Semiflexible polymer in a strip

We study the thermodynamic properties of a semiflexible polymer confined inside strips of widths L<=9 defined on a square lattice. The polymer is modeled as a self-avoiding walk and a short range interaction between the monomers and the walls is included through an energy e associated to each monomer placed on one of the walls. Also, an additional energy is associated to each elementary bend of the walk. The free energy of the model is obtained exactly through a transfer matrix formalism. The profile of the monomer density and the force on the walls are obtained. We notice that as the bending energy is decreased, the range of values of e for which the density profile is neither convex nor concave increases, and for sufficiently attracting walls (e<0) we find that in general the attractive force is maximum for situations where the bends are favored.Comment: 5 pages, 6 figure

Nature of the collapse transition in interacting self-avoiding trails

We study the interacting self-avoiding trail (ISAT) model on a Bethe lattice of general coordination $q$ and on a Husimi lattice built with squares and coordination $q=4$. The exact grand-canonical solutions of the model are obtained, considering that up to $K$ monomers can be placed on a site and associating a weight $\omega_i$ for a $i$-fold visited site. Very rich phase diagrams are found with non-polymerized (NP), regular polymerized (P) and dense polymerized (DP) phases separated by lines (or surfaces) of continuous and discontinuous transitions. For Bethe lattice with $q=4$ and $K=2$, the collapse transition is identified with a bicritical point and the collapsed phase is associated to the dense polymerized phase (solid-like) instead of the regular polymerized phase (liquid-like). A similar result is found for the Husimi lattice, which may explain the difference between the collapse transition for ISAT's and for interacting self-avoiding walks on the square lattice. For $q=6$ and $K=3$ (studied on the Bethe lattice only), a more complex phase diagram is found, with two critical planes and two coexistence surfaces, separated by two tricritical and two critical end-point lines meeting at a multicritical point. The mapping of the phase diagrams in the canonical ensemble is discussed and compared with simulational results for regular lattices.Comment: 12 pages, 13 figure

A general creation-annihilation model with absorbing states

A one dimensional non-equilibrium stochastic model is proposed where each site of the lattice is occupied by a particle, which may be of type A or B. The time evolution of the model occurs through three processes: autocatalytic generation of A and B particles and spontaneous conversion A to B. The two-parameter phase diagram of the model is obtained in one- and two-site mean field approximations, as well as through numerical simulations and exact solution of finite systems extrapolated to the thermodynamic limit. A continuous line of transitions between an active and an absorbing phase is found. This critical line starts at a point where the model is equivalent to the contact process and ends at a point which corresponds to the voter model, where two absorbing states coexist. Thus, the critical line ends at a point where the transition is discontinuous. Estimates of critical exponents are obtained through the simulations and finite-size-scaling extrapolations, and the crossover between universality classes as the voter model transition is approached is studied.Comment: 9 pages and 17 figure

The nature of attraction between like charged rods

Comment on the paper of Ha and Liu (Phys. Rev. Lett. {\bf 79}, 1289 (1997)) regarding the nature of attraction between like charged rods. We demostrate that their results do not produce the correct low temperature limit.Comment: Comment to appear in Phys. Rev. Let

Thermodynamic Behavior of Polymers on the Anisotropic Husimi Lat tice

We study a model for equilibrium polymerization on an anisotropic Husimi lattice of coordination number equal&apos;to four, so that an additional energy E is associated with each bond of the polymer in a particular direction of the lattice. Two different polymerized phases are found in the phase diagram of the model, one of them having all lattice sites visited by the polymer. We compare our results with earlier Bethe lattice calculations on the same model

Cooperative gas adsorption without a phase transition in metal-organic frameworks

Cooperative adsorption of gases by porous frameworks permits more efficient uptake and removal than does the more usual non-cooperative (Langmuir-type) adsorption. Cooperativity, signaled by a step-like isotherm, is usually attributed to a phase transition of the framework. However, the class of metal-organic frameworks mmen-M$_2$(dobpdc) exhibit cooperative adsorption of CO2 but show no evidence of a phase transition. Here we show how cooperativity emerges in these frameworks in the absence of a phase transition. We use a combination of quantum and statistical mechanics to show that cooperativity results from a sharp but finite increase, with pressure, of the mean length of chains of CO2 molecules that polymerize within the framework. Our study provides microscopic understanding of the emergent features of cooperative binding, including the position, slope and height of the isotherm step, and indicates how to optimize gas storage and separation in these materials.Comment: 18 pages, 11 figure

Kinetic model for a polmer in one dimension

We consider a model for a directed polymer on a one-dimensional lattice of width 2, with attractive interactions between monomers that occupy first-neighbor sites on the lattice and are not consecutive along the chain. We show that this model is equivalent to the one-dimensional Ising model with first- and second-neighbor interactions. We study the kinetic behavior of the model in the region of the phase diagram where the ground state is not frustrated, using a Glauber ansatz for the time evolution of the configurations. In order to decouple the dynamical equations, we use the pair approximation. In this approximation, we show that the dynamical exponent of the model is a function of the ratio between second- and first-neighbor interaction strengths

Kinetic model for a polmer in one dimension

We consider a model for a directed polymer on a one-dimensional lattice of width 2, with attractive interactions between monomers that occupy first-neighbor sites on the lattice and are not consecutive along the chain. We show that this model is equivalent to the one-dimensional Ising model with first- and second-neighbor interactions. We study the kinetic behavior of the model in the region of the phase diagram where the ground state is not frustrated, using a Glauber ansatz for the time evolution of the configurations. In order to decouple the dynamical equations, we use the pair approximation. In this approximation, we show that the dynamical exponent of the model is a function of the ratio between second- and first-neighbor interaction strengths