Crystal shapes and crystallization in continuum modeling

A crystallization model appropriate for application in continuum modeling of complex processes is presented. As an extension to the previously developed Schneider equations [ W. Schneider, A. Köppel, and J. Berger, "Non-isothermal crystallization of polymers," Int. Polym. Proc. 2, 151 (1988) ], the model presented here allows one to account for the growth of crystals of various shapes and to distinguish between one-, two-, and three-dimensional growth, e.g., between rod-like, plate-like, and sphere-like growth. It is explained how a priori knowledge of the shape and growth processes is to be built into the model in a compact form and how experimental data can be used in conjunction with the dynamic model to determine its growth parameters. The model is capable of treating transient processing conditions and permits their straightforward implementation. By using thermodynamic methods, the intimate relation between the crystal shape and the driving forces for phase change is highlighted. All these capabilities and the versatility of the method are made possible by the consistent use of four structural variables to describe the crystal shape and number density, irrespective of the growth dimensionality

On the selection of AGN neutrino source candidates for a source stacking analysis with neutrino telescopes

The sensitivity of a search for sources of TeV neutrinos can be improved by grouping potential sources together into generic classes in a procedure that is known as source stacking. In this paper, we define catalogs of Active Galactic Nuclei (AGN) and use them to perform a source stacking analysis. The grouping of AGN into classes is done in two steps: first, AGN classes are defined, then, sources to be stacked are selected assuming that a potential neutrino flux is linearly correlated with the photon luminosity in a certain energy band (radio, IR, optical, keV, GeV, TeV). Lacking any secure detailed knowledge on neutrino production in AGN, this correlation is motivated by hadronic AGN models, as briefly reviewed in this paper. The source stacking search for neutrinos from generic AGN classes is illustrated using the data collected by the AMANDA-II high energy neutrino detector during the year 2000. No significant excess for any of the suggested groups was found.Comment: 43 pages, 12 figures, accepted by Astroparticle Physic

All-particle cosmic ray energy spectrum measured with 26 IceTop stations

We report on a measurement of the cosmic ray energy spectrum with the IceTop air shower array, the surface component of the IceCube Neutrino Observatory at the South Pole. The data used in this analysis were taken between June and October, 2007, with 26 surface stations operational at that time, corresponding to about one third of the final array. The fiducial area used in this analysis was 0.122 km^2. The analysis investigated the energy spectrum from 1 to 100 PeV measured for three different zenith angle ranges between 0{\deg} and 46{\deg}. Because of the isotropy of cosmic rays in this energy range the spectra from all zenith angle intervals have to agree. The cosmic-ray energy spectrum was determined under different assumptions on the primary mass composition. Good agreement of spectra in the three zenith angle ranges was found for the assumption of pure proton and a simple two-component model. For zenith angles {\theta} < 30{\deg}, where the mass dependence is smallest, the knee in the cosmic ray energy spectrum was observed between 3.5 and 4.32 PeV, depending on composition assumption. Spectral indices above the knee range from -3.08 to -3.11 depending on primary mass composition assumption. Moreover, an indication of a flattening of the spectrum above 22 PeV were observed.Comment: 38 pages, 17 figure

Crystal shapes and crystallization in continuum modeling

A crystallization model appropriate for application in continuum modeling of complex processes is presented. As an extension to the previously developed Schneider equations [ W. Schneider, A. Köppel, and J. Berger, "Non-isothermal crystallization of polymers," Int. Polym. Proc. 2, 151 (1988) ], the model presented here allows one to account for the growth of crystals of various shapes and to distinguish between one-, two-, and three-dimensional growth, e.g., between rod-like, plate-like, and sphere-like growth. It is explained how a priori knowledge of the shape and growth processes is to be built into the model in a compact form and how experimental data can be used in conjunction with the dynamic model to determine its growth parameters. The model is capable of treating transient processing conditions and permits their straightforward implementation. By using thermodynamic methods, the intimate relation between the crystal shape and the driving forces for phase change is highlighted. All these capabilities and the versatility of the method are made possible by the consistent use of four structural variables to describe the crystal shape and number density, irrespective of the growth dimensionality

Polyethylene {201} crystal surface: interface stresses and thermodynamics

We describe a method to determine the mechanical and thermodynamic properties of the interface between a polyethylene crystal and melt by united-atom Monte Carlo simulations. In particular, the {201} fold surface is studied in the temperature range 380450 K. The interface properties are defined by using the concept of a sharp Gibbs dividing surface, which in turn is used to define the interface internal energy and the interface stresses. We find that the internal energy of the interface is of the order 0.30.35 J/m2. The interface stresses are anisotropic for the {201} crystal surface with values of approximately −0.27 and −0.4 J/m2 for the xx- and yy-components, respectively. By way of the Herring equation, the surface tension of the fold surface is independent of shear strains in the interface. The temperature and strain derivatives of the interface properties are also measured and discussed in detail. The influence of the interface internal energy and of phase change contributions on the macroscopic heat capacity of the semi-crystalline material is examined

Temperature-dependent thermal and elastic properties of the interlamellar phase of semicrystalline polyethylene by molecular simulation

We present the first theoretical estimates for thermoelastic properties of the noncrystalline domain (the interlamellar phase) of semicrystalline polyethylene obtained by Monte Carlo simulations. The interlamellar phase is prescribed to be thermodynamically metastable, with the constraints that it have an average density less than that of the crystal and that it be bounded by two static crystalline lamellae oriented with the {201} crystal plane parallel to the interface. Polyethylene was modeled using a realistic united atom force field with inclusion of torsional contributions, and the results are compared to those of prior studies that used a freely rotating chain model. Parallel tempering between 350 and 450 K was used to simulate several isochoric/isothermal ensembles simultaneously and efficiently, from which the heat capacity, thermal expansion coefficients, Grneisen coefficients, and the elastic stiffness tensor were determined at atmospheric pressure. The noncrystalline interlamellar phase exhibits properties intermediate between that of the semicrystalline solid and the amorphous melt

Flow-induced crystallization

Molecular properties are reflected in the rheological and crystallization behavior. The first task is to design and use some well&hyphen;defined experiments that reveal all these features. Second, the experimental findings should be translated into mathematically formulated physical models, suited to be implemented in numerical codes for simulation of polymer shaping processes. Third, this modeling should be validated for a range of conditions including processing conditions. This chapter focuses on these three aspects and addresses general questions: How do the different structures observed relate to the flow conditions: deformation rates, stress, pressure, thermal conditions, material parameters, additives, and so on? and How can one model this on a continuum level so it is applicable in numerical codes for process simulation? The chapter also focuses on the effect of flow on crystallization of polymer melts

Electrospray as a Tool for Drug Micro- and Nanoparticle Patterning

Carbamazepine (CBZ) microparticles of different sizes and shapes, including spheres, q-tips, elongated spheres, and tear-shaped particles, were formed by electrospraying solutions of different CBZ concentrations. The particle characteristics were determined by the interplay between jet formation, droplet breakup, solvent evaporation, and eventual particle solidification. The average particle size increased with increasing CBZ concentration, with particles of different shapes being observed for different CBZ concentrations. The cascade of sizes and shapes observed was interpreted in terms of Rayleigh instability theory as applied to charged jets and droplets, with the final sizes depending upon the time needed to evaporate the solvent sufficiently for CBZ to solidify; the lower the initial concentration of CBZ, the smaller the final droplets/particles that are formed