488/CMP.16.43004 http://www.icmp.lviv.ua/journal �-� )LNYTSKYI SYSTEMS EXHIBIT A SIMILAR SET OF LAMELLAR� COLUMNAR AND VARIOUS CUBIC PHASES ;�� ÿ��=� 3TRICTLY SPEAKING� THE INTERIOR OF THESE TYPES OF MACROMOLECULES IS RATHER DIFFERENT� 2EXIBLE HYPERBRANCHED POLYMER SCAFFOLD VSSOLID NANOPARTICLE� RESPECTIVELY� 4HIS IMPLIES A DIFFERENT TYPE OF GRAFTING IN EACH CASE� MORE OF ANNEALED TYPE FOR ,# DENDRIMER �THE LEVEL OF REARRANGEMENT FREEDOM FOR GRAFTED BEADS DEPENDS ON THE DENDRIMER GENERATION ;�� = � AND MORE OF QUENCHED TYPE FOR GOLD METAPARTICLE� .EVERTHELESS� THE GENERAL ASPECTS OF A SELF ASSEMBLY TURNED OUT TO BE MORE DEPENDENT ON THE SPACE 1LLING CAPABILITIES OF GRAFTED CHAINS AND ON THE STRENGTH OF THE MESOGEN MESOGEN INTERACTION ;�� = THAN ON THE DETAILS OF INTERNAL STRUCTURE OF THE MACROMOLECULE� 4HE SIMILARITIES BETWEEN THE ,# DENDRIMERS AND ,# GOLD METAPARTICLES OPEN UP A POSSIBILITY TO DE SCRIBE THEIR SELF ASSEMBLY BY SOME GENERIC COARSE GRAINEDMODEL� IN WHICH LESS RELEVANT INTERNAL DEGREES OF FREEDOM OF A CENTRAL CORE ARE NEGLECTED AND ONLY REARRANGEMENT OF THE ATTACHED POLYMER CHAINS WITH TERMINATING MESOGENS IS TAKEN INTO ACCOUNT� 4HE GROUNDS FORSUCH COARSE GRAINING �BESIDES GENERAL ARGU MENTS GIVEN ABOVE ARE TO BE FOUND IN SOME PREVIOUS SIMULATION STUDIES ;��ÿ��=� WHERE� IN PARTICULAR� IT WAS FOUND THAT THE CENTRAL CORE OF THE GENERATION THREE CARBOSILANE DENDRIMER IS ON AVERAGE SPHERICALLY SYMMETRIC IN ALL �ISOTROPIC� NEMATIC AND SMECTIC ! PHASES OF ,# SOLVENT ;��=� 4HE MODELS THAT EXPLOIT THIS FACT HAVE ALREADY BEEN CONSIDERED� NAMELY IN THE FORM OF A SPHERE WITH ATTACHED CHAINS� EACH CONTAINING A MESOGEN ;�� =� AS WELL AS A SPHERE DECORATED BY 'AY "ERNEPARTICLES DIRECTLY ON ITS SURFACE ;��=� 4HE NUMBER OF BULK PHASES HAVE BEEN FOUND IN THESE SIMULATION WORKS� 4HE MODELS� HOWEVER� PERMIT TUNING IN A NUMBER OF WAYS �THE NUMBER AND LENGTH OF GRAFTED CHAINS� THE PRECISE WAY OF GRAFTING� THE WAY TER MINAL MESOGENS ARE ATTACHED� ETC� AND THE EFFECTS OF ALL THESE CHANGES STILL AWAIT TO BE ANALYSED IN DETAIL BY COMPUTER SIMULATIONS� 4HE EXPERIMENTAL STUDIES REVEAL THE EXISTENCE OF STRONG DEPENDENCE BETWEEN THE DENSITY OF MESO GENS ON THE MACROMOLECULE SURFACE� MOLECULAR CONFORMATIONIN BULK PHASE AND THE SYMMETRY OF THE LATTER ;�� ÿ��=� !S REMARKED IN REFERENCE ;�=� THE GRAFTING DENSITY �CAN EFFECTIVELY CHANGE THE OVERALL GROSS SHAPE OF THE STRUCTURE OF THE SUPERMOLECULE FROM BEINGROD LIKE� TO DISC LIKE� TO SPHERULITIC� 4HUS� THE STRUCTURE OF THE SYSTEMS AT A MOLECULAR LEVEL CAN BE CONSIDERED AS BEING DEFORMABLE� WHERE EACH TYPE OF MOLECULAR SHAPE WILL SUPPORT DIFFERENT TYPES OF SELF ORGANIZED MESOPHASE STRUCTURE� 4HUS� FOR SU PERMOLECULAR MATERIALS� ROD LIKE SYSTEMS WILL SUPPORT THEFORMATION OF CALAMITIC MESOPHASES �INCLUDING VARIOUS POSSIBILITIES OF SMECTIC POLYMORPHISM � DISC LIKE SYSTEMS TEND TO SUPPORT COLUMNAR MESOPHASES� AND SPHERULITIC SYSTEMS FORM CUBIC PHASES� � 4HE CURRENT STUDY ADDRESSES THIS EFFECT BY MEANS OF COMPUTER SIMULATION� 4HE WORK IS A CONTINUATION OF THE STUDY PERFORMED IN REFERENCE ;��=� WHERE THE COARSE GRAINED GENERIC MODEL FOR THE ,# METAPARTICLE WAS INTRODUCED AND STUDIED ON ASUBJECT OF A BULK SELF ASSEMBLY� 4HE MODEL CONTAINED A CENTRAL SPHERE AND �� FREE SLIDING CHAINS EACH TERMINATED BY A MESOGEN AND THE SIMULATIONS WERE PERFORMED BY MEANS OF A COARSE GRAINED MOLECULAR DYNAMICS �#'-$ � )T HAS BEEN FOUND THAT THE MELT SELF ASSEMBLE INTO EITHER SMECTIC LAMELLAR OR HEXAGONAL COLUMNAR MORPHOLOGY WHEN AIDED BRIE2Y BY AN UNIAXIAL OR PLANAR EXTERNAL1ELD� RESPECTIVELY� 4HE MOLECULAR SHAPE IS PREDOMINANTLY ROD LIKE IN THE SMECTIC PHASE AND DISC LIKE IN THE COLUMNAR ONE� 4HIS SHAPE BISTABILITY WAS ANALYSED BY MEANS OF AVERAGE METRIC PROPERTIES �GYRATION TENSOR� AVERAGE ASPHERICITY�ETC� � /N THE CONTRARY� THE UNAIDED �SPONTANEOUS SELF ASSEMBLY BY MEANS OF EITHER SLOW COMPRESSION OR COOLING THE MELT DOWN WAS FOUND TO ALWAYS RESULT IN THE POLYDOMAIN PHASE� (ERE� THESE1NDINGS ARE EXTENDED IN TWO DIRECTIONS� &IRSTLY� THE MODEL ISGENER ALIZED TO THE CASE OF AN ARBITRARY NUMBER OF GRAFTED CHAINSN ch � WHICH ALLOWS ONE TO STUDY THE INTERVALS OF STABILITY FOR EACH BULK PHASE ONN ch BY MEANS OF #'-$ SIMULATIONS� 3ECONDLY� BOTH AIDED AND SPON TANEOUS SELF ASSEMBLY IS ANALYSED IN DETAIL BY SPLITTING THE MELT INTO SUBSYSTEMS OF ROD LIKE AND DISC LIKE MOLECULES AND MONITORING THE HISTOGRAMS OF THEIR ASPHERICITIES� 4HE PHASE BOUNDARIES OBTAINED BY MEANS OF #'-$ ARE ALSO COMPARED WITH THE RESULTS OF PURELY GEOMETRIC ANALYSIS FOR ATHERMAL SPACE 1LLED ROD� DISC AND SPHERE� 4HE FOLLOWING SECTION CONTAINS A DESCRIPTION OF THE MODEL AND A SPACE 1LLING ANALYSIS� 3ECTION � CON TAINS THE RESULTS FOR THE #'-$ SIMULATIONS OF THE BULK PHASESBY MEANS OF SPONTANEOUS AND AIDED SELF ASSEMBLY� AS WELL AS A DETAILED ANALYSIS OF MOLECULAR CONFORMATIONS� #ONCLUSIONS ARE PROVIDED IN SEC TION �� 3ELF ASSEMBLY OF ,# MACROMOLECULES �� -ODELLING AND COMPUTATIONAL DETAILS 4HE COARSE GRAINED MODEL FOR ,# DENDRIMER OR ,# GOLD METAPARTICLE �HEREAFTER REFERRED TO AS� GENERIC MODEL� IS DEPICTED SCHEMATICALLY IN1GURE �� ,ARGE CENTRAL SPHERE REPRESENTS A COARSE GRAINED CORE OF A MACROMOLECULE WITH ITS INTERNAL DEGREES OF FREEDOM BEING NEGLECTED� &OUR SMALLER SPHERES �EACH BEING A FRAGMENT OF A POLYMER CHAIN OF A FEW HYDROCARBONS FORM A SPACER� 4HE LATTER IS TERMINATED BY A SPHERO CYLINDER REPRESENTING A COARSE GRAINED MESOGENIC �,# GROUP� &IGURE ��#OLOR ONLINE 'ENERIC COARSE GRAINED MODEL OF LIQUID CRYSTAL COLLOID CONSISTING OF LARGE CENTRAL SPHERE ANDN ch FREELY GRAFTED CHAINS EACH TERMINATED BY A MESOGEN� 4HIS MODEL� INTRODUCED IN REFERENCE ;��= AND STUDIED THERE FOR THE CASE OFN ch Æ 32 ATTACHED CHAINS ONLY� IS GENERALISED HERE FOR THE CASE OF ARBITRARYN ch � 4HE1RST BEAD OF EACH CHAIN CAN BE ATTACHED TO THE SURFACE OF A CENTRAL SPHERE IN A NUMBER OF WAYS� IN PARTICULAR� �I QUENCHED LIKE GRAFTING TO A PARTICULAR POINT ON A SURFACE� �II SEMI QUENCHED LIKE GRAFTING WITH THE EMPLOYMENT OF AN ANGULAR ELASTIC SPRING WITH RESPECT TO A PARTICULAR POINT� �III ANNEALEAD LIKE GRAFTING� WHEN THE END BEAD IS CAPABLE OF SLIDING FREELY ON THE SURFACE� )N ALL CASES� RADIAL ELASTIC SPRING CAN BE USED TO ENSURE THAT THE1RST BEAD IS ALWAYS LOCATED ON THE SURFACE OF A LARGE SPHERE� )T IS EVIDENT THAT OPTION �I WOULD BE THE BEST SUITED TO MODEL THE ,# GOLD METAPARTICLE� WHEREAS OPTION �II WOULD REPRESENT THE,# DENDRIMER �E�G�� SUCH OPTION WAS APPLIED IN ;��= � /PTION �III CAN BE SEEN AS SOME LIMIT CASE REPRESENTING THE IN1NITE GENERATION ,# DENDRIMER OR THE METAMOLECULE WITH AN ADDITIONAL SYMMETRY OF CHAINS INTEREXCHANGE� 4HE LATTER IS NOT UNREASONABLE FOR THE EQUILIBRATION SPEED UP AND IS� IN FACT� ON PAR WITH HIGH INTERPENETRABILITY OF SOFT BEADS IN #'-$ MODELLING EMPLOYED HERE� 4HE OPTION �III WITH ANNEALED GRAFTING IS USED IN THIS STUDY� 4HE EFFECTIVE DIMENSIONS OF SOFT BEADS ARE BASED ON THE COARSE GRAINING OF THE ATOMISTIC MODEL FOR THE GENERATION � ,# DENDRIMER ;��=� 4HESE ARE�¾ 1 Æ 21.37 „ FOR A LARGE SPHERE�¾ 2 Æ 6.23 „ FOR THE1RST BEAD OF A SPACER�¾ 3 Æ 4.59 „ FOR ALL THE REST BEADS OF THE SPACER ANDD Æ 3.74 „� L / D Æ 3 FOR THE MESOGEN BREADTH AND ELONGATION� RESPECTIVELY� 4HESE DIMENSIONS ARE ALSO USED FOR THE VISUALISATION PURPOSE� 4HE INTERACTION POTENTIAL BETWEEN ANY TWO SPHERES HAS A QUADRATIC FORM� V sp ¡ sp i j Æ ( U sp ¡ sp MAX (1 ¡ r ¤ i j ) 2 , r ¤ i j Ç 1, 0, r ¤ i j Ê 1, �� WHEREr ¤ i j Æ r i j / ¾ i j IS THE SCALED DISTANCE BETWEEN THE CENTERS OFi TH ANDj TH SPHERE� AND USUAL MIXING RULES¾ i j Æ ( ¾ i Å ¾ j )/2 ARE EMPLOYED FOR THE SPHERES WITH DIFFERENT DIAMETERS¾ i AND ¾ j � 4HE VALUE OF U sp ¡ sp MAX Æ 70 ¢ 10 ¡ 20 IS THE SAME FOR ALL COMBINATIONS OF INTERACTING SPHERES� 4HE SAME POTENTIAL FORM IS USED FOR INTERACTION BETWEEN THE SPHERE AND THE SPHEROCYLINDER� V sp ¡ sc i j Æ ( U sp ¡ sc MAX (1 ¡ d ¤ i j ) 2 , d ¤ i j Ç 1, 0, d ¤ i j Ê 1, �� WHEREd ¤ i j Æ d i j / ¾ i j IS A DIMENSIONLESS CLOSEST DISTANCE BETWEEN THE CENTER OF THE i TH SPHERE AND THE CORE OF THEj TH SPHEROCYLINDER� WITH THE SCALING FACTOR¾ i j Æ ( ¾ i Å D )/2 � 0ARAMETERU sp ¡ sc MAX IS EQUAL TOU sp ¡ sp MAX �SEE ABOVE � �� �-� )LNYTSKYI 3PHEROCYLINDER SPHEROCYLINDER PAIRWISE INTERACTION HASTHE FORM INTRODUCED BY ,INTUVUORI AND 7IL SON ;��=� V sc ¡ sc i j Æ 8 > < > : U sc ¡ sc MAX (1 ¡ d ¤ i j ) 2 Å ² ¤ , d ¤ i j Ç 1, U sc ¡ sc MAX (1 ¡ d ¤ i j ) 2 ¡ U ¤ attr ( ˆ r i j , ˆ e i , ˆ e j )(1 ¡ d ¤ i j ) 4 Å ² ¤ , 1 É d ¤ i j Ç d ¤ c , 0, d ¤ i j È d ¤ c , �� WHEREd ¤ i j Æ d i j / D IS THE DIMENSIONLESS NEAREST DISTANCE BETWEEN THE CORES OF SPHEROCYLINDERS ;��=�d ¤ c IS THE EFFECTIVE CUTOFF DISTANCE FOR THE ATTRACTIVE INTERACTION THAT DEPENDS ON THE ATTRACTIVE PART OF THE POTENTIAL U ¤ attr ( ˆ r i j , ˆ e i , ˆ e j ) Æ U ¤ attr ¡ £ 5 ² 1 P 2 ( ˆ e i ¢ ˆ e j ) Å 5 ² 2 ( P 2 ( ˆ r i j ¢ ˆ e i ) Å P 2 ( ˆ r i j ¢ ˆ e j ) ¤ . �� 4HE LATTER DEPENDS ON THE ORIENTATIONSˆ e i � ˆ e j OF THE LONG AXES OF SPHEROCYLINDERS AND THE UNIT VECTORˆ r i j THAT CONNECT THEIR CENTERS� AS DISCUSSED IN MORE DETAIL ELSEWHERE ;��=� P 2 ( x ) Æ 1/2(3 x 2 ¡ 1) IS THE SECOND ,EGENDRE POLYNOMIAL� THE ENERGY PARAMETERS ARE AS FOLLOWS�U sc ¡ sc MAX Æ 70 ¢ 10 ¡ 20 � U ¤ attr Æ 1500 ¢ 10 ¡ 20 � ² 1 Æ 120 ¢ 10 ¡ 20 AND² 2 Æ ¡ 120 ¢ 10 ¡ 20 � 4HE PHASE DIAGRAM OF THE SYSTEM OF ,# PARTICLES INTERACTING VIA THIS POTENTIAL IS DISCUSSED IN ;��=� "ONDED INTERACTIONS INCLUDE HARMONIC BOND AND HARMONIC PSEUDO VALENT ANGLE �INTRODUCED TO MIMIC SPACER RIGIDITY ON A COARSE GRAINED LEVEL CONTRIBUTIONS� V bonded Æ N b X i Æ 1 k b ( l i ¡ l k 0 ) 2 Å N a X i Æ 1 k a ( µ i ¡ µ 0 ) 2 , �� WHEREl i AND µ i ARE INSTANT VALUES FORi TH BOND LENGTH ANDi TH PSEUDO VALENT ANGLE �DE1NED BETWEEN EACH THREE CONSECUTIVE BEADS IN A SPACER � RESPECTIVELY�N b ANDN a BEING THEIR MAXIMUM NUMBERS� &ORCE CONSTANTS ARE�k b Æ 50 ¢ 10 ¡ 20 � „ 2 ANDk a Æ 20 ¢ 10 ¡ 20 �RAD2 � BOND LENGTH CONSTANTS ARE�l 1 0 Æ 14.9 „ �LARGE SPHEREÿ1RST SPHERE OF SPACER �l 2 0 Æ 3.6 „ � 1RSTÿSECOND SPHERE OF SPACER �l 3 0 Æ 3.62 „ �ALL OTHER BONDS BETWEEN SPHERES IN THE SPACER �l 4 0 Æ 2.98 „ �LAST SPHERE OF A SPACERÿMESOGEN NEAREST CAP CENTER � 4HE PSEUDO VALENT ANGLE CONSTANT ISµ 0 Æ ¼ � ,ET ME NOW CONSIDER POSSIBLE CONFORMATIONS THAT CAN BE OBSERVED IN SUCH MODEL MACROMOLECULE DE PENDING ON A NUMBER OF ATTACHED CHAINSN ch � &OLLOWING EXPERIMENTAL WORK ;�� ÿ��=� ONE WOULD EXPECT THE POSSIBILITY FOR THE ROD LIKE� DISC LIKE AND SPHERULITIC SHAPES� )T IS OBVIOUS THAT ONE OF THE CRUCIAL FACTORS THAT WILL DE1NE THE MOST FAVOURABLE SHAPE�S AT GIVENN ch IS THE CAPABILITY OF THE AVAILABLE MOLECULAR ELE MENTS OF SPACE 1LLING INTO A REQUIRED FORM� )T IS ALSO KNOWN FROM BOTH EXPERIMENTAL ;�� = AND SIMULATION ;��= WORKS THAT THE MESOGENS OF ADJACENT MOLECULES HIGHLY INTERDIGITATE� &OR THE CASE OF A ROD LIKE CONFOR MATION �IN THE SMECTIC PHASE � ONE MAY CONSIDER THE� SLIM ROD� LIMIT WHEN THE BREADTH OF THE MOLECULAR ROD IS EQUAL TO THE DIAMETER OF THE LARGE SPHERE¾ 1 � )F SUCH TWO RODS INTERDIGITATE� THEN THE MESOGENS FROM BOTH MOLECULES CROSS THE MID DISTANCE CROSS SECTION OF DIAMETER¾ 1 �SHOWN IN GREY IN1GURE �� ON THE LEFT � 4HE CONDITION OF TIGHT SPACE1LLING OF EACH MOLECULE INTO A ROD IS REDUCED THEN TO CLOSE PACKING OF �$ DISCS OF DIAMETERD INSIDE THE CIRCLE OF DIAMETER¾ 1 � 4HE NUMBER OF HEXAGONALLY CLOSELY PACKED MESOGENS PER CROSS SECTION CIRCLE ISN 0 Æ k ¼ r 2 1 ¼ ( D /2) 2 Æ k ¡ r 1 D /2 ¢ 2 ¼ 30 � WHEREk Æ 0.91 IS A PACKING FRACTION FOR �$ HEXAGONAL LATTICE ANDr 1 Æ ¾ 1 /2 � (ALF OF THESE �SHOWN AS BLUE BELONG TO THE LOWER MOLECULE ONLY� BUT EACH MOLECULAR ROD HAS TWO TAILS� 4HEREFORE� THE NUMBER OF CHAINS PER MOLECULE IN THE� SLIM ROD� LIMIT ISN rod Æ N 0 ¼ 30 � 4HIS IS AN ESTIMATE FOR THE AVERAGE NUMBER OF CHAINS TO FORM A TIGHTLY SPACE 1LLED ROD� 3IMILAR ESTIMATES CAN BE PERFORMED FOR THE CASE OF A DISC LIKE CONFORMATION �IN THE COLUMNAR PHASE IN A � SLIM DISC� LIMIT �SEE�1GURE �� ON THE RIGHT � )N THIS CASE� THE WIDTH OF THE DISC IS EQUAL TO¾ 1 Æ 2 r 1 AND ITS RADIUSR d CAN BE ESTIMATED FROM THE SUMS OF BOND LENGTHS IN THE SPACER AND HALF A LENGTH OF THE MESOGEN� YIELDINGR d ¼ 34.3 „ �THE HALF OF THE MESOGEN LENGTH IS TAKEN INTO ACCOUNT DUE TO MESOGENS INTERDIGITATION WITH THOSE FROM SIX NEIGHBORING MOLECULES � 4HE NUMBER OF CLOSELY PACKED MESOGENS ON THE SIDE SURFACE OF A DISC IS� THEREFORE�N 00 Æ k 2 ¼ R d ¢ 2 r 1 ¼ ( D /2) 2 ¼ 382 � /NLY HALF OF THESE MESOGENS BELONG TO A GIVEN MOLECULE �SHOWN AS BLUE DISCS IN THE CROSS SECTION REGION IN1GURE � � HENCE THE NUMBER OF CHAINS PER MOLECULE IN A� SLIM DISC� LIMIT ISN disc Æ N 00 /2 ¼ 191 � 4HIS NUMBER� HOWEVER� TURNS OUT TO BE UNREALISTIC FOR OUR MODEL� BECAUSE ONE SHOULD TAKE INTO ACCOUNT THAT THE DENSITY OF CHAINS INCREASES CLOSER TO THE CENTRAL SPHERE� )NDEED� THE NUMBER OF CLOSELY PACKED GRAFTING BEADS �OF RADIUSr 2 Æ ¾ 2 /2 ATTACHED TO THE SIDE SURFACE OF A SMALL DISC OF A RADIUSr 1 Å r 2 �MADE AROUND A CENTRAL SPHERE IS ONLYN ¤ Æ k 2 ¼ ( r 1 Å r 2 ) ¢ 2 r 1 ¼ r 2 2 ¼ 55 � FOUR TIMES �� 3ELF ASSEMBLY OF ,# MACROMOLECULES &IGURE ��#OLOR ONLINE /N THE LEFT� CROSS SECTION REGION �SHOWN AS GRAY CIRCLE BETWEEN THE TAILS OF TWO ADJACENT MOLECULAR RODS PACKED IN AN INTERDIGITATED SMECTIC LAYER� 4HE ARROW POINTS TO �$ ILLUSTRATION OF MESOGENS CROSS SECTIONS PACKING INSIDE THE CROSS SECTIONREGION �BLUE AND GREEN DISCS REPRESENT MESOGENS FROM DIFFERENT MOLECULES � /N THE RIGHT� THE SAME FOR MOLECULAR DISCS PACKED INTO INTERDIGITATED HEXAGONAL COLUMNAR PHASE� 4HE SIDE SURFACE OF DISCS �SHOWN BELOW IS THE CROSS SECTION REGION IN THIS CASE� BLUE AND GREEN DISCS REPRESENT MESOGENS FROM THE CENTRAL AND NEIGHBOURING MOLECULES� RESPECTIVELY� LESS THAN IT IS REQUIRED FOR CLOSE PACKED MESOGENS ON THE EDGESURFACE OF A DISC LIKE MOLECULE� 4HEREFORE� ATN ch È N ¤ ONE WOULD FACE A TREMENDOUS CROWDING OF BEADS NEAR THE SURFACE OF A LARGE SPHERE AND THE REASONABLE ESTIMATE FORN ch TO FORM SPACE 1LLED �NEAR THE CENTRAL SPHERE ONLY DISC WOULD BEN ¤ ¼ 55 � &OR THE CASE OF SPHERULITIC CONFORMATION� THE SITUATION IS SIMILAR AND THE CLOSE PACKED EXTERNAL SHELL CANNOT BE ACHIEVED DUE TO LIMITATIONS ON THE GRAFTING DENSITY AT THESURFACE OF A CENTRAL SPHERE� 4HE NUMBER OF CLOSELY GRAFTED POLYMER BEADS IN THIS CASE IS ESTIMATED ASN † Æ k 4 ¼ ( r 1 Å r 2 ) 2 ¼ r 2 2 ¼ 71 � 4HIS ANALYSIS� BASED ON SPACE 1LLING OF MOLECULAR ELEMENTS� RESULTS IN A VERY ROUGH ESTIMATE FOR THE AVERAGE NUMBER OF CHAINSN ch » 30, 55, 71 THAT ARE OPTIMAL TO FORM A ROD LIKE� DISC LIKE AND SPHERULITIC SPACE 1LLED CONFORMATIONS� RESPECTIVELY� )T LEAVES BEYOND THE EFFECT OF CONFORMATIONAL ENTROPY� WHICH RESULTS IN SWELLING OF BOTH RODS AND DISCS� AND THIS WILL BE TEMPERATURE DEPENDENT� 4HE EQUILIBRIUM CON FORMATION �AND THE RESULTING BULK MORPHOLOGY WILL BE THE RESULT OF THE COMPETITION BETWEEN ENTHALPY OF THE MESOGEN MESOGEN INTERACTIONS AND VARIOUS ENTROPIC CONTRIBUTIONS TO THE FREE ENERGY� 4HE EFFECTS ARE TAKEN INTO ACCOUNT MOST NATURALLY IN THE #'-$ SIMULATIONS PRESENTED IN THE FOLLOWING SECTION� �� "ULK PHASES� AIDED AND SPONTANEOUS SELF ASSEMBLY� ANALYSIS OF MOLEC ULAR CONFORMATIONS VIA #'-$ SIMULATIONS (ERE� ) USE THE SAME COARSE GRAINED -$ APPROACH AS WAS USED INREFERENCE ;��=� 4HIS IS A PRETTY STANDARD -$ TECHNIQUE ONLY TO BE APPLIED TO THE SYSTEM WITH SOFT COARSE GRAINED POTENTIALS� THE DETAILS CAN BE FOUND IN REFERENCES ;�� =� 4HE NUMBER OF MACROMOLECULES BEING SIMULATED ISN mol Æ 100 FOR EACH CASE OFN ch Æ 8 ¡ 64 GRAFTED CHAINS� THEN P T ANDN P x x P y y P z z T ENSEMBLES ARE USED AT THE PRESSURE OF53 ATM� THE TIMESTEP IS20 FS AND THE LEAP FROG INTEGRATOR IS EMPLOYED� )T IS ASSUMED THAT THE GENERIC MODEL FOR ,# MACROMOLECULE �INTRODUCED IN THE PREVIOUS SECTION AND SHOWN IN1GURE � IS CAPABLE OF SELF ASSEMBLING INTO THE FOLLOWING BULK PHASES� LAMELLAR SMECTIC �MACRO MOLECULES ADOPT A ROD LIKE CONFORMATION � HEXAGONAL COLUMNAR �MACROMOLECULES ADOPT A DISC LIKE CON FORMATION AND CUBIC PHASE OF POSSIBLY VARIOUS SYMMETRIES�!S ALREADY MENTIONED ABOVE� THE GROUNDS FOR THIS ARE TO BE FOUND IN BOTH EXPERIMENTAL ;�� = AND SIMULATION ;��= STUDIES� 3LOW SELF ASSEMBLY OF ,# MACROMOLECULAR MELTS POSES SERIOUS PROBLEMS TO COMPUTER SIMULATIONS� %S SENTIAL SPEED UP FOR MICROPHASE SEPARATION CAN BE ACHIEVEDBY USING SOFT POTENTIALS ;E�G�� EQUATIONS �� ÿ �� �-� )LNYTSKYI &IGURE ��#OLOR ONLINE 3NAPSHOTS FOR LAMELLAR SMECTIC PHASES OBTAINED VIA SPONTANEOUS SELF ASSEMBLY OF GENERIC MODEL BY COOLING THE SAMPLE FROMT Æ 500 + DOWN TO450 + WITH THE COOLING RATE OF2.5 +�NS� 4OP LEFT�N ch Æ 8 � TOP RIGHT�N ch Æ 12 � BOTTOM LEFT�N ch Æ 20 � BOTTOM RIGHT�N ch Æ 24 � �� =� SINCE IN THIS CASE THE BEADS ARE SEMI TRANSPARENT AND MAY OVERLAP AND CROSS EACH OTHER DURING THE EQUILIBRATION �SEE� E�G�� ;�� ÿ��= � (OWEVER� FOR THE CASE OF THE MODEL DEPICTED IN1GURE �� THE SPONTA NEOUS SELF ASSEMBLY WAS STILL FOUND TO TYPICALLY LEAD TO THEPOLYDOMAIN �GLOBALLY ISOTROPIC PHASE� BOTH IN THE CASE OF SLOW COOLING DOWN OR SLOW COMPRESSING �THE RESULTS FORN ch Æ 32 CHAINS ARE DISCUSSED EARLIER ;��= � 3IMILARLY TO THESE1NDINGS� SPONTANEOUS SELF ASSEMBLY AT A BROADER INTERVAL OFVALUES OFN ch Æ 8 ¡ 64 TURNS OUT TO BE ALSO MORE� HIT AND MISS� � ) USED RELATIVELY SLOW COOLING� WHEN THE TEMPERATURE WAS LOW ERED LINEARLY FROMT Æ 500 + DOWN TO450 + DURING1RST20 NS �COOLING RATE IS2.5 +�NS � FOLLOWED BY ANOTHER RUN FOR20 NS AT1XEDT Æ 450 +� !S THE RESULT� RELATIVELY DEFECT FREE SMECTIC LAYERS AREFOUND FOR THE CASES OFN ch Æ 12 AND N ch Æ 20 � WHEREAS AT OTHER VALUES OFN ch É 24 � THE POLYDOMAIN LAYERED STRUC TURES HAVE BEEN OBTAINED �SEE�1GURE � WITH THE SAMPLE PREPARATION PATH BEING THE SAME IN ALLCASES� 4HERE SEEM TO BE SEVERAL REASONS FOR HAMPERING THE SPONTANEOUS SELF ASSEMBLY OF OUR MODEL� 4HE1RST ONE COULD BE RELATED TO THE ANNEALED GRAFTING OF CHAINS� WHICH RESULTS IN A BROAD UNCONTROLLED DISTRIBUTION OF MOLECULAR ASPHERICITY �SEE BELOW AS WELL AS MAY ENHANCE MICROPHASE SEPARATION BETWEEN LARGE AND SMALL SPHERES� AS EVIDENCED FOR THE CASE OFN ch Æ 8 �SEE�1GURE � � 4HE SECOND REASON IS HIGH METASTABILITY OF THE MELT BELOW ,# TRANSITION� &OR INSTANCE� WHEN THE SYSTEM IS COOLED DOWN� ONCE THE MESOGENS START TO FORM ,# DOMAINS� IT IS LOCKED INTO A RANDOM NETWORK FORMED BY PHYSICAL CROSSLINKS BETWEEN MESOGENS� !S A RESULT� THE SYSTEM IS STUCK IN A METASTABLE STATE AND CANNOT BE DRIVEN FURTHER TO THE GLOBAL MINIMUM MORPHOLOGY WITHOUT APPLYING A CERTAIN EXTERNAL STIMULUS� )N REAL LIFE� THE PERTURBATIONS OF VARIOUS KIND DO EXIST� E�G�� RANDOM2OWS �WHEN MELT IS POURED INTO SOME VESSEL � CENTRIFUGAL FORCES �WHEN SPIN COATING IS USED � POSSIBILITY TO APPLY SHEAR� LAMINAR2OW OR EXTERNAL1ELDS� 4HESE STIMULI CONSTANTLY� SHAKE� THE MOLECULES IN VARIOUS WAYS AND DRIVE THE MELT TOWARDS THE EQUILIBRIUM STATE� 3IMILAR APPROACHES COULD BE ALSO USED IN -$ SIMULATIONS� )N REFERENCE ;��= THE EXTERNAL1ELDS ACTING ON THE MESOGENS WERE USED TO AID THE FORMATION OF BULK PHASES� THIS APPROACH BEING ALSO ADOPTED IN OUR STUDY� 4HE EXTERNAL1ELD IS INTRODUCED VIA ADDITIONAL ENERGY TERM� V rot i Æ ¡ F ( ˆ e i ¢ ˆ f ) 2 , �� WHEREF IS THE AMPLITUDE OF THE1ELD �THE REDUCED AMPLITUDEf WILL BE DE1NED ASF Æ f ¢ 10 ¡ 20 * � ˆ e i IS THE UNIT VECTOR DIRECTED ALONG THE LONG AXIS OFi TH MESOGEN ANDˆ f IS THE UNIT VECTOR THAT DE1NES THE DIRECTION OF THE1ELD� 7HEN F È 0 � THE1ELD HAS AN UNIAXIAL SYMMETRY� WHENF Ç 0 � ITS SYMMETRY IS PLANAR �PRO MOTING THE ORIENTATION OF THE MESOGENS IN A PLANE PERPENDICULAR TOˆ f VECTOR � 4HE LATTER CASE IS INSPIRED BY SIMULATIONS OF AZOBENZENE POLYMERS ;�� =� 4HE APPROACH CAN BE TERMED AS� AIDED SELF ASSEMBLY� � IN CONTRAST TO THE SPONTANEOUS ONE� /NE SHOULD REMARK THAT THE EXTERNAL1ELD ONLY PROMOTES CERTAIN SYMME TRY FOR THE MOLECULAR CONFORMATIONS BUT THE MOLECULES ORGANISE THEMSELVES INTO A BULK PHASE BY MEANS OF SELF ASSEMBLY� 4HE SMECTIC ISOTROPIC AND COLUMNAR ISOTROPIC TRANSITIONTEMPERATURES ARE FOUND TO BE IN THE RANGE OF 490 ¡ 500 + AND WEAKLY DEPENDENT ON THE NUMBER OF ATTACHED CHAINSN ch IF N ch É 40 � 4HIS IS ATTRIBUTED �� 3ELF ASSEMBLY OF ,# MACROMOLECULES f^ f^ N =8ch f=5 f=-5 &IGURE ��#OLOR ONLINE 2ESULTS FOR AN AIDED SELF ASSEMBLY OF GENERIC MODEL WITHN ch Æ 8 GRAFTED CHAINS� ,EFT HAND FRAME� UNIAXIAL AIDING 1ELD� RIGHT HAND FRAME� PLANAR AIDING 1ELD� 1ELD DIRECTIONˆ f IS SHOWN AS ARROW �POINTS TOWARDS THE READER IN THE RIGHT HAND FRAME � .OTE THAT THE SAME LAMELLAR SMECTIC PHASE IS FORMED IN BOTH CASES� TO THE FACT THAT THE MESOGEN MESOGEN INTERACTIONS ARE THE SAME IN ALL THE CASES� 4HEREFORE� TO SEARCH FOR ORDERED PHASES� THE FOLLOWING STEPS ARE PERFORMED� &IRST� THE INITIAL SYSTEM IS FORMED BY1LLING THE SIMULATION BOX RANDOMLY BY ,# MACROMOLECULES WITHN ch CHAINS DIRECTED RADIALLY OUT OF A CENTRAL SPHERE� 4HEN� THE SHORTN V T RUN IS PERFORMED ATT Æ 500 + WITH THE TIME STEP OF2 FS TO REMEDY THE BEADS OVERLAPPING� !FTER THAT� SEVERAL AIDED SELF ASSEMBLY RUNSOF DURATION20 NS ARE PERFORMED ATT Æ 520 + �ABOVE THE ,# TRANSITION WITH THE TIMESTEP OF20 FS INN P x x P y y P z z T ENSEMBLE �FOR MORE DETAILS ON THIS ENSEMBLE� SEE ;��= � 4HE RUNS DIFFER BY THE VALUE OF A REDUCED1ELD STRENGTH CHOSEN FROM THE INTERVAL OFf Æ [3; 5] FOR THE UNIAXIAL1ELD ANDf Æ [ ¡ 5; ¡ 3] FOR THE PLANAR ONE� &INALLY� THE FOLLOWING RUNS ARE PERFORMED �MOSTLY ATT Æ 450 +� ABOUT50 + BELOW THE ,# TRANSITION IN WHICH THE EXTERNAL1ELD IS REMOVED� TO CHECK ON THE STABILITY OF EACH BULK PHASE� !LL THESE RUNS ARE PERFORMED AT NON ZERO EXTERNAL PRESSURE� AS FAR THE SYSTEM IS MOSTLY DENSITY DRIVEN �OUT OF ALL THE NON BONDED INTERACTIONS� EQUATIONS �� ÿ�� ONLY THE MESOGEN MESOGEN PAIR POTENTIAL HAS AN ATTRACTIVE CONTRIBUTION � 4HE PRESSURE OF53atm IS FOUND TO BE QUITE ADEQUATE FOR THIS PURPOSE� AS WAS FOUND IN AN EARLIER STUDY ;��=� !T THE LOWER END OFN ch VALUES� THE ROD LIKE MOLECULAR CONFORMATION AND BULK LAMELLAR SMECTIC PHASE ARE EXPECTED� 4HE SELF ASSEMBLY OF THIS PHASE IS AIDED BY AN UNIAXIAL1ELD WITHf È 0 ATT Æ 520 +� .EV ERTHELESS� FOR THE SAKE OF COMPARISON� ) ALSO PERFORMED RUNSFORf Ç 0 �ATTEMPTING TO FORCE A DISCOTIC CONFORMATION � )N BOTH CASES�ˆ f IS ORIENTED ALONGZ AXIS AND THE RUNS OF10 NS DURATION ARE PERFORMED� !FTER THAT� THE1ELD IS REMOVED AND THE SYSTEM IS EQUILIBRATED FOR ANOTHER20 NS ATT Æ 450 +� 2EMARKABLY� THE SAME LAMELLAR SMECTIC MORPHOLOGY IS OBTAINED IN BOTH CASES �OFf È 0 AND f Ç 0 � THE LAYERS ONLY DIFFER IN THEIR ARRANGEMENT WITH RESPECT TO THE SPATIAL AXES �SEE�1GURE � � )N PARTICULAR� ATf Æ 5 THE LONG AXES OF MOLECULAR RODS ARE DIRECTED ALONGZ AXIS� WHEREAS ATf Æ ¡ 5 THEY ARE CON1NED WITHINX Y PLANES� )N THE LATTER CASE� THE QUASI �$ SPONTANEOUS SELF ASSEMBLY OCCURS INSIDE THESE PLANES RESULTING IN THE FORMATION OF THE SMECTIC LAYERS� )N BOTH SIMULATIONS WITH UNIAXIAL ANDPLANAR1ELDS� THE ROD LIKE CONFORMATION IS OBSERVED ONLY �THE HISTOGRAMS WILL BE PROVIDED BELOW � WHICH SAYS IN FAVOUR OF THE AIDING1ELD APPROACH� )NDEED� THE SYMMETRY OF THE1ELD IS NOT CAPABLE OF FORCING A CERTAIN CONFORMATION TO OCCUR�IN THIS CASE ÿ A DISCOTIC ONE � IF IT IS NOT A NATIVE ONE FOR A GIVEN VALUE OFN ch � 4HE SAME SCENARIO HOLDS FOR AT LEAST N ch Æ 16 ATTACHED CHAINS� AND IN ALL THESE CASES THE LAMELLAR SMECTICPHASE IS OBSERVED ONLY� !T THE RANGE OF VALUES OFN ch Æ 24 ¡ 40 � THE MODEL DISPLAYS CONFORMATIONAL BISTABILITY� DISCUSSED EARLIER IN ;��=� )N THIS CASE� THE SYMMETRY OF THE AIDING1ELD ACTS AS A CONFORMATION SWITCHER� 4HE LARGEST NUMBER OF CHAINS AT WHICH THE SMECTIC PHASE IS OBSERVED IS40 � HIGHER THAN THE CLOSE PACKING ESTIMATE FOR THE� SLIM ROD� MODEL �SEE� PREVIOUS SECTION N 0 Æ 30 � THUS� INDICATING A� SWOLLEN ROD� CONFORMATION� !T A LARGER NUMBER OF CHAINS�N ch Æ 48 � THE LAMELLAR SMECTIC PHASE CAN BE FORCED BY THE1ELDf Æ 5 � BUT IT TURNS OUT TO BE UNSTABLE IF THE1ELD IS REMOVED AND THE TEMPERATURE REDUCED TO450 + �SEE�1GURE � � 0RELIMINARY RUNS� PERFORMED FORN ch Æ 48 IN A TEMPERATURE RANGE OFT Æ [300, 500] +� INDICATE THAT THE SMECTIC ISOTROPIC TRANSITION TEMPERATURE IN THIS CASE IS MUCH LOWER THAN FOR THE CASE OFN ch Æ 32 � NAMELYT » 400 + VS T » 490 +� RESPECTIVELY� 4HESE EFFECTS WILL BE COVERED IN DETAIL IN ASEPARATE STUDY� �� �-� )LNYTSKYI &IGURE ��#OLOR ONLINE &ORCED LAMELLAR SMECTIC PHASE FOR A GENERIC MODEL WITHN ch Æ 48 CHAINS KEPT BY MEANS OF UNIAXIAL 1ELD �LEFT HAND FRAME AND BREAK UP OF THISPHASE WHEN THE 1ELD IS SWITCHED �OFF� �RIGHT HAND FRAME � 4HE APPLICATION OF THE PLANAR1ELD WITHf Ç 0 INDUCES A DISC LIKE CONFORMATION AND AIDS SELF ASSEMBLY OF A DEFECT FREE HEXAGONALLY PACKED COLUMNAR PHASE FORN ch Æ 24 ¡ 48 � INCLUDING THE CASE OFN ch Æ 32 DISCUSSED IN DETAIL IN REFERENCE ;��=� 4HE PROPERTIES OF THIS PHASE AND THE SNAPSHOTS ARE TO BE FOUND THERE AND ARE NOT REPEATED HERE� !TN ch » 56 ¡ 64 � THE DISCOTIC CONFORMATION TRANSFORMS INTO A SPHERULITIC AND� AS A RESULT� THE CUBIC PHASE IS FORMED �SEE�1GURE � � 4WO VIEWS OF THE CUBIC PHASE ARE SHOWN IN THIS 1GURE� AND ON THE R�H�S� ONE MAY IDENTIFY THE STRUCTURE OF SWOLLEN COLUMNS OF THE FORMER COLUMNAR PHASE� 4HE INTERVAL OF STABILITY FOR THE DISC LIKE CONFORMATION INTERMS OFN ch IS NOT SPANNING UP TO THE VALUE PREDICTED BY CLOSE PACKING OF THE GRAFTING POINTS�N ¤ ¼ 55 � INDICATING NOT TIGHTLY PACKED DISCS� ,ET ME SWITCH NOW TO THE QUANTITATIVE ANALYSIS OF CONFORMATIONS IN THE OBSERVED BULK PHASES� 4O DO SO ) SPLIT THE SYSTEM INTO RODS AND DISCS AND BUILD HISTOGRAMSFOR ASPHERICITY OF THEIR CONFORMATIONS� &IRST OF ALL� THE COMPONENTS OF GYRATION TENSOR ARE EVALUATED FOR EACHk TH MOLECULE� G [ k ] ®¯ Æ 1 N [ k ] N [ k ] X i Æ 1 ³ r [ k ] i , ® ¡ R [ k ] ® ´ ³ r [ k ] i , ¯ ¡ R [ k ] ¯ ´ , ~ R [ k ] Æ 1 N [ k ] N [ k ] X i Æ 1 ~ r i [ k ] , �� WHEREN [ k ] PARTICLE CENTERS WITH COORDINATESr [ k ] i , ® ARE TAKEN INTO ACCOUNT�R [ k ] ® IS THE MOLECULAR CENTER OF MASS�® � ¯ DENOTE #ARTESIAN AXES� 4O ACCOUNT FOR AN EXTENDED SHAPE OF MESOGENS� EACH IS REPLACED BY A LINE OF FOUR CENTERS� 4HE EIGENVALUES OF GYRATION TENSOR�¸ [ k ] max � ¸ [ k ] med ANḐ [ k ] min �WHERE THE INDICES DENOTE &IGURE ��#OLOR ONLINE 4WO VIEWS SHOWING THE SYMMETRY OF THE CUBIC PHASE OBTAINED AS THE RESULT OF EITHER SPONTANEOUS OR AIDED WITH PLANAR1ELD SELF ASSEMBLY OF GENERIC MODEL WITHN ch Æ 64 CHAINS� 4HE IMAGE ON THE RIGHT RESEMBLES COLUMNAR STRUCTURE BEING SWOLLEN DUE TO THE CHANGE OF MOLECULAR CONFOR MATIONS FROM DISC TO A SPHERE� �� 3ELF ASSEMBLY OF ,# MACROMOLECULES -0.5 0.0 0.5 8 16 24 32 64 40 a 0 p(a 0 ) f = 0 -0.5 0.0 0.5 8 16 24 40 48 a 0 p(a 0 ) f > 0, then f = 0 -0.5 0.0 0.5 16 22 40 56 24 64 a 0 p(a 0 ) f < 0, then f = 0 &IGURE ��(ISTOGRAMS FOR THE DISTRIBUTIONS OF MOLECULAR ASPHERICITYp ( a 0 ) �SEE TEXT FOR EXPLANATIONS SHOWN FOR A SPONTANEOUS SELF ASSEMBLY �LEFT HAND IMAGE � UNIAXIAL1ELD AIDED SELF ASSEMBLY �MIDDLE IMAGE AND PLANAR1ELD AIDED SELF ASSEMBLY �RIGHT HAND IMAGE � /NLY CHARACTERISTICN ch CASES ARE SHOWN IN EACH CASE� MAXIMUM� MEDIUM AND MINIMUM VALUE� RESPECTIVELY ARE EVALUATED NEXT� 4HESE ARE USED TO INTRODUCE MOLECULAR� RODDICITY� �ALWAYS POSITIVE � a [ k ] r Æ · ¸ [ k ] max ¡ 1 2 ( ¸ [ k ] med Å ¸ [ k ] min ) ¸ [ R [ k ] g ] ¡ 2 �� AND MOLECULAR� DISCOTICITY� �ALWAYS NEGATIVE � a [ k ] d Æ · ¸ [ k ] min ¡ 1 2 ( ¸ [ k ] med Å ¸ [ k ] max ) ¸ [ R [ k ] g ] ¡ 2 , �� FOR EACHk TH MOLECULE� (ERE�[ R [ k ] g ] 2 Æ ¸ [ k ] max Å ¸ [ k ] med Å ¸ [ k ] min IS SQUARED RADIUS OF GYRATION� )F� FOR A GIVENk � THE� RODDICITY� PREVAILS�j a [ k ] r j È j a [ k ] d j � THEN IT IS CLASSI1ED AS A ROD AND ITS ASPHERICITY IS SET TOa 0 Æ a [ k ] r � OTHERWISE THE MOLECULE IS CLASSI1ED AS A DISC WITH ITS ASPHERICITY SET TOa 0 Æ a [ k ] d � !S A RESULT� THE SYSTEM SPLITS INTO RODS AND DISCS SUBSYSTEMS� WITH THEIR FRACTIONSf r AND f d � RESPECTIVELY� 4HE HISTOGRAMS FORa 0 DISTRIBUTIONp ( a 0 ) ARE BUILT OVER ALL THE MOLECULES IN THE SYSTEM AVERAGED OVER TIME TRAJECTORY� 4HESE ARE SHOWN IN1GURE � FOR SOME CHARACTERISTIC VALUES OFN ch IN EACH CASE OF SPONTANEOUS SELF ASSEMBLY �LEFT HAND FRAME � AND SELF ASSEMBLY AIDED BY AN UNIAXIAL �MIDDLE FRAME AND PLANAR �RIGHT HAND FRAME 1ELDS� ) DID NOT INCLUDE THE HISTOGRAMS FORN ch Æ 12 AND 20 �SEE�1GURE � INTO LEFT HAND FRAME� AS THE SELF ASSEMBLY IN THESE TWO CASES WERE RATHER ATYPICAL AS COMPARED WITH OTHER CASES OF SPONTANEOUS SELF ASSEMBLY �THESE FOLLOW THE ROUTE SIMILAR TO AN AIDED SELF ASSEMBLY � 4HE DISTRIBUTIONS OF DISCOTICITY AND RODDICITY ARE CONVENIENTLY SEPARATED ON THESE PLOTS AS FAR AS THE FORMER IS NEGATIVE AND THE LATTER IS POSITIVE� THE VALUES CLOSE TO ZERO INDICATE SPHERULITIC CONFORMATIONS� /NE CAN ALSO SEE THE RELATIVE WEIGHT OF ROD AND DISC LIKE CONFORMATIONS VIA THE HEIGHT OF EACH WING� AS WELL AND THE BREADTH OF EACH DISTRIBUTION� /NE MAY MAKE THE FOLLOWING OBSERVATIONS FROM THE HISTOGRAMS SHOWN IN1GURE �� )N THE CASE OF A POLYDOMAIN PHASE� AS A RESULT OF SPONTANEOUS SELF ASSEMBLY �LEFT HAND FRAME � RODS AND DISCS ALWAYS COEXIST AND THE DISTRIBUTIONSOF THEIR ASPHERICITIES ARE RATHER BROAD� 7ITH AN INCREASE OFN ch � TWO MAXIMA GRADUALLY MERGE INTO A SPHERULITIC SHAPE FROM BOTH SIDES OFa 0 Æ 0 �AT ABOUTN ch Æ 64 AND HIGHER � 4HE HISTOGRAMS FOR THE1ELD AIDED SELF ASSEMBLY ARE ESSENTIALLY NARROWER� )N THE CASE OF UNIAXIAL1ELD �MIDDLE FRAME THE DISCOTIC CONFORMATIONS ARE COMPLETELY ELIMINATED �EXCEPT THE �� �-� )LNYTSKYI 8 16 24 32 40 48 56 64 72 0.0 0.2 0.4 0.6 0.8 1.0 Nch rods discs 8 16 24 32 40 48 56 64 72 0.0 0.2 0.4 0.6 0.8 1.0 Nch rods discs smectic columnar cubic &IGURE ��#OLOR ONLINE &RACTION OF RODS AND DISCS FOR SPONTANEOUS SELF ASSEMBLY �LEFT FRAME�f r Å f d Æ 1 � 4HE SAME PROPERTIES ARE SHOWN ON THE RIGHT BUT FRACTION OF RODS IS SHOWN FOR UNIAXIAL1ELD AIDED RUNS AND FRACTION OF DISCS ÿ FOR PLANAR1ELD AIDED RUNS�f r Å f d , 1 IN THIS CASE� 4HE1GURE ON R�H�S� SHOWS ALSO THE APPROXIMATE PHASE BOUNDARIES FOR THE SMECTIC� COLUMNAR ANDCUBIC PHASES �DASHED COLOURED HORIZONTAL TEXT BOXES AND THE OPTIMAL NUMBERS FOR SPACE 1LLING OF ROD� DISC AND SPHERE FROM GEOMETRY ESTIMATES �VERTICAL RED� BLUE AND BLACK DASHED LINES� RESPECTIVELY � CASE OFN ch Æ 48 WHERE SMECTIC PHASE IS NOT OBSERVED ANY MORE � AS THESE ARE INCOMPATIBLE WITH THE �$ SYMMETRY OF THE AIDING1ELD� )N THE CASE OF PLANAR1LED �RIGHT HAND FRAME � WHICH HAS A �$ SYMMETRY� THE ROD LIKE CONFORMATIONS ARE NOT ELIMINATED AND DO APPEAR WITHIN X Y PLANE� AND ARE� IN FACT� THE DOMINANT ONES AT SMALLER VALUES OFN ch �AS DISCUSSED ABOVE FOR THE CASE OFN ch Æ 8 � SEE1GURE � � 7ITH AN INCREASE OFN ch ABOVE24 � THE DISC LIKE CONFORMATIONS DOMINATE� (ERE� ) WOULD LIKE TO REMIND AGAIN THAT THE AIDING 1ELD IS SWITCHED� ON� ONLY AT THE BEGINNING OF EACH RUN� TO PROMOTE THE1RST� KICK� � FOLLOWED BY AN EXTEN SIVE SIMULATION WITH THE1ELD SWITCHED� OFF� � 4HE COMPARISON OF HISTOGRAMS FOR SPONTANEOUS AND AIDED SELF ASSEMBLY CASES REVEALS THE EFFECT OF THE AIDING1ELD IN THE FORM OF CONFORMATION SWITCHING�ENRICHING� !FTER THE REQUIRED CONFORMATIONS ARE ENRICHED� THE MELT IS CAPABLE OF SELF ASSEMBLING INTO AN APPROPRIATE PHASE� 4HE FRACTIONS OF RODS AND DISCS�f r AND f d � AS FUNCTIONS OFN ch ARE DISPLAYED IN1GURE � FOR VARIOUS SELF ASSEMBLY RUNS� ,EFT HAND FRAME CONTAINS THE DATA FOR A SPONTANEOUS SELF ASSEMBLY AND IT INDICATES A BROAD REGION FOR A ROD DISC COEXISTENCE AT INTERMEDIATE VALUES OFN ch � !T N ch Æ 64 � THE SYSTEM APPROACHES A SYMMETRIC CASE WITH BOTH CONFORMATIONS TRANSFORMING INTOA SPHERULITIC SHAPE� 4HE RIGHT HAND FRAME CONTAINS DATA FORf r FOR UNIAXIAL1ELD AIDED SELF ASSEMBLY AND DATA FORf d FOR PLANAR1ELD AIDED SELF ASSEMBLY� 4HEREFORE�f r Å f d , 1 AS BOTH ARE OBTAINED FOR DIFFERENT CASES� /NE CAN SEE THAT THESHAPES OF BOTH CURVES ARE MUCH STEEPER IN THIS CASE AS COMPARED TO THE LEFT HAND FRAME PLOT INDICATING ONCE MORE THE POSSIBILITY TO CONTROL THE MOLECULAR CONFORMATION BY MEANS OF INITIAL1ELD OF APPROPRIATE SYMMETRY� 4HE COMPARISON BETWEEN THE INTERVALS WITH HIGH MOLECULAR RODDICITY AND DISCOTICITY WITH THE INTERVALS OF STABILITY FOR THE SMECTIC AND COLUMNAR PHASE �SHOWN AS COLOURED TEXT BOXES IN1GURE �� ON THE RIGHT SHOWS THEIR EXACT COINCIDENCE� THUS INDICATING A STRONG CORRELATION BETWEEN THE AVERAGE MOLECULAR SHAPE AND THE SYMMETRY OF THE BULK PHASE� 4HE SPACE 1LLING GEOMETRICAL ESTIMATES FOR SLIM ROD AND DISC ARE �� ÿ�� TIMES LARGER THAN THE APPROXIMATE MID POINTS OF THE RESPECTIVE INTERVALS OF STABILITY OF EACH PHASE� 4HEREFORE� THE REAL CONFORMATIONS CONSIDERABLY DEVIATE FROM THE� SLIM� LIKE MODELS� �� #ONCLUSIONS #OMPUTER SIMULATIONS PERFORMED AND DISCUSSED IN THIS STUDYPROVIDE SOME MORE INSIGHT ON A MACRO MOLECULAR SELF ASSEMBLY OF LIQUID CRYSTAL COLLOIDS� ! GENERIC MODEL BEING USED CONSISTS OF A LARGE CENTRAL SPHERE AND IS MODI1ED ON ITS SURFACE BY GRAFTED CHAINS EACH TERMINATED BY A MESOGEN� 4HE FOCUS OF CUR RENT STUDY IS ON THE ROLE PLAYED BY THE SURFACE DENSITY OF CHAINS ON PHASE DIAGRAM AND TYPICAL MOLECULAR CONFORMATIONS� 3IMPLE GEOMETRY ESTIMATES BASED ON SPACE 1LLING OF MACROMOLECULE INTO A ROD LIKE� DISC LIKE AND SPHERULITIC SHAPE PROVIDED SOME REASONABLE STARTING POINTFOR THE RELATION BETWEEN THE NUMBER OF GRAFTED CHAINS AND EQUILIBRIUM CONFORMATION� -OLECULAR DYNAMICS SIMULATIONS USING SOFT INTERACTION MODELS RE �� 3ELF ASSEMBLY OF ,# MACROMOLECULES PEAT THE EXPERIMENTAL EVIDENCE FOR THE LAMELLAR COLUMNAR CUBIC SEQUENCE OF PHASES WITH AN INCREASE OF SURFACE DENSITY� ) FOUND THE MODEL BEING CONFORMATIONALLY BISTABLE AT A WIDE RANGE OF SURFACE DENSITY WITH THE POSSIBILITY TO FORM EITHER LAMELLAR SMECTIC OR COLUMNAR PHASE� #ONFORMATIONAL ANALYSIS IS PERFORMED BY INTRODUCING� RODDICITY� AND� DISCOTICITY� OF THEIR SHAPE AND� THEREFORE� SORTING THE MOLECULES AT EACH TIME INSTANCE INTORODS AND DISCS� 4HE FRACTION OF MOLECULES IN EACH SUBSYSTEM PROVIDES SOME PRELIMINARY INFORMATION ON THE DISTRIBUTION OF THEIR CONFORMATIONS� -ORE DETAILS ARE PROVIDED BY THE HISTOGRAMS OF THEIR ASPHERICITY� THESE ALSO SHED SOME LIGHT ON A PROCESS OF MACROMOLECULAR SELF ASSEMBLY� )N THIS RESPECT� THE MAIN OBSTACLE IN EWCIENT SELF ASSEMBLY INTO A MON ODOMAIN PHASES IS SEEN IN A LACK OF CONTROL OVER THE MOLECULARCONFORMATIONS� )N VIRTUALLY ALL THE CASES OF SURFACE DENSITY BEING CONSIDERED� THE ROD AND DISC LIKE CONFORMATIONS COEXIST AND HAVE RELATIVELY BROAD DISTRIBUTION OF THEIR ASPHERICITY� 4HE PROBLEM CAN BE PARTIALLY REMEDIED BY AN AIDED SELF ASSEMBLY USED IN THIS STUDY� )T IMPLIES THE USE OF AN EXTERNAL1ELD OF CERTAIN SYMMETRY �UNIAXIAL� PLANAR� ETC� WHICH ACTSON THE MESOGENS ORIENTATIONS TO PROMOTE SPECI1C CONFORMATIONS �ROD � DISC LIKE� ETC� � 7HEN THE BULK PHASE IS FORMED� THE1ELD IS REMOVED AND THE SYSTEM IS EQUILIBRATED AT A DESIRED TEMPERATURE TO CHECK FOR THE STABILITY OF THUS FORMED PHASE AND TO EVALUATE ITS PROPERTIES� 4HE PROBLEM OF THIS APPROACHIS A LIMITED CHOICE FOR THE SYMMETRY OF THE 1ELD AND A BIAS TOWARDS SPECI1C PHASE WHICH SHOULD BE KNOWNA PRIORI� !NOTHER POSSIBLE REASON FOR� IN GENERAL� POOR SELF ASSEMBLY OF THIS PARTICULAR MODEL COULDBE CONNECTED WITH THE FACT THAT GRAFTED CHAINS ARE FREELY SLIDING ON THE LARGE SPHERE RESULTING IN BROAD DISTRIBUTIONS FOR MOLECULAR ASPHERICITY AND� AS OBSERVED IN SOME CASES� AN ENHANCED MICROPHASE SEPARATION BETWEEN LARGE AND SMALL SPHERES� 4HIS DIRECTS THE FOLLOWING RESEARCH IN THIS AREA INTO RE1NING THE GENERIC MODEL TOWARDS REAL SYSTEMS AND INTO DEVELOPING SOME SPECI1C TECHNIQUES TO DRIVE MACROMOLECULAR SELF ASSEMBLY� !CKNOWLEDGEMENTS 4HE PAPER IS DEDICATED TO THE ��TH BIRTHDAY ANNIVERSARY OF PROFESSOR -YROSLAV (OLOVKO� GREAT SCIENTIST AND TEACHER� 4HE AUTHOR ACKNOWLEDGES PARTICIPATION IN ONE OF THE WORKSHOPS FROM THE� -ATHEMATICS OF ,IQUID #RYSTALS� SERIES BY ).)-3 �#AMBRIDGE� 5+ � � ÿ�� -ARCH �� AND BENE 1TED FROM EXCHANGE VISITS IN THE FRAMES OF %5 'RANT .O� 0)23%3 �� 2EFERENCES �� 2IESS '�� 0ROG� 0OLYM� 3CI�� DOI��3�� /LSEN "�$�� 3EGALMAN 2�!�� -AT� 3CI� %NG� 2� �� DOI��J�MSER�� :ENG &�� :IMMERMAN 3�#�� #HEM� 2EV�� DOI��CR�� $ISCHER $�%�� %ISENBERG !�� 3CIENCE� �� DOI��SCIENCE�� 'ITTINS 0��� 4WYMAN ,��� 3UPRAMOL� #HEM�� DOI�� 0ERCEC 6�� -ITCHELL #�-�� #HO 7� $�� 5CHIDA 3�� 'LODDE -�� 5NGAR '�� :ENG 8�� ,IU 9�� "ALAGURUSAMY 6�3�+�� (EINEY 0�!�� � !M� #HEM� 3OC�� DOI��JA��J� �� 4SCHIERSKE #�� � -ATER� #HEM�� DOI��B��M� �� 3AEZ )�-�� 'OODBY �7�� � -ATER� #HEM�� DOI��B��H� �� 4SCHIERSKE #�� #HEM� 3OC� 2EV�� DOI��B��K� �� 3AEZ )�-�� 'OODBY �7�� 3TRUCT� "OND�� ,IQUID #RYSTALLINE &UNCTIONAL !SSEMBLIES AND 4HEIR 3UPRAMOLECULAR 3TRUC TURES� �� DOI��?��?�� $RAPER -�� 3AEZ )�-�� #OWLING 3��� 'AI 0�� (EINRICH "�� $ ONNIO "�� 'UILLON $�� 'OODBY �7�� !DV� &UNCT� -ATER�� DOI��ADFM�� "ISOYI (�+�� +UMAR 3�� #HEM� 3OC� 2EV�� DOI��B��N� �� 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)ÔØÙÏÙÚÙ ÛIÎÏÑÏ ÑÕÔËÌÔØÕÉÇÔÏÜ ØÏØÙÌÓ ´§´ ºÑ×ÇíÔÏ� ÉÚÒ� ¸ÉêÔÝIÝãÑÕÊÕ� �� ²ãÉIÉ� ºÑ×ÇíÔÇ ·ÕÎÊÒæÔÚÙÕ ÚÎÇÊÇÒãÔÌÔÚ ÓÕËÌÒã� Ö×ÏËÇÙÔÚ ËÒæ ÕÖÏØÚ ÕÈ�êÓÔÕÊÕ ÉÖÕ×æËÑÚÉÇÔÔæ ×IËÑÕÑ×ÏØÙÇÒIÞÔÏÜ �·± ÓÇ Ñ×ÕÓÕÒÌÑÚÒ �ÔÇÖ×ÏÑÒÇË� ·± ËÌÔË×ÏÓÌ×IÉ� ÔÇÔÕÞÇØÙÏÔÕÑ ÎÕÒÕÙÇ� ÓÕËÏÛIÑÕÉÇÔÏÜ ÖÕÒIÓÌ×ÔÏÓÏ ÒÇÔÝåÍÑÇ ÓÏ IÎ ÑIÔÝÌÉÏÓÏ ·± Ê×ÚÖÇÓÏ ÙÕàÕ � «ÕØÒIËÍÌÔÔæ ÑÕÔÝÌÔÙ×ÚêÙãØæ ÔÇ ÉÎÇêÓÕÎÉ�æÎÑÚ ÓIÍ ÑIÒãÑIØÙå Ö×ÏêËÔÇ ÔÏÜ ÒÇÔÝåÍÑIÉN ch ÙÇ ØÏÓÌÙ×Iêå ÉÖÕ×æËÑÕÉÇÔÕí ÛÇÎÏ� ©ÏÑÕ×ÏØÙÕÉÚåÞÏ Ö×ÕØÙI ÊÌÕÓÌÙ×ÏÞÔI ÕÈÞÏØÒÌÔÔæ ØÖÕÞÇÙÑÚ ÕÝIÔÌÔÕ IÔÙÌ×ÉÇÒÏ ØÙÇÈIÒãÔÕØÙI ËÒæ ØÙÌ×ÍÔÌ � ËÏØÑÕ ÙÇ ØÛÌ×Õ ÖÕËIÈÔÏÜ ÓÕÒÌÑÚÒæ×ÔÏÜ ÑÕÔÛÕ× ÓÇÝIÐ ÎÇÒÌÍÔÕ ÉIËN ch � «ÇÒI ÉÏÑÕÔÇÔÕ ÓÕËÌÒåÉÇÔÔæ ÎÇ ËÕÖÕÓÕÊÕå ÓÕÒÌÑÚÒæ×ÔÕí ËÏÔÇÓIÑÏ ËÒæ ØÖÕÔÙÇÔ ÔÕÊÕ ÙÇ ÑÌ×ÕÉÇÔÕÊÕ ØÇÓÕÉÖÕ×æËÑÚÉÇÔÔæ ·± ÓÇÑ×ÕÓÕÒÌÑÚÒ É ÕÈ�êÓÔI ÛÇÎÏ� ¶IË ÞÇØ ØÖÕÔÙÇÔÔÕÊÕ ØÇÓÕÉÖÕ ×æËÑÚÉÇÔÔæ ßÒæÜÕÓ ÇÔÇÒIÎÚ ÊIØÙÕÊ×ÇÓ ËÒæ ÓÕÒÌÑÚÒæ×ÔÕí ÇØÛÌ×ÏÞÔÕØÙI ÉÏæÉÒÌÔÕ ØÖIÉIØÔÚÉÇÔÔæ ØÙÌ×ÍÔÌ ÙÇ ËÏØÑÕ ÖÕËIÈÔÏÜ ÑÕÔÛÕ×ÓÇÝIÐ É ßÏ×ÕÑÕÓÚ IÔÙÌ×ÉÇÒIN ch � àÕ ÖÌ×ÌßÑÕËÍÇê ÛÕ×ÓÚÉÇÔÔå ÈÌÎËÌÛÌÑÙÔÏÜ ØÙ×ÚÑÙÚ×� ©ÏÑÕ×ÏØÙÇÔÔæ ÕËÔÕÉIØÔÕÊÕ ÇÈÕ ÖÒÇÔÇ×ÔÕÊÕ ÑÌ×ÚåÞÏÜ ÖÕÒIÉ ØÚÙÙêÉÕ ÖÕÑ×ÇàÚê ØÇÓÕÉÖÕ×æËÑÚ ÉÇÔÔæ ÉIËÖÕÉIËÔÏÜ ÓÕÔÕËÕÓÌÔÔÏÜ ÛÇÎ ßÒæÜÕÓ ØÌÒÌÑÝIí ÑÕÔÛÕ×ÓÇÝIÐ Î ÉIËÖÕÉIËÔÕå ØÏÓÌÙ×Iêå� ¸ÏÒãÔÇ ÎÇÒÌÍÔIØÙã ÓIÍ ÛÕ×ÓÕå ÓÕÒÌÑÚÒÏ ÙÇ ØÏÓÌÙ×Iêå ÛÇÎÏ� æÑÇ ØÖÕØÙÌ×IÊÇêÙãØæ ÌÑØÖÌ×ÏÓÌÔÙÇÒãÔÕ� ÙÇÑÕÍ ÉÏ æÉÒæêÙãØæ I Ö×Ï ÓÕËÌÒåÉÇÔÔI ÿ ÞÌ×ÌÎ ØÖIÉÖÇËIÔÔæ IÔÙÌ×ÉÇÒIÉØÙÇÈIÒãÔÕØÙI ÉIËÖÕÉIËÔÏÜ ÑÕÔÛÕ×ÓÇÝIÐ ÙÇ ÕÈ�êÓÔÏÜ ÛÇÎ� ±ÒåÞÕÉI ØÒÕÉÇ�ÓÇÑ×ÕÓÕÒÌÑÚÒÏ� ×IËÑI Ñ×ÏØÙÇÒÏ� ØÇÓÕÉÖÕ×æËÑÚÉÇÔÔæ� ÓÕÒÌÑÚÒæ×ÔÇ ËÏÔÇÓIÑÇ �� Introduction Modelling and computational details Bulk phases, aided and spontaneous self-assembly, analysis of molecular conformations via CGMD simulations
id	nasplib_isofts_kiev_ua-123456789-120848
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn	1607-324X
language	English
last_indexed	2025-12-07T18:22:57Z
publishDate	2013
publisher	Інститут фізики конденсованих систем НАН України
record_format	dspace
spelling	Ilnytskyi, J.M. 2017-06-13T05:45:15Z 2017-06-13T05:45:15Z 2013 Relation between the grafting density of liquid crystal macromolecule and the symmetry of self-assembled bulk phase: coarse-grained molecular dynamics study / J.M. Ilnytskyi // Condensed Matter Physics. — 2013. — Т. 16, № 4. — С. 43004:1-12. — Бібліогр.: 35 назв. — англ. 1607-324X PACS: 02.70.Ns;61.30.Vx;61.30.Cz;61.30.Gd; DOI:10.5488/CMP.16.43004 arXiv:1312.4416 https://nasplib.isofts.kiev.ua/handle/123456789/120848 I consider a generic coarse-grained model suitable for the study of bulk self-assembly of liquid crystal (LC) macromolecules. The cases include LC dendrimers, gold nanoparticles modified by polymer chains with terminating LC groups and oth. The study is focused on the relation between a number of grafted chains, Nch, and the symmetry of the self-assembled bulk phases. Simple space-filling arguments are used first to estimate stability intervals for a rod-like, disc-like and spherulitic conformations in terms of Nch. These are followed by coarse-grained molecular dynamics simulations for both spontaneous and aided self-assembly of LC macromolecules into bulk phases. In spontaneous self-assembly runs, essential coexistence of rod-like and disc-like conformations is observed (via analysis of the histograms for the molecular asphericity) in a broad interval of Nch, which prevents formation of defect-free structures. The use of uniaxial and planar aiding fields is found to improve self-assembly into monodomain phases by promoting conformations of respective symmetry. Strong shape-phase relation, observed experimentally, is indicated also by the simulations by the coincidence of the stability intervals for the respective conformations with those for the bulk phases. Розглянуто узагальнену модель, придатну для опису об’ємного впорядкування рiдкокристалiчних (РК) макромолекул (наприклад, РК дендримерiв; наночастинок золота, модифiкованих полiмерними ланцюжками iз кiнцевими РК групами тощо). Дослiдження концентрується на взаємозв’язку мiж кiлькiстю приєднаних ланцюжкiв N ch та симетрiєю впорядкованої фази. Використовуючи простi геометричнi обчислення спочатку оцiнено iнтервали стабiльностi для стержне-, диско- та сферо-подiбних молекулярних конформацiй залежно вiд N ch . Далi виконано моделювання за допомогою молекулярної динамiки для спонтанного та керованого самовпорядкування РК макромолекул в об’ємнi фази. Пiд час спонтанного самовпорядкування шляхом аналiзу гiстограм для молекулярної асферичностi виявлено спiвiснування стержне-та дископодiбних конформацiй в широкому iнтервалi N ch , що перешкоджає формуванню бездефектних структур. Використання одновiсного або планарного керуючих полiв суттєво покращує самовпорядкування вiдповiдних монодоменних фаз шляхом селекцiї конформацiй з вiдповiдною симетрiєю. Сильна залежнiсть мiж формою молекули та симетрiєю фази, яка спостерiгається експериментально, також виявляється i при моделюваннi – через спiвпадiння iнтервалiв стабiльностi вiдповiдних конформацiй та об’ємних фаз. The paper is dedicated to the 70th birthday anniversary of professor Myroslav Holovko, great scientist and teacher. The author acknowledges participation in one of the workshops from the “Mathematics of Liquid Crystals” series by INIMS (Cambridge, UK), 8–22 March 2013 and beneﬁted from exchange visits in the frames of EU Grant No. PIRSES 268498. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics Relation between the grafting density of liquid crystal macromolecule and the symmetry of self-assembled bulk phase: coarse-grained molecular dynamics study Взаємозв’язок мiж поверхневою густиною рiдкокристалiчної макромолекули та симетрiєю її саморганiзованої фази: дослiдження за допомогою методу огрубленої молекулярної динамiки Article published earlier
spellingShingle	Relation between the grafting density of liquid crystal macromolecule and the symmetry of self-assembled bulk phase: coarse-grained molecular dynamics study Ilnytskyi, J.M.
title	Relation between the grafting density of liquid crystal macromolecule and the symmetry of self-assembled bulk phase: coarse-grained molecular dynamics study
title_alt	Взаємозв’язок мiж поверхневою густиною рiдкокристалiчної макромолекули та симетрiєю її саморганiзованої фази: дослiдження за допомогою методу огрубленої молекулярної динамiки
title_full	Relation between the grafting density of liquid crystal macromolecule and the symmetry of self-assembled bulk phase: coarse-grained molecular dynamics study
title_fullStr	Relation between the grafting density of liquid crystal macromolecule and the symmetry of self-assembled bulk phase: coarse-grained molecular dynamics study
title_full_unstemmed	Relation between the grafting density of liquid crystal macromolecule and the symmetry of self-assembled bulk phase: coarse-grained molecular dynamics study
title_short	Relation between the grafting density of liquid crystal macromolecule and the symmetry of self-assembled bulk phase: coarse-grained molecular dynamics study
title_sort	relation between the grafting density of liquid crystal macromolecule and the symmetry of self-assembled bulk phase: coarse-grained molecular dynamics study
url	https://nasplib.isofts.kiev.ua/handle/123456789/120848
work_keys_str_mv	AT ilnytskyijm relationbetweenthegraftingdensityofliquidcrystalmacromoleculeandthesymmetryofselfassembledbulkphasecoarsegrainedmoleculardynamicsstudy AT ilnytskyijm vzaêmozvâzokmižpoverhnevoûgustinoûridkokristaličnoímakromolekulitasimetriêûíísamorganizovanoífazidoslidžennâzadopomogoûmetoduogrublenoímolekulârnoídinamiki

Relation between the grafting density of liquid crystal macromolecule and the symmetry of self-assembled bulk phase: coarse-grained molecular dynamics study

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