Determination of the critical parameters of polymer solutions

The contribution of short-range orientation order to the chemical potentials of components in a polymer-solvent system was determined. The temperature dependence of the degree of orientation of solvent molecules relative to polymer chains in a polyisobutylene-benzene system was obtained. It was shown that the short-range order in the polymer-solvent system fails with temperature to a much lesser extent than in the pure solvent. The expressions for the upper and lower critical solution temperatures with allowance for the contribution of short-range order to the entropy and the free energy of solution, as well as to the chemical potentials of components, were found. It was demonstrated that, in the polymer-solvent system, two upper and two lower critical solution temperatures can exist.     

Tetranuclear and Octanuclear Manganese Carboxylate Clusters: Preparation and Reactivity of (NBu(n)(4))[Mn(4)O(2)(O(2)CPh)(9)(H(2)O)] and Synthesis of (NBu(n)(4))(2)[Mn(8)O(4)(O(2)CPh)(12)(Et(2)mal)(2)(H(2)O)(2)] with a "Linked-Butterfly" Structure

The reaction of Mn(O(2)CPh)(2).2H(2)O and PhCO(2)H in EtOH/MeCN with NBu(n)(4)MnO(4) gives (NBu(n)(4))[Mn(4)O(2)(O(2)CPh)(9)(H(2)O)] (4) in high yield (85-95%). Complex 4 crystallizes in monoclinic space group P2(1)/c with the following unit cell parameters at -129 degrees C: a = 17.394(3) ?, b = 19.040(3) ?, c = 25.660(5) ?, beta = 103.51(1) degrees, V = 8262.7 ?(3), Z = 4; the structure was refined on F to R (R(w)) = 9.11% (9.26%) using 4590 unique reflections with F > 2.33sigma(F). The anion of 4 consists of a [Mn(4)(&mgr;(3)-O)(2)](8+) core with a "butterfly" disposition of four Mn(III) atoms. In addition to seven bridging PhCO(2)(-) groups, there is a chelating PhCO(2)(-) group at one "wingtip" Mn atom and terminal PhCO(2)(-) and H(2)O groups at the other. Complex 4 is an excellent steppingstone to other [Mn(4)O(2)]-containing species. Treatment of 4 with 2,2-diethylmalonate (2 equiv) leads to isolation of (NBu(n)(4))(2)[Mn(8)O(4)(O(2)CPh)(12)(Et(2)mal)(2)(H(2)O)(2)] (5) in 45% yield after recrystallization. Complex 5 is mixed-valent (2Mn(II),6Mn(III)) and contains an [Mn(8)O(4)](14+) core that consists of two [Mn(4)O(2)](7+) (Mn(II),3Mn(III)) butterfly units linked together by one of the &mgr;(3)-O(2)(-) ions in each unit bridging to one of the body Mn atoms in the other unit, and thus converting to &mgr;(4)-O(2)(-) modes. The Mn(II) ions are in wingtip positions. The Et(2)mal(2)(-) groups each bridge two wingtip Mn atoms from different butterfly units, providing additional linkage between the halves of the molecule. Complex 5.4CH(2)Cl(2) crystallizes in monoclinic space group P2(1)/c with the following unit cell parameters at -165 degrees C: a = 16.247(5) ?, b = 27.190(8) ?, c = 17.715(5) ?, beta = 113.95(1) degrees, V = 7152.0 ?(3), Z = 4; the structure was refined on F to R (R(w)) = 8.36 (8.61%) using 4133 unique reflections with F > 3sigma(F). The reaction of 4 with 2 equiv of bpy or picolinic acid (picH) yields the known complex Mn(4)O(2)(O(2)CPh)(7)(bpy)(2) (2), containing Mn(II),3Mn(III), or (NBu(n)(4))[Mn(4)O(2)(O(2)CPh)(7)(pic)(2)] (6), containing 4Mn(III). Treatment of 4 with dibenzoylmethane (dbmH, 2 equiv) gives the mono-chelate product (NBu(n)(4))[Mn(4)O(2)(O(2)CPh)(8)(dbm)] (7); ligation of a second chelate group requires treatment of 7 with Na(dbm), which yields (NBu(n)(4))[Mn(4)O(2)(O(2)CPh)(7)(dbm)(2)] (8). Complexes 7 and 8 both contain a [Mn(4)O(2)](8+) (4Mn(III)) butterfly unit. Complex 7 contains chelating dbm(-) and chelating PhCO(2)(-) at the two wingtip positions, whereas 8 contains two chelating dbm(-) groups at these positions, as in 2 and 6. Complex 7.2CH(2)Cl(2) crystallizes in monoclinic space group P2(1) with the following unit cell parameters at -170 degrees C: a = 18.169(3) ?, b = 19.678(4) ?, c = 25.036(4) ?, beta = 101.49(1) degrees, V = 8771.7 ?(3), Z = 4; the structure was refined on F to R (R(w)) = 7.36% (7.59%) using 10 782 unique reflections with F > 3sigma(F). Variable-temperature magnetic susceptibility studies have been carried out on powdered samples of complexes 2 and 5 in a 10.0 kG field in the 5.0-320.0 K range. The effective magnetic moment (&mgr;(eff)) for 2 gradually decreases from 8.61 &mgr;(B) per molecule at 320.0 K to 5.71 &mgr;(B) at 13.0 K and then increases slightly to 5.91 &mgr;(B) at 5.0 K. For 5, &mgr;(eff) gradually decreases from 10.54 &mgr;(B) per molecule at 320.0 K to 8.42 &mgr;(B) at 40.0 K, followed by a more rapid decrease to 6.02 &mgr;(B) at 5.0 K. On the basis of the crystal structure of 5 showing the single Mn(II) ion in each [Mn(4)O(2)](7+) subcore to be at a wingtip position, the Mn(II) ion in 2 was concluded to be at a wingtip position also. Employing the reasonable approximation that J(w)(b)(Mn(II)/Mn(III)) = J(w)(b)(Mn(III)/M(III)), where J(w)(b) is the magnetic exchange interaction between wingtip (w) and body (b) Mn ions of the indicated oxidation state, a theoretical chi(M) vs T expression was derived and used to fit the experimental molar magnetic susceptibility (chi(M)) vs T data. The obtained fitting parameters were J(w)(b) = -3.9 cm(-)(1), J(b)(b) = -9.2 cm(-)(1), and g = 1.80. These values suggest a S(T) = (5)/(2) ground state spin for 2, which was confirmed by magnetization vs field measurements in the 0.5-50.0 kG magnetic field range and 2.0-30.0 K temperature range. For complex 5, since the two bonds connecting the two [Mn(4)O(2)](7+) units are Jahn-Teller elongated and weak, it was assumed that complex 5 could be treated, to a first approximation, as consisting of weakly-interacting halves; the magnetic susceptibility data for 5 at temperatures >/=40 K were therefore fit to the same theoretical expression as used for 2, and the fitting parameters were J(w)(b) = -14.0 cm(-)(1) and J(b)(b) = -30.5 cm(-)(1), with g = 1.93 (held constant). These values suggest an S(T) = (5)/(2) ground state spin for each [Mn(4)O(2)](7+) unit of 5, as found for 2. The interactions between the subunits are difficult to incorporate into this model, and the true ground state spin value of the entire Mn(8) anion was therefore determined by magnetization vs field studies, which showed the ground state of 5 to be S(T) = 3. The results of the studies on 2 and 5 are considered with respect to spin frustration effects within the [Mn(4)O(2)](7+) units. Complexes 2 and 5 are EPR-active and -silent, respectively, consistent with their S(T) = (5)/(2) and S(T) = 3 ground states, respectively.     

Dynamics of Diels–Alder reactions involving 2-trialkylsilyloxyfurans

Increasing the size of the silyl group on 2-trialkylsilyloxyfurans reduces the rate of Diels–Alder reactions with maleic acid derivatives. While the exo-adduct resulted from the reaction between 2-silyloxyfurans and maleic anhydride, endo-adducts resulted from the reactions with maleate esters. Analysis of transition state structures for the cycloaddition, calculated at the B3LYP/6-31G1 level of theory, revealed significant stretch-mode asynchronicity in the forming bonds, with selectivity arising from steric interactions that affect torsional strain about the shorter of the forming bonds.     

On the cubic convergence of the Paardekooper method

We show a simple way how asymptotic convergence results can be conveyed from a simple Jacobi method to a block Jacobi method. Our pilot methods are the well known symmetric Jacobi method and the Paardekooper method for reducing a skew-symmetric matrix to the real Schur form. We show resemblance in the quadratic and cubic convergence estimates, but also discrepances in the asymptotic assumptions. By numerical tests we confirm that our asymptotic assumptions for the Paardekooper method are most general.