Orientation characterization

When a suspension of several fibers needs to be described, the distribution function, also called the probability density funetion, is the most general way to present the orientation state. This function, p,t), is defined as the probability to find a fiber orientated in the range between p and p -b at time t. 

The range of i/ (p, t) is [0, 1]. The integral of this funetion over aU possible values of p must equal unity, i.e., 

The distribution function satisfies the Fokker-Planck equation  

Although the distribution function provides a general description of the orientation state in the suspension, the numerical solution of the Fokker-Planck equation is computationally expensive. One needs a more compact and efficient description of fiber orientation for use in modeling of process. A proper approach is to use orientation tensors (Advani and Tucker 1987). Orientation tensors are defined in term of the ensemble average of the dyadic products of the unit vector p, i.e.. 

5 Flow-Induced Alignment in Short-Fiber Reinforced Polymers 

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The simple system of hardware and software described above provides data for orientation characterization of polymer specimens. The system is used to conduct research on a wide variety of materials rather than to provide analytical results for process control. 

IR spectroscopy is a powerful and readily available orientation characterization technique. It offers a high chemical selectivity since most functional groups absorb at distinct wavelengths (typically in the 2.5-25 pm range (4,000 00 cm-1 range)), which often depend on their local environment. IR spectroscopy thus provides qualitative and quantitative information about the chemical nature of a sample, its structure, interactions, etc. The potential of IR spectroscopy for orientation characterization stems from the fact that absorption only occurs if the electric field vector of the incident radiation, E, has a component parallel to the transition dipole moment, M, of the absorbing entity. The absorbance, A, is given... 

Ecke, H., Menad, N. Lagerkvist, A. 2002. Treatment-oriented characterization of dry scrubber residue from municipal solid waste incineration. Journal of Material Cycles Waste Management, 4, 117-126. 

Molecular Orientation Characterization of molecular orientation is important as many physical and mechanical properties of polymers depend on the extent and uniformity of the orientation [2,4,25]. Orientation can be measured by using a variety of techniques [2,4,25,33,34]. IR spectroscopy not only allows the characterization of amorphous and crystalline phases separately, it also provides morphological data and can be used to map orientation with high spatial resolution [35]. 

Subsequent falling-ball experiments performed with suspended rods (Graham et al., 1987 Milliken et al., 1989) replacing the spheres revealed significant and systematic differences between quiescent values of the suspension viscosity and those derived from Couette and capillary viscometer flow measurements. This is attributed by Graham, Mondy, and co-workers to fundamental differences in the distributions of rod orientations characterizing the quiescent and sheared suspensions. 

Equation 3.23 is derived without truncation above any order by assuming that the geometrical order parameters, A2, of the orientational distribution of the A and B isomers are equal at the photostationary state of irradiation. Although this assumption physically mirrors a uniform molecular orientational distribution, it does simplify considerably the expression of the photostationary-state orientational order and provides a simple law for steady-state photo-orientation characterization. Equation 3.23 holds when analysis is performed at the irradiation wavelength, and fits by Equations 3.22 and 3.23 allow for the measurement of 2 (cos [Pg.78]

A battery of complementary techniques is often necessary (and always desirable) to provide reliable, applications-oriented characterization of the bulk properties of (catalytic) carbon materials. Arguably the most useful ones are transmission electron microscopy (TEM), thermoelectric power (TEP) measurements, electron spin resonance (ESR) spectroscopy coupled with a superconducting quantum interference device (SQUID), and Raman spectroscopy. For example, among the recently reported virtues of Raman spectroscopy is the identification of graphite whiskers [152,153] in three carbonaceous chondrite meteorites (M. Fries and A. Steele, Science Online, Feb. 28, 2008), which contain some of the oldest matter in the solar system and has thus generated tremendous interest among astrophysicists. 

Nevertheless, the liquid-phase methylation displays the typical features of the aromatic substitution by an extremely reactive, unselective electrophile such as CTs", which, however, appears capable of discriminating between the aromatic substrates ( T/fca 2), and gives a predominantly ortho/para orientation, characterized by a para Vi meta ratio of 2.5 in the formation of the xylenes. 

B. Hu et al., Recycling-oriented characterization of polyolefin packaging waste. Waste Manage. 33(3), 574-584 (2013)... 

Assigning surface bonding and configuration Determining surface species and adsorption orientation Characterizing interfacial stmcture and co-adsoibed species Proposing reaction intermediates and products Correlating to theoretical calculation... 

The solid angle il can be decomposed into a polar angle 0 e [0, n] and an azimuthal angle (f) e [0, 2tc]. In (5.24) Vexci(i, v) is the excluded volume of the added scaled spherocylinder with orientation SI and a spherocylinder of the fluid with orientation characterized by the solid angle Si ,... 

With equation (3.55), Qads can be calculated from the adsorption isotherms measured at different temperatures. Figure 3.12 shows the adsorption isotherm of CO on a platinum surface with an orientation characterized by the Miller indices (111) [2]. 

An arbitrary distribution is expected to depend on, in addition to the position r, the orientation characterized by three angles. An arbitrary distribution includes a dipole. 

In addition to the orientational characterization via WAXS, some information regarding the phase state and the degree of crystallhiity was obtained from the DSC analysis. The measmements were performed on the stai-ting components and the intermediate and final products, as well as on some of them after annealing. The evaluated data are summarized in Table 5.4. 

The polymer is subjected to a biaxial stretching, which creates orientation both in the crystalline and in the amorphous phases. As in fiber spinning, many studies have been dedicated to orientation characterization, especially in the crystalline phase, but biaxial orientation requires more sophisticated methods. More recently, much effort has been devoted to the description of the morphology at the lamellar scale, for example, by electron microscopy. 

A vicinal orientation is one with a small angle deviation from a singular orientation, characterized by broad terraces separated by monomolecular steps. 

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