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     

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.     

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.     

Low-molecular-weight poly(alpha-methyl beta,L-malate) of microbial origin: synthesis and crystallization

Low-molecular-weight poly(alpha-methyl beta,L-malate) made of approximately 25-30 units was prepared from microbial poly(beta,L-malic acid) by treatment with diazomethane. The thermal characterization of the polymalate methyl ester was carried out and its crystalline structure was preliminary examined. Its ability to crystallize both from solution and from the melt was comparatively evaluated.     

Contact phase modulation method for acoustic nonlinear parameter measurement in solid

In this work, a new method to measure in contact the nonlinearity parameter beta of solid plates is presented. A high frequency (HF) tone-burst signal of 20 MHz is inserted in the material by a contact-transducer (with a suitable coupling). A low frequency (LF) pulse (2.5 MHz) is applied to the other face, in the opposite direction, so that the nonlinear interaction of the two waves takes place during the back propagation toward the HF transducer. This collinear interaction creates a phase modulation of the HF tone-burst which is proportional to the beta coefficient and the particle velocity of the LF wave. To determine this particle velocity, in time domain, an extended self-reciprocity calibration of the contact LF transducer is used. A numeric phase demodulation is then performed, giving the beta coefficient of the sample. The proposed method is validated by nonlinearity parameter measurements in Fused Silica. The nonlinear parameter of Fused Silica measured is found to be in good agreement with the literature, and specially the negative sign of this parameter.