The Importance of Chain-Length Dependent Kinetics in Free-Radical Polymerization: A Preliminary Guide

The effect of chain-length dependent propagation at short chain lengths on the observed kinetics in low-conversion free-radical polymerization (frp) is investigated. It is shown that although the values of individual propagation rate coefficients quickly converge to the high chain length value (at chain lengths, i, of about 10), its effect on the average propagation rate coefficients, 〈k_p〉, in conventional frp may be noticeable in systems with an average degree of polymerization (DP_n) of up to 100. Furthermore it is shown that, unless the system is significantly retarded, the chain-length dependence of the average termination rate coefficient, 〈k_t〉, is not affected by the presence of chain-length dependent propagation and that there exists a simple (fairly general) scaling law between 〈k_t〉 and DP_n. This latter scaling law is a good reflection of the dependence of the termination rate coefficient between two i-meric radicals, k, on i. Although simple expressions seem to exist to describe the dependence of 〈k_p〉 on DP_n, the limited data available to date does not allow the generalization of these expressions.     

Long-range magnetic ordering of quasi-one-dimensional S=1/2 Heisenberg antiferromagnet Sr2Cu(PO4)2

Magnetic properties of quasi-one-dimensional S=1/2 Heisenberg antiferromagnet Sr₂Cu(PO₄)₂ were investigated by temperature and field dependence of AC susceptibility down to 0.03 K. A sharp peak was observed at on the temperature dependence of AC susceptibility indicating long-range magnetic ordering. Taking into account the exchange constant, (Hamiltonian =J∑S_iS_i+1), the ratio k_BT_N/J is 0.06%. Sr₂Cu(PO₄)₂ is, therefore, one of the best one-dimensional Heisenberg antiferromagnet known so far.     

Magnetic and transport properties of RCr0.3Ge2 (R=Tb, Dy, Ho and Er) compounds

The magnetic and transport properties of ternary rare-earth chromium germanides RCr_0.3Ge₂ (R=Y and Tb-Er) have been determined. X-ray and neutron diffraction studies indicate that these compounds have the CeNiSi₂-type structure (space group Cmcm) [1]. Magnetic measurements reveal the antiferromagnetic ordering below T_N equal to 18.5 K (R=Tb), 11.8 K (Dy), 5.8 K (Ho) and 3.4 K (Er). From the neutron diffraction data the magnetic structures have been determined. For TbCr_0.3Ge₂ and DyCr_0.3Ge₂ at low temperatures the magnetic ordering can be described by two vectors k₁=(,0,0) and k₂=(,0,), and k₁′=(,0,0) and k₂′=(,0,), respectively. In HoCr_0.3Ge₂ and ErCr_0.3Ge₂ the ordering can be described by one propagation vector equal to (,,0) and (0,0,0.4187(2)), respectively. In DyCr_0.3Ge₂ some change in the magnetic ordering is observed at T_t=5.1 K. In temperature range from T_t to T_N the magnetic ordering is given by one propagation vector k=(,0,0). YCr_0.3Ge₂ is a Pauli paramagnet down to 1.72 K which suggests that in the entire RCr_0.3Ge₂ series the Cr atoms do not carry magnetic moments. All compounds studied exhibit metallic character of the electrical conductivity. The temperature dependencies of the lattice parameters reveal strong magnetostriction effect at the respective Nèel temperatures.     

Elastic behavior of poly(ethylene terephthalate) chains

The Monte Carlo (MC) method based on the rotational-isomeric-state (RIS) model is adopted in studying the elastic behavior of poly(ethylene terephthalate) (PET) chains in this paper. The mean-square end-to-end distance 〈R²〉, the mean-square radius of gyration 〈S²〉, and the ratio of 〈R²〉/〈S²〉 all increase with elongation ratio λ. The interior conformations are also investigated through calculating the a priori probability of rotational state in the process of tensile elongation. The radius of gyration tensor S is introduced here in order to measure the shape of PET chains, and increases with elongation ratio λ, however, some different behaviors are obtained for . Here , and are the eigenvalues of the radius of gyration tensor . The average energy per repeat unit 〈U〉 and the average free energy per repeat unit 〈A〉 are also calculated, and we find that the average energy decreases with elongation ratio λ, however, the average free energy per repeat unit increases with elongation ratio λ. Elastic force f, energy contribution to force f_U, and entropy contribution to force f_S are also investigated. Both elastic force f and entropy contribution to force f_S increases with λ, however, energy contribution to force f_U and the ratio f_U/f decreases with λ. The ratio of f_U/f is less than zero and almost independent of chain length. The results of these microscopic calculations may explain some macroscopic phenomena of rubber elasticity.     

Binding of fluoride and carbonate by open chain polyammonium cations

The formation of open chain polyammonium cation-fluoride and -carbonate complexes was studied by potentiometric and calorimetric techniques at t=25 °C. Several species of H_iAL (A=amine; L=F⁻, CO₃²⁻) are formed in both systems with a mean stability (ζ=|z_anion×z_cation|) and for fluoride and carbonate, respectively. The comparison with analogous systems (chloride and acetate for fluoride and hydrogenphosphate, sulfate and malonate for carbonate) showed that fluoride and carbonate form the most stable species with open chain polyammonium cations, among low molecular weight anions. The N-alkyl substitution does not play negligible role in the stability of these complexes, the species formed by substituted amines being more stable.     

A TEM study of Ni ordering in the Ni6Se5−xTex, 0<x<∼1.7, system

The Ni₆Se_5−xTe_x, 0<x<∼1.7, system has been carefully investigated via electron diffraction and TEM imaging. They reveal a somewhat disordered modulated superstructure phase arising from Ni ion ordering within an essentially well-defined chalcogen sub-structure. As x, and the underlying parent substructure cell dimensions increase, the incommensurate primary modulation wave-vector q characteristic of this Ni ion ordering quickly swings from close to for x=0 towards for x?0.5. A lock-in to would formally transform the underlying parent Bmmb (a_p, b_p, c_p) structure into a P1a1 (a_s=2a_p, b_s=b_p, c_s=a_p+c_p) superstructure phase.     

Isomorphy of structural phase transitions in LiTaOSiO4, LiTaOGeO4 and titanite, CaTiOSiO4

Structural phase transitions in LiTaOGeO₄ (LTGO) and LiTaOSiO₄ (LTSO) have been observed using differential scanning calorimetry, X-ray diffraction and MAS NMR spectroscopy. LTGO transforms from P2₁/c to C2/c space group symmetry at , while the isomorphic transition occurs at in LTSO. An analogous phase transition is known to occur in the structurally related mineral titanite, CaTiOSiO₄. Spontaneous strain accompanying this phase transition in LTSO is significantly stronger than in titanite. As in titanite non-vanishing strain components are observable for T_c<T<T_i, with a similar ratio T_i/T_c. MAS NMR spectroscopy in combination with computation of the electric field gradient by first principle methods confirms that the tetrahedral Li coordination environment is retained during the phase transitions in LTGO and in LTSO. In LTSO substantial motional narrowing is observed, indicating increased mobility of the Li cation above . The narrowing of the spinning sidebands is significantly modified immediately above and below the critical temperature.     

X-ray powder diffraction studies and thermal behaviour of NaK2B9O15, Na(Na.17K.83)2B9O15, and (Na.80K.20)K2B9O15

The crystal structures of NaK₂B₉O₁₅ (, , , β=94.080(1)°, R_p=0.047, R_wp=0.059, R_B=0.026), Na(Na_.17K_.83)₂B₉O₁₅ (, , , β=94.228(2)°, R_p=0.053, R_wp=0.068, R_B=0.026), and (Na_.80K_.20)K₂B₉O₁₅ (, , , β=94.071(1)°, Z=4, R_p=0.041, R_wp=0.052, R_B=0.023) were refined in the monoclinic space groups P2₁/c(Z=4) using X-ray powder diffraction data and the Rietveld method. These nonaborates are isostructural to K₃B₉O₁₅. Their crystal structure consists of a three-dimensional open framework built up from three crystallographically independent triborate groups. The alkali metal cations are located on three different sites in the voids of the framework. High-temperature X-ray diffraction studies show that NaK₂B₉O₁₅ decomposes at about 700 °C in accordance with the peritectic reaction NaK₂B₉O₁₅↔K₅B₁₉O₃₁+liquid. The thermal expansion of NaK₂B₉O₁₅ and Na(Na_.17K_.83)₂B₉O₁₅ is highly anisotropic. A similarity of the thermal and compositional (Na-K substitution) deformations of NaK₂B₉O₁₅ is revealed: heating of NaK₂B₉O₁₅ by 1 °C leads to the same deformations of the crystal structure as increasing the amount of K atoms in (Na_1−xK_x)₃B₉O₁₅ by 0.04 at% K.     

Monitoring structural transformations in crystals. Part 4. Monitoring structural changes in crystals of pyridine analogs of chalcone during [2+2]-photodimerization and possibilities of the reaction in hydroxy derivatives

We studied the [2+2]-photodimerization in crystals of pyridine analogs and hydroxy derivatives of chalcone using the X-ray structure analysis. The mutual orientation of adjacent molecules in the crystals was analyzed in a quantitative way and the results were compared with data for known photoactive crystals undergoing the [2+2]-photodimerization. In the case of one pyridine analog, we processed the single-crystal-to-single-crystal photodimerization and determined the structure for the mixed crystal containing both the substrate and the product. We also explained a role of hydrogen bonds in the [2+2]-photodimerization in the case of the hydroxy derivatives of chalcone. C₅H₄N-CO-CHCH-C₆H₅: , , , β=91.318(10)°, monoclinic, . The irradiated crystal of the above analog: , , , β=91.870(10)°, monoclinic, . C₆H₅-CO-CHCH-C₅H₄N: , , , β=110.01(3)°, monoclinic, C2/c,Z=8. C₆H₅-CO-CHCH-C₆H₄(o-OH): , , , β=109.73(5)°, monoclinic, . C₆H₅-CO-CHCH-C₆H₄(p-OH): , , , orthorhombic, .     

The thermodynamic dissociation constants of ambroxol, antazoline, naphazoline, oxymetazoline and ranitidine by the regression analysis of spectrophotometric data

The mixed dissociation constants of five drug acids—ambroxol, antazoline, naphazoline, oxymetazoline and ranitidine—at various ionic strengths I of range 0.01 and 1.0 and at temperatures of 25 and 37 °C were determined using SQUAD(84) regression analysis of the pH-spectrophotometric titration data. A proposed strategy of efficient experimentation in a protonation constants determination, followed by a computational strategy for the chemical model with a protonation constants determination, is presented on the protonation equilibria of ambroxol. The thermodynamic dissociation constant pK_a^T was estimated by non-linear regression of {pK_a, I} data at 25 and 37 °C: for ambroxol and 8.25 (4), log  and 11.83 (8), for antazoline and 7.83 (6), and 9.55 (2), for naphazoline and 10.63 (1), for oxymethazoline and 10.77 (7), pK_a,2^T=12.03(3) and 11.82 (4) and for ranitidine and 1.77 (1). Goodness-of-fit tests for various regression diagnostics enabled the reliability of the parameter estimates to be found.     

Chain-length dependent termination in pulsed-laser polymerization, 1. Interaction with propagation

Using a new simulation procedure in which each individual propagation step is subjected to a Poisson process it was proved that in case of chain-length dependent termination the apparent rate of propagation no longer coincides with the true one. This is caused by the polydispersity of the chain-length distribution of the growing chains: shorter chains are removed preferentially. This effect is comparatively small although significant. The consequences for the determination of the rate constant of chain propagation k_p are nearly negligible.     

C2- and Cs-symmetric diamidodichlorotitanium complexes: Syntheses, structures and 1-hexene polymerization catalysis

The complexes l-[CMe₂{CHMeN(2-Prⁱ-C₆H₄)}₂TiCl₂] (2) and (3), C₂- and C_s-symmetric analogues, respectively, of McConville’s C_2v hexene polymerization precatalyst (1), were prepared by high-dilution salt-elimination from the lithium amides and characterized spectroscopically and crystallographically. Complex 2, though less active than 1, was a highly active catalyst of polymerization of 1-hexene when activated by MAO. Complex 3 was inactive under similar conditions. NMR analysis confirmed that there were more mmmm pentads in polymer produced by 2 than in the statistically atactic material produced by 1, though the isotacticity index was not high. The results are interpreted in terms of an isotactic/atactic block structure, caused by syn/anti fluxion of the two 2-isopropylphenyl rings in 2. Kinetic profiles and polydispersities were consistent with a slow initiation step involving monomer, followed by rapid propagation, with some chain transfer to aluminium and only a small extent of β-hydride elimination. The rubber-like polymers were indistinguishable by thermal analysis from those prepared by Ziegler-Natta catalyst systems.     

Structure of δ-Bi2O3 from density functional theory: A systematic crystallographic analysis

A systematic crystallographic analysis of the 〈110〉 and 〈111〉 vacancy-ordered structure of cubic δ-Bi₂O₃ obtained from electronic-structure calculations is presented. The ordering of vacancies leads to a doubling of the unit-cell that results in a 2×2×2 fluorite super-structure, with an associated reduction in its space group symmetry from to . The Bi atoms present inside the 〈111〉 vacancy-ordered oxygen sublattice have equal Bi-O bond lengths, whereas, those present inside the 〈110〉 vacancy-ordered oxygen sublattice have three different pairs of Bi-O bond lengths. The specific ionic displacements and electronic charge configurations also depend on the nature of vacancy ordering in the oxygen sub-lattice.