Novel ethero atoms containing polyesters based on 2,6‐naphthalendicarboxylic acid: A comparative study with poly(butylene naphthalate)

Poly(butylene naphthalate) (PBN), poly(diethylene naphthalate) (PDEN), and poly(thiodiethylene naphthalate) (PTDEN) were synthesized and characterized in terms of chemical structure and molecular weight. The polyesters were examined by TGA, DSC, and DMTA. All the polymers showed a good thermal stability, even though depending on chemical structure. At room temperature they appeared as semicrystalline materials; the effect of the introduction along the PBN polymer chain of ether oxygen atoms or sulfur ones was a lowering in the T_g value, a decrement of T_m, and a decrease of the crystallization rate. Changing in chemical structure also affects the main α absorption associated with the glass transition which moves to lower temperature and whose energetic requirements decrease. The results were explained as due to the presence of highly flexible C? S? C or C? O? C bonds in the polymeric chain. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1694–1703, 2007     

From clusters to ionic complexes: structurally characterized thallium titanium double alkoxides

A series of sterically varied titanium alkoxides [[Ti(OR)(4)](n)(), n = 4, OR = OCH(2)CH(3) (OEt); n = 1, OCH(CH(3))(2) (OPr(i)); n = 2, OCH(2)C(CH(3))(3) (ONep); n = 1, OC(6)H(3)(CH(3))(2)-2,6 (DMP)] were reacted with a series of thallium alkoxides [[Tl(OR)](x) (x = 4, OR = OEt, ONep; n = infinity, DMP)]. The resultant products of the [Tl(mu(3)-OEt)](4)-modified [Ti(OR)(4)](n)() (OR = OEt, OPr(i), ONep) were found by X-ray analysis to be Tl(4)Ti(2)(mu-O)(mu(3)-OEt)(8)(OEt)(2) (1), Tl(4)Ti(2)(mu-O)(mu(3)-OPr(i))(5)(mu(3)-OEt)(3)(OEt)(2) (2), and TlTi(2)(mu(3)-OEt)(2)(mu-OEt)(mu-ONep)(2)(ONep)(4) (3), respectively. The reaction of [Tl(mu(3)-OEt)](4), 12HOEt, and 4[Ti(mu-ONep)ONep)(3)](2) to generate 3 in a higher yield resulted in the isolation of TlTi(2)(mu(3)-OEt)(mu(3)-ONep)(mu-OEt)(mu-ONep)(2)(ONep)(4) (4). Compounds 1 and 2 possess an octahedral (Oh) arrangement of two Ti and four Tl metal atoms around a mu-O central oxide atom (the Tl-O distance is too long to be considered a bond). For both compounds, each Ti atom adopts a distorted Oh geometry with one terminal OEt ligand. The Tl atoms are formally 4-coordinated, adopting a distorted pyramidal geometry using four mu(3)-OR (OR = OEt or OPr(i)) ligands to complete their coordination sphere. The Tl atoms reside approximately 1.4 A below the basal plane of oxygens. In contrast to these structures, both 3 and 4 utilize ONep ligands and display reduced oligomerization yielding trinuclear complexes without oxo formation. The two Ti cations are Oh, and the single Tl cation is in a formal distorted pyramidal (PYD) arrangement. If the lone pair of the Tl cations are considered in the geometry, each Tl adopts a square base pyramidal geometry. Two terminal ONep ligands are bound to each Ti with the remainder of the molecule consisting of mu(3)- and mu-ONep ligands. The reaction of [Tl(mu(3)-ONep)](4) with two equivalents of [Ti(mu-ONep)(ONep)(3)](2) also led to the isolation of the homoleptic trinuclear complex TlTi(2)(mu(3)-ONep)(2)(mu-ONep)(3)(ONep)(4) (5) which is analogous in structure to the mixed ligand species of 3 and 4. Each Ti is Oh coordinated with six ONep ligands, and the single Tl is PYD bound by ONep ligands. A further increase in the steric bulk of the pendant ligands, using [Tl(mu-DMP)](infinity) and [Ti(mu-ONep)(ONep)(3)](2), resulted in a further decrease in the nuclearity yielding the dinuclear species TlTi(mu-DMP)(mu-ONep)(DMP)(ONep)(2) (6). For 6, the two metals are bound by a mu-ONep and a mu-DMP ligand. The Tl metal center was solved in a bent geometry while the Ti adopted a distorted trigonal bipyramidal (TBP) geometry using three ONep and two DMP ligands to fill its coordination sphere. Further increasing the steric bulk of the ancillary ligands using Ti(DMP)(4) and [Tl(mu-DMP)](infinity) led to the formation of [Tl(+)][(-)(eta(2-3)-DMP)Ti(DMP)(4)] (7). The Ti metal center is in a TBP geometry, and the "naked" Tl cation resides unencumbered by solvent molecules but was found to have a strong pi-interaction with four DMP ligands of neighboring Ti(DMP)(5)(-) anions. For this novel set of compounds, (205)Tl NMR spectroscopy was used to investigate the solution behavior of these compounds. Multiple (205)Tl resonances were observed for the solution spectra of the crystalline material of 1-6, and a broad singlet was observed for 7. The large number of minor resonances noted for these compounds was attributed to sensitivity of the Tl cation based on small variations due to ligand rearrangement. However, the major resonance noted in the (205)Tl NMR solution spectra of 1-7 are in agreement with their respective solid-state structures.     

Novel random poly(propylene isophthalate/adipate) copolyesters: Synthesis and characterization

Poly(propylene adipate) (PPA) and poly(propylene isophthalate/adipate) (PPI-PPA) random copolymers of various compositions were synthesized in bulk and characterized in terms of chemical structure and molecular weight. Furthermore, the thermal behavior was examined by thermogravimetric analysis and differential scanning calorimetry. All the polymers showed a good thermal stability. At room temperature they appeared as semicrystalline materials, except the copolymers containing 20 and 30 mol% of PI units: the main effect of copolymerization was a lowering in the amount of crystallinity and a decrease of melting temperature with respect to homopolymers. The crystalline phase of PPI and PPA was evidenced at high content of propylene isophthalate or propylene adipate units, respectively. Amorphous samples were obtained after melt quenching and an increment of T_g as the content of PI units is increased was observed. This behavior was explained as due to the stiff phenylene groups in the polymeric chain. The Wood equation was found to describe well T_g-composition data. Lastly, the presence of a rigid-amorphous phase was evidenced in the copolymers, differently from PPA homopolymer.     

Evidence of early stage precursors of polymer crystals by dielectric spectroscopy

Dielectric spectra of the polyester poly(propylene succinate) were measured upon crystallization. For this model aliphatic polyester the alpha and beta relaxations appear simultaneously and are well resolved in the experimental frequency window. During isothermal crystallization, this fact allows one to use the beta relaxation to characterize the crystalline structural development while the alpha relaxation provides information about the evolution of the amorphous phase dynamics. In this way structure development and dynamics evolution can be characterized by a single experiment during the crystallization process. The unambiguous analysis of the dielectric loss clearly supports the existence of precursors of crystallization in the induction period.     

Flat-on lamellae in spin-coated, stable films of poly(propylene azelate)

Thin films (5-500 nm thick) of the linear aliphatic polyester (3,7) poly(propylene azelate) (PPAz) were prepared by spin-coating of CHCl(3) polymer solutions with different polymer concentrations. The morphology and structure of the spin-coated thin films were investigated by atomic force microscopy (AFM) and by grazing incidence wide-angle X-ray scattering (GIWAXS) techniques. AFM revealed the continuous nature of the flat, spherulitic films which are stable against dewetting even for polymer coatings as thin as 15 nm. GIWAXS patterns revealed a high crystal orientation of the films. A sharp reflection on the meridian whose spacing is related to the polymer chain unit length (c-axis) supports the presence of flat-on lamellae morphology in the whole range of film thicknesses investigated. The flat-on lamellae morphology is also supported by AFM images. A triclinic unit cell with the c*-axis perpendicular to the substrate is proposed for PPAz. The repulsion of the long aliphatic spacer by the Si-substrate is invoked as the main reason for the flat-on morphology observed.     

(2‐Hydroxy isobutyric) acid containing poly(glycolic acid): Structure–properties relationship

Poly(glycolic acid) (PGA) and a series of novel random copolymers of PGA containing 2‐hydroxyisobutyrric acid (PGAPHIB) (HIB unit content from 1.5 to 7.4 mol %) were synthesized and characterized in terms of chemical structure and molecular weight. Afterward, the polyesters were examined by thermogravimetric analysis, differential scanning calorimetry, and X‐ray diffraction techniques. The copolymers, which displayed a better thermal stability than PGA, at room temperature appeared as semicrystalline materials: the main effect of copolymerization was a lowering in the amount of crystallinity and a decrease of the melting temperature with respect to homopolymer PGA. Baur's equation described well the T_m‐composition data. X‐ray diffraction measurements allowed the identification of the PGA crystalline structure in all cases. After melt quenching, semicrystalline samples were obtained with the exception of PGAPHIB7.4 copolymer. The introduction of HIB units decreased the crystallization rate compared with pure PGA. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1901–1910, 2010     

Adaptive solution of infinite linear systems by Krylov subspace methods

In this paper we consider the problem of approximating the solution of infinite linear systems, finitely expressed by a sparse coefficient matrix. We analyse an algorithm based on Krylov subspace methods embedded in an adaptive enlargement scheme. The management of the algorithm is not trivial, due to the irregular convergence behaviour frequently displayed by Krylov subspace methods for nonsymmetric systems. Numerical experiments, carried out on several test problems, indicate that the more robust methods, such as GMRES and QMR, embedded in the adaptive enlargement scheme, exhibit good performances.     

Rounding Error Analysis in Solving M-Matrix Linear Systems of Block Hessenberg Form

The problem of solving large M-matrix linear systems with sparse coefficient matrix in block Hessenberg form is here addressed. In previous work of the authors a divide-and-conquer strategy was proposed and a backward error analysis of the resulting algorithm was presented showing its effectiveness for the solution of computational problems of queueing theory and Markov chains. In particular, it was shown that for block Hessenberg M-matrices the algorithm is weakly backward stable in the sense that the computed solution is the exact solution of a nearby linear system, where the norm of the perturbation is proportional to the condition number of the coefficient matrix. In this note a better error estimate is given by showing that for block Hessenberg M-matrices the algorithm is even backward stable.     

Poly(propylene isophthalate), poly(propylene succinate), and their random copolymers: Synthesis and thermal properties

Poly(propylene isophthalate) (PPI), poly(propylene succinate) (PPS), and poly(propylene isophthalate/succinate) (PPI‐PPS) random copolymers were synthesized and characterized in terms of chemical structure and molecular weight. The thermal behavior was examined by TGA and DSC. All the polymers showed a good thermal stability. At room temperature, they appeared as semicrystalline materials, except 20PPI‐PPS and 30PPI‐PPS: the main effect of copolymerization was a lowering in the amount of crystallinity and a decrease of T_m with respect to homopolymers. A crystalline phase of PPI and PPS was evidenced at high content of PI or PS units, respectively. Amorphous samples were obtained after melt quenching and an increment of T_g, with the increment of PI units, was observed. This behavior was explained as due to the presence of stiff phenylene groups. The Wood equation described well T_g‐composition data. Lastly, the presence of a rigid‐amorphous phase was evidenced in copolymers, differently from the two homopolymers. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 310–321, 2007.