A mean-field monomer-dimer model with random monomer activities. Exact solution and rigorous results

Independent random monomer activities are considered on a mean-feld monomer-dimer model. Under very general conditions on the randomness the model is shown to have a self-averaging pressure density that obeys a solvable variational principle. The dimer density is exactly computed in the thermodynamic limit and shown to be a smooth function.Comment: 20 page

Exact Solution of a Monomer-Dimer Problem: A Single Boundary Monomer on a Non-Bipartite Lattice

We solve the monomer-dimer problem on a non-bipartite lattice, the simple quartic lattice with cylindrical boundary conditions, with a single monomer residing on the boundary. Due to the non-bipartite nature of the lattice, the well-known method of a Temperley bijection of solving single-monomer problems cannot be used. In this paper we derive the solution by mapping the problem onto one on close-packed dimers on a related lattice. Finite-size analysis of the solution is carried out. We find from asymptotic expansions of the free energy that the central charge in the logarithmic conformal field theory assumes the value $c=-2$.Comment: 15 pages, 1 figure, submitted to Phy. Rev. E; v2: revised Acknowledgment

Symmetry-breaking in chiral polymerisation

We propose a model for chiral polymerisation and investigate its symmetric and asymmetric solutions. The model has a source species which decays into left- and right-handed types of monomer, each of which can polymerise to form homochiral chains; these chains are susceptible to `poisoning' by the opposite handed monomer. Homochiral polymers are assumed to influence the proportion of each type of monomer formed from the precursor. We show that for certain parameter values a positive feedback mechanism makes the symmetric steady-state solution unstable. The kinetics of polymer formation are then analysed in the case where the system starts from zero concentrations of monomer and chains. We show that following a long induction time, extremely large concentrations of polymers are formed for a short time, during this time an asymmetry introduced into the system by a random external perturbation may be massively amplified. The system then approaches one of the steady-state solutions described above.Comment: 26pages, 6 Figure

Random Polyelectrolytes and Polyampholytes in Solution

The behavior of polyelectrolytes and polyampholytes in semi-dilute solutions is investigated theoretically. Various statistical charge distributions along the polyelectrolyte chains are considered: smeared, annealed, permuted and quenched. Annealed polyampholytes are also considered. Path integral formulation was used to derive mean field free energies for the different models. Self-consistent field equation is obtained for the polymer order parameter and a Poisson-Boltzmann like equation for the electrostatic potential. The random phase approximation is used to calculate the monomer-monomer structure factor S(q) for the different statistical charge distribution models. We show that in the annealed model, fluctuations of the the monomer charges contribute to the electrostatic screening in addition to the free ions in the solution. The strength of this screening depends on the variance of the monomer charge distribution and is especially important for polyampholytes in bad solvent conditions where the mesophase separation is enhanced. The ratio between the variance and the net average charge determines whether polyampholytes behave as polyelectrolytes or as neutral chains.Comment: 18 pages, 5 figures, submitted to Eur. Phys. J.

The Pfaffian solution of a dimer-monomer problem: Single monomer on the boundary

We consider the dimer-monomer problem for the rectangular lattice. By mapping the problem into one of close-packed dimers on an extended lattice, we rederive the Tzeng-Wu solution for a single monomer on the boundary by evaluating a Pfaffian. We also clarify the mathematical content of the Tzeng-Wu solution by identifying it as the product of the nonzero eigenvalues of the Kasteleyn matrix.Comment: 4 Pages to appear in the Physical Review E (2006

Driven translocation of a polymer: role of pore friction and crowding

Force-driven translocation of a macromolecule through a nanopore is investigated by taking into account the monomer-pore friction as well as the "crowding" of monomers on the {\it trans} - side of the membrane which counterbalance the driving force acting in the pore. The set of governing differential-algebraic equations for the translocation dynamics is derived and solved numerically. The analysis of this solution shows that the crowding of monomers on the trans side hardly affects the dynamics, but the monomer-pore friction can substantially slow down the translocation process. Moreover, the translocation exponent $\alpha$ in the translocation time - vs. - chain length scaling law, $\tau \propto N^{\alpha}$, becomes smaller when monomer-pore friction coefficient increases. This is most noticeable for relatively strong forces. Our findings may explain the variety of $\alpha$ values which were found in experiments and computer simulations.Comment: 12 page

Effect of ester impurities in PMR-polyimide resin

Spectral and chomatographic studies were conducted which established the presence of tri- and tetraester impurities in aged monomer solutions employed in fabrication of PMR-polyimide resin composites. The equilibrium constant and apparent rate of the esterification were determined. It was demonstrated, using differential scanning calorimetry, that the ortho-ester moiety of these impurities does not completely react at typical cure conditions. It is concluded that voids formed in composites fabricated with aged monomer solution are due to gaseous decomposition products evolved by ester impurities and/or unreacted amine during elevated temperature post-cure treatment

The Force-Velocity Relation for Growing Biopolymers

The process of force generation by the growth of biopolymers is simulated via a Langevin-dynamics approach. The interaction forces are taken to have simple forms that favor the growth of straight fibers from solution. The force-velocity relation is obtained from the simulations for two versions of the monomer-monomer force field. It is found that the growth rate drops off more rapidly with applied force than expected from the simplest theories based on thermal motion of the obstacle. The discrepancies amount to a factor of three or more when the applied force exceeds 2.5kT/a, where a is the step size for the polymer growth. These results are explained on the basis of restricted diffusion of monomers near the fiber tip. It is also found that the mobility of the obstacle has little effect on the growth rate, over a broad range.Comment: Latex source, 9 postscript figures, uses psfig.st