Simulation of bulk phases formed by polyphilic liquid crystal dendrimers
A coarse-grained simulation model for a third generation liquid crystalline dendrimer (LCDr) is presented. It allows, for the rst time, for a successful molecular simulation study of a relation between the shape of a polyphilic macromolecular mesogen and the symmetry of a macroscopic phase. The mod...
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irk-123456789-321042012-04-09T12:22:22Z Simulation of bulk phases formed by polyphilic liquid crystal dendrimers Ilnytskyi, J.M. Lintuvuori, J.S. Wilson, M.R. A coarse-grained simulation model for a third generation liquid crystalline dendrimer (LCDr) is presented. It allows, for the rst time, for a successful molecular simulation study of a relation between the shape of a polyphilic macromolecular mesogen and the symmetry of a macroscopic phase. The model dendrimer consists of a soft central sphere and 32 grafted chains each terminated by a mesogen group. The mesogenic pair interactions are modelled by the recently proposed soft core spherocylinder model of Lintuvuori and Wilson [J. Chem. Phys, 128, 044906, (2008)]. Coarse-grained (CG) molecular dynamics (MD) simulations are performed on a melt of 100 molecules in the anisotropic-isobaric ensemble. The model LCDr shows conformational bistability, with both rod-like and disc-like conformations stable at lower temperatures. Each conformation can be induced by an external aligning eld of appropriate symmetry that acts on the mesogens (uniaxial for rod-like and planar for disc-like), leading to formation of a monodomain smectic A (SmA) or a columnar (Col) phase, respectively. Both phases are stable for approximately the same temperature range and both exhibit a sharp transition to an isotropic cubic-like phase upon heating. We observe a very strong coupling between the conformation of the LCDr and the symmetry of a bulk phase, as suggested previously by theory. The study reveals rich potential in terms of the application of this form of CG modelling to the study of molecular self-assembly of liquid crystalline macromolecules. Розроблено огрублену модель рідкокристалічного дендримера (РКД) 3-ї генерації, завдяки чому вперше в літературі вивчено взаємозв'язок між формою рідкокристалічної макромолекули та симетрією макроскопічної фази за допомогою молекулярної динаміки. Модель складається з м'якої центральної сфери, до якої приєднано 32 ланцюжки, кожен із яких закінчується мезогенною групою. Останні взаємодіють за допомогою недавно запропонованого анізотропного потенціалу з м'якою серцевиною Лінтувуорі та Вілсона [J. Chem. Phys, 128, 044906, (2008)]. За допомогою методу огрубленої молекулярної динаміки змодельовано розплав 100 молекул РКД в анізотропно-ізобаричному ансамблі. Запропонована модель РКД продемонструвала конформаційну бістабільність, за якої як паличкоподібна, так і дископодібна конформації виявляються стабільними за низьких температур. Кожна з цих 2-х конформацій може ініціюватись зовнішнім полем із відповідною симетрією, в результаті в розплаві спонтанно формуються або монодоменна смектична фаза (із паличкоподібних конформацій, ініційованих одновісним полем), або стовпцева фаза (із дископодібних конформацій, ініційованих планарним полем). Обидві фази є стабільними приблизно в тому ж температурному інтервалі та у процесі нагрівання переходять в ізотропну кубічну фазу через яскраво виражений фазовий перехід. Спостережено сильний зв'язок між конформацією РКД і симетрією об'ємної фази, на що вказано раніше в теоретичних роботах. Дослідження виявляє великий потенціал в застосуванні огрубленого моделювання до опису просторової самоорганізації рідкокристалічних макромолекул. 2010 Article Simulation of bulk phases formed by polyphilic liquid crystal dendrimers / J.M. Ilnytskyi, J.S. Lintuvuori, M.R. Wilson // Condensed Matter Physics. — 2010. — Т. 13, № 3. — С. 33001:1-16. — Бібліогр.: 55 назв. — англ. 1607-324X PACS: 02.70.Ns, 61.30.Vx, 61.30.Cz, 61.30.Gd http://dspace.nbuv.gov.ua/handle/123456789/32104 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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| description |
A coarse-grained simulation model for a third generation liquid crystalline dendrimer (LCDr) is presented. It allows, for the rst time, for a successful molecular simulation study of a relation between the shape of a polyphilic macromolecular mesogen and the symmetry of a macroscopic phase. The model dendrimer consists of a soft central sphere and 32 grafted chains each terminated by a mesogen group. The mesogenic pair interactions are modelled by the recently proposed soft core spherocylinder model of Lintuvuori and Wilson [J. Chem. Phys, 128, 044906, (2008)]. Coarse-grained (CG) molecular dynamics (MD) simulations are performed on a melt of 100 molecules in the anisotropic-isobaric ensemble. The model LCDr shows conformational bistability, with both rod-like and disc-like conformations stable at lower temperatures. Each conformation can be induced by an external aligning eld of appropriate symmetry that acts on the mesogens (uniaxial for rod-like and planar for disc-like), leading to formation of a monodomain smectic A (SmA) or a columnar (Col) phase, respectively. Both phases are stable for approximately the same temperature range and both exhibit a sharp transition to an isotropic cubic-like phase upon heating. We observe a very strong coupling between the conformation of the LCDr and the symmetry of a bulk phase, as suggested previously by theory. The study reveals rich potential in terms of the application of this form of CG modelling to the study of molecular self-assembly of liquid crystalline macromolecules. |
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Article |
| author |
Ilnytskyi, J.M. Lintuvuori, J.S. Wilson, M.R. |
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Ilnytskyi, J.M. Lintuvuori, J.S. Wilson, M.R. Simulation of bulk phases formed by polyphilic liquid crystal dendrimers Condensed Matter Physics |
| author_facet |
Ilnytskyi, J.M. Lintuvuori, J.S. Wilson, M.R. |
| author_sort |
Ilnytskyi, J.M. |
| title |
Simulation of bulk phases formed by polyphilic liquid crystal dendrimers |
| title_short |
Simulation of bulk phases formed by polyphilic liquid crystal dendrimers |
| title_full |
Simulation of bulk phases formed by polyphilic liquid crystal dendrimers |
| title_fullStr |
Simulation of bulk phases formed by polyphilic liquid crystal dendrimers |
| title_full_unstemmed |
Simulation of bulk phases formed by polyphilic liquid crystal dendrimers |
| title_sort |
simulation of bulk phases formed by polyphilic liquid crystal dendrimers |
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Інститут фізики конденсованих систем НАН України |
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2010 |
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http://dspace.nbuv.gov.ua/handle/123456789/32104 |
| citation_txt |
Simulation of bulk phases formed by polyphilic liquid crystal dendrimers / J.M. Ilnytskyi, J.S. Lintuvuori, M.R. Wilson // Condensed Matter Physics. — 2010. — Т. 13, № 3. — С. 33001:1-16. — Бібліогр.: 55 назв. — англ. |
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Condensed Matter Physics |
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2025-07-03T12:36:59Z |
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2025-07-03T12:36:59Z |
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| fulltext |
Condensed Matter Physics 2010, Vol. 13, No 3, 33001: 1–16
http://www.icmp.lviv.ua/journal
Simulation of bulk phases formed by polyphilic liquid
crystal dendrimers
J.M. Ilnytskyi1, J.S. Lintuvuori2, M.R. Wilson2
1 Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine,
1 Svientsitskii Str., 79011 Lviv, Ukraine
2 Department of Chemistry, University Science Laboratories, University of Durham,
South Road, Durham, DH1 3LE, UK
Received April 21, 2010, in final form June 8, 2010
A coarse-grained simulation model for a third generation liquid crystalline dendrimer (LCDr) is presented.
It allows, for the first time, for a successful molecular simulation study of a relation between the shape of
a polyphilic macromolecular mesogen and the symmetry of a macroscopic phase. The model dendrimer
consists of a soft central sphere and 32 grafted chains each terminated by a mesogen group. The mesogenic
pair interactions are modelled by the recently proposed soft core spherocylinder model of Lintuvuori and
Wilson [J. Chem. Phys, 128, 044906, (2008)]. Coarse-grained (CG) molecular dynamics (MD) simulations
are performed on a melt of 100 molecules in the anisotropic-isobaric ensemble. The model LCDr shows
conformational bistability, with both rod-like and disc-like conformations stable at lower temperatures. Each
conformation can be induced by an external aligning field of appropriate symmetry that acts on the mesogens
(uniaxial for rod-like and planar for disc-like), leading to formation of a monodomain smectic A (SmA) or a
columnar (Col) phase, respectively. Both phases are stable for approximately the same temperature range
and both exhibit a sharp transition to an isotropic cubic-like phase upon heating. We observe a very strong
coupling between the conformation of the LCDr and the symmetry of a bulk phase, as suggested previously
by theory. The study reveals rich potential in terms of the application of this form of CG modelling to the study
of molecular self-assembly of liquid crystalline macromolecules.
Key words: liquid crystals, dendrimers, self-assembling, molecular dynamics
PACS: 02.70.Ns, 61.30.Vx, 61.30.Cz, 61.30.Gd
1. Introduction
Polyphilic liquid crystal (LC) molecules are mesogenic molecules composed of segments with
different types of interaction. It has proved possible to engineer molecules to contain aliphatic,
aromatic, hydrogen bonding and fluorinated segments, all of which can be combined together (in
different ways) to produce differing molecular architectures. In one sense the simplest polyphilic
mesogens are linear or star-shaped ABC triblock copolymers, which undergo microphase separation
to produce interesting mesophase structures [1–4].However, the range of molecular architectures
possible are limited only by the ingenuity of chemists. Recent interesting examples include the use
of calamitic bolaamphiphiles with a rigid rod-like aromatic unit, two hydrophilic terminal groups,
and a liphophilic or semifluorinated lateral alkyl chain [5–7]; and the use of ‘Janus molecules’ with
two groups of differing mesogens tethered to a molecular core via semi-flexible spacers [8].
A further architectural motif involves the combination of flexible and rigid segments within
a mesogen. In combination with different types of interaction, this provides the possibility for
polyphilic molecules to change structure on formation of mesophases. Interesting examples include
dendrimers, where a central dendritic core has been functionalised by a flexible chain and a terminal
mesogenic group [9, 10], multipedal mesogens containing a central octasilsesquioxane core [11] and
fullerene containing liquid crystals [12, 13]. Some of the recent exciting work in this area has
been summarised in a number of excellent review articles [14–19], which draw parallels between
polyphilic thermotropic liquid crystals, block copolymers and self-assembly in amphiphilic and
biological systems.
c© J.M. Ilnytskyi, J.S. Lintuvuori, M.R. Wilson 33001-1
http://www.icmp.lviv.ua/journal
J.M. Ilnytskyi, J.S. Lintuvuori, M.R. Wilson
In principle, computer simulation provides a convenient way of studying the effect of structure
on bulk phase behaviour for polyphilic liquid crystals. The effect of small changes in structure
can be seen through changes in predicted phase stability and, crucially, simulation can provide a
microscopic picture of how changes in structure can direct local packing and orientational ordering.
In practice, however, efficacious simulation studies of polyphilic mesogens can be a difficult to
achieve. At the atomistic level, simulations of polyphilic systems are often impractical. This is
because polyphilic systems are composed of several different fragments, each consisting of a large
number of individual atomic sites and ordering of molecules may take place over tens of nanometers
requiring a minimum of a few hundred molecules of reasonably high molecular weight. Moreover, the
self-assembly of such structures in a simulation can be very slow, requiring hundreds of nanoseconds
of dynamics. CG simulations provide a more natural way of studying polyphilic systems. However,
even here, large system sizes and long time scales associated with processes such as microphase
separation can prove problematic.
In recent years, a number of successful theoretical attempts have been made to study polyphilic
liquid crystals. The molecular cubic-block model has been employed to model the self-organization
of fullerenomesogens [20, 21]. Progress has also been made with off-lattice coarse-grained models.
For example, quite recently, successful attempts to study the phase behaviour of bolaamphiphiles
were accomplished using both molecular dynamics [22, 23] and dissipative particle dynamics ap-
proaches [24, 25]. Both methodologies used spherical sites and represented rigid parts of a mesogen
structure by a combination of spherical sites. As in previous studies of block copolymer mesophases
[26–31], such models work quite well because there is strong enthalpic driving force towards mi-
crophase separation, which aids in the formation of mesophase structures.
A slightly different class of models attempt to combine spherical and anisotropic potentials.
Most notably, Gay-Berne particles have been combined with spherical sites to look at the struc-
ture of liquid crystal dimers [32], fullerene containing mesogens [33, 34], main chain [35] and side
chain LC polymers [36, 37]; and hard repulsive spherocylinders have been combined with repulsive
spheres [38]. Such mixed models are potentially very powerful because they allow for the shape
and/or anisotropy of the attractive interactions between mesogenic units to be altered to mimic
the different types of interactions found in real mesogens. While quite successful, to date these
models have proved relatively slow to equilibrate.
Most recently, the drive for new effective potentials for polyphilic liquid crystals has led to the
development of anisotropic soft core potentials [39–42]. Here, the lack of infinite repulsion between
molecules at close distances allows for longer time-steps in dynamics simulations and quicker move-
ment of particles through phase space. An important proviso to note is that particles should be
repulsive enough to allow for realistic site-site radial distribution functions to be obtained, i. e.,
should not be able to pass through each other [39]. With this proviso anisotropic soft core poten-
tials provide the possibility for studying complex liquid crystal molecules composed of segments
with different types of interaction.
In the current paper, we use anisotropic soft core particles to study the phase behaviour of a
polyphilic macromolecule consisting of a model liquid crystalline dendrimer (LCDr) functionalised
by terminal mesogenic groups. The coarse-grained model contains three constituent parts, a central
dendritic core, flexible spacer groups (characterised by 32 flexible chains bonded to the core), and
mesogenic groups terminating each spacer. We use the soft core model of Lintuvuori and Wilson
[40], in combination with an efficient parallel simulation program developed by two of the current
authors in earlier work [43, 44]. More details on modelling and simulation technique will be given
in section 2. In sections 3-4 bulk ordered phases will be obtained with the aid of external fields
with appropriate symmetry. We will concentrate on the structure of ordered phases, on their phase
transition into an isotropic phase upon heating and on equilibrium conformations of LCDrs in each
phase. In section 5 attempts will be made to obtain LCDr self-assembly spontaneously from the
isotropic phase by means of temperature decreasing. Conclusions will be given in section 6.
33001-2
Bulk phases in liquid crystalline dendrimers
2. Modelling and computational details
To study self-assembly of the LCDr in the bulk we used a coarse-grained molecular dynamics
(CGMD) approach, in which relevant groups of atoms are represented as single particles. The
repulsive part of effective potentials can be made softer in this case, in comparison with atom-atom
potentials (i. e., 1/r12 or exp(−ar)), but not as soft as the underlying potentials used in typical
dissipative particle dynamics studies [45]. Consequently, one can still use Newtonian dynamics due
to sufficient energy exchange in a system via collisions of particles.
The model used in this study is based on the CG LCDr of [38] but makes use of a recently
published anisotropic potential, developed by Lintuvuori and Wilson [40], which, in turn, has its
origins in the potential of Steuer et al. [46]. Schematically, the model is shown in left frame of
figure 1. The LCDr is built from a central sphere, representing the core of the dendrimer, and
32 flexible polymer chains that are (effectively) grafted on its surface but are free to surf on it
(freely grafted chains). Each chain is terminated by a terminal spherocylindrical mesogen. The
number of chains corresponds to a generation three carbosilane dendrimer. Such a coarse-grained
representation for this macromolecule can be justified by earlier findings by Wilson and coworkers
[47]. In particular, in solution, the dendritic core was found not to respond significantly to changes
in the ordering of an LC solvent, keeping a spherical conformation. However, there was sufficient
flexibility in the molecule for the chains with attached mesogenic units to rearrange in response to
changes in the orientational and/or translational order of the solvent.
Figure 1. Schematic model for a CG LCDr of generation three (only 12 out of 32 mesogenic
branches are shown for the sake of clarity), left frame. Schematic representation showing the
definition of sizes and distances for pairs of interacting particles is shown in the right frame.
The model contains three types of spherical sites (designated thereafter as ‘sp’) and one type
of spherocylindrical site (‘sc’). The largest, type 1, spheres represent the dendritic core, type 2
spheres are bonded to them and represent adjacent chemical groups Si(Me2)-O-Si(Me2), subsequent
polymer beads are constructed of the smallest, type 3, spheres, each representing a group of three
methylenes: CH2-CH2-CH2. The terminal spherocylindrical mesogen represents a cyanobiphenyl
group.
The non-bonded pair interaction between all spheres is of soft repulsive type and is represented
by a quadratic form
V sp−sp
ij =
{
U sp−sp
max (1− r∗ij)2, r∗ij < 1,
0, r∗ij > 1,
(1)
where r∗ij = rij/σij is the scaled distance between centers of i-th and j-th sphere, and usual
mixing rules σij = (σi + σj)/2 are implied for the spheres with different diameters σi and σj (see
right frame of figure 1). In this study the same value of U sp−sp
max is used for all combinations of
33001-3
J.M. Ilnytskyi, J.S. Lintuvuori, M.R. Wilson
interacting spheres. Spherocylinders are of breadth D and of elongation L/D and interact via the
soft anisotropic potential of Lintuvuori and Wilson [40]:
V sc−sc
ij =
U sc−sc
max (1− d∗ij)2, d∗ij < 1,
U sc−sc
max (1− d∗ij)2 − U∗
attr(r̂ij , êi, êj)(1− d∗ij)4 + ε∗, 1 6 d∗ij < d∗c ,
0, d∗ij > d∗c ,
(2)
where d∗ij = dij/D is the dimensionless nearest distance between the cores of spherocylinders [48]
(see right frame of figure 1), d∗c is the effective cutoff for the attractive interaction that depends
on the attractive part of the potential
U∗
attr(r̂ij , êi, êj) = U∗
attr − [5ε1P2(êi · êj) + 5ε2(P2(r̂ij · êi) + P2(r̂ij · êj)] . (3)
The latter depend on orientations êi, êj of the long axes of spherocylinders and the unit vector
r̂ij that connect their centers, as discussed in more detail in [40]. P2(x) = 1/2(3x2 − 1) is the
second Legendre polynomial, whereas energy parameters U ∗
attr, ε1 and ε2 are constants defined
below. We would like to stress that the inclusion of the attractive contribution to the potential in
(2) effectively shifts the region for liquid crystal stability towards elongations L/D ∼ 3 that are
realistic for many typical thermotropic mesogens [40], as compared to the case of purely repulsive
interactions, where elongations of L/D ∼ 6− 8 were required for the formation of ordered phases
[38].
Mixed nonbonded interactions are evaluated in a way similar to (1)
V sp−sc
ij =
{
U sp−sc
max (1− d∗ij)2, d∗ij < 1,
0, d∗ij > 1,
(4)
where d∗ij = dij/σij is a dimensionless distance between the center of the i-th sphere and the core
of the j-th spherocylinder (see right frame of figure 1), with the scaling factor σij = (σi +D)/2.
Parameter U sp−sc
max is chosen in this study to be equal to U sp−sp
max , but values U sp−sc
max > U sp−sp
max can
be used to enhance segregation between sp and sc sites.
Intramolecular interactions for the model include bond and angle interactions terms
Vbonded =
Nb
∑
i=1
kb(li − lk0)2 +
Na
∑
i=1
ka(θijk − θ0)2, (5)
where li is the instantaneous separation between the centers of two bonded spheres (or between
the center of a sphere and the end of a spherocylinder line segment) for the i-th bond, {lk0} is
the set of effective bond lengths. Bond angles terms introduce a certain level of stiffness into a
CG polymer chain. Following typical choices for similar CG chains, θ0 = π is chosen (instead of
∼ 109◦ found in atomistic models) and the magnitude of harmonic springs constants kb and ka
are lower than their atomistic counterparts. A complete set of the force field parameters used in
this study is presented in table 1. The simulations were carried out with the GBMOLDD program
written by two of the current authors [43, 44], which has been extended recently to the case of
anisotropic-isobaric ensemble NPxxPyyPzzT in [37].
We should mention that the model, employed in this study, is aimed at reproducing some
general features of LCDr, namely, its dendritic architecture, flexibility of terminal chains and liquid
crystallinity of terminal mesogens. Chemically detailed coarse graining, that involves a thorough
parametrization of the potentials, is required to describe particular dendritic macromolecules in
terms of packing densities and phase transition points.
We used relatively simple thermostatting for the system, in particular, a single Nóse-Hoover
thermostat [49, 50] was employed for translational and rotational degrees of freedom and, in some
cases, velocity rescaling was performed (when rapid heating or cooling was required). The timestep
∆t ∼ 20 fs was used for velocity rescaling runs, whereas smaller timesteps ∆t ∼ 10 − 15 fs were
required for the runs with the thermostat. To control the pressure in the NPxxPyyPzzT ensemble,
33001-4
Bulk phases in liquid crystalline dendrimers
Table 1. Force field parameters for the CG LCDr model used in this study.
parameter description value
σ1 diameter of sp1 21.37 Å
σ2 diameter of sp2 6.23 Å
σ3 diameter of sp3 4.59 Å
D diameter of sc cap sphere 3.74 Å
L/D elongation of sc 3
U sp−sc
max maximum repulsive energy, sp-sp 70 · 10−20J
U sp−sc
max maximum repulsive energy, sp-sc 70 · 10−20J
U sp−sc
max maximum repulsive energy, sc-sc 70 · 10−20J
U∗
attr attractive energy parameter, sc-sc 1500 · 10−20J
ε1 attractive energy parameter, sc-sc 120 · 10−20J
ε2 attractive energy parameter, sc-sc −120 · 10−20J
m1 mass of sp1 62.44 · 10−25kg
m2 mass of sp2 2.20 · 10−25kg
m3 mass of sp3 0.70 · 10−25kg
m mass of sc 3.94 · 10−25kg
I moment of inertia of sc 6.00 · 10−24kg · Å
2
l1−2 bond length sp1-sp2 14.9 Å
l2−3 bond length sp2-sp3 3.60 Å
l3−3 bond length sp3-sp3 3.62 Å
l3−sc bond length sp3-sc 2.98 Å
kb bond interaction spring constant 50 · 10−20J/ Å
2
θ0 pseudo-valent angle π
ka angle interaction spring constant 20 · 10−20J/rad2
three global separate barostats were used, one for each diagonal component of the pressure Pαα.
All components were fixed at Pαα = P/3, where P is the assigned value for the total external
pressure. Thermostat and barostat masses (Q and Qp, respectively) are chosen according to the
relations
Q = (3(Nsp +Nsc) + 2Nsc)kBTτ
2, Qp = (3(Nsp +Nsc))kBTτ
2, (6)
where kB is Boltzmann’s factor and Nsp, Nsc are the total numbers of spheres and spherocylinders
in a melt, respectively. A time constant was chosen equal to τ = 3 ps.
Preliminary runs were aimed at preparing an isotropic melt of the LCDr using the methodology
described in reference [38]. Equilibration runs were undertaken at T = 500 K with a small timestep
to relax any internal stress. Initial configurations for further runs were prepared at P = 50 atm
and at T = 400 K in the isotropic-isobaric (NPT ) ensemble, corresponding to an average density
of ρ ∼ 0.7 g/cm3.
3. Smectic phase and the smectic-isotropic phase transition
As already mentioned above, LCDrs self-assemble into a number of ordered phases depending on
the dendrimer generation, chemical composition, temperature and other factors [14–19]. One of the
most striking features is the ability of these molecules to adopt distinctly different conformations
in different phases [51]. For instance, generation five carbosilane LCDrs most likely adopt rod-like
conformations in the smectic phase at lower temperatures and disc-like ones in columnar phases,
until the spherically-symmetric conformation is finally adopted in a higher temperature cubic
phase [9].
Previous studies performed on a pseudo-atomistic level, showed that the presence of a nematic
solvent promotes rod-like conformations of a generation three LCDr [47]. This effect of the solvent
can be interpreted as providing an effective aligning field, which may be mimicked by an external
potential
Urot = −F cos2(θi), (7)
33001-5
J.M. Ilnytskyi, J.S. Lintuvuori, M.R. Wilson
where θi is the angle between the long axis of the i-th spherocylinder and the direction of the
field (directed in this study always along the Z axis), F is the maximum in the aligning potential
and determines the strength of the applied field (F = f · 10−20J, f is a reduced field strength,
with f > 0 favouring alignment parallel to the rod-axis and f < 0 favouring in-plane alignment
perpendicular to the rod-axis).
Starting with an isotropic phase at T = 520 K, application of a field with the strength f = 2
while keeping constant pressure of P = 50 atm induced the formation of defect free lamellae.
Stronger fields induced lamellae with defects, similarly to the case of side chain LC polymers
[36, 37]. The phase grown under these conditions was identified as a SmAphase (see below). It
was subsequently studied in a series of anisotropic-isobaric runs in the NPxxPyyPzzT ensemble
performed at P = 50 atm and at a range of temperatures T ∈ [350 K, 650 K] for durations of
between 20 ns and 40 ns each.
During these runs we monitored the density of the melt ρ and the order parameter Sz of
mesogens with respect to the Z axis of the simulation box. It was calculated as
Sz = 〈P2(ezi )〉, (8)
where ezi is Z-th component of the orientation of the i-th mesogen, P2(x) is the second Legendre
polynomial and averaging was performed on all mesogens in a melt. The spatial distribution of the
molecular mass for the k-th molecule was characterised by components of the gyration tensor
G
[k]
αβ =
1
N [k]
N [k]
∑
i=1
(r
[k]
i,α −R[k]
α )(r
[k]
i,β −R
[k]
β ), ~R[k] =
1
N [k]
N [k]
∑
i=1
~
r
[k]
i , (9)
calculated over N [k] particle centers, α, β denote Cartesian axes. When evaluating G
[k]
αβ each sphe-
rocylinder was replaced by a line of four centers. G
[k]
αβ was averaged over the set {k} of molecules in
a melt and subsequently along the time trajectory in equilibrium phase. Its diagonal elements will
be denoted as Gxx, Gyy and Gzz. The mean squared radius of gyration is R2
g = Gxx +Gyy +Gzz ,
and the asphericity of the molecular mass distribution with respect to the Z axis is given by
a = [Gzz − 1
2 (Gxx +Gyy)]R−2
g . The latter is positive for prolate asphericity and negative for the
case of oblate particles.
The simulation data (table 2) show gradual changes upon heating the SmAphase from T = 350 K
to 600 K. From these data, the SmAphase is stable in the range T = 350 K− 480 K (T = 350 K is
the lowest temperature being simulated), with a transition to the isotropic phase taking place in
the temperature range T = 490 K− 500 K.
Partial contributions to the potential energy, Vtotal, are listed in table 3. Changes in Vtotal
across the transition region (characteristic bend in the curve with increasing temperature) occur
mainly from changes to the sc-sc pair contribution, Vsc−sc. Bonded interactions Vbonds and Vangles
are found to grow monotonously with the increase of T , whereas Vsp−sp and Vsp−sc decrease. These
values suggest that in the SmAphase, the flexible chains occupy low energy conformations; and that
spheres are fairly tightly packed, with the energy penalty for the high sphere-sphere interaction
energy compensated for by strong attractions between mesogens, reflected by low negative values
of Vsc−sc.
A snapshot of the SmAphase at T = 470 K is shown in figure 2, where an ideal lamellar structure
is observed with alternating layers of dendrimer scaffold (central sphere and linking chains) and
ordered mesogens (see, figure 2, left frame). The two-dimensional arrangement of central cores and
mesogens in respective layers is shown in the same figure (right frame). The spatial distribution of
the central spheres of each dendrimer was examined by calculating the radial distribution function
g(r). To extend the range of distances up to the simulation box dimensions, the box was replicated
in space in a 2 × 2 × 2 way. The behaviour of g(r) is very similar in the temperature range
T = 350 K − 470 K and indicates the presence of two distinctive maxima, one at r ∼ 27 Å for
the short-range order of cores within each layer, and another at r ∼ 65 Å, which is related to
the interlayer distance (figure 3, left frame). The two characteristic distances can be examined
33001-6
Bulk phases in liquid crystalline dendrimers
Table 2. Temperature, T , density, ρ, nematic order along the Z axis, Sz, components of the
averaged gyration tensor, Gαα, asphericity, a, squared radius of gyration, R2
g, and type of the
ordered phase obtained on heating the SmAphase.
T ,K ρ, g/cm3 Sz Gxx, Å
2
Gyy, Å
2
Gzz, Å
2
R2
g , Å
2
a phase
350 0.700 0.773 112.0 113.9 476.4 702.3 0.518 SmA
400 0.677 0.756 113.3 119.1 466.9 699.3 0.502 SmA
440 0.656 0.714 120.5 125.5 452.8 698.8 0.472 SmA
460 0.633 0.667 126.6 131.8 439.0 697.4 0.444 SmA
470 0.614 0.632 131.3 137.1 428.2 696.6 0.422 SmA
480 0.556 0.435 170.9 145.8 377.0 693.7 0.315 SmA
490 0.488 0.140 200.0 209.0 281.4 690.4 0.111 transition
500 0.455 0.045 238.5 201.6 247.1 687.2 0.039 transition
510 0.416 0.007 246.6 227.2 206.8 680.6 –0.044 I (cubic-like)
520 0.404 –0.003 229.6 224.2 225.4 679.2 –0.002 I (cubic-like)
540 0.394 –0.004 228.4 227.0 222.6 678.0 –0.008 I (cubic-like)
560 0.386 0.003 225.4 224.6 227.2 677.2 0.003 I (cubic-like)
600 0.375 0.002 225.9 223.6 225.7 675.2 0.001 I (cubic-like)
640 0.367 –0.005 226.2 223.7 223.2 673.1 –0.003 I (cubic-like)
Table 3. Mean potential energies (in 10−20J units) on heating through the temperature induced
SmA–I transition.
T ,K Vsp−sp Vsc−sc Vsp−sc Vbonds Vangles Vtotal phase
350 1049.7 –23505.3 315.0 4262.8 8148.3 –9729.5 SmA
400 1040.1 –21902.7 338.2 4827.5 8783.4 –6913.4 SmA
440 1041.5 –20157.1 347.9 5294.8 9279.9 –4193.1 SmA
460 1004.5 –18060.2 341.6 5531.5 9432.9 –1749.7 SmA
470 980.3 –17273.8 338.3 5636.8 9548.7 –769.7 SmA
480 908.5 –14372.0 296.0 5775.3 9450.8 2058.6 SmA
490 803.8 –10026.1 239.0 5870.7 9468.5 6355.8 transition
500 744.3 –7063.2 222.1 5998.7 9611.4 9513.3 transition
510 647.2 –3330.1 206.7 6114.6 9831.1 13469.4 I (cubic-like)
520 630.5 –2448.2 208.6 6242.9 10016.6 14650.4 I (cubic-like)
540 623.9 –1813.4 215.1 6459.6 10332.1 15817.4 I (cubic-like)
560 626.5 –1538.7 219.6 6683.2 10693.6 16684.2 I (cubic-like)
600 643.1 –1201.2 233.2 7177.8 11376.1 18229.0 I (cubic-like)
640 664.8 –1022.0 245.5 7656.4 12063.9 19608.6 I (cubic-like)
separately by evaluating pair distribution functions gz(r) (along the Z axis) and gxy(r) (in XY
planes). The former allows for the estimation of an interlayer distance at ∼ 59 Å. The latter
indicates some degree of local (but not long-ranged) positional order within the layers (figure 3,
middle frame), characteristic of a 2D liquid. Therefore the phase is identified as SmA. Snapshot
of the frozen SmAphase at T = 350 K looks virtually identically to the one at 470 K and is not
shown. Plots of gz(r) indicate a small increase of interlayer spacing ∼ 56 Å in frozen SmAphase at
350 K (see, figure 3, right frame).
It is interesting to note that the volume occupied by the terminal mesogenic units is not
sufficient to completely fill mesogen-rich lamellae (figure 2). This situation, that normally never
happens in atomistic MD simulations, can be explained by the following two reasons. The first one
is connected with the need of precise parametrization of the repulsive interactions in CG model to
reproduce packing of underlying atomic model. The second reason is relative rigidity of the chains
in our CG model which also might prevent efficient space filling in the melt. We would also predict
that it would be possible to fill the voids by adding a small amount of mesogenic solvent with only
minimal disruption of the bulk mesophase structure shown in figure 2.
A typical molecular conformation in the SmAphase is shown in figure 2. Molecules show a
33001-7
J.M. Ilnytskyi, J.S. Lintuvuori, M.R. Wilson
Figure 2. Snapshots of the SmAphase induced by the uniaxial field (f = 2) and with subsequent
equilibration at T = 470 K with no field applied. A lamellar structure is shown in the left frame
with a typical molecular conformation shown above it. 2D structure of the phase is shown in
the right frame via slicing in the middle of core-rich and mesogen-rich lamellae.
0 20 40 60 80 100 120
0
1
2
r, Å
g(r)
0 20 40 60 80 100 120
0
1
2
r, Å
gxy(r)
0 50 100 150 200 250
0
5
10
15
r, Å
gz(r)
Figure 3. Pair distribution functions for dendritic cores in the SmAphase at T = 350 K (solid
lines) and at T = 470 K (dashed lines). Radial distribution function g(r) (left frame), 2D radial
distribution function gxy(r) in XY planes (middle frame) and 1D pair distribution function
gz(r) along the Z axis (right frame).
strong preference for a rod-shaped geometry with uniaxial symmetry, leading to a large anisotropy
in the mean gyration tensor Gαα and high molecular asphericity (see table 2). Close to the SmA–I
transition the anisotropy decreases (between T = 350 K and T = 470 K the asphericity drops by
≈ 18%) and fluctuates around zero in the isotropic phase.
At T > 500 K a macroscopically isotropic, cubic-like phase is observed. A snapshot of the
phase at T = 560 K is shown in figure 4 (left frame). Dendritic cores appear to be arranged
on a loosely defined FCC lattice, but the order is smeared by a number of dislocations. This is
supported by the form of a radial distribution function g(r) for the molecular cores, which shows
liquid-like characteristics. g(r) shape is found to be very similar over a wide range of temperatures
T = 500 K − 640 K indicating similar structure to the phase throughout this temperature range
(see figure 4, right frame). Molecular anisotropy in this cubic-like phase is practically zero (see,
table 2 and the single molecule snapshot in figure 4). While individual molecules are spherical
in shape (visually resembling spherical micellar structures) the outer layers contain considerable
free space, allowing for interdigitation of mesogens from adjacent molecules. This suggests that
macroscopically ordered cubic phases might be not achievable for this model dendrimer, as these
phases require a denser surface structure to ensure true spherical shape of the LCDr.
33001-8
Bulk phases in liquid crystalline dendrimers
0 50 100 150
0
1
2
r, Å
g(r)
� 640K
� 520K
Figure 4. Snapshot of the cubic phase at T = 560 K (left frame) and its section showing LCDr
cores only (middle frame) and the radial distribution function g(r) built for the temperature
interval T = 520 K − 640 K (right frame).
4. Columnar phase and the columnar-isotropic transition
Application of a planar field (f < 0) along the Z axis leads to the formation of a Col phase.
As for the SmAsimulations, well-annealed structures were best achieved through slow growth in
the presence of a moderate field (f = −2) at P = 50 atm, T ∼ 520 K. The resulting Col phase was
subsequently studied in a series of isobaric runs performed at P = 50 atm and at temperatures in
the range T ∈ [350 K, 650 K]. The duration of the runs was similar to those in the case of SmAphase.
The temperature dependence of the density, order parameter and gyration tensor of the Col phase
between 350 K and 600 K are shown in table 4. As observed for the SmAphase, the Col phase is
stable in the range T = 350 K− 490 K (T = 350 K is the lowest temperature simulated), and at
T ∼ 500 K undergoes a transition to the isotropic phase.
Table 4. Temperature dependence of the density ρ, nematic order along Z axis Sz, components
of the averaged gyration tensor Gαα, asphericity a, squared radius of gyration R2
g and type of
the ordered phase obtained for the Col phase.
T ,K ρ, g/cm3 Sz Gxx, Å
2
Gyy, Å
2
Gzz, Å
2
R2
g , Å
2
a phase
350 0.535 –0.433 320.6 308.6 81.7 710.9 –0.328 Col
400 0.524 –0.403 318.5 303.7 88.0 710.2 –0.314 Col
440 0.527 –0.379 313.4 299.3 94.7 707.4 –0.299 Col
470 0.516 –0.328 294.8 296.6 109.1 700.5 –0.266 Col
480 0.518 –0.302 290.7 289.2 119.0 698.9 –0.245 Col
490 0.498 –0.270 277.1 288.3 127.5 692.9 –0.224 Col
500 0.446 –0.046 237.0 235.6 212.8 685.4 –0.034 transition
505 0.446 0.053 254.9 179.0 252.2 686.1 0.051 I (cubic-like)
510 0.423 0.058 215.1 214.2 252.2 681.5 0.055 I (cubic-like)
515 0.408 0.009 225.1 223.7 230.7 679.5 0.009 I (cubic-like)
520 0.402 0.006 226.9 223.3 228.5 678.7 0.005 I (cubic-like)
530 0.398 0.002 225.4 225.3 227.6 678.3 0.003 I (cubic-like)
540 0.394 0.001 224.0 227.3 226.1 677.4 0.001 I (cubic-like)
560 0.386 0.000 225.0 226.2 225.7 676.9 0.000 I (cubic-like)
The Col phase exhibits the same trends in potential energy contributions (table 5) as those
observed for the SmAphase (table 3). The SmAphase is found to have a lower potential energy
than the Col phase at the same temperature. The true thermodynamic stability of each phase
33001-9
J.M. Ilnytskyi, J.S. Lintuvuori, M.R. Wilson
can only be gauged by free energy calculations. Free energy calculations would be very difficult to
achieve for model molecules and model phases of this complexity. While such calculations may not
be computationally achievable at the current time, we note that some success has recently been
achieved for simple bead-spring block copolymer models [52]. Here, in elegant work by Mart́ınez-
Veracoechea and Escobedo, chemical potentials were calculated by an expanded ensemble method
that gradually inserts or deletes a target chain.
Table 5. Mean potential energies (in 10−20J units) on heating through the temperature induced
Col–I phase transition.
T ,K Vsp−sp Vsc−sc Vsp−sc Vbonds Vangles Vtotal phase
350 1024.9 –22329.3 272.6 4284.0 7404.8 –9343.0 Col
400 1036.6 –20170.0 280.0 4805.0 8052.8 –5995.6 Col
440 1005.7 –17467.1 278.1 5294.8 8602.2 –2286.3 Col
470 940.4 –14609.8 272.0 5640.8 9040.8 1284.2 Col
480 931.1 –13316.5 260.7 5785.1 9172.2 2832.6 Col
490 863.9 –11231.1 249.7 5883.3 9398.7 5164.5 Col
500 723.6 –6655.3 219.6 5995.4 9648.2 9931.4 transtition
510 651.7 –3549.6 205.4 6121.9 9831.0 13260.4 I (cubic-like)
515 623.5 –2611.3 207.5 6176.6 9920.1 14316.4 I (cubic-like)
520 630.5 –2512.9 208.8 6228.0 10015.1 14569.5 I (cubic-like)
530 616.1 –1904.9 212.5 6332.5 10190.5 15446.7 I (cubic-like)
540 617.5 –1737.3 218.7 6480.2 10357.2 15936.3 I (cubic-like)
560 631.5 –1564.7 217.8 6688.7 10702.6 16676.0 I (cubic-like)
Figure 5. Snapshots of the Col phase (at T = 490 K) and frozen Col phase (at T = 350 K). A
tight vertical arrangement of dendrimers into columns are seen in the side view of the Col phase
(left frame), top view of the same phase indicates a hexagonal arrangement of columns (middle
frame), typical molecular conformations are shown above each snapshot. Frozen Col phase has
highly ordered columnar structure with the LCDrs adopting a hexamer-like conformation (right
frame).
Snapshots for the Col phase are shown in figure 5. Both single molecule snapshots and data
presented in table 4 indicate a disc-like oblate molecular shape, with Gxx ≈ Gyy > Gzz and,
subsequently, negative values for asphericity a. Similarly to the SmAphase, raising the temperature
leads to a reduction in asphericity (between T = 350 K and T = 490 K the absolute value for the
asphericity decreases by ≈ 32%), which can be seen as the reason behind an increase of the
33001-10
Bulk phases in liquid crystalline dendrimers
molecular spacing within the columns at T = 490 K. Similar trends for the decrease in density and
nematic order parameter at higher temperatures reflects the move of the melt towards the Col–I
transition. The resulting isotropic phase is of the same structure as that formed upon heating the
SmAphase (see above).
r
r
r
r
r
r
r
r
r
r
r
r
r
r
r r r
r
r
r
r r
r
r
r
r r
r
r
r
r
r
r
r
r
r
r
r
r
r
r
r r
r
r
r r r
r
r
r
r r
r
r
r
r r r
r
r
r
b
b b
b
b b b
b b
b
b
b
b b
b b
b b
b
b b b
b
b
b
b b
b b b
b
b
b b b
b b b
b b b b
b
b
b b b b b b b b
b b b
b
b
b
b
b b b
φ0 π/2 π 3π/2
520K, f = −2
r 400K 440K 490K b 500K 560K
Figure 6. Polar distribution of mesogens centers in XY plane of oblate shape in Col phase (φ
is polar angle) at various temperatures. Field induced Col phase is shown as a dashed line.
Let us concentrate on the shape of LCDr in Col phase. It is oblate (as was shown above),
but the arrangement of the arms within the ‘disc’ depends on the temperature. In Col phase at
T = 490 K both uniformly filled discs and hexamer-like discs are found, whereas in frozen Col
phase at T = 350 K the shape is distinctly hexamer-like (see figure 5). One should also mention
that in the latter case the arms of the hexamers stacked within each column are strongly correlated
spatially. This effect is a result of pure self-assembly, since the sole effect of an external field is
promotion of an oblate shape of each LCDr. Polar distribution of the centers of mesogens within
the discs indicates that the ‘hexamericity’ is present to various degree at all temperatures where
Col phase is observed (see figure 6). In another set of simulations we checked that the level of
the ‘hexamericity’ found in frozen Col phase at T = 350 K is independent of the history of the
sample preparation. In this respect, the behaviour of our model can be related to that of the
TTF-containing hexamers with a flexible disc structure that demonstrate strong ability to form
hexagonal columnar phase [53]. We may suggest that some features of the frozen Col phase are
related to the peculiarities of the model being employed in this study. One of those is constant
(relatively large) stiffness of terminal chains, which may mimick a polymer rather below the glass
transition. We may also suggest that with an increase of the number of arms in our model, the
hexamer-like discs might give place to uniform discs.
0 20 40 60 80
0
1
2
3
4
5
6
r, Å
g(r)
0 50 100 150 200
0
1
2
3
4
5
6
r, Å
gxy(r)
0 20 40 60 80
0
5
10
15
20
25
30
35
r, Å
gz(r)
Figure 7. Pair distribution functions for dendritic cores in the Col phase at T = 350 K (solid
lines) and at T = 470 K (dashed lines): radial distribution function g(r) (left frame), 2D radial
distribution function gxy(r) in XY planes (middle frame) and 1D pair distribution function
gz(r) along Z axis (right frame).
The structure of Col phase is reflected in the behaviour of the pair distribution functions, shown
in figure 7. Hexagonal arrangement of columns is clearly indicated in the form of gxy(r), while the
peaks in gz(r) allow the distance between dendritic cores within a column to be estimated as ∼ 18 Å
for the Col phase at T = 350 K and ∼ 20 Å at T = 490 K.
33001-11
J.M. Ilnytskyi, J.S. Lintuvuori, M.R. Wilson
350 400 450 500 550 600
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
b
b
b
b
b
b
b
b
b b b b b b
r
r
r
r
r
r
r
r
r r r r r r
T , K
ρ
a
Sz
350 400 450 500 550
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
b b b b b
b
bb
bbb b b b
r
r
r
r
r
r
r
rr
rr r r r
T , K
ρ
a
Sz
Figure 8. Synchronicity in the changes of molecular asphericity, system density and order pa-
rameter at the SmA–I and Col–I phase transitions.
The simulations performed support the view that a strong link exists between the shape of
a LCDr and the type of bulk phase exhibited [9, 51]. In particular, rod shapes are compatible
with the SmAphase (figure 2), discotic shapes are compatible with Col phases (figure 5) and an
isotropic molecular shape is compatible with an isotropic liquid phase. The shape changes prolate-
to-isotropic or oblate-to-isotropic take place synchronously with the LC–I phase transition, as
shown in figure 8. It is the preferential selection of two groups of energetically similar conformations
which makes phases of radically different symmetries possible within the same system. In both cases
the transition to the isotropic phase leads to a massive conformational rearrangement reflected in
the change in both intramolecular and intermolecular contributions to Vtotal. This conclusion was
elegantly predicted in the early theoretical work by Photinos and coworkers [54, 55], and is seen in
the current study for the first time for a CG molecular model of this type.
We note in passing that conformational changes are relatively easy to achieve in our model,
both because of the CG nature of the polymer chains and due to free grafting of the chains to the
surface of the core. Arguably, the latter mimicks generations of LCDr higher than three, which
have very flexible scaffolds. It is also worth noting that in the case of some real fifth generation
carbosilane LCDrs, Col phases are observed at higher temperatures than smectic phases [9], while
in our model, the Col phase thermal stability is similar to that of the SmAphase. In our model,
at lower temperatures, we might reasonably expect a Col-SmAtransition, at the point where the
temperature becomes sufficiently low for the chains to straighten, such that the mesogens can no
longer fill the space in a planar arrangement around the cores. Unfortunately, at such temperatures,
(even for this relatively efficient CG model), phase space sampling is not sufficient to overcome the
free energy barrier needed to see a transition to SmAordering.
Stability of both SmAand Col phases at approximately the same thermodynamical conditions
raise an interesting question as to whether direct phase transitions between the two phases are
possible by means of some external stimuli (i. e., the applied field). Starting from the spatial
arrangement of the Col phase shown in figure 5, left frame, we performed two further simulations.
In the first, a uniaxial field with the strength f = 2 was applied along the Z axis (aiming at a
massive reorientation of mesogens), whereas in the other simulation the field was applied along
the Y axis (directed at ‘flipping’ circularly distributed mesogens into uniaxial ‘bunches’). In both
cases perfect monodomain SmAphases were formed, but only if the simulation was performed just
above the phase transition point, e. g. at T = 520 K. In the case of lower temperatures, simulations
were locked into polydomain smectics. Below both transitions the interactions between terminal
mesogenic groups strongly lock the melt into one symmetry, and the reassembly into another
ordered phase is very slow on the time scale possible in the simulations of the current CG model.
We note in passing that many real systems of this type are also extremely viscous; requiring strong
electric or magnetic fields to produce uniformly aligned samples [10].
We note that the conformational bistability found here is much harder to simulate than the
shape changes seen recently in simulations of an octapedal liquid crystal [40]. The octapedal system
was able to self-assemble spontaneously into a smectic phase [40] by conformational rearrangement
33001-12
Bulk phases in liquid crystalline dendrimers
on cooling from an isotropic melt. In the case of an octamer, the far smaller number of arms leads
to a complete supression of discotic conformations in which the mesogens are unable to fill the
space around a central core.
5. Spontaneous self-assembly
As it may be expected from the observations above, with no external field applied, conforma-
tional bistability of the LCDr is a serious obstacle towards the formation of a single monodomain
phase. This was confirmed by further simulations, in which isotropic melt either cooled or com-
pressed. In the first series of runs an isotropic phase at 520 K (see table 2) was cooled to 400 K
at a constant pressure of P = 50 atm using different cooling rates. With cooling rates as slow as
30 K/ ns, frozen, random polydomain structures were observed with relatively small domain sizes.
For lower cooling rates, below 12 K/ ns, a clear mixture of Col and SmAclusters was obtained with
Figure 9. Snapshot of all particles (left frame) and dendritic cores only (right frame) for the
spontaneously assembled mixture of smectic and columnar phases. This phase is obtained by
isobaric (P = 50 atm) cooling of an isotropic phase from 520 K down to 400 K at a rate 12 K/ ns
(for 10 ns) and then keeping the constant temperature at 400 K (for another 15 ns). Approximate
domain boundaries are shown by dotted contours.
relatively large domain sizes (see figure 9). Prevailance of the Col clusters is revealed in figure 10,
with the shape of the pair distribution functions resembling those found for the monodomain Col
phase in figure 7.
0 20 40 60 80
0
1
2
r, Å
g(r)
0 50 100 150 200
0
1
2
3
4
5
r, Å
gxz(r)
0 20 40 60
0
5
10
15
r, Å
gy(r)
Figure 10. Radial distribution function g(r) (left frame), 2D radial distribution function gxz(r)
in XZ planes (middle frame) and 1D pair distribution function gy(r) along Y axis (right frame)
for a polydomain phase obtained by cooling the melt down to 400 K (figure 9).
The second set of runs was performed at constant temperature T = 500 K but at a range of
pressures P = 10−2 atm − 80 atm imposed on the melt at the beginning of each run. The evolution
of the shape of the radial distribution function g(r) with the increase of the pressure is shown in
33001-13
J.M. Ilnytskyi, J.S. Lintuvuori, M.R. Wilson
0 50 100 150 r, Å
g(r) 0.01 atm
1 atm
5 atm
40 atm
50 atm
80 atm
20 atm
Figure 11. Evolution of the radial distribution function obtained by imposing various pressures
to an isotropic melt at constant T = 500 K (left frame). Snapshot of a cubic phase obtained at
P = 5 atm (a), of a polydomain phase obtained at P = 50 atm (b) and of a polydomain phase
obtained by slow compressing of the system from P = 20 atm up to P = 80 atm with the rate
6 atm/ ns (c) are shown in right frame.
figure 11 (left frame). At lower pressures P = 10−2 atm − 20 atm a cubic phase (snapshot (a) in
figure 11) is observed with the maxima positions being gradually shifted towards smaller distances
as the melt is compressed further. At a threshold pressure ∼ 40 atm the system starts to undergo
a phase transition and at P > 50 atm a polydomain ordered phase is found with typically two
peaks at approximately 21 Å and 64 Å. The polydomain phase, shown in figure 11, snapshot (b),
is obtained by imposing a pressure of P = 50 atm. As with the temperature induced self-assembly,
we also undertook runs with gradual compression. The snapshots, obtained by compression from
P = 20 atm up to P = 80 atm with various compression rates are very similar to the one shown
in figure 9 and demonstrate domains of both SmAand Col phases (the one obtained at the rate
6 atm/ ns is shown in figure 11, snapshot (c)). The radial distribution functions are also similar
to those in figure 10 and are not shown. Therefore, no essential gain towards monodomainity was
achieved due to slow compression method.
Therefore, with no symmetry breaker such as an external field, self-assembly of the conforma-
tionally bistable LCDr model into a single monodomain phase is difficult to achieve.
6. Conclusions
The coarse-grained model for the LCDr exploited in this study is found to exhibit both rod-like
and disc-like conformations. The symmetry of this conformational bistability can be broken by
application of a suitable external factor, such as the application of an external field or by solvent
castings or by surface alignment. In this study we apply a uniform external field, that acts on
terminal mesogens and plays the role of a conformational trigger.
In a uniaxial field the dendrimer adopts a rod-like shape and the melt assembles into a smectic
A phase on cooling. In the case of a planar field the LCDrs adopt disc-like conformations and
columnar phase is formed. In the latter case, the disc is not uniform but of a hexamer form, but
this can be attributed to the number of arms in this particular model. The thermal stability of both
smectic A and columnar phases is very similar with a sharp transition to an isotropic (cubic-like)
phase taking place at T ∼ 500− 510 K for isobaric runs at a pressure of P = 50 atm.
Conformational bistability of the model LCDr prevents spontaneous self-assembly of the isotropic
33001-14
Bulk phases in liquid crystalline dendrimers
melt into one single ordered phase, a polydomain mixture of both smectic A and columnar phase is
observed instead. In real systems, the symmetry of shape bistability might be broken not only by
external conditions, but also by additional conformational rigidity of the central core (particularly
on cooling). The effect of this can be taken into account in future work.
We also note that, for this model, field-induced phase transitions between the SmAand Col
phases are possible only at, or close to, the transition to the isotropic phase. Application of the
field below the clearing point leads only to the formation of random domains. We see the reason
for this in terms of strong mesogenic interactions at lower temperatures, which effectively produces
physical crosslinks that prevent rearrangements of macromolecules.
The simulations demonstrate the power and capabilities of CG approaches and are, to our best
knowledge, the first computer simulations of bulk dendritic phases that show macromolecules with
switchable shapes that can exist in different bulk ordered phases.
Acknowledgements
MRW and JSL wishes to thank the EPSRC for the award of a DTA studentship to JSL (2006–
2009). JI thanks S. Soko lowski and M. Schoen for fruitful discussions.
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Моделювання об’ємних фаз у розплавi полiфiльних
рiдкокристалiчних дендримерiв
Я.М. Iльницький1, Ю.С. Лiнтувуорi2, М.Р. Вiлсон2
1 Iнститут фiзики конденсованих систем НАН України, вул.Свєнцiцького, 1, 79011, м.Львiв, Україна,
2 Факультет хемiї, Унiверситет м. Дарема, Саус роад, Дарем, DH1 3LE, Великобританiя
Розроблено огрублену модель рiдкокристалiчного дендримера (РКД) третьої генерацiї, завдяки чо-
му вперше в лiтературi вивчено взаємозв’язок мiж формою рiдкокристалiчної макромолекули та си-
метрiєю макроскопiчної фази за допомогою молекулярної динамiки. Модель складається iз м’якої
центральної сфери, до якої приєднано 32 ланцюжки, кожен iз яких закiнчується мезогенною групою.
Останнi взаємодiють за допомогою недавно запропонованого анiзотропного потенцiалу iз м’якою
серцевиною Лiнтувуорi i Вiлсона [J. Chem. Phys, 128, 044906, (2008)]. За допомогою методу огру-
бленої молекулярної динамiки виконано моделювання розплаву 100 молекул РКД в анiзотропно-
iзобаричному ансамблi. Запропонована модель РКД демонструє конформацiйну бiстабiльнiсть, при
якiй як паличкоподiбна, так i дископодiбна конформацiї виявляються стабiльними при низьких тем-
пературах. Кожна з цих двох конформацiй може iнiцiюватись зовнiшнiм полем iз вiдповiдною си-
метрiєю, в результатi в розплавi спонтанно формуються або монодоменна смектична фаза (iз па-
личкоподiбних конформацiй, iнiцiйованих одновiсним полем) або стовпцева фаза (iз дископодiбних
конформацiй, iнiцiйованих планарним полем). Обидвi фази стабiльнi приблизно в тому ж темпера-
турному iнтервалi i при нагрiваннi переходять в iзотропну кубiчну фазу через яскраво виражений
фазовий перехiд. Спостережено сильний зв’язок мiж конформацiєю РКД та симетрiєю об’ємної фа-
зи, на що було вказано ранiше в теоретичних роботах. Дослiдження виявляє великий потенцiал
в застосуваннi огрубленого моделювання до опису просторової самоорганiзацiї рiдкокристалiчних
макромолекул.
Ключовi слова: рiдкi кристали, дендримери, самоорганiзацiя, молекулярна динамiка
33001-16
Introduction
Modelling and computational details
Smectic phase and the smectic-isotropic phase transition
Columnar phase and the columnar-isotropic transition
Spontaneous self-assembly
Conclusions
|