The ionization of sulfurous acid in Na−Mg−Cl solutions at 25°C

The stoichiometric pK ₁ ^* and pK ₂ ^* for the ionization of sulfurous acid has been determined from emf measurements in NaCl solutions with varying concentrations of added MgCl₂ (m=0.1, 0.2 and 0.3) from I=0.5 to 6.0 molal at 25°C. These experimental results have been treated using both the ion pairing and Pitzer's specific ion-interaction models. The Pitzer parameters for the interaction of Mg²⁺ with SO₂ and HSO ₃ ^– yielded =0.085±0.004, ⁽⁰⁾ = 0.35±0.02, ⁽¹⁾ = 1.2±0.04, and C = –0.072±0.007. The Pitzer parameters ⁽⁰) = –2.8±0.4, ⁽¹⁾ = 12.9±2.9 and ⁽²⁾ = –2071±57 have been determined for the interactions of Mg²⁺ with SO ₃ ^2– . The calculated values of pK ₁ ^* and pK ₂ ^* using Pitzer's equations reproduce the measured values to within ±0.04 pK units. The ion pairing model with log K_MgSO3=2.36±0.02 and log_MgSO3 = 0.1021, reproduces the experimental values of pK ₂ ^* to ±0.01. These results demonstrate that treating the data by considering the formation of MgSO₃ yields a better fit of the experimental measurements with fewer adjustable parameters. With these derived coefficients obtained from the Pitzer equations and the ion pairing model, it is possible to make reliable estimates of the activity coefficients of HSO ₃ ^– and SO ₃ ^2– in seawater, brines and marine aerosols containing Mg²⁺ ions.     

The class reconstruction number of maximal planar graphs

The reconstruction numberrn(G) of a graphG was introduced by Harary and Plantholt as the smallest number of vertex-deleted subgraphsG _i =G – v _i in the deck ofG which do not all appear in the deck of any other graph. For any graph theoretic propertyP, Harary defined theP-reconstruction number of a graph G P as the smallest number of theG _i in the deck ofG, which do not all appear in the deck of any other graph inP We now study the maximal planar graph reconstruction numberrn(G), proving that its value is either 1 or 2 and characterizing those with value 1.     

Synthesis, structure, and nonlinear optical properties of cross-conjugated perphenylated iso-polydiacetylenes

Monodisperse, cross-conjugated perphenylated iso-polydiacetylene (iso-PDA) oligomers, ranging from monomer 15 to pentadecamer 25, have been synthesized by using a palladium-catalyzed cross-coupling protocol. Structural characteristics elucidated by X-ray crystallographic analysis demonstrate a non-planar backbone conformation for the oligomers due to the steric interactions between alkylidene phenyl groups. The electronic absorption spectra of the oligomers show a slight red-shift of the maximum absorption wavelength as the chain length increases from dimer 17 b to pentadecamer 25, a trend that has saturated by the stage of nonamer 22. Fluorescence spectroscopy confirms that the pendent phenyl groups present on the oligomer framework enhance emission, and the relative emission intensity consistently increases as a function of chain length n. The molecular third-order nonlinearities, gamma, for this oligomer series have been measured via differential optical Kerr effect (DOKE) detection and show a superlinear increase as a function of the oligomer chain length n. Molecular modeling and spectroscopic studies suggest that iso-PDA oligomers (n>7) adopt a coiled, helical conformation in solution.