Persistence length/ratio

The sedimentation coefficient provides a useful indicator of polysaccharide conformation and flexibility in solution, particiflarly if the dependence of on Mw is known [62]. There are two levels of approach (i) a general level in which we are delineating between overall conformation types (coil, rod, sphere) (ii) a more detailed representation where we are trying to specify particle aspect ratios in the case of rigid structures or persistence lengths for linear, flexible structures. 

Recently a very detailed study on the single chain dynamic structure factor of short chain PIB (M =3870) melts was undertaken with the aim to identify the leading effects limiting the applicability of the Rouse model toward short length scales [217]. This study was later followed by experiments on PDMS (M =6460), a polymer that has very low rotational barriers [219]. Finally, in order to access directly the intrachain relaxation mechanism experiments comparing PDMS and PIB in solution were also carried out [186]. The structural parameters for both chains were virtually identical, Rg=19.2 (21.3 A). Also their characteristic ratios C =6.73 (6.19) are very similar, i.e. the polymers have nearly equal contour length L and identical persistence lengths, thus their conformation are the same. The rotational barriers on the other hand are 3-3.5 kcal/mol for PIB and about 0.1 kcal/mol for PDMS. We first describe in some detail the study on the PIB melt compared with the PDMS melt and then discuss the results. 

When the temperature is increased above the 0-temperature the enhanced local viscosity at higher concentration drops. The variation is the same as observed for the macroscopic viscosity [329]. In [328] polyisoprene (PI) and PS in different solvents have also been investigated and the authors observe that the slopes of the concentration dependence of the scaled local viscosities for PS and PI have a ratio of 1.7, which matches the value of the concentration ratio either on the Kuhn length (1.6) or the persistence length (1.7) for the two polymers. 

Chanzy and Peguy (13) were the first to report that cellulose forms a lyotropic mesophase. They used a mixture of N-methyl-morpholine-N-oxide (MMNO) and water as the solvent. Solution birefringence occurred at concentrations greater than 20% (w/w) cellulose. The concentration at which an ordered phase formed increased as the cellulose D.P. decreased. The persistence length of cellulose in MMNO-H2O is not known but presumably it has an extended chain configuration in this solvent. Again the question arises as to what is the relevant axial ratio to be used for cellulose. This will be discussed further below. 

Chain for which the contour length is greater than the persistence length but for which their ratio is still below the Gaussian limit. 

The light-scattering behavior of those polysilanes studied indicates that they are slightly extended and stiffened compared with typical polyolefins. One measure of chain flexibility is the characteristic ratio C, which is also shown in the table. The values of C for most polysilanes of about 20 are larger than those for typical hydrocarbon polymers (—10), indicating that the polysilanes are somewhat less flexible than polyolefins. However, poly(diarylsilylene)s are much more rod-like and inflexible, with persistence lengths greater than 100 46... 

Fig. 17 (a-d) Cryo-TEM images of diblock (sphere-rod) liposomes comprised of liquid-phase lipid nanorods (white arrows) connected to spherical vesicles. The lipid nanorods are stiff cylindrical micelles with an aspect ratio RilOOO. Their diameter equals the thickness of a lipid bilayer ( 4 nm) and their length reaches up to several micrometers, with a persistence length on the order of millimeters, (c) An inset of B, demonstrating the thickness of the nanorod white arrow heads point out a thickness of rj4 nm (approximate bilayer thickness, identical for the spherical vesicle and the nanorods), (d) Schematic of a MVLBisG2/DOPC sphere-rod diblock liposome. Reprinted with permission from [58]. Copyright 2008 American Chemical Society... 

Later Flory (1978) extended his theory to semi-flexible particles. For that purpose he suggested that the persistence length would determine the effective aspect ratio. If the persistence length is temperature dependent then the phase behaviour will also be temperature dependent and thus, in addition, concentration dependent. He made use of Cifferri s suggestion for the temperature dependence of the persistence length... 

Valenti et al. noted a transition to the mesophase under the effect of the applied external field for those semirigid-chain polymers which do not exhibit the liquid crystalline transition under normal conditions. A moderately concentrated solution of polyterephthalamide of p-aminobenzylhydrazide (X-500) in dimethyl sulphoxide does not exhibit the transition into the liquid crystalline state, which can be explained by a relatively low axial ratio for the macromolecules. The persistence length for this polymer is estimated being equal to 50 A. At the same time, according to the data from the literature, high-modulus fibres have been obtained from the solutions of this polymer, which can be connected only with the appearance of the liquid crystalline state in the process of fibre formation. The authors of believe that this... 

For example, PBLG molecules have a persistence length of around 120 nm (Jackson and Shaw 1991 Ookubo et al. 1976) in the solvent metacresol and a diameter J of 1.54 nm, so that the aspect ratio kp fd of a single persistence length of the molecule is around 78. According to the Semenov-Khokhlov theory, for long PBLG molecules the phase transition to a nematic should occur at a polymer volume fraction of 02 0.073, not far from the experimental value of around 0.080. Further details can be found in Sato and Teramoto (1996). 

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) ... 

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