Segment Motion in the Reptation Model of Polymer Dynamics. I. Analytical Investigation

We analyze the motion of individual beads of a polymer chain using a discrete version of De Gennes' reptation model that describes the motion of a polymer through an ordered lattice of obstacles. The motion within the tube can be evaluated rigorously, tube renewal is taken into account in an approximation motivated by random walk theory. We find microstructure effects to be present for remarkably large times and long chains, affecting essentially all present day computer experiments. The various asymptotic power laws, commonly considered as typical for reptation, hold only for extremely long chains. Furthermore, for an arbitrary segment even in a very long chain, we find a rich variety of fairly broad crossovers, which for practicably accessible chain lengths overlap and smear out the asymptotic power laws. Our analysis suggests observables specifically adapted to distinguish reptation from motions dominated by disorder of the environment.Comment: 38 pages in latex plus 8 ps figures, submitted to J. Stat. Phys. on September 18, 1997, please note part II on cond-mat/971006

Segment Motion in the Reptation Model of Polymer Dynamics. II. Simulations

We present simulation data for the motion of a polymer chain through a regular lattice of impenetrable obstacles (Evans-Edwards model). Chain lengths range from N=20 to N=640, and time up to $10^{7}$ Monte Carlo steps. For $N \geq 160$ we for the central segment find clear $t^{1/4}$-behavior as an intermediate asymptote. The also expected $t^{1/2}$-range is not yet developed. For the end segment also the $t^{1/4}$-behavior is not reached. All these data compare well to our recent analytical evaluation of the reptation model, which shows that for shorter times (t \alt 10^{4}) the discreteness of the elementary motion cannot be neglected, whereas for longer times and short chains (N \alt 100) tube renewal plays an essential role also for the central segment. Due to the very broad crossover behavior both the diffusion coefficient and the reptation time within the range of our simulation do not reach the asymptotic power laws predicted by reptation theory. We present results for the center-of-mass motion, showing the expected intermediate $t^{1/2}$-behavior, but again only for very long chains. In addition we show results for the motion of the central segment relative to the center of mass, where in some intermediate range we see the expected increase of the effective power beyond the $t^{1/4}$-law, before saturation sets in. Analysis and simulations agree on defining a new set of criteria as characteristic for reptation of finite chains.Comment: 19 pages in latex plus 13 ps figures, submitted to J. Stat. Phys. on September 18, 199

On the orientational ordering of long rods on a lattice

We argue that a system of straight rigid rods of length k on square lattice with only hard-core interactions shows two phase transitions as a function of density, rho, for k >= 7. The system undergoes a phase transition from the low-density disordered phase to a nematic phase as rho is increased from 0, at rho = rho_c1, and then again undergoes a reentrant phase transition from the nematic phase to a disordered phase at rho = rho_c2 < 1.Comment: epl.cl

Estabilidade de agregados, distribuição e perda de carbono em um latossolo vermelho amarelo sob diferentes manejos no bioma Amazônia.

O objetivo deste estudo foi avaliar as alterações causadas na estabilidade de agregados, distribuição e perda de C em agregados em solo submetido a sistemas exclusivos de cultivo em comparação ao sistema de integração lavoura-pecuária-floresta.. As avaliações foram realizadas em Sinop-MT, em Latossolo Vermelho Amarelo. Os tratamentos foram: Floresta: (floresta plantada com eucalipto); Lavoura: (lavoura com sucessão soja na safra e milho segunda safra consorciado com braquiária); Pastagem: (pastagem de B. brizantha (U. brizantha) cv Marandu); ILPF: (sistema integração lavoura-pecuária-floresta com floresta de eucalipto e cultivo entre renques de soja na safra e milho consorciado com pasto na segunda safra). O delineamento utilizado foi de blocos ao acaso com quatro repetições. Para as análises de estabilidade de agregados e distribuição de carbono foram retiradas de cada tratamento amostras indeformadas (monólitos), nas camadas de 0-5 cm, 5-10 cm e 10-20 cm. Ao analisar os agregados não foram observadas diferenças para DMP (diâmetro médio ponderado) e DMG (diâmetro médio geométrico) nas camadas de 0-5 e 10-20 cm. Porém, na camada de 5-10 cm o tratamento pastagem mostrou os maiores DMP (4,91 mm) e DMG (3,35 mm). As classes de agregados retidas nas peneiras 1,00 e 0,50 mm apresentaram os maiores teores de C nas três camadas estudadas, porém entre manejos não houve diferença significativa. No período considerado, apenas o DMG foi sensível às mudanças ocasionadas pelo sistema ILPF na camada superficial ao longo das distâncias dos renques de árvores. Após três anos de implantação, o sistema ILPF não promoveu alterações na agregação do solo comparado com os cultivos exclusivos.Dissertação (Mestrado em Agronomia) ­- Universidade Federal de Mato Grosso. Orientador: Eduardo da Silva Matos, CPAMT

Phase Transitions of Single Semi-stiff Polymer Chains

We study numerically a lattice model of semiflexible homopolymers with nearest neighbor attraction and energetic preference for straight joints between bonded monomers. For this we use a new algorithm, the "Pruned-Enriched Rosenbluth Method" (PERM). It is very efficient both for relatively open configurations at high temperatures and for compact and frozen-in low-T states. This allows us to study in detail the phase diagram as a function of nn-attraction epsilon and stiffness x. It shows a theta-collapse line with a transition from open coils to molten compact globules (large epsilon) and a freezing transition toward a state with orientational global order (large stiffness x). Qualitatively this is similar to a recently studied mean field theory (Doniach et al. (1996), J. Chem. Phys. 105, 1601), but there are important differences. In contrast to the mean field theory, the theta-temperature increases with stiffness x. The freezing temperature increases even faster, and reaches the theta-line at a finite value of x. For even stiffer chains, the freezing transition takes place directly without the formation of an intermediate globule state. Although being in contrast with mean filed theory, the latter has been conjectured already by Doniach et al. on the basis of low statistics Monte Carlo simulations. Finally, we discuss the relevance of the present model as a very crude model for protein folding.Comment: 11 pages, Latex, 8 figure

Interacting Crumpled Manifolds: Exact Results to all Orders of Perturbation Theory

In this letter, we report progress on the field theory of polymerized tethered membranes. For the toy-model of a manifold repelled by a single point, we are able to sum the perturbation expansion in the strength g of the interaction exactly in the limit of internal dimension D -> 2. This exact solution is the starting point for an expansion in 2-D, which aims at connecting to the well studied case of polymers (D=1). We here give results to order (2-D)^4, where again all orders in g are resummed. This is a first step towards a more complete solution of the self-avoiding manifold problem, which might also prove valuable for polymers.Comment: 8 page

Anomalous Dynamics of Translocation

We study the dynamics of the passage of a polymer through a membrane pore (translocation), focusing on the scaling properties with the number of monomers $N$. The natural coordinate for translocation is the number of monomers on one side of the hole at a given time. Commonly used models which assume Brownian dynamics for this variable predict a mean (unforced) passage time $\tau$ that scales as $N^2$, even in the presence of an entropic barrier. However, the time it takes for a free polymer to diffuse a distance of the order of its radius by Rouse dynamics scales with an exponent larger than 2, and this should provide a lower bound to the translocation time. To resolve this discrepancy, we perform numerical simulations with Rouse dynamics for both phantom (in space dimensions $d=1$ and 2), and self-avoiding (in $d=2$) chains. The results indicate that for large $N$, translocation times scale in the same manner as diffusion times, but with a larger prefactor that depends on the size of the hole. Such scaling implies anomalous dynamics for the translocation process. In particular, the fluctuations in the monomer number at the hole are predicted to be non-diffusive at short times, while the average pulling velocity of the polymer in the presence of a chemical potential difference is predicted to depend on $N$.Comment: 9 pages, 9 figures. Submitted to Physical Review