Control over Nanostructures and Associated Mesomorphic Properties of Doped Self‐Assembled Triarylamine Liquid Crystals

We have synthesized a series of triarylamine‐cored molecules equipped with an adjacent amide moiety and dendritic peripheral tails in a variety of modes. We show by ¹H NMR and UV/Vis spectroscopy that their supramolecular self‐assembly can be promoted in solution upon light stimulation and radical initiation. In addition, we have probed their molecular arrangements and mesomorphic properties in the bulk by integrated studies on their film state by using differential scanning calorimetry (DSC), variable‐temperature polarizing optical microscopy (VT‐POM), variable‐temperature X‐ray diffraction (VT‐XRD), and atomic force microscopy (AFM). Differences in the number and the disposition of the peripheral tails significantly affect their mesomorphic properties associated with their lamellar‐ or columnar‐packed nanostructures, which are based on segregated stacks of the triphenylamine cores and the lipophilic/lipophobic periphery. Such structural tuning is of interest for implementation of these soft self‐assemblies as electroactive materials from solution to mesophases.     

Comparison of fast field-cycling magnetic resonance imaging methods and future perspectives

ABSTRACT

Fast field-cycling (FFC) nuclear magnetic resonance relaxometry is a well-established method to determine the relaxation rates as a function of magnetic field strength. This so-called nuclear magnetic relaxation dispersion gives insight into the underlying molecular dynamics of a wide range of complex systems and has gained interest especially in the characterisation of biological tissues and diseases. The combination of FFC techniques with magnetic resonance imaging (MRI) offers a high potential for new types of image contrast more specific to pathological molecular dynamics. This article reviews the progress in FFC-MRI over the last decade and gives an overview of the hardware systems currently in operation. We discuss limitations and error correction strategies specific to FFC-MRI such as field stability and homogeneity, signal-to-noise ratio, eddy currents and acquisition time. We also report potential applications with impact in biology and medicine. Finally, we discuss the challenges and future applications in transferring the underlying molecular dynamics into novel types of image contrast by exploiting the dispersive properties of biological tissue or MRI contrast agents.     

Absolutely indecomposable symmetric matrices

Let A be a symmetric matrix of size n×n with entries in some (commutative) field K. We study the possibility of decomposing A into two blocks by conjugation by an orthogonal matrix T∈Mat_n(K). We say that A is absolutely indecomposable if it is indecomposable over every extension of the base field. If K is formally real then every symmetric matrix A diagonalizes orthogonally over the real closure of K. Assume that K is a not formally real and of level s. We prove that in Mat_n(K) there exist symmetric, absolutely indecomposable matrices iff n is congruent to 0, 1 or −1 modulo 2s.     

Spinors and multivectors as a unified tool for spacetime geometry and for elementary particle physics

From the definition of spinors as the minimal left (right) modules of multivectors (that is, of vectors and their outer products), we can construct a unified mathematical approach for the study of matter and its interaction fields, which are either defined as fields in the geometrical spacetime or considered as generators of the physical spacetime. It is also shown how matter and interaction fields can be represented either by spinor fields or by multivector fields, both types of fields carrying the same information as the traditional corresponding spinors, vectors, or tensors. Geometry is more transparent in one representation (multivector form), and physics is more obvious in the spinor representation. Our theory provides a unified and totally self-consistent representation of quarks (barions), leptons, and all their known interactions.