The cross-over from 2D to 3D percolation and its relationship to glass transition in thin films. Theory and numerical simulations

We consider here the percolation problem in thin films, both in the direction normal to the film and in the direction parallel to the film. We thereby describe here the cross-over between 2D and 3D percolation, which we do on cubic and square lattices. The main relations are derived using scaling and real space renormalisation arguments. They are checked by numerical simulations, which also provide the numerical prefactors. We calculate in particular the correlation length parallel to the film, the average mass and the mass distribution $n(m)$ of the clusters. In particular, we show that the latter is given by a master function of $h^{-D+1/\sigma_{2}\nu_{3}}| p-p_{c}(h)|^{1/\sigma_{2}} m$, where $h$ is the thickness of the film and $D,\nu_3,\sigma_2$ are tabulated 2D and 3D critical exponents. $p_c(h)$ is the percolation threshold of the film which we also calculate. These results are of interest in particular for describing the glass transition in thin polymer films.Comment: 14 figure

Dragging a polymer chain into a nanotube and subsequent release

We present a scaling theory and Monte Carlo (MC) simulation results for a flexible polymer chain slowly dragged by one end into a nanotube. We also describe the situation when the completely confined chain is released and gradually leaves the tube. MC simulations were performed for a self-avoiding lattice model with a biased chain growth algorithm, the pruned-enriched Rosenbluth method. The nanotube is a long channel opened at one end and its diameter $D$ is much smaller than the size of the polymer coil in solution. We analyze the following characteristics as functions of the chain end position $x$ inside the tube: the free energy of confinement, the average end-to-end distance, the average number of imprisoned monomers, and the average stretching of the confined part of the chain for various values of $D$ and for the number of monomers in the chain, $N$. We show that when the chain end is dragged by a certain critical distance $x^*$ into the tube, the polymer undergoes a first-order phase transition whereby the remaining free tail is abruptly sucked into the tube. This is accompanied by jumps in the average size, the number of imprisoned segments, and in the average stretching parameter. The critical distance scales as $x^*\sim ND^{1-1/\nu}$. The transition takes place when approximately 3/4 of the chain units are dragged into the tube. The theory presented is based on constructing the Landau free energy as a function of an order parameter that provides a complete description of equilibrium and metastable states. We argue that if the trapped chain is released with all monomers allowed to fluctuate, the reverse process in which the chain leaves the confinement occurs smoothly without any jumps. Finally, we apply the theory to estimate the lifetime of confined DNA in metastable states in nanotubes.Comment: 13pages, 14figure

Local chain deformation and overstrain in reinforced elastomers: An NMR study

A molecular-level understanding of the strain response of elastomers is a key to connect microscopic dynamics to macroscopic properties. In this study we investigate the local strain response of vulcanized, natural rubber systems and the effect of nanometer-sized filler particles, which are known to lead to highly improved mechanical properties. A multiple-quantum NMR approach enables the separation of relatively low fractions of network defects and allows to quantitatively and selectively study the local deformation distribution in the strained networks matrix on the microscopic (molecular) scale. We find that the presence of nondeformable filler particles induces an enhanced local deformation of the matrix (commonly referred to as overstrain), a slightly increased local stress/strain heterogeneity, and a reduced anisotropy. Furthermore, a careful analysis of the small nonelastic defect fraction provides new evidence that previous NMR and scattering results of strained defect-rich elastomers cannot be interpreted without explicitly taking the nonelastic defect fraction into account

Quantificação da biomassa na floresta estadual do Amapá: alometria e estimativas de estoque de carbono.

Material e métodos; Localização e caracterização da área; Inventário de biomassa; Inventário florestal das parcelas de biomassa; Estimativas de biomassa; Compartimentos da biomassa área e raízes das árvores; Equação de biomassa; Inventário florestal; Estimativa da biomassa fresca na FLOTA do Amapá; Estoque de carbono na FLOTA do Amapá; Teor de umidade; Teor de carbono; Estoque de carbono; Custo do levantamento de dados em campo para a quantificação da biomassa.bitstream/item/114961/1/CPAF-AP-2012-Quantificacao-da-biomassa.pd