XII
International Conference on the Discrete Simulation of Fluid Dynamics,
Augist
25-29 (2003), Beirut, Lebanon
XI
international Conference of Discrete Simulation of Fluid Dynamics and
Soft
Condensed Matter
August
5-9 (2002), Shanghai, China
| Polyelectrolytes
& Colloids |
Hydrodynamics
&
Brownian Motion |
Phase Transitions & Critical Behavior | Coulombic
Fluids |
Many important biological
macromolecules, such as e.g. DNA, are Polyelectrolytes. Solutions
of Polyelectrolytes
and of Charged Colloidal paricles
exhibit very interesting phase behavior: Phase transitions may be accompanied
by a sudden change of a gyration
radius of a polymer chain, of an average charge of a macromolecule,
etc. We
developed a theory of electrostatically
driven chain collapse in dilute polyelectrolyte solutions,
which occurs as a
first-order phase transition (PRL
81, 1998). Later this phase transition has been detected in
experiments
(Mel'nikov et al, JACS, 121
(1999) 1130). We also developed a theory of phase transitions in
colloidal solutions
of particles with variable
surface charges.
My main publications on the topic are:
N.V.Brilliantov, D.V.Kuznetsov
and R.Klein,
Chain Collapse and Counterion
Condensation in Dilute Polyelectrolyte Solutions,
Phys. Rev. Lett., 81, (1998)
1433. pdf file (171 kB)
N.V.Brilliantov,
Phase Transitions
in Solutions of Variably Ionizable Particles,
Phys. Rev. E., 48, (1993) 4536.
pdf file (2283 kB)
N.V.Brilliantov, and V.V.Malinin,
Liquid-liquid type phase transitions
and variation of the particle charge in colloidal solutions,
Colloidal Journal, 64, (2002)
261.
Hydrodynamics
&
Brownian Motion
Particles in Complex Fluids, such
as solutions of Polyelectrolyte or Colloids, often carry a considerable
charge. Hence, the local properties
of the solvent, such as e.g. viscosity, around the particles may
be
altered by the strong electric
field. The other effect which is called the dielectric friction may also
significantly
influence the Brownian motion of
particles in Complex Fluids. The molecular motion in these systems
may be analyzed using the hydrodynamics
of fluids with the internal degrees of freedom. For the case of polar
solvents such hydrodynamic equations
are called Hubbard-Onsager equations. Solving the these hydrodynamic
equations we obtain the generalization
of Stokes-Einstein and Stokes-Einstein-Debye relations for translational
and rotational Brownian motion.
My main publications on the topic are:
N.V.Brilliantov, N.G.Vostrikova and O.P.Revokatov,
Role of electrical interactionss in
rotational motion of
charged solute in polar solvents.
J. Phys. Chem.B, 102, (1998) 6299.
pdf
file (75 kB)
N.V.Brilliantov, and N.G.Vostrikova
Rotational motion of Brownian
particles with surface charge,
Molecular Physics, 77, (1992) 957
N.V.Brilliantov, and P.L.Krapivsky,
Stokes laws for ions in solutions with ion-induced
inhomogeneity,
J. Phys. Chem., 95, (1991) 6055-6057.
N.V.Brilliantov, V.P.Denisov, and P.L.Krapivsky,
Generalized Stokes-Einstein-Debye relation
for charged
Brownian particles in solution, Physica
A, 175, (1991) 293-304.
Phase Transitions
&
Critical Behavior
The critical behavior of simple
fluids as well as of other fluids with a short-range interaction
potential corresponds to that of
the Ising universality class. This follows from experiments,
computer simulations and theoretical
reasonings. For the Coulombic
Fluids however, it is still
not completely clear to which universality
class do these fluids belong. The most direct analysis of
the critical properties of the
system may be performed using the Landau-Ginzburg-Wilson
(LGW) form of the system Hamiltonian.
We develop a method which allows a rigorous mapping of
the fluid Hamiltonian onto the
effective field-theoretical LGW Hamiltonian, which coefficients
may be calculated analytically.
Using this approach we derive some relations between critical
parameters, which have been confirmed
in numerical experiments (Camp P.J., Patey G.N.,
J. Chem.Phys. 114 (2001) 399) and
analyze the coulombic
criticality.
My main publications on the topic are:
N.V.Brilliantov,
Effective magnetic Hamiltonian and Ginzburg
criterion for fluids,
Phys.Rev.E, 58, (1998) 2628.
pdf file
(136 kB)
N.Brilliantov, and J.Valleau,
Thermodynamic Scaling Monte Carlo Study of
the Liquid--Gas Transition in the Square--Well Fluid,
J.Chem.Phys., 108, (1998) 1115.
N.Brilliantov, and J.Valleau,
Effective Hamiltonian Analysis of Fluid Criticality
and Application to the Square--Well Fluid,
J.Chem.Phys., 108, (1998) 1123.
N.V.Brilliantov, A.Yu.Loskutov and V.V.Malinin
Field-Theoretic analysis of critical behavior
of a symmetric binary fluid,
Theor. Math. Phys., 130, (2002)
p.123-135 (in russian).
Fluids with long-range coulombic
interactions, such as ionic solutions, plasma, etc.
are called coulombic fluids. The
problem of critical behavior of such fluids, i.e. of the
coulombic
criticality, is still under discussion, since some the ionic fluids
demonstrate
Ising criticality, while other
- the classical one. Using the effective LGW
Hamiltonian
and nonperturbative
RG approach, we show that very long crossover
from the classical
to Ising critical behavior may
be observed. For the simplest model of the coulombic fluid,
for the model of One Component
Plasma we derived the equation of state (EOS) which is
very accurate for all values of
plasma parameter, from the Debye-Huckel limit up to the
Wigner crystallization point.
To derive this EOS we propose the Restricted Random Phase
Approximation.
My main publications on the topic are:
N.V. Brilliantov,
C. Bagnuls and C.Bervillier,
Peculiarity of the Coulombic Criticality?,
Phys. Lett. A, 245, (1998) 274.
pdf file
N.V. Brilliantov,
Accurate First-Principle Equation of State
for the One-Component Plasma,
Contrib. to Plasma Physics, 38, (1998) 489.
N.V.Brilliantov, V.V.Malinin and R.R.Netz,
Systematic Field-Theory for the Hard-Core
One-Component Plasma,
Eur. Phys. J. D, 18, (2002) 339. pdf
file