Multiaxial deformations of end‐linked poly(dimethylsiloxane) networks. III. Effect of entanglement density on strain‐energy density function

Strain‐energy density functions (W) of end‐linked polydimethylsiloxane (PDMS) networks with different entanglement densities were estimated as a function of the first and second invariants I₁ and I₂ of Green's deformation tensor on the basis of the quasi‐equilibrium biaxial stress‐strain data. Entanglement densities in the PDMS networks were controlled by varying the precursor PDMS concentration (?₀) in end‐linking. The deduced functional form of W [W = C₁₀(I₁ ? 3) + C₀₁(I₂ ? 3) + C₁₁(I₁ ? 3)(I₂ ? 3) + C₂₀(I₁ ? 3)² + C₀₂(I₂ ? 3)²] is independent of the degree of dilution at network preparation. The contribution of each term in I₁ and I₂ to total energy depends on whether the precursor PDMS solution before end‐linking belongs to the concentrated regime ?₀ > ?_c where many entanglement couplings of precursor chains exist or the moderately concentrated regime ?₀ < ?_c where pronounced entanglement couplings of precursor chains are absent. These results suggest that the rubber elasticity of the end‐linked networks is significantly influenced by the entangled state of precursor chains before end‐linking, and the extra terms in the estimated W that are absent in the prediction of the classical rubber elasticity theories [W = C (I₁ ? 3)] mainly originate from the effect of trapped entanglements. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2780–2790, 2002     

Length scale hierarchy in sol,gel, and coacervate phases of gelatin

Length scale hierarchy in gelatin sol, gel, and coacervate (induced by ethanol) phases, having same concentration of gelatin in aqueous medium (13% w/v), has been investigated through small angle neutron scattering and rheology measurements. The static structure factor profile, I(q) versus wave vector q, was found to be remarkably similar for all these samples. This data could be split into three distinct q‐regimes: the low‐q regime, I_ex(q) = I_ex(0)/(1+q²ζ²)² valid for q < 3R_g^?1; the intermediate q‐regime, I(q) = I(0)/(1+q²ξ²) for 3R_g^?1 < q < ξ^?1; and the asymptotic regime, I(q) = (c/q) exp(?R_c²q²/2) for q > ξ^?1. Consequently, three distinct length scales could be deduced from structure factor data: (a) inhomogeneity of size, ζ = 20 ± 1 nm for all the three phases; (b) average mesh size, ξ₀ = 2.6 ± 0.2 nm for sol and gel, and smaller mesh size, ξ_os = 1.2 ± 0.2 nm for coacervate; and (c) cross section of gelatin chains, R_c = 0.35 ± 0.04 nm. In addition, the structure factor data obtained from coacervating solution analyzed in the Guinier region, I(q) = exp(?q²R_g²/3), yielded value of typical radius of gyration of clusters, R_g ≈ 69 nm that indicated existence of triple‐helices of length, L ≈ 239 nm; (d) Frequency and temperature sweep measurements conducted on coacervate samples revealed two other length scales: (e) viscoelastic length, ξ_ve = 14 ± 2 nm and (f) correlation length at melting, ξ_T = 500 ± 70 nm. Thus, existence of six distinct length scales, (a–f), ranging from 1.2 to 500 nm has been established in the coacervate phase of gelatin–ethanol–water system. Results are discussed within the framework of Landau‐Ginzburg treatment of dynamically asymmetric systems (Prog Theor Phys 1977, 57, 826; Phys Rev A 1991, 44, R817; J Phys II (France) 1992, 2, 1631). © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1653–1667, 2006     

Evidence for hydrophobic attraction between latex particles in aqueous systems as investigated by turbidimetry

We report the evidence for attractive interaction of latex particles which are covered by poly(ethylene oxide) chains. These particles are suspended in aqueous solutions of ammonium sulfate. The interaction is probed by measurements of the turbidity of the suspensions up to 70 g/l. Turbidity is insensitive to multiple scattering and allows the static structure factor, S(q) [q=(4πn ₀/λ₀)sin(θ/2), where θ is the scattering angle, n₀ is the refractive index of the medium and λ₀ is the wavelength in vacuo], to be determined at small q values. The analysis of S(q) at small q values yields information about possible attraction of the particles. The analysis of the turbidity data furthermore shows that no aggregation took place in these systems. A weak but long-range attractive interaction was found at ammonium sulfate concentrations of 0.01 and 0.1 M. The relation of this attractive force to hydrophobic forces is discussed. Received: 9 March 2000/Accepted: 28 June 2000     

Calculation of X‐ray scattering intensities by means of the coupled cluster singles and doubles model

Total X‐ray scattering intensity σ_ee(q) is very sensitive to electron correlation effects. In this study σ_ee(q) of N₂, CO, and N₂O have been computed by the coupled cluster singles and doubles (CCSD) method and compared with configuration interaction singles and doubles (CISD) calculations as well as experimental observations. σ_ee(q) curves by CCSD calculations are rather close to those by CISD, but although small, there still exist some discrepancies between calculated and observed values. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1315–1320, 2001     

Binuclear Iron(I) Complex Containing Bridging Phenanthrene‐4,5‐dithiolate Ligand: Preparation,Spectroscopy, Crystal Structure,and Electrochemistry

A diiron hexacarbonyl complex containing bridging phenanthrene‐4,5‐dithiolate ligand is prepared by oxidative addition of Phenanthro[4,5‐cde][1,2]dithiin to Fe₂(CO)₉. The complex is investigated as a model for the active site of the [Fe–Fe] hydrogenase enzyme. The compound, [(μ‐PNT)Fe₂(CO)₆]; (PNT = phenanthrene‐4,5‐dithiolate), was characterized by spectroscopic methods (IR, UV/Vis and NMR) and X‐ray crystallography. The IR and proton NMR spectra of [(μ‐PNT)Fe₂(CO)₆] ( 4 ) are in agreement with a PNT ligand attached to a Fe₂(CO)₆ core. The infrared spectrum of 4 recorded in dichloromethane contains three peaks at 2001, 2040, and 2075 cm^–1 corresponding to the stretching frequency of terminal metal carbonyls. X‐ray crystallographic study unequivocally confirms the structure of the complex having a butterfly shape with an Fe–Fe bond length of 2.5365 Å close to that of the enzyme (2.6 Å). Electrochemical properties of [(μ‐PNT)Fe₂(CO)₆] have been investigated by cyclic voltammetry. The cyclic voltammogram of [(μ‐PNT)Fe₂(CO)₆] recorded in acetonitrile contains one quasi‐irreversible reduction (E_1/2 = –0.84 V vs. Ag/AgCl, I_pc/I_pa = 0.6, ΔE_p = 131 V at 0.1 V · s^–1) and one irreversible oxidation (E_pa = 0.86 V vs. Ag/AgCl). The redox of [(μ‐PNT)Fe₂(CO)₆] at E_1/2 = –0.84 V can be assigned to the one‐electron transfer processes; [Fe^I–Fe^I] → [Fe^I–Fe⁰] and [Fe^I–Fe⁰] → [Fe^I–Fe^I].     

Identification of unknown diffusion and convection coefficients in ion transport problems from flux data: an analytical approach

This article presents an analytical approach for identification problems related to ion transport problems. In the first part of the study, relationship between the flux j_L : = (D(x)u_x(0, t)_x=0{\varphi_L := (D(x)u_x(0, t)_{x=0}} and the current response I(t){{\mathcal I}(t)} is analyzed for various models. It is shown that in pure diffusive linear model case the flux is proportional to the classical Cottrelian I_C(t){{\mathcal I}_C(t)}. Similar relationship is derived in the case of nonlinear model including diffusion and migration. These results suggest acceptability of the flux data as a measured output data in ion transport problems, instead of nonlocal additional condition in the form an integral of concentration function. In pure diffusive and diffusive-convective linear models cases, explicit analytical formulas between inputs (diffusion or/and convection coefficients) and output (measured flux data) are derived. The proposed analytical approach permits one to determine the unknown diffusion coefficient from a single flux data given at a fixed time t ₁ > 0, and unknown convection coefficient from a single flux data given at a fixed time t ₂ > t ₁ > 0. Linearized model of the nonlinear ion transport problem with variable diffusion and convection coefficients is analyzed. It is shown that the measured output (flux) data can not be given arbitrarily.     

Spinodal decomposition and phase separation kinetics in nanoclay–biopolymer solutions

Intensity of light, I(q,t), scattered from homogeneous aqueous solutions, of nanoclay (Laponite) and protein (gelatin‐A), was studied to monitor the temporal and spatial evolution of the solution into a phase‐separated nanoclay–protein‐rich dense phase, when the sample temperature was quenched below spinodal temperature, T_s (=311 ± 3 K). The zeta potential data revealed that the dense phase comprised charge‐neutralized intermolecular complexes of nanoclay and protein chains of low surface charge. The early stage, t < 500 s, of phase separation could be described adequately through Cahn‐Hilliard theory of spinodal decomposition where the intensity grows exponentially, I(q, t) = I₀ exp.(2R(q)t). The wave vector, q dependence of the growth parameter, R(q) exhibited a maxima independent of time. Corresponding correlation length, 1/q_c = ξ_c was found to be ≈75 ± 5 nm independent of quench depth. In the intermediate regime, anomalous growth described by I(q, t) ～ t^α with α = 0.1 ± 0.02 independent of q was observed. Rheological studies established that there was a propensity of network structures inside the dense phase. Isochronal temperature sweep studies of the dense phase determined the melting temperature, T_m = 312 ± 4 K, which was comparable with the spinodal temperature. The stress‐diffusion coupling prevailing in the dense phase when analyzed in the Doi‐Onuki model yielded a viscoelastic correlation length, ξ_v determined from low‐frequency storage modulus, G ′₀ ≈ k_B T/ξ, which was ξ_v ≈ 35 ± 3 nm indicating 2ξ_v ≈ ξ_c. It is concluded that the early stage of phase separation in this system was sufficiently described by linear Cahn‐Hilliard theory, but the same was not true in the intermediate stage. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 555–565, 2010     

Bis‐Triiodide von 1,2‐Ethandiaminkomplexen am Beispiel des Metalls Kupfer

In bis­(1,2‐ethanedi­amine‐N,N′)­bis­[tri­iodo(1?)‐I]copper, [Cu(I₃)₂­(C₂H₈N₂)₂], the triiodide anions form chains parallel to [001]. The central metal ion (site symmetry 2/m) of the complex cation is coordinated to four N atoms and to two I atoms. The geometry of the square‐bipyramidal complex is as expected, with d(Cu—N) = 2.006 (5) and d(Cu—I) = 3.3600 (9) Å.     

Pair distribution function and related properties of star‐branched chains

Pair configurations of linear and star‐branched chains with F = 4, 8 and 12 arms embedded in the tetrahedral lattice were investigated. Pair data were determined by exact enumeration of all possible pair configurations. When the separation between two (linear) chains reached zero (r → 0) the pair distribution function g (r) read ≈ 0.15 for athermal and ≈ 0.6 for theta conditions in full accordance with former work. For star‐branched chains, g (r) approached a value zero at small separations for both thermodynamic conditions and the range of g (r) = 0 increased with an increase of the number of arms. As a consequence, the characteristic maximum of g (r) for theta conditions was the more pronounced the larger the number of arms. For stars, the extent to which mean squared dimensions and shape parameters depend on intermolecular distance was similar to that of linear chains, at least in the region of intermediate and large intermolecular separations. Transformation of the data into a concentration dependence revealed that with an increase in concentration, the dimensions decreased in the case of athermal solvents while they increased for θ‐solvents regardless of the functionality given.     

Characteristic lengths and the structure of salt free polyelectrolyte solutions. A small angle neutron scattering study

We have studied salt free semi dilute polyelectrolyte solutions by small angle neutron scattering. Specific labelling associated with an extrapolation method has allowed the separation of the form factor of a single polyelectrolyte chainS ₁(q) and the structure factorS ₂(q). Two lengths are deduced from these two factors: the persistence lengthb _t which characterizes the electrostatic interactions along the chain by a fitting ofS ₁(q) with calculation of the scattering function for a wormlike chain, and fromS ₂(q),q _m ^–1 which characterizes the interactions between chains. These two lengths vary in the same way with the concentration of polyions (b _t C _p ^–1/2 ,q _m ^–1 C _p ^–1/2 ) and a constant relation exists between them: only one length is then necessary to describe the structure of polyelectrolyte soltuion on this semidilute concentration range.Laboratoire Commun CEA-CNRS.     

Novel Method of Producing Polymer Gels in Aqueous Solution Using UV Irradiation

Summary: We developed a novel method of producing polymer gels in aqueous solution using UV irradiation. Persulfates were effective photosensitive initiators of polymerization and/or gelation of acryloyl‐type monomers/polymers. The gelation was confirmed by an abrupt increase in light scattering intensity, 〈I(q)〉_T, at the gelation point. The gelation method entails significant advantages: it does not need any cross‐linkers, temperature control (heating), and additives except the persulfate.

The UV irradiation time dependence of light scattering intensity, 〈I(q)〉_T, for pre‐gel solutions containing N‐isopropylacrylamide (NIPAm) and/or ammonium persulfate (APS).     

Two polymorphs,with Z′ = 1 and 2, of 2‐amino‐4‐chloro‐6‐morpholino­pyrimidine in P21/c,and 2‐amino‐4‐chloro‐6‐piperidino­pyrimidine,which is isomorphous and almost isostructural with the Z′ = 2 polymorph

Crystallization of 2‐amino‐4‐chloro‐6‐morpholino­pyrimidine, C₈H₁₁ClN₄O, (I), yields two polymorphs, both with space group P2₁/c, having Z′ = 1 (from diethyl ether solution) and Z′ = 2 (from di­chloro­methane solution), denoted (Ia) and (Ib), respectively. In polymorph (Ia), the mol­ecules are linked by an N—H⋯O and an N—H⋯N hydrogen bond into sheets built from alternating R(8) and R(40) rings. In polymorph (Ib), one mol­ecule acts as a triple acceptor of hydrogen bonds and the other acts as a single acceptor; one N—H⋯O and three N—H⋯N hydrogen bonds link the mol­ecules in a complex chain containing two types of R(8) and one type of R(18) ring. 2‐Amino‐4‐chloro‐6‐piperidino­pyrimidine, C₉H₁₃ClN₄, (II), which is isomorphous with polymorph (Ib), also has Z′ = 2 in P2₁/c, and the mol­ecules are linked by three N—­H⋯N hydrogen bonds into a centrosymmetric four‐mol­ecule aggregate containing three R(8) rings.     

Two polymorphs of 5‐cyclohexyl‐5‐ethylbarbituric acid and their packing relationships with other barbiturates

Polymorph (Ia) (m.p. 474 K) of the title compound, C₁₂H₁₈N₂O₃, displays an N—H...O=C hydrogen‐bonded layer structure which contains R₆⁶(28) rings connecting six molecules, as well as R₂²(8) rings linking two molecules. The 3‐connected hydrogen‐bonded net resulting from these interactions has the hcb topology. Form (Ib) (m.p. 471 K) displays N—H...O=C hydrogen‐bonded looped chains in which neighbouring molecules are linked to one another by two different R₂²(8) rings. Polymorph (Ia) is isostructural with the previously reported form II of 5‐(2‐bromoallyl)‐5‐isopropylbarbituric acid (noctal) and polymorph (Ib) is isostructural with the known crystal structures of four other barbiturates.     

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.     

Formation and Stability of Gaseous WS2Cl2, WS2Br2 and WS2I2 – A Combined Experimental and Theoretical Study

Gaseous WS₂Cl₂ and WS₂Br₂ are formed by the reaction of solid WS₂ with chlorine resp. bromine at temperatures of about 1000 K. This could be shown by mass spectrometric measurements. The heats of formation and entropies of WS₂Cl₂ and WS₂Br₂ have been determined by means of mass spectrometry (MS) and quantum chemical calculations (QC). WS₂I₂ could not be detected by experimental methods. This is in line with the quantum chemically determined equilibrium constant of the formation reaction. The following values are given:, Δ_fH⁰₂₉₈(WS₂Cl₂) = –230.8 kJ · mol^–1 (MS), Δ_fH⁰₂₉₈(WS₂Cl₂) = –235.0 kJ · mol^–1 (QC),, S⁰₂₉₈(WS₂Cl₂) = 370.7 J · K^–1 · mol^–1 (QC) and, c_p⁰_T(WS₂Cl₂) = 103.78 + 7.07 × 10^–3 T – 0.93 × 10⁵ T^–2 – 3.25 × 10^–6 T² (298.15 K < T < 1000 K) (QC). Δ_fH⁰₂₉₈(WS₂Br₂) = –141.9 kJ · mol^–1 (MS), Δ_fH⁰₂₉₈(WS₂Br₂) = –131.5 kJ · mol^–1 (QC),, S⁰₂₉₈(WS₂Br₂) = 393.9 J · K^–1 · mol^–1 (QC) and, c_p⁰_T(WS₂Br₂) = 104.84 + 5.32 × 10^–3 T – 0.75 × 10⁵ T^–2 – 2.45 × 10^–6 T² (298.15 K < T < 1000 K) (QC). Δ_fH⁰₂₉₈(WS₂I₂) = –18.0 kJ · mol^–1 (QC), S⁰₂₉₈(WS₂I₂) = 409.9 J · K^–1 · mol^–1 (QC) and, c_p⁰_T(WS₂I₂) = 105.17 + 4.77 × 10^–3 T – 0.67 × 10⁵ T^–2 – 2.19 × 10^–6 T² (298.15 K < T < 1000 K) (QC). These molecules have the expected C_2v‐symmetry.     

The interpenetrated three‐dimensional framework of a new mixed lithium/ammonium perchlorate grown in a gel medium

Mixed lithium/ammonium perchlorate, Li_0.41(NH₄)_0.59ClO₄, has been prepared by gel diffusion using agar agar gel as the medium of growth at ambient temperature. The Cl and mixed Li/N atoms are located on the 4a (, , ) and 4b (, 0, ) special positions, respectively, in the space group I2d. The structure features a twofold interpenetrated three‐dimensional entanglement architecture, in which single three‐dimensional networks are constructed from tetrahedral coordination based on [–(ClO₄)–(Li/NH₄)–(ClO₄)–]_∞ diamondoid arrays. A comparison of the crystal structures of Li_0.41(NH₄)_0.59ClO₄, LiClO₄·3H₂O, LiClO₄ and NH₄ClO₄ is given.     

Electron-pair radial density functions

We introduce and discuss a generalized electron-pair radial density function G(q; a) that represents the probability density for the electron-pair radius |r ₁+ar ₂| to be q, where a is a real-valued parameter. The density function G(q; a) is a projection of the two-electron radial density D ₂(r ₁, r ₂) along lines r ₁ + ar ₂ ± q = 0 in the r ₁ r ₂ plane onto a point in the qa plane, and connects three densities S(s), D(r), and T(t), defined independently in the literature, as a smooth function of a: For an N-electron (N ≥ 2) system, S(s) = G(s; + 1), D(r) = 2G(r; 0)/(N − 1), and T(t) = G(|t|;−1)/2, where S(s) and T(t) are the electron-pair radial sum and difference densities, respectively, and D(r) is the single-electron radial density. Simple illustrations are given for the helium atom in the ground 1s² and the first excited 1s2s ³S states.     

Quasielastic scattering of neutrons from freely jointed polymer chains in dilute solutions

Starting with Kirkwood's Fokker–Planck equation for the polymer configuration-space distribution function and using the Zwanzig–Mori projection operator technique we have calculated the scattering law S_(q,w) for a freely jointed model polymer chain in a dilute solution. When memory effects are neglected, the theory predicts a Lorentzian for S_(q,w) with a halfwidth Ω_(q), which we have determined as a function of the momentum transfer q for all values of q. The results are compared with recent neutron scattering experiments on deuterated polytetrahydrofuran and polystyrene in dilute solution in CS₂. It is found that the observed q dependence of Ω(q) is represented satisfactorily by the present theory with a bond length b of about 6.3 Å for polystyrene and 3.8 Å for polytetrahydrofuran, and a friction coefficient ζ = 4πη0b where η₀ is the viscosity of the solvent.