Nonlinear viscoelasticity of polystyrene solutions. II. Non-Newtonian viscosity

The steady shear viscosity η(k) and the stress decay function \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \eta \left({t,k} \right)$\end{document} (the shear stress divided by the rate of shear k after cessation of steady shear flow) were measured for concentrated solutions of polystyrene in diethyl phthalate. Ranges of molecular weight M and concentration c were 7.10 × 10⁵ to 7.62 × 10⁶ and 0.112–0.329 g/cm³, respectively. Measurements were performed with a rheometer of the cone-and-plate type in the range 10^?4 < k < 1 sec^?1. The Cox–Merz relation η(k) = |η^*(ω)|_ω=k was tested with the experimental result (|^*(ω)| is the magnitude of the complex viscosity). It was found to be applicable to solutions of relatively low M or c but not to those of high M and c. For the latter η(k) began to decrease at a lower rate of shear than |η^*(ω)|_ω=k did; the Cox–Merz law underestimated the effect of rate of shear. The stress decay function was assumed to have a functional form \documentclass{article}\pagestyle{empty}\begin{document}$\tilde \eta \left( {t,k} \right) = \sum {\eta _p \left( k \right)e^{ - t/\tau p\left( k \right)} } $\end{document} where τ₁ > τ₂ > …, and the values of τ₁, τ₂ η₁ and η₂ were determined for some solutions. The relaxation times τ₁ and τ₂ were found to be independent of k and equal to the relaxation times of linear viscoelasticity. At the limit of k → 0, η₁ and η₂ were approximately 60 and 20–30%, respectively, of η and the non-Newtonian behavior was due to large decreases of η₁ and η₂ with increasing k. It was shown that η₁(k) may be evaluated from the relaxation strength G₁(s) for the longest relaxation time of the strain-dependent relaxation modulus with a constitutive model for relatively high c–M systems as well as for low c–M systems.     

Rheological properties of rodlike polymers in solution. 2. Linear and nonlinear transient behavior

Rheological and rheo-optical studies are reported for isotropic solutions of the mesogenic rodlike polymer poly(1,4-phenylene-2,6-benzobisthiazole) (PBT). Several PBT samples were used with average contour lengths from 95 to 135 nm. Concentrations were varied over a range just below the concentration C_c for the formation of an ordered (nematic) state. The predictions of a single-integral constitutive equation of the BKZ type utilizing experimental estimates of the distribution of discrete relaxation times is compared with experimental data on the steady-state viscosity η_κ, the recoverable compliance function R_κ, and the steady-state flow birefringence as functions of the shear rate κ, with satisfactory results. The relaxation of the shear stress and the flow birefringence on cessation of steady-state flow at shear rate κ are also compared with the single-integral constitutive equation, and it is found that in the nonlinear response range the data can be superposed over a wide range in κ. The overall behavior is qualitatively similar to that for flexible chains, which can also be fitted by the single-integral constitutive equations over similar ranges of η₀R₀κ, with η₀ and R₀ the limiting values of η_k and R_κ for small κ. Of course, the dependence of η₀ and R₀ on concentration and molecular weight differs markedly for rodlike and flexible-chain polymers.     

Stress overshoot of polymer solutions at high rates of shear; Polystyrene with bimodal molecular weight distribution

Overshoot of shear stress, σ, and the first normal stress difference, N₁, in shear flow was investigated for dilute solutions of polystyrene with very high molecular weight in concentrated solution of low M PS. In the case that the matrix was a nonentangled system, behavior of overshoot was similar to that of dilute solution of high M PS in pure solvent. The magnitudes of shear, γ_σm and γ_Nm, corresponding to the peaks of σ and N₁ lay on the universal functions of γ˙τ_R, respectively, proposed for dilute solutions in pure solvent. Here τ_R is the Rouse relaxation time for high M PS in the blend evaluated from dynamic modulus at high frequencies. In the case that the matrix was an entangled system, an additional σ peak was observed at high rates of shear at times corresponding to γ_σm = 2–3. This peak can be assigned to the motion of low M chains in entanglement network. When the matrix was entangled, stress overshoot was observed even at relatively low rates of shear, say γ˙τ_R < 10⁻². This is probably due to the motion of high M chains in entanglement of all the chains. In this case the γ_σm and γ_Nm values were higher than those expected for entangled chains of monodisperse polymer in pure solvent. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2043–2050, 2000     

Dynamic mechanical properties of moderately concentrated polystyrene solutions

The storage (G′) and loss (G″) shear moduli have been measured in the frequency range from 0.04 to 630 Hz for solutions of narrow distribution polystyrenes with molecular weights (M) 19,800 to 860,000, and a few of poly(vinyl acetate), M = 240,000. The concentration (c) range was 0.014–0.40 g/ml and the viscosities of the solvents (diethyl phthalate and chlorinated diphenyls) ranged from 0.12 to 70 poise. Data at different temperatures (0–40°C) were combined by the method of reduced variables. Two types of behavior departing from the usual frequency dependence describable by the Rouse-Zimm-Tschoegl theories were observed. First, for M ? 20,000, the ratio (G″ ? ωη_s)/G′ in the neighborhood of ωτ₁ = 1 was abnormally large and the steady-state compliance J was abnormally small, especially at the lowest concentrations studied. Here ω is circular frequency, η_s solvent viscosity, and τ₁ terminal relaxation time. Related anomalies have been observed by others in undiluted polymers at still lower molecular weights. Second, at the highest concentrations and molecular weights, a “crossover” region of the logarithmic frequency scale appeared in which G″ ? ωη_s < G′. The width of this region is a linear function of log c; the frequency dependence under these conditions can be represented by a sequence of Rouse relaxation times grafted on to a sequence of Zimm relaxation times. For each molecular weight, the terminal relaxation time τ₁ was approximately a single function of c for different solvents of widely different η_s. At lower concentrations, τ₁ was close to the Rouse prediction of 6ηM/π²cRT, where η is the steady-flow viscosity; but at higher concentrations, τ₁ was proportional to η/c² and corresponded, according to a recent theory of Graessley, to an average molecular weight of 20,000 between entanglement coupling points in the undiluted polymer.     

Relaxation dynamics of salt‐free polyelectrolyte solutions using flow birefringence and rheometry

Relaxation dynamics of salt‐free, aqueous solutions of sodium poly(styrene sulfonate) (NaPSS) were investigated by mechanical rheometry and flow birefringence measurements. Two semidilute concentration regimes were studied in detail for a range of polymer molecular weights. At solution concentrations c < 10 mg mL, limiting shear viscosity η₀ was found to scale with molecular weight and concentration as η₀ ∼ c^0.5M_w over nearly two decades in concentration. At higher solution concentrations, c > 10 mg mL, a change in viscosity scaling was observed η₀ ∼ c^1.5M, consistent with a change from simple Rouse dynamics for unentangled polyions to near‐perfect reptation dynamics for entangled chains. Characteristic relaxation times τ deduced from shear stress and birefringence relaxation measurements following start‐up of steady shearing at high rates reveal very different physics. For c < 10 mg mL, both methods yield τ ∼ c^−0.42M and τ ∼ c⁰M for c > 10 mg mL. Curiously, the concentration scalings seen in both regimes are consistent with theoretical expectations for salt‐free polyelectrolyte solutions undergoing Rouse and reptation dynamics, respectively, but the molecular weight scalings are not. Based on earlier light scattering studies using salt‐free NaPSS solutions, we contend that the unusual relaxation behavior is likely due to aggregation and/or coupled polyion diffusion. Simultaneous stress and birefringence measurements suggest that in concentrated solution, NaPSS aggregates are likely well permeated by solvent, supporting a loose collective of aggregated chains rather than the dense polymer aggregates previously supposed. Nonetheless, polyion aggregates of either variety cannot account for the inverse dependence of relaxation time on polymer molecular weight for c < 10 mg mL. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 825–835, 1999     

Eight-arm star polystyrene in methylcyclohexane: Cloud-point curves,critical lines,and coexisting densities and viscosities

We measured the cloud-point curves of eight-arm star polystyrene (sPS) in methylcyclohexane (MCH) for polymer samples of three total molecular masses [weight-average molecular weight (M_w) × 10⁻³ = 77, 215, or 268]. We found a downward shift of 5–15 K in the critical temperature (T_c) of the star polymer solutions with respect to linear polystyrene (PS) solutions of the same M_w. The shift in T_c became smaller as M_w increased. The critical volume fraction for eight-arm sPS in MCH was equal within experimental uncertainty (10–40%) to that of linear PS in MCH. For sPS of M_w = 77,000 in MCH, we studied the mass density (ρ) as a function of temperature (T). As for linear polymers in solution, the difference in ρ between coexisting phases (Δρ) could be described over t = (T_c − T)/T_c for 1.1 × 10⁻⁴ < t < 4.7 × 10⁻³ with the Ising value of the exponent β in the expression Δρ = B t^β. Both ρ(T) above T_c and the average value of ρ below T_c were linear functions of temperature; no singular corrections were observed. The measurements of the shear viscosity (η) near T_c for sPS (M_w = 74,000) in MCH indicated a strong critical anomaly in η, but the data were not precise enough for a quantitative analysis. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 129–145, 2004     

Non-newtonian behavior of polymers with log-normal molecular weight distribution

By choosing suitable approximations to Bueche's function, it is possible to calculate the viscosity versus shear stress for log-normal molecularly distributed linear polymers. For bulk polymers the mixing rules M?_w, M?_w, M?_z are considered. For values of η/η0 > 0.1 and heterogeneities with M?_w/M?_n > 1.5 the result obtained with any mixing rule is η/η0 = erfc [(1/delta;) log (M₀Q^h/aK)], where a = π²/6_pRT and where the δ and K values are dependent on the heterogeneity ratio Q = M?_w/M?_n and on the type of mixing rule; on the other hand, the h value is independent of the heterogeneity, but depends on the mixing rule. Most experimental data should fit the M?_w mixing rule as one would expect from the zero shear stress mixing rule. Experimental data are compared with the theoretical results.     

Relaxation spectra of concentrated polystyrene solutions

The relaxation modulus G(t) and the stress decay after cessation of steady shear flow were measured on concentrated solutions of polystyrenes in diethyl phthalate. Ranges of concentration c and molecular weight M of the polymer were from 0.112 to 0.329 g/ml and from 1.23 × 10⁶ to 7.62 × 10⁶, respectively. The relaxation spectrum H(τ) as calculated from G(t) for the solution of very high M was found to be composed of two parts. One, at relatively short times, was a broad distribution (plateau zone) with height proportional to c². The second, at the long-time end, was very sensitive to concentration and gave rise to a maximum in H(τ) for very high concentrations. The behavior of H(τ) at long times was examined quantitatively by evaluating the longest relaxation time τ₁⁰ and the corresponding relaxation strength G₁⁰ from G(t) and from the stress decay function, on the assumption of a discrete distribution of relaxation times at long times. The longest relaxation time was approximately proportional to M^3.5, even at relatively low concentrations where the zero-shear viscosity was not proportional to M^3.5. The strengths of relaxation modes with the longest few relaxation times are proportional to the third power of concentration.     

New Quaternary Chalcogenides BaLnMQ3 (Ln = Rare Earth or Sc; M = Cu, Ag; Q= S, Se): II. Structure and Property Variation vs Rare-Earth Element

Some new quaternary compounds of the type BaLnMQ₃ (Ln = rare earth or Sc; M = Cu, Ag; Q = S, Se) have been synthesized by the reaction of the constituent binary chalcogenides and elements at 1000°C. The crystal structures of two of these compounds have been determined by single-crystal X-ray diffraction techniques and are isostructural. Crystal data: BaErCuS₃—space group D¹⁷_2h —Cmcm, M= 464.32, Z = 4 , a = 3.987(1), b = 13.377(3), c = 10.101(2) Å (T = 115 K), V = 538.7(4) ų, R_w (F²) = 0.095 for 848 observations and 24 variables, R(F) = 0.037 for 840 observations having F²₀ > 2σ (F²₀); BaYAgSe—space group D¹⁷_2h —Cmcm, M = 571.0, Z = 4, a = 4.239(1), b = 14.030(2), c = 10.636(2) Å (T = 115 K), V = 632.6(2) ų, R_w (F²) = 0.057 for 645 observations and 24 variables, R(F) = 0.023 for 595 observations having F²₀ > 2σ(F²₀). These two compounds adopt the layered KZrCuS₃ structure type. The layers, which are separated by Ba²⁺ ions, consist of edge-sharing octahedral chains and corner-sharing tetrahedral chains. The other compounds synthesized crystallize either with this same structure or with that of β-BaLaCuSe₃, a slightly distorted variation, which is isostructural with Eu₂CuS₃. The diffuse reflective UV-visible spectra of several of these compounds have been measured. From magnetic susceptibility measurements, both BaNdCuS₃ and BaGdCuS₃ show Curie-Weiss behavior, whereas BaCeCuS₃ and BaCeCuSe₃ show in addition temperature-independent paramagnetism.     

Stress overshoot of polymer solutions at high rates of shear

Overshoot of shear stress, σ, and the first normal stress difference, N₁, in shear flow were investigated for polystyrene solutions. The magnitudes of shear corresponding to these stresses, γ_σm and γ_Nm, for entangled as well as nonentangled solutions were universal functions of γ˙τ_eq, respectively, and γ_Nm was approximately equal to 2γ_σm at any rate of shear, γ˙. Here τ_eq = τ_R for nonentangled systems and τ_eq = 2τ_R for entangled systems, where τ_R is the longest Rouse relaxation time evaluated from the dynamic viscoelasticity at high frequencies. Only concentrated solutions exhibited stress overshoot at low reduced rates of shear, γ˙τ_eq < 1. The behavior at very low rates, γ˙τ_eq < 0.2, was consistent with the Doi–Edwards tube model theory for entangled polymers. At high rates, γ˙τ_eq > 1, γ_σm and γ_Nm were approximately proportional to γ˙τ_eq. At very high rates of shear, the peak of σ is located at t = τ_R, possibly indicating that the polymer chain shrinks with a characteristic time τ_R in dilute solutions. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1917–1925, 2000     

Generalized correlations for molecular weight and concentration dependence of zero-shear viscosity of high polymer solutions

Data are presented to show that two correlations of viscosity–concentration data are useful representations for data over wide ranges of molecular weight and up to at least moderately high concentrations for both good and fair solvents. Low molecular weight polymer solutions (below the critical entanglement molecular weight M_c) generally have higher viscosities than predicted by the correlations. One correlation is η_sp/c[η] versus k′[η], where η_sp is specific viscosity, c is polymer concentration, [η] is intrinsic viscosity, and k′ is the Huggins constant. A standard curve for good solvent systems has been defined up to k′[η]c ≈? 3. It can also be used for fair solvents up to k′[η]c ≈? 1.25· low estimates are obtained at higher values. A simpler and more useful correlation is η_R versus c[η], where η_R is relative viscosity. Fair solvent viscosities can be predicted from the good solvent curve up to c[η] ≈? 3, above which estimates are low. Poor solvent data can also be correlated as η_R versus c[η] for molecular weights below 1 to 2 × 10⁵.     

Scaling analysis of cotton cellulose/LiCl·DMAc solution using light scattering and rheological measurements

Semidilute solution of cotton lint (CC1) in 8 wt % LiCl/N,N‐dimethylacetamide was investigated using static light scattering (SLS) and rheological measurements. The reduced osmotic modulus estimated by SLS measurements for CC1 solutions are proportional to c^1.16 in the semidilute region. From the exponent of 1.16, de Gennes' scaling theory derives the relationship between radius of gyration, R_g, and molecular weight, M_w, of CC1 as R_g ∝ M^0.62 This corresponds to the Mark‐Houwink‐Sakurada exponent of 0.86. This exponent is very close to that estimated from scaling analysis of zero shear rate viscosity, that is 0.85. Apparent radius of gyration, R_g,app, estimated by SLS measurements for CC1 solutions are proportional to c^?0.5 in the semidilute region. R_g,app indicates the mesh size of polymer entanglement in the semidilute region. On the assumption of the Gaussian behavior of CC1 molecule in the semidilute region, the exponent of ?0.5 gives the relationship between the molar mass between entanglements, M_e, and c as following relationship: M_e ∝ c^?1. This agrees with the concentration dependence on plateau modulus estimated from the dynamic viscoelastic measurements. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2155–2160, 2006     

Copper-indium ordering in RECu6In6 (RE=Y, Ce, Pr, Nd, Gd, Tb, Dy)

The rare earth metal-copper-indides RECu₆In₆ (RE=Y, Ce, Pr, Nd, Gd, Tb, Dy) were synthesized from the elements by arc-melting. Well-crystallized samples were obtained by slowly cooling the melted buttons from 1320 to 670 K in sealed silica tubes in a muffle furnace. They were investigated by X-ray diffraction on powders and single crystals: ThMn₁₂ type, space group I4/mmm, Z=2, a=916.3(2), c=535.8(2) pm, wR₂=0.063, 216 F² values, 15 variables for YCu₆In₆, a=926.5(4), c=543.5(3) pm, wR₂=0.064, 314 F² values, 15 variables for CeCu₆In₆, a=925.7(4), c=540.1(3) pm, wR₂=0.075, 219 F² values, 15 variables for PrCu₆In₆, a=923.1(4), c=540.3(3) pm, wR₂=0.071, 218 F² values, 15 variables for NdCu₆In₆, a=917.7(4), c=540.2(3) pm, wR₂=0.076, 207 F² values, 15 variables for GdCu₆In₆, a=917.0(5), c=540.5(4) pm, wR₂=0.062, 215 F² values, 15 variables for TbCu₆In₆, a=915.2(8), c=540.7(7) pm, wR₂=0.108, 218 F² values, 15 variables for DyCu₆In₆. The structures have been refined with a split position (50% Cu+50% In) for the 8j site. They can be explained by a tetragonal body-centered packing of CN 20 polyhedra (10Cu+10In) around the rare earth atoms. The ordering models of the copper and indium atoms and the limitations/resolution of X-ray diffraction for this topic are discussed.     

Assemblies of brilliant cresyl violet to DNA in the presence of γ-cyclodextrin

The interactions of brilliant cresyl violet (BCV) with herring sperm DNA in γ-cyclodextrin (γ-CD) supramolecular system were studied by UV-vis absorption spectroscopy and cyclic voltammetry (CV). Both UV-vis absorption and CV data show that the interaction of BCV with DNA depends on the concentration ratio of BCV to DNA (R), the initial concentration of BCV and γ-CD. The binding constants of BCV monomer, (BCV)₂ dimer and (BCV)₂-γ-CD inclusion complex with DNA are 1.64 × 10⁵, 2.56 × 10⁴ and 2.32 × 10³ M⁻¹, respectively. It was observed that γ-CD can affect the interactive mode of BCV with DNA. If R is larger than 0.5, the (BCV)₂-γ-CD inclusion complex will retain intact and bind to DNA via the electrostatic attraction forces. By contrast, when R is smaller than 0.5, the inclusion complex will be partially dissociated and the free BCV monomer is intercalated into the double-helix structure of DNA attributing to the more favorable microenvironment of DNA for the BCV monomer. Our work postulates the importance of the initial concentration of dye and host molecule on the interaction of dye with DNA in living bodies.     

Determination of chain stiffness and polydispersity from static light-scattering

Chain stiffness is often difficult to distinguish from molecular polydisperity. Both effects cause a downturn of the angular dependence at large q² (q = (4π/λ)sin θ/2) in a Zimm plot. A quick estimation of polydisperity becomes possible from a bending rod (BR) plot in which lim (c → 0) qRθ/Kc is plotted against q(〈S²〉_z)^1/2 = u. Flexible and semiflexible chains show a maximum whose position is shifted from u_max = 1.41 for monodisperse chains towards larger values as polydispersity is increased, while simultaneously, the maximum height is lowered. Stiff chains display a constant plateau at large q, its value is πM_L where M_L is the linear mass density. Using Koyama's theory, the number of Kuhn segments can be determined from the ratio of the maximum height to the plateau height, if the polydispersity index z = (M_w/M_n ? 1)^?1 is known. Thus, if the weight-average molecular weight M_w, is known, the contour length L_w, the number of Kuhn segments (N_k)_w, the Kuhn segment length l_k and the polydispersity of the stiff chains can be determined. The influence of excluded volume is shown to have no effect on this set of data. The reliability of this set can be cross-checked with the mean-square radius of gyration 〈s²〉_z which can be calculated from the Benoit-Doty equation for polydisperse chains. Rigid and slightly bending rods exhibit no maximum in the BR plot, and the effect of polydispersity can no longer be distinguished from a slight flexibility if only static scattering techniques are applied.     

Explanation for the 3.4-power law for viscosity of polymeric liquids on the basis of the tube model

The viscosity η₀(M) of polymeric liquids of molecular weight M is calculated on the basis of the tube model formulated by Doi and Edwards (ref. 3). The contour length fluctuation of polymers along the tube, which was neglected in ref. 3, is now explicitly taken into account. The result is where M_c = 2M_e, and M_e is the molecular weight between the entanglement points. This result is numerically close to the empirical 3.4-power law, η₀(M) = η₀(M_c)(M/M_c)^3.4, for 10M_c ? M ? 100M_c but approaches the result in ref. 3 for very high molecular weight. We thus conclude that the 3.4-power law is actually an approximate expression for the real curve which slowly approaches the asymptotic form calculated in ref. 3.     

Nonlinear viscoelasticity of polystyrene solutions. I. Strain-dependent relaxation modulus

Strain-dependent relaxation moduli G(t,s) were measured for polystyrene solutions in diethyl phthalate with a relaxometer of the cone-and-plate type. Ranges of molecular weight M and concentration c were from 1.23 × 10⁶ to 7.62 × 10⁶ and 0.112 to 0.329 g/cm³. Measurements were performed at various magnitudes of shear s ranging from 0.055 to 27.2. The relaxation modulus G(t,s) always decreased with increasing s and the relative amount of decrease (i.e.,–log[G(t,s)/G(t,0)]) increased as t increased. However, the detailed strain dependences of G(t,s) could be classified into two types according to the M and c of the solution. When cM < 10⁶, the plot of log G(t,s) versus log t varied from a convex curve to an S-shaped curve with increasing s. For solutions of cM > 10⁶, the curves were still convex and S-shaped at very small and large s, respectively, but in a certain range of s (approximately 3 < s < 7) log G(t,s) decreased rapidly at short times and then very slowly; a peculiar inflection and a plateau appeared on the plot of log G(t,s) versus log t. The strain-dependent relaxation spectrum exhibited a trough at times corresponding to the plateau of log G(t,s). The longest relaxation time τ₁(s) and the corresponding relaxation strength G₁(s) were evaluated through the “Procedure X” of Tobolsky and Murakami. The relaxation time τ₁(s) was independent of s for all the solutions studied while G₁(s) decreased with s. The reduced relaxation strength G₁(s)/G₁(0) was a simple function of s (The plot of log G₁(s)/G₁(0) against log s was a convex curve) and was approximately independent of M and c in the range of cM <10⁶. This behavior of G₁(s)/G₁(0) was in agreement with that observed for a polyisobutylene solution and seems to have wide applicability to many polymeric systems. On the other hand, log G₁(s)/G₁(0) as a function of log s decreased in two steps and decreased more rapidly when M or c was higher. It was suggested that in the range of cM < 10⁶, a kind of geometrical factor might be responsible for a large part of the nonlinear behavior, while in the range of cM > 10⁶, some “intrinsic” nonlinearity of the entanglement network system might be important.     

Mononuclear Complexes of Cr(II) and Fe(II) with Terminal -SH Groups. Synthesis and X-Ray Crystal Structures of trans-M(SH)2(dmpe)2 (M = Cr,Fe; dmpe = 1,2-Bis(Dimethylphosphino)Ethane)

Abstract

The reaction of two equivalents of NaSH with MCl₂(dmpe)₂ (M = Cr, Fe,) at—78°C gives trans-M(SH)₂(dmpe)₂ (M = Cr, (1), 30%; Fe, (2) 98%). The complexes have been characterized spectroscopically, and the trans geometry has been confirmed by single crystal X-ray diffraction studies. Crystal data (1): C₁₂H₃₄CrP₄S₂, M= 418.42, monoclinic, P2₁/n, a = 8.857 (I), b= 12.719 (2), c = 9.648 (I) Å, β = 92.14(1)°, U= 1086.2 (5)Å, D _c = 1.279gcm^?3, Z = 2, λ(MoK_a) = 0.71073 Å, (graphite mono-chromator), μ(MoK_a) = 9.80cm^?1. Methods: MULTAN, difference Fourier, full-matrix least-squares. Refinement of 1149 reflections (I > 3σ(I)) out of 1901 unique observed reflections (3.0° < 29 < 48.0°) gave R and R _w values of 0.092 and 0.096, respectively. Crystal data (2): C₁₂H₃₄FeP₄S₂, M = 422.28, monoclinic, P2₁/n, a = 8.834 (2), b = 12.594 (2), c = 9.532 (2) Å, β = 90.66 (2)°, U = 1060.3 (5) ų, D _c = 1.323 g cm^?3, Z = 2, γ(MoK_a) = 0.71073 Å, (graphite monochromator), μ(MoK_a) = 11.87 cm^?1. Methods: same as for (1). Refinement of 1178 reflections (I > 3σ (I)) out of 2086 unique observed reflections (2.0° < 20 < 50.0°) gave R and R _w values of 0.056 and 0.059, respectively.     

Synthesis and Characterization of a MetastableLnTh2F11Series (Ln=La–Lu, Y) with Cationic and Anionic Disorder: Crystal Structure of SmTh2F11

A series of apparently stoichiometric and metastable phases of compositionLnTh₂F₁₁(Ln=La–Lu) was prepared for the first time. The crystal structure of SmTh₂F₁₁was determined from single-crystal data with direct methods and refined toR₁=0.043 and wR₂=0.107 [space group:Pnma;a=861.0(2) pm,b=413.7(1) pm,c=722.5(2) pm;Z=1.33]. This new structure type is characterized by a (Th+Sm) disorder on the 4ccationic site and by the presence of anionic vacancies on three of the four 4canionic sites. The idealMF₄structure is a three-dimensional network of interconnectedMF₁₁polyhedra but the coordination number of the cations is locally reduced to eight for Sm³⁺. The structural relationship with the LaF₃(tysonite) type is discussed.     

Kristallstruktur von Trimethylisocyanursäure, (CH3NCO)3, und von Trichlorisocyanursäure-1/2-Ethylenchlorid, (ClNCO)3·1/2C2H4Cl2

X-ray crystal structure analyses of (CH₃NCO)₃ (M) and (ClNCO)₃·1/2C₂H₄Cl₂ (C) were carried out at room temperature (MoK, graphite monochromator, =0.71069 Å): 1.M=171.16, monochlinic, P2₁/c,a=14.848 (1) Å,b=13.400 (2) Å,c=8.149 (1) Å, =100.87 (1)°,V=1 592.3 ų,Z=8,F(000)=720,d _x =1.428 Mgm^–3, =76m^–1,R=6.51%,R _w =7.01% (964 reflections, 218 parameters). 2.M=281.89, monochlinic, P 2₁/c,a=9.416 (3) Å,b=5.728 (1) Å,c=18.199 (8) Å, =98.64 (2)°,V=970.4 Å₃,Z=4,F(000)=556,d _x =1.929 Mgm^–3, =1.11 mm^–1,R=3.96%,R _w =3.44% (605 reflections, 132 parameters). The ring systems together with the C atoms of the methyl groups in (M) and with the Cl atoms in (C) are planar and have D_3h-symmetry. Bond lengths and bond angles are discussed with regard to¹⁴N-NQR,³⁵Cl-NQR and vibrational spectroscopic data.