Scientific publications

During the cycling of a lithium-ion battery, the active storage materials experience a volume change due to the intercalation process, often causing fracture, loss of contact among the active particles, and finally the degradation of the whole electrode. Here, we present a model for the lithium diffusion and stress generation in a particle of active material having a phase change. In our approach the driving force for diffusion is deduced from basic thermodynamics and statistical physics. The parameters of our model may be obtained from experimental measurements, or from ab-initio density functional theory calculations if the values are experimentally not accessible, as in the evaluation of new, as yet unsynthesized, computer-designed materials. We present results from simulations representing graphite known to experience phase-changes or staging. In some of our simulations, the particles are coupled to a battery simulator to apply conditions experienced in a functioning cell. We find that staging causes a significant increase in particle stress in comparison to when it is absent.

We utilize a model for birefringence/permittivity based on the statistical mechanics of a Gaussian polymer chain to construct a relationship for the dependence of the dielectric permittivity of an elastomer on a general 3-dimensional state of deformation. The model, due to Kuhn and Grün (1942 [1]), expresses the birefringence/permittivity of a Gaussian polymer chain elastomer as a function of the end-to-end distance of the chains, and assumes that the motions of the chains are affine to the overall deformation. The outcome is an expression for the permittivity tensor of the elastomer as a function of its stretch ratios. The permittivity is isotropic in the undeformed state and under pure dilatation, but otherwise becomes anisotropic during deformation. With this model, we use the free energy of the elastomer to compute the response of a neo-Hookean thin film in an actuator configuration subject to electric and mechanical loading for conditions where the permittivity in the through thickness direction is allowed to increase or decrease with the in-plane extension of the thin film. With such an approach, we study the deformation characteristics of the actuator and its stability under through thickness electric fields. Our calculations show that the deformation dependent permittivity can hasten or postpone an electromechanical instability that can cause a sudden thinning of the dielectric, accompanied by in-plane stretching, when the through thickness electric field is raised above a critical magnitude. Specifically, we consider the case of an actuator exhibiting a through thickness permittivity that decreases with in-plane extension. We observe that in such an actuator the instability is delayed to a higher electric field than would be the case if the dielectric permittivity were independent of strain. Furthermore, we establish that upon removal of the electric field the system follows a different path in terms of potential versus charge, and so develops a hysteresis loop, similar to that identified by Zhao et al. (2007 [2]) for dielectric elastomers with constant isotropic permittivity, but that stiffen during straining.

In this paper the problem of transformation toughening in anisotropic solids is addressed in the framework of Stroh formalism. The fundamental solutions for a transformed strain nucleus located in an infinite anisotropic elastic plane are derived first. Furthermore, the solution for the interaction of a crack tip with a residual strain nucleus is obtained. On the basis of these expressions, fundamental formulations are presented for the toughening arising from transformations using the Green's function method. Finally, a representative example is studied to demonstrate the relevance of the fundamental formulation.

Optimization of composition and microstructure is important to enhance performance of solid oxide fuel cells (SOFC) and lithium-ion batteries (LIB). For this, the porous electrode structures of both SOFC and LIB are modeled as a binary mixture of electronic and ionic conducting particles to estimate effective transport properties. Particle packings of 10 000 spherical, binary sized and randomly positioned particles are created numerically and densified considering the different manufacturing processes in SOFC and LIB: the sintering of SOFC electrodes is approximated geometrically, whereas the calendering process and volume change due to intercalation in LIB are modeled physically by a discrete element approach. A combination of a tracking algorithm and a resistor network approach is developed to predict the connectivity and effective conductivity for the various densified structures. For SOFC, a systematic study of the influence of morphology on connectivity and conductivity is performed on a large number of assemblies with different compositions and particle size ratios between 1 and 10. In comparison to percolation theory, an enlarged percolation area is found, especially for large size ratios. It is shown that in contrast to former studies the percolation threshold correlates to varying coordination numbers. The effective conductivity shows not only an increase with volume fraction as expected but also with size ratio. For LIB, a general increase of conductivity during the intercalation process was observed in correlation with increasing contact forces. The positive influence of calendering on the percolation threshold and the effective conductivity of carbon black is shown. The anisotropy caused by the calendering process does not influence the carbon black phase.

The effect of stress on storage particles within a lithium ion battery, while acknowledged, is not fully understood. In this study we identify three non-dimensional parameters which govern the stress response within a spherical storage particle, and we carry out numerical simulations to characterize the stresses that are developed. The non-dimensional parameters are developed using system properties such as the diffusion coefficient, particle radius, lithium partial molar volume and Young’s modulus. Stress maps are generated for various values of these parameters for fixed rates of insertion, with boundary conditions applied to particles similar to those found in a battery. Stress and lithium concentration profiles for various values of these parameters show that the coupling between stress and concentration is magnified depending on the values of the parameters. The resulting maps can be used for different materials, depending on the value of the dimensionless parameters. Finally, the value of maximum stress generated is calculated for extraction of lithium from the particle and compared with those generated during insertion.

Recent experiments in which arrays of compliant fibrils are compressed axially against a rigid surface and then released have shown that there is load-displacement hysteresis during this process, accompanied by buckling and unbuckling of the fibrils. Furthermore, the adhesive performance of the system is decreased by such prior buckling. We present a model describing the buckling and postbuckling characteristics of a fibril with an aspect ratio of 10 or greater. The possibility during buckling of partial detachment of the end of the fibril is taken into account. The results are presented and discussed for both load and displacement control and the load-displacement hysteresis is identified. It is found that due to instabilities sudden spreading and shrinkage of the adhered area at the end of the fibril can accompany the hysteresis. Numerical results are provided to substantiate the findings and possible reasons for the observed influence of buckling on adhesive performance are reviewed.

Event related potentials (ERPs) represent a noninvasive and widely available means to analyze neural correlates of sensory and cognitive processing. Recent developments in neural and cognitive engineering proposed completely new application fields of this wellestablished measurement technique when using an advanced singletrial processing. We have recently shown that twodimensional diffusion filtering methods from image processing can be used for the denoising of ERP singletrials in matrix representations, also called ERP images. In contrast to conventional onedimensional transient ERP denoising techniques, the twodimensional restoration of ERP images allows for an integration of regularities over multiple stimulations into the denoising process. Advanced anisotropic image restoration methods may require directional information for the ERP denoising process. This is especially true if there is a lack of a priori knowledge about possible traces in ERP images. However due to the use of event related experimental paradigms, ERP images are characterized by a high degree of selfsimilarity over the individual trials. In this paper, we propose the simple and easy to apply nonlocal means method for ERP image denoising in order to exploit this selfsimilarity rather than focusing on the edgebased extraction of directional information. Using measured and simulated ERP data, we compare our method to conventional approaches in ERP denoising. It is concluded that the selfsimilarity in ERP images can be exploited for singletrial ERP denoising by the proposed approach. This method might be promising for a variety of evoked and eventrelated potential applications, including non stationary paradigms such as changing exogeneous stimulus characteristics or endogenous states during the experiment. As presented, the proposed approach is for the a posteriori denoising of singletrial sequences.

Nanoparticles may be taken up into cells via endocytotic processes whereby the foreign particles are encapsulated in vesicles formed by lipid bilayers. After uptake into these endocytic vesicles, intracellular targeting processes and vesicle fusion might cause transfer of the vesicle cargo into other vesicle types, e.g., early or late endosomes, lysosomes, or others. In addition, nanoparticles might be taken up as single particles or larger agglomerates and the agglomeration state of the particles might change during vesicle processing. In this study, liposomes are regarded as simple models for intracellular vesicles. We compared the energetic balance between two liposomes encapsulating each a single silica nanoparticle and a large liposome containing two silica nanoparticles. Analytical expressions were derived that show how the energy of the system depends on the particle size and the distance between the particles. We found that the electrostatic contributions to the total energy of the system are negligibly small. In contrast, the van der Waals term strongly favors arrangements where the liposome snugly fits around the nanoparticle(s). Thus the two separated small liposomes have a more favorable energy than a larger liposome encapsulating two nanoparticles.

This paper proposes an advanced image enhancement method that is specifically tailored towards 3-D confocal and STED microscopy imagery. Our approach unifies image denoising, deblurring and interpolation in one joint method to handle the typical weaknesses of these advanced microscopy techniques: out-of-focus blur, Poisson noise and low axial resolution. In detail, we propose the combination of (i) Richardson–Lucy deconvolution, (ii) image restoration and (iii) anisotropic inpainting in one single scheme. To this end, we develop a novel PDE-based model that realizes these three ideas. First we consider a basic variational image restoration functional that is turned into a joint interpolation scheme by extending the regularization domain. Next, we integrate the variational representation of Richardson–Lucy deconvolution into our model, and illustrate its relation to Poisson distributed noise. In the following step, we supplement the components of our model with sub-quadratic penalization strategies that increase the robustness of the overall method. Finally, we consider the associated minimality conditions, where we exchange the occurring scalar-valued diffusivity function by a so-called diffusion tensor. This leads to an anisotropic regularization that is aligned with structures in the evolving image. As a further contribution of this paper, we propose a more efficient and faster semi-implicit iteration scheme that also increases the stability. Our experiments on real data sets demonstrate that this joint model achieves a superior reconstruction quality of the recorded cell.