NEMD of Simple and Polymeric Liquids
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Transcript of NEMD of Simple and Polymeric Liquids
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614
Nonequilibrium dynamics simulations of simple and
polymeric fluids
artin roger
Computer simulations on classic model systems are
continuing to enable significant progress to be made in
research concerning the inter-relation between dynamics,
structure and rheology of simple and polymeric fluids that are
under the influence of an external field. This work includes
studies on flow-induced alignment, self-assembly, phase
transitions, anisotropic diffusion and the validation and
improvement of the underlying models and techniques. The
best insight into chain-structure relationships has come from
idealized models.
Addresses
Institute of Polymers,Polymer Physics, ETHZentrum, CH 8092 ZOrich,
Switzerland; e-mail: [email protected]
Current Opinion in Colloid Interface Science 1998, 3:614 619
Electronic identifier: 1359 0294 003 00614
~
Current Chemistry Ltd ISSN 1359 0294
Abbreviations
DlMC (dynamic)Monte Carlo
FENE finitely extendable nonlinear elastic
U Lennard-Jones
MD molecular dynamic
NE nonequilibrium
NEBD nonequilibrium Brownian dynamics
WCA Weeks-Chandler-Andersen
Introduction
Molecular simulations
aim
to provide
a d ir ec t r ou te from
th e
classic microscopic world
to th e
macroscopic world
an d
thus yield information that may be difficult to
obtain
from
real experiments. Fo r simple, hard an d soft sphere model
fluids, an d also for polymeric
an d
surfactant-based fluids,
agreement with
experimental
data has b ee n o btaine d in
predicting th e formation of micro- an d mesoscopic struc
tures and
n on -N ew to nia n p he no me na
such as
shear-thinning/thickening and normal stress differences.
On the other hand, modern
research is often
devoted
to
studying
a pp li ed p ro bl em s in making usc
of methods
which a rc n ot ye t understood. One of th e challenges in th e
field of molecular simulations concerns th e appropriate for
mulation
of
equations
of
change for variables
of
complex
systems -
an d
their relationship to th e stress
tensor
- by
means of nonequilibrium thermodynamics.
T he most convenient and precise
method
to investigate
th e
response
of
a
complex
fluid to an external, for example, flow
field, is th e nonequilibrium
NE )
molecular dynamics
~ [ O
technique. This technique is based on th e numerical solu
tion of Newton s equations of motion for a many-part ic le
system
whose
interm olec ular p oten tials
are given.
Stochastic simulation m et ho ds , s uc h as nonequilibrium
Brownian dynamics
NEBD)
an d
their equivalent
-
Fokkcr-Planck equations - treat th e dissipative part of th e
N E ~ [ O
mot ions in a less preci se way. In th e .dynamic 0 )
Monrc Carlo ~ [ C approach configurations are generated
using random
numhers
obeying rules which e ns ur e t ha t
mean values taken over
th e
sample correspond to
ensemble
averages
rather
t han t im e averages as for
N E ~ [ D N E B D
Other approaches are arising which treat particles as fields or
usc particles which have
memory of their
own past;
s ee t he
later section on micro-macro modeling.
Here, I review advances in th e science of classic continuum
models which have been published within th e past year.
Quantum
mechanical and lattice models have been exclud
ed from
th e
discussion; an art icle
collection covering
achievements in
both
fields appear ed in 1996 [1]. In this
review I shall try to cover
th e
area concerning
th e
ranges
of
applications and attempts to meliorate coarse grained models
in the mentioned fields.
Simple and Gay erne fluids
Simple
model fluids, made
of
hard spheres,
Weeks-Chandler-Anderson
WCt\) or Lennard-jones
LJ ) particles, serve as models for colloidal suspensions
and
solvents. These m od el s ys te ms
exhibit
liquid, solid,
an d
metastable phases,
an d i nd ee d
provide a good first
approximation
for real
systems
of
such properties
as liquid
structure,
transport properties,
an d
both
liquid- and solid
phase
thermodynamic
features. Fo r hard sphere fluids at
moderate
densities a
tractable kinetic Enskog) equation
exists, which - for
steady-shear
- has
been
solved by a
m o me n t m etho d [2], whose lowest order solution gives a
good quantitative description of nonlinear viscoelastic
effects, as
substantiated
by
N E ~ [ D
Only r ec en tl y h av e
th e thermo-mechanical properties of th e frequently used,
since short-ranged,
truncated
LJ i .e ., WCA
simple
model
systems in
their
fluid
an d
fcc crystalline s ta te s w er e care
fully computed [3 ]
via
~ [ O .
It s
thermodynamic
quantities, in th e fluid
state
were successfully compared
with
t he or et ic al e xp re ssi on s ba se d
on a
modified
Carnahan-Stirling theory. This theory provides a handy
description
of
th e shear modulus tensor) and th e
Born-Green a nd f lu ct ua ti on c on ti bu ri on s to all
th e
thermo-mechanical properties of th e W C A s ys te m.
T he
shear modulus tensor
an d
its Born-Green
and
fluctuation
contributions of
th e
W CA s ys te m w er e i de n ti fi ed O]
T h e transient-time
c or re la ti on f un ct io n
technique
of
Morriss a nd E va ns has been applied [5,6°] to th e case
o f
an
LJ fluid undergoing
steady
isothermal uniaxial a nd p la na r
clongationul flow. Such calculations of stresses arc extreme
ly
efficient
for .small
applied
s train ra tes ,
where
th e
signal-co-noise ratio for
th e
equivalent direct time-averaged
stresses is far roo low. At higher strain rates,
the m etho d
is
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Nonequilibrium dynamics simulations of simple and polymeric fluids Kroger 6
seen to faithfully
reproduce th e
long-time steady-state val
ues, bu t is
unable
to
account
for
transient
oscillations.
Enormous
progress has b ee n m ad e recently in the s tu dy
of
a
variety
of phase
transitions
an d th e rheological behavior
of Gay-Berne fluids [7-13]. T h e Gay-Berne potential has
been
u se d o ye r th e past decade to describe inter-molecu
lar potential between tw o
identical
anisotropic molecules.
T h e Gay-Berne potential is similar in form to th e LJ
potential but has an ansisotropic
shape
a nd s tr en g th para
meter describing th e interaction between tw o anisotropic
molecules.
Nematic viscosities
w er e o bt ai ne d,
an d th e
structure of
these f luids in the ir b u lk
a n d c on fi ne d
states,
sueh
as f il ms, have been
worked
out.
Model
fluids com
posed of Gay-Berne particles
already
capture the essential
dynamics of th e isotropic-nematic bulk ordering
transition
of simple
liquid
crystals.
T h e dynamical
properties of real
liquid crystals are known to be affected by th e
conforma
tional
freedom,
particularly
shape an d
semi
flexibility
o f
molecules. Tw o of th e promising
steps
in making progress
ar c
provided
by Br ownian
dynamics studies
of
single
poly
mer chains [14] as a
sequence
of Gay-Berne particles
connected to each
other
by f lexibl e
spacers,
an d by
studies
of suspensions
o f oblong
particles [15]
consisting
of linear
ly connected
WCA
spheres.
T h e
latter investigation
revealed a shear-induced formation
of
a
layered
and hexag
onal
structure with an unexpected step-wise
dynamics.
lexible polymers
T h e rheological properties o f macromolecular fluids are of
fundamental interest
to a
number
of
chemical,
biochemical
and manufacturing
industries,
such
as th e
polymer and
oil
industries. While manufacturing
techniques arc well
estab
lished, a detailed
microscopic
understanding
of the
rheological behavior is
often
difficult to
obtain
experimen
tally. In
recent
years
this knowledge deficit
has been
reduced with
th e aid
o f
high-powered supercomputing.
In
th e
study o fth e dynamics and structure of bulk polymer
ic liquids, made of shor t or l ong, casuall y entangled chains,
th e
finitely extendable nonlinear elastic FEN E) force an d
th e
united
atom model
arc
promising
candidates for
future
work. There is
ongoing
progr ess in
adjusting united
atom
mo d el p a ra meter s
in order to ge t quantitative
agreement
with
rheological data [16]. Th e FEN E model has less p ar a
meters,
bu t disregards
chemical
details, has, however ,
been
shown
that th e
dynamics
on time scales of
relevance
for
th e
rheological, optical an d structural properties of real
p ol ym er s as well as these properties arc described well by
th e F E N E model. Both th e models an d
th e
effect of their
microscopic
parameters such
as
chain length,
polydispersity,
temperature,
density,
concentration,
flexibility an d flow
parameters on th e macroscopic dynamics can be only
obtained by simulation
methods.
T h e
rheology
an d
flow-alignment
of
a
monodisperse
poly
mer melt, modeled as a collection of flexible FEN E
chains
which was
subjected
to a u nia xi al
elongational
flow [17], a
shear
flow
[ S ] an d
pu t
through
a
channel with
a re
entrant corner [19°],
were
determined by N E1 .I O. This
modeling
approach also e na bl ed t he
detailed
analysis
of
t he e nt an gl em en t
network
[20]. In addition, scattering
functions became
available
for th e e x te nd e d, bidispersc
model [21]. S pe ct ra l s im ul at io n a n d Brownian dynamics
were combined to s tu dy t he recovery of
F E N E
polymer
fluids after shear flow [22°]. T h e dynamics o f p h as e s ep a
ration of a quenched polymer solution in two-dimensions
has been characterized for F E N E polymer solutions with
explicit LJ
solvent
particles [ YO] a basic but
powerful
approach
FEI m -C
where
C indicates a cu t of th e
poten
t ial) to t he s tu dy of th e
detailed
rheology an d
structure
of
flexible
equilibrium
polymers
an d wo rm- lik e mice lle s u s es
a modified F EN E potential which
accounts
for sci ssion
and recombination of molecules [24].
Conventional 1 .10 simulations of u ni te d a to m m od el s for
alkane melts
allowed
for a
test
of
a
memory function theo
ry of flexible polymers [25°]. Fo r th e s am e model th e
equivalence of
th e
Grecn-Kubo a n d E i ns te i n
approach to
th e calculation of viscosity in
both
th e
atomic an d
molecu
lar representations ha s been reported [26]; th e
inapplicability o f
th e Rouse
model
on
time
scales shorter
t han t he Rouse time for th e
united
a to m m od el has also
been proven [27,28]. T he dynamics of
hexagonal
cluster
in g of short
un it ed ato m chains, subjected
to sudden
cooling has been inspected [29]. All these investigations
were devoted
to resolve
th e
relationships between
microstructure an d
th e
observed macroscopic thermody
n am ic al , o pt ic al
or
m ec ha ni ca l b eh av io r
o f
polymeric
mat er ials. A
relationship between chain
conformation
an d
rheology gives
valuable information
since it
ca n
be
used
to
refine constitutive equations
between
stress an d
deforma
tion
history,
an d
se t u p more
simple
models which capture
th e behavior of th e more detailed
models.
Within th e next decade simplified and efficient)
models,
which
profit from such investigations will
enter
th e market
to be of
relevance
for
th e
development
an d
characteriza
tion
of
ne w
materials
a nd t he ir d yn am ic
behavior, I am
c on vi nc ed t ha t r e ce n t t re n ds
in
specific modeling
areas ca n
be
obtained
from Table 1.
emiflexible polymers
Semi flexible model polymers
with
a f in it e bending rigidi
ty arc of us c to l oo k into th e dynamics of
actin
filaments,
DN A
an d polyclcctrolytcs,
Birefringence overshoots,
various
steady-state effects
of
semi
flexible macromolecules
undergoing shear
flow
an d
extensional flow have been
obtained
by NEBO [30],
NEBD/1 .IC [31]
an d
NE1 .IO [32°].
T h e underlying
model
u ti li ze s a discrete version of th e Krurky-Porod worm-like
or persistent)
chain.
T h e
investigation
of double-stranded
scmiflcxiblc polymers
using
both
analytical
techniques
an d 1 .10
clarified
-t he t em pe ra tu re driven
transition
b et we en t he worm-like
an d
twist
structures
[33°].
Fo r
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6 6 Dynamic aspects of col lo ids and interfaces
weakly charged semi flexible chains within
th e
Debye-Hucckel
approximation [34] and in
the
presence
of
counterions [35] the two concurrent, intrinsic and electro
static-interaction-induced dynamical mechanisms produce
an extraordinary scaling behavior
of
conformational quan
tities; inhomogeneous charge distributions and
th e
formation
of
ion pairs can
produce
a collapse
of
the whole
chain. The study
of
the dynamics
of
scmiflexible polymers
is particularly useful to validitate assumptions in physical
theories on this topic and to determine and influence the
speed
of mass transport and the mechanical properties of
biological cells.
luids in confined geometries
Geometrical confinement
of
fluids tends to slow down
their relaxation processes - caused by the
reduction
of
the
systems
degrees of
freedom
- when compared with
the
corresponding
bulk system.
Contacts
with interfaces
arc realized, for
example
in films
and
brushes.
For these
geometries
experimental characterization techniques are
now widely available.
Many of the
experimental investi
gations focus on slip
effects
and velocit y profile s,
rheological
and
optical
properties,
sur face tension,
anisotropic diffusion, and
the
influence
of
interfacial
properties on these phenomena.
In the following I will summarize
recent
works which
extend the simulation
methods
validated for
bulk
fluids
(see the
preceding
sections) to the above
mentioned
model fluids in confined geometries.
The
shear rheology
of wet
polymer brushes and
of
inter
acting brushes has been analyzed [36] via
NEBD
and [37J
D;\IC, respectively. The adsorption and surface tension for
FENE polymer solutions in contact with attractive or
repulsive planar walls, as well as their phase behavior has
been explored [3sooJ by
D ~ I C
For brushes of end-grafted,
polar FENE polymer chains in a good, nonpolar solvent a
charge-induced collapse of the chain and its dielectric
properties have been probed [39J
under the
influence of an
electric field by NE;\ID.
The steady shear flow
of
scmiflexible chains (modeling n
alkanes) [400°] and the oscillatory shear flow
of FENE
polymer melts [41°] confined between parallel plates have
been carefully inspected .via NE1 .ID. Generalized bead
spring model polymer films under the . action
of
external
bending
forces were also
studied
[42°J using
N E ~ I
The
rheological behavior of molecular (simple fluid) films is also
a topic of current interest, and has
been
probed, for exam
ple, via isosrress-isosrrain
ensemble
i\IC simulations
[43J.
The interfacial s tructure and tension between the two
immiscible phases for binary polymer blends composed
of
FENE chains [ l l J has
been
determined via 1 .10 and ;\IC.
Capillary
W,H CS
were observed and it has been indicated that
for relatively short time scales
the
dynamical scaling expo
ncnt for an
FENE
polymer chain in solution is anomalous in
two dimensions, contrary to
the
prediction of the Zirnrn
model [45 ,46J.
By means
of
NE1 .ID a new method
to
calculate growth
rate constants
of
various crystal faces from the fluctua
tions
of
interfaces - ba sed on Onsagcr s hypothesis - has
been validated [47°J. Results
of
the first
combined
Grand
Canonical
\ I C I N E ~ I D
study
of
transport of a gas mixture
through carbon nanopore, in the
presence
of an external
chemical potential gradient are available [4SJ.
Micro macro modeling
In order to close the gap between different length and time
scales in molecular simulations, models have appeared
which will
embed
the information
contained
in the micro
scopic conformations of macromolecules into
th e
simulation
of
macroscopic flows. From my view three
of
them arc
of
particular interest.
An efficient model in which whole polymer chains arc rep
resented
as soft particles has been
presented
[49 ]. These
particles arc characterized by their shapes and internal free
energies, which are calculated from
the
distribution
of
con
formations
of
microscopic chains, for example FENE
chains. The inonomer density within a soft par ticle is cal
culated from all conformations that possess its size and the
intermolecular interaction strength between soft particles
is assumed to be equal to the spatial overlap of
monomer
density distributions.
Another new
model for macroscopic flows, without
the
need
for a constitutive relationship between stress and
deformation has been tested [50
J.
Here, the collection
of
individual polymer chains is replaced by an ensemble
of
configuration fields, representing the internal degrees
of
f reedom, which are subjected to Brownian motion. The
comparison with a parallel, equilibr ium simulat ion as a
method to reduce the influence
of
stochastic noise on the
calculated viscoelastic properties, called variance reduc
t ion , has shown to be applicable [51J with this model.
A third
method, smooth
particle applied mechanics
([52J
and references therein), allows thermo-mechanical contin
uum
equations
on a moving grid to
be
solved. By
eliminating t he ordered grid, smooth particle applied
mechanics resembles 1 .10. Complex hydrodynamics prob
lems can be solved and its irnplcmcnrarion on parallel
computers
has been shown to be straightforward.
Nonequilibrium thermodynamics
The consistent
jumping
between different levels of descrip
tion for complex fluids requires further developments and a
better understanding
of
the theory
of
noncquilibriurn ther
modynamics. I will briefly summarize approaches which
should increase the quality of basic simulation concepts.
The
so-called matrix model, a
thermodynamic
framework
for micro-rheological modeling,
seems
to be applicable for
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Nonequilibrium dynamics simulations of
simple
and polymeric f lu ids Kroger 617
Table 1
Publications
per year fo r keywords; relative
changes
may
also reflect
the trends in corresponding
research
areas.
Yearfor topic,
199
1991
1992 1993 1994 1995 1996
1997
1998
Dynamics simulation 2705 2954 3312
3943
4665
5383 5998 588 58
Molecular dynamics simulation 15 6 1642 1866
1985
2 44
2 5
2298
2317 26
Brownian dynamics simulation 62 78 86 111 112 114 132 145 200
Molecular dynamics algorithm
56
62 81 101 112
13
128
13
100
Surfactants computer simulation 7 9 10 6 10 11
22
8 21
Fokker-Planck equation
222
168 199 219 269
25
278 268 280
Lennard-Jones potential 136 140 177
16
176 200 240 25 250
Coarse-grained model
15
23 14 31 41 40 46 57
50
FENE potential 4 5 6 8 6 9 13 18
25
Gay-Berne potential 2 3 4
7
6 15 16 23 25
United atom potential
2
4
8 6 7 10
12
12 18
Entangled polymers 2 5 4 2 6 6 8 6
7
Polymer rheology 119 91
124
139 165 137 183 203 270
Surfactant rheology 4 1 0 6 8 21 22 21
9
Polymer flow
257 225 241
3 6
339
339
397
399
430
Simple fluid flow 15 165 173 19 223 250
255
25
280
The numbers given for
1998
are extrapolated from the period January-May 1998,
m od el s f or mu la te d at
th e
c on fi gu ra ti on t en so r l ev el of
description.
Combining
th e
matrix
model with
a
Lagrangian simulation
method
an e xp li ci t s ol ut io n of
th e
configuration space distribution is
obtained.
Recently,
th e
elastic
dumbbell
model
under shear
has
been
worked
ou t
[53) a nd c om pa re d with
NEBD
results.
This
model an d
also th e Bracket formalism of Bcris an d E dw ar ds can be
embedded w it hi n a m or e g en er al , s o- ca ll ed GENERIC
framework
[5-l°
and r ef er en ce s t he re in ), w hi ch u se s [ \ \
separate
g en er at or s for
th e
reversible
an d
irreversible
dynamics, together w it h c er ta in
symmetry
requirements.
By applying
th e
projection operator method
th e
equations
for
th e nonequilibrium
reversible-irreversible
coupling
were stated
and mic ro sco pi c e xp re ss io ns - wh ic h s ho ul d
be
further
e xp lo re d by N E: - I D/ Br ow ni an d yn am ic s - for
th e GENERIC building
blocks
were
derived.
A n on li ne ar r es po ns e theory for autonomous systems has
been generalized in [55°) so that it describes
th e
response
of classic many-body systems to large time-dependent
external fields.
The
expressions were
checked
against
N ~ I
simulation results for both
time-dependent
linear
response an d
steady
nonlinear response.
-Hard
sphere fluids
Therrnosratting of
molecular
dynamics
is a field
of
ongo
ing discussion. Fo r
example
th e multifracral states found
in reversibly
thermostated
hard-particle simulations have
isomorphic counterparts in adiabatic flows [56). This
recent
finding
supports
th e quality of
f re quentl y use d
reversible thermostats.
on lusions
I have
highlighted recent advances
in
th e study
of classic
continuum
m od el s for
complex
fluids. In a dd it io n,
on e
may find an
amount
of research concerning too simplified
m od el s. wh ic h is caused by
th e
fact that
th e
increase of
available
computing
power is no t strong
enough
to co m
pensate
th e
speed
of
development
of
approximations
[57,58).
Often m od el s w er e
p ro po se d at
one
level
an d
subsequent
approximation allows experimental
data
to be
reproduced. Such models
arc missing
much of their
early
physical motivation. There is considerable
interest
in seri
ous simulation results
[59° an d
efforts are
underway
to
confirm th e underlying
methods
such as rhermostatting
ensembles
in simulations. Basic research on noncquilibri
um
thermodynamics
even
applied
to
simple
s ys te ms , is
still a challenging field. Overall improvements arc g oi ng
to
take
place
when
information obtained from experi
ments atomistic
microscopic,
coarse-grained
macroscopic simulations
and theory
is
combined an d
every
result may be
regarded
as a part of this
attempt
either
positive or negative.
Reasonable coarse-grained modeling for polymers
avoiding
assumptions
related to
hydrodynamic
interac
tions,
a nd e xc lu de d
volume
stretching mechanisms
for
m ole cula r ba ckbone s
diffusion
behavior
an d
phase
space equilibrium
is p ar ti cu la rl y w el l done
using
th e
FE N E model
- an d its
slightly
modified
versions
which
for
example account
for semif le xi bi li ty or scis
sion -
an d
also by
simulating
explicit
solvent
particles.
But
for
entangled polymers
in
confined
geometries
for
example
most
relevant
time scales arc j ust c omi ng into
reach of simulations.
Trends for th e increase in relevance of selected molecu
lar models
simulation
techniques
an d
r es ea rc h a re as arc
reflected
by th e relative
changes
o f s u bs e qu e nt
entries
in
Table
1.
It
seems
to
be inescapable,
that
serious validation
of
mod
els will have to pr oce ed from small to large scales,
hence
retrospectively, in future works.
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8 Dynamic aspec ts
of
colloids
and interfaces
eferences nd recommended re ding
Papersof particular interest, published within the annualperiod of review,
havebeen highlighted as:
• of special interest
•• of outstanding interest
1. Binder K,Ciccolti G Eds): Monte Carlo and molecular dynamics of
condensed matter systems. IPS Conference Proceedings: 1996
July
3 8;
Bologna Bologna: Editrice Compositoria; 1996
2. Lutsko JF:Approximate solut ion of the Enskog equation far from
equilibrium. Phys Rev Lett 1997, 78:243-246.
3. Hess S , K roger M ,
Voigt
H: Thermomechanical properties of the
WCA·Lennard·Jones model system in its fluid and solid states.
Physica A 1998,250:58-82.
The WCA potentialis quite popular in molecularsimulation studies of simple
and complex fluids. For the first time precise simulation data and analytic
expressions arepresentedfor the thermomechanical propertiesof WCA fluids.
4. Hess S, Kroger M , Hoover WG: Shear m od ul us of f lu id s and s ol id s.
Physica A 1997,239:449·466.
This paper shows that the shear modulus proves to be a good indicator for
the fluid-solid phase transition of the WCA model system.
5. ToddBD: Application of transient-t ime correlation functions to
nonequilibrium molecular-dynamics simulations of elongational
flow. Phys Rev E 1997,56:6723-6728.
6. ToddBD, DaiviesPJ:Elongational viscosities from nonequilibrium
molecular dynamics simulations of oscillatory elongational flow.
J
Chem Phys 1997,107:1617-1624.
An easynew technique to simulatethe elongationalflow of a simple atomic
fluid by NEMD.
7. GruhnT,SchoenM: A grand canonical ensemble Monte Carlo
study of confined planar and homeotropically anchored
Gay-Berne films.
J
Chern Phys 1998, 108:9124-9136.
8. S arman S : Flow p ro pe rt ie s of l iq ui d c ry st al phases of the
Gay-Berne fluid. J Chem Phys 1998, 108:7909-7916..
9. Brown
JT
Allen MP, del Rio EM, de Miguel E: Effects of elongation
on the phase behavior of the Gay-Berne fluid. Phys Rev E 1998
57:6685·6699. .
10. Wilson MR: Molecular dynamics simulations of flexible liquid
crystal molecules using a Gay-BernelLennard·Jones model.
J
Chem Phys 1997,107:8654·8663.
11. Wall GD, Cleaver DJ:Computer simulation studies of confined
llquld-crystal films.
Phys Rev E
1997,56:4306-4316.
12. StelzerJ,LongaL,Trebin H-R: Homeotropic surface anchoring of a
Gay-Berne nematic liquid crystal. Phys Rev E 1997,55:7085-7089.
13. PereraA, Ravichandran S, MoreauM, Bagchi B: Single particle and
collective orientational relaxation in an anisotropic liquid near the
isotropic-nematic transition.
J
Chern Phys 1997, 106:1280-1283.
14. Lyulin
V
AI-Barwani MS, Allen MP,Wilson MR, NeelovI, Allsopp NK:
Molecular dynamics simulation of main chain liquid crystalline
polymers.
Macromolecules
1998, 31:4626-4634.
15. Mori N, KumagaeM, NakamuraK: Brownian dynamics simulation
for suspensions of oblong-particles under shear flow. Rheol Acta
1998,37:151-157.
16. LahtelaM, PakkanenTA:Nonequilibrium molecular dynamics
simulations of 3-methylhexane: the effect of inter- and
intramolecular potential models on simulated viscosity.
J
Phys
Chern 1997, 101:3449-3453.
17. KrogerM, LuapC, MullerR: Polymer melts under uniaxial
elongational flow: stress-optical behavior from experiments and
NEMD computer simulations. Macromolecules 1997,30:526.
18. Hess S, Aust C, Bennett L,Kroger M,PereiraBorgmeyer C, Weider T:
Rheology: from simple and to complex fluids. Physica A 1997,
240:126-144.
The method of NEMD is reviewed. Special emphasisis placed on the simu
lation of plane Couelte f low, and results for simple and complex fluids.
Particular emphasisis placed on olymericliquids and anisotropic fluids such
as nematic liquid crystals ferro-fluids, magneto- or electro-rheological fluids.
19. Koplic J,BanavarJR: Molecular simulation of reentrant corner flow.
Phys Rev Lett 1997,78:2116-2119.
The authors haveshown again see [60]) how molecular calculations of the
FENE multibead chain model can elucidate some of the important subcon
tinuum properties of macromolecular liquids, such as the regularization of
apparent divergences and the relation between flow and structure.
2 Voigt
H: Investigation of the entanglement network in polymer
melts. Appl Rheo/1997
7:105-110.
21. Cui ST,Cochran HD, CummingsPT,KumarSK: Computer
simulations of the static scattering from model polymer blends.
Macromolecules 1997,30:3375-3382. .
22. BellTW, NylandGH, de Pablo JJ,GrahamMD: Combined Brownian
dynamics and spectral simulation of the recovery of polymeric
fluids after shear flow. Macromolecules 1997,30: 1806-1812.
Demonstratesthat the spectral technique is significantly more computation
ally efficient than the traditional finite element method in one dimension.
23. BhattacharyaA, Mahanti SD, Chakrabarti A: Networklike pattern
formation in phase separating polymer solutions: a molecular
dynamics study. Phys Rev Lett 1998,80:333-336.
A detailed understanding of such a network pattern formation will be of
utmost importance not just in phase separating polymer solutions, but also
in other diverse complex fluid systems such as gels, an interpenetrating net
work of cross-linked polymers and polymeric surfactants.
24. Carl W,MakhloufiR,Kroger M: On the shape and rheology of l inear
micelles in dilute solutions.
J
Phys 111997 7:931·9 46
25. KostovKS,FreedKF,Webb EB, MondelloM, Grest GS: Dynamics of
linear and branched alkane melts: molecular dynamics test of
theory for long
time
dynamics.
J
Chern Phys 1998, .
108:9155-9167.
Excellentagreementwith the simulationsis found for all correlation functions
and all times for the decane dynamics, provided the theory employs one,
temperature dependent scale factor to compensate for the inadequacy of
the Rouse model.
26. Mondello M,Grest GS: Viscosity calculations of n-alkanes by
equilibrium molecular dynamics.
J
Chern Phys 1997
106:9327-9336.
27. PaulW,Smith GD, Yoon
DY
FaragoB: Chain motion in an
unentangled polyethylene melt: a critical
test
of the rouse model
by molecular dynamics simulations and neutron spin echo
spectroscopy. Phys Rev Lett 1998,80:2346-2349.
28. PaulW,Smith GO, YoonDY:Static and dynamic propert ies of a
n-ClooH202 melt
from molecular dynamics simulations.
Macromolecules 1997, 30:7772-7780.
29. FujiwaraS, Sato T: Molecular dynamics simulation of structural
formation of short polymer chains.
Phys Rev Lett 1998
80:991-994.
30. Andrews NC, McHugh AJ: Conformational and rheological
dynamics of semiflexible macromolecules undergoing shear flow:
a nonequilibrium Brownian dynamics study.
J
Rheo/1
99
42:281-305.
31. Andrews NC, McHugh
J
Schieber JD: Configuration biased Monte
Carlo and Brownian dynamics simulations of semiflexible
polymers in extensional flows. Macromol Theory Simul 1998
7:19-26.
32. Liu
Yang
Srolovitz OJ YeeAF: Extended ensemble molecular
dynamics method for constant strain rate uniaxial deformation of
polymer systems.
J
Chem Phys 1997, 107:4396-4407.
Bond length constraints were applied to a macromolecularsystem together
with an extended ensemble in which the simulationcell shape was allowed
to fluctuate.
33. Liverpool TB, KremerK: Statistical mechanics of double-stranded
semiflexible polymers. Phys Rev Lett 1998, 80:405-408.
In the low temperature phase,the polymersdevelopa kink·rodstructure which
could clarify some recent puzzling experiments on actin [61). It is known that
biopolymers, such as microtubules, can also be multistrandedobjects.
34. Micka U,KremerK: Persistence length of weakly charged
polyelectrolytes with variable intrinsic stiffness. Europhys Lett
1997,38:279-284.
35. Winkler RG, Gold M, ReineckerP: Collapse of polyelectrolyte
macromolecules by counterion condensation and ion pair
formation: a molecular dynamics simulation study. Phys Rev Lett
1998, 80:3731-3734.
36. DoylePS, Shaqfeh ESG, Gast AP: Rheology of wet polymer
brushes via Brownian dynamics simulation: steady vs. oscillatory
shear.
Phys Rev Lett
1997,78: 1182-1185.
37. Neelov
M
Borisov
av
Binder K: Shear deformation of two
interpenetrating polymer brushes: stochastic dynamics
simulation.
J
Chern Phys 1998, 108:6973-6988.
-
8/17/2019 NEMD of Simple and Polymeric Liquids
6/6
Nonequilibrium
dynamics
simulations
of
simple
and
polymeric
fluids Kroger 619
38. PandeyRB, Milchev A,Binder K: Semidilute and concentrated
polymer solutions near attractive walls: dynamic Monte Carlo
simulation of density and pressure profiles of a coarse-qralned
model. Macromolecules 1997,30:1194-1204.
Therehavebeennumerous previous
simulations
addressing static properties only
whileinthis
state of the art
studyanalready
validated
DMC methodhasbeenused
to resolve the interplay betweenstaticanddynamicproperties of polymer brushes.
39. Kaznessis YN, Hill DA, Maginn EJ: Molecular dynamics
simulations
of
polar polymer
brushes.
Macromolecules
998
31:3116-3129.
40. Stevens MJ,Mondello M, Grest GS, Cui ST,Cochran HD,
Cummings PT: Comparison of shear
flow
of hexadecane in a
confined geometry and in bulk. J Chern Phys 1997, 106:7303-7314.
State-of-the-artsimulationofa confined unitedatom model polymerunder flow.
41. Koike A: Molecular dynamics study of viscoelastic properties of
confined oligomer melts. Macromolecules 1998,31 :4605-4613.
This paper gives simulation results of the dynamic viscosities of confined
oligomer meltsvia NEMD.In myview,investigations in thisfield arestilltoo rare.
42. Hapke T,LinkeA, Patzold G, HeermannDW: Modeling of
amorphous
polymer surfaces in
computer
simulation.
Surf Sci
1997,373:109-124.
Analysis of the results qives an advanced characterization of the deformed
states for such polymer films.
43. Schoen M: Rheology and local structure of thin films confined
between thermally corrugated walls. Physica A 1997, 240:328-339.
44. Lacasse M, Grest GS, LevineAJ: Capillary-wave and chain-length
effects at polymer/polymer interfaces. Phys Rev Lett 998
80:309-312.
Theauthorselucidate a method of measuring the interfacialwidth in terms of
second moments of the different contributions to the first derivative of the
interfacial profile.
45. Shannon SR, Choy TC: Dynamical scaling anomaly for a
two
dimensional polymer chain in solution.
Phys Rev Lett 997
·79:1455-1458.
Although the Zimm model equations may offer some insight into this result,
a re-examinationof the scaling argument in 2D is called for in order to fully
understand and explainthe anomalous exponent.
46. Okuzono T: Computer simulation of shear-induced phase
separation and rheology in
two-component
viscoelastic fluid.
Mod
Phys Lett B 1997, :379-389.
47. Biels WJ, TepperHL: Crystal growth of the Lennard-Jones 100)
surface by means of equilibrium and nonequilibrium molecular
dynamics. Phys Rev Lett 1997, 79:5074-5077.
Theuse of Onsager s hypothesisto derivethe microscopic expressionfor the
growth rate constant serves as an examplefor applications in other fields.
48. LifangX, Sedigh MG, Sahimi M,TsotsisTI : Nonequilibrium
molecular dynamics simulation of transport of gas mixtures in
nanopores. Phys Rev Lett 1998, 80:3511-3514.
49. MuratM, KremerK: From many monomers to many polymers: soft
ellipsoid model for polymer melts and mixtures. J Chern Phys
1998, 108:4340-4348.
Since the internal degrees of freedom of a chain are integrated out, a large
number -10000 of long 100 beads) chains can be simulated within rea
sonable computer time on a single work-station processor.
50. Hulsen MA, van Heel APG, van der Brule BHAA: Simulation of
viscoelastic
flows
using Brownian configuration fields.
J
Non-
Newtonian Fluid Mech 1997, 70:79-101.
Presents a new approach for calculating inhomogeneous viscoelastic flows
of polymers. The polymer stress is determined from an arbitrary microscop
ic model. Particle tracking is circumvented.
51. Ottinger HC, van der Brule BHAA, Hulsen MA: Brownian
configuration fields and variance reduced CONNFFESSIT.
Non-
Newtonian Fluid Mech 1997, 70:255-261.
52. Hoover WG, HessS: Equilibrium and nonequilibrium
thermomechanics for an effective pair potential used in
smooth
particle applied mechanics.
Physica
A 1996,231 :425-438.
53. Jongschaap
RJJ
DennemanAIM, Conrads W: Thermodynamic
approach to rheological modeling and simulations at the
configuration space level of description.
J
Rheol 1997, 41:219-235.
54. Ottinger HC: General projection operator formalism for the
dynamics and thermodynamics of complex fluids. Phys Rev E
1998,57:1416-1420.
Recent approach to the consistent formulation of equations of motion at dif
ferent levels of description for arbitrary complex systems. Prominent rheo
logical models havebeen reformulated in this new, intriguing language.
55. Dellago C, HooverWG, Posch HA: Isomorphic multifractal shear
flows
for hard
disks
via adiabatic and isokinetic nonequilibrium
molecular dynamics. Phys Rev E 1998, 57:4969-4975.
56. PetravicJ, EvansDJ:Nonlinear response for time-dependent
external fields.
Phys Rev Lett
1997, 78:1199-1202.
Their formalism represents the first practical application of response theory
to such problems. The leiter describes an entirelynew approach to the treat
ment of nonlinear autonomeous systems.
57. PodtelezhnikovA, Vologodskii A: Simulations of polymer cyclization
by Brownian dynamics. Macromolecules 1997,30:6668·6673.
58. Srinivasalu Gupta J,KhakharDV: Brownian dynamics simulation of
diffusion-limited polymerization of rodlike molecules: anisotropic
translation diffusion.
J
Chern Phys
1998,108:5626-5634.
59. van Gunsteren WF, MarkAE:Validation of molecular dynamics
simulation.
J
Chern Phys 1998, 108:6109-6116.
This paper is of notable interest for any researcher in the field of molecular
dynamics since it offers a route to validate a new molecular dynamics com
puter program.
60. KrogerM, Loose W, Hess S: Structural changes and rheology of
polymer
melts
via nonequilibrium molecular dynamics.
J
Rheol
1993, 37:1057-1080.
61. Kas J,Strey H, Barmann M, SackmannE: Direct measurement of
the wave-vector-dependent bending stiffness of freely flickering
actin-filaments. Europhys Lett
1993, 21:863·865.
