Complex tracer mobilities in polymer networks revealed by fluorescence correlation spectroscopy

Gels are elastic porous polymer networks that are accompanied by pronounced mechanical properties. Due to their biocompatibility, ‘responsive hydrogels’ (HG) have many biomedical applications ranging from biosensors and drug delivery to tissue engineering. They respond to external stimuli such as temperature and salt by changing their dimensions. Of paramount importance is the ability to engineer penetrability and diffusion of interacting molecules in the crowded HG environment, as this would enable one to optimize a specific functionality. Even though the conditions under which biomedical devices operate are rather complex, a bottom-up approach could reduce the complexity of mutually coupled parameters influencing tracer mobility. The present thesis focuses on the interaction-induced tracer diffusion in polymer solutions and their homologous gels, probed by means of Fluorescence Correlation Spectroscopy (FCS). This is a single-molecule-sensitive technique having the advantage of optimal performance under ultralow tracer concentrations, typically employed in biosensors. Two different types of hydrogels have been investigated, a conventional one with broad polydispersity in the distance between crosslink points and a so-called ‘ideal’, with uniform mesh size distribution. The former is based on a thermoresponsive polymer, exhibiting phase separation in water at temperatures close to the human body temperature. The latter represents an optimal platform to study tracer diffusion. Mobilities of different tracers have been investigated in each network, varying in size, geometry and in terms of tracer-polymer attractive strength, as perturbed by different stimuli. The thesis constitutes a systematic effort towards elucidating the role of the strength and nature of different tracer-polymer interactions, on tracer mobilities; it outlines that interactions can still be very important even in the simplified case of dilute polymer solutions; it also demonstrates that the presence of permanent crosslinks exerts distinct tracer slowdown, depending on the tracer type and the nature of the tracer-polymer interactions, expressed differently by each tracer with regard to the selected stimulus. In aqueous polymer solutions, the tracer slowdown is found to be system-dependent and no universal trend seems to hold, in contrast to predictions from scaling theory for non-interacting nanoparticle mobility and empirical relations concerning the mesh size in polymer solutions. Complex tracer dynamics in polymer networks may be distinctly expressed by FCS, depending on the specific synergy among-at least some of - the following parameters: nature of interactions, external stimuli employed, tracer size and type, crosslink density and swelling ratio.

Chiral properties of two-flavour QCD at zero and non-zero temperature

Lattice Quantum Chromodynamics (LQCD) is the preferred tool for obtaining non-perturbative results from QCD in the low-energy regime. It has by nowrnentered the era in which high precision calculations for a number of phenomenologically relevant observables at the physical point, with dynamical quark degrees of freedom and controlled systematics, become feasible. Despite these successes there are still quantities where control of systematic effects is insufficient. The subject of this thesis is the exploration of the potential of todays state-of-the-art simulation algorithms for non-perturbativelyrn$\mathcal{O}(a)$-improved Wilson fermions to produce reliable results in thernchiral regime and at the physical point both for zero and non-zero temperature. Important in this context is the control over the chiral extrapolation. Thisrnthesis is concerned with two particular topics, namely the computation of hadronic form factors at zero temperature, and the properties of the phaserntransition in the chiral limit of two-flavour QCD.rnrnThe electromagnetic iso-vector form factor of the pion provides a platform to study systematic effects and the chiral extrapolation for observables connected to the structure of mesons (and baryons). Mesonic form factors are computationally simpler than their baryonic counterparts but share most of the systematic effects. This thesis contains a comprehensive study of the form factor in the regime of low momentum transfer $q^2$, where the form factor is connected to the charge radius of the pion. A particular emphasis is on the region very close to $q^2=0$ which has not been explored so far, neither in experiment nor in LQCD. The results for the form factor close the gap between the smallest spacelike $q^2$-value available so far and $q^2=0$, and reach an unprecedented accuracy at full control over the main systematic effects. This enables the model-independent extraction of the pion charge radius. The results for the form factor and the charge radius are used to test chiral perturbation theory ($\chi$PT) and are thereby extrapolated to the physical point and the continuum. The final result in units of the hadronic radius $r_0$ is rn$$ \left\langle r_\pi^2 \right\rangle^{\rm phys}/r_0^2 = 1.87 \: \left(^{+12}_{-10}\right)\left(^{+\:4}_{-15}\right) \quad \textnormal{or} \quad \left\langle r_\pi^2 \right\rangle^{\rm phys} = 0.473 \: \left(^{+30}_{-26}\right)\left(^{+10}_{-38}\right)(10) \: \textnormal{fm} \;, $$rn which agrees well with the results from other measurements in LQCD and experiment. Note, that this is the first continuum extrapolated result for the charge radius from LQCD which has been extracted from measurements of the form factor in the region of small $q^2$.rnrnThe order of the phase transition in the chiral limit of two-flavour QCD and the associated transition temperature are the last unkown features of the phase diagram at zero chemical potential. The two possible scenarios are a second order transition in the $O(4)$-universality class or a first order transition. Since direct simulations in the chiral limit are not possible the transition can only be investigated by simulating at non-zero quark mass with a subsequent chiral extrapolation, guided by the universal scaling in the vicinity of the critical point. The thesis presents the setup and first results from a study on this topic. The study provides the ideal platform to test the potential and limits of todays simulation algorithms at finite temperature. The results from a first scan at a constant zero-temperature pion mass of about 290~MeV are promising, and it appears that simulations down to physical quark masses are feasible. Of particular relevance for the order of the chiral transition is the strength of the anomalous breaking of the $U_A(1)$ symmetry at the transition point. It can be studied by looking at the degeneracies of the correlation functions in scalar and pseudoscalar channels. For the temperature scan reported in this thesis the breaking is still pronounced in the transition region and the symmetry becomes effectively restored only above $1.16\:T_C$. The thesis also provides an extensive outline of research perspectives and includes a generalisation of the standard multi-histogram method to explicitly $\beta$-dependent fermion actions.