The vibrational spectrum and ultimate modulus of polyethylene

We have performed the first completely ab initio lattice dynamics calculation of the full orthorhombic cell of polyethylene using periodic density functional theory in the local density approximation (LDA) and the generalized gradient approximation (GGA). Contrary to current perceptions, we show that LDA accurately describes the structure whereas GGA fails. We emphasize that there is no parametrization of the results. We then rigorously tested our calculation by computing the phonon dispersion curves across the entire Brillouin zone and comparing them to the vibrational spectra, in particular the inelastic neutron scattering (INS) spectra, of polyethylene (both polycrystalline and aligned) and perdeuteriopolyethylene. The F-point frequencies (where the infrared and Raman active modes occur) are in good agreement with the latest low temperature data. The near-perfect reproduction of the INS spectra, gives confidence in the results and allows Lis to deduce a number of physical properties including the elastic moduli, parallel and perpendicular to the chain. We find that the Young's modulus for an infinitely long, perfectly crystalline polyethylene is 360.2 GPa at 0 K. The highest experimental value is 324 GPa, indicating that current high modulus fibers are similar to 90% of their maximum possible strength.

Effect of ethanol on the micellization and gelation of Pluronic P123

In certain applications copolymer P123 (E21P67E21) is dissolved in water-ethanol mixtures, initially to form micellar solutions and eventually to gel. For P123 in 10, 20, and 30 wt % aqueous ethanol we used dynamic light scattering from dilute solutions to confirm micellization, oscillatory rheometry, and visual observation of mobility (tube inversion) to determine gel formation in concentrated solutions and small-angle X-ray scattering (SAXS) to determine gel structure. Except for solutions in 30 wt % aqueous ethanol, a clear-turbid transition was encountered on heating dilute and concentrated micellar solutions alike, and as for solutions in water alone (Chaibundit et al. Langmuir 2007, 23, 9229) this could be ascribed to formation of wormlike micelles. Dense clouding, typical of phase separation, was observed at higher temperatures. Regions of isotropic and birefringent gel were defined for concentrated solutions and shown (by SAXS) to have Cubic (fcc and hcp) and hexagonal structures, consistent with packed spherical and elongated micelles, respectively. The cubic gels (0, 10, and 20 wt % ethanol) were clear, while the hex gels were either turbid (0 and 10 wt % ethanol), turbid enclosing a clear region (20 wt % ethanol), or entirely clear (30 wt % ethanol). The SAXS profile was unchanged between turbid and clear regions of the 20 wt % ethanol gel. Temperature scans of dynamic moduli showed (as expected) a clear distinction between high-modulus cubic gels (G'(max) approximate to 20-30 kPa) and lower modulus hex gels (G'(max) < 10 kPa).

Nematic and columnar ordering of a PEG-peptide conjugate in aqueous solution

The self-assembly in aqueous solution of a PEG-peptide conjugate is studied by spectroscopy, electron microscopy, rheology and small-angle Xray and neutron scattering (SAXS and SANS). The peptide fragment, FFKLVFF is based on fragment KLVFF of the amyloid beta-peptide, A beta(16-20), extended by two hydrophobic phenylalanine units. This is conjugated to PEG which confers water solubility and leads to distinct self-assembled structures. Small-angle scattering reveals the formation of cylindrical fibrils comprising a peptide core and PEG corona. This constrained structure leads to a model parallel beta-sheet self-assembled structure with a radial arrangement of beta sheets. Oil increasing concentration, successively nematic and hexagonal columnar phases are formed. The flow-induced alignment of both structures was studied in situ by SANS using a Couette cell. Shear-induced alignment is responsible for the shear thinning behaviour observed by dynamic shear rheometry. Incomplete recovery of moduli after cessation of shear is consistent with the observation from SANS of retained orientation in the sample.

Block copolymers of ethylene oxide and phenyl glycidyl ether: micellization, gelation, and drug solubilization

Three triblock copolymers of ethylene oxide and phenyl glycidyl ether, type E(m)G(n)E(m), where G = OCH2-CH(CH2OC6H5) and E = OCH2CH2, were synthesized and characterized by gel-permeation chromatography, matrix-assisted laser desorption ionization time-of-flight mass spectrometry, and NMR spectroscopy. Their association properties in aqueous solution were investigated by surface tensiometry and light scattering, yielding values of the critical micelle concentration (cmc), the hydrodynamic radius, and the association number. Gel boundaries in concentrated micellar solution were investigated by tube inversion, and for one copolymer, the temperature and frequency dependence of the dynamic moduli served to confirm and extend the phase diagram and to highlight gel properties. Small-angle X-ray scattering was used to investigate gel structure. The overall aim of the work was to define a block copolymer micellar system with better solubilization capacity for poorly soluble aromatic drugs than had been achieved so far by use of block copoly(oxyalkylene)s. Judged by the solubilization of griseofulvin in aqueous solutions of the E(m)G(n)E(m) copolymers, this aim was achieved.

Viscoelastic properties of high pressure and heat induced tofu gels

Tofu gels were rheologically examined to determine their storage or elastic (G′) and loss or viscous (G″) moduli as a function of frequency within their linear viscoelastic limits. The tofu gels were made using either glucono-δ-lactone (GDL) or calcium sulphate (CaSO4·2H2O), followed by either heat treatment (heated soymilk at 97 °C prior to coagulation and subsequently held at 70 °C for 60 min, HT) or high pressure treatment (400 MPa at 20 °C for 10 min, HP). The overall moduli values of the GDL gels and CaSO4·2H2O gels of both physical treatments were similar, each gave frequency profiles expected for weak viscoelastic materials. However, although both temperature and high pressure treatments could be used to produce tofu gels, the final products were not the same. Pressure formed gels, despite having a higher overall “consistency” (increasing values of their moduli), had a proportionately higher contribution from the loss modulus (increased tan δ). Differences could also be observed using confocal scanning laser microscopy. While such treatment may give rise to differing systems/structures, with new or modified organoleptic properties, the more “open” structures obtained by pressure treatment may well cause processing difficulties if subsequent reworking or moulding is required.

Viscoelastic properties of high pressure and heat induced tofu gels

Tofu gels were rheologically examined to determine their storage or elastic (G') and loss or viscous (G '') moduli as a function of frequency within their linear viscoelastic limits. The tofu gels were made using either glucono-delta-lactone (GDL) or calcium sulphate (CaSO4 center dot 2H(2)O), followed by either heat treatment (heated soymilk at >= 97 degrees C prior to coagulation and subsequently held at 70 degrees C for 60 min, HT) or high pressure treatment (400 MPa at 20 degrees C for 10 min, HP). The overall moduli values of the GDL gels and CaSO4 center dot 2H(2)O gels of both physical treatments were similar, each gave frequency profiles expected for weak viscoelastic materials. However, although both temperature and high pressure treatments could be used to produce tofu gels, the final products were not the same. Pressure formed gels, despite having a higher overall "consistency" (increasing values of their moduli), had a proportionately higher contribution from the loss modulus (increased tan delta). Differences could also be observed using confocal scanning laser microscopy. While such treatment may give rise to differing systems/structures, with new or modified organoleptic properties, the more "open" structures obtained by pressure treatment may well cause processing difficulties if subsequent reworking or moulding is required. (c) 2007 Elsevier Ltd. All rights reserved.

Effects of endogenous flour lipids on the quality of semisweet biscuits

Fractionation and reconstitution techniques were used to study the contribution of enclogenous flour lipids to the quality of semisweet (Rich Tea-type) biscuits. Biscuit flour was defatted with chloroform and baked with bakery fat but without enclogenous lipid addition. Semisweet biscuits baked from defatted flour were flatter, denser, and harder and showed collapse of gas cells during baking when compared with control biscuits. Defatted flour semisweet doughs exhibited a different rheological behavior from the control samples showing higher storage and loss moduli (G' and G" values), that is, high viscoelasticity. Functionality was restored when total nonstarch flour lipids were added back to defatted flour. Both the polar and nonpolar lipid fractions had positive effects in restoring flour quality, but the polar lipid fraction was of greatest benefit. Both fractions were needed for complete restoration of both biscuit quality and dough rheological characteristics.

Effects of endogenous flour lipids on the quality of short-dough biscuits

Fractionation and reconstitution techniques were used to study the contribution of endogenous flour lipids to the quality of short-dough (shortcake type) biscuits. Biscuit flour was defatted with chloroform and baked with bakery fat, but without endogenous lipid. Short-dough biscuits baked from defatted flour had smaller diameters, and were flatter, denser and harder than control biscuits. Defatted flour shortcake doughs exhibited different rheological behaviour from the control samples, showing higher storage and loss moduli (G' and G" values), ie higher viscoelasticity. Functionality was restored when total non-starch flour lipids were added back to defatted flour. The polar lipid fraction had a positive effect in restoring flour quality whereas the non-polar lipid fraction had no effect. Both fractions were needed for complete restoration of both biscuit quality and dough rheological characteristics. A study of the microstructure of defatted biscuits revealed that their gluten protein was more hydrated and developed than the gluten of the control biscuits. This conclusion was supported by the higher water absorption of the defatted gluten. (C) 2004 Society of Chemical Industry.

Effects of hydrocolloid addition and high pressure processing on the rheological properties and microstructure of a commercial ostrich meat product "Yor" (Thai sausage)

"Yor" is a traditional sausage like product widely consumed in Thailand. Its textures are usually set by steaming, in this experiment ultra-high pressure was used to modify the product. Three types of hydrocolloid; carboxymethylcellulose (CMC), locust bean gum (LBG) and xanthan gum, were added to minced ostrich meat batter at concentration of 0-1% and subjected to high pressure 600 Mpa, 50 degrees C, 40 min. The treated samples were analysed for storage (G) and loss (G '') moduli by dynamic oscillatory testing as well as creep compliance for control stress measurement. Their microstructures using confocal microscopy were also examined. Hydrocolloid addition caused a significant (P < 0.05) decrease in both the G' and G '' moduli. However the loss tangent of all samples remained unchanged. Addition of hydrocolloids led to decreases in the gel network formation but appears to function as surfactant materials during the initial mixing stage as shown by the microstructure. Confocal microscopy suggested that the size of the fat droplets decreased with gum addition. The fat droplets were smallest on the addition of xanthan gum and increased in the order CMC, LBG and no added gum, respectively. Creep parameters of ostrich yors with four levels of xanthan gum addition (0.50%, 0.75%, 1.00% and 1.25%) showed an increase in the instantaneous compliance (J(0)), the retarded compliance (J(1)) and retardation time (lambda(1)) but a decrease in the viscosity (eta(0)) with increasing levels of addition. The results also suggested that the larger deformations used during creep testing might be more helpful in assessing the mechanical properties of the product than the small deformations used in oscillatory rheology. (c) 2007 Elsevier Ltd. All rights reserved.

Comparison of the rheology of mozzarella-type curd made from buffalo and cows’ milk

Curd rheology and calcium distribution in buffalo and cows’ milk, were compared at their natural pH and during acidification (pH 6.5–5.6). Buffalo milk displays a curd structure and rheology different from that of cows’ milk and the casein-bound calcium, as well as the contents of fat, protein and calcium, are also higher. Due to these higher amounts of casein-bound calcium, the overall curd strength with buffalo milk (as indicated by the dynamic moduli) was higher, at similar pH values, than those of equivalent gels produced from cows’ milk. The curd rheology was adversely affected at lower pH (5.8–5.6) in both of the milk types, due to the loss of casein-bound calcium from casein micelles. The degree of solubilisation of calcium in buffalo milk during acidification is quite different from that observed in cows’ milk with a lower proportion of the calcium being solubilised in the former. The maximum curd firmness was obtained at pH 6.0 in both milk types. For both species, these rheological and micellar changes were qualitatively the same but quantitatively different, due to the different milk compositions.

Self-assembly of Fmoc-tetrapeptides based on the RGDS cell adhesion motif

Self-assembly in aqueous solution has been investigated for two Fmoc [Fmoc ¼ N-(fluorenyl)-9-methoxycarbonyl] tetrapeptides comprising the RGDS cell adhesion motif from fibronectin or the scrambled sequence GRDS. The hydrophobic Fmoc unit confers amphiphilicity on the molecules, and introduces aromatic stacking interactions. Circular dichroism and FTIR spectroscopy show that the self-assembly of both peptides at low concentration is dominated by interactions among Fmoc units, although Fmoc-GRDS shows b-sheet features, at lower concentration than Fmoc-RGDS. Fibre X-ray diffraction indicates b-sheet formation by both peptides at sufficiently high concentration. Strong alignment effects are revealed by linear dichroism experiments for Fmoc-GRDS. Cryo-TEM and smallangle X-ray scattering (SAXS) reveal that both samples form fibrils with a diameter of approximately 10 nm. Both Fmoc-tetrapeptides form self-supporting hydrogels at sufficiently high concentration. Dynamic shear rheometry enabled measurements of the moduli for the Fmoc-GRDS hydrogel, however syneresis was observed for the Fmoc-RGDS hydrogel which was significantly less stable to shear. Molecular dynamics computer simulations were carried out considering parallel and antiparallel b-sheet configurations of systems containing 7 and 21 molecules of Fmoc-RGDS or Fmoc-GRDS, the results being analyzed in terms of both intermolecular structural parameters and energy contributions.

Rheology of milk foams produced by steam injection

Rheology of milk foams generated by steam injection was studied during the transient destabilization process using steady flow and dynamic oscillatory techniques: yield stress (τ_y) values were obtained from a stress ramp (0.2 to 25 Pa) and from strain amplitude sweep (0.001 to 3 at 1 Hz of frequency); elastic (G') and viscous (G") moduli were measured by frequency sweep (0.1 to 150 Hz at 0.05 of strain); and the apparent viscosity (η_a) was obtained from the flow curves generated from the stress ramp. The effect of plate roughness and the sweep time on τ_y was also assessed. Yield stress was found to increase with plate roughness whereas it decreased with the sweep time. The values of yield stress and moduli—G' and G"—increased during foam destabilization as a consequence of the changes in foam properties, especially the gas volume fraction, φ, and bubble size, R_32 (Sauter mean bubble radius). Thus, a relationship between τ_y, φ, R_32, and σ (surface tension) was established. The changes in the apparent viscosity, η, showed that the foams behaved like a shear thinning fluid beyond the yield point, fitting the modified Cross model with the relaxation time parameter (λ) also depending on the gas volume fraction. Overall, it was concluded that the viscoelastic behavior of the foam below the yield point and liquid-like behavior thereafter both vary during destabilization due to changes in the foam characteristics.

Extended factorizations of exponential functionals of Lévy processes

Pardo, Patie, and Savov derived, under mild conditions, a Wiener-Hopf type factorization for the exponential functional of proper Lévy processes. In this paper, we extend this factorization by relaxing a finite moment assumption as well as by considering the exponential functional for killed Lévy processes. As a by-product, we derive some interesting fine distributional properties enjoyed by a large class of this random variable, such as the absolute continuity of its distribution and the smoothness, boundedness or complete monotonicity of its density. This type of results is then used to derive similar properties for the law of maxima and first passage time of some stable Lévy processes. Thus, for example, we show that for any stable process with $\rho\in(0,\frac{1}{\alpha}-1]$, where $\rho\in[0,1]$ is the positivity parameter and $\alpha$ is the stable index, then the first passage time has a bounded and non-increasing density on $\mathbb{R}_+$. We also generate many instances of integral or power series representations for the law of the exponential functional of Lévy processes with one or two-sided jumps. The proof of our main results requires different devices from the one developed by Pardo, Patie, Savov. It relies in particular on a generalization of a transform recently introduced by Chazal et al together with some extensions to killed Lévy process of Wiener-Hopf techniques. The factorizations developed here also allow for further applications which we only indicate here also allow for further applications which we only indicate here.

A Nyström method for a class of integral equations on the real line with applications to scattering by diffraction gratings and rough surfaces

We propose a Nystr¨om/product integration method for a class of second kind integral equations on the real line which arise in problems of two-dimensional scalar and elastic wave scattering by unbounded surfaces. Stability and convergence of the method is established with convergence rates dependent on the smoothness of components of the kernel. The method is applied to the problem of acoustic scattering by a sound soft one-dimensional surface which is the graph of a function f, and superalgebraic convergence is established in the case when f is infinitely smooth. Numerical results are presented illustrating this behavior for the case when f is periodic (the diffraction grating case). The Nystr¨om method for this problem is stable and convergent uniformly with respect to the period of the grating, in contrast to standard integral equation methods for diffraction gratings which fail at a countable set of grating periods.

First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.