The collapse of linear polyelectrolyte chains in a poor solvent: When does a collapsing polyelectrolyte collect its counter ions?

The collapse of linear polyelectrolyte chains in a poor solvent: When does a collapsing polyelectrolyte collect its counter ions? The collapse of polyions in a poor solvent is a complex system and is an active research subject in the theoretical polyelectrolyte community. The complexity is due to the subtle interplay between hydrophobic effects, electrostatic interactions, entropy elasticity, intrinsic excluded volume as well as specific counter-ion and co-ion properties. Long range Coulomb forces can obscure single molecule properties. The here presented approach is to use just a small amount of screening salt in combination with a very high sample dilution in order to screen intermolecular interaction whereas keeping intramolecular interaction as much as possible (polyelectrolyte concentration cp ≤ 12 mg/L, salt concentration; Cs = 10^-5 mol/L). This is so far not described in literature. During collapse, the polyion is subject to a drastic change in size along with strong reduction of free counterions in solution. Therefore light scattering was utilized to obtain the size of the polyion whereas a conductivity setup was developed to monitor the proceeding of counterion collection by the polyion. Partially quaternized PVP’s below and above the Manning limit were investigated and compared to the collapse of their uncharged precursor. The collapses were induced by an isorefractive solvent/non-solvent mixture consisting of 1-propanol and 2-pentanone, with nearly constant dielectric constant. The solvent quality for the uncharged polyion could be quantified which, for the first time, allowed the experimental investigation of the effect of electrostatic interaction prior and during polyion collapse. Given that the Manning parameter M for QPVP4.3 is as low as lB / c = 0.6 (lB the Bjerrum length and c the mean contour distance between two charges), no counterion binding should occur. However the Walden product reduces with first addition of non solvent and accelerates when the structural collapse sets in. Since the dielectric constant of the solvent remains virtually constant during the chain collapse, the counterion binding is entirely caused by the reduction in the polyion chain dimension. The collapse is shifted to lower wns with higher degrees of quaternization as the samples QPVP20 and QPVP35 show (M = 2.8 respectively 4.9). The combination of light scattering and conductivity measurement revealed for the first time that polyion chains already collect their counter ions well above the theta-dimension when the dimensions start to shrink. Due to only small amounts of screening salt, strong electrostatic interactions bias dynamic as well as static light scattering measurements. An extended Zimm formula was derived to account for this interaction and to obtain the real chain dimensions. The effective degree of dissociation g could be obtained semi quantitatively using this extrapolated static in combination with conductivity measurements. One can conclude the expansion factor a and the effective degree of ionization of the polyion to be mutually dependent. In the good solvent regime g of QPVP4.3, QPVP20 and QPVP35 exhibited a decreasing value in the order 1 > g4.3 > g20 > g35. The low values of g for QPVP20 and QPVP35 are assumed to be responsible for the prior collapse of the higher quaternized samples. Collapse theory predicts dipole-dipole attraction to increase accordingly and even predicts a collapse in the good solvent regime. This could be exactly observed for the QPVP35 sample. The experimental results were compared to a newly developed theory of uniform spherical collapse induced by concomitant counterion binding developed by M. Muthukumar and A. Kundagrami. The theory agrees qualitatively with the location of the phase boundary as well as the trend of an increasing expansion with an increase of the degree of quaternization. However experimental determined g for the samples QPVP4.3, QPVP20 and QPVP35 decreases linearly with the degree of quaternization whereas this theory predicts an almost constant value.

Methods for the Quantification of Motor Stability for the Assessment of Fall Risk

The research field of the Thesis is the evaluation of motor variability and the analysis of motor stability for the assessment of fall risk. Since many falls occur during walking, a better understanding of motor stability could lead to the definition of a reliable fall risk index aiming at measuring and assessing the risk of fall in the elderly, in the attempt to prevent traumatic events. Several motor variability and stability measures are proposed in the literature, but still a proper methodological characterization is lacking. Moreover, the relationship between many of these measures and fall history or fall risk is still unknown, or not completely clear. The aim of this thesis is hence to: i) analyze the influence of experimental implementation parameters on variability/stability measures and understand how variations in these parameters affect the outputs; ii) assess the relationship between variability/stability measures and long- short-term fall history. Several implementation issues have been addressed. Following the need for a methodological standardization of gait variability/stability measures, highlighted in particular for orbital stability analysis through a systematic review, general indications about implementation of orbital stability analysis have been showed, together with an analysis of the number of strides and the test-retest reliability of several variability/stability numbers. Indications about the influence of directional changes on measures have been provided. The association between measures and long/short-term fall history has also been assessed. Of all the analyzed variability/stability measures, Multiscale entropy and Recurrence quantification analysis demonstrated particularly good results in terms of reliability, applicability and association with fall history. Therefore, these measures should be taken in consideration for the definition of a fall risk index.

Caratterizzazione della misura di entropia di singolo nodo nell'ambito della teoria statistica dei network

In questo lavoro si è affrontata la definizione e la caratterizzazione di una misura di entropia di singolo nodo nell’ambito della teoria statistica dei network, per ottenere informazioni a livello di singolo nodo a fini di analisi e classificazione. Sono state introdotte e studiate alcune proprietà di questi osservabili in quanto la Network Entropy, precedentemente definita e utilizzata nello stesso contesto, fornisce un’informazione globale a livello dell’intero network. I risultati delle analisi svolte con questa definizione sono stati confrontati con una seconda definizione di entropia di singolo nodo proveniente dalla letteratura, applicando entrambe le misure allo stesso problema di caratterizzazione di due classi di nodi all’interno di un network

Topologisch kontrollierte Interpolyelektrolytkomplexe aus kettensteifen Polyelektrolyten

Interpolyelektrolytkomplexe bilden sich spontan bei Mischung von Lösungen entgegengesetzt geladener Polyelektrolyte. Dabei sind die Haupttriebkräfte der Entropiegewinn durch die Freisetzung von niedermolekularen Gegenionen sowie die elektrostatischen Wechselwirkungen. In der letzten Zeit sind sie aufgrund ihrer zahlreichen biologischen und technischen Anwendungen in den Fokus des wissenschaftlichen Interesses gerückt. Vor allem die Anwendung von Komplexen aus DNA und kationischen Polyelektrolyten in der nonviralen Gentherapie wird vielfältig diskutiert. rnIn dieser Arbeit wird eine Polystyrolsulfonat-Bürste mit einer Pfropfdichte von 100 % mit einem kationischen Tensid komplexiert und der Komplex in verschiedenen organischen Lösungsmitteln charakterisiert. Dabei zeigt sich eine signifikante Abhängigkeit des Lösungsverhaltens von der Art und der Konzentration zugesetzter Salze. Dieser Polyelektrolyt-Tensid-Komplex wird anschließend als vereinfachtes Modellsystem für die Komplexierung von DNA verwendet. Als kationische Komponente dient zunächst ein kommerzielles PAMAM-Dendrimer der 5. Generation. Dabei steht die Erhaltung der zylindrischen Topologie der anionischen Polyelektrolytbürste in den gebildeten Komplexen im Vordergrund. Durch Variation des Lösungsmittels und des Protonierungsgleichgewichts werden die experimentellen Bedingungen eingegrenzt, bei denen eine solche topologische Kontrolle möglich ist. Es zeigt sich, dass durch die Verwendung von aprotischen organischen Lösungsmitteln gute Erfolge erzielt werden können. Des Weiteren wird das Komplexierungsverhalten stark durch den Zusatz einer Säure oder einer Base beeinflusst, sodass eine topologische Kontrolle mit einem großen Überschuss einer organischen Base auch in protischen Lösungsmitteln wie Wasser und Methanol möglich wird. Anschließend wird das gleiche Polyanion noch mit einer geschützten Polylysin-Bürste in DMF komplexiert, was zur Bildung von kinetisch kontrollierten Aggregaten führt. Die Bildung dieser Aggregate kann durch den Zusatz eines großen Überschusses an Base verhindert werden und es werden zylindrische Komplexe erhalten, die nur aus einer Polylysin-Bürste bestehen. rn

Correlations and Quantum Dynamics of 1D Fermionic Models: New Results for the Kitaev Chain with Long-Range Pairing

In the first part of the thesis, we propose an exactly-solvable one-dimensional model for fermions with long-range p-wave pairing decaying with distance as a power law. We studied the phase diagram by analyzing the critical lines, the decay of correlation functions and the scaling of the von Neumann entropy with the system size. We found two gapped regimes, where correlation functions decay (i) exponentially at short range and algebraically at long range, (ii) purely algebraically. In the latter the entanglement entropy is found to diverge logarithmically. Most interestingly, along the critical lines, long-range pairing breaks also the conformal symmetry. This can be detected via the dynamics of entanglement following a quench. In the second part of the thesis we studied the evolution in time of the entanglement entropy for the Ising model in a transverse field varying linearly in time with different velocities. We found different regimes: an adiabatic one (small velocities) when the system evolves according the instantaneous ground state; a sudden quench (large velocities) when the system is essentially frozen to its initial state; and an intermediate one, where the entropy starts growing linearly but then displays oscillations (also as a function of the velocity). Finally, we discussed the Kibble-Zurek mechanism for the transition between the paramagnetic and the ordered phase.

Statistical mechanics formalism and methods for the analysis of real networks

This thesis provides a thoroughly theoretical background in network theory and shows novel applications to real problems and data. In the first chapter a general introduction to network ensembles is given, and the relations with “standard” equilibrium statistical mechanics are described. Moreover, an entropy measure is considered to analyze statistical properties of the integrated PPI-signalling-mRNA expression networks in different cases. In the second chapter multilayer networks are introduced to evaluate and quantify the correlations between real interdependent networks. Multiplex networks describing citation-collaboration interactions and patterns in colorectal cancer are presented. The last chapter is completely dedicated to control theory and its relation with network theory. We characterise how the structural controllability of a network is affected by the fraction of low in-degree and low out-degree nodes. Finally, we present a novel approach to the controllability of multiplex networks

Generatore di entropia basato su dinamica caotica con interfaccia usb

È impossibile implementare sorgenti autenticamente casuali su hardware digitale. Quindi, storicamente, si è fatto ampio uso di generatori di numeri pseudo-casuali, evitando così i costi necessari per la progettazione di hardware analogico dedicato. Tuttavia, le sorgenti pseudo-casuali hanno proprietà (riproducibilità e periodicità) che si trasformano in vulnerabilità, nel caso in cui vengano adottate in sistemi di sicurezza informatica e all’interno di algoritmi crittografici. Oggi la richiesta di generatori di numeri autenticamente casuali è ai suoi massimi storici. Alcuni importanti attori dell’ICT sviluppato proprie soluzioni dedicate, ma queste sono disponibili solo sui sistemi moderni e di fascia elevata. È quindi di grande attualità rendere fruibili generatori autenticamente casuali per sistemi già esistenti o a basso costo. Per garantire sicurezza e al tempo stesso contenere i costi di progetto è opportuno pensare ad architetture che consentano di riusare parti analogiche già disponibili. Particolarmente interessanti risultano alcune architetture che, grazie all’utilizzo di dinamiche caotiche, consentono di basare buona parte della catena analogica di elaborazione su ADC. Infatti, tali blocchi sono ampiamente fruibili in forma integrata su architetture programmabili e microcontrollori. In questo lavoro, si propone un’implementazione a basso costo ed elevata flessibilità di un architettura basata su un ADC, inizialmente concepita all’Università di Bologna. La riduzione di costo viene ottenuta sfruttando il convertitore già presente all’interno di un microcontrollore. L’elevata flessibilità deriva dal fatto che il microcontrollore prescelto mette a disposizione una varietà di interfacce di comunicazione, tra cui quella USB, con la quale è possibile rendere facilmente fruibili i numeri casuali generati. Quindi, l’intero apparato comprende solo un microcontrollore e una minima catena analogica di elaborazione esterna e può essere interfacciato con estrema facilità ad elaboratori elettronici o sistemi embedded. La qualità della proposta, in termini di statistica delle sequenze casuali generate, è stata validata sfruttando i test standardizzati dall’U.S. NIST.

Polykation-DNA-Komplexe : Eigenschaften und Anwendung in der Gentransfektion

Polykationen bilden mit DNA spontan Komplexe. Triebkraft ist der Entropiegewinn durch Freisetzung der Gegenionen auf den Polyelektrolyten. Solche Komplexe können in der Gentechnik verwendet werden, um fremde DNA in eine Zelle einzuschleusen. Dies bezeichnet man als Gentransfektion. In dieser Arbeit werden erstmals bürstenförmige Polykationen mit wurmförmiger Topologie zur Gentransfektion verwendet. Dazu wurde die Komplexierung von DNA mit Bürstenpolymeren mit Poly-L-Lysin- und Polyvinylpyridinium-Seitenketten und linearen Polykationen untersucht. Die Komplexbildung verläuft in allen Fällen kinetisch kontrolliert, alle Polykationen bilden sphärische Komplexe, die Topologie hat keinen Einfluss auf die Komplexgröße. Komplexe aus Bürstenpolymeren transfizieren mehr als 25% der gesamten Zellpopulation bei Schweinehirnendothelzellen. Gegenüber dem kommerziellen Transfektionsmittel Lipofektamin konnte eine deutliche Steigerung um bis zu 400% erreicht werden. Komplexe, die mit linearen Analoga gebildet wurden, zeigten bei gleicher Komplexgröße Transfektionsraten unter 5%. Freisetzungsversuche zeigen, dass die Komplexe, die gut transfizieren, recht labil sind, also die DNA unter Kompetitoreinfluss freisetzen können. Stabile Komplexe haben geringe Transfektionseffizienzen. Ebenso wichtig ist der Schutz der DNA vor Abbau durch DNase. Die PVP-Bürste bietet als einziges der untersuchten Polykationen diesen Schutz und zeigt auch die besten Transfektionsraten. Zusätzlich zu der medizinischen Anwendung wurde die Kinetik der Komplexbildung untersucht. Dazu wurde ein spezieller Aufbau entwickelt, der es ermöglicht die Streuintensität der Komplexlösung bei kleinen Streuwinkeln zeitaufgelöst im Millisekundenbereich zu detektieren. Die Komplexbildung verläuft diffusionskontrolliert, im Bereich von Ladungsverhältnissen (positive zu negativen Ladungen) von 1.8 bis 4.0 schließt sich ein fraktales Wachstum an.

Improvement of photon transport model by including coupled photon-electron transport and kernel refinement

The first part of this work deals with the inverse problem solution in the X-ray spectroscopy field. An original strategy to solve the inverse problem by using the maximum entropy principle is illustrated. It is built the code UMESTRAT, to apply the described strategy in a semiautomatic way. The application of UMESTRAT is shown with a computational example. The second part of this work deals with the improvement of the X-ray Boltzmann model, by studying two radiative interactions neglected in the current photon models. Firstly it is studied the characteristic line emission due to Compton ionization. It is developed a strategy that allows the evaluation of this contribution for the shells K, L and M of all elements with Z from 11 to 92. It is evaluated the single shell Compton/photoelectric ratio as a function of the primary photon energy. It is derived the energy values at which the Compton interaction becomes the prevailing process to produce ionization for the considered shells. Finally it is introduced a new kernel for the XRF from Compton ionization. In a second place it is characterized the bremsstrahlung radiative contribution due the secondary electrons. The bremsstrahlung radiation is characterized in terms of space, angle and energy, for all elements whit Z=1-92 in the energy range 1–150 keV by using the Monte Carlo code PENELOPE. It is demonstrated that bremsstrahlung radiative contribution can be well approximated with an isotropic point photon source. It is created a data library comprising the energetic distributions of bremsstrahlung. It is developed a new bremsstrahlung kernel which allows the introduction of this contribution in the modified Boltzmann equation. An example of application to the simulation of a synchrotron experiment is shown.

EPR spectroscopy as a tool for the elucidation of non-covalent structuring principles in complex soft matter

This thesis aims at connecting structural and functional changes of complex soft matter systems due to external stimuli with non-covalent molecular interaction profiles. It addresses the problem of elucidating non-covalent forces as structuring principle of mainly polymer-based systems in solution. The structuring principles of a wide variety of complex soft matter types are analyzed. In many cases this is done by exploring conformational changes upon the exertion of external stimuli. The central question throughout this thesis is how a certain non-covalent interaction profile leads to solution condition-dependent structuring of a polymeric system.rnTo answer this question, electron paramagnetic resonance (EPR) spectroscopy is chosen as the main experimental method for the investigation of the structure principles of polymers. With EPR one detects only the local surroundings or environments of molecules that carry an unpaired electron. Non-covalent forces are normally effective on length scales of a few nanometers and below. Thus, EPR is excellently suited for their investigations. It allows for detection of interactions on length scales ranging from approx. 0.1 nm up to 10 nm. However, restriction to only one experimental technique likely leads to only incomplete pictures of complex systems. Therefore, the presented studies are frequently augmented with further experimental and computational methods in order to yield more comprehensive descriptions of the systems chosen for investigation.rnElectrostatic correlation effects in non-covalent interaction profiles as structuring principles in colloid-like ionic clusters and DNA condensation are investigated first. Building on this it is shown how electrostatic structuring principles can be combined with hydrophobic ones, at the example of host-guest interactions in so-called dendronized polymers (denpols).rnSubsequently, the focus is shifted from electrostatics in dendronized polymers to thermoresponsive alkylene oxide-based materials, whose structuring principles are based on hydrogen bonds and counteracting hydrophobic interactions. The collapse mechanism in dependence of hydrophilic-hydrophobic balance and topology of these polymers is elucidated. Complementarily the temperature-dependent phase behavior of elastin-like polypeptides (ELPs) is investigated. ELPs are the first (and so far only) class of compounds that is shown to feature a first-order inverse phase transition on nanoscopic length scales.rnFinally, this thesis addresses complex biological systems, namely intrinsically disordered proteins (IDPs). It is shown that the conformational space of the IDPs Osteopontin (OPN), a cytokine involved in metastasis of several kinds of cancer, and BASP1 (brain acid soluble protein one), a protein associated with neurite outgrowth, is governed by a subtle interplay between electrostatic forces, hydrophobic interaction, system entropy and hydrogen bonds. Such, IDPs can even sample cooperatively folded structures, which have so far only been associated with globular proteins.

Liquid crystalline elastomers as stimuli-responsive microactuators

Liquid crystalline elastomers (LCEs) are known to perform a reversible change of shape upon the phase transition from the semi-ordered liquid crystalline state to the chaotic isotropic state. This unique behavior of these “artificial muscles” arises from the self-organizing properties of liquid crystals (mesogens) in combination with the entropy-elasticity of the slightly crosslinked elastomer network. In this work, micrometer-sized LCE actuators are fabricated in a microfluidic setup. The microtubular shear flow provides for a uniform orientation of the mesogens during the crosslinking, a perquisite for obtaining actuating LCE samples. The scope of this work was to design different actuator geometries and to broaden the applicability of the microfluidic device for different types of liquid crystalline mesogens, ranging from side-chain to main-chain systems, as well as monomer and polymer precursors. For example, the thiol-ene “click” mechanism was used for the polymerization and crosslinking of main-chain LCE actuators. The main focus was, however, placed on acrylate monomers and polymers with LC side chains. A LC polymer precursor, comprising mesogenic and crosslinkable side-chains was synthesized. Used in combination with an LC monomer, the polymeric crosslinker promoted a stable LC phase, which allowed the mixture to be isothermally handled in the microfluidic reactor. If processed without the additional LC components, the polymer precursor yielded actuating fibers. A suitable co-flowing continuous phase facilitates the formation of a liquid jet and lowers the tendency for drop formation. By modification of the microfluidic device, it was further possible to prepare core-shell particles, comprised of an LCE shell and filled with an isotropic liquid. In analogy to the heart, a hollow muscle, the elastomer shell expels the inner liquid core upon its contraction. The feasibility of the core-shell particles as micropumps was demonstrated. In general, the synthesized LCE microactuators may be utilized as active components in micromechanical and lab-on-chip systems.

Classical and quantum aspects of black hole dynamics

Il contenuto fisico della Relatività Generale è espresso dal Principio di Equivalenza, che sancisce l'equivalenza di geometria e gravitazione. La teoria predice l'esistenza dei buchi neri, i più semplici oggetti macroscopici esistenti in natura: essi sono infatti descritti da pochi parametri, le cui variazioni obbediscono a leggi analoghe a quelle della termodinamica. La termodinamica dei buchi neri è posta su basi solide dalla meccanica quantistica, mediante il fenomeno noto come radiazione di Hawking. Questi risultati gettano una luce su una possibile teoria quantistica della gravitazione, ma ad oggi una simile teoria è ancora lontana. In questa tesi ci proponiamo di studiare i buchi neri nei loro aspetti sia classici che quantistici. I primi due capitoli sono dedicati all'esposizione dei principali risultati raggiunti in ambito teorico: in particolare ci soffermeremo sui singularity theorems, le leggi della meccanica dei buchi neri e la radiazione di Hawking. Il terzo capitolo, che estende la discussione sulle singolarità, espone la teoria dei buchi neri non singolari, pensati come un modello effettivo di rimozione delle singolarità. Infine il quarto capitolo esplora le ulteriori conseguenze della meccanica quantistica sulla dinamica dei buchi neri, mediante l'uso della nozione di entropia di entanglement.

Accretion of Mass and Angular Momentum onto The Discs of Spiral Galaxies

In this Thesis, we study the accretion of mass and angular momentum onto the disc of spiral galaxies from a global and a local perspective and comparing theory predictions with several observational data. First, we propose a method to measure the specific mass and radial growth rates of stellar discs, based on their star formation rate density profiles and we apply it to a sample of nearby spiral galaxies. We find a positive radial growth rate for almost all galaxies in our sample. Our galaxies grow in size, on average, at one third of the rate at which they grow in mass. Our results are in agreement with theoretical expectations if known scaling relations of disc galaxies are not evolving with time. We also propose a novel method to reconstruct accretion profiles and the local angular momentum of the accreting material from the observed structural and chemical properties of spiral galaxies. Applied to the Milky Way and to one external galaxy, our analysis indicates that accretion occurs at relatively large radii and has a local deficit of angular momentum with respect to the disc. Finally, we show how structure and kinematics of hot gaseous coronae, which are believed to be the source of mass and angular momentum of massive spiral galaxies, can be reconstructed from their angular momentum and entropy distributions. We find that isothermal models with cosmologically motivated angular momentum distributions are compatible with several independent observational constraints. We also consider more complex baroclinic equilibria: we describe a new parametrization for these states, a new self-similar family of solution and a method for reconstructing structure and kinematics from the joint angular momentum/entropy distribution.

Stabilità e variabilità del cammino in acqua

La camminata, sia in acqua sia a secco, è un esercizio praticato frequentemente in ambito riabilitativo. Lo scopo di questa tesi è di confrontare variabilità e stabilità del cammino dentro e fuori dall’acqua, al fine di comprendere le caratteristiche dei due tipi di cammino. L’analisi si è focalizzata sulla valutazione di misure di stabilità e variabilità che non erano mai state indagate prima per la camminata in acqua: Harmonic Ratio, Plot di Poincarè, moltiplicatori di Floquet, esponenti di Lyapunov, multiscale entropy, recurrence rate, determinism, averaged diagonal line length, maximum diagonal line length e divergenza. Gli indici sono stati calcolati su camminate di 30 e di 90 passi. Da questa analisi possiamo stimare anche quale parametro è già affidabile a 30 passi e non cambia se analizzato a 90 o se un parametro necessita di più passi per risultare affidabile. Inoltre è stata effettuata indagine statistica tramite test di Kruskal-Wallis. Dall'analisi è emerso che la camminata in acqua è più stabile, meno smooth, c’è un maggiore controllo posturale lungo gli assi antero-posteriore e medio-laterale e che il cammino è condotto in maniera meno automatica.

The Role of Anharmonicity in Hydrogen-Bonded Systems: The Case of Water Clusters

The nature of vibrational anharmonicity has been examined for the case of small water clusters using second-order vibrational perturbation theory (VPT2) applied on second-order Møller–Plesset perturbation theory (MP2) potential energy surfaces. Using a training set of 16 water clusters (H2O)n=2–6,8,9 with a total of 723 vibrational modes, we determined scaling factors that map the harmonic frequencies onto anharmonic ones. The intermolecular modes were found to be substantially more anharmonic than intramolecular bending and stretching modes. Due to the varying levels of anharmonicity of the intermolecular and intramolecular modes, different frequency scaling factors for each region were necessary to achieve the highest accuracy. Furthermore, new scaling factors for zero-point vibrational energies (ZPVE) and vibrational corrections to the enthalpy (ΔHvib) and the entropy (Svib) have been determined. All the scaling factors reported in this study are different from previous works in that they are intended for hydrogen-bonded systems, while others were built using experimental frequencies of covalently bonded systems. An application of our scaling factors to the vibrational frequencies of water dimer and thermodynamic functions of 11 larger water clusters highlights the importance of anharmonic effects in hydrogen-bonded systems.