Selective mixed coupling of carboxylic acids (I). - Electrolysis,thermolysis and photolysis of unsymmetrical diacyl peroxides with acyclic and cyclic alkyl groups

14 Unsymmetrical diacyl peroxides (R¹CO₂-O₂CR₂ with R¹: undecyl; R²: e.g. methyl, propyl, pentyl, nonyl, 2-methylpropyl, 2-propyl, 2-pentyl, cyclopropyl, cyclobutyl, cyclohexyl) are prepared in 85 to 92 % yield. Square pulse electrolysis of dodecanoyl octanoyl peroxide ($\text{li}$) affords the unsymmetrical coupling product octadecane($\text{4}$)ins poor yield and selectivity. Thermolysis or photolysis in solution produces preferentially $\text{4}$, but also considerable amounts of disproportionation products. At ?78°C the neat peroxides are photolysed selectively to the mixed dimers. With straight chain and β-branched alkyl groups high yields are obtained (63 – 76 %), with cycloalkyl groups medium yields (42 – 56 %), and with α-branched diacyl peroxides moderate yields (20 – 33 %). A comparison of the mixed Kolbe-electrolysis with the low temperature photolysis of the neat peroxide demonstrates the superiority of the latter method in small scale conversion with regard to yield and selectivity.     

Further Gurtin-type Variational Principles for Linear Initial Value Problems

Following the variational principles for linear initial valueproblems associated with the wave and heat conduction equationsdiscussed by Gurtin and Leitmann and using time convolutionsit is shown that general variational principles exist for theseproblems with sources on the boundaries and within the regionunder consideration.     

Spectroscopic information on ground-state Ar2, Kr2, and Xe2 from interatomic potentials

Calculations of vibrational and rotational level spacings of homonuclear inert gas diatomic molecules by numerical integration of the radial Schrödinger equation are presented. The potentials which were used for the ground states of Ar₂, Kr₂, and Xe₂ were obtained from accurate fits to the molecular beam scattering data. From the calculated $\text{Δ}\text{G}{}_{\mathrm{<mtext>v+</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{'}\text{s}$ and B_v's, the following spectroscopic constants (in cm^?1) were fitted: for Ar₂ω_e = 31.92, ω_ex_e = 3.31, ω_ey_e = 0.11, B_e = 0.060, α_e = 0.004; for $\text{Kr}{}_2\text{ω}{}_{\mathrm{e}}\text{? 23.99}$, $\text{ω}{}_{\mathrm{e}}\text{x}{}_{\mathrm{e}}\text{? 1.30}$, $\text{ω}{}_{\mathrm{e}}\text{y}{}_{\mathrm{e}}\text{? 0.021}$, $\text{B}{}_{\mathrm{e}}\text{? 0.024}$, $\text{α}{}_{\mathrm{e}}\text{? 0.001}$; for $\text{Xe}{}_2\text{ω}{}_{\mathrm{e}}\text{? 21.26}$, $\text{ω}{}_{\mathrm{e}}\text{x}{}_{\mathrm{e}}\text{? 0.75}$, $\text{ω}{}_{\mathrm{e}}\text{y}{}_{\mathrm{e}}\text{? 0.008}$, $\text{B}{}_{\mathrm{e}}\text{? 0.013}$, $\text{α}{}_{\mathrm{e}}\text{? 0.0004}$.     

Modified Locally One Dimensional Methods for Parabolic Partial Differential Equations in Two Space Variables

In this note we consider the locally one dimensional methodas discussed in Gourlay & Mitchell (1969, 1972) and indicatehow this scheme can be used to solve accurately a parabolicpartial differential equation in two space variables.     

Frequency domain studies of intersubband optical transitions in Si inversion layers

Fourier Transform Spectroscopic studies of inter-electric-field subband transitions in Silicon inversion layers are compared with optical properties calculated with a 5 media model and a classical dielectric function representation of the inversion layer. Qualitative discrepancies in relative intensities of the subband transitions are interpreted in terms of many-body effects.     

Three-dimensional chemical concentration maps in a microfluidic device using two-photon absorption fluorescence imaging

Two-photon absorption fluorescence is employed within a microfluidic device to create a three-dimensional chemical concentration map for mixing uniformity characterization. This multiphoton technique images fluorescence intensity directly and provides a simple, rapid, and readily employed route to composition characterization within microfluidic systems.