Fourier phase microscopy for investigation of biological structures and dynamics

By use of the Fourier decomposition of a low-coherence optical image field into two spatial components that can be controllably shifted in phase with respect to each other, a new high-transverse-resolution quantitative-phase microscope has been developed. The technique transforms a typical optical microscope into a quantitative-phase microscope, with high accuracy and a path-length sensitivity of lambda/5500, which is stable over several hours. The results obtained on epithelial and red blood cells demonstrate the potential of this instrument for quantitative investigation of the structure and dynamics associated with biological systems without sample preparation.     

Scaling laws for diffusion coefficients in mixtures of alkanes

Natural fluids, such as crude oils, are often mixtures of a broad range of different molecules, and in situ measurement of their composition is highly desirable. Furthermore, the relationship between their composition and their physical properties has always been a challenge for such mixtures. We have analyzed diffusion in alkane mixtures to find a power law for the self-diffusion coefficient in terms of molecular sizes. We demonstrate that this power law can be used to obtain the molecular size distribution of crude oils using noninvasive measurements of diffusion distributions.     

Existence of Self-Similar Solutions to Smoluchowski’s Coagulation Equation

The existence of self-similar solutions to Smoluchowskis coagulation equation has been conjectured for several years by physicists, and numerical simulations have confirmed the validity of this conjecture. Still, there was no existence result up to now, except for the constant and additive kernels for which explicit formulae are available. In this paper, the existence of self-similar solutions decaying rapidly at infinity is established for a wide class of homogeneous coagulation kernels.     

Measured and predicted band model parameters of BF3(v3) at high temperatures

Two experimental techniques were used to determine the high temperature infrared absorption coefficients of the v₃ band of BF₃. A high temperature flow tube fitted with a multipass infrared absorption cell was used to determine the BF₃ absorption coefficients at 295, 585, 870, 1150, and 1440K. BF₃ was also used in a flame emission-absorption apparatus to determine the BF₃ absorption coefficients at 2400 K.A generalized formulation for predicting the S/d and 1/d band model parameters of symmetric top perpendicular bands of MX₃ molecules is presented. The effect of including nuclear spin statistics in computing the S/d and 1/d band model parameters is considered. It is shown that nuclear spin statistic?s effect only the 1/d parameter and are significant only for the case of zero nuclear spin. A number of practical considerations, which arise in designing a computer algorithm to calculate the S/d and 1/d parameters, are discussed.Comparisons of the theoretical and experimental BF₃ absorption coefficients are made. Good agreement between theory and experiment at all temperatures was obtained by adjusting only two vibrational energy coupling constants, _χ23 and _χ34. Predicted S/d and 1/d band model parameters at 300, 600, 900, 1200, 1500, 2000, 2500, and 3000 K are presented.     

Solvent-equilibrated ion pairs from carbene fragmentation reactions

[R(+) OC Cl(-)] ion pairs were generated in methanol/dichloroethane solutions, with R(+) as the 1-bicyclo[2.2.2]octyl, 1-adamantyl, or 3-homoadamantyl cation. Ion pairs were produced either by the direct fragmentation of alkoxychlorocarbenes (ROCCl), with R = 1-bicyclo[2.2.2]octyl, 1-adamantyl, or 3-homoadamantyl, or by the ring expansion-fragmentation of R'CH(2)OCCl, with R' = 1-norbornyl, 3-noradamantyl, or 1-adamantyl. Correlations of the [ROMe]/[RCl] product ratios as a function of the mole fraction of MeOH in dichloroethane showed that the homoadamantyl chloride ion pairs, produced by either the direct or ring expansion-fragmentations, were identical, solvent- and anion-equilibrated, and precursor independent. Laser flash photolysis experiments gave 20-30 ps as the time required for solvent equilibration and precursor independence. Methanol/chloride selectivities of the (less-stable) 1-adamantyl chloride and 1-bicyclo[2.2.2]octyl chloride ion pairs were not independent of their ROCCl or R'CH(2)OCCl precursors. Computational studies provided transition states for the fragmentations and for the structures of the ion pairs.     

The Discrete Coagulation Equations with Collisional Breakage

The discrete coagulation equations with collisional breakage describe the dynamics of cluster growth when clusters undergo binary collisions resulting either in coalescence or breakup with possible transfer of matter. Each of these two events may happen with an a priori prescribed probability depending for instance on the sizes of the colliding clusters. We study the existence, density conservation and uniqueness of solutions. We also consider the large time behaviour and discuss the possibility of the occurrence of gelation in some particular cases.     

Air-stable,long-length,solution-based graphene nanoribbons

Within the context of nanoelectronics, general strategies for the development of electronically tunable and air stable graphene nanoribbons are crucial. Previous studies towards the goal of processable nanoribbons have been complicated by ambient condition instability, insolubility arising from aggregation, or poor cyclization yield due to electron deficiency. Herein, we present a general strategy for the elongation of smaller graphene nanoribbon fragments into air-stable, easily processed, and electronically tunable nanoribbons. This strategy is facilitated by the incorporation of electron-rich donor units between electron-poor acceptor perylene diimide oligomeric units. The ribbons are processed in solution via a visible-light flow photocyclization using LEDs. The resulting long nanoribbons can be solution-cast and imaged, which are necessary characteristics for device fabrication. The ribbons become conductive after thermolysis of the pendent side-chains. The electron-accepting character of these nanoribbons in solution is reversible, and the conductivity of the thermolyzed species as a solid remains stable. This work highlights our general strategy for the mild and reliable fabrication of tunable and ambient-stable graphene nanoribbons, and charts a straightforward route for facile device incorporation.

A strategy is shown for the elongation of graphene nanoribbon (GNR) fragments into air-stable, solution processable and electronically tunable GNRs, aided by incorporating electron-rich donor units between electron-poor oligomeric acceptor units.