The derivation of homogenized diffusion kurtosis models for diffusion MRI.

We use homogenization theory to establish a new macroscopic model for the complex transverse water proton magnetization in a voxel due to diffusion-encoding magnetic field gradient pulses in the case of biological tissue with impermeable membranes. In this model, new higher-order diffusion tensors emerge and offer more information about the structure of the biological tissues. We explicitly solve the macroscopic model to obtain an ordinary differential equation for the diffusion MRI signal that has similar structure as diffusional kurtosis imaging models. We finally present some validating numerical results on synthetic examples showing the accuracy of the model with respect to signals obtained by solving the Bloch-Torrey equation.

Tuning relaxation dynamics and mechanical properties of polymer films of identical thickness.

Using dewetting as a characterization tool, we demonstrate that physical properties of thin polymer films can be regulated and tuned by employing variable processing conditions. For different molecular weights, the variable behavior of polystyrene films of identical thickness, prepared along systematically altered pathways, became predictable through a single parameter P, defined as the ratio of time required over time available for the equilibration of polymers. In particular, preparation-induced residual stresses, the corresponding relaxation times as well as the rupture probability of such films (of identical thickness) varied by orders of magnitude following scaling relations with P. Our experimental findings suggest that we can predictably enhance properties and hence maximize the performance of thin polymer films via appropriately chosen processing conditions.

Time Allowed for Equilibration Quantifies the Preparation Induced Nonequilibrium Behavior of Polymer Films.

Performance and properties of materials may strongly depend on processing conditions. This is particularly so for polymers, which often have relaxation times much longer than the processing times and therefore may adopt preparation dependent nonequilibrated molecular conformations that potentially cause novel properties. However, so far it was not possible to predictably and quantitatively relate processing steps and resulting properties of polymer films. Here, we demonstrate that the behavior of polymer films, probed through dewetting, can be tuned by controlling preparation pathways, defined through a dimensionless parameter [Formula: see text], which is the appropriate preparation time normalized with the characteristic relaxation time of the polymer. We revealed scaling relations between [Formula: see text] and the amount of preparation-induced residual stresses, the corresponding relaxation time, and the probability of film rupture. Intriguingly, films of the same thickness exhibited hole nucleation densities and subsequent dewetting kinetics differing by up to an order of magnitude, indicating possibilities to adjust the desired properties of polymer films by preparing them in appropriate ways.