Dynamic scaling of polymer gels comprising nanoparticles

We present dynamic light scattering (DLS) measurements of soft poly(methyl-methacrylate) (PMMA) and polyacrylamide (PA) polymer gels prepared with trapped bodies (latex spheres or magnetic nanoparticles). We show that the anomalous diffusivity of the trapped particles can be analyzed in terms of a fractal Gaussian network gel model for the entire time range probed by DLS technique. This model is a generalization of the Rouse model for linear chains extended for structures with power law network connectivity scaling, which includes both percolating and uniform bulk gel limits. For a dilute dispersion of strongly scattering particles trapped in a gel, the scattered electric field correlation function at small wavevector ideally probes self-diffusion of gel portions imprisoning the particles. Our results show that the time-dependent diffusion coefficients calculated from the correlation functions change from a free diffusion regime at short times to an anomalous subdiffusive regime at long times (increasingly arrested displacement). The characteristic time of transition between these regimes depends on scattering vector as approximately q(-2), while the time decay power exponent tends to the value expected for a bulk network at small q. The diffusion curves for all scattering vectors and all samples were scaled to a single master curve.     

Viscoelastic scaling in polymer gels

New scaling laws for chain networks are derived to describe the fundamental relationships between the viscosity exponent (k), viscoelastic exponent (m), stretched exponent (β), spatial dimension (d). fractal dimension (d_f), and a universal constant (γ). The scaling of the total number of monomers and the radius of gyration is defined by d_f. We have discovered γ = m/β to be a universal constant which relates the shear modulus of a polymer gel melt to the shear modulus near the glass transition. Analyzing the size-dependent shear viscosity, we have determined γ = 3d_fcd/(7d−5d_fc) = 2.647 for d = 3 where d_fc is the fractal dimension of critical clusters at the gel point. By using γ, the present theory extends previous work pertaining to systems near the sol-gel transition, and shows how properties far from the critical point can be explained. The theoretical prediction is in good agreement with viscoelastic measurements.     

Heat capacity and thermodynamic properties of tellurites Yb2(TeO3)3, Dy2(TeO3)3 and Er2(TeO3)3

The experimental results obtained for the specific molar heat capacity of the tellurites Yb₂(TeO₃)₃, Dy₂(TeO₃)₃ and Er₂(TeO₃)₃ are processed by the least squares method. The temperature dependence of the specific molar heat capacity derived is used to determine the thermodynamic properties: entropy ( \Updelta_T￠^T S_m⁰ ), \left( {\Updelta_{T\prime }^{T} S_{m}^{0} } \right), enthalpy ( \Updelta_T￠^T H_m⁰ ) \left( {\Updelta_{T\prime }^{T} H_{m}^{0} } \right) and Gibbs function ( \Updelta_T￠^T G_m⁰ ) \left( {\Updelta_{T\prime }^{T} G_{m}^{0} } \right) of the tellurites Yb₂(TeO₃)₃, Dy₂(TeO₃)₃ and Er₂(TeO₃)₃.     

Rheological properties of the methylcellulose gels in N,N-dimethyl formamide: Validity of scaling laws

The rheological behavior of the methylcellulose (MC) gels in N,N-dimethylformamide (DMF) was studied under dynamic compression with respect to the presence of various concentrations c (1, 2, 2.5 and 3 wt %) and different molecular weight M (4.1 × 10⁴, 6.3 × 10⁴ and 8.8 × 10⁴) of MC in the gels. The temperature scan for the 1 wt % MC gel (M = 8.8 × 10⁴) in DMF shows double crossover of the storage modulus E′ with the loss modulus E″. This indicates that two types of transitions namely the phase separated MC-DMF mixture to MC-DMF gel and MC-DMF gel to solution are present. The plot of storage modulus E′ with temperature shows almost plateau like behavior. This plateau like behavior may reflect the equilibrium between the core formation and core disintegration. In the frequency scan of MC gels, the modulus increases with an increase in the concentration. This can be explained by the increase in core structure of the gel. The core formation in the MC-DMF gel is a concentration dependent parameter. While comparing the different molecular weight grades of MC, it is observed that the storage modulus increases with an increase in the molecular weight of the MC. The validity of three scaling laws is also investigated with respect to various concentration of MC-88.000. The modified scaling law in terms of relative frequency and modulus $\left( {\eta '_r = \frac{{\left| {\frac{{E''}} {\omega } - \left( {\frac{{E''}} {\omega }} \right)_c } \right|}} {{\left( {\frac{{E''}} {\omega }} \right)_c }}andE'_r = \frac{{\left| {E' - E'_c } \right|}} {{E'_c }}} \right) $ is seemed to be applicable.     

Lanthanoidtellurate Ln2TeO6

Lanthanoid Tellurates Ln₂TeO₆ The crystal structure of La₂TeO₆, orthorhombic, a = 551.0, b = 944.1, c = 1038.7 pm, and crystallographic data of other isostructural lanthanoid tellurates (up to Yb₂TeO₆) formerly described as hexagonal, have been determined. For a second modification of the Yb compound, the Na₂SiF₆ structure has been confirmed.     

Vibrational spectra of Hg3TeO6 and Hg2TeO5

The infrared and Raman spectra of the crystalline hexaoxotellurates Hg3TeO6 and Hg2TeO5 were recorded and discussed on the basis of a site symmetry analysis derived from known structural data. Approximate values for the Te-O bond force constants are reported and some comparisons with related species are made.     

Specific thermal and thermodynamic properties of the tellurites Fe2(TeO3)3, Fe2TeO5 and Fe2Te4O11

The temperature dependence of the molar heat capacities of the tellurites Fe₂(TeO₃)₃, Fe₂TeO₅ and Fe₂Te₄O₁₁ were determined. By statistical manipulation of the values obtained, the parameters in the equations for the corresponding compounds showing this dependence were determined using the least-squares method. These equations together with the standard molar entropies were used to determine the thermodynamic functions Δ₀^T S _m⁰, Δ_T^T,H _m⁰ and (Φ_m⁰ + Δ₀^T’ H _m⁰ / T) for T’=298.15 K.     

Hydrogen sorption properties of non-stoichiometric ZrMn2-based systems

Hydrogen sorption by several non-stoichiometric ZrMn₂-based alloys was studied at pressures up to 50 atm and over a temperature range from 23 to about 200°C. The dissociation pressure of the hydrides is raised by a factor of 500–1000 for ZrMn₂T_0.8 or ZrMn₂T_1.2 (T ≡; transition element or Cu) as the host material compared with that for ZrMn₂ as the host material. Among the hydrides studied, ZrMn₂Co_0.8-H exhibited the highest value for the plateau pressure. Measurements of the experimental densities of the non-stoichiometric host materials show good agreement with the substitutional model in which manganese and/or T partially replace zirconium at the zirconium sites. The hydrides have remarkably low heats of formation and entropies of 12–19 kJ (mol H₂)⁻¹ and 50–80 J (mol H₂)⁻¹ K⁻¹ respectively. The hydrogen absorption or desorption is extremely rapid, e.g. 90% of the hydrogen was released or absorbed in about 1 min. The hydrides studied exhibit features which strongly suggest that they have technological potential.     

Characterization of emission properties of Er3+ ions in TeO2-CdF2-WO3 glasses

TeO(2)-CdF(2)-WO(3) glasses with various compositions and Er(3+) concentrations were prepared by conventional melting method. Their optical properties were studied by measuring the absorption, luminescence spectra and the decay patterns at room temperature. From the optical absorption spectra the Judd-Ofelt parameters (Ω(t)), transition probabilities, branching ratios of various transitions, and radiative lifetimes were calculated. The absorption and emission cross-section spectra of the (4)I(15/2) to (4)I(13/2) transition of erbium were determined. Emission quantum efficiencies and the average critical distance R(0) which provides a measure for the strength of cross relaxation were determined.     

Photocatalytic and antifouling properties of TiO2-based photocatalytic membranes

Photocatalysis has been extensively studied due to its potential ability to avoid the excessive use of chemical reagents and reduce the energy consumption by employing solar energy. Moreover, to alleviate the reduction in the membrane permeation selectivity, separation efficiency, and membrane service life caused by the emerging micro-pollutants and membrane fouling, membrane technology is often coupled with microbial, electrochemical, and catalytic processes. However, although physical/chemical cleaning and membrane module replacement can overcome the inherent limitations caused by membrane fouling and other membrane separation processes, high operating costs limit their practical applications. In this review, common preparation methods for TiO₂ photocatalytic membranes are described in detail, and the main approaches to enhancing their photocatalytic performance are discussed. More importantly, the mechanism of the TiO₂ photocatalytic membrane antifouling process is elucidated, and some applications of photocatalytic membranes in other areas are described. This review systematically outlines future research directions in the field of photocatalytic membrane modification, including metal and non-metal doping, fabrication of heterojunction structures, control over reaction conditions, increase in hydrophilicity, and increase in membrane porosity.     

Intermolecular interaction in TeO2 crystal

It is shown that the abnormal long-range Te-Te intermolecular interaction in TeO(2) crystals may be related to the tunneling of electrons from the 5s(2) active lone pairs of Te(4+) ions and their partial delocalization on neighboring Te(4+).     

Scattering properties of agarose gels

Static light scattering and small angle neutron scattering measurements are reported for agarose hydrogels prepared under various conditions of concentration and temperature. For the wide range of transfer wave vector explored, these measurements show that the gels do not display fractal behaviour. Their structure is better described by a stretched exponential form, in which the value of the exponent is n = 0.2. As found by other authors, a maximum in the scattering intensity is observed in the light scattering spectra. The position of the maximum, q_max, depends on the concentration and on the thermal history of the sample. The inverse length 1/q_max is in good agreement with published measurements of the pore size D in this system. Preliminary measurements by small angle scattering indicate that the sol-gel transition is not of spinodal type.     

Die Kristallstruktur von Li2TeO3

Crystal Structure of Li₂TeO₃ Crystals of Li₂TeO₃ were prepared from melts. Li₂TeO₃ crystallizes in the monoclinic system, space group C2/c. The lattice parameters are a = 5.06₉, b = 9.56₆, c = 13.72₇ Å, β = 95.4°. The formular unit is 8. The crystal structure has been determined by Patterson and threedimensional differential Fourier synthesis refined by least squares using isotropic temperature corrections. The final R-value of 772 observed reflections is 0.101. Li₂TeO₃ forms a layer lattice consisting of trigonal TeO₃ pyramids and deformed LiO₄ tetrahedrons. The TeO₃ pyramids are only connected with the corners of LiO₄ groups, which are linked one with another by common corners and edges.     

Crystal structure of the new compound Co6(TeO3)2(TeO6)Cl2

The new compound Co₆(TeO₃)₂(TeO₆)Cl₂ has been isolated during an investigation of the system CoO:CoCl₂:TeO₂. The new compound is deep purple in color and crystallizes in the tetragonal system, space group P4₂/mbc, a=8.3871(7) Å, c=18.5634(19) Å, Z=4. The Co(II) ions have octahedral [Co1O₆] and tetrahedral [Co2O₃Cl] coordinations. Tellurium is present both as Te(IV) with a tetrahedral [Te1O₃E] coordination, where E is the 5s² lone-pair and as Te(VI) with an octahedral [Te2O₆] coordination. The structure is made up of intersecting layers of tetrahedra forming channels comprising octahedra chains that run along the c-axis. The new compound is the first cobalt tellurium oxochloride described.     

Intermolecular Interaction in TeO2 Crystal.

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Thermodynamic studies on Pr2TeO6

The standard Gibbs energy of formation of Pr₂TeO₆ $ (\Updelta_{\text{f}} G^{^\circ } \left( {{ \Pr }_{ 2} {\text{TeO}}_{ 6} ,\;{\text{s}}} \right)) $ was derived from its vapour pressure in the temperature range of 1,400–1,480 K. The vapour pressure of TeO₂ (g) was measured by employing a thermogravimetry-based transpiration method. The temperature dependence of the vapour pressure of TeO₂ over the mixture Pr₂TeO₆ (s) + Pr₂O₃ (s) generated by the incongruent vapourization reaction, Pr₂TeO₆ (s) = Pr₂O₃ (s) + TeO₂ (g) + ½ O₂ (g) could be represented as: $ { \log }\left\{ {{{p\left( {{\text{TeO}}_{ 2} ,\;{\text{g}}} \right)} \mathord{\left/ {\vphantom {{p\left( {{\text{TeO}}_{ 2} ,\;{\text{g}}} \right)} {{\text{Pa}} \pm 0.0 4}}} \right. \kern-0em} {{\text{Pa}} \pm 0.0 4}}} \right\} = 19. 12- 27132\; \left({\rm{{{\text{K}}}}/T} \right) $ . The $ \Updelta_{\text{f}} G^{^\circ } \;\left( {{ \Pr }_{ 2} {\text{TeO}}_{ 6} } \right) $ could be represented by the relation $ \left\{ {{{\Updelta_{\text{f}} G^{^\circ } \left( {{ \Pr }_{ 2} {\text{TeO}}_{ 6} ,\;{\text{s}}} \right)} \mathord{\left/ {\vphantom {{\Updelta_{\text{f}} G^{^\circ } \left( {{ \Pr }_{ 2} {\text{TeO}}_{ 6} ,\;{\text{s}}} \right)} {\left( {{\text{kJ}}\,{\text{mol}}^{ - 1} } \right)}}} \right. \kern-0em} {\left( {{\text{kJ}}\,{\text{mol}}^{ - 1} } \right)}} \pm 5.0} \right\} = - 2 4 1 5. 1+ 0. 5 7 9 3\;\left(T/{\text{K}}\right) .$ Enthalpy increments of Pr₂TeO₆ were measured by drop calorimetry in the temperature range of 573–1,273 K and heat capacity, entropy and Gibbs energy functions were derived. The $ \Updelta_{\text{f}} H_{{298\;{\text{K}}}}^{^\circ } \;\left( {{ \Pr }_{ 2} {\text{TeO}}_{ 6} } \right) $ was found to be $ {{ - 2, 40 7. 8 \pm 2.0} \mathord{\left/ {\vphantom {{ - 2, 40 7. 8 \pm 2.0} {\left( {{\text{kJ}}\,{\text{mol}}^{ - 1} } \right)}}} \right. \kern-0em} {\left( {{\text{kJ}}\,{\text{mol}}^{ - 1} } \right)}} $ .     

Ag2Hg2(TeO4)3

Red single crystals of disilver(I) dimercury(II) tris­[tetra­oxo­tellurate(VI)], Ag₂Hg₂(TeO₄)₃, were obtained under hydro­thermal conditions at 523 K. The structure is built up of _∞¹[(TeO_2/1O_4/2)({TeO_2/1O_2/2}₂O_4/2)] chains, with an overall composition [TeO₄]²⁻, that run parallel to the crystallographic a axis. Distorted AgO₆ and HgO₆ polyhedra (the latter with two short and nearly collinear Hg—O bonds) link the tellurate chains into a three‐dimensional network. Except for one Te atom situated on an inversion center, all atoms occupy general positions.     

Dynamic scaling method and interface growth

The dynamic scaling approach is an important tool for describing the time evolution of rough interfaces. It computes dynamic scaling parameters alpha and beta, which characterize surface and time correlations. Applications of dynamic scaling to random deposition and ballistic deposition are discussed. A model of random adsorption on fractal substrates is presented. Then the influence of surface diffusion on adsorption is analyzed. The dependence of alpha and beta on the substrate fractal dimension, together with the dependence of the fractal dimension of the gas-solid interface on adsorption coverage are computed.