2,169 research outputs found
A rigorous model for constraint release in the bulk and the near-wall region
In the present work an attempt is made to build a rigorous theoretical model for the constraint release mechanism found to play an important role in the dynamics of polymer melts. Our goal is a formalism free of adjustable parameters and ''ad-hoc'' assumptions which are inherent to existing theories for constraint release. Our model is capable to describe both thermal and convective constraint release. These processes have the same effect on chains and accordingly can be unified in a single framework. Since polymer chains in the bulk and in the near-wall layer may experience different types of constraint release, the latter case is studied separately. This topic is closely related to the long-standing problem of polymer melt flow instabilities encountered during extrusion. Nowadays it is believed that constraint release plays a crucial role in the dynamics of tethered chains preventing them from being squeezed against the wall. The resulting non-monotonous slip-law is the most probable reason of the so-called spurt instability. \u
A universal constitutive model for the interfacial layer between a polymer melt and a solid wall
In a preceeding report we derived the evolution equation for the bond vector probability distribution function (BVPDF) of tethered molecules. It describes the behavior of polymer molecules attached to a solid wall interacting with an adjacent flowing melt of bulk polymer molecules and includes all the major relaxation mechanisms such as constraint release, retraction and convection. The derived equation is quite universal and valid for all flow regimes. In the present paper the developed formalism is further analyzed. We begin our analysis with the simple case of slow flows. Then, as expected, a remarkable reduction of the theory is possible. Later on the more general case is considered. \u
Dynamics of chains grafted on solid wall during polymer melt extrusion
The objective of the present work is the mathematical modeling of the dynamics of polymer molecules grafted on a solid boundary during polymer melt extrusion. This topic is closely related to the long-standing problem of polymer flow instabilities encountered in industry when extruding melts. In order to describe the behavior of the tethered chains, we introduce the bond vector probability distribution function (BVPDF) which appears to be a simple, yet effective mathematical 'tool'. The bond vector, i.e. the tangent vector to a polymer chain depending on the position along the chain and on time, describes the local geometry via its direction and the local stretching of the chain via its length. The BVPDF contains all information about the geometry of the ensemble of chains. Via averaging over the BVPDF we can calculate all interesting macrsocopic quantities, e.g. the thickness of and stress in the layer of tethered molecules. The time dependence of the BVPDF yields the time evolution of the system. We derive the equation of motion for the BVPDF taking into account all important mechanisms, such as reptation and (convective) constraint release. Besides that, we show that all macroscopic quantities of practical interest can be expressed via second order moments of this distribution function. \u
Flow-induced correlation effects within a linear chain in a polymer melt
A framework for a consistent description of the flow-induced correlation effects within a linear polymer chain in a melt is proposed. The formalism shows how correlations between chain segments in the flow can be incorporated into a hierarchy of distribution functions for tangent vectors. The present model allows one to take into account all the major relaxation mechanisms. Special cases of the derived set of equations are shown to yield existing models and shed some light on the connection between them. Consequences of several assumptions widely used in the literature are analyzed within the developed framework
The influence of polydispersity and inhomogeneity on EXAFS of bimetallic catalysts
The effect of polydispersity and inhomogeneity of supported bimetallic catalysts on the EXAFS analysis is investigated with some simple model calculations. These show that EXAFS is very insensitive to polydispersity. Polydispersity and inhomogeneous distribution of the metals over the particles however have only limited influence on the ability to distinguish between core-shell particles and particles with random distribution of both metals
Studies of a Terawatt X-Ray Free-Electron Laser
The possibility of constructing terawatt (TW) x-ray free-electron lasers
(FELs) has been discussed using novel superconducting helical undulators [5].
In this paper, we consider the conditions necessary for achieving powers in
excess of 1 TW in a 1.5 {\AA} FEL using simulations with the MINERVA simulation
code [7]. Steady-state simulations have been conducted using a variety of
undulator and focusing configurations. In particular, strong focusing using
FODO lattices is compared with the natural, weak focusing inherent in helical
undulators. It is found that the most important requirement to reach TW powers
is extreme transverse compression of the electron beam in a strong FODO
lattice. The importance of extreme focusing of the electron beam in the
production of TW power levels means that the undulator is not the prime driver
for a TW FEL, and simulations are also described using planar undulators that
reach near-TW power levels. In addition, TW power levels can be reached using
pure self-amplified spontaneous emission (SASE) or with novel self-seeding
configurations when such extreme focusing of the electron beam is applied.Comment: 10 pages, 12 figure
Using ultra-short pulses to determine particle size and density distributions
We analyze the time dependent response of strongly scattering media (SSM) to
ultra-short pulses of light. A random walk technique is used to model the
optical scattering of ultra-short pulses of light propagating through media
with random shapes and various packing densities. The pulse spreading was found
to be strongly dependent on the average particle size, particle size
distribution, and the packing fraction. We also show that the intensity as a
function of time-delay can be used to analyze the particle size distribution
and packing fraction of an optically thick sample independently of the presence
of absorption features. Finally, we propose an all new way to measure the shape
of ultra-short pulses that have propagated through a SSM.Comment: 15 pages, 29 figures, accepted for publication in Optics Express will
update with full reference when it is availabl
Surface acoustic waves for acousto-optic modulation in buried silicon nitride waveguides
We theoretically investigate the use of Rayleigh surface acoustic waves
(SAWs) for refractive index modulation in optical waveguides consisting of
amorphous dielectrics. Considering low-loss SiN waveguides with a
standard core cross section of 4.40.03 m size, buried 8 m
deep in a SiO cladding we compare surface acoustic wave generation in
various different geometries via a piezo-active, lead zirconate titanate film
placed on top of the surface and driven via an interdigitized transducer (IDT).
Using numerical solutions of the acoustic and optical wave equations, we
determine the strain distribution of the SAW under resonant excitation. From
the overlap of the acoustic strain field with the optical mode field we
calculate and maximize the attainable amplitude of index modulation in the
waveguide. For the example of a near-infrared wavelength of 840 nm, a maximum
shift in relative effective refractive index of 0.7x10 was obtained for
TE polarized light, using an IDT period of 30 - 35 m, a film thickness of
2.5 - 3.5 m, and an IDT voltage of 10 V. For these parameters, the
resonant frequency is in the range 70 - 85 MHz. The maximum shift increases to
1.2x10, with a corresponding resonant frequency of 87 MHz, when the
height of the cladding above the core is reduced to 3 m. The relative
index change is about 300-times higher than in previous work based on
non-resonant proximity piezo-actuation, and the modulation frequency is about
200-times higher. Exploiting the maximum relative index change of
1.210 in a low-loss balanced Mach-Zehnder modulator should allow
full-contrast modulation in devices as short as 120 m (half-wave voltage
length product = 0.24 Vcm).Comment: 19 pages, 8 figure
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