The Softness Parameters of Ions. Prediction of the Occurrence of Miscibility Gaps in Molten Salt Mixtures

Softness parameters σ_M for cations and σ_X for anions, have been calculated as dimensionless quantities for approx. 90 cations and 18 anions. They are given by σ_M = [σ_A (M^m+) - σ_A(H⁺)]/σ_A(H⁺) and σ_X = [σ_B(X^a?) - σ_B(OH^?)]/σ_A(H⁺) where σ_A = [σI_i(M) + ΔH⁰_h(M^m+)]/m and σ_B = [-E_a(X) + ΔH⁰_h(X^a?)]/a are Ahrland's parameters. The new normalized and comparative (to the test ions H⁺ and OH^?) softness parameters are positive for soft ions and negative for hard ones. These parameters, obtained independently, are used with a four-coefficient equation to calculate coordinate bond energies for metal halides with acceptable accuracy. Considerations of the average coordination in reciprocal molten salt mixture lead to an expression for the metathesis energy change as proportional to the product of the differences in softness parameters of the two cations and the two anions. An empirical one-coefficient equation involving the softness parameters is proposed to deal with next-nearest-neighbor interactions in binary common-ion molten salt mixtures. These relationships are then used with Blander and Topol's equation to predict the occurrence of irascibility gaps in uni-univalent reciprocal salt mixtures. The gaps found in other systems are also discussed in terms of the softness of the constituent ions.     

Rheological behavior of compatible polymer blends. I. Blends of poly(styrene-Co-acrylonitrile) and poly(ε-caprolactone)

The rheological behavior of blends of poly(styrene-co-acrylonitrile) (SAN) and poly(ε-caprolactone) (PCL) was investigated, using a cone-and-plate rheometer. For the study, blends of various compositions were prepared by melt blending using a twin-screw compounding machine. The rheological properties measured were shear stress (σ₁₂), viscosity (η), and first normal stress difference (N₁) as functions of shear rate (γ) in steady shearing flow, and dynamic storage modulus (G′) and loss modulus (G″) as functions of angular frequency (ω) in oscillatory shearing flow, at various temperatures. It has been found that logarithmic plots of N₁ versus σ₁₂, and logarithmic plots of G′ versus G″, become virtually independent of temperature but vary regularly with blend composition, and that the zero-shear viscosity of the blends, (η_o)_blend, follows the relationship, 1/log(η_o)_blend = w_A/log η_0A + w_B/log η_0B, where η_0A and η_0B are the zero-shear viscosities of components A and B, respectively, and w_A and w_B are the weight fractions of components A and B, respectively. The physical implications of the relationship found are discussed.     

Molecular weight distribution and rheological properties of polyisobutylene solutions

The molecular weight distribution of a series of polyisobutylenes was determined using osmotic pressure measurements, gel permeation chromatography, and intrinsic viscosity. All of the polymers except for one, a blend of the highest and lowest molecular weight constituents, had similar moderate molecular weight distributions. The “extended chain length” method of calibrating the gel permeation chromatograph for polyisobutylenes was found to be effective. Steady state and transient shear stresses and normal stresses were measured on 5% decalin solutions of these polymers. The zero shear viscosity increased with the 3.3 power of molecular weight, and the zero shear normal stress coefficient (σ₁₁ ? σ₂₂)/Γ² varied with the 7.5 power. Relative elastic memory as measured by (σ₁₁ ? σ₂₂)/σ₁₂ or stress relaxation increased with increasing molecular weight (and at constant number- or weight-average molecular weight) with breadth of distribution. Stress overshoot also correlated with this tendency.     

Stress growth and relaxation of a molten polyethylene in a modified weissenberg rheogoniometer

A Weissenberg rheogoniometer was modified^1-3 to improve sample temperature uniformity and constancy (to within ±0.5°C) and to give a quicker response to normal thrust changes (estimated gap change ≤0.1 μm/kg thrust; gap angle = 8.046°; gap radius = 1.2 cm; servomechanism replaced by an open-loop cantilever spring of 10 kg/μm stiffness). Low-density polyethylenes (IUPAC samples A and C, melt index at 190°C = 1.6) at 150°C were used in step-function shear rate experiments. Inspection of marked sectors in the samples showed substantial uniformity of shear at values of ? = 0.1, 2, and 5 sec^?1; for ? = 10 sec^?1 and S ≤ 2 shear units (S = ?t), the shear was highly nonuniform at and near the free boundary. Using selected premolded samples A, scatter in seven replicate tests at ? = 1.0 sec^?1 did not exceed ±6% for N₁(t) and ±5% for σ(t) (N₁ = primary normal stress difference; σ = shear stress; t = time of deformation from the initiation of experiment at zero time). N₁(t) and σ(t) data agreed with Meissner's¹; for ? = 0.1, 2.0, 5.0, and 10.0 sec^?1, torque maxima occurred at S = 6 shear units, and thrust maxima occurred in the range of 10 to 20 shear units. σ(t) and N₁(t) data do not satisfy the van Es and Christensen⁴ test for rubber-like liquids with strain rate invariants included in the memory function. On cessation of shear (after a shear strain S at constant shear rate ?), initial values of ?dσ(t)/dt and ?dN₁(t)/dt were found to depend strongly on S, in some cases passing through maxima as S was increased. After shearing at ? = 0.1 sec^?1 for 500 sec, such that stresses became constant, stress relaxation data satisfied Yamamoto's⁵ equation of dN₁(t)/dt = ?2?σ(t).     

Anomalous galvanomagnetic properties of graphite in the quantum limit

Recent experiments on the galvanomagnetic effects of graphite in the quantum limit revealed that (1), σ_xyH is not a constant but depends on the field strength; (2), the resistivity ? ? σ_xx^?1 at low temperatures has a field dependence of? = ∣(A + BHⁿ), n ? 1; and (3), the ? vs T curve has a maximum at about T = 25K. These results cannot be explained by a simple theory. However, in consideration of the appearance of the bound states D⁰ and A⁰ in the quantum limit we can provide a qualitative explanation of the above observed results, where D correspond to donor and A represents acceptor. In the quantum limit the possibility of the transitions D⁺ + (?e) → D⁰ and A^? + (+e) → A⁰ is pointed out. Co-existence of the ionized impurity scattering and the neutral impurity scattering explains the qualitative features of the (H,T)-dependence of the resistivity at low temperatures. At high temperatures it is necessary to consider the phonon scattering and the carrier-carrier scattering. Without the carrier-carrier scattering the (H,T)-dependence of ? at T > 25K cannot be explained.     

Stress-strain behavior of polychloroprene vulcanizates containing polymer-gel particles

The equations of stress-strain of gel-filled polymer under large deformation were derived by using a simple model i.e. a sphere in a cubic matrix. The author finds for no adhesion between the phases: In case of perfect adhesion between the phases: where σ(α) is the stress of a blend at an elongation ratio of α, σ_R(α) the stress of a rubber matrix at α, σ_G(α_G) the stress of a gel component at α_G, σ_R (α_R) the stress of a rubber matrix at α_R, ? the volume fraction of gel. The validity of Eq 1 was shown for the polychloroprene vulcanizates containing polystyrene-gel which exhibits no adhesion with the polychloroprene matrix. This result shows the value of the model proposed here. The tensile strength of polychloroprene vulcanizates filled with polychloroprene-gel at break is discussed by the use of Eqs 2–4.     

Steady‐shear rheology properties of polydimethylsiloxane (PDMS) colloids as a new contrast agent for nuclear magnetic resonance imaging

This work investigated the toxicity, the nuclear magnetic resonance (NMR) spectra, the NMR imaging, and the steady‐rheology properties concerning polydimethylsiloxane (PDMS) colloids. These experiments illustrate low toxicity, strong NMR signal intensity, as well as clear images, and render the colloids the potential application as contrast agent for gastrointestinal NMR imaging. The steady‐shear rheology data are fitted very well by the model τ = τ₀ + AÝ^m. According to the theory of Princen and Kiss, 12 we found the yield stresses (τ₀) of the colloids are proportional to φ^1/3/D in 0.72 ≦ φ ≦ 0.81. Based on the model and the definition of the capillary number Ca = τ/(σ/R), a linear relationship between log(D) and m was discovered if the assumptions that 2Ca σ/A and Ý_eff are constants are satisfied. We also proved these assumptions are rational in the investigated range 0.62 ≦ φ ≦ 0.81. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 1888–1896, 2002     

Relationships between mechanical properties and microhardness of polyethylenes

The values of the elastic modulus (E) and the yield stress (Y) and the shape of the strain-stress curves of different polyethylenes have been related to the microhardness (MH) of these materials, considering the roles that the crystalline, amorphous, and interfacial regions play in the deformation of semicrystalline polymers. Linear relations between microhardness and degree of crystallinity, (1 – λ)_d, and between the logarithms of E and MH have been found. The variations of the parameters 100Y/E and σ_min/Y (σ_min is the relative minimum value of the nominal stress for elongations above the yield point) as a function of (1–λ)_d follow different trends for linear and branched polyethylenes. Moreover, it has been found that the ratio MH/Y is smaller than three for these materials, approaching this theoretical value (Tabor relation) only for the highest crystallinity levels.     

New techniques for measuring maximum reflectance of vitrinite and dispersed vitrinite in sediments

Maximum reflectance, R_max, can be calculated by the following equation: $\text{R}{}_{\max }\text{= (}\text{R}{}_1\text{+ R}{}_3\text{2}\text{) + (}\text{(R}{}_1\text{? R}{}_2\text{)}{}^2\text{+ (R}{}_2\text{? R}{}_3\text{)}{}^2\text{2}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ in which R₁, R₂, and R₃ are three separate reflectance readings on the same vitrinite grain at 45° angular intervals. The equation is derived from the reflectance distribution function for a central section of a reflectance indicatrix: R_α = R_maxcos²α + R′_minsin²α where R_α is the reflectance measured in the direction α degrees from R_max, R′_min is an apparent minimum which has the minimum value on this central section, and R_max ? R′_min ? R_min. This new technique can be further simplified by rotating the polarizer in 45-degree intervals to obtain three photometer readings and then converting them to R₁, R₂, and R₃, by the use of empirically-established conversion factors. The new techniques do not require the full revolution of the microscope stage and, therefore, are particularly suitable for measuring small grains of vitrinite.     

Flow property analysis of irregular powders

Accurate yield locus analysis using computer techniques can now be carried out on simple and complex irregular powders, as well as on regular powders, by performing a least squares regression on the equation n log(τ_i/τ_L) = log [(T_s + σ_i/σ_L)/(T_s + 1)]This equation reduces any number of yield loci having a common shear index value, n, to a single straight line of slope n provided that all individual shear stress,τ_i, and normal stress, σ_i points are divided by their respective steadystate stress values τ_L and σ_L, and that the correct value for specific tension, T_s = T/σ_L is entered for each locus. Improved values for both n and T_s are found by successive reiteration of the above regression and by subsequent regeneration of individual yield locus values for cohesion, C, and tension, T, from a solution of the equation.

Simple irregular powders which show a constant n, but a variable angle of static internal friction, ψ_s, are easily handled by this technique. Complex irregular powders, in which both n and ψ_s vary, present greater difficulty, but can be analysed by taking a large number of points and operating on individual loci in pairs or one at a time. Examples are given of industrial powders showing both simple and complex irregularity, and particular reference is made to the effect of variable friction characteristics on overall flowability, ζ_i.     

Luminescence properties of Dy3+-doped alkali lead alumino borosilicate glasses

A new series of Dy³⁺-doped sodium lead alumino borosilicate glasses are prepared by the melt quenching technique with the chemical composition 20Na₂O- 10PbO-(5-x)Al₂O₃-40B₂O₃–25SiO₂-xDy2O3 (where x?=?0, 0.5, 1.0 and 1.5?mol%) and are characterized by various spectroscopic techniques such as XRD, FT-IR, Optical absorption spectra, Fluorescence spectra and Decay measurements. Optical and Luminescence spectra of all the glasses are recorded at room temperature. From the optical absorption spectra, optical band gap and Urbach energies of Dy³⁺-doped titled glasses have been evaluated. The oscillator strengths and the intensity parameters, Ω_λ (λ?=?2, 4 and 6) are calculated using Judd-Ofelt analysis. The various lasing parameters like transition probability (A_T), branching ratio (β_R), stimulated emission cross-section (σ_e) and the radiative lifetime (τ_rad) for different emission levels of Dy³⁺ ions have been evaluated. Fluorescence spectra show sharp emission peaks are observed at 482?nm (blue), 575?nm (yellow) and 665 (red) under 385?nm excitation, which are attributed to ⁴F_9/2→⁶H_15/2, ⁶H_13/2 and ⁶H_11/2 transitions respectively. The yellow-to-blue intensity ratio (Y/B) increase up to 1.0?mol% Dy³⁺ ion content and beyond it decreases because of concentration quenching which occurs due to the energy transfer between Dy³⁺ and Dy³⁺ ions. The x, y coordinates of the prepared glasses pass through the white light region in the CIE 1931 chromaticity diagram. The results reveal that these glasses emit quality white light which is suitable for the development of W-LEDs. The color purity and the correlated color temperature (CCT) are also calculated for the present work. Various physical parameters such as density, refractive index, and ion concentration etc., are calculated. Among the prepared glasses, NPABSDy10 glass exhibits higher σ_e, β_R, σ_exτ_R, and σ_exΔλ_eff values corresponding to the ⁴F_9/2→⁶H_13/2 emission band and these are in turn specifies its suitability for W-LEDs and visible laser applications.     

Effect of hydrostatic pressure on the deformation behavior of polyethylene and polycarbonate in tension and in compression

The stress-strain response of crystalline high density polyethylene and of amorphous polycarbonate has been determined in tension and in compression at superimposed pressures up to 1104 MPa(160 ksi). Strain softening occurred in the polycarbonate at low pressures but was inhibited by pressure. Tensile necking occurred in both materials, but was promoted by pressure in polyethylene and inhibited in polycarbonate. The initial modulus, E, and the flow stress, σ, at a given offset strain varied linearly with the mean pressure, P, with essentially the same pressure coefficient, α. Thus, E = (1+αP)E₀ and σ = (1+αP)σ₀, where E₀ and σ₀ are values at zero mean pressure. In polyethylene, the coefficient, σ₀, was the same in tension and compression, indicating that the strength differential between tension and compression was a simple manifestation of pressure-dependent yielding. In polycarbonate the coefficient, σ₀, was different in tension and in compression, implying an effect due to the third stress invariant or to anisotropy. The results suggest a constitutive model for polymers in which the flow stress is linearly dependent on mean pressure, but in which inelastic volume change is negligible. The results also suggest that the pressure dependence of flow stress in polymers is the same as that of the initial modulus.     

Mixing of pharmaceutical solids. I. Effect of particle size on mixing in cylindrical shear and V-shaped tumbling mixers

The mixing of a cohesive drug with a cohesive, non-cohesive and free-flowing excipient was studied using two types of mixers, cylindrical shear and V-shaped tumbling. Two mixing indices, one based on complete random mixing, s/σ_R, and the other based on standard specifications, s/σ_A, were used to evaluate the data. Both indices gave similar results for mixing cohesive drug with a free-flowing or non-cohesive excipient and were suitable for evaluating homogeneity. However, for mixing a cohesive drug with a cohesive excipient, s/σ_R was not a suitable index, while s/σ_A could be used. The ‘mixing margin’, a concept proposed by Hersey [3], is not a very useful tool in assessing mix-ability of powders having too large or too small particle size distributions. Because of electrostatic charging, preferential sticking of the drug to the walls of the mixer resulted in a lower mean value of the drug in the mixture. Although the mixing indices suggested that the desired mixedness was reached, it is proposed that the mean percent of the active ingredient should be checked in addition to the mixing indices for ensuring the uniformity and potency of the drug content in solid state mixtures.     

Shear-induced gelation of associative polyelectrolytes

Copolymer of N,N-dimethylacrylamide (DMA) and acrylic acid (AA) was functionalized with pendant alkyl groups. Their dynamic mechanical properties in aqueous solution were investigated using continuous shear and oscillatory shear. Shear flow showed an abrupt divergence of the viscosity at a critical shear stress (σ_c). Oscillatory shear showed, with increasing applied stress, slight shear thinning followed by strong shear thickening above σ_c. The effect of the polymer concentration and the oscillation frequency (ω) was investigated. The behaviour at all concentrations and frequencies was fully determined by the product of the oscillation frequency and the terminal relaxation time (τ) of the systems at rest. Master curves of the data determined at different concentrations and frequencies were obtained if the reduced shear modulus was plotted versus the reduced applied stress at constant ω.τ. The effect of shear increased with decreasing value of ω.τ. At low frequencies the storage shear modulus crossed the loss modulus with increasing shear. A model is proposed for this phenomenon of shear-induced gelation.     

Flow behavior of well characterized polyethylene melts

A careful characterization and rheological study of low density polyethylene (LDPE) reveals that long-chain branching (LCB) plays a decisive role. At constant molecular weight (M?_w) higher LCB reduces the Newtonian viscosity η_o and the shear sensitivity, increases the activation energy E_o, and finally delays transition to pseudoplastic flow to higher shear rates and the onset of melt fracture to higher shear stresses (τ_d). The flow parameters η_o, \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma _{cr} $\end{document}_cr, τ_d, and the derived flow relaxation times are uniquely correlatable by means of a modified molecular weight (gM?_w) incorporating the LCB effect. High density polyethylene are less shear sensitive than their low-density counterparts, have a lower activation energy, fracture at higher shear stress levels and cannot be regarded as branchless LDPE's.     

Conductance studies in amide—water mixtures—III. Tetraethylammonium iodide in N,N-dimethylacetamide-water mixtures at 35°C

Conductance data of tetraethylammonium iodide in N,N-dimethylacetamide (DMA)—water mixtures (44.01 ? D ? 66.96) in the concentration range 0.001–0.06N and densities, viscosities and dielectric constants of the solvent mixtures (DMA—water) at 35°C are reported. Limiting equivalent conductance A_o, association constant K_A and pairing radius R are derived from Fuoss (1978) equation. Most structuredness of the solvent mixture indicated by the maximum viscosity is obtained at 1(DMA):3(H₂O) mole ratio. Walden product passes through a maximum with change of DMA content in the solvent mixture. Ionic association is found negligible (K_A < 10) in all the solvent compositions studied.     

Polarographic behaviour of hansa yellow- like dyes. Reduction mechanism and substituent effects

The electroreduction of a series of 3-phenyl-2,3-dioxopropionanilide 2-arylhydrazones (III) on the dropping mercury electrode (dme) was investigated in ethanolic Britton-Robinson buffers. In each case, the polarographic curves showed two waves, A and B, corresponding to a four- and a two-electron process, respectively. The E_1/2 values for the wave A at pH 8.0 were shown to be a linear function of the Hammett substituent constant σ; -(E_1/2)_A(V) = 0.982 + 0.145 σ (r = 0.989). A mechanism for the polarographic reduction of III is proposed.     

Stress relaxation behaviour of liquid crystalline solutions of ethyl celluloses with different molecular weight in m-cresol

The stress relaxation behaviour of liquid crystal-forming ethyl celllulose (EC) solutions in m-cresol was determined by means of a cone-plate type viscometer at 30°C. The effect of molecular weight (MW) on the behaviour was also determined. The relaxation behaviour could be fitted with the following equation: where σ_i and σ_f are steady-state shear stresses at shear rate $\dot \gamma _{\rm i}$ and $\dot \gamma _{\rm f}$, σ(t) is time- dependent stress, A₁ and A₂ are constants, τ₁ and τ₂ are relaxation times, t is time, and t_c is a characteristic time. When log σ* was plotted against time, one straight line was obtained for isotropic solutions, whereas anisotropic solutions yielded two straight lines. This suggests that the liquid crystalline solutions have two separate relaxation processes: Process 1 has a relatively short relaxation time, and process 2 has a long one. The parameters τ₁, τ₂, and A₂ were greatly dependent on polymer concentration, combination of $\dot \gamma _{\rm i}$ and $\dot \gamma _{\rm f}$, and MW, whereas A₁ was independent thereof and was close to unity. The process 1 was supposed to be valid for individual molecules, and process 2 for liquid crystalline domains or randomly aggregated or entangled molecules.     

Formation of β-cylindrites under supercooled extrusion of isotactic polypropylene at low shear stress

Formation of β-cylindrites of isotactic polypropylene under various wall shear stress (σ_w), supercooled temperature of melt (T_e) and crystallization temperature (T_c) has been investigated by polarized light microscopy (PLM), wide angle X-ray diffraction (WAXD), and differential scanning calorimeter (DSC). To have better control over the thermomechanical history, instead of a reciprocating screw, the samples were prepared by extruding supercooled melt through capillary die. β-cylindrites can be observed by PLM in the extruded specimen even at a lower σ_w (0.020 MPa), and the number of β-cylindrites nuclei increases rapidly with the lowering of T_e. The nucleation density of β-cylindrites increases with the raising of wall shear stress under a given T_e of 160 °C. Furthermore, at lower supercooled temperature of melt (145 °C), the radius of β-cylindrites decreases with the increasing of σ_w, and the number of β-cylindrites nuclei almost remain invariant. At relatively higher σ_w (0.090 MPa), a saturation of β-cylindrites nuclei is observed with decreasing T_c. A modified model based on above results has been proposed to explain the effect of the original structure of quiescent supercooled melt on the formation of β-cylindrites under low shear stress.     

Calorimetric study of quinoline interaction with o-phenylphenol and coal-derived asphaltenes

A calorimetric method is presented for the simultaneous evaluation of equilibrium constant, K, and molar enthalpy, ΔH^o, for 1:1 adduct formation of quinoline (Qu) with coal-derived asphaltenes in solvent benzene. Asphaltene (A), together with its acid/neutral (AA), and base (BA) fractions used in this study were isolated from a centrifuged liquid product (CLP) sample prepared from Kentucky hvAb coal at 27.6 MPa hydrogen pressure and 723 K, with reactor charged with glass pellets. The computed K values for the interaction of Qu and A, AA, and BA are, within experimental error, the same, 18–19 dm³ mol^?1; whereas there is large variation in the ΔH^o values (Qu-A, ?16.92 ± 0.21 kJ mol^?1; Qu-AA, ?14.74 ± 0.04 kJ mol^?1; Qu-BA, ?11.76 ± 0.04 kJ mol^?1). For Qu-A and Qu-AA systems, hydrogen-bonding occurs between the aromatic phenols (present in A and AA) and quinoline, which is a strong hydrogen-bond acceptor, in addition to other molecular interactions. The hydrogen-bonding interaction in the Qu-BA system is lacking because both Qu and BA are hydrogen-bond acceptors. Since asphaltenes are really mixtures, we have taken a pure compound, o-phenyl-phenol (OPP), and obtained thermodynamic parameters for its interaction with quinoline (Qu). OPP was chosen to represent the aromatic phenols found in coal liquefaction products. Results obtained are: K (dm³ mol^?1): 10.4 (in CS₂), 6.2 (in CCl₄); ΔH^o (kJ mol^?1): ?31.40 (inCS₂) ?27.80 (inCCl₄). The solvent effect is apparent. By using o-phenylanisole as a model non-hydrogen-bonding donor (Dietz Blaha, Li J. Chem. Thermodynamics, 1977, 9, 783), the relative contribution of H-bond to π-interactions in the total enthalpy change for the OPP—Qu system is estimated to be 3:1.