Kinetic Analysis and Optimization for the Catalytic Esterification Step of PPT Polymerization

Summary: A well‐validated kinetic scheme has been studied for PPT, poly(propylene terephthalate) polymerization process in batch and semi‐batch mode with tetrabutoxytitanium (TBOT), a proven catalyst. Optimization study and analysis for PPT are rare, as the industrial relevance of PPT just became vibrant due to the commercial availability of one of its monomers in industrial scale in the recent past. Correctness of the analysis is checked by a new approach and parameters for the model are estimated from available experimental data. Solubility of terephthalic acid (TPA) is less in reaction medium and this effect is also considered along with the reaction scheme. Several simulations have been performed to see various process dynamics and this ultimately helps in formulating optimization problems. Using recently developed and well tested real‐coded non‐dominated sorting genetic algorithm‐II, a state‐of‐the art evolutionary optimization algorithm, a couple of three objective optimization problems have been solved and corresponding Pareto sets are presented. Results show remarkably promising aspects of productivity enhancement with an improvement in product quality. Sensitivity analysis for relatively uncertain solubility parameter is also performed to estimate its effect over the proposed optimal solutions.

Multiobjective Pareto front for 3 objectives: degree of polymerization, time and (bTPA + bPG).     

Studies on binuclear hydroxo/carboxylato-bridged manganese(III) complexes and a mononuclear manganese(III) complex involving salen type ligands

Synthesis of six hydroxo-bridged binuclear manganese(III) complexes of formulae [MnL-X-MnL](ClO₄) [X = OH (1–6)] along with a mononuclear manganese(III) complex (7) [Mn(L)(L′)(MeOH)₂] [HL′ = 2-(2-hydroxy-phen-yl)benzimidazole] and two carboxylate-bridged binuclear manganese(III) complexes (8) and (9) are described. The complexes have been characterized by the combination of i.r., u.v.-vis spectroscopy, magnetic moments and by their redox properties. The electronic spectra of all the complexes exhibit almost identical features consisting of two d–d bands at ca. 550 and 600 nm, one MLCT band at ca.400 nm, together with two π–π^* intra-ligand transitions at ca. 250 nm and ca.300 nm. Room temperature magnetic data range from μ = 2.7–3.0 BM indicates some super-exchange between the binuclear metal centers via bridging hydroxo/carboxylato groups. The X-ray crystal structure of the binuclear complex (5) revealed that it has a symmetric Mn^IIIN₂O₂ core bridged by a hydroxyl group. The X-ray analysis of the mononuclear complex (7) showed that the manganese-center possesses a distorted octahedral geometry. Electrochemical properties of hydroxo-bridged manganese(III) complexes (1–6) show identical features consisting of an irreversible and a quasi-reversible reduction corresponding to the Mn₂^III → Mn^IIMn^III → Mn^IIMn^II couples in the voltammogram. It was found that electron withdrawing substituents on the ligand result in easier reduction. Complex (7) displays an irreversible reduction at 0.08 V and a reversible oxidation at 0.45V assignable to the Mn^III → Mn^II reduction and Mn^III → Mn^IV oxidation, respectively. The carboxylate-bridged compound (8) exhibits two irreversible oxidations at 0.4 and 0.6 V, probably due to Mn₂^III → Mn^IIIMn^IV → Mn^IVMn^IV oxidations and shows a quasi-reversible reductive wave at −0.85 V, tentatively assigned to Mn₂^III → Mn^IIMn^III reduction.     

Synthesis,Characterization and Crystal Structures of new Palladium(II) Complexes and the first Platinum(III) Complex Containing ATT (ATT = 6‐Aza‐2‐thiothymine)

Treatment of the ligand 6‐aza‐2‐thiothymine (ATT, HL, 1 ) with palladium chloride in methanol forms the ionic complex [(HL)₄Pd]Cl₂·8MeOH ( 2 ), while its reaction with palladium iodide in same solvent produces the neutral complex trans‐[(HL)₂PdI₂]·2MeOH ( 3 ) in high yields. The reaction of 1 with Na₂[PdCl₄] in the presence of sodium acetate in a molar ratio of 2:1:2 and with platinum(II) chloride in presence of sodium acetate led to the dimer tetranuclear complexes [(L₄Pd₂)NaCl]₂·8MeOH ( 4 ) and [L₄Pt₂Cl₂]·6MeOH·H₂O ( 5 ). The latter is the first Pt^III complex of the ligand. All complexes were characterized by elemental analyses and IR spectroscopy and the crystal structures of 2 , 3 , 4 and 5 are determined by single‐crystal X‐ray diffraction. Crystal data for 2 at ?80 °C: triclinic space group , a = 1006.6(1), b = 1006.9(1), c = 1158.1(1) pm, α = 85.20(1)°, β = 83.84(1)°, γ = 88.91(1)°, Z = 1, R₁ = 0.0278; for 3 at ?80 °C: triclinic space group , a = 490.5(1), b = 977.2(2), c = 1116.8(2) pm, α = 90.26(1)°, β = 102.33(1)°, γ = 96.08(1)°, Z = 1, R₁ = 0.0394; for 4 at ?80 °C: orthorhombic space group Ccca, a = 1791.7(2), b = 1874.1(2), c = 2044.0(1) pm, Z = 4, R₁ = 0.0341 and for 5 at ?80 °C: monoclinic space group P2₁/c, a = 1464.3(1), b = 2003.7(1), c = 1368.5(1) pm, β = 95.66(1)°, Z = 4, R₁ = 0.0429.     

Recoil reactions of38Cl and128I in some heterocyclic systems

Halogen recoil following /n, / reaction has been studied in some heterocyclic systems. The organic yields are 60% for irradiation as solids: exceptions are dioxanide furoate /34%/ and 5-chloro isatoic anhydride /31%/. As solutions in 11 THF + benzene and 11 HTF+DMSO, these yields are lower by 10% and decrase further when only THF is the solvent. Mass-spectroscopy data revealed the possible fragmentation pattern.     

Synthesis of Some Novel Class of Peptides from α‐Amino Nitrones and Their Potential Biological Activities

α‐amino nitrones are found to have a great significance in the synthesis of peptides. Simple reaction methodology, high yield, and atom efficiency in these reactions have made this protocol highly attractive. The synthetic route may be extended to the synthesis of dipeptides in enantiomerically pure form. Potential biological activity of the newly synthesized peptides is the major application in this new methodology.     

Copper phthalocyanine films deposited by liquid-liquid interface recrystallization technique (LLIRCT)

The simple recrystallization process is innovatively used to obtain the nanoparticles of copper phthalocyanine by a simple method. Liquid-liquid interface recrystallization technique (LLIRCT) has been employed successfully to produce small sized copper phthalocyanine nanoparticles with diameter between 3-5 nm. The TEM-SAED studies revealed the formation of 3-5 nm sized with beta-phase dominated mixture of alpha and beta copper phthalocyanine nanoparticles. The XRD, SEM, and the UV-vis studies were further carried out to confirm the formation of copper phthalocyanine thin films. The cyclic voltametry (CV) studies conclude that redox reaction is totally reversible one electron transfer process. The process is attributed to Cu(II)/Cu(I) redox reaction.     

Studies on the exchange of gramicidin in liposomes

The exchange of gramicidin between liposomes made of two different kinds of phospholipids has been studied using a fluorescent probe (pyranine). The experimentally observed rate of exchange is compared with that of nigericin, which is a simple carrier. Possible reasons for the difference in the rate of exchange are discussed and probable mechanisms suggested. It is proposed that gramicidin exchanges between vesicles by a contact mechanism.     

Limiting Spectral Distribution of Random k-Circulants

Consider random k-circulants A _k,n with n????,k=k(n) and whose input sequence {a _l } _l??0 is independent with mean zero and variance one and $\sup_{n}n^{-1}\sum_{l=1}^{n}\mathbb{E}|a_{l}|^{2+\delta}<\infty$ for some ??>0. Under suitable restrictions on the sequence {k(n)} _n??1, we show that the limiting spectral distribution (LSD) of the empirical distribution of suitably scaled eigenvalues exists, and we identify the limits. In particular, we prove the following: Suppose g??1 is fixed and p ₁ is the smallest prime divisor of g. Suppose $P_{g}=\prod_{j=1}^{g}E_{j}$ where {E _j }_1??j??g are i.i.d. exponential random variables with mean one. (i) If k ^g =?1+sn where s=1 if g=1 and $s=o(n^{p_{1}-1})$ if g>1, then the empirical spectral distribution of n ^?1/2 A _k,n converges weakly in probability to $U_{1}P_{g}^{1/(2g)}$ where U ₁ is uniformly distributed over the (2g)th roots of unity, independent of P _g . (ii) If g??2 and k ^g =1+sn with $s=o(n^{p_{1}-1})$ , then the empirical spectral distribution of n ^?1/2 A _k,n converges weakly in probability to $U_{2}P_{g}^{1/(2g)}$ where U ₂ is uniformly distributed over the unit circle in ?², independent of P _g . On the other hand, if k??2, k=n ^o(1) with gcd?(n,k)=1, and the input is i.i.d. standard normal variables, then $F_{n^{-1/2}A_{k,n}}$ converges weakly in probability to the uniform distribution over the circle with center at (0,0) and radius $r=\exp(\mathbb{E}[\log\sqrt{E}_{1}])$ .     

Laguerre minimal surfaces,isotropic geometry and linear elasticity

Laguerre minimal (L-minimal) surfaces are the minimizers of the energy \(\int (H^2-K)/K d\!A\). They are a Laguerre geometric counterpart of Willmore surfaces, the minimizers of \(\int (H^2-K)d\!A\), which are known to be an entity of Möbius sphere geometry. The present paper provides a new and simple approach to L-minimal surfaces by showing that they appear as graphs of biharmonic functions in the isotropic model of Laguerre geometry. Therefore, L-minimal surfaces are equivalent to Airy stress surfaces of linear elasticity. In particular, there is a close relation between L-minimal surfaces of the spherical type, isotropic minimal surfaces (graphs of harmonic functions), and Euclidean minimal surfaces. This relation exhibits connections to geometrical optics. In this paper we also address and illustrate the computation of L-minimal surfaces via thin plate splines and numerical solutions of biharmonic equations. Finally, metric duality in isotropic space is used to derive an isotropic counterpart to L-minimal surfaces and certain Lie transforms of L-minimal surfaces in Euclidean space. The latter surfaces possess an optical interpretation as anticaustics of graph surfaces of biharmonic functions.