Separation of long linear polymers in gel electrophoresis with alternating electric fields: a theoretical study using the necklace model.

The necklace model, which mimics the reptation of a chain of N beads in a square lattice, is used to study the drift velocity of charged linear polymers in gels under an applied electric field that periodically changes its direction. The characteristics of the model allow us to determine the effects of the alternating electric field on the chains' dynamics. We explain why chains of different N can be made to move in opposite directions with a nonuniform electric field with certain values of intensity and frequency. The key point is that, when alternating electric fields are applied, longer chains spend more time out of the steady-state regime than lower chains. Numerical results are obtained by means of Monte Carlo simulations and they are qualitatively in agreement with experiments of DNA migration in gel electrophoresis.

Diffusion in the two-dimensional necklace model for reptation.

An extension of a recently introduced one-dimensional model, the necklace model, is used to study the reptation of a chain of N particles in a two-dimensional square lattice. The mobilities of end and middle particles of a chain are governed by three free parameters. This new model mimics the behavior of a long linear and flexible polymer in a gel. Noninteracting and self-avoiding chains are considered. For both cases, analytical approximations for the diffusion coefficient of the center of mass of the chain, for all values of N , are proposed. The validity of these approximations for different values of the free parameters is verified by means of Monte Carlo simulations. Extensions to higher dimensions are also discussed.

Drift velocity for a chain of beads in one dimension.

The one-dimensional motion of a chain of N beads is studied to determine its drift velocity when an external field is applied. The dependences of the drift velocity with the chain length and field strength are addressed. Two cases are considered, chains with all their beads charged and chains having an end bead charged. In the last case, an analytical expression for the drift velocity is proposed for all N . Results are tested with the help of Monte Carlo simulations.

Effects of island disaggregation in growth models.

We introduced two point island models with island disaggregation. In the first one, particles can detach from islands with an odd number of particles and from those with two particles. In the second model, particles can detach from all islands with more than two particles. The scaling exponents are analytically obtained and verified with Monte Carlo simulations. Specially, the power-law scalings of the island and monomer densities are analyzed. Comparison with other models indicates that the models introduced here present different scaling behaviors.

Window effect in a discretized model for diffusion of a chain in one dimension.

We introduce a model to study the diffusion of chains in microporous solids. The difficulties a chain has to escape from a pore where it is confined is found to strongly depend on the ratio between the chain length and the cage size. This dynamic effect implies a nonstandard behavior of the diffusion coefficient. We found a window effect that can be explained without using any energy argument.

Exact diffusion coefficient for a chain of beads in one dimension using the Einstein relation.

The one-dimensional motion of a chain of N beads is studied to determine its diffusion coefficient. We found an exact analytical expression for all through two methods by resorting to the Einstein relation. Results are tested with the help of Monte Carlo simulations.

Growth model with disaggregation of islands having an odd number of particles.

A simple model of deposition of particles and growth of point islands in a two-dimensional substrate is introduced and studied. The detachment of particles from islands with an odd number of particles can occur with a probability P. The power-law scalings of the island, monomer, and odd island densities are analytically obtained and verified by Monte Carlo simulations. The universality class of the model depends on P, and the island density exponent chi changes from chi=1/3 (for P=0 ) to chi=0 (for P>0 ).

Discretized model for diffusion of a chain in one dimension.

With the help of Monte Carlo simulations, the one-dimensional diffusion motion of a chain of N beads is studied to determine its diffusion coefficient and viscosity. We found that the end bead movements with respect to that of the central beads play a key role. There is no memory between bead hops but they become correlated as a consequence of the chain dynamics. This determines the scaling exponents and the relation connecting them. In particular, the scaling exponent for the viscosity can be smaller or greater than 3 but it must scale as N3 in the asymptotic regime (N--> infinity ). We analyze in detail the dynamics of a chain with three beads to explain why the expected relation between diffusivity and viscosity exponents is not satisfied.

Effects of the sticking probability on the scaling of the island density in a point island model.

The behavior of the island density exponent chi for a model of deposition, nucleation, and aggregation of particles, forming point islands with a sticking probability p in one dimension, is analyzed. Using Monte Carlo simulation we found that chi depends on p. For p=1 we obtain chi congruent with 1/4, the well-known result for perfect sticking and one-dimensional diffusion. Interestingly, as p is decreased, chi adopts higher values. Possible reasons for this behavior are addressed. The universal result for a one-dimensional diffusion, chi=1/4, is expected to be recovered, for all p, only in the asymptotic regime.