Lattice Monte Carlo investigations on copolymer systems, 1. Diblock copolymers

Symmetric diblock copolymers in dilute solution were examined by means of Monte Carlo simulations on a cubic lattice with respect to chain- and block dimensions, shape, local structure and number of contacts. The solvent was either a common good one, a common θ-solvent or a selective one for the two blocks. In all cases, repulsive interactions are operative between the blocks. In addition, the underlying homopolymers (athermal and θ) were divided into two parts (and treated as a block copolymer) for comparison. Chain-length was varied from 40 to 1280 segments leading to the expected values for the critical exponent 2v ≈ 1.2 for good solvent quality and 2v ≈ 1.0 for θ-solvent. Copolymers in a selective solvent scale with an intermediate exponent, 2v ≈ 1.13. The deviation of the mean squared dimensions of the copolymers from the sum of those of two homopolymers of the same length and for the same solvent quality as the blocks is largest for block copolymers in a common θ-solvent (where it exceeds 20%), while the blocks themselves have mostly the same dimensions as their underlying homopolymers of equal length. The shape of the copolymers, expressed by the parameter δ (asphericity) becomes more rod-like with increasing chain-length if there are (compact) θ-blocks in the molecule which are subject to mutual repulsive interaction. In these cases, θ exceeds the value of the homopolymers in the limit of infinite chain-length. The number of contacts per segment approaches a limiting value with increasing chain-length which is ≈0.20 for athermal chains and athermal blocks. For θ-chains and θ-blocks, a limiting value is not yet reached within the range of chainlengths investigated. The number of contacts per segment between two different blocks quickly tends to zero with increasing chain-length.     

The incorporation of side reactions into pseudostationary polymerization, 3. The closed solution of a kinetic scheme for pulsed-laser polymerization comprising concomitant continuous initiation

A procedure is developed that allows the calculation of chain-length distributions of polymers prepared by periodic modulation of the initiation process considering concomitant continuous initiation. For the case of a (pseudostationary) laser-pulse initiated polymerization process a closed solution could be derived for the pseudostationary radical concentration and for the chain-length distribution of dead polymer terminated by disproportionation or stabilized by chain-transfer to monomer or solvent. The analysability of the characteristic peaks appearing in the chain-length distributions of laser-pulse initiated polymers (which is the key for determining the rate constant k_p) is only moderately influenced by continuous thermal radical formation if the extent of this side reaction is not pathologically large, i.e. as long as the amount of primary radicals created by the laser-pulse appreciably exceeds that produced in the dark reaction.     

Simulation of pseudostationary radical polymerization, 3. Periodic modulation of the termination process for termination by disproportionation

A procedure is developed that allows the calculation of chain-length distributions of polymers prepared by periodic modulation of the termination rate constant, considering termination by disproportionation. Applying some (hypothetical) field which suppresses — or at least diminishes — the termination rate constant periodically, results in step-function-like chain-length distributions. In principle, the same information may be obtained as in the case of periodical variation of the rate of initiation.     

Solvent stabilized transition metal cations as initiators for cyclopentadiene polymerization

Solvent stabilized transition metal cations are excellent initiators for the polymerization of cyclopentadiene. The product yield is – in first approximation – directly proportional to the reaction time. Partial substitution of the solvent molecules by ligands with different donor strength and charge allows the synthesis of initiators with tailor made activity. The presence of a metal-metal multiple bond seems not to be of significant importance for the catalytic activity of the initiator systems. The crucial point for the activity of the complexes described here is the presence of labile and therefore easily replacable ligands in equatorial coordination sites.     

Column space equalities for orthogonal projectors

In their paper [Y. Tian, G.P.H. Styan, Rank equalities for idempotent and involutory matrices. Linear Algebra Appl. 335 (2001) 101-117], Tian and Styan established several rank equalities involving a pair of idempotent matrices P and Q. Subsequently, these results are reinvestigated from the point of view of the following question: provided that idempotent P, Q are Hermitian, which relationships given in the aforementioned paper remain valid when ranks are replaced with column spaces? Simultaneously, some related results are established, which shed additional light on the links between subspaces attributed to various functions of a pair of orthogonal projectors.     

Bayesian log-periodic model for financial crashes

This paper introduces a Bayesian approach in econophysics literature about financial bubbles in order to estimate the most probable time for a financial crash to occur. To this end, we propose using noninformative prior distributions to obtain posterior distributions. Since these distributions cannot be performed analytically, we develop a Markov Chain Monte Carlo algorithm to draw from posterior distributions. We consider three Bayesian models that involve normal and Student’s t-distributions in the disturbances and an AR(1)-GARCH(1,1) structure only within the first case. In the empirical part of the study, we analyze a well-known example of financial bubble – the S&P 500 1987 crash – to show the usefulness of the three methods under consideration and crashes of Merval-94, Bovespa-97, IPCMX-94, Hang Seng-97 using the simplest method. The novelty of this research is that the Bayesian models provide 95% credible intervals for the estimated crash time.     

Multi-conjugate solar adaptive optics at the Vacuum Tower Telescope on Tenerife

We present a breadboard multi-conjugate adaptive optics (MCAO) system for high angular resolution solar observations which we operate at the Vacuum Tower Telescope. We have developed methods to estimate quantitatively the performance of solar adaptive optics from science data. Several sets of short exposure images of the solar photosphere were analyzed to assess the performance of the MCAO. We demonstrate that a 30 arcsec field of view is substantially improved when the MCAO system is turned on. This compares favourably with an improvement of a 10 arcsec field with conventional solar adaptive optics. We also show how irradiance fluctuations in the MCAO compensated focus can be suppressed. To cite this article: O. von der Lühe et al., C. R. Physique 6 (2005).     

Isobutene Polymerization Using [CuII(NCMe)6]2+ with Non‐Coordinating Anions as Catalysts

Cu^II compounds coordinated octahedrally with nitriles and associated with bulky, non‐coordinating counter ions can be applied in the polymerization of isobutene at 30 °C. High yields and a high content of terminal double bonds are reached in the resulting highly reactive polyisobutylenes, while the molecular masses are moderate. Two of the coordinating nitriles are more weakly coordinated than the other four, as can be concluded from an exemplary X‐ray structure and from vibrational spectra, thus providing easily accessible sites for substrate coordination.

     

Polymer‐Bound Thiol Groups on Poly(2‐oxazoline)s

A new 2‐oxazoline monomer with a protected thiol group, 2‐[2‐(4‐methoxybenzylsulfanyl)ethyl]‐2‐oxazoline, MOB‐SOx , was synthesized from commercially available compounds. MOB‐SOx and 2‐ethyl‐2‐oxazoline (EtOx) were simultaneously polymerized yielding well defined copolymers with narrow molar mass distributions and target polymer chain length. The copolymerization was initiated by N‐methyl‐2‐methyl‐2‐oxazolinium triflate ( MeOxOTf ). After quantitative deprotection, poly(2‐oxazoline) with pendant thiol groups was obtained. The thiol groups were quantitatively added to the double bond of N‐phenyl‐acrylamide ( PhA ) and benzylmaleimide ( BzM ). Graft copolymers were obtained by reaction of those SH containing polymers with poly(2‐methyl‐2‐oxazoline)s bearing acrylamide ( PMeOx ₁₀ A ) and maleimide ( PMeOx ₁₀ M ) as terminal reactive groups.

     

Stereoselective Cyclopolymerization of Polar 1,6‐Heptadiynes by Novel,Tailor‐Made Ruthenium‐Based Metathesis Catalysts

Summary: The cyclopolymerization of 4,4‐bis(hydroxymethyl)‐1,6‐heptadiyne ( M1 ), 4‐(carboxyethyl)‐1,6‐heptadiyne ( M2 ), 4‐(hydroxymethyl)‐1,6‐heptadiyne ( M3 ), and 4‐carboxy‐1,6‐heptadiyne ( M4 ) using five different well‐defined metathesis initiators was investigated. Control of molar mass was achieved with catalysts bearing trifluoroacetate ligands. ¹³C NMR experiments showed that poly‐ M2 , prepared by the action of any catalyst consisted solely of five‐membered ring structures, i.e., 1,2‐(cyclopent‐1‐enylene)vinylene units. Effective conjugation lengths of all polymers were calculated from the corresponding UV‐Vis absorption maxima, which varied reversibly with temperature.