9 research outputs found

    Mathematik in der Tradition des Neukantianismus / Siegener Beiträge zur Geschichte und Philosophie der Mathematik 2019

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    Enthält nicht nur Beiträge der internationalen Tagung "Mathematik in der Tradition des Neukantianismus" an der Universität Siegen, Emmy-Noether-Campus, 15.-16.3.2018"Mathematik in der Tradition des Neukantianismus" war das Thema einer internationalen Tagung, die im März 2018 in Siegen stattfand. Dass die Philosophie der Mathematik für die Autoren dieser Denktradition ein zentrales Anliegen war, ist einerseits selbstverständlich. Spielt doch bereits für Kant das ’Phänomen Mathematik’ in vielerlei Hinsicht eine Schlüsselrolle. Auf der anderen Seite werden der historische Blick auf das frühe 20. Jahrhundert wie auch die aktuellen Überlegungen zur Philosophie der Mathematik dominiert von Autoren analytischer Prägung. Der erste Teil des Bandes enthält die Tagungsbeiträge. Drei weitere Beiträge zu Kurt Gödel, Nikolaus Cusanus und Heinrich Behmann runden die farbenfrohe Palette dieser Siegener Beiträge ab.Inhalt: Mathematik in der Tradition des Neukantianismus: Gottfried Gabriel & Sven Schlotter: Freges Philosophie der Mathematik im Kontext des Neukantianismus Kay Herrmann: Leonard Nelson: Mathematische Erkenntnis als synthetisches Apriori Daniel Koenig: Ernst Cassirer und der mathematische Raum – vom Erkenntnisproblem zum Symbolproblem Thomas Mormann: Mathematische Wissenschaftsphilosophie im Marburger Neukantianismus Matthias Neuber: Cassirer, der Grundlagenstreit und die „idealen Elemente“ der Mathematik Shafie Shokrani: Die Philosophie der Mathematik und die Sokratische Methode Leonard Nelsons – Ein Überblick Siegener Beiträge zur Geschichte und Philosophie der Mathematik: Merlin Carl & Eva-Maria Engelen: Einige Bemerkungen Kurt Gödels zur Mengenlehre Gregor Nickel: Nec finitum – nec infinitum. Überlegungen zur Rolle der Mathematik in der Kosmologie des Nikolaus Cusanus Christian Thiel: Heinrich Behmanns Beitrag zur Grundlagendebatt

    Construction of biocompatible and electrically conductive coatings consisting of carbon nanotubes and polyelectrolytes

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    The combination of the Layer-by-Layer (LbL) method, a nano-material such as carbon nanotubes (CNTs), and charged polyelectrolytes (PEs) is a reliable approach to produce highly functionalized surface coatings. These coatings are stable, controllable, ultra-thin, and most importantly, biocompatible. The ability to tune their properties by varying the preparation conditions and the terminating layer opens up a wide range of applications in the fields of biology and medicine. Here, the goal was to create electrically conductive coatings on which cells grow and proliferate. To achieve this goal, a coating with a stable conductive film structure, a suitable film surface topography, and suitable surface potential (and -potential) must be prepared. At the beginning of this thesis, the focus was on the fabrication of electrically conductive multilayer films, whose electrical properties should be stable and adjustable in a controlled manner (Article 1). The combination of chemically modified CNTs as polyanions, a strong linear polycation like poly(diallyldimethylammonium chloride) (PDADMA), and the LbL-method allowed us to prepare such films. Their characterization was carried out in air at ambient conditions. Since PDADMA is non-conductive, the charge transfer within the film and thus the electrical conductivity itself depends mainly on the CNTs and their arrangement. It was found that four CNT/PDADMA bilayers (BL) were always necessary to create a lateral network structure with multiple CNT crossing points to enable and support electron transport within the film. Moreover, additional CNT/PDADMA BL resulted in decreasing sheet resistance, while the conductivity remained constant at ≈ 4 kS/m regardless of the number of bilayers. Increasing the PDADMA molecular weight (Mw) from 44.4 kDa to 322 kDa did not affect film properties such as thickness or electrical conductivity. However, increasing the CNT concentration from 0.15 mg/ml to 0.25 mg/ml in the deposition suspension resulted in thicker and less conductive films. This is attributed to a faster adsorption process of the CNTs leading to more adsorption sites for the polycation. We found an increased PDADMA monomer/CNT ratio compared to films prepared with the lower CNT concentration in the deposition suspension. The electrical conductivity decreased by a factor of four down to 1.1 kS/m, which can be attributed to fewer contact points between the CNTs. Overall, we were able to prepare stable and electrically conductive multilayer films. Additionally, by varying the preparation conditions tuning of the electrical conductivity is possible. To fulfill requirements regarding i.e., medical implants, film properties not only have to be stable and controllable in a dry state (described in Article 1) but also in a biological aqueous environment. Therefore, in Article 2 we immersed our coated samples in three different solutions usually employed in biological research and compared their properties with their dry state, respectively. Also, hydration/swelling effects that normally occur for polyelectrolyte multilayer films (PEMs) in solutions were investigated. For the film preparation, PDADMA (Mw = 322 kDa) and a deposition suspension of modified CNTs with two different concentrations (0.15 mg/ml and 0.25 mg/ml), which aged for two years, were used. Independent of the CNT suspension concentration, it turned out that the film thickness of the samples, prepared from the aged suspension, decreased significantly compared to the film thickness previously measured in Article 1. As a cross-check a new and fresh CNT suspension was made, which allowed us to reproduce the film thickness described in Article 1. These results indicated that something happened with the CNT suspension over a two-year period. An analysis via X-ray photoelectron spectroscopy (XPS) showed a decrease in the percentage of functional groups in the CNTs from the aged suspension. The loss of functional groups resulted in less negatively charged CNTs and thus in fewer adsorption sites for the polycation PDADMA. Consequently, the PDADMA monomer/CNT ratio decreased, which lowered the thickness per bilayer by a factor of three, compared to films prepared with a freshly prepared CNT suspension. The lower linear charge density of the aged CNTs also enhanced their hydrophobicity, which is, in combination with the electrostatic forces, another important factor for multilayer cohesion. In contrast to PEMs made from polycations and polyanions, no swelling of the films occurred when immersed in solutions. This can be attributed to the fact that the increased hydrophobicity of the CNTs and the hydrophobic nature of the PDADMA backbone prevent the incorporation of water into the multilayer film. In solution, the films slightly shrink (by ≈ 2 nm), which makes them even more compact. Yet they remain stable. The result is an increased electrical conductivity from 9.6 kS/m, in the dry state, up to 15.3 kS/m immersed in solutions. To summarize, we showed that by tuning the interpolyelectrolyte forces the swelling and the ensuing decrease of the electrical conductivity of the films can be prevented. Regarding the application in biology and medicine, we must consider that long-term exposure of cells to nano-materials like CNTs could lead to damage and inflammation of adjacent tissue. Therefore, it is necessary to prevent direct contact between the electrically conductive multilayer, i.e., CNT/PDADMA film, and the cells. The solution to this problem is a biocompatible top film that covers the CNT/PDADMA multilayer completely and still provides a lateral surface structure that supports cell adhesion and proliferation. Additional layers consisting solely of PEs could provide such a top film. In Article 3 we investigated the self-patterning of PEM films as function of deposition steps. After preparation in water, the films were dried, characterized in air, and in vacuum. The films were built with high and low molecular weight PEs. PDADMA was used as polycation and poly(styrene sulfonate) sodium salt (PSS) as polyanion. The observation via Atomic Force Microscopy (AFM) showed that films prepared with high molecular weight PEs are laterally homogeneous and form no patterns, due to the chain immobility. The flat surfaces are ineligible as a substrate for cell adhesion. In contrast, films built with a short PSS, especially at Mw, PSS = 10.7 kDa, began to self-pattern after seven deposited PDADMA/PSS bilayers. With each additionally deposited bilayer, the surface got more and more structured, from grooves over stripes to circular domains. Increasing film thickness led to an increased lateral mean distance between the surface structures. Scanning Electron Microscopy (SEM) images showed that exposure to a vacuum resulted in a decrease in the film thickness attributed to water removal, while the mean distance between the domains increased. Thus, by using this self-pattering process we are able to prepare PEMs with a highly structured surface. By adding PDADMA/PSS bilayers, not only the CNT/PDADMA film can be covered completely, but also a suitable surface morphology for cells can be created. Controlling the number of deposited bilayers allows the preparation of suitable coatings for cells. To further improve the interaction of the cell and coated substrate not only the lateral structure but also the interacting electrostatic forces between cells and substrate are important for the nature of cell adhesion, function, and proliferation. In Article 4 we investigated PEMs, consisting of strong PEs with a low (PDADMA) and high (PSS) linear charge density. We performed asymmetric force measurements with the help of the colloidal probe technique (CP). Here, the forces between a PEM-covered surface and a colloidal probe (silica sphere) glued to a cantilever were investigated. The colloidal probe was either bare or covered with polycation poly(ethylenimine) (PEI). The surfaces were immersed in NaCl solutions with different ionic strengths (INaCl), starting with deionized water, then enriched up to 1 mol/L NaCl. The interaction force between a CP and the surface was measured. Thus, insight into the surface potential/charge was obtained. During film preparation, two growth regimes (parabolic and linear) exist. These regimes and the terminating layer determine the surface force of the PEM. PEMs with a terminating PSS layer are predominantly flat and negatively charged when the ion concentration is low and the film is in the parabolic growth regime (between 1 and ≈ 15 BL). This indicates charge reversal on PSS adsorption. At the transition point between the parabolic and linear growth regimes, the ratio between polyanion and polycation monomers starts to switch and some cationic monomers are neutralized not by anionic monomers but by monovalent ions. Therefore, the surface charge density in diluted NaCl solutions changed from slightly positive near the transition to positive in the linear growth regime. At the lowest ionic strengths (INaCL) the range of the surface potential goes from – 40.5 mV (9 BL, parabolic) up to + 50 mV (19 BL, linear). In contrast, polycation (PDADMA) terminated films are overall positive in diluted NaCl solutions. At the beginning of the parabolic growth regime, the layers are more compact and flat. However, with each additional layer deposited, the film becomes less compact and the chains begin to loosen. The now more loosely bound chains start to protrude into the solution and form pseudo-brushes. This could already be observed for 10.5 BL. It intensifies in the linear growth regime (begin at ≈ 15 BL) and results in steric surface forces. Changing the surrounding INaCl affects this behavior and the pseudo-brushes scale as polyelectrolyte brushes. By controlling the number of bilayers (thus the growth regime), the surrounding ionic strength, and the conformation of PEs at the PEM surface, it is possible to prepare a suitable range of surface properties i.e., for cell adhesion and proliferation. To prove that these multilayers can provide a suitable surface and have a positive effect on cell behavior, we coated in Article 5 titanium-covered samples with PEMs. Investigated was the cell interaction with the surface at different zeta(ζ) - potentials, a parameter for dynamic surface potential. Here the cell activity is measured by the mobilization of calcium (Ca2+) within the cell as a function of the ζ - potential of the substrate and the externally applied electrical potential. The cell activity indicates if the ζ - potential, provided by the sample surface, is suitable or not for the cells. The favorable interaction with the substrate is also reflected in the cell morphology and proliferation. The results showed that highly negative ζ - potentials between - 90 and - 3 mV led to a decreasing/reduced Ca2+ mobilization which correlates with reduced cell activity. Nearly neutral to moderate positive surfaces (ζ - potential + 1 to + 10 mV) i.e., PSS-terminated PEMs are able to promote cell adhesion and growth as demonstrated by an increased Ca2+ mobilization. The access to the intracellular Ca2+ stores, provided by the external stimulus, is now more effective and suggests a higher cell activity. Increasing the ζ - potentials up to ≈ + 50 mV (highly positive), i.e., PDADMA - terminated PEMs with pseudo-brushes, resulted in restricted cell viability and impaired Ca2+ mobilization, which led to a disturbed cell morphology and proliferation. In conclusion, only surfaces, terminated with i.e., PEI, with moderate positive charges (ζ - potential + 1 to + 10 mV) are able to improve the Ca2+ mobilization and thus the cell activity and proliferation. PEMs with a PSS termination provide negative −potentials, onto which cells adhere, and proliferate. Therefore, they are a good alternative for surface functionalization for implant surfaces. In summary, the objective set at the beginning of the thesis is addressed within articles written as part of this thesis. It is possible to fabricate PEMs with modified CNTs to produce coatings that are electrically conductive with tunable sheet resistance, whether dry in air or immersed in an aqueous solution (Articles 1 and 2). Also, for pure PEMs, it is shown that with the right molecular weight of PEs and a certain number of bilayers, a suitable surface structure for cell adhesion can be produced (Article 3). Additional surface properties such as a suitable surface charge density can be provided by PEMs which can improve the cell activity as monitored with Ca2+ mobilization (Articles 4 and 5). The next step is to combine the knowledge gained from Articles 1 – 5 and link it to the application of external electrical fields to cells

    Influence of Different Solutions on Electrically Conductive Films Composed of Carbon Nanotubes and Polydimethyldiallylammonium

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    For engineering and biomedical applications, nanometer-thin films with high electrical conductivity in aqueous solutions are desirable. Multilayers of polydimethyldiallylammonium chloride (PDADMA) and oxidized carbon nanotubes (CNTs) were built using the layer-by-layer technique. CNTs with a low linear charge density were used. The surface coverage of the CNTs was monitored with optical absorption. The film thickness and the surface coverage of the CNTs increased linearly with the number of CNT/PDADMA bilayers deposited. On immersion into aqueous solutions, the film thickness decreased or remained constant. This finding is attributed to the hydrophobic character of the CNTs and the backbone of PDADMA. The films showed ohmic behavior, both in air and in solutions. The electrical conductivity was 0.95 × 104 S/m in air and increased to 1.36 × 104 S/m in solution, provided the thickness of the CNT/PDADMA bilayers was as low as 1.9 nm. We suggest that high electrical conductivity can be achieved by flat adsorption of the CNTs

    Response of Osteoblasts to Electric Field Line Patterns Emerging from Molecule Stripe Landscapes

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    Molecular surface gradients can constitute electric field landscapes and serve to control local cell adhesion and migration. Cellular responses to electric field landscapes may allow the discovery of routes to improve osseointegration of implants. Flat molecule aggregate landscapes of amine- or carboxyl-teminated dendrimers, amine-containing protein and polyelectrolytes were prepared on glass to provide lateral electric field gradients through their differing zeta potentials compared to the glass substrate. The local as well as the mesoscopic morphological responses of adhered osteoblasts (MG-63) with respect to the stripes were studied by means of Scanning Ion Conductance Microscopy (SICM) and Fluorescence Microscopy, in situ. A distinct spindle shape oriented parallel to the surface pattern as well as a preferential adhesion of the cells on the glass site have been observed at a stripe and spacing width of 20 μm. Excessive ruffling is observed at the spindle poles, where the cells extend. To explain this effect of material preference and electro-deformation, we put forward a retraction mechanism, a localized form of double-sided cathodic taxis

    Automatic Actin Filament Quantification and Cell Shape Modeling of Osteoblasts on Charged Ti Surfaces

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    Surface charges at the cell–biomaterial interface are known to determine cellular functions. Previous findings on cell signaling indicate that osteoblastic cells favor certain moderately positive surface charges, whereas highly positive charges are not tolerated. In this study, we aimed to gain deeper insights into the influence exerted by surface charges on the actin cytoskeleton and the cell shape. We analyzed surfaces with a negative, moderately positive, and highly positive zeta (ζ) potential: titanium (Ti), Ti with plasma polymerized allylamine (PPAAm), and Ti with a polydiallyldimethylammonium chloride (PDADMA) multilayer, respectively. We used the software FilaQuant for automatic actin filament quantification of osteoblastic MG-63s, analyzed the cell edge height with scanning ion conductance microscopy (SICM), and described the cellular shape via a mathematical vertex model. A significant enhancement of actin filament formation was achieved on moderately positive (+7 mV) compared with negative ζ-potentials (−87 mV). A hampered cell spreading was reflected in a diminished actin filament number and length on highly positively charged surfaces (+50 mV). Mathematical simulations suggested that in these cells, cortical tension forces dominate the cell–substrate adhesion forces. Our findings present new insights into the impact of surface charges on the overall cell shape and even intracellular structures

    Enhancement of Intracellular Calcium Ion Mobilization by Moderately but Not Highly Positive Material Surface Charges

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    Electrostatic forces at the cell interface affect the nature of cell adhesion and function; but there is still limited knowledge about the impact of positive or negative surface charges on cell-material interactions in regenerative medicine. Titanium surfaces with a variety of zeta potentials between -90 mV and +50 mV were generated by functionalizing them with amino polymers, extracellular matrix proteins/peptide motifs and polyelectrolyte multilayers. A significant enhancement of intracellular calcium mobilization was achieved on surfaces with a moderately positive (+1 to +10 mV) compared with a negative zeta potential (-90 to -3 mV). Dramatic losses of cell activity (membrane integrity, viability, proliferation, calcium mobilization) were observed on surfaces with a highly positive zeta potential (+50 mV). This systematic study indicates that cells do not prefer positive charges in general, merely moderately positive ones. The cell behavior of MG-63s could be correlated with the materials' zeta potential; but not with water contact angle or surface free energy. Our findings present new insights and provide an essential knowledge for future applications in dental and orthopedic surgery
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