Orientation distribution molecular

FIG. 3 Left density profile, p z), from a 500 ps simulation of a thin film consisting of 200 TIP4P water molecules at room temperature. Right orientational distribution, p cos d), with 3 the angle between the molecular dipole moment p and the surface normal z. The vertical lines in the left plot indicate the boundary z-ranges,... 

The left side of Fig. 7 shows the orientational distribution of the molecular dipole moment relative to the surface normal in various distance... 

While thin polymer films may be very smooth and homogeneous, the chain conformation may be largely distorted due to the influence of the interfaces. Since the size of the polymer molecules is comparable to the film thickness those effects may play a significant role with ultra-thin polymer films. Several recent theoretical treatments are available [136-144,127,128] based on Monte Carlo [137-141,127, 128], molecular dynamics [142], variable density [143], cooperative motion [144], and bond fluctuation [136] model calculations. The distortion of the chain conformation near the interface, the segment orientation distribution, end distribution etc. are calculated as a function of film thickness and distance from the surface. In the limit of two-dimensional systems chains segregate and specific power laws are predicted [136, 137]. In 2D-blends of polymers a particular microdomain morphology may be expected [139]. Experiments on polymers in this area are presently, however, not available on a molecular level. Indications of order on an... 

The anisotropy of the liquid crystal phases also means that the orientational distribution function for the intermolecular vector is of value in characterising the structure of the phase [22]. The distribution is clearly a function of both the angle, made by the intermolecular vector with the director and the separation, r, between the two molecules [23]. However, a simpler way in which to investigate the distribution of the intermolecular vector is via the distance dependent order parameters Pl+(J") defined as the averages of the even Legendre polynomials, PL(cosj r)- As with the molecular orientational order parameters those of low rank namely Pj(r) and P (r), prove to be the most useful for investigating the phase structure [22]. 

We begin, however, with the singlet orientational distribution function which is shown for the three liquid crystal phases in Fig. 6. In each phase the distribution is peaked at cos of 1 showing that the preferred molecular orientation is parallel to the director. The form of the distribution function is well represented by the relatively simple function... 

It may be worthwhile to compare briefly the PECD phenomenon discussed here, which relates to randomly oriented chiral molecular targets, with the likely more familiar Circular Dichroism in the Angular Distribution (CDAD) that is observed with oriented, achiral species [44 7]. Both approaches measure a photoemission circular dichroism brought about by an asymmetry in the lab frame electron angular distribution. Both phenomena arise in the electric dipole approximation and so create exceptionally large asymmetries, but these similarities are perhaps a little superficial. 

Solid-state NMR methods have been much used to study the characteristics of the network chains themselves, particularly with regard to orientations [265], molecular motions [266], and their effects on the diffusion of small molecules [267], Aspects related to the structures of the networks include the degree of cross-linking [268,269], the distributions of cross-links [270] and stresses [271], and topologies [272,273]. Another example is the use of NMR to clarify some issues in the areas of aging and phase separation [274],... 

As will be shown in this report, polymer fibres gain additional strength by an increase of the molecular weight and by a more contracted orientation distribution, i.e. a higher modulus. For the wet-spun fibres, a strength increase can be achieved by improvement of the coagulation process, which makes for a more uniform structure and chain orientation in the cross section of the fibre, and by a reduction of the amount of impurities. 

M. Tanaka and R.J. Young, Molecular orientation distributions in uniaxiaUy oriented poly(L-lactic acid) films determined by polarized Raman spectroscopy. Macromolecules, 39, 3312-3321 (2006). 

M. Tanaka and R.J. Yoimg, Review Polarised Raman spectroscopy for the smdy of molecular orientation distributions in polymers, J. Mater. Sci, 41, 963-991 (2006). 

The partition of molecular distance correlations into intra- and intermolecular contributions allows us to interpret these correlations in terms of a simple geometrical model. By this means, we are able to elicit structural units as for example segment-clusters that include intermolecular interference phenomena. These clusters are the primary structure units which we call monodomains . These natural units characterize the basic symmetry of the whole structure. If we keep in mind this basic symmetry, we can construct our structure model from a molecular level up to the level of the monodomain treating intra- and intermolecular correlations independently. If we do so, every X-ray pattern can be represented by accounting for the orientation distribution of these monodomains. 

Orientational Distribution Function and Order Parameter. In a liquid crystal a snapshot of the molecules at any one lime reveals that they arc not randomly oriented. There is a preferred direction for alignment of the long molecular axes. This preferred direction is called the director, and it cun be used to define- an orienlalional distribution function, f W). where flH win Vilb is proportional to the fraction of molecules with their long axes within the solid angle sinbdw. 

The applied electric field perturbs the orientational distribution function of the dipolar molecules. Dielectric relaxation due to classical molecular reorientational motions is a form of pure absorption spectroscopy whose frequency range of interest for materials, including polymers, is between 10 6 and 1011 Hz. 

In Fig. 13.8, Sample 1 shows that the outline (shape) of the front is circular in the deep section and becomes somewhat distorted upon entering the thinner region. The flow is split by the T insert and reunites past the insert, forming a weld line. The location and the shape of the weld line are determined by the flow profile around the insert. The insert strongly affects the direction of the advancing front which, as we see later, determines the direction of molecular orientation. We would expect, therefore, a highly nonuniform orientation distribution in such a mold. 

The Front Region The front region was analyzed by Tadmor (29) in an attempt to model the experimentally observed molecular orientation distribution in molded articles. 

If Ae 0 the reaction/cavity fields, and then the molecular property /, depend on the molecular orientation. Such a dependence affects the physical observables, which are obtained by averaging over the orientational distribution. Considering in general a tensorial property, we can express the average value as ... 

In elastomer samples with macroscopic segmental orientation, the residual dipolar couplings are oriented as well, so that also the transverse relaxation decay depends on orientation. Therefore, the relaxation rate 1/T2 of a strained rubber band exhibits an orientation dependence, which is characteristic of the orientational distribution function of the residual dipolar interactions in the network. For perfect order the orientation dependence is determined by the square of the second Legendre polynomial [14]. Nearly perfect molecular order has been observed in porcine tendon by the orientation dependence of 1/T2 [77]. It can be concluded, that the NMR-MOUSE appears suitable to discriminate effects of macroscopic molecular order from effects of temperature and cross-link density by the orientation dependence of T2. 

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