Fractional Kinetics in Kac–Zwanzig Heat Bath Models

We study a variant of the Kac–Zwanzig model of a particle in a heat bath. The heat bath consists of n particles which interact with a distinguished particle via springs and have random initial data. As n → ∞ the trajectories of the distinguished particle weakly converge to the solution of a stochastic integro-differential equation—a generalized Langevin equation (GLE) with power-law memory kernel and driven by 1/f ^α -noise. The limiting process exhibits fractional sub-diffusive behaviour. We further consider the approximation of non-Markovian processes by higher-dimensional Markovian processes via the introduction of auxiliary variables and use this method to approximate the limiting GLE. In contrast, we show the inadequacy of a so-called fractional Fokker–Planck equation in the present context. All results are supported by direct numerical experiments.     

Collisional quenching of resonance states of rare gases

We report an experimental study of Xe(³P₁) → Xe(³P₂) electronic quenching by Ar in Xe/Ar mixtures optically excited by the 1470 Å line of Xe. The quenching process was monitored by the observation of the Xe^*₂ second emission continuum at low Xe pressures.     

Perturbations of molecular extravalence excitations by rare-gas fluids

In this paper we report the results of an experimental study of the vacuum ultraviolet absorption spectra of molecular impurity states of methyl iodide in Ar (density range ? = 0–1.4 g cm^?3) and in Kr (? = 0–2.3 g cm^?3), of carbon disulphide in Ar (? = 0–1.4 g cm^?3) and of formaldehyde in Ar (? = 0–1.25 g cm^?3). The experimental results provide new information regarding medium perturbations of intravalenc transitions, of the lowest extravalence transitions and of transitions to mixed valence—Rydberg configurations, which serve as a diagnostic tool to distinguish between different types of electronic excitations. All the lowest extravalence molecular excitations exhibit appreciable blue spectral shifts at moderate and at high fluid densities, intravalence transitions are practically insensitive to medium effects, while excitations to mixed valence—Rydberg configurations are characterized by a moderate blue spectral shift. New information has been obtained concerning the energetics of molecular ionization processes in a dense fluid. The high n = 2–5 Rydberg states of CH₃l exhibit a large red shift at moderate (? = 0–0.5 cm^?3) Ar densities. The ionization potential E_g and the effective Rydberg constant G for CH₃I in Ar was found to decrease from G = 13.6 eV and E_g = 9.55 eV at ? = 0 and E_g = 9.08 eV and constant G for CH₃l in Ar was found to decrease from G = 13.6 eV and E_g = 9.55eV at ? = 0 and E_g = 9.08 eV and G ≈ 7.15 eV at ? = 0.5 g cm^?3. Experimental evidence was obtained for the identification of n = 2 molecular Wannier impurity states of CH₃I and of CH₂O in liquid Ar. These spectroscopic data result in E_g ≈ 8.6 eV for CH₃I in liquid Ar and E_g ≈ 10.2 eV for CH₂O in liquid Ar.     

Synthesis of 2-oxazolines mediated by N,N′-diisopropylcarbodiimide

N-(β-Hydroxy)amides can be cyclised by reaction with diisopropylcarbodiimide (DIC) to give the corresponding 2-oxazolines in high yields. The reaction requires only very mild Lewis-acid catalysis (5 mol % Cu(OTf)₂) and can be accomplished with simple heating, or in very short reaction times under microwave irradiation.     

Synthesis,self-assembly,and photomechanical actuator performance of a sequence-defined polyviologen crosslinker

ABSTRACT

Although it is well known that viologen radical cations can self-assemble into stacks or complexes on account of radical-radical pairing interactions, it has only recently been demonstrated that reduction of main-chain polyviologens integrated into hydrogel networks can trigger actuation. In these earlier examples, hydrogels comprising oligoethylene glycol-based polyviologens and poly(ethylene glycol) were functionalized with terminal azide groups to prepare ‘click’-based gels. Here, we report a new structural design for the functional polyviologen that consists of main-chain viologen subunits separated by hexamethylene groups instead of glycols and is capped at each end with styrene groups. Activation of this viologen-based macrocrosslinker was achieved using chemical- and photoreduction methods and its ability to undergo intramolecular chain-folding was monitored by absorption spectroscopy. Acrylate-based organogels and hydrogels were also prepared and a comparison was carried out to assess the actuator performance in each gel in terms of the rate of contraction and changes in stiffness.