Non-orientability

Anisotropic behaviour is also exhibited in optical properties and orientation effects can be observed and to some extent measured by birefringence methods. In such oriented materials the molecules are in effect frozen in an unstable state and they will normally endeavour to take up a more coiled conformation due to rotation about the single bonds. If an oriented sample is heated up the molecules will start to coil as soon as they possess sufficient energy and the mass will often distort. Because of this oriented materials usually have a lower heat distortion temperature than non-oriented polymers. 

Channelling. When the incoming beam is aligned with any low-index axis or plane in a crystal it can be channelled, so that the probe atoms are steered down the channels. Under these conditions the backscattering yield will decrease to a few percent of its original non-oriented value (the random yield ). 

Molecular orientation and the testing direction strongly influence the observed modulus of a polymer sample. Fibers are typically highly oriented and exhibit much higher modulus values than non-oriented samples prepared from the same polymer. In the case of films, we typically observe anisotropy a film exhibits a range of modulus values depending upon the testing direction. 

Fig. 2 Mechanically oriented bilayer samples as a membrane model for ssNMR. (a) Illustration of the hydrated lipid bilayers with MAPs embedded, the glass supports, and the insulating wrapping, (b) A real sample consists of 15 stacked glass slides, (c) Schematic solid-state 19F-NMR lineshapes from an oriented CF3-labelled peptide (red), and the corresponding powder lineshape from a non-oriented sample (grey), (d) Illustration of typical orientational defects in real samples - the sources of powder contribution in the spectra...

Fig. 7 Comparison of the solid-state 31P-NMR spectra from erythrocyte ghosts (left column) and of DMPC model membranes (right column). Samples are prepared as a non-oriented suspension in excess water (a, d), and as macroscopically oriented membranes on glass slides that are aligned either parallel (b, e) or perpendicular (c, f) to the static magnetic field...

Considerable interest has been shown in the potential of PEN for cosmetic and pharmaceutical containers. Many cosmetics require the increased chemical resistance of PEN. These, generally, are small, amorphous, non-oriented containers that can resist solvent crystallization by the specific chemicals involved. Similar PET containers develop an unacceptable, solvent-induced hazy appearance. PEN has been used successfully to contain liquid anesthetics [28], while PEN blood tubes have also been demonstrated [29],... 

Fibres are, as a result of the spinning process, molecularly oriented, and they have, therefore, a 2 to 3 times higher stiffness than the non-oriented polymer (e.g. polyamide and polyester textile fibres). With the highest attainable orientation, such as in aromatic polyamides (Twaron and Kevlar), and in the PE-fibre (Dyneema) the stiffness can be a hundred times higher than the one in the unoriented condition ... 

With the exception of PC, amorphous, non-oriented polymers did not produce measurable amounts of broken segments when subjected to tension. As has been shown in previous paragraphs, large axial stresses capable of chain scission in amorphous polymers can only be transmitted into the chain by friction of slipping chains requiring strong intermolecular interactions. In addition, macroscopic fracture occurs before a widespread chain overloading and scission occurs, which is opposite to the behavior of semicrystalline polymers. 

The main method used to distinguish the relative quantities of neoformed illite is by the polymorph or structure of the material. Using the criteria that 2M and 3T polymorphs of dioctahedral potassic mica are high temperature forms (Velde, 1965a), the determination of the relative quantities of lMd, and 1M vs. 2M, 3T polymorphs permits a semi-quantitative estimation of the proportion of neo-formed or low temperature illite present in a specimen. A method commonly used is a determination of relative intensities of X-ray diffraction peaks of non-oriented mica (Velde and Hower, 1963 Maxwell and Hower, 1967). Usually only 2M and lMd polymorphs are present in illite specimens which simplifies the problem. The 1M polymorph is typical of ferric illites and celadonite-glauconites, the more tetrasilicic types. 

These investigations agree well with experiments by Trillat [129] who found that the X-ray diagram of colloidal nitrocellulose showing a non-oriented structure of crystallites (interference rings), altered after being stretched to indicate a fibrous structure in which the crystallites were oriented along the axis in the direction in which the film was stretched. 

The viscosity of nitrostarch solutions is appreciably lower than the viscosity of the corresponding nitrocellulose solutions. Taking the viscosity of water as 100, the viscosity of 1% nitrostarch solutions varies within the relative values of 45 and 70. Due to such low viscosity and non-oriented crystal structure, nitrostarch solutions leave very fragile film after evaporation. Hence nitrostarch is valueless for varnish production, and for smokeless powder making. 

Besides polymerization, another type of polyreaction can be used for stabilizing model membrane systems. Recently, Fukuda et al.28) described polyamide formation via polycondensation in monolayers at the gas/water interface (definition of mono-layers see Sect. 3.2). Long-chain esters of glycine and alanine were polycondensed to yield non-oriented polyamide films of polyglycine and polyalanine. 

The projective plane arises as a quotient space of the sphere, the required group being C,-. It is obtained by identifying antipodal points of the spherical surface in other words, it is the antipodal quotient of the sphere (see Section 1.2.2). P2 is the simplest compact non-orientable surface in the sense that it can be obtained from the sphere by adding just one cross-cap. 

Prisntm, m > 2 (on S2, with two m-gons seen as holes) and their non-orientable quotients, for m> 2 even (on projective plane, with one hole),... 

Proof. Hike such a polycycle. Its universal cover is an elementary (5,3)-polycycle, whose automorphism group contains some fixed-point-free transformation. Inspection of the list of elementary (5,3)-polycycles in Figure 7.2 yields only Eg = snub Prismoo as a possibility. Snub Prismm is obtained from the group of translations by m faces and the non-orientable quotients if the group contains also some translation followed by reflection. ... 

Let us now determine all elementary ( 2,3,4,5), 3)gOT-polycycles. Hie universal cover P of such a polycycle P is an elementary ( 2,3,4,5, 3)-polycycle, whichhas a non-trivial fixed-point-free automorphism group in Aut(P). Consideration of the above list of polycycles yields snub Prisma, as the only possibility. The polycycles snub Prismm and its non-orientable quotients arise in this process. ... 

If P is an elementary ( 2,3], 5)ge -polycycle, which is not a ( 2,3, 5)-polycycle, then its universal cover P is an elementary ( 2,3, 5)-polycycle, which has a fixed-point-free automorphism group included in Aut(P). Clearly, only snub APrismoo is such and it yields the infinite series of snub APrisnim and its non-orientable quotients. ... 

In Sect. 1.3 we described cycles of two types, oriented and non-oriented. The oriented cycle can be passed by if we move in the direction of the arrows. For a cycle of a general type it can be different since it is a sequence of the vertices Z1(.. ., Zk where the pairs of vertices Zt and Zi+1(i = 1,.. ., /e-l)and also of Zk and Z, are connected by edges. As usual, we will consider simple cycles with no edge and no Z vertex appearing twice. 

Here is a fixed integer, the Euler characteristic that marks the particular topology of the surface on which the polyhedron is embedded. However, in order to describe the topology completely, one also has to specify the orientability of the surface [3]. A surface is orientable if there is no walk on the surface that would take you from the outside to the inside. Such is the case of a sphere with handles. Otherwise, it is non-orientable. This is the case of a sphere with crosscaps. Based on this orientability, the infinite class of surfaces can be divided into two subclasses ... 

Take the sphere and attach q crosscaps to form the non-orientable surface Nq which has the Euler characteristic x(Nq) = 2 — q. For example the projective plane is homeomorphic to the sphere with one crosscap and has... 

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