Polyimides derived from cyclooctadiene dianhydrides

1,5-Cyclooctadiene-1,2,5,6-tetracarboxylic dianhydride reacts with diamines in m-cresol at 110°C to give high molecular weight polymides soluble in m-cresol and tetrachloroethane. Films can be cast from solution and fibers drawn by dry and wet spinning. These polyimides showed rather low thermal stability, but high hydrolytic stability and good mechanical properties. The polyamic acid intermediates cannot be isolated due to spontaneous cyclization even at room temperature. This is discussed in terms of the strain in the cyclooctadiene ring.     

Nanoscale probing of the enamel nanorod surface using polyamidoamine dendrimers

Although it is known that noncollagenous proteins of dental origin bind to the hydroxyapatite crystal surfaces, no measure of their binding strength has been calculated. This experiment used -COOH-capped generation 7 PAMAM dendrimers as nanoprobes of the biological hydroxyapatite nanorod surfaces. Dendrimer distribution was characterized using AFM. The results showed dendrimers to be spaced at intervals along the c-axis of the crystals. From these observations and assuming a fully ionized -COOH dendrimer, a mathematical model of the binding capacity of the crystal surface with the dendrimer was developed. The Monte Carlo method was used to simulate the binding process between the dendrimer and crystal surface, and the binding strength of the -COOH groups to the surface was calculated to be 90 +/- 20 kJ/mol. These results support the CFM studies which have described alternating bands of charge domains on the crystal surface and that the binding strength will be dependent on both the intensity of the charge on the protein and the crystal surface.     

An analysis of the vanishing interfacial tension technique for determination of minimum miscibility pressure

Observations of interfacial tensions for mixtures of a gas and oil have been proposed as a way to measure the minimum miscibility pressure for displacement of a multicomponent oil by a gas mixture in a porous medium. The experimental approach known as the “vanishing interfacial tension technique” (VIT) is to measure interfacial tensions for a gas–oil mixture at a sequence of pressures. The estimate of the minimum miscibility pressure (MMP) is taken to be the pressure at which the interfacial tension extrapolates to zero when plotted against pressure. In this paper, the behavior observed in the VIT experiment is analyzed by performing phase equilibrium calculations with an equation of state and calculations of interfacial tensions using a parachor approach. The analysis shows that the VIT estimate of the MMP depends strongly on the overall composition of the gas–oil mixture used in the VIT experiment. Comparison of the estimates obtained for systems with three and four components and for a multicomponent crude oil system with MMPs calculated from solutions of the differential equations that describe the interactions of flow and phase equilibria indicates that the VIT approach can give estimates of the MMP that differ substantially from the MMP that would be observed in a displacement experiment. For some choices of the composition of the fluid mixture in the cell and the compositions of the oil and gas, however, it can also give estimates that are reasonably close to the value that would be obtained in a slim tube displacement experiment. However, the overall composition that gives the smallest error in the MMP estimate and the magnitude of the error cannot be determined from the VIT experiment alone. The uncertainty in the VIT estimate of the MMP arises from a fundamental limitation of the experiment: it investigates mixture compositions that are linear combinations of the initial oil and injection gas that are quite different from the critical mixture that forms at the MMP in a gas–oil displacement in a porous medium. The results indicate that the VIT approach to determine the MMP for multicomponent gas–oil displacements should be used with caution given the potential for significant errors in the resulting estimate of the MMP.     

The Orienteering Problem with Time Windows

The orienteering problem with time windows, denoted by OPTW, belongs to a class of routeing and scheduling problems that arise in physical distribution. It may be modelled as a problem on a graph. It considers a set of nodes (customers), each with an associated profit and service duration (time window), and a set of arcs, each with an associated travel time. The objective of the problem is to construct an acyclic path beginning at a specified origin and ending at a specified destination that maximizes the total profit while observing time window constraints on all nodes and not exceeding a designated time limit. The problem is classified as NP-hard and, thus, an exact algorithm that executes in reasonable computational time is unlikely to exist. Since the problem is highly-constrained, we were able to develop a heuristic (referred to as the ‘tree’ heuristic) based upon an exhaustive search of the feasible solution space. The tree heuristic systematically generates a list of feasible paths and then selects the most profitable path from the list. In comparison with an insertion heuristic, the tree heuristic was found to produce improved values of total profit for heavily-constrained, modest-sized problems with reasonable computational effort.     

A queueing network with a single cyclically roving server

A queueingnetwork that is served by asingle server in a cyclic order is analyzed in this paper. Customers arrive at the queues from outside the network according to independent Poisson processes. Upon completion of his service, a customer mayleave the network, berouted to another queue in the network orrejoin the same queue for another portion of service. The single server moves through the different queues of the network in a cyclic manner. Whenever the server arrives at a queue (polls the queue), he serves the waiting customers in that queue according to some service discipline. Both the gated and the exhaustive disciplines are considered. When moving from one queue to the next queue, the server incurs a switch-over period. This queueing network model has many applications in communication, computer, robotics and manufacturing systems. Examples include token rings, single-processor multi-task systems and others. For this model, we derive the generating function and the expected number of customers present in the network queues at arbitrary epochs, and compute the expected values of the delays observed by the customers. In addition, we derive the expected delay of customers that follow a specific route in the network, and we introduce pseudo-conservation laws for this network of queues.Summary of notation B_i, B _i ^* (s) service time of a customer at queue i and its LST - b_i, b_i ⁽²⁾ mean and second moment of B_i - R_i, R _i ^* (s) duration of switch-over period from queue i and its LST - r_i, r_i mean and second moment of R_i - r, r⁽²⁾ mean and second moment of _i ^N =₁R_i - _i external arrival rate of type-i customers - _i total arrival rate into queue i - _i utilization of queue i; _i=_i - system utilization _i ^N =_1i - c=E[C] the expected cycle length - X _i ^j number of customers in queue j when queue i is polled - X_i=X _i ⁱ number of customers residing in queue i when it is polled - f_i(j) - X _i ^* number of customers residing in queue i at an arbitrary moment - Y_i the duration of a service period of queue i - W_i,T_i the waiting time and sojourn time of an arbitary customer at queue i - F^*(z₁, z₂,..., z_N) GF of number of customers present at the queues at arbitrary moments - F_i(z₁, z₂,..., z_N) GF of number of customers present at the queues at polling instants of queue i - ¯F_i(z₁, z₂,...,z_N) GF of number of customers present at the queues at switching instants of queue i - V_i(z₁, z₂,..., z_N) GF of number of customers present at the queues at service initiation instants at queue i - ¯V_i(z₁,z₂,...,z_N) GF of number of customers present at the queues at service completion instants at queue i The work of this author was supported by the Bernstein Fund for the Promotion of Research and by the Fund for the Promotion of Research at the Technion.Part of this work was done while H. Levy was with AT&T Bell Laboratories.     

A Characterization of Cancellation Ideals

An ideal of a commutative ring with identity is called a cancellation ideal if whenever for ideals and of , then . We show that an ideal is a cancellation ideal if and only if is locally a regular principal ideal.

     

Multicolor polymeric carbon dots: synthesis,separation and polyamide-supported molecular fluorescence

Multicolor carbon dots (CDs) have been developed recently and demonstrate great potential in bio-imaging, sensing, and LEDs. However, the fluorescence mechanism of their tunable colors is still under debate, and efficient separation methods are still challenging. Herein, we synthesized multicolor polymeric CDs through solvothermal treatment of citric acid and urea in formamide. Automated reversed-phase column separation was used to achieve fractions with distinct colors, including blue, cyan, green, yellow, orange and red. This work explores the physicochemical properties and fluorescence origins of the red, green, and blue fractions in depth with combined experimental and computational methods. Three dominant fluorescence mechanism hypotheses were evaluated by comparing time-dependent density functional theory and molecular dynamics calculation results to measured characteristics. We find that blue fluorescence likely comes from embedded small molecules trapped in carbonaceous cages, while pyrene analogs are the most likely origin for emission at other wavelengths, especially in the red. Also important, upon interaction with live cells, different CD color fractions are trafficked to different sub-cellular locations. Super-resolution imaging shows that the blue CDs were found in a variety of organelles, such as mitochondria and lysosomes, while the red CDs were primarily localized in lysosomes. These findings significantly advance our understanding of the photoluminescence mechanism of multicolor CDs and help to guide future design and applications of these promising nanomaterials.

Understanding the origin and sensitivity of carbon dot emission will improve their utility in various applications.

Since the accidental discovery of luminescent carbon fragments in 2004,¹ carbon dots (CDs) have attracted great research interest due to the diverse synthetic methods, tunable luminescence, and applicability in a broad range of fields, including bio-imaging,^2–4 sensing,^5,6 and light emitting diodes (LEDs).^7,8 Typically, CDs are fluorescent carbon nanostructures of sizes less than 10 nm, composed of carbon, oxygen, and nitrogen.^9–12 CDs can be produced through bottom-up methods, which involve small molecular precursors like citric acid, malic acid, urea, ethylenediamine, and so on.^13–15 In a high temperature reaction, polymerization and dehydration occur among various functional groups, and the resulting products are usually a mixture of small molecule residues, oligomers, and long chain polymers.¹⁶ The unclear fluorescence mechanisms and poorly understood internal structure of CDs limit the ability to understand, tune, and fully exploit their fluorescence properties.Fortunately, in recent years, breakthrough syntheses of multicolor CDs have been achieved.^17–19 Several different multicolor CDs have been synthesized with aromatic compounds such as phenylenediamine.^4,20–22 However, it should be noted that precursors such as aniline and phenol may have toxic effects on human health and the environment,^23,24 and thus should be avoided where possible. Syntheses of colorful CDs from non-aromatic compounds such as citric acid and urea often employ solvothermal methods. Utilizing different solvents such as formamide and dimethylformamide have been shown to play a significant role in tuning CD emission.^25,26 In addition, chromatographic post-treatment of as-made CDs plays a critical role in obtaining different colored fractions, using techniques such as anion-exchange column chromatography,²⁶ normal phase silica chromatography,²⁷ and reversed phase silica chromatography.¹⁵ Compared with high performance liquid chromatography (HPLC), the aforementioned column chromatography techniques help to separate CDs on a larger scale. These separations are based on charge²⁶ or polarity,²¹ and are efficient in isolating the desired fractions with distinct colors so that detailed structural characterization can be performed.To gain insight into the fluorescence mechanism of these multicolor CDs, researchers have considered three hypotheses: quantum size effects,²⁸ the inclusion of molecular fluorophores,²⁹ and surface state-induced emission.³⁰ For example, Rogach and coworkers developed solid-state CDs with tunable fluorescence via the seeded growth method. They attributed the tunable emission to the size of π-conjugated domains.³¹ Yang and coworkers synthesized CDs by hydrothermal treatment of citric acid and ethylenediamine. They identified a small molecule fluorophore, IPCA (1,2,3,5-tetrahydro-5-oxo-imidazo[1,2-α]pyridiine-7-carboxylic acid) from CD column separation fractions, which contributed to the blue fluorescence.¹³ Xiong and coworkers synthesized CDs from urea and p-phenylenediamine that emitted a range of colors and separated them with silica column chromatography. They found the degree of carbon oxidation increased as the emission redshifted and thus, they endorsed the surface state hypothesis.²¹ In addition to the above mechanisms, computational methods such as density functional theory (DFT) have also been applied to analyze the fluorescence origins of CDs. The charge transfer between functional groups on the polymeric unit of CDs made from citric acid and ethylenediamine was found to facilitate blue emission.¹⁶The goal of present work is to understand the fluorescence origin of multicolor CDs. The model multicolor CDs were obtained by reacting citric acid and urea in formamide via a microwave-assisted hydrothermal treatment. An automated chromatographic apparatus was employed to separate as-made CD mixtures into distinct color fractions. The individual separation process took around 20 minutes, and the obtained CD fractions exhibit discrete illumination-induced emission throughout the visible region of the spectrum. Interestingly, the sizes of separated CD fractions are not statistically different from one another, suggesting that the quantum size effects are not the source of differential emission. Solvatochromism experiments showed that the blue and green fractions have similar fluorescence behavior as a function of solvent polarity, but the red fraction behaved differently. Using computational simulations, three models of the fluorescence origin were constructed and evaluated, showing that the formation of small blue fluorescent molecules is likely and pyrene analogs could be the origins for various emission colors. Moreover, two representative CD fractions, the blue- and red-emitting fractions, were chosen for subsequent cell imaging experiments. The localization pattern for the CD fractions differed: blue-emitting CDs were observed in a wide range of organelles, while red-emitting CDs were primarily enclosed in lysosomes. Understanding the origin and the sensitivity of CD emission will improve their utility in bioimaging applications.