Chain longitudinal

According to the reptation theory, the polyelectrolyte (it can be DNA in this case) is assumed to be something which consists of N units (length = a, the number of bases in case of DNA). The total length of DNA is equal to Na. In the reptation theory, only the force along the DNA chain (longitudinal force) is taken into account in the electric field. The mobihty of DNA, /t, therefore, is then expressed by... 

Traditionally, two major classes of thermotropic liquid crystalline polymers have been identified the so called main chain (longitudinal) and side chain (comb) types (MCLCPs and SCLCPs, respectively) (Fig. 2.5). More recently other variants have appeared these are combined LCPs which are hybrid between MCLCPs and SCLCPs, and the rigid rod types described by Watanabe et A great wealth of literature already exists in the form of unified texts and reviews which detail both the major classes of LCPs. Bibliographic data have been compiled" and reviews more or less specific to main chain or comb " polymer systems have appeared. We shall be concerned here only with main chain and side chain LCPs. 

These concepts are tested in Fig. 7(a,b) where one can see that both in the non-adsorbed case (Fig. 7(a)) and in the adsorbed case (Fig. 7(b)) the data is compatible with normal diffusion of the parallel (longitudinal) component, g2/(t) = 4Djyt. For e = —1.5, the chains are freely diffusing in the 3d bulk, far away from the adsorbing wall, g / = For e = —3 most monomers... 

Single chains confined between two parallel purely repulsive walls with = 0 show in the simulations the crossover from three- to two-dimensional behavior more clearly than in the case of adsorption (Sec. Ill), where we saw that the scaling exponents for the diffusion constant and the relaxation time slightly exceeded their theoretical values of 1 and 2.5, respectively. In sufficiently narrow slits, D density profile in the perpendicular direction (z) across the film that the monomers are localized in the mid-plane z = Djl so that a two-dimensional SAW, cf. Eq. (24), is easily established [15] i.e., the scaling of the longitudinal component of the mean gyration radius and also the relaxation times exhibit nicely the 2 /-exponent = 3/4 (Fig. 13). 

In fact, the further longitudinal growth of a bundlelike nucleus will be hindered by such factors as chain... 

Hence, the main aim of the technological process in obtaining fibres from flexible-chain polymers is to extend flexible-chain molecules and to fix their oriented state by subsequent crystallization. The filaments obtained by this method exhibit a fibrillar structure and high tenacity, because the structure of the filament is similar to that of fibres prepared from rigid-chain polymers (for a detailed thermodynamic treatment of orientation processes in polymer solutions and the thermokinetic analysis of jet-fibre transition in longitudinal solution flow see monograph3. ... 

According to Hosemann-Bonart s model8), an oriented polymeric material consists of plate-like more or less curved folded lamellae extended mostly in the direction normal to that of the sample orientation so that the chain orientation in these crystalline formations coincides with the stretching direction. These lamellae are connected with each other by some amount of tie chains, but most chains emerge from the crystal bend and return to the same crystal-forming folds. If this model adequately describes the structure of oriented systems, the mechanical properties in the longitudinal direction are expected to be mainly determined by the number and properties of tie chains in the amorphous regions that are the weak spots of the oriented system (as compared to the crystallite)9). 

Many of the mesogenic molecules are stericaUy asymmetric, which is determined by the fractures and bending of the molecular core as well as by the presence of the tail chains of different nature, including the branched, biforked or polyphilic moieties (Fig. 2c-f). In terms of the multipole model of molecular asymmetry introduced by Petrov and Derzhanski [34], we can speak about longitudinal or transverse steric dipoles or multipoles (Fig. 3). 

Figure 3 Frequency-dispersion curves of the longitudinal polarizability per unit cell of infinite periodic chains of hydrogen molecules according to the method used (RPA (bottom) and UCHF (top)). AH the values are in a.u.. The position of the first excitation energies which corresponds to the poles is indicated by vertical bars.

The longitudinal layer of smooth muscle in the small intestine is continuous. In the large intestine, this layer of muscle is concentrated into three flat bands referred to as taniae coli. Furthermore, the large intestine appears to be subdivided into a chain of pouches or sacs referred to as haustra. The haustra are formed because the bands of taniae coli are shorter than the underlying circular layer of smooth muscle and cause the colon to bunch up, forming the haustra. 

Lateral crystallite growth is permitted by a contingent of amorphous chains. All earlier theories allow longitudinal (along the chain axis) growth only. 

Lateral growth occurs in real systems but is not accounted for in the model of Flory. What allows its incorporation into these new calculations is the assignation of the chains to their most probable positions the chains continuously seek positions of equilibrium as crystallization proceeds. This means that all amorphous links have the same propensity for crystallization, which therefore tends to eliminate a distinction between lateral and longitudinal crystal growth (keep in mind that different levels of crystallinity favor one growth pattern over the other -low crystallinity favors fibrils, high crystallinity favors lamellae). 

Carbon nanotubes have been also used as a macromolecular scaffold for Gdm complexes. An amphiphilic gadolinium(III) chelate bearing a C16 chain was adsorbed on multiwalled carbon nanotubes (264). The resulting suspensions were stable for several days. Longitudinal water proton relaxivities, r] showed a strong dependence on the GdL concentration, particularly at low field. The relaxivities decreased with increasing field as predicted by the SBM theory. Transverse water proton relaxation times, T2, were practically independent of both the frequency and the GdL concentration. An in vivo feasibility MRI study has been... 

The computed 6-31G values for the longitudinal polarizability and longitudinal hyperpolarizability per unit cell are given in Table 7. It can be observed that the longitudinal polarizability and longitudinal hyperpolarizability increase with the chain length. However, the rate of variation of these magnitudes decreases with N, in such a way that ay/N... 

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