Stiff molecule

The freedom to vary < ) and i so extensively—even if exaggerated here owing to the absence of other molecules—renders cellulose fragments such as an octamer, surprisingly flexible. Cellulose is generally considered to be a stiff molecule, but at least single-molecule simulations in vacuum at 400 K show it to have considerable internal mobility. The range of conformations that result from this mobility are quite apparent when the molecular shape is... 

Up to this point, rather flexible molecules are considered. However, it is necessary to note that the theory of Gotlib and Svetlov should in first instance be applicable to rather stiff molecules, as very flexible molecules cannot be approximated by a worm-like chain. The applicability to stiff molecules is demonstrated in Fig. 5.6, with the aid of results obtained... 

The proof given by Meixner (79) (Section 3.1) is only valid, if no energy is dissipated during the building up of the free energy. However, with kinetically stiff molecules the hydrodynamic part of intrinsic viscosity corresponds to such a dissipation (Section 5.1.3). For an elementary discussion see ref. (117). 

For these measurements, temperature has been varied between 55 and 110° C. In this temperature range, the solvent viscosity changes by a factor three 4.7 to 1.5 cps). It is very improbable that a noticeable internal friction factor would change just by the same factor. Moreover, as has already been pointed out at the end of Section 5.2.2, the curves obtained by plotting cot2 c vs reduced shear stress fjN are practically coinciding for dilute solutions of cellulose tricarbanilate fractions with M S 500,000 and for anionic polystyrenes. So one can conclude that the internal friction of the thermodynamically stiff molecules of cellulose tricarbanilate must be rather low. 

Melt viscosity is the most critical practical property for the process engineer. When stiff molecules give high viscosity and slow flow... 

The rheology of isotropic suspensions and solutions of stiff molecules and particles is covered in Section 6.3. The rheology of lyotropic and thermotropic nematic liquid crystals composed of long, stiff molecules is described in Chapter 11. 

Brownian rod-like objects of high aspect ratio are usually molecules, not colloidal particles. As exception is tobacco mosaic virus (TMV), which is a Brownian particle of length 300 nm and diameter 18 nm (Caspar 1963). For completeness, we shall discuss the theory of Brownian rod-like particles in this chapter, with the understanding that the theory for such particles is actually more relevant to long stiff molecules than to rod-like fibers. The behavior of non-Brownian fiber suspensions is covered in Section 6.3.2.2.------------------... 

The viscous and elastic properties of orientable particles, especially of long, rod-like particles, are sensitive to particle orientation. Rods that are small enough to be Brownian are usually stiff molecules true particles or fibers are typically many microns long, and hence non-Brownian. The steady-state viscosity of a suspension of Brownian rods is very shear-rate- and concentration-dependent, much more so than non-Brownian fiber suspensions. The existence of significant normal stress differences in non-Brownian fiber suspensions is not yet well understood. 

From slow-shear-rate solutions of the Smoluchowski equation, Eq. (11-3), with the Onsager potential, Semenov (1987) and Kuzuu and Doi (1983, 1984) computed the theoretical Leslie-Ericksen viscosities. They predicted that ai/a2 < 0 (i.e., tumbling behavior) for all concentrations in the nematic state. The ratio jai is directly related to the tumbling parameter X by X = (1 -h a3/a2)/(l — aj/aa). Note the tumbling parameter X is not to be confused with the persistence length Xp.) Thus, X < I whenever ai/a2 < 0. As discussed in Section 10.2.4.1, an approximate solution of Eq. (11-3) predicts that for long, thin, stiff molecules, X is related to the second and fourth moments Sa and S4 of the molecular orientational distribution function (Stepanov 1983 Kroger and Sellers 1995 Archer and Larson 1995) ... 

From Fig. 1 one might conclude that the general theoretical form of Eq. (4.26) is satisfactory. However, it has been found that stiff molecules... 

Fig. 18. Two isomers of the random copolymer (E XEEX)N a stiff molecule of linear polyethylene En=(C4H8)n (x=0) with a larger statistical segment length a and a flexible chain of branched poly(ethyl ethylene) EEN=(C2H3(C2H5))N (x=l) with a smaller statistical segment length a...

Most natural polymers are greatly heterogeneous, having specific structures, and polymer theory can only be used in a broad, semiquanti-tative sense. For most polysaccharides and for some proteins (gelatin, casein) the theory nevertheless is useful. For most polysaccharides, the solvent quality of water is rather poor, but many of them nevertheless have a quite expanded conformation, because they are relatively stiff molecules (starch being an exception). For globular proteins other theory is needed. Proteins and several of the polysaccharides are polyelectrolytes. 

The angles (6t, i) represent the orientation angles of segment / in a laboratory-fixed spherical polar coordinate system. Note that in Eq. (8.9.5) the last term contains a cross term in Pa. For large stiff molecules this term does not, in general, vanish. In the limit q - 0, however, the Pa term vanishes and Eqs. (8.9.1) and (8.9.2) are valid. 

In this next sections an attempt will be made to collect on the examples of poly(p-phenylenebenzobisthiazole), poly-p-oxybenzoate and poly(p-ptenylene ter-ephthalamide) the sparse evidence suggesting that dynamic disorder may sometimes also be of importance for the understanding of stiff molecules. 

Fig. 2.8. A quantum-mechanical analogy of the stable positions of a chair on the floor. A stiff molecule CioHlo with the shape shown here, when interacting with a crystal surface, would acquire several stable positions similar to those of the chair on the floor. They would correspond to some vibrational states (the molecule would vibrate about these positions) of a given electronic state ( the same bond pattern" ), which in this analogy would correspond to the fixed structirre of the chair.

These materials exhibit mechanical properties (e.g., modulus, tensile) which are significantly greater than those exhibited by conventional thermoplastic resins. In fabricated articles these properties are highly anisotropic. This anisotropy is caused by the sensitivity of these stiff molecules to the imposed elongational flow fields which cause molecular orientation in the longitudinal direction. 

Intramolecular zwitterion pair formation presupposes a quite flexible molecule chain. So, in contrast, stiff molecules form intermolecular chains, which are a kind of polybetaine. 

In this section, additional details on the conformations of macromolecules are given to further the understanding of flexible molecules. Details on computer simulation are presented to evaluate mobility. Increasingly stiff molecules are described to make the link to rigid macromolecules. 

Our group developed a novel strategy consisting in the use of planar stiff molecules bearing two identical reactive functions at the opposite end of their structure [14—17]. The working hypothesis was that only one of the functions can react with the wood OH group, whereas the other should be left to copolymerize with a subsequently... 

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