Chain semi-flexible

From the dynamic point of view, as illustrated in Fig. 4.3, polymer coUs are rather ellipsoids with their anisotropy depending upon chain semi-flexibility, and their hydrodynamic radii are usually larger than their radii of gyration. Thus, a dynamic overlap concentration C < C exists, which is of practical importance for characterizing the hydrodynamic property of the polymers in solutimis. 

Angstroms by the optical properties of the materials used, it will be necessary in the future to use much longer polymer chains. Semi-flexible chains with long persistence lengths, such as some of the water-soluble polysaccharides, are good potential candidates. 

The expression for entropic Fa in Eq. 23 describes the data with the X = 0.07 samples and the results by Jinnai et al. [75] very well assuming z = 5.7 nearest neighbors. Because of obvious Umitations inherent in any lattice model, the parameter z is allowed to vary freely to compensate for deficiencies of the model. The closeness of z = 5.7 to the theoretical z = 6 is, however, quite convincing. According to the theory, there seems to be no isotope effect on Fa. Deviations from theory were found for the dPB(l,2)/ PB(1,2 1,4) blend, which shows a positive F that cannot be described without possibly including chain semi flexibility effects. 

The changes in the average chain length of a solution of semi-flexible selfassembling chains confined between two hard repulsive walls as the width of the sht T> is varied, have been studied [61] using two different Monte Carlo models for fast equihbration of the system, that of a shthering snake and of the independent monomer states. A polydisperse system of chain molecules in conditions of equilibrium polymerization, confined in a gap which is either closed (with fixed total density) or open and in contact with an external reservoir, has been considered. 

Semi-Flexible Chains Worm-Like Cods. 241... 

The molecule is either fully flexible or semi-flexible. The fully flexible chains are generally harder to crystallize than semi-flexible chains [35]. In the latter part of the paper (Sect. 5), where we discuss crystallization from the melt, we consider a semi-flexible chain, the flexibility of which is adjusted to reproduce the characteristic ratio of real polyethylene. We there make the... 

The polymer we consider here is a semi-flexible chain which has some bending stiffness (Eq. 3). We first estimated the chain conformation in the melt. The calculated mean-square end-to-end distance R2n between atoms n-bond apart has shown that the chains have an ideal Gaussian conformation R2 is a linear function of n (see Fig. 35 given later). The value of R2 for n = 100... 

Flory, P. J. Statistical thermodynamics of semi-flexible chain molecules. Proc. Roy. Soc. (London) A234,60-73 (1956). 

Fig. 8 General structure of semi-flexible oligobenzoate Hekates 34—36. (a) These stars may consist of three identical arms (34), two (35) or three (36) different arms. Thereby the length (n,m,l), the peripheral chains (R, R", R "), the linking groups X (OOC, COO, CONH) to the core and the substituents Y (H, I) can he adjusted, (b) Borderline conformers - star-shaped, f.-shaped and cone-shaped conformers - for a non-symmetric oligobenzoate scaffold (X = OOC). They can be created by rotation about the C-O single bond within the carboxy linking group to the core...

It is noted that the UV absorbance of the 10(g)-32(sc) sample decreased after the annealing treatment, as shown in Fig. 28a. Presumably, most polysilane chains lie down before annealing in the quartz substrate plane, as the film was prepared by the spin-coating technique. However, the thermal annealing treatment of semi-flexible 32 tends to orient some of the polymer chain segments perpendicularly and/or tilt them to the substrate plane, leading to the decrease in the apparent UV absorbance at 321 nm, as illustrated in Fig. 27. 

The alternative method [46] of analyzing the data is based on the treatment by Odijk and Houwaart [36] of the excluded volume effect on the electrostatic stiffening of semi flexible chains. The total persistence length lt of a stiff polyelectrolyte is the sum of the intrinsic persistence length lp=hl2 and the electrostatic persistence length le,... 

The discussion of the influence of the interphase need not be limited to just linear polyethylenes. Interphases of several nm have been reported in polyesters and poly-hydroxy alkanoates. One major difference between the interphase of a flexible polymer like polyethylene and semi-flexible polymers like PET, PEN and PBT is the absence of regular chain folding in the latter materials. The interphase in these semi-flexible polymers is often defined as the rigid amorphous phase (or rigid amorphous fraction, RAF) existing between the crystalline and amorphous phases. The presence of the interphase is more easily discerned in these semi-flexible polymers containing phenylene groups, such as polyesters. 

The conformation parameter a (=A/Af, where Af is A of a hypothetical chain with free internal rotation) for cellulose and its derivatives lies between 2.8-7.5 2 119,120) and the characteristic ratio ( = A2Mb//2, where Ax is the asymptotic value of A at infinite molecular weight, Mb is the mean molecular weight per skeletal bond, and / the mean bond length) is in the range 19-115. These unexpectedly large values of a and Cffi suggest that the molecules of cellulose and its derivatives behave as semi-flexible or even inflexible chains. For inflexible polymers, analysis of dilute solution properties by the pearl necklace model becomes theoretically inadequate. Thus, the applicability of this model to cellulose and its derivatives in solution should be carefully examined. 

The qnD values of cellulose and its derivatives lie between 3 and 25 nm and are larger than those of typical vinyltype polymer ( 1 nm), but markedly smaller than those of typical stiff chain polymers, such as DNA (Table 14)67). Thus, the chains of cellulose and its derivatives can be considered as semi-flexible. It may be concluded that both the pearl-necklace chain and the wormlike chain models are adequately applicable to these polymers. 

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