Characterization of the structure and the size distribution of branched polymers formed by co-polymerization of MMA and EGDMA

Free radical co-polymerization of methyl methacrylate (MMA) and ethyl glycol dimethyl methacrylate (EGDMA) in solution leads to the formation of polydisperse branched PMMA which grows in size until the system gels. The structure and the size distribution of the PMMA aggregates were characterized at infinite dilution using static and dynamic light scattering and size exclusion chromatography (SEC). The reaction extent was measured using SEC and Raman spectroscopy. The results show that the structure and size distribution of PMMA aggregates formed close to the gel point are compatible with those of percolating clusters. The structure factor of semi-dilute solutions of PMMA aggregates is the same as that of dilute solutions at distance scales much smaller than the correlation length of the concentration fluctuations (). However, the cut-off function of the pair correlation function at for semi-dilute solutions is more gradual than the cut-off function at for dilute solutions. Received 11 May 1998 and Received in final form 22 October 1998     

Dynamic and static light scattering study of the formation of cross-linked PMMA gels

Free radical co-polymerization of methyl methacrylate (MMA) and ethyl glycol dimethyl metacrylate (EGDMA) was investigated in solution at different molar ratios R = [EGDMA]/[MMA] between 0 and 0.05. Initially mainly linear PMMA was formed with weight average molar mass 7.5 g/mol independent of R. At larger reaction extents branched polymers were formed and the systems gelled. The scattering intensity rose initially with the reaction extent, but reached a plateau value at larger reaction extents. The plateau value increased strongly with R. Dynamic light scattering showed the appearance of a slow relaxation not observed in linear PMMA solutions. The data can be interpreted by assuming that the excess scattering originates from the branching points and relaxes through self diffusion of the branched particles. The results agree with predictions of the percolation model for gelation and Rouse dynamics. Viscosity measurements corroborate this interpretation. Measurements on a progressively diluted sample quenched close to the gel point again showed quantitative agreement with the percolation model for gelation. Received 11 May 1998 and Received in final form 22 October 1998     

Growth morphology of nanoscale sputter-deposited Au films on amorphous soft polymeric substrates

The growth of a room-temperature sputter-deposited thin Au film on two soft polymeric substrates, polystyrene (PS) and poly(methyl methacrylate) (PMMA), from nucleation to formation of a continuous film is investigated by means of atomic force microscopy. In particular, we studied the surface morphology evolution of the film as a function of the deposition time observing an initial Au three-dimensional island-type growth. Then the Au film morphology evolves, with increasing deposition time, from hemispherical islands to partially coalesced worm-like island structures, to percolation, and finally to a continuous and rough film. The overall Au morphology evolution is discussed in the framework of the interrupted coalescence model, allowing us to evaluate the island critical radius for the partial coalescence R _c=8.7±0.9 nm for Au on PS and R _c=7.6±0.8 nm for Au on PMMA. Furthermore, the application of the kinetic freezing model allows us to evaluate the room-temperature surface diffusion coefficient D _s≈1.8×10⁻¹⁸ m²/s for Au on PS and D _s≈1.1×10⁻¹⁸ m²/s for Au on PMMA. The application of the Vincent model allows us, also, to evaluate the critical coverage (at which the percolation occurs) P _c=61% for Au on PS and P _c=56% for Au on PMMA. Finally, the dynamic scaling theory of a growing interface was applied to characterize the kinetic roughening of the Au film on both PMMA and PS. Such analyses allow us to evaluate the dynamic scaling, growth, and roughness exponents z=3.8±0.4, β=0.28±0.03, α=1.06±0.05 for the growth of Au on PS and z=4.3±0.3, β=0.23±0.03, α=1.03±0.05 for the growth of Au on PMMA, in agreement with a non-equilibrium but conservative and linear growth process in which the surface diffusion phenomenon plays a key role.     

TDPAC studies of Hf doped YBCO

Time differential perturbed angular correlation measurements of the 133–482 keVγ-γ cascade of¹⁸¹Ta in Hf-doped YBa₂Cu₃O_7−x are presented. The¹⁸¹Hf precurser nuclei are incorporated into the sample by thermal neutron irradiation. Two quadrupole interaction frequencies are observed in the as-irradiated sample:v _Q1=161±10 MHz with intensityf ₁=75%, asymmetry parameterη ₁=0.32 and damping parameter Λ₁=0.42, andv _Q2=1108±40 MHz withf ₂=25%,η ₂=0.62, and Λ₂=0.60. On annealing the sample in air at various temperaturesT _a and quenching to room temperature,f ₁ remained nearly constant forT _a<600°C andv _Q1 for all annealing temperatures indicating that these are insensitive to oxygen stoichiometry. This frequency is interpreted to be due to¹⁸¹Hf substitutingY sites. BeyondT _a=600°C,f ₁ increased and reached a constant value of 90% forT _a=800°C. The value ofv _Q2 showed a slight variation between 1086 and 1160 MHz, whilef ₂ remained nearly constant at 25% forT _a<600°C. This component is identified to be due to¹⁸¹Hf substituting Cu 1 sites in the Cu-O chains of YBCO. Above 600°Cv _Q2 decreased and reached a value of 808 MHz beyond 750°C.     

Neutron scattering study of short-range correlations and ionic diffusion in copper selenide

The paper reports the results of a neutron scattering study of Cu_{2 - d}Se {\hbox{C}}{{\hbox{u}}_{{2 - \delta }}}{\hbox{Se}} superionic compounds. The crystallographic model fitted to the diffraction data shows the occupation of 8c and 32f sites by Cu atoms. Observed diffuse background is related to correlated thermal vibrations of Se and Cu atoms, with Se↔Cu (8c,32f) and Cu (8c)↔Cu (8c) correlations being most important. The quasi-elastic neutron experiments show the decrease of the self-diffusion coefficient with the deviation from the stoichiometry due to the longer residence time of Cu ions between diffusion hops. Combination of neutron diffraction, diffuse scattering and quasi-elastic scattering experimental data suggests that the Cu atoms diffuse between the nearest 8c sites through the 32f sites.     

The Newtonian Limit for Perfect Fluids

We prove that there exists a class of non-stationary solutions to the Einstein-Euler equations which have a Newtonian limit. The proof of this result is based on a symmetric hyperbolic formulation of the Einstein-Euler equations which contains a singular parameter ∈ =  v _T /c, where v _T is a characteristic velocity scale associated with the fluid and c is the speed of light. The symmetric hyperbolic formulation allows us to derive ε independent energy estimates on weighted Sobolev spaces. These estimates are the main tool used to analyze the behavior of solutions in the limit ∈ ↘ 0.     

| m | Partial wave treatment for two-dimensional Coulomb-scattering and Regge pole

The symmetry and |m| partial-wave analysis for two-dimensional (2D) Coulomb-scattering is investigated. As a function of energyE, the |m| partial-wave scattering amplitudef _|m|(θ) is analytically continuated to the, negativeE (complexk) plane, and it is found that the bound state energy eigenvalues (E<0) are just located at the poles off _|m|(θ) on the positive imaginaryk axis as is expected. In addition, as a function of |m|,f _|m|(θ) is analytically continuated to the complex |m| plane, the bound state energy eigenvalues are just located at the poles off _|m|(θ) on the positive real |m| axis.     

On the maximum in the differential cross sections of the F + H2 reaction in the region of small scattering angles

By means of quantum mechanical simulation of the reaction F + H₂(v = 0; j = 0, 1, 2) → H + HF(v′, j′) on the Stark-Werner ground state potential energy surface at collision energies of 1.84, 2.74, and 3.42 kcal/mol, we have analyzed interference of the “partial waves” corresponding to different values of the total angular momentum J. As the vibrational quantum number v′ of the HF(v′, j′) product increases, the interference for the HF forward scattering becomes noticeably more constructive. This is probably the reason for the maximum in the angular distributions of the HF(v′= 3) molecules at small scattering angles that was discovered experimentally by D.M. Neumark, A.M. Wodtke, G.N. Robinson, C.C. Hayden, and Y.T. Lee, J. Chem. Phys. 82 (7), 3045 (1985) at the same collision energies. We have also determined the intervals of J values most effective for forward scattering of the HF(v′, j′) molecules.     

Measurements of the refractive indices and refractive index increment of a synthetic PMMA solutions at 488 nm

We describe a Mach–Zehnder interferometer (MZI) method for measuring the refractive index (RI) of polymethyl-methacrylate (PMMA) solution in both acetone and methyl-ethyl-ketone (MEK). The measurements are made as a function of concentration values 4, 8, 12, 16 and 20 g/l at a wavelength of 488 nm with a high degree of accuracy tends to 1.4×10⁻⁵. The refractive index increments (RIIs) dn/dc of PMMA in both investigated solvents are determined too. In addition, the RIIs Δn as a function of concentration and the RIIs at zero concentration (dn/dc)_c=0 are determined for both solvents accurately. The PMMA solutions in acetone and MEK solvents are chosen for laser light scattering investigations.     

Muon spin relaxation study on magnetism in high quality single crystal of a high transition temperature superconductor La2−xSrxCuO4−σ (0.11≤x≤0.14)

The positive muon spin relaxation method is applied to probe magnetic ordering in the superconducting phase of a high quality single crystal of La_2−xSr_xCuO_4−σ (0.11≤x≤0.14). The well characterized crystal ofx=0.11 (T _c=34.5 K) with nearly complete flux exclusion exhibits spin freezing at 8K(T _f) with significant spin fluctuation up to 20 K. The onset of spin fluctuation andT _f decrease against increasingx towardsx=0.15, suggesting an existence of a magnetic phase boundary aroundx whereT _c becomes maximum.     

Vacancy formation energies from positron trapping measurements

The threshold temperatureT _t at which thermally generated vacancies produce measurable positron trapping is a linear function of the energy of self-diffusionQ. SinceQ is also linearly related to the vacancy formation energyE _1v ^f , a measurement ofT _t leads directly to a determination of the latter. It is possible to make a precise determination ofE _1v ^f without approaching the melting point—a major advantage in dealing with refractories or with metals having a high vapour pressure in the solid state.     

Effect of PMMA on crystallization behavior and hydrophilicity of poly(vinylidene fluoride)/poly(methyl methacrylate) blend prepared in semi-dilute solutions

Films of poly(vinylidene fluoride) (PVDF)/poly(methyl methacrylate) (PMMA) blend were derived from a special procedure of casting semi-dilute solutions. Hydrophilic character and crystallization of PVDF were optimized by variation of PMMA concentration in PVDF/PMMA blends. It was found that a PVDF/PMMA blend containing 70 wt% PMMA has a good performance for the potential application of hydrophilic membranes via thermally induced phase separation. The films presented β crystalline phase regardless of PMMA content existed in the blends. Thermal analysis of the blends showed a promotion of crystallization of PVDF with small addition of PMMA which induced larger lamellar thickness of PVDF, leading to the largest spherulitic crystal of PVDF (10 wt% PMMA) is about 8 μm. SEM micrographs illustrated no phase separation occurred in blends, due to the high compatibility between PVDF and PMMA.     

Kinematics of Cherenkov’s effect with noninvariant velocity of light

The kinematics of Cherenkov’s effect is considered for an electron moving in the Minkowski space with universal time and velocity of light c = c ₀ (1 + v ²/c ₀²)^1/2, where c ₀ = 3⋅10 m/s is the invariant constant and v is the particle velocity. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 47–50, January, 2009.     

On the Poisson Limit Theorems of Sinai and Major

Let f(ϕ) be a positive continuous function on 0 ≤ϕ≤Θ, where Θ≤ 2 π, and let ξ be the number of two-dimensional lattice points in the domain Π _R (f) between the curves r=(R+c ₁/R)f(ϕ) and r=(R+c ₂/R)f(ϕ), where c ₁<c ₂ are fixed. Randomizing the function f according to a probability law P, and the parameter R according to the uniform distribution μ _L on the interval [a ₁ L,a ₂ L], Sinai showed that the distribution of ξ under P×μ _L converges to a mixture of the Poisson distributions as L→∞. Later Major showed that for P-almost all f, the distribution of ξ under μ _L converges to a Poisson distribution as L→∞. In this note, we shall give shorter and more transparent proofs to these interesting theorems, at the same time extending the class of P and strengthening the statement of Sinai. Received: 15 June 1999 / Accepted: 11 February 2000     

Analytical calculations and properties of γ-rays polymerization of novel acrylates copolymer system

A detailed study of some physical properties of pure PMMA (polymethyl methacrylate) film and MMA/Ani (methyl methacrylate/aniline) films is presented. Films of thicknesses ranged from 0.04 to 0.72 mm for MMA/Ani were prepared while it is 0.68 mm for PMMA. The structure of the sample is analyzed by X-ray diffraction technique and is found to be amorphous (PMMA) and partially crystalline (MMA/Ani). Ultra violet–visible electronic absorption spectra measurements were analyzed to obtain some important parameters such as molar extrication coefficient, oscillator strength, dipole strength and having good thermal stability (T_d >300 °C) was also reported. TGA studies revealed that the thermal stability of polymethyl methacrylate, prepared by radiation polymerization of methyl methacrylate, improved after copolymerization with aniline. Also, optical behavior of film samples was analyzed by obtaining transmission spectra, in the wavelength range of 200–1100 nm. It was found that all studied samples lead to the appearance of a second edge at lower photon energy due to the formation of the induced energy states. From the intensity of absorption interband transitions (B and Q) which are assigned as type π–π^* for both PMMA and MMA/Ani films, the energy gaps E_g1 and E_g2 were calculated respectively. The optical conductivity (σ) was determined and it was found that with the increase of thicknesses optical energy gap decreases monotonically and the refractive index increases.     

Investigation of dibutyl phthalate as plasticizer on poly(methyl methacrylate)–lithium tetraborate based polymer electrolytes

Polymer electrolyte membranes, comprising of poly(methyl methacrylate) (PMMA), lithium tetraborate (Li₂B₄O₇) as salt and dibutyl phthalate (DBP) as plasticizer were prepared using a solution casting method. The incorporation of DBP enhanced the ionic conductivity of the polymer electrolyte. The polymer electrolyte containing 70 wt.% of poly(methyl methacrylate)–lithium tetraborate and 30 wt.% of DBP presents the highest ionic conductivity of 1.58 × 10⁻⁷ S/cm. The temperature dependence of ionic conductivity study showed that these polymer electrolytes obey Vogel–Tamman–Fulcher (VTF) type behaviour. Thermogravimetric analysis (TGA) was employed to analyse the thermal stability of the polymer electrolytes. Fourier transform infrared (FTIR) studies confirmed the complexation between poly(methyl methacrylate), lithium tetraborate and DBP.     

Study of CdSe/CdS quantum dots in solutions and gels by small-angle X-ray scattering

The sizes of semiconductor nanocrystals of CdSe/CdS quantum dots (QDs) synthesized by the colloidal method were estimated using small-angle X-ray scattering. The distribution of QD nanocrystals in organic solvents of different polarities and in polymer gels and matrices is studied. Structural invariants of scattering QD particles (heterogeneities of the electron density)—namely, inertia radii and sizes, forms, and dispersive composition of particles—are determined. The contribution of scattering by QDs in solutions and gels is calculated. The effective sizes of particles and their aggregates are determined, and the parameters of the distribution over the QD sizes in organic solvents and polymer matrices are estimated. The typical distance between particles in samples is determined. The position of the maximum at the beginning of the small-angle scattering curves corresponds to the distance d _m = 2π/h ₀ between the planes (here, h ₀ is the position of the maximum on the scale h). It is 74–76.9 ? for solutions, 60 ? for gels, and 99 ? for polymer matrices with concentrations of up to 0.15% and 77 ? for those with the concentrations exceeding 0.15%, which is close to the estimation of the sizes of separate CdSe QDs that was obtained from the distribution histograms (60–80 ?). This result shows that CdSe/CdS QDs introduced in the polymer matrices disperse to form either separate particles or small aggregates and located at a distance on the order of 80 ? from each other.     

Study of B c → J / ψ π , η c π decays with?perturbative?QCD?approach

The B _c →J/ψ π, η _c π decays are studied with the perturbative QCD approach. It is found that the form factors and for the B _c →J/ψ, η _c transitions and the branching ratios are sensitive to the parameters ω, v, f _J/ψ and , where ω and v are the parameters of the charmonium wave functions for a Coulomb potential and the harmonic-oscillator potential, respectively, and f _J/ψ and are the decay constants of the J/ψ and η _c mesons, respectively. The large branching ratios and the clear signals of the final states make the B _c →J/ψ π, η _c π decays the prospective channels for measurements at the hadron colliders.     

Determination of low-energy parameters of neutron-proton scattering in the the shape-parameter approximation from present-day experimental data

On the basis of the total cross sections for neutron-proton scattering in the region of laboratory energies below 150 keV, the value of σ₀ = 20.4288(146) b was obtained for the total cross sections for neutron-proton scattering at zero energy. This value is in very good agreement with the experimental cross sections obtained by Houke and Hurst, but it is at odds with Dilg’s experimental cross section. By using the value that we found for σ₀ and the experimental values of the neutron-proton coherent scattering length f, the deuteron binding energy ɛ _t , the deuteron effective radius ρ _t (−ɛ _t , −ɛ _t ), and the total cross section in the region of energies below 5 MeV, the following values were found in the shape-parameter approximation for the low-energy parameters of neutron-proton scattering in the spin-triplet and spin-singlet states: a _t = 5.4114(27) fm, r _0t = 1.7606(35) fm, v _2t = 0.157 fm³, a _s = −23.7154(80) fm, r _0s = 2.706(67) fm, and v _2s = 0.491 fm³.