No abstract

The design and effective application of supramolecular transient polymer networks based on the assembly of entangled polymer building blocks requires not only precise description of relaxation mechanisms of the chain segments but also inclusion of the kinetics of reversible formation and breakage of reversible supramolecular interactions. In this work we extend the tube-based time marching algorithm to the entangled associative polymers with sticky side groups, with special emphasis on the effect of hindered fluctuations, besides sticky Rouse and sticky reptation. Two different approaches are introduced for inclusion of hindered fluctuations comprising fluctuations with extra penalty for deeper segments and stepwise fluctuations by extra friction. It is shown that there is a transition zone in dynamic moduli between the characteristic lifetime of the stickers and emergence of the final relaxation slopes, which can be characterized by almost parallel drop of loss and storage moduli with slope of 0.5 that can be assigned to hindered fluctuations alongside the blinking of stickers. Theoretical guidelines are drawn for practical application of the model by inclusion of secondary association of sticky groups in clusters with longer lifetimes.

The spectrum of the hydrogen atom has played a central part in fundamental physics over the past 200 years. Historical examples of its importance include the wavelength measurements of absorption lines in the solar spectrum by Fraunhofer, the identification of transition lines by Balmer, Lyman and others, the empirical description of allowed wavelengths by Rydberg, the quantum model of Bohr, the capability of quantum electrodynamics to precisely predict transition frequencies, and modern measurements of the 1S-2S transition by Hänsch 1 to a precision of a few parts in 10 15 . Recent technological advances have allowed us to focus on antihydrogen-the antimatter equivalent of hydrogen 2-4 . The Standard Model predicts that there should have been equal amounts of matter and antimatter in the primordial Universe after the Big Bang, but today's Universe is observed to consist almost entirely of ordinary matter. This motivates the study of antimatter, to see if there is a small asymmetry in the laws of physics that govern the two types of matter. In particular, the CPT (charge conjugation, parity reversal and time reversal) theorem, a cornerstone of the Standard Model, requires that hydrogen and antihydrogen have the same spectrum. Here we report the observation of the 1S-2S transition in magnetically trapped atoms of antihydrogen. We determine that the frequency of the transition, which is driven by two photons from a laser at 243 nanometres, is consistent with that expected for hydrogen in the same environment. This laser excitation of a quantum state of an atom of antimatter represents the most precise measurement performed on an anti-atom. Our result is consistent with CPT invariance at a relative precision of about 2 × 10 −10 .

In 1928, Dirac published an equation that combined quantum mechanics and special relativity. Negative-energy solutions to this equation, rather than being unphysical as initially thought, represented a class of hitherto unobserved and unimagined particles-antimatter. The existence of particles of antimatter was confirmed with the discovery of the positron (or anti-electron) by Anderson in 1932, but it is still unknown why matter, rather than antimatter, survived after the Big Bang. As a result, experimental studies of antimatter, including tests of fundamental symmetries such as charge-parity and charge-parity-time, and searches for evidence of primordial antimatter, such as antihelium nuclei, have high priority in contemporary physics research. The fundamental role of the hydrogen atom in the evolution of the Universe and in the historical development of our understanding of quantum physics makes its antimatter counterpart-the antihydrogen atom-of particular interest. Current standard-model physics requires that hydrogen and antihydrogen have the same energy levels and spectral lines. The laser-driven 1S-2S transition was recently observed in antihydrogen. Here we characterize one of the hyperfine components of this transition using magnetically trapped atoms of antihydrogen and compare it to model calculations for hydrogen in our apparatus. We find that the shape of the spectral line agrees very well with that expected for hydrogen and that the resonance frequency agrees with that in hydrogen to about 5 kilohertz out of 2.5 × 10 hertz. This is consistent with charge-parity-time invariance at a relative precision of 2 × 10-two orders of magnitude more precise than the previous determination -corresponding to an absolute energy sensitivity of 2 × 10 GeV.

Metal−ligand interactions are extensively used for the development of biomimetic polymers. Macroscopic properties of such systems are closely tied to the microscopic structure and dynamics of not only the polymer precursor but also metallosupramolecular bonds. Despite many researchers that have tried to develop a clear understanding of the strength and stability of transient bonds, the role of the coordination geometry is often overlooked. In this work, we utilize a flexible platform that allows us to vary the coordination geometry preference of junctions and study the consequences on the macroscopic scale. We graft tetraand bi-functional poly(ethylene glycol) precursors with bidentate phenanthroline ligands, which, in combination with different divalent transition metal ions, demonstrate different coordination geometries. Specifically, despite the universality of the dynamics in such ideal transient networks, Fe 2+ ions form stable gels at ligand-deficient conditions, in sharp contrast to Co 2+ or Ni 2+ . Modeling of the evolution of the UV−vis absorption spectra of the ligand in the presence of various concentrations of metal ions suggests that while they all contain a remarkable fraction of tris-complexes on top of bis-complexes, the equilibrium constants of these two are inversely correlated in networks formed by Fe 2+ or the other ions. Moreover, DFT simulations show subtle differences between the structures and ground-state energies of the mono-, bis-, and tris-complexes made by different ions. Accordingly, the corresponding free energies of formation prove that Fe 2+ has a significantly larger affinity toward the tris-complex while other ions rather other geometries. These findings propose a new dimension for regulating the structure and dynamics of metallo-supramolecular polymers.

We introduce a theoretical model based upon the kinetic Monte Carlo (KMC) simulation approach capable of quantifying chain shuttling copolymerization (CSP) of ethylene and 1-octene in a semibatch operation. To make a deeper understanding of kinetics and evolution of microstructure, the reversible transfer reaction is first investigated by applying each of the individual catalysts to the reaction media, and the competences and shortcomings of a qualified set of CSP catalysts are discussed based on coordinative chain transfer copolymerization (CCTP) requirements. A detailed simulation study is also provided, which reflects and compares the contributions of chain transfer reversibility and other chain breaking reactions in controlling distribution fashion of molecular weight and chemical composition. The developed computer code is executed to capture developments in dead chain concentration and time-driven composition drift during CCTP. Also, the effect of chain shuttling agent (CSA) on the copolymerization kinetics is theoretically studied by simultaneous activation of both catalysts. In this way, it is attempted to make control over comonomer incorporation in the course of copolymerization. The molecular-level criteria reflecting copolymer properties, i.e., ethylene sequence length distribution and longest ethylene sequence length, as the signature of CSA performance, are virtually simulated in the presence and absence of hydrogen to capture an image on gradient copolymers in CCTP and blocks with gradually changing composition in CSP.

The properties and function of supramolecular polymer networks are determined not only by pairwise interchain transient associations but also by chain entanglement and nanoscopic phase separation of the associative groups. To unravel the impact and interplay of these different factors, we devise a set of model supramolecular polymer networks in which the number of entanglements and the density of associative groups are systematically varied. Rheological data show that by increasing the density of associative groups, the plateau modulus grows to a steady level and extends over a distinct frequency range. This is credited to the presence of binary associations with unique partner exchange time. For samples where the high-frequency plateau stays at the constant level, a second plateau emerges at low frequencies in addition. This plateau, which is well below the entanglement plateau of the precursor, is attributed to the presence of collective assemblies of nanophase-separated associative groups, as confirmed by FTIR spectroscopy. The contributions of these two different levels of interchain associations are decoupled on the basis of a tube-based model. The obtained model parameters show that by increasing the number of network junctions, including both interchain associations and entanglements, the fraction of binary associations decreases, while the density of collective ones approaches a constant level.

Multiple energy dissipating modes are introduced into a model network hydrogel by metallo-supramolecular bonds and regulated by their association thermodynamics.