Finite extensibility and orientational effects in rubbers. A physical interpretation of the ‘van der Waals equation’ for the elastic force

We propose a physical interpretation of the so-called van der Waals equation of state for rubbers, which gives a relation between the force and the deformation. On a phenomenological basis this equation takes the finite extensibility and a non-defined interaction into account. Here the fininte extensibility is discussed for the dilute case (no entanglements) and the highly entangled limit. The intramolecular interactions are described by orientational effects. The resulting equation of state for the force shows the same features as the van der Waals equation.Dedicated to Prof. H.-G. Kilian on the occasion of his 60th birthday.     

Analysis of sterol oxidation products in foods

The main aspects related to the analysis of sterol oxidation products (SOP) in foods are comprehensively reviewed. Special emphasis is placed on the critical and controversial points of this analysis because these points affect crucial analytical parameters such as precision, accuracy, selectivity, and sensitivity. The effect of sample preparation and the conditions of quantification by gas chromatography and liquid chromatography on these parameters are also reviewed. The results show that, in order to choose an adequate method to analyze SOP in a certain food, the analyst must consider its SOP concentration and matrix complexity. The term SOP includes both cholesterol oxidation products (COP) and phytosterol oxidation products (POP). The state of the art of COP and POP analysis is quite different; many more studies have dealt with the analysis of COP than of POP. However, most of the results presented here about COP analysis may be extrapolated to POP analysis because both groups of compounds show similar structures and characteristics.     

Effect of diffusion on rates and molecular weights in graft polymerization

A theoretical analysis has been made of the graft polymerization process in terms of the quantitative interrelationship between the initiation rate R_i, the k_p/k_t^1/ ratio of the monomer, the equilibrium solubility M of the monomer in the polymer, the polymer film thickness L, and the diffusivity D of the monomer in the polymer. It is shown how the values of these parameters in any grafting system interact to lead to diffusion-controlled graft polymerization. Whether graft polymerization is diffusion-free or diffusion-controlled depends on the values of K_p, d, k_p/k_p^1/2, and L as gathered in the parameter A = [(K_p/k_t^1/2)R_i, D,/^1/2] L/2. When the values of the various terms are such that A is less than 0.1 (i.e., D is large while R_i, k_p, and L are small), the reaction is diffusion-free. When A is greater than 3 (i.e., D is small while R_i, k_p, and L are large), the reaction is diffusion-controlled. The derived equations showing the relationship between kinetic and diffusional parameters are theoretically applicable to all grafting systems, i.e., for all monomer-polymer combinations under all conditions of reaction temperature, radiation intensity and polymer film thickness. The theoretical analysis has been verified for the rate and degree of polymerization for the radiation-induced graft polymerization of styrene to polyethylene.     

Poly(ethylene terephthalate) copolymers containing nitroterephthalic units. III. Methanolytic degradation

The methanolytic degradation of poly(ethylene terephthalate) (PET) copolymers containing nitroterephthalic units was investigated. Random poly(ethylene terephthalate‐co‐nitroterephthalate) copolyesters (PETNT) containing 15 and 30 mol % nitrated units were prepared from ethylene glycol and a mixture of dimethyl terephthalate and dimethyl nitroterephthalate. A detailed study of the influence of the nitro group on the methanolytic degradation rate of the nitrated bis(2‐hydroxyethyl) nitroterephthalate (BHENT) model compound in comparison with the nonnitrated bis(2‐hydroxyethyl) terephthalate (BHET) model compound was carried out. The kinetics of the methanolysis of BHENT and BHET were evaluated with high‐performance liquid chromatography and ¹H NMR spectroscopy. BHENT appeared to be much more reactive than BHET. The methanolytic degradation of PET and PETNT copolyesters at 80 °C was followed by changes in the weight and viscosity, gel permeation chromatography, differential scanning calorimetry, scanning electron microscopy, and ¹H and ¹³C NMR spectroscopy. The copolyesters degraded faster than PET, and the degradation increased with the content of nitrated units and occurred preferentially by cleavage of the ester groups placed at the meta position of the nitro group in the nitrated units. For both PET and PETNT copolyesters, an increase in crystallinity accompanied methanolysis. A surface degradation mechanism entailing solubilization of the fragmented polymer and consequent loss of mass was found to operate in the methanolysis of the copolyesters. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2276–2285, 2002     

Provably stable and time‐accurate extensions of Runge–Kutta schemes for CFD computations on moving grids

Extending fixed‐grid time integration schemes for unsteady CFD applications to moving grids, while formally preserving their numerical stability and time accuracy properties, is a nontrivial task. A general computational framework for constructing stability‐preserving ALE extensions of Eulerian multistep time integration schemes can be found in the literature. A complementary framework for designing accuracy‐preserving ALE extensions of such schemes is also available. However, the application of neither of these two computational frameworks to a multistage method such as a Runge–Kutta (RK) scheme is straightforward. Yet, the RK methods are an important family of explicit and implicit schemes for the approximation of solutions of ordinary differential equations in general and a popular one in CFD applications. This paper presents a methodology for filling this gap. It also applies it to the design of ALE extensions of fixed‐grid explicit and implicit second‐order time‐accurate RK (RK2) methods. To this end, it presents the discrete geometric conservation law associated with ALE RK2 schemes and a method for enforcing it. It also proves, in the context of the nonlinear scalar conservation law, that satisfying this discrete geometric conservation law is a necessary and sufficient condition for a proposed ALE extension of an RK2 scheme to preserve on moving grids the nonlinear stability properties of its fixed‐grid counterpart. All theoretical findings reported in this paper are illustrated with the ALE solution of inviscid and viscous unsteady, nonlinear flow problems associated with vibrations of the AGARD Wing 445.6. Copyright © 2011 John Wiley & Sons, Ltd.     

Band structures of symmetrical graphene superlattice with cells of three regions

We study the electronic band structures of massless Dirac fermions in symmetrical graphene superlattice with cells of three regions. opening gaps and additional Dirac points. Finally, we inspect the potential effect on minibands, the anisotropy of group velocity and the energy bands contours near Dirac points. We also discuss the evolution of gap edges and cutoff region near the vertical Dirac points.     

Synthesis of New Pyrimidine,Quinazoline and Diazatricyclo Derivatives by Multicomponent Reaction and Evaluation of Their Biological Activity

Abstract

A series of new pyrimidine and quinazoline derivatives was synthesized by a Biginelli-like reaction of urea/thiourea, aldehyde, and ketone in the presence of hydrochloric acid as a catalyst. In a similar way, some novel diazatricyclo derivatives were obtained via a Biginelli-like reaction followed by an intramolecular Michael-type addition. The yields of products were reasonable after recrystallization from ethanol. All newly synthesized compounds were characterized using IR and NMR (¹H and ¹³C) spectroscopy and elemental analysis. The antibacterial activity of these compounds was investigated against Staphylococcus aureus (RTCC, 1885), and Escherichia Coli (ATCC, 35922).

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.     

Efficient synthesis of branched poly(acrylic acid) derivatives via postpolymerization modification

The utility of pentafluorophenyl esters for the selective introduction of functional units and branch points in well-defined poly(acrylic acid) (PAA) derivatives is demonstrated using a combination of controlled radical polymerization and postpolymerization modification. Reversible addition-fragmentation chain transfer enables the synthesis of well-defined copolymers—poly(pentafluorophenyl acrylate-co-tert-butyl acrylate)—with the active ester repeat units serving as attachment points for reaction with primary amines, specifically tris(2-(t-butoxycarbonyl)ethyl)methyl amine (Behera's amine). Deprotection using trifluoroacetic acid removes both the backbone and side chain t-butyl esters to give a series of branched PAA derivatives containing novel tricarboxylic acid side chains that are well suited to complexation and multidentate interactions. Surprisingly, the active ester homopolymer is shown to have the highest reactivity with Behera's amine when compared to copolymers with lower incorporation of pentafluorophenyl esters, suggesting an intriguing interplay of neighboring group effects and steric interactions. The ability to tune the efficiency of postpolymerization modification gives a library of PAA derivatives.     

Structure of Zinc and Nickel Histidine Complexes in Solution Revealed by Molecular Dynamics and Raman Optical Activity

The histidine residue has an exceptional affinity for metals, but solution structure of its complexes are difficult to study. For zinc and nickel complexes, Raman and Raman optical activity (ROA) spectroscopy methods to investigate the link between spectral shapes and the geometry were used. The spectra were recorded and interpreted on the basis of ionic equilibria, molecular dynamics, ab initio molecular dynamics, and density functional theory. For zwitterionic histidine the dominant tautomer was determined by the decomposition of experimental spectra into calculated subspectra. An octahedral structure was found to prevail for the ZnHis₂ complex in solution, in contrast to a tetrahedral arrangement in the crystal phase. The solution geometry of NiHis₂ is more similar to the octahedral structure found by X-ray. The Raman and ROA structural determinations of metal complexes are dependent on extensive computations, but reveal unique information about the studied systems.     

1,3-Migration of Trimethylsilyl Group from Carbon to Oxygen in Highly Sterically Hindered Silanol of the Type (Me 3 Si) 3 CSi(C 6 H 4 Me- p )MeOH and Reaction of the Related Iodide with Iodine Monochloride and Iodine Monobromide

The silanol (Me 3 Si) 3 CSi(C 6 H 4 Me- p )MeOH has been shown to isomerize to (Me 3 Si) 2 CHSi(C 6 H 4 Me- p )(Me)(OSiMe 3 ) when it was kept at room temperature for 10 h in 0.2 M NaOMe/MeOH. Corresponding isomerizations of the above silanol (to give (Me 3 Si) 2 CHSi(C 6 H 4 Me- p ) (Me)(OSiMe 3 )) are complete after 26 h under reflux in pyridine. The reaction involve 1,3-migration from carbon to oxygen within a silanolate ion to give a carbanion, which rapidly acquires a proton from the solvent. Treatment of (Me 3 Si) 3 CSi(C 6 H 4 Me- p )MeOH with MeLi in Et 2 O/THF give, by the same rearrangement, the organolithium reagent (Me 3 Si) 2 CLiSi(C 6 H 4 Me- p )(Me)(OSiMe 3 ) which on treatment with Me 2 SiHCl gives (Me 3 Si) 2 C(SiMe 2 H)Si(C 6 H 4 Me- p )(Me)(OSiMe 3 ) and (Me 3 Si) 2 CHSi(C 6 H 4 Me- p )(Me)(OSiMe 3 ). When the experiment was repeated, but with Me 3 SiCl in place of Me 2 SiHCl, it gives exclusively (Me 3 Si) 2 CHSi(C 6 H 4 Me- p )(Me)(OSiMe 3 ). Treatment of the organolithium reagent (Me 3 Si) 2 CLiSi(C 6 H 4 Me- p )(Me)(OSiMe 3 ) with Mel gives exclusively (Me 3 Si) 2 CMeSi(C 6 H 4 Me- p )(Me)(OSiMe 3 ). The related iodide (Me 3 Si) 3 CSi(C 6 H 4 Me- p )Mel reacts with ICI and IBr to give rearranged (Me 3 Si) 2 C(SiMe 2 X)Si(C 6 H 4 Me- p )Me 2 and unrearranged products (Me 3 Si) 3 CSi(C 6 H 4 Me- p )MeX, (X = Cl, Br) respectively. The rearranged bromide (Me 3 Si) 2 C(SiMe 2 Br)Si(C 6 H 4 Me- p )Me 2 reacts with a range of silver [I] salts AgY (Y = OOCCH 3 , SO 4 2 m ) and Mercury [II] salt HgY 2 (Y = OOCCH 3 , SO 4 2 m ) in glacial CH 3 COOH to give the corresponding species (Me 3 Si) 2 C(SiMe 2 OOCCH 3 )Si(C 6 H 4 Me- p )Me 2 . The reaction of the bromide with AgBF 4 in MeOH or i -PrOH give the corresponding rearranged products (Me 3 Si) 2 C(SiMe 2 Y)Si(C 6 H 4 Me- p )Me 2 (Y = --OMe, --OPr i ).