On signed graphs and gramians

Let A be a symmetric matrix with entries (0, 1, -1) and ¹(A) its smallest eigenvalue. We consider the question of how closely A–¹(A)I can be approximated by a gramian KK ^T , where each entry in K is 0, 1, or -1.This work was supported (in part) by the U.S. Army Research Office under Contract DAAG 29-74-C-0007.     

Synthesis and structural characterization of integrally oxidized, metal-free phthalocyanine compounds: [H(2)(pc)][IBr(2)] and [H(2)(pc)](2)[IBr(2)]Br.C(10)H(7)Br

The first integrally oxidized metal-free phthalocyanine compounds have been synthesized by chemical oxidation. Phthalocyanine (H(2)(pc), pc = phthalocyaninato) was oxidized with IBr to afford the compounds [H(2)(pc)][IBr(2)] (1) and [H(2)(pc)](2)[IBr(2)]BrAC(10)H(7)Br (2), whose structures were determined by means of single-crystal X-ray diffraction methods: [H(2)(pc)][IBr(2)], P2(1)/c, a = 8.0272(9) A, b = 21.258(2) A, c = 18.1439(2) A, beta = 113.975(2) degrees, V = 2828.8(5) A(3), T = 153 K, Z = 4; [H(2)(pc)](2)[IBr(2)]Br.C(10)H(7)Br, P, a = 8.4724(6) A, b = 13.5794(10) A, c = 13.8403(10) A, alpha = 90.854(1) degrees, beta = 103.417(1) degrees, gamma = 97.049(1)E degrees, V = 1535.61(19) A(3), T = 153 K, Z = 1. The extended structure of [H(2)(pc)][IBr(2)] comprises slipped columns of pc rings stacked along the a axis in adjacent columns at approximately 70 degrees to one another. IBr(2-) ions occupy the interstitial columns. The extended structure of [H(2)(pc)](2)[IBr(2)]Br.C(10)H(7)Br comprises slant stacks of pc rings along the crystallographic a axis with IBr(2-) ions, Br(-) ions, and disordered 1-bromonaphthalene molecules in the adjacent, parallel columns. The overall reaction for the formation of 1 is 2H(2)(pc) + 4IBr --> 2[H(2)(pc)][IBr(2)] + I(2), and the overall reaction for the formation of 2 (not including solvent) is 2H(2)(pc) + 3IBr --> [H(2)(pc)](2)Br[IBr(2)] + I(2).     

Electrostatic influence on rotational mobilities of sol-gel-encapsulated solutes by NMR and EPR spectroscopies

The rotational mobilities of small solute molecules encapsulated in tetramethyl orthosilicate (TMOS) sol-gels have been investigated by EPR spectroscopy of encapsulated nitroxide probes and by high-resolution NMR spectroscopic measurements of transferred NOE's (trNOE's), of T(1)'s, and of T(1)'s in the rotating frame (T(1)rho). The two spectroscopic methods are sensitive to motions on different time scales and hence, are nicely complementary. Suites of neutral, positively, and negatively charged nitroxide probes (EPR) and of simple diamagnetic small molecules (NMR) were selected to disclose influences of electrostatic interactions with the sol-gel walls and to probe the presence of multiple populations of molecules in distinct regions of the sol-gel pores. For neutral and negatively charged solute probes, both techniques disclose a single population with a significantly increased average rotational correlation time, which we interpret at least in part as resulting from exchange between free-volume and transiently immobilized surface populations. The electrostatic attraction between cationic probes and the negatively charged sol-gel walls causes the positively charged probes to be more effectively immobilized and/or causes a greater percentage of probes to undergo this transient immobilization. The EPR spectra directly disclose a population of cationic probes which are immobilized on the X-band EPR time scale: tau(c) greater than or approximately equal 10(-7) s. However, NMR measurements of trNOE's and of T(1)rho demonstrate that this population does exchange with the free-volume probes on the slower time scale of NMR. This approach is equally applicable to the study of solutes within other types of confined spaces, as well.     

Microrheology probes length scale dependent rheology

We exploit the power of microrheology to measure the viscoelasticity of entangled F-actin solutions at different length scales from 1 to 100 microm over a wide frequency range. We compare the behavior of single probe-particle motion to that of the correlated motion of two particles. By varying the average length of the filaments, we identify fluctuations that dissipate diffusively over the filament length. These provide an important relaxation mechanism of the elasticity between 0.1 and 30 rad/sec.     

The millimeter-wave spectrum of acetaldehyde in its two lowest torsional states

A large number of new millimeter-wave spectral lines of gaseous acetaldehyde have been measured at frequencies up to 250 GHz. These lines arise from rotational transitions of acetaldehyde in its two lowest (v_t = 0,1) torsional states and involve angular momentum quantum numbers J ≤ 12 and K ≤ 10. A global data set consisting of 562 lines has been obtained by combining the millimeter-wave lines with previously measured lower frequency data involving the two lowest torsional states. This data set has been analyzed via an internal axis method previously used to study the spectra of CH₃OH and CH₃SH. The root-mean-square deviation of the fit is only 685 kHz. An analogous least-squares fit to 335v_t = 0 lines yields a root-mean-square deviation of 269 kHz.     

Site specific effects in alloy surface reactivity probed by Li ions

We investigated site specific reactivity of the α-Cu-Al(17 at.%)(1 0 0) alloy surface versus that of Al and Cu by measuring neutralisation of Li⁺ ions. Experiments show that Li⁺ neutralisation on the α-CuAl(1 0 0) alloy surface does not occur efficiently on Al and is somewhat more efficient on Cu as compared to a pure Cu sample, indicating depletion of electron density on Al and transfer to neighboring Cu. It can thus be concluded that Cu sites in presence of Al are more reactive in the sense that processes involving electron capture from the surface would proceed more efficiently on these.     

Test of sum rules in nucleon transfer reactions

The quantitative consistency of nucleon transfer reactions as a probe of the occupancy of valence orbits in nuclei is tested. Neutron-adding, neutron-removal, and proton-adding transfer reactions were measured on the four stable even Ni isotopes, with particular attention to the cross section determinations. The data were analyzed consistently in terms of the distorted wave Born approximation to yield spectroscopic factors. Valence-orbit occupancies were extracted, utilizing the Macfarlane-French sum rules. The deduced occupancies are consistent with the changing number of valence neutrons, as are the vacancies for protons, both at the level of <5%. While there has been some debate regarding the true "observability" of spectroscopic factors, the present results indicate that empirically they yield self-consistent results.