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Despite the popularity of thermoresponsive polymers, much is still unknown about their behavior, how it is triggered, and what factors influence it, hindering the full exploitation of their potential. One particularly puzzling phenomenon is called co-nonsolvency, in which a polymer is soluble in two individual solvents, but counter-intuitively becomes insoluble in mixtures of both. Despite the innumerous potential applications of such systems, including actuators, viscosity regulators and as carrier structures, this field has not yet been extensively studied apart from the classical example of poly(N isopropyl acrylamide) (PNIPAM) in mixtures of water and methanol. Therefore, this thesis focuses on evaluating how changes in the chemical structure of the polymers impact the thermoresponsive, aggregation and co-nonsolvency behaviors of both homopolymers and amphiphilic block copolymers. Within this scope, both the synthesis of the polymers and their characterization in solution is investigated. Homopolymers were synthesized by conventional free radical polymerization, whereas block copolymers were synthesized by consecutive reversible addition fragmentation chain transfer (RAFT) polymerizations. The synthesis of the monomers N isopropyl methacrylamide (NIPMAM) and N vinyl isobutyramide (NVIBAM), as well as a few chain transfer agents is also covered. Through turbidimetry measurements, the thermoresponsive and co-nonsolvency behavior of PNIPMAM and PNVIBAM homopolymers is then compared to the well-known PNIPAM, in aqueous solutions with 9 different organic co-solvents. Additionally, the effects of end-groups, molar mass, and concentration are investigated. Despite the similarity of their chemical structures, the 3 homopolymers show significant differences in transition temperatures and some divergences in their co-nonsolvency behavior. More complex systems are also evaluated, namely amphiphilic di- and triblock copolymers of PNIPAM and PNIPMAM with polystyrene and poly(methyl methacrylate) hydrophobic blocks. Dynamic light scattering is used to evaluate their aggregation behavior in aqueous and mixed aqueous solutions, and how it is affected by the chemical structure of the blocks, the chain architecture, presence of cosolvents and polymer concentration. The results obtained shed light into the thermoresponsive, co-nonsolvency and aggregation behavior of these polymers in solution, providing valuable information for the design of systems with a desired aggregation behavior, and that generate targeted responses to temperature and solvent mixture changes.
Synchronization – the adjustment of rhythms among coupled self-oscillatory systems – is a fascinating dynamical phenomenon found in many biological, social, and technical systems.
The present thesis deals with synchronization in finite ensembles of weakly coupled self-sustained oscillators with distributed frequencies.
The standard model for the description of this collective phenomenon is the Kuramoto model – partly due to its analytical tractability in the thermodynamic limit of infinitely many oscillators. Similar to a phase transition in the thermodynamic limit, an order parameter indicates the transition from incoherence to a partially synchronized state. In the latter, a part of the oscillators rotates at a common frequency. In the finite case, fluctuations occur, originating from the quenched noise of the finite natural frequency sample.
We study intermediate ensembles of a few hundred oscillators in which fluctuations are comparably strong but which also allow for a comparison to frequency distributions in the infinite limit.
First, we define an alternative order parameter for the indication of a collective mode in the finite case. Then we test the dependence of the degree of synchronization and the mean rotation frequency of the collective mode on different characteristics for different coupling strengths.
We find, first numerically, that the degree of synchronization depends strongly on the form (quantified by kurtosis) of the natural frequency sample and the rotation frequency of the collective mode depends on the asymmetry (quantified by skewness) of the sample. Both findings are verified in the infinite limit.
With these findings, we better understand and generalize observations of other authors. A bit aside of the general line of thoughts, we find an analytical expression for the volume contraction in phase space.
The second part of this thesis concentrates on an ordering effect of the finite-size fluctuations. In the infinite limit, the oscillators are separated into coherent and incoherent thus ordered and disordered oscillators. In finite ensembles, finite-size fluctuations can generate additional order among the asynchronous oscillators. The basic principle – noise-induced synchronization – is known from several recent papers. Among coupled oscillators, phases are pushed together by the order parameter fluctuations, as we on the one hand show directly and on the other hand quantify with a synchronization measure from directed statistics between pairs of passive oscillators.
We determine the dependence of this synchronization measure from the ratio of pairwise natural frequency difference and variance of the order parameter fluctuations. We find a good agreement with a simple analytical model, in which we replace the deterministic fluctuations of the order parameter by white noise.