The Crystal Chemistry of Lithium in the Alluaudite Structure: A Study of the (Na1−xLix)CdIn2(PO4)3 Solid Solution (x=0 to 1)

Several compounds of the (Na_1−xLi_x)CdIn₂(PO₄)₃ solid solution were synthesized by a solid-state reaction in air, and pure alluaudite-like compounds were obtained for x=0.00, 0.25, and 0.50. X-ray Rietveld refinements indicate the occurrence of Cd²⁺ in the M(1) site, and of In³⁺ in the M(2) site of the alluaudite structure. This non-disordered cationic distribution is confirmed by the sharpness of the infrared absorption bands. The distribution of Na⁺ and Li⁺ on the A(1) and A(2)′ crystallographic sites cannot be accurately assessed by the Rietvled method, probably because the electronic densities involved in the Na⁺→Li⁺ substitution are very small. A comparison with the synthetic alluaudite-like compounds, (Na_1−xLi_x)MnFe₂(PO₄)₃, indicates the influence of the cations occupying the M(1) and M(2) sites on the coordination polyhedra morphologies of the A(1) and A(2)′ crystallographic sites.     

Polystyrene-supported organotin dichloride as a recyclable catalyst in lactone ring-opening polymerization: assessment and catalysis monitoring by high-resolution magic-angle-spinning NMR spectroscopy

Dialkyltin dichloride grafted to a cross-linked polystyrene, with the formula [P-H]((1-t))[P-(CH2)nSnBuCl2]t (P=[CH2CH(pC6H4)], t=the degree of functionalization, and n=6 or 11), is investigated as a recyclable catalyst in the ring-opening polymerization (ROP) of epsilon-caprolactone (CL). It is demonstrated that high-resolution magic-angle-spinning (HR-MAS) NMR spectroscopy is an invaluable tool to characterize completely the supported catalyst. The 2D 1H-13C HSQC HR-MAS spectrum, in particular, allowed extensive assignment of the 1H and 13C resonances, as well as accurate measurement of the (n)J((1)H-(117/119)Sn) and (n)J((13)C-(117/119)Sn) coupling constants. 1H and 119Sn HR-MAS NMR spectroscopy is presented as a monitoring tool for catalytic processes based on organotin compounds, particularly for the investigation of the extent to which polymerization residues are observable in situ in the material pores and for the assessment of the chemical integrity and recycling conditions of the grafted catalyst. From polymerization experiments with CL, initiated by n-propanol and with [P-H]((1-t))[P-(CH2)nSnBuCl2]t of various compositions as the supported catalyst, it appears that a partial 'burst' of the polystyrene support occurs when the length of the alkyl spacer is limited to n=6, as a result of polymer chains growing within the pores of the support. However, extension of the length of the aliphatic polymethylene spacer from 6 to 11 carbon atoms preserves the support integrity and allows the production of catalyst-deprived poly(epsilon-caprolactone) (PCL) oligomers. A preliminary attempt to recycle the heterogeneous catalyst has shown that very good reproducibility can be obtained, in terms of both catalyst activity and molecular-weight parameters of the as-recovered PCL polyester chains.     

Synthesis, structure and anion binding properties of lower rim α-hydroxyamide calix[4]arene derivatives

A new family of p-tert-butylcalix[4]arenes functionalized at the lower rim with α-ketoamide or α-hydroxyamide functions has been prepared. The ¹H and ¹³C NMR spectra indicate that the macrocycles preferably adopt a cone conformation. X-ray crystal study of the α-ketoamide derivative 4a shows the flattened cone conformation in the solid state. Reduction of α-ketoamide 4ab has produced the α-hydroxyamide derivatives 6ab. The introduction of chiral moieties on the lower rim position of the calix[4]arene allowed the synthesis of the chiral derivatives 7 and 8. Host-guest complexation properties towards various anions of the chiral α-hydroxyamide 8 have been examined by ¹H NMR spectroscopy. This new receptor has shown promising selectivity for and N-tosyl-(L)-alaninate.     

Influence of stereochemistry on the thermal properties of partially cycloaliphatic polyamides

The effects of the partial substitution of 1,4‐disubstituted cyclohexane monomers for linear aliphatic monomers in polyamides are discussed. More specifically, the relation between the stereochemistry of the cycloaliphatic residues and the thermal properties [melting temperature (T_m) and crystallization temperature (T_cr)] was investigated. For this purpose, two different types of copolyamides were synthesized: in polyamides 12.6, the adipic acid residues were partially replaced by cis/trans‐1,4‐cyclohexanedicarboxylic acid (1,4‐CHDA), whereas in polyamides 4.14, the 1,4‐diaminobutane residues were partially substituted with cis/trans‐1,4‐diaminocyclohexane (1,4‐DACH). For both systems, increasing the degree of substitution of cycloaliphatic residues for linear aliphatic residues resulted in a rise of both T_m and T_cr. This points to the isomorphous crystallization of the linear and cycloaliphatic residues. In contrast to the use of 1,4‐DACH as a comonomer, 1,4‐CHDA residues showed isomerization upon thermal treatment of the polyamides. This isomerization of the cyclohexane residues influenced the thermal properties of the copolyamides. The use of a nonisomerizing cis–trans mixture of 1,4‐DACH exhibited the large influence of the stereochemistry of the cycloaliphatic residues on the T_m of the copolyamides. For both the 1,4‐CHDA‐ and 1,4‐DACH‐based copolyamides, differential scanning calorimetry analysis revealed that recrystallization occurs during melting. This exothermal effect becomes less pronounced with an increasing content of rigid cycloaliphatic residues. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 1962–1971, 2002     

The importance of vibronic perturbations in ferrocytochrome c spectra: a reevaluation of spectral properties based on low-temperature optical absorption, resonance Raman, and molecular-dynamics simulations

We have measured and analyzed the low-temperature (T=10 K) absorption spectrum of reduced horse heart and yeast cytochrome c. Both spectra show split and asymmetric Q(0) and Q(upsilon) bands. The spectra were first decomposed into the individual split vibronic sidebands assignable to B(1g) (nu15) and A(2g) (nu19, nu21, and nu22) Herzberg-Teller active modes due to their strong intensity in resonance Raman spectra acquired with Q(0) and Q(upsilon) excitations. The measured band splittings and asymmetries cannot be rationalized solely in terms of electronic perturbations of the heme macrocycle. On the contrary, they clearly point to the importance of considering not only electronic perturbations but vibronic perturbations as well. The former are most likely due to the heterogeneity of the electric field produced by charged side chains in the protein environment, whereas the latter reflect a perturbation potential due to multiple heme-protein interactions, which deform the heme structure in the ground and excited states. Additional information about vibronic perturbations and the associated ground-state deformations are inferred from the depolarization ratios of resonance Raman bands. The results of our analysis indicate that the heme group in yeast cytochrome c is more nonplanar and more distorted along a B(2g) coordinate than in horse heart cytochrome c. This conclusion is supported by normal structural decomposition calculations performed on the heme extracted from molecular-dynamic simulations of the two investigated proteins. Interestingly, the latter are somewhat different from the respective deformations obtained from the x-ray structures.     

Thermodynamic properties of naphthalene and uric acid in ethylene glycol-water mixtures

The solubility of naphthalene and uric acid was measured as function of temperature (5–45°C) in water(W)-ethylene glycol(EG) mixtures over the entire composition range. The molar solubility data were used to calculate transfer Gibbs energies G _tr ⁰ (WW-EG) (from water to water-ethylene glycol mixtures) and the temperature dependence of G⁰ was used to compute the corresponding transfer enthalpies and heat capacities. The thermodynamic quantities are interpreted in terms of two contributions; a cavity term which is estimated using the scaled particle theory (SPT) and a solute-solvent interaction term. The latter is inferred from comparisons involving the SPT results and the naphthalene data, or the data for naphthalene and uric acid. The solvation effects in W-EG mixtures are discussed with reference to thermodynamic properties of the solvent mixtures available from previous work.     

Phase Behavior in Blends of Ethylene Oxide–Propylene Oxide Copolymer and Poly(ether sulfone) Studied by Modulated-Temperature DSC and NMR Relaxometry

The state diagram of a blend consisting of a copolymer containing ethylene oxide and propylene oxide, P(EO-ran-PO), and poly(ether sulfone), PES, is constructed by using modulated-temperature differential scanning calorimetry (MTDSC), T₂ NMR relaxometry, and light scattering. The apparent heat capacity signal in MTDSC is used for the characterization of polymer miscibility and morphology development. T₂ NMR relaxometry is used to detect the onset of phase separation, which is in good agreement with the onset of phase separation in the apparent heat capacity from MTDSC and the cloud-point temperature as determined from light scattering. The coexistence curve can be constructed from T₂ values at various temperatures by using a few blends with well-chosen compositions. These T₂ values also allow the detection of the boundary between the demixing zones with and without interference of partial vitrification and are in good agreement with stepwise quasi-isothermal MTDSC heat capacity measurements. Important interphases are detected in the heterogeneous P(EO-ran-PO)/PES blends.     

An algorithm for the generalized quadratic assignment problem

This paper reports on a new algorithm for the Generalized Quadratic Assignment problem (GQAP). The GQAP describes a broad class of quadratic integer programming problems, wherein M pair-wise related entities are assigned to N destinations constrained by the destinations’ ability to accommodate them. This new algorithm is based on a Reformulation Linearization Technique (RLT) dual ascent procedure. Experimental results show that the runtime of this algorithm is as good or better than other known exact solution methods for problems as large as M=20 and N=15. Current address of P.M. Hahn: 2127 Tryon Street, Philadelphia, PA 19146-1228, USA.     

Semidefinite bounds for the stability number of a graph via sums of squares of polynomials

Lovász and Schrijver (SIAM J. Optim. 1:166–190, 1991) have constructed semidefinite relaxations for the stable set polytope of a graph G = (V,E) by a sequence of lift-and-project operations; their procedure finds the stable set polytope in at most α(G) steps, where α(G) is the stability number of G. Two other hierarchies of semidefinite bounds for the stability number have been proposed by Lasserre (SIAM J. Optim. 11:796–817, 2001; Lecture Notes in Computer Science, Springer, Berlin Heidelberg New York, pp 293–303, 2001) and by de Klerk and Pasechnik (SIAM J. Optim. 12:875–892), which are based on relaxing nonnegativity of a polynomial by requiring the existence of a sum of squares decomposition. The hierarchy of Lasserre is known to converge in α(G) steps as it refines the hierarchy of Lovász and Schrijver, and de Klerk and Pasechnik conjecture that their hierarchy also finds the stability number after α(G) steps. We prove this conjecture for graphs with stability number at most 8 and we show that the hierarchy of Lasserre refines the hierarchy of de Klerk and Pasechnik.