International
School of Liquid Crystals 10^{th} Workshop COMPUTATIONAL METHODS
FOR POLYMERS AND
LIQUID CRYSTALLINE POLYMERS A NATO
Advanced Research Workshop Erice (TP), Centre E. Majorana, July 16 
22, 2003 Directors of
the Workshop: P. Pasini, S. Žumer 
INVITED TALKS

G. Allegra 
PolymerMediated Adhesion. A Statistical Approach 

G. Allegra 
Polymer Internal Viscosity. Friction Against a Hard Surface 

J. H.R. Clarke and W. den Otter 
Mesoscopic modelling of polymers
and liquid crystals 

J. H.R. Clarke, A. Sunaidi and W. den Otter 
Simulation of phase transitions in
polymer liquid crystals 

O. Guzmán, E. Doxastakis,
and J. J. de Pablo 
Advanced Monte Carlo simulation
methods for colloidpolymer mixtures 

O. Guzmán, S. Grollau, E. B. Kim and J. J. de Pablo 
Multiscale simulation of liquid
crystals 

S. Hess 
NonEquilibrium Molecular Dynamics
(NEMD) studies of the flow properties of polymeric melts 

S. Hess 
Regular and chaotic rheological
behavior of tumbling polymeric liquid crystals. 

S. Hess 
Rotation and deformation of
polymers in solutions subjected to a shear flow. 

A. R. Khokhlov 
Sequence Design in Functional
Copolymers: Computer Simulations Intramolecular Ordering in Copolymer
Globules 

K. Kremer 
Simulations of Polymers: Link between different scales,
energy entropy interplay 

K. Kremer 
Entangled Polymer Melts and
Solutions 

W. Paul 
Some things we can learn from
chemically realistic polymer melt
simulations. 

W. Paul 
Monte Carlo simulations of
semiflexible polymers: From single chains to nematic
melts 

A. Polimeno 
Computational approaches to
coarsegraining methods for the description of collective dynamics in
nematics and nematic polymers 

M. Vacatello 
Monte Carlo simulations of liquids
of mesogenic oligomers 

M. Vacatello 
Molecular arrangements in
polymernanofiller systems 

M. R. Wilson 
Parallel Computer Simulation
Techniques for the Study of Macromolecules 

M. R. Wilson 
Computer Simulation of Liquid
Crystal Polymers and Dendrimers 

C. Zannoni 
Computer simulations of some liquid crystal and polymer liquid crystal models 

C. Zannoni 
Molecular and atomistic simulations of liquid crystals: what can be achieved now? 

S. Žumer 
Polymer
Stabilized Liquid Crystals:
Simulation of Physical
Properties 
PolymerMediated Adhesion.
A Statistical
Approach
Giuseppe Allegra
Dept. of Chemistry,
Materials and Chemical Engineering "Giulio
Natta",
Polytechnic, Milan, ITALY
The statistical behavior of linear chains confined in
a thin slab is investigated theoretically as a model of polymermediated
adhesion. We apply transitionmatrix methods to two lattice models of the
polymer: model A consists of endgrafted monodisperse polymer chains, model B
of randomly grafted, infinitely long chains.
We evaluate both the elongational and the tangential
moduli, the first being generally larger than the latter. By a FloryHuggins
approach we also derive the contribution to the elongational modulus of the
polymer compressibility.
Polymer Internal Viscosity.
Friction Against a Hard Surface
Giuseppe
Allegra
Dept. of Chemistry,
Materials and Chemical Engineering "Giulio
Natta",
Polytechnic, Milan, ITALY
Polymer internal viscosity arises from energy loss
through the rotational energy barriers, according to Eyring's model.
The theory explains several aspects of polymer
dynamics on the local scale, such as the highfrequency complex modulus of
polystyrene in Aroclor solvents and the dynamic structure factor of polyisobutylene as compared with PDMS
(Richter et al., 2001).
The theory is applied to the problem of polymer
friction against a hard surface; it is shown that the effective friction
coefficient varies with the relative velocity V as V^{1/2} and as V^{2},
depending whether V is smaller or larger than a critical limit, in qualitative
agreement with recent experimental observations by Israelachvili et al.
Mesoscopic modelling of polymers
and liquid crystals
J. H.R. Clarke
and W. den Otter
Chemistry Department, UMIST,
Manchester, UK
Dynamic processes in synthetic and biopolymers extend
over a very wide range of length and time scales and this presents a particular
challenge to computer simulation.
Exciting advances in polymer simulation methodology however are now providing
access to an increasingly wide range of phenomena.
Whilst
atomistic level molecular dynamics (MD) simulations can be used to probe the
dynamics of segmental motion in pure homopolymers, new mesoscopic 'coarse
grain' simulation techniques such as dissipative particle dynamics (DPD)
operate on structurally a much less detailed scale and give access to the dynamics of polymer
solutions, copolymer microphase separation and blend miscibility.
DPD particles can represent many monomers on a polymer
chain; the particles interact through ultrasoft potentials so there is a finite
probablity that chains will pass through each other! In this presentation we discuss the advantages and limitations of
using DPD to study liquid crystals and polymers.
References
[1] Hoogerbrugge & Koelman, Europhys. Lett. 21 363
(1993)
[2] W. den Otter and J.H.R. Clarke, Europhys. Lett., 53, 426 (2001)
Simulation of phase transitions
in polymer liquid crystals
J. H.R. Clarke,
A. Sunaidi and W. den Otter
Chemistry Department, UMIST,
Manchester, UK
Liquid crystal polymers are copolymers in which
mesogenic molecular units are connected either in a backbone polymer chain or
as side chains [1]; they have potentially important applications in
microelectronics, optical memory devices and high modulus plastics. Experimental work has revealed several
interesting phenomena relating to the size of the polymer connections such as
the oddeven effect on clearing temperatures, but to date simulations have made
a limited impact on the understanding of these complex materials.
The problem is that they are not only atomistically
complicated but exhibit complex microphase behaviour due to the interplay of
orderdisorder and mesophase transitions.
Using mesoscale dissipative particle
dynamics [2] (DPD) simulations, which ignore all atomistic detail, together
with a simple model of rodshaped mesogens connected by loosely jointed polymer
chains, we show the formation of smectic and nematic forms of lamella
microphases obtained by cooling a fully disordered system.
Equilibration is achieved very rapidly using DPD and
the various transitions can be observed either by heating or cooling. An interesting pseudonematic phase can be
characterised if the ODT is above the clearing temperature.
[1] A. White and A.H. Windle, Liquid Crystalline
Polymers (CUP)
[2] W. den Otter and J.H.R. Clarke, Europhys. Lett., 53, 426 (2001)
Advanced Monte Carlo simulation methods
for colloidpolymer mixtures
O. Guzmán, E.
Doxastakis, and J. J. de Pablo
Department of Chemical Engineering, University of
Wisconsin,
Madison WI 537061691, USA
We present Monte Carlo methods that permit the
simulation of coarsegrained models of colloidpolymer mixtures (CPM) in a
continuum. The sampling of independent configurations is enhanced by using
advanced techniques such as configurational bias, single chain rebridging, and
also rebridging between two different chains.
We present the application of these methods to the
computation of the potential of mean force between pairs of colloids, obtained
by inversion of the OrnsteinZernike equation for the radial distribution
function of colloids immersed in the mixture.
We analyze the dependence of this effective
interaction in terms of simple scaling arguments.
Finally, we discuss the computation of phase diagrams
for CPM by Monte Carlo simulations (both in lattices and the continuum) as well
as by thermodynamic perturbation theories.
Multiscale simulation of liquid crystals
O. Guzmán, S.
Grollau, E. B. Kim and J. J. de Pablo
Department of Chemical Engineering, University of
Wisconsin,
Madison WI 537061691, USA
Nematic liquid crystals are characterized by the
occurrence of disclination lines,
topological defects where the average molecular orientation changes abrubtly. Besides their application in
displays, recent experiments have shown
that liquid crystals permit the detection
of ligandreceptor binding by optical amplification.
The optimal design
of LCbased biosensors requires to understand the effects of the presence of biomolecules on the structure
and dynamics of nematic liquid
crystals.
We present a multiscale approach that combines
molecular simulation and mesoscale
modeling: Monte Carlo simulations are used to
study the interactions of dilute colloidal particles, as well as
the structure of topological defects;
these results compare satisfactorily
with the corresponding theoretical calculations at the mesoscale
level.
The mesoscale modeling of a multiparticle sensor shows
that adsorbed biomolecules modify the
relaxation dynamics in the device: at low
surfacecovering densities, the equilibrium structure is characterized by a slightly perturbed uniform nematic
order; at a critical density, the dynamics exhibits a slowdown at late stages,
characteristic of the inability of the
nematic to arrive at a uniform order.
These results are
compared with the experimental observations of the nematic response
in biosensors.
NonEquilibrium Molecular Dynamics (NEMD) studies
of the flow properties of polymeric melts
S. Hess
Institut f. Theoretische Physik Techn. Univ. Berlin,
PN 71Hardenbergstr. 36, D  10623 Berlin, Germany
The flow properties of polymeric melts are studied via
NEMD computer simulations. The method is introduced and results are presented
for the nonnewtonian viscosity and for the normal stress differences of a
model polymer melt composed of flexible chain molecules of FENEtype [1,2].
The dependence of these quantities on the chain length
is studied. Comparison with Kinetic Theory is made. Furthermore, the
shearflowinduced structural changes as revealed by the static structure
factor, the gyration tensor and the flow alignment are analyzed.
[1] S. Hess: Flow properties and structure of anisotropic fluids studied by
NonEquilibrium Molecular Dynamics and Flow properties of other complex fluids: polymeric liquids, ferrofluids and magnetorheological fluids in: P. Pasini and C. Zannoni (eds.)
Advances in the computer simulation of liquid crystals, pp. 189233 (Kluwer,
Dordrecht, 2000)
[2] M. Kröger and S. Hess: Rheological evidence for a
dynamical crossover in polymer melts via nonequilibrium molecular dynamics,
Phys. Rev. Lett. 85 (2000) 11281131
Regular and chaotic rheological behavior
of tumbling polymeric liquid crystals.
S. Hess
Institut f. Theoretische Physik Techn. Univ. Berlin,
PN 71Hardenbergstr. 36, D  10623 Berlin, Germany
The rheological properties of nematic liquid
crystalline polymers are strongly affected by the dynamic behavior of the
molecular alignment. Starting from a closed nonlinear inhomogeneous relaxation
equation for the 5 components of the alignment tensor [1] which, in turn, can
be inferred from a generalized FokkerPlanck equation [2], it has recently been
demonstrated that the rathercomplex orientation behavior of "tumbling" nematics can even be
chaotic [3] in a certain range of the relevant control variables.These are the
shear rate and tumbling parameter.
A similar conclusion was reached in [4] where 65
moments were used in a solution of the FokkerPlanck equation. In this talk,
the rheological consequences, in particular the shear stress and the normal
stress differences are computed and discussed for such a nematic. Longtime
averages are evaluated both for imposed constant shear rate and constant shear
stress. The time response of the shear stress to steplike and ramplike shear
rates as well as to reversal of the shear rate areanalyzed in the regular and
in the irregular, i.e. chaotic regimes.
[1] S. Hess, Z. Naturforsch. 30a 728, 1224 (1975); 31a, 1224 (1976).
[2] S. Hess, Z. Naturforsch. 31a, 1034 (1976); M. Doi,
J.Poly,.Sci.Polymer.Phys. Ed. 19, 229 (1981).
[3] G. Rienaecker,Thesis, TU Berlin 2000 (Shaker Verlag
Aachen 2000); G. Rienaecker, M. Kroeger, and S. Hess, Phys.Rev. E 040702 (R)
(2002), Physica A 315, 537 (2002).
[4] M. Grosso, R. Keunings, S. Crescitelli, and P.L.
Maffettone, Phy.Rev.Lett. 86, 3184 (2001).
Rotation and deformation of polymers
in solutions subjected to a shear flow.
S. Hess
Institut f. Theoretische Physik Techn. Univ. Berlin,
PN 71Hardenbergstr. 36, D  10623 Berlin, Germany
The rotation, the orientation and the conformational
changes of flexible chain molecules in a streaming solution are studied by NEMD
computer simulations [1] and for a simple modelsystem of a nonlinear elastic
dumbbell subjected to a flow field and timereversible thermostats [2] and
twirlers [3].
The similarities and differences of the results
inferred from the many particle calculations and from the simple model are
outlined. The occurrence of a chaotic behavior for a range of shear rates is
discussed.
[1] C. Aust, S. Hess, and M. Kröger: Rotation and
deformation of a finitely extendable flexible polymer molecule in a steady shear
flow Macromolecules 35 (2002)
86218630.
[2] S. Hess and G.
Morriss: Regular and chaotic rotation of a polymer molecule subjected to
shear flow,to be published
[3] S. Hess: Construction and test of thernostats and
twirlers for molecular rotations, Z.znaturforsch. 58 a, .... (2003)
Sequence Design in Functional Copolymers:
Computer Simulations Intramolecular Ordering
in Copolymer Globules
A. R. Khokhlov
Physics Department, Moscow State University,
Moscow 117234, Russia
Email: khokhlov@polly.phys.msu.ru
The
possibility of design of sequences of synthetic copolymers in order to achieve
desired functional properties is considered. The adopted approach is biomimetic
in its nature: we look at the properties of primary structure in biopolymers
and try to implement similar ideas in the sequence design of synthetic
copolymers. One of the examples corresponds to "proteinlike
copolymers" which collapse to a nanostructured globule with a welldefined
hydrophobic core wrapped in a hydrophilic envelope. These proteinlike
copolymers can be easily generated in computer simulations.
The real synthetic procedures based on
polymeranalogous reactions, on the copolymerization in poor solvent with
simultaneous formation of copolymer globule, as well as on the direct solid
phase polypeptide synthesis, will be also described. As a result, it becomes
possible to synthesize a copolymer macromolecule which undergoes coilglobule
transition without simultaneous intermolecular aggregation and precipitation.
The kinetics
of the collapse transition of proteinlike copolymers is described and compared
with the collapse of random and random block copolymers. For the designed
copolymers collapse occurs at a markedly higher rate. Still it is possible to
select champion “fast folders”. Those normally have larger mean length of
hydrophobic and hydrophilic blocks, wider distribution of block length and the
average hydrophobicity decreasing towards the chain ends.
The
statistical properties of primary sequences of proteinlike copolymers designed
as described above are considered as well. It is shown, both by computer
simulations and by exact analytical calculation that for large globules and
flexible polymers such sequences exhibit longrange correlations which can be described
by Levyflight statistics.
The concept of
evolution of sequences of synthetic copolymers is introduced, and some of the
examples of experimental realization of such evolution are described. The
parallels with the evolution of sequences in biopolymers are discussed. Both
ascending and descending branches of the evolution of sequences are modeled. It
is shown that via evolution of sequences, it is possible to obtain copolymer
chains with more perfect statistical characteristics in comparison with the
synthetic procedures mentioned above. Thus, such chains are even more designed
for implementation of specific functions. As a measure of sequence complexity
emerging in the course of evolution, the socalled JensenShannon divergence
measure is used. This characteristic correlates well with our intuitive notion
of complexity of the sequence, contrary to Shannon entropy or sequence
compressibility. For the sequences designed in the course of evolution, the
JensenShannon divergence measure exhibits a maximum just at the threshold of
the transition towards the evolution degeneracy of sequences.
Other examples
of the functiontuned copolymer sequences are considered: copolymers tuned to
the adsorption on plane surface, copolymers tuned to absorb small colloidal
particles or proteins (molecular dispensers), copolymers which mimic proteins
with active enzymatic center etc. One of the most important problems in this
field is the design of copolymers capable to recognize certain specific
nanopatterns on the surfaces via preferential adsorption on these nanopatterns.
Entangled Polymer Melts and Solutions
Kurt Kremer
Max Planck Institute for Polymer Research
Ackermannweg 10, D55128 Mainz, GERMANY
Polymer melts, solutions, and networks display unique
(visco)elastic and relaxational properties. Though there is a huge quantitative
variation depending on chemical species and e. g. temperature, the general
properties are universal.
The presentation will review the role of the fact,
that long chain molecules (flexible threads) exhibit special dynamic and
elastic properties due to the fact that the threads cannot cut through each
other. This is of no relevance for the question of the overall chain
conformation.
By comparing analytic theoretical approaches, computer
simulations as well as experiments, the effect of conserved topology of linked
threads will systematically be isolated and demonstrated. Simulation approaches
to study static and dynamic properties of such melts will be discussed in
detail. In this context we also show, that the concepts of Gaussian linking
numbers and more advanced ones between pairs of closed paths and standard
approaches from knot theory are not sufficient to understand the systems,
because "many chains" effects are needed to stabilize the complex
topological structure of a polymer melt or network.
Employing a new topology conserving approach the
entanglement molecular weight for different model systems as well as specific
polymers can be determined. To do so the analysis of the melt conformations is
sufficient.
Simulations of Polymers:
Link between different scales, energy entropy
interplay
Kurt Kremer
Max Planck Institute for Polymer Research
Ackermannweg 10, D55128 Mainz, GERMANY
Unlike low molecular weight compounds, polymers have a
huge intramolecular entropy, which is proportional to the molecular weight of
the object. This entropy dominates the packing of the beads with each other and
the overall conformations. This part of the free energy is generic and qualitatively
the same for all polymers, leading to universal static and dynamic properties.
It can be understood on a mesoscopic or ''scaling'' level.
On a microscopic, atomistic scale energies originating
from chemical bonds and beadbead interactions dominate the structure. These
energetic contributions differ significantly for different chemical species and
have a magnitude also proportional to the polymer molecular weight. Thus both,
the energetic and the intrachain entropic contributions are of the same order.
To understand the properties of a given polymer system quantitatively, both
aspects have to be properly taken into account. It can be shown that a brute
force atomistic simulation of e.g. a polymer melt is neither possible for
almost all systems of interest, nor very useful, since most of the generated
information is not needed for the quantities of interest.
The lecture gives some examples of attempts to
systematically link simulations on different length scales and by this to
generate well equilibrated conformations of dense polymer systems. For the
example of polycarbonates different modifications are considered. This allows
e.g. studies of the vacancy structure and penetrant diffusion in polymer
matrices. In a next step specific interactions of bead fragments with metal
surfaces have been studied by a combination of ab initio and coarse grained
simulations.
Some things we can learn
from chemically realistic polymer melt simulations.
W. Paul
Institut f. Physik, University of Mainz, Germany
In the last decade chemically realistic and
quantitatively correct Molecular Dynamics simulations of polymer melt dynamics
have become feasible. These simulations start from well optimized quantum
chemistry based force fields.
The most important part of these force fields for the
understanding of the relaxation properties of polymer melts are the torsional
potentials. I will exemplify the model building for the case of 1,4
polybutadiene. These force fields are then used in Molecular Dynamics simulations
which span time scales of 100 nano seconds routinely today for a simulation box
of some 5000 force centers.
An analysis of the times series of configurations
generated in these simulations allows for the calculations of several
experimentally accessible spectra, like, for example, dielectric relaxation,
nuclear magnetic resonance and neutron scattering. On small length scales and
short time scales these are dependent on the chemical structure of the specific
polymer.
The relaxation behavior on large length scales is,
however, universal and can be scaled between so different simulation models as
chemically realistic MD simulations and Monte Carlo simulations of a
coarsegrained polymer lattice model.
Monte Carlo simulations of semiflexible polymers:
From single chains to nematic melts
W. Paul
Institut f. Physik, University of Mainz, Germany
The physics of stiffchain macromolecules for which
the chain length L is of the same size or order of magnitude as the persistence
length p on which the bending of such a chain occurs is of great importance in
the context of biomacromolecules. DNA typically has a persistence length of
around 50 nanometers whereas the one of the building blocks of the
cytosceleton, Actin, has a persistence length of around 15 micrometers. We have
performed Monte Carlo simulations of a lattice model of such stiff or
semiflexible chains to study the following questions:
1. Under which conditions does a semiflexible chain
collapse into a toroidal structure typical for DNA folded into the cell nucleus
and what is the general phase diagram for the coilglobule transition of these
semiflexible chains?
2. Long semiflexible chain with attractive
interactions between them show two types of phase transitions, a liquidgas
transition and an isotropic nematic transition. What type of phase diagram
results from the competition between these two phase transitions?
Computational approaches to coarsegraining methods
for the description of collective dynamics
in nematics and nematic polymers
Antonino Polimeno
Universitŕ
degli Studi di Padova  Dipartimento di Chimica Fisica
Via Loredan 2,
I35131 Padova, Italy
We shall consider in our discussion different
approaches to coarsegraining descriptions of liquid crystalline fluids, with
the purpose of highlighting the potential applications of theoretical and
computational mesoscopic treatments to the interpretation of complex behaviors
observed for nematics lowweight fluids and nematic polymers, expecially in the
framework of shear experiments. Coarsegraining toptobottom (i.e. from
macroscopic to mesoscopic) and bottomtotop (from molecular to mesoscopic)
methods are nowadays increasing spreading as effective simulation techniques
applied profitably to isotropic fluids, but analogous treatments of anisotropic
phases are lacking. In order to discuss some examples of coarsegraining
techniques applied to nematics, and without any pretence of being truly
representative of the field, this presentation will be therefore divided in
three parts.
* First a systematic discussion of the basic
theoretical foundations of nonlinear fluctuations in continuum descriptions of
anisotropic liquids will be reviewed, to bridge the stochastic description of
compressible isotropic and uniaxial nematic fluids, both in the Langevin and
FokkerPlanck formulations
* Next an example of a computational application
founded on a coarsegrained FokkerPlanck formulation of a nematic fluid will
be discussed, in connection with existing experimental rheological data
obtained for nematic and nematic polymers
* Finally a more phenomenological approach, based on a
nonstandard Dissipative Particle Dynamics description will be described for
understanding qualitative aspect of shear properties of nematic polymers.
References
[1] D. Forster, Hydrodynamics Fluctuations, Broken
Symmetry, and Correlation Functions, (Benjamin, New York, 1975); G.L. Eyink,
J.L. Lebowitz, and H. Spohn, J. Stat. Phys. 65, 385 (1996).
[2] S. Nguyen and L.A. Turski, Physica A 272, 48
(1999); S. Nguyen and L.A. Turski, J. Phys. A: Math. Gen. 34, 9281 (2001).
[3]. Hoogerbrugge, P.J.; Koelman, J.M.V.A., Europhys.
Lett. 1992, 19, 155. Koelman, J.M.V.A.; Hoogerbrugge, P.J., Europhys.
Lett.,1993, 21, 369.
Monte Carlo simulations
of liquids of mesogenic oligomers
Michele Vacatello
Dip. di
Chimica  Univ. di Napoli Federico II
Via Cintia –
80126 Napoli (Italy)
Monte Carlo simulations have been performed for model
liquids of dimers and trimers consisting of rigid cores connected by
semiflexible spacers.
Though highly idealized, the models take into account
the three principal factors responsible for the onset of nematic order in
liquids of segmentedchain oligomers and polymers, i.e. the anisometry of the
rigid cores, the anisotropy of their attractive interactions and the intrinsic
conformational properties of the molecules under study. In a first set of
simulations, the conformation of model trimers has been approximately regulated
to mimic idealized systems of rigid cores separated by (CH_{2})_{n}
spacers with n odd or even.
The simulated systems show reversible
isotropic/nematic phase transitions at well defined temperatures, with oddeven
oscillations in good agreement with experiments.
The transitions are coupled with a conformational selection
favoring extended conformations in the nematic liquids.
Simulations of model oligomers with conformational
properties approximating those of a well characterized series of mesogenic
oligoesters are currently underway.
Molecular
arrangements in polymernanofiller systems
Michele Vacatello
Dip. di
Chimica  Univ. di Napoli Federico II
Via Cintia –
80126 Napoli (Italy)
Polymers containing randomly distributed spherical
filler particles have been simulated by Monte Carlo methods for various particle
sizes (4 to 28 times the transverse diameter of the polymer chains) and partial
volumes of filler (10% to 50%).
The polymer/filler interface consists of densely
packed and partly ordered shells of polymer units of thickness nearly twice the
diameter of the units. A number of parameters
characterizing the molecular arrangements in these systems have been
analyzed, leading to a general picture in which the chains are considered to be
sequences of interface, bridge and loop segments.
The results can be approximately predicted on a
quantitative level using a few simple rules.
It is also
shown that phantom chains can be utilized in the simulations, provided that the
interaction energy between chains and filler is modified in order to
counterbalance the intrinsic tendency of the chain segments to avoid the filler
surfaces. This makes possible to study systems that cannot be simulated at full
density (i.e. systems with long chains, and/or with large particles and small
filling density).
Parallel Computer Simulation Techniques
for the Study of Macromolecules
Mark R. Wilson
Department of Chemistry, University of Durham
South Road, Durham DH1 3LE, U. K.
In recent years two important developments have
occurred. At the highcost end, supercomputers have become parallel computers.
The ultrafast (specialist) processors and the expensive vectorcomputers of a
few years ago, have largely given way to systems which combine extremely large
numbers of processors with fast interprocessor communications. At the lowcost
end, cheap PC processors have started to dominate the market. This has led to
the growth of distributed computing, with PC clusters linked with slow (but
very cheap) communications such as simple ethernet. For both of these types of
computer systems, new parallel simulation techniques are essential if we are to
utilize parallel machines effectively in macromolecular simulations.
This talk will review some of the progress that has
been made in developing parallel simulation techniques for macromolecules. It
will start with simple methods for molecular dynamics, involving replicated
data techniques; and go onto show how parallel performance can be improved by
careful loadbalancing and reduction of message passing. Domain decomposition
MD methods are then presented as a way of reducing message passing further, so
that effective parallelization can occur with even the slowest of communication
links (ethernet).
Finally, parallel techniques for conducting Monte
Carlo are reviewed, and ways of combining parallel methods are presented, which
can make effective use of massively parallel architectures without the need to
simulate huge systems of molecules.
Computer Simulation
of Liquid Crystal Polymers and Dendrimers
Mark R. Wilson
Department of Chemistry, University of Durham
South Road, Durham DH1 3LE, U. K.
There is considerable interest in the properties of
new mesomorphic materials, which are composed of molecules with novel
architectures. These include rodcoil molecules, polyphilic molecules,
blockcopolymers and dendritic molecules. In each of these systems it is
possible to combine "molecular building blocks" containing radically
different types of molecular interactions (for example aliphatic, aromatic,
fluoro, and siloxanebased) to induce microphase separation. This opens up a
widevariety of possibilities for the formation of new self assembled
structures.
This paper describes some of our preliminary work to
simulate (and attempt to understand) these types of system. Simulations of a
sidechain liquid crystalline polymer are described in which a hybrid
GayBerne/LennardJones model is used. Mesogenic groups are represented by
GayBerne particles, which are attached to a flexible polymer backbone via a
short alkyl spacer. The model system shows spontaneous microphase separation
into mesogenrich and polymerrich regions, which (under the application of an
aligning field) grow to form smecticA layers. Here, the polymer backbone is
sandwiched between mesogenic regions, and becomes surrounded by a sheath
composed of the flexible spacer groups.
We also describe a multiscale approach to the
simulation of a polyphilic third generation liquid crystalline dendrimer, in
which cyanobiphenyl mesogenic groups are bound to a carbosilane dendritic core
via flexible alkyl chains. Fully atomistic simulations predict a structural
change for the dendrimer on the application of a mean field ordering potential.
Simulations of a hybrid atomistic/GayBerne dendrimer in isotropic, nematic and
smecticA liquid crystalline solvents, demonstrate a sphere to rod transition
for the dendrimer as the solvent order parameter changes. Finally, simulations
of the bulk phase of the dendrimer (employing a coarsegrained
sphere/spherocylinders model), demonstrate entropy driven microphase separation
into mesogenrich and dendritic corerich regions.
Computer simulations of some liquid
crystal
and polymer liquid crystal models
C. Zannoni
V.le
Risorgimento 4, Bologna, ITALY.
We present a brief introduction to the computer simulation of
liquid crystalline systems, concentrating on the coarse grained, molecular
resolution, level.
We discuss in particular GayBerne type models where a mesogenic molecule
is replaced by a simple ellipsoidal particle with attractive repulsive
interactions and illustrate on one hand the key observables relevant for these
anisotropic systems and on the other the variety of phases that can be obtained
for rodlike and disclike molecules [1].
We then discuss a possible generalization of the model to the
treatment of polymerization in liquid crystals at coarse grain level, with a
simple GayBerne beads and spring approach.
We discuss a first simple application to the effect of the
anisotropic medium on the polymer chains [2].
[1]
for a review, cf. C. Zannoni, J. Mater. Chem., 11, 2637 (2001)
[2] R. Berardi, D. Micheletti,M. Ricci,
and C. Zannoni, to be published
(2003)
Molecular and atomistic simulations of liquid crystals: what can be achieved now?
C. Zannoni
V.le
Risorgimento 4, Bologna, ITALY.
In the first lecture we have shown that simple GayBerne (GB)
models with uniaxial prolate or oblate particles can provide a number of the
classical liquid crystalline phases. However, the model has various
shortcomings even in a molecular resolution representation. For instance real
molecules have dipoles or more complex charge distributions and shapes that can
be biaxial or non centrosymmetric, even if the rigid particle approximation is
maintained.
We show that generalized GB potentials can yield biaxial, tilted
and ferroelectric phases [1,2] that cannot be obtained with the basic GB
interactions, thus considerably extending the range of the molecular resolution
approach and providing hints for the synthetic chemists wishing to design
molecules with an improved chance of yielding mesophases with specific
properties of interest (such as ferroelectricity).
The ultimate goal of modelling and simulation is, ideally, the
prediction of realistic properties and when the molecular structure of a liquid
crystal forming compound is known, one could expect that atomistic modelling
and simulations should allow calculating transition temperatures, molecular
organization and phase properties. This has not really happened until now,
although an increasing number of significant atomistic simulations have started
to appear [3]. We show that reasonable
estimates for disordering temperatures are now becoming feasible and discuss
how this can help our understanding of a classical problem in liquid crystals,
the oddeven effect [4].
[1] C. Zannoni, J. Mater. Chem.,
11, 2637 (2001) and references therein.
[2] R. Berardi, S. Orlandi, C. Zannoni,
Phys. Rev. E, 67, 041708 (2003)
[3]
see, e.g. the contributions by M. Wilson, M. Glaser, P. Procacci in P. Pasini
and C. Zannoni, eds., Advances in the
computer simulations of liquid crystals, Kluwer, Dordrecht (2000)
[4] R. Berardi, L. Muccioli, C. Zannoni,
submitted (2003)
S. Žumer
University of Ljubljana, Dept. of Physics,
Jadranska 19,
1000 Ljubljana, SLOVENIA
Liquid crystal  polymer dispersions ranging from low liquid crystal content (polymer dispersed liquid crystals) to low polymer content (polymer stabilized systems) are still a fast developing research field.
Recent developments realized in collaboration of groups at University of Bologna, Brown University, and University of Ljubljana are briefly reported.
Ordering in nematic liquid crystals with dispersed polymer networks is studied using Monte Carlo simulations. Results of simulations are used to predict measurable physical properties.
Simulated NMR spectrum, electrical capacitance, and effective birefringence are represented. In particular the effect of networktopography on the field induced switching in nematic cell is simulated.
With increasing network irregularity the transition is less Freedericksz like but nevertheless effectively sharper.