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 
ORAL CONTRIBUTIONS

M. A. Bates 
Computer simulation of large flexible liquid crystal
molecules 

J.I.Ilnytskyi
and M.R.Wilson 
Computer simulations of the dendritic molecules with the
aid of configurational biased Monte Carlo 

G. Raffaini and F. Ganazzoli 
Protein adsorption on a hydrophobic graphite surface 

A. Soldera 
Molecular Simulation of the Glass Transition in PMMA of
Different Tacticities 

P. N.
VorontsovVelyaminov, N. A.
Volkov, A.A. Yurchenko. 
Entropic sampling of simple polymer models within
WangLandau algorithm. 
of
large flexible liquid crystal molecules
Martin A. Bates
Department
of Chemistry, University of Southampton,
Southampton
SO17 1BJ, United Kingdom.
The techniques necessary for the
simulation of high molar mass liquid crystals are no different to those used
for low molar mass molecules. However, even relatively simple models, such as
those in which single site potentials are used to model the mesogenic units and
the flexible chains linking the mesogens are modelled by a string of
LennardJones atoms, are computationally expensive to simulate. This is
partially due to the fact that, whilst the liquid crystal units are modelled at
the coarse grained molecular level, the chains are modelled using atomic like
potentials. To be able to simulate high molar mass, flexible liquid crystalline
molecules, we require models which are computationally cheaper, but retain the
essential physics of the molecules.
We highlight some preliminary results
for a new model for the study of flexible, high molar mass liquid crystals,
based on the bond fluctuation model which has proved to be an extremely useful
model for studying polymeric systems.
The model consists of flexible chains in
which the subunits are designated as either mesogenic or alkyl units, with
appropriate interactions between these. In this model, the chains are modelled
at the same level of detail as the mesogenic units. The phase diagram for a low
molar mass system composed solely of monomers exhibits nematic and smectic A
phases, in addition to an isotropic phase at high temperature.
Main chain liquid crystal polymers can
easily be constructed without changing the density by joining a number of these
monomers together by their terminal flexible chains. Simulations using such
models indicate that the nematic phase is destabilised with respect to the
smectic A phase on changing the topology of the molecules at fixed density.
Computer
simulations of the dendritic molecules
with
the aid of configurational biased Monte Carlo
J.I.Ilnytskyi and M.R.Wilson
Dept.
of Chemistry, University of Durham,
South
Road, Durham, DH1 3LE UK
We have developed a variant of the
configurational bias Monte Carlo approach that is suitable for simulations of
highly branched macromolecules.
The main targets are dendritic and
elastomeric polyatomics, including ones with “internal" or “external"
mesogenic groups.
The efficiency of the method described
is tested using singlemolecule and bulk systems of dendritic molecules of
different generations.
Protein adsorption on a hydrophobic graphite surface
Giuseppina Raffaini and Fabio Ganazzoli
Dipartimento di Chimica, Materiali e Ingegneria Chimica "G.
Natta",
Sez. Chimica, Politecnico di Milano,
via L. Mancinelli 7, 20131 Milano
We report our recent results about the
adsorption of some protein fragments on a flat graphite surface. Using atomistic simulations for both the
proteins and the surface, we first carry out direct energy minimizations in an
effective dielectric medium, considering different orientations of the
fragments close to the surface.
Afterwards, we perform long Molecular Dynamics simulation (12 ns) of
selected optimized geometries in the same medium, and finally we optimize a
large number of the instantaneous snapshots in search of the absolute energy
minima. We propose that this procedure
yields both the initial and the final adsorption stage on a bare surface,
allowing for possible rearrangements and denaturation. Short MD runs are also carried out
explicitly including a very large number of water molecules to study the system
hydration in both adsorption stages.
We consider two albumin fragments with
different hydrophobicity patterns, and a fibronectin type I module (Protein
Data Bank entries 1AO6 and 1FBR). These
globular proteins of the human serum have a wholly different secondary
structure, since albumin contains only ahelices, while the selected fibronectin module is made up
of bsheets (both molecules also comprise
random strands, of course).
Our results indicate that the initial
adsorption takes place with significant conformational rearrangements close to
the surface. This feature is
particularly noticeable in the albumin fragments, which loose their ahelical structure at the interface, though otherwise
preserving the secondary structure and the globular shape. Conversely, the fibronectin fragment
undergoes minor changes upon the initial adsorption. In the long MD runs, the fragments show much larger
rearrangements and an almost complete denaturation in order to maximize the
surface covering. In this way, in spite
of a greater intramolecular strain they achieve a much larger interaction
energy. Interestingly, we also find
that the surface may induce partially ordered arrangements.
Finally, the hydration pattern shows
significant changes upon adsorption. In
fact, the large molecular rearrangements expose all the residues to water, thus
enhancing their solvation. Accordingly,
the protein fragments optimize both the interaction energy with the surface and
their hydration energy.
Molecular
Simulation of the Glass Transition
in
PMMA of Different Tacticities
A. Soldera
Département de Chimie, Université de Sherbrooke,
Sherbrooke,
J1K 2R1, Canada
Poly(methyl methacrylate), PMMA, has
the special feature of exhibiting different glass transition temperatures, T_{g}s,
according to the tacticity of its chain.
Actually this difference can be interpreted only in changes in molecular
characteristics. Consequently,
molecular modeling offers an ideal tool to understand, from the probing of the
molecular interactions, the reasons that give rise to such a difference, and
accordingly, to better understand the tricky problem of glass transition.
The difference in the T_{g}s
between the two PMMA configurations has been accurately simulated using
molecular dynamics simulation in the bulk.
Variations in the nonbond energy, intradiade angles, and in the local
dynamics, are reported.
An energetic analysis shows that the nonbond energy
and the bending angle energy associated to the intradiad backbone angle,
principally contribute to the energetic difference between the two PMMA
configurations. These two energetic
contributions actually result from the substitution of the hydrogen atom
attached to the chiral carbon atom in the PMA repeat unit by a methyl group,
giving the PMMA. Such a substitution
also implies a variation in the local dynamics.
To reveal local motions, correlation
times are computed: flexibilities of the backbone and the sidechain are thus
looked at. At a specific temperature,
both configurations display different backbone and side chain flexibilities,
but at T + T_{g}, only a difference in the sidechain mobility is
observed. Considering the mode coupling
theory, cooperativity can be revealed.
A coupling is thus clearly observed between the sidechain and the
backbone. Moreover, this coupling is
different according to the chain tacticity.
Such a behavior tends to explain the difference in the Tgs between the
two configurations in PMMA.
Molecular modeling is thus used as a
tool to probe the molecular interactions, and to guide the understanding of the
glass transition, that is still a striky and conceptually unresolved thermal
transition.
Entropic
sampling of simple polymer models
within WangLandau algorithm.
P. N.
VorontsovVelyaminov, N. A.
Volkov, A.A. Yurchenko.
Faculty
of Physics, St. Petersburg State University,
198504,
St. Petersburg, RUSSIA
email:
voron.wgroup@pobox.spbu.ru
A new Monte Carlo simulation technique
proposed by Wang and Landau (WL) in [1]
is applied to sampling of 3dimensional lattice and continuous models of
polymer chains. Density of states obtained by homogeneous (unconditional) random walk is compared with
the result of entropic sampling (ES)
[24] within WLalgorithm. While homogeneous sampling gives reliable results typically in the range of
45 orders of magnitude the WL entropic
sampling yields them in the range of 2030 orders and even larger. A combination of homogeneous and WLsampling
provides reliable data for events with
probabilities down to 1.E35.
For the lattice model we consider both
the athermal case (selfavoiding walks, SAWs) and the thermal case when an
energy is attributed to each contact between nonbonded monomers in a
selfavoiding walk. For short chains the simulation results are checked by
comparison with the exact data. In
WLcalculations for chain lengths up to N=300 the scaling relation for SAWs
[5,6] is well reproduced. In the thermal case distribution over the number of
contacts is obtained in the Nrange
up to N=100 and the canonical averages  internal energy, heat capacity,
excess canonical entropy, mean square endtoend distance – are calculated as a
result in a wide temperature range.
The continuous model is studied in the
athermal case. By sorting conformations of a continuous phantom freely joined
Nbonded chain with a unit bond length over a stochastic variable – the minimum
distance between nonbonded beads  we determine probability distribution for
the Nbonded chain with hard sphere monomers over its diameter a in
the complete diameter range, 0 < a < 2,
within a single ES run. This distribution provides us with excess
specific entropy for a set of diameters
a in this range. Calculations
were made for chain lengths up to N=100 and results were extrapolated to N
tending to infinity for a in the range
0 < a < 1.25.
[1] F.Wang, D.P.Landau, Phys.Rev.Lett.
86, 2050 (2001).
[2] B.A.Berg, T.Neuhaus, Phys.Rev.Lett.
68, 9 (1992).
[3] J.Lee, Phys.Rev.Lett. 71, 211
(1993).
[4] Y.Iba, Int.J.Modern Phys. C 12, 623
(2001).
[5] P.G. de Gennes, Scaling Concepts in
Polymer Science, Cornell University Press, Itaca & London (1979).
[6] J.Douglas, C.M.Guttman, A.Mah,
T.Ishinabe, Phys.Rev. E 55, 738 (1997).