Spectroscopic investigations on polypropylene‐carbon nanofiber composites. I. Raman and electron spin resonance spectroscopy

Isotactic polypropylene‐vapor grown carbon nanofiber composites containing various fractions of carbon nanofibers, ranging from 0 to 20 wt %, have been prepared. Raman spectroscopy was used to analyze the effect of the dispersion of carbon nanofibers within polypropylene and the interactions between carbon nanofibers and macromolecular chains. The as‐recorded Raman spectra have been successfully fitted by a linear convolution of Lorentzian lines. Changes of the Raman lines parameters (position, intensity, width, and area) of polypropylene and carbon nanofibers were analyzed in detail. The Raman spectra of the polymeric matrix—at low concentrations of nanofibers—show important modifications that indicate strong interactions between carbon nanofibers and the polymeric matrix reflecting by vibrational dephasing of macromolecular chains. The Raman spectrum of carbon nanofibers is sensitive to the loading with carbon nanofibers, showing changes of the resonance frequencies, amplitudes, and width for both D‐ and G‐bands. Raman data reveals the increase of the disorder, as the concentration of carbon nanofibers is increased. The presence of the typical ESR line assigned to conducting electrons delocalized over carbon nanofibers is confirmed and the presence of a spurious magnetic line due to catalyst's residues is reported. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1644–1652, 2009     

Animal bone meal as an efficient catalyst for crossed-aldol condensation

α,α′-Bis(substituted benzylidene)cycloalkanones were efficiently prepared from cycloalkanones and benzaldehydes in water by using animal bone meal (ABM) or ABM modified as a catalyst. It is shown that ABM modified can be quantitatively recovered and be reused effectively for many times. A comparison of catalytic activity of these catalysts is discussed.     

Some class of analytic functions related to conic domains

For q ∈ (0, 1) let the q-difference operator be defined as follows $$\partial _q f(z) = \frac{{f(qz) - f(z)}} {{z(q - 1)}} (z \in \mathbb{U}),$$ where \(\mathbb{U}\) denotes the open unit disk in a complex plane. Making use of the above operator the extended Ruscheweyh differential operator R _q ^λ f is defined. Applying R _q ^λ f a subfamily of analytic functions is defined. Several interesting properties of a defined family of functions are investigated.     

Third-Order Differential Subordinations for Analytic Functions Associated with Generalized Mittag-Leffler Functions

In this paper, third-order differential subordination results are obtained for analytic functions associated with an operator defined by the normalized form of the generalized Mittag-Leffler functions. Some particular cases involving Mittag-Leffler and hyperbolic functions are also considered.     

Coarsening in one dimension: invariant and asymptotic states

We study a coarsening process of one-dimensional cell complexes. We show that if cell boundaries move with velocities proportional to the difference in size of neighboring cells, then the average cell size grows at a prescribed exponential rate and the Poisson distribution is precisely invariant for the distribution of the whole process, rescaled in space by its average growth rate. We present numerical evidence toward the following universality conjecture: starting from any finite mean stationary renewal process, the system when rescaled by e ^?2t converges to a Poisson point process. For a limited case, this makes precise what has been observed previously in experiments and simulations, and lays the foundation for a theory of universal asymptotic states of dynamical cell complexes.     

A note on line forces in gradient elasticity

The theory of gradient elasticity is applied to line forces. Line forces acting on a point within the body and a concentrated normal force (Flamant problem) which acts on a half plane are studied. Closed analytical solutions which have a simple form are obtained for displacement fields of these forces. The gradient elasticity solutions are free from undesirable displacement singularities predicted by classical elasticity.