Self-diffusion of polymers in cartilage as studied by pulsed field gradient NMR

Pulsed field gradient (PFG) nuclear magnetic resonance (NMR) was used to investigate the self-diffusion behaviour of polymers in cartilage. Polyethylene glycol and dextran with different molecular weights and in different concentrations were used as model compounds to mimic the diffusion behaviour of metabolites of cartilage. The polymer self-diffusion depends extremely on the observation time: The short-time self-diffusion coefficients (diffusion time Delta approximately 15 ms) are subjected to a rather non-specific obstruction effect that depends mainly on the molecular weights of the applied polymers as well as on the water content of the cartilage. The observed self-diffusion coefficients decrease with increasing molecular weights of the polymers and with a decreasing water content of the cartilage. In contrast, the long-time self-diffusion coefficients of the polymers in cartilage (diffusion time Delta approximately 600 ms) reflect the structural properties of the tissue. Measurements at different water contents, different molecular weights of the polymers and varying observation times suggest that primarily the collagenous network of cartilage but also the entanglements of the polymer chains themselves are responsible for the observed restricted diffusion. Additionally, anomalous restricted diffusion was shown to occur already in concentrated polymer solutions

Dimer diffusion in a washboard potential

The transport of a dimer, consisting of two Brownian particles bounded by a harmonic potential, moving on a periodic substrate is investigated both numerically and analytically. The mobility and diffusion of the dimer center of mass present distinct properties when compared with those of a monomer under the same transport conditions. Both the average current and the diffusion coefficient are found to be complicated non-monotonic functions of the driving force. The influence of dimer equilibrium length, coupling strength and damping constant on the dimer transport properties are also examined in detail.Comment: Final revised version. 7 pages, 6 figure

The impact of draping effects on the stiffness and failure behavior of unidirectional non-crimp fabric fiber reinforced composites

Unidirectional non-crimp fabrics (UD-NCF) are often used to exploit the lightweight potential of continuous fiber reinforced plastics (CoFRP). During the draping process, the UD-NCF fabric can undergo large deformations that alter the local fiber orientation, the local fiber volume content (FVC) and create local fiber waviness. Especially the FVC is affected and has a large impact on the mechanical properties. This impact, resulting from different deformation modes during draping, is in general not considered in composite design processes. To analyze the impact of different draping effects on the mechanical properties and the failure behavior of UD-NCF composites, experimental results of reference laminates are compared to the results of laminates with specifically induced draping effects, such as non-constant FVC and fiber waviness. Furthermore, an analytical model to predict the failure strengths of UD laminates with in-plane waviness is introduced. The resulting stiffness and strength values for different FVC or amplitude to wavelength configurations are presented and discussed. In addition, failure envelopes based on the PUCK failure criterion for each draping effect are derived, which show a clear specific impact on the mechanical properties. The findings suggest that each draping effect leads to a “new fabric” type. Additionally, analytical models are introduced and the experimental results are compared to the predictions. Results indicate that the models provide reliable predictions for each draping effect. Recommendations regarding necessary tests to consider each draping effect are presented. As a further prospect the resulting stiffness and strength values for each draping effect can be used for a more accurate prediction of the structural performance of CoFRP parts

Collective shuttling of attracting particles in asymmetric narrow channels

The rectification of a single file of attracting particles subjected to a low frequency ac drive is proposed as a working mechanism for particle shuttling in an asymmetric narrow channel. Increasing the particle attraction results in the file condensing, as signalled by the dramatic enhancement of the net particle current. Magnitude and direction of the current become extremely sensitive to the actual size of the condensate, which can then be made to shuttle between two docking stations, transporting particles in one direction, with an efficiency much larger than conventional diffusive models predict

Diffusion of Tagged Particle in an Exclusion Process

We study the diffusion of tagged hard core interacting particles under the influence of an external force field. Using the Jepsen line we map this many particle problem onto a single particle one. We obtain general equations for the distribution and the mean square displacement of the tagged center particle valid for rather general external force fields and initial conditions. A wide range of physical behaviors emerge which are very different than the classical single file sub-diffusion $ \sim t^{1/2}$ found for uniformly distributed particles in an infinite space and in the absence of force fields. For symmetric initial conditions and potential fields we find $ = {{\cal R} (1 - {\cal R})\over 2 N {\it r} ^2} $ where $2 N$ is the (large) number of particles in the system, ${\cal R}$ is a single particle reflection coefficient obtained from the single particle Green function and initial conditions, and $r$ its derivative. We show that this equation is related to the mathematical theory of order statistics and it can be used to find even when the motion between collision events is not Brownian (e.g. it might be ballistic, or anomalous diffusion). As an example we derive the Percus relation for non Gaussian diffusion

Diffusion in nanopores recorded by microscopic measuring techniques

The poster presents two measuring techniques which, by their very nature, can be focused on, exclusively, microscopic dimensions, including the interior of the individual particles (crystallites) of the material under study. Correspondingly, they are referred to as “microscopic measuring techniques”. The examples presented refer, in particular, to the potentials of these techniques for investigating mass transfer in complex systems

On the applicability of thermoforming characterization and simulation approaches to glass mat thermoplastic composites

Chopped fiber composite materials offer the potential to be used for complex geometries, including local thickness changes, ribs and beads, offering significant potential for functional lightweighting. Depending on the initial mold coverage and flowability of the material, the processing behaves either more like a compression molding or a thermoforming process. The latter is applicable to high initial mold coverages and includes typical thermoforming defects such as local wrinkling. Such defects are not predictable by conventional compression molding simulation approaches usually adopted for this material class. Therefore, thermoforming characterization and simulation approaches and their applicability to glass mat thermoplastic (47 vol.% long glass fiber, Tepex Flowcore) for high initial mold coverages is investigated. Abaqus in combination with several user-subroutines is applied. Valid material characterization results from torsion bar and rheometer bending tests are obtained and applied to an automotive structure in thermoforming simulation. Results indicate that the high stiffness and high viscosity captured by the rheometer bending test at low shear-rates are necessary to reproduce the wrinkling behavior observed in the experimental results. Discrepancy is most likely reducible to thermomechanical effects, and that the modelling approach does not account for thickness deformation due to transverse compression

Langevin formulation for single-file diffusion

We introduce a stochastic equation for the microscopic motion of a tagged particle in the single file model. This equation provides a compact representation of several of the system's properties such as Fluctuation-Dissipation and Linear Response relations, achieved by means of a diffusion noise approach. Most important, the proposed Langevin Equation reproduces quantitatively the \emph{three} temporal regimes and the corresponding time scales: ballistic, diffusive and subdiffusive.Comment: 9 pages, 5 figures, 1 table, to appear in Physical Review

Exact results for the reactivity of a single-file system

We derive analytical expressions for the reactivity of a Single-File System with fast diffusion and adsorption and desorption at one end. If the conversion reaction is fast, then the reactivity depends only very weakly on the system size, and the conversion is about 100%. If the reaction is slow, then the reactivity becomes proportional to the system size, the loading, and the reaction rate constant. If the system size increases the reactivity goes to the geometric mean of the reaction rate constant and the rate of adsorption and desorption. For large systems the number of nonconverted particles decreases exponentially with distance from the adsorption/desorption end.Comment: 4 pages, 2 figure

Surface self-diffusion of organic molecules adsorbed in porous silicon

The pulsed field gradient nuclear magnetic resonance method has been employed to probe self-diffusion of organic guest molecules adsorbed in porous silicon with a 3.6 nm pore size. The molecular self-diffusion coefficient and intrapore adsorption were simultaneously measured as a function of the external vapor pressure. The latter was varied in a broad range to provide pore loading from less than monolayer surface coverage to full pore saturation. The measured diffusivities are found to be well-correlated with the adsorption isotherms. At low molecular concentrations in the pores, corresponding to surface coverages of less than one monolayer, the self-diffusion coefficient strongly increases with increasing concentration. This observation is attributed to the occurrence of activated diffusion on a heterogeneous surface. Additional experiments in a broad temperature range and using binary mixtures confirm this hypothesis. © 2005 American Chemical Society