Complex Fluids & Phase Transitions
Polyelectrolytes & Colloids
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.
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.
N.V.Brilliantov,
Phase Transitions in Solutions of Variably Ionizable Particles,
Phys. Rev. E., 48, (1993) 4536.
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.
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.
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).
Coulombic Fluids
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.
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.
