Kinking-units

Some of the kinked units discussed in the previous section, such as —0— and — S—, are simple examples of flexible spacers that space the meso-genic units into separate structural sequences of smaller length-to-diameter ratios. Other segments often used as flexible spacers include oligomeric polymethylenes, polyoxyethylenes, polysiloxanes, and so forth. The following series of molecules, (3.5) with n = 1-8, make up one of the oldest examples of the flexible spacer concept in the molecular design of liquid crystals (Vorlander, 1927) ... 

As is for low mass liquid crystals, incorporation of kinked moieties will result in destructive effects on the liquid crystallinity of polymers (Figure 3.4). 2,2-diphenylpropane, diphenylmethane, diphenyl ether, diphenyl ketone, 1,2-phenylene, 1,3-phenylene, and 1,2-naphthalene are examples of kinked moieties used in the modification of liquid crystalline polymers. They are very effective in destroying the linearity of rigid rods. Polymers with kinked units have less crystallinity and lower phase transition temperatures. Appropriate use of kinked units is thus of help from case to case. However, the type and amount of kinked units should be carefully determined so as to maintain desirable liquid crystallinity. 

This study on i-carrageenan is aimed at exploring the gel formation in aqueous systems of i-carrageenan containing small amounts of v-units (kinking units). 

Figure 22.12 Three concrete examples of kinked pol-yarylenes 55-57 in which the kinked units are alternately connected by 1,4-phenylenes.

The introduction of kinked linkages into the polymer backbone effectively reduces the regularity of the molecule and lowers the melting temperature. However, the incorporation of kinked units has an unfavorable influence on the liquid crystallinity because the kinks disrupt the molecular linearity. Frequently used kinked monomers include isophthalic acid (with the meta linked core angle of 120°), 2,5 substituted thiophene (with a core angle of 148°), and so on. The induction of kinks into the molecular chain tends to lower the thermal stability of theLCPs [4,19]. 

The different forms of carbynes were assumed to be polytypes with different numbers of carbon atoms in the chains lying parallel to the hexagonal axis and different packing arrangements of the chains within the crystallite. Heimaim et al [23] proposed that the sizes of the unit cells were determined by the spacing between kinks in extended carbon chains, Fig. 3A. They were able to correlate the Cg value for the different carbyne forms with assumed numbers of carbon atoms, n (in the range n = 6 to 12), in the linear parts of the chains. 

Figure 5.4 Attachment of a growth unit into a kink site...

The seeond-order dependenee of the growth rate on the supersaturation ean be explained by a number of growth theories. The most eonvineing, however, is that of Burton etal. (1951). In their BCF theory about the serew disloeation eentred surfaee spiral step, it is assumed that growth units enter at kinks with a rate proportional to cr and that the kink density is also proportional to cr whieh gives the faetor cr in the rate expression. 

The y relaxation takes place at the lowest temperature, overlaps with the )3 relaxation (Fig. 15), and coincides in location and activation energy with the typical y relaxation of polyethylene [35,36], and also of polyethers [37], and polyesters [38] with three or more consecutive methylene units. It appears, for 3 Hz and tan6 basis, at - 120°C (P7MB) and - 126°C (P8MB), and its location and activation energy (35-45 kJ mol ) agree with the values of a similar relaxation associated with kink motions of polymethylenic sequences. 

The disruption of chain regularity by the introduction of lateral substituents or kinks on repeating units is a supplementary means to decrease the melting temperature of aromatic polyesters.72 This is illustrated in Table 2.9, where the melting temperatures of unsubstituted and methyl-substituted aromatic-aliphatic and aliphatic acids are reported. Regularity disruptions often cause significant... 

Introduction of nonmesogenic units in polymer chains. (E.g., using meta-substituted aromatic monomers such as isophthalic acid or resorcinol). This results in the formation of kinks in polymer chain, which disrupt lateral interactions. 

The shear work done for one atomic (molecular) displacement, b is the applied force times the displacement, or xb3. This work must equal the promotion energy 2Eg. Therefore, letting b3 equal the molecular volume, Vm, the required shear stress is approximately 2Eg/Vm. The parameter [Eg/Vm] is called the bond modulus. It has the dimensions of stress (energy per unit volume). The numerator is a measure of the resistance of a crystal to kink movement, while the denominator is proportional to the work done by the applied stress when a kink moves one unit distance. Overall, the bond modulus is a measure of the shear strengths of covalent bonds. 

The motion of a single kink is analogous with an embedded chemical reaction of the simple exchange type (Gilman, 1993). A pair of atoms, above and below the glide plane exchange partners when a kink moves a unit b amount. 

The crystal structure of NiAl is the CsCl, or (B2) structure. This is bcc cubic with Ni, or A1 in the center of the unit cell and Al, or Ni at the eight comers. The lattice parameter is 2.88 A, and this is also the Burgers displacement. The unit cell volume is 23.9 A3 and the heat of formation is AHf = -71.6kJ/mole. When a kink on a dislocation line moves forward one-half burgers displacement, = b/2 = 1.44 A, the compound must dissociate locally, so AHf might be the barrier to motion. To overcome this barrier, the applied stress must do an amount of work equal to the barrier energy. If x is the applied stress, the work it does is approximately xb3 so x = 8.2 GPa. Then, if the conventional ratio of hardness to yield stress is used (i.e., 2x3 = 6) the hardness should be about 50 GPa. But according to Weaver, Stevenson and Bradt (2003) it is 2.2 GPa. Therefore, it is concluded that the hardness of NiAl is not intrinsic. Rather it is determined by an extrinsic factor namely, deformation hardening. 

The distance that the small segment of a dislocation line moves when a kink moves is called the Burgers displacement, b. Figure 11.2 illustrates it for the case of quartz. It determines the amount of work that is done by the advance of a kink (per unit width of the kink) which is acted upon by the virtual force generated by the applied shear stress, x. This force is xb per unit length of the dislocation line. Letting the kink width be b since the displacement is b, the work done is xb3. This is resisted by the strength, U (eV) of a Si-O bond which... 

The intrinsic energy band-gap of YAG is about 6.6 eV., and the Burgers displacement is about half the unit cell size, or 6 A. Then, if a kink volume is taken to be 6 x 3 x 3 = 54 A3, the bond modulus is 0.11 eV/A3, or 1800 kg/mm2. Given how little is known about dislocation motion in garnet, this agreement with the room temperature hardness value is largely fortuitous. 

Jefferson s studies of the pyroxenoids has added greatly to our application of the way in which, through the intermediary of planar - or planar and Kinke - faults one structure is converted into another (45). And Audier, Jones and Bowen (46) have revealed how unit cell strips of Fe C may be accommodated as extended defects in the Fe C structure. Both these carbidic phases can be readily identified by HREM at the interface of iron catalysts used for the disproportionation of CO (to yield C j+CC ). 

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