Microgels for the encapsulation and stimulus-responsive release of molecules with distinct polarities

A microfluidic strategy for the encapsulation and stimulus-responsive release of molecules with distinct polarities from the interior of microgels is reported. The approach relies on (i) the generation of a primary O/W emulsion by the ultrasonication method, (ii) MF emulsification of the primary emulsion, and (iii) photopolymerization of the monomer present in the aqueous phase of the droplets, thereby transforming them into microgels. Non-polar molecules are dissolved in oil droplets embedded in the microgels. Polar molecules are physically associated with the hydrogel network. Upon heating, the microgels contract and release polar and non-polar cargo molecules. The approach paves the way for stimuli-responsive vehicles for multiple drug delivery.     

Numerical ranges of cube roots of the identity

The numerical range of a bounded linear operator T on a Hilbert space H is defined to be the subset W(T)={〈Tv,v〉:v∈H,∥v∥=1} of the complex plane. For operators on a finite-dimensional Hilbert space, it is known that if W(T) is a circular disk then the center of the disk must be a multiple eigenvalue of T. In particular, if T has minimal polynomial z³-1, then W(T) cannot be a circular disk. In this paper we show that this is no longer the case when H is infinite dimensional. The collection of 3×3 matrices with three-fold symmetry about the origin are also classified.     

Absorption and transport properties of ultra-fine cellulose webs

Characterization of transport and absorption properties of nanofiber webs is a challenge, because in many cases the material is soft and cannot withstand the stresses exerted by the standard instruments. In this paper, we report on development of a new technique for materials characterization. We propose to conduct wicking and permeability experiments for full characterization of the nanowebs. As an example, we used electrospun cellulose acetate nanowebs. The wicking experiments showed very good reproducibility, demonstrating the square-root-of-time dependence of wetting front position vs time. The prefactor depends on a product of capillary pressure and materials permeability. We developed a technique to independently measure the permeability of small samples of nanowebs. Wicking and permeability data allow one to estimate the pore size; SEM micrographs confirmed the obtained estimates of pore radius. In general, the proposed method allows one to characterize the transport and absorption parameters of the nanofibrous materials for which the standard procedures are inapplicable.     

Computational thinking and constructionism: creating difference equations in spreadsheets

The invention of the computer has led to the establishment of a new research paradigm, computation, which has recently become more and more popular in scientific exploration. However, computation is not well represented in high school and university curricula in science and engineering, although it applies to a wide range of disciplines beyond computer science and software engineering. In light of the increasing need to provide students with computational education, this paper presents a novel way to develop computational thinking among students. The proposed approach is based on the implementation of Papert's theory of constructionism in electronic spreadsheets. In this approach, students build their knowledge while constructing the difference equation that describes a physical (or engineering) phenomenon, based on specific cases investigated in the spreadsheet. The method does not require the students to write code or perform complex calculations in the spreadsheet and makes it possible to teach advanced subjects at a relatively early stage. The method is demonstrated through contents taken from the secondary and tertiary curricula in mechanics and electromagnetism.     

The Kinetics of Formation of Microporous Polytriazine in Diphenyl Sulfone

This study highlights the value of nonisothermal kinetic methods in selecting temperature conditions for the isothermal preparation of microporous polymeric materials. A dicyanate ester is synthesized and the kinetics of its polymerization in diphenyl sulfone are studied by calorimetry under nonisothermal conditions. The kinetics are analyzed by a model-based approach, using the Kamal model, as well as by a model-free approach, using an advanced isoconversional method. Both approaches correctly predict the time to completion of polymerization at a given temperature. The material prepared independently at the predicted temperature is characterized by electron microscopy and CO₂ adsorption measurements and is confirmed to possess a microporous structure with a multimodal distribution of micropores with two major maxima at ~0.5 and 0.8 nm.     

Quantum-chemical study of the interface formed by carboxylic species on TiO<Subscript>2</Subscript> nanoparticles. 1. Nanoparticle surface

The current paper presents results of a quantum-chemical study of the surface structure of nanoparticles of both rutile and anatase crystallographic modifications. Different stages of the surface relaxation are discussed. Water adsorption is considered. The calculations were performed in the spd-basis by using semi-empirical quantum-chemical codes, both sequential and parallel. The results are mainly addressed to the study of the interface formed by titania nanoparticles and a set of carboxylated species, namely, benzoic, bi-isonicotinic acids as well as tris-(2,2′-dcbipyridine) Fe(II) complex placed on the surface of either rutile or anatase polymorphs.This revised version was published online in August 2005 with a corrected issue number.     

The Subadditive Ergodic Theorem and generic stretching factors for free group automorphisms

Let F _k be a free group of rank k ≥ 2 with a fixed set of free generators. We associate to any homomorphism φ from F _k to a group G with a left-invariant semi-norm a generic stretching factor, λ(φ), which is a noncommutative generalization of the translation number. We concentrate on the situation where φ: F _k → Aut(X) corresponds to a free action of F _k on a simplicial tree X, in particular, where φ corresponds to the action of F _k on its Cayley graph via an automorphism of F _k . In this case we are able to obtain some detailed “arithmetic” information about the possible values of λ = λ(φ). We show that λ ≥ 1 and is a rational number with 2kλ ∈ ℤ[1/(2k − 1)] for every φ ∈ Aut(F _k ). We also prove that the set of all λ(φ), where φ varies over Aut(F _k ), has a gap between 1 and 1+(2k−3)/(2k ²−k), and the value 1 is attained only for “trivial” reasons. Furthermore, there is an algorithm which, when given φ, calculates λ(φ). The second and the third author were supported by the NSF grant DMS#0404991 and the NSA grant DMA#H98230-04-1-0115.     

Quantum-Chemical Investigation of the Mechanism of Fluorocyclization of Norbornenecarboxylic Acids by the Action of F-TEDA-BF4

Possible paths for the reaction of norbornenecarboxylic acids with model F-TEDA-BF₄ were studied by the semiempirical PM3 method. The activation energies of the main transformations in the initial reagents and intermediates were determined. Conclusions were reached about the effect of their reaction mechanisms on the distribution of the products.