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Phase transitions in molecular crystals are often determined by intermolecular interactions. The cage complex of [Co(C12H30N8)](3+) . 3 NO3- is reported to undergo a disorder-order phase transition at T-c1 approximate to 133 K upon cooling. Temperature-dependent neutron and synchrotron diffraction experiments revealed satellite reflections in addition to main reflections in the diffraction patterns below T-c1. The modulation wave vector varies as function of temperature and locks in at T-c3 approximate to 98 K. Here, we demonstrate that the crystal symmetry lowers from hexagonal to monoclinic in the incommensurately modulated phases in T-c1<T<T-c3. Distinctive levels of competitions: trade-off between longer N-H...O and shorter C-H...O hydrogen bonds; steric constraints to dense C-H...O bonds give rise to pronounced modulation of the basic structure. Severely frustrated crystal packing in the incommensurate phase is precursor to optimal balance of intermolecular interactions in the lock-in phase.
Fluorination of organic spacer impacts on the structural and optical response of 2D perovskites
(2020)
Low-dimensional hybrid perovskites have triggered significant research interest due to their intrinsically tunable optoelectronic properties and technologically relevant material stability. In particular, the role of the organic spacer on the inherent structural and optical features in two-dimensional (2D) perovskites is paramount for material optimization. To obtain a deeper understanding of the relationship between spacers and the corresponding 2D perovskite film properties, we explore the influence of the partial substitution of hydrogen atoms by fluorine in an alkylammonium organic cation, resulting in (Lc)(2)PbI4 and (Lf)(2)PbI4 2D perovskites, respectively. Consequently, optical analysis reveals a clear 0.2 eV blue-shift in the excitonic position at room temperature. This result can be mainly attributed to a band gap opening, with negligible effects on the exciton binding energy. According to Density Functional Theory (DFT) calculations, the band gap increases due to a larger distortion of the structure that decreases the atomic overlap of the wavefunctions and correspondingly bandwidth of the valence and conduction bands. In addition, fluorination impacts the structural rigidity of the 2D perovskite, resulting in a stable structure at room temperature and the absence of phase transitions at a low temperature, in contrast to the widely reported polymorphism in some non-fluorinated materials that exhibit such a phase transition. This indicates that a small perturbation in the material structure can strongly influence the overall structural stability and related phase transition of 2D perovskites, making them more robust to any phase change. This work provides key information on how the fluorine content in organic spacer influence the structural distortion of 2D perovskites and their optical properties which possess remarkable importance for future optoelectronic applications, for instance in the field of light-emitting devices or sensors.
Fluorination of organic spacer impacts on the structural and optical response of 2D perovskites
(2020)
Low-dimensional hybrid perovskites have triggered significant research interest due to their intrinsically tunable optoelectronic properties and technologically relevant material stability. In particular, the role of the organic spacer on the inherent structural and optical features in two-dimensional (2D) perovskites is paramount for material optimization. To obtain a deeper understanding of the relationship between spacers and the corresponding 2D perovskite film properties, we explore the influence of the partial substitution of hydrogen atoms by fluorine in an alkylammonium organic cation, resulting in (Lc)(2)PbI4 and (Lf)(2)PbI4 2D perovskites, respectively. Consequently, optical analysis reveals a clear 0.2 eV blue-shift in the excitonic position at room temperature. This result can be mainly attributed to a band gap opening, with negligible effects on the exciton binding energy. According to Density Functional Theory (DFT) calculations, the band gap increases due to a larger distortion of the structure that decreases the atomic overlap of the wavefunctions and correspondingly bandwidth of the valence and conduction bands. In addition, fluorination impacts the structural rigidity of the 2D perovskite, resulting in a stable structure at room temperature and the absence of phase transitions at a low temperature, in contrast to the widely reported polymorphism in some non-fluorinated materials that exhibit such a phase transition. This indicates that a small perturbation in the material structure can strongly influence the overall structural stability and related phase transition of 2D perovskites, making them more robust to any phase change. This work provides key information on how the fluorine content in organic spacer influence the structural distortion of 2D perovskites and their optical properties which possess remarkable importance for future optoelectronic applications, for instance in the field of light-emitting devices or sensors.
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.
We analyze the cross-over of a homogeneous, weakly interacting Bose gas in one dimension from the ideal gas into the dense quasi-condensate phase. We review a number of mean-field theories, perturbative or self-consistent, and provide accurate evaluations of equation of state, density fluctuations, and correlation functions. A smooth crossover is reproduced by classical-field simulations based on the stochastic Gross-Pitaevskii equation and the Yang-Yang solution to the one-dimensional Bose gas.
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.
The subject of the present thesis is the one-dimensional Bose gas. Since long-rang order is destroyed by infra-red fluctuations in one dimension, only the formation of a quasi-condensate is possible, which exhibits suppressed density fluctuations, but whose phase fluctuates strongly. It is shown that modified mean-field theories based on a symmetry-breaking approach can even characterise phase coherence properties of such a quasi-condensate properly. A correct description of the transition from the degenerate ideal Bose gas to the quasi-condensate, which is a smooth cross-over rather than a phase transition, is not possible though. Basic conditions for the applicability of the theories are not fulfilled in this regime, such that the existence of a critical point is predicted.
The theories are compared on the basis of their excitation sprectum, equation of state, density fluctuations and related correlation functions. High-temperature expansions of the corresponding integrals are derived analytically for the numerical evaluation of the self-consistent integral equations. Apart from that, the Stochastic Gross-Pitaevskii equation (SGPE), a non-linear Langevin equation, is analysed numerically by means of Monte-Carlo simulations and the results are compared to those of the mean-field theories. In this context, a lot of attention is payed to the appropriate choice of the parameters. The simulations prove that the SGPE is capable of describing the cross-over properly, but highlight the limitations of the widely used local density approximation as well.