“…Long ago, this problem with the simple wormlike chain model motivated the incorporation of a "shift factor" in order to improve agreement between the model and the behavior of real chains of finite molecular weight. 3,[28][29][30][31][32] The "shift factor" introduces another parameter into the model, which permits a more accurate fitting of the model to experimental data. A new parameter can be introduced into the wormlike chain in other ways, as in the helical wormlike chain.…”
Often experiments with chains containing a finite number of bonds, n, are interpreted with the assumption that the characteristic ratio, C n, is determined completely by C∞ and n. This assumption is supported by some, but not all, textbook models for simple flexible chains. The freely jointed chain, freely rotating chain with fixed bond angle, and simple wormlike chain predict C n ) f(C∞,n). These three models share the feature that the stiffness of the chain is specified by no more than one parameter. However, when more than one parameter affects the stiffness of the chain, as in the model with fixed bond angle and symmetric hindered rotation about independent bonds, C n is no longer determined by C∞ and n alone, Cn * f(C∞,n). Since virtually all real chains have hindered rotation, they cannot be expected to have the dimensions given by Cn ) f(C∞,n). This conclusion is supported by numerical calculations using previously published rotational isomeric state models for polyethylene, polyisobutylene, and poly-(dimethylsiloxane). Although these three polymers have similar values of C ∞, they may have quite different values of Cn. This conclusion from the calculations is consistent with the observed behavior of polyisobutylene and poly(dimethylsiloxane), as reported by Arbe et al. (Macromolecules 2001, 34, 1281 and by Sluch et al. (Macromolecules 2003, 36, 2721. The finite n effect in these polymers is three times stronger for the mean square unperturbed radius of gyration than for the mean square unperturbed end-to-end distance.
“…Long ago, this problem with the simple wormlike chain model motivated the incorporation of a "shift factor" in order to improve agreement between the model and the behavior of real chains of finite molecular weight. 3,[28][29][30][31][32] The "shift factor" introduces another parameter into the model, which permits a more accurate fitting of the model to experimental data. A new parameter can be introduced into the wormlike chain in other ways, as in the helical wormlike chain.…”
Often experiments with chains containing a finite number of bonds, n, are interpreted with the assumption that the characteristic ratio, C n, is determined completely by C∞ and n. This assumption is supported by some, but not all, textbook models for simple flexible chains. The freely jointed chain, freely rotating chain with fixed bond angle, and simple wormlike chain predict C n ) f(C∞,n). These three models share the feature that the stiffness of the chain is specified by no more than one parameter. However, when more than one parameter affects the stiffness of the chain, as in the model with fixed bond angle and symmetric hindered rotation about independent bonds, C n is no longer determined by C∞ and n alone, Cn * f(C∞,n). Since virtually all real chains have hindered rotation, they cannot be expected to have the dimensions given by Cn ) f(C∞,n). This conclusion is supported by numerical calculations using previously published rotational isomeric state models for polyethylene, polyisobutylene, and poly-(dimethylsiloxane). Although these three polymers have similar values of C ∞, they may have quite different values of Cn. This conclusion from the calculations is consistent with the observed behavior of polyisobutylene and poly(dimethylsiloxane), as reported by Arbe et al. (Macromolecules 2001, 34, 1281 and by Sluch et al. (Macromolecules 2003, 36, 2721. The finite n effect in these polymers is three times stronger for the mean square unperturbed radius of gyration than for the mean square unperturbed end-to-end distance.
“…In addition, the presence of sulfur (probably as sulfate ion) in the film of the cationic system (Figure c) may lead to the distorted spherulite structure, which is different from the other surfactant systems. A close view of the SEM picture at high magnification shows the starlike image of the morphology (Figure d−f), especially for the cationic surfactant system, implying a higher degree of aromaticity (>80%) and lower degree of cross-linking as supported by the IR results. − 6 Scanning electron micrograph (SEM) of PPP films synthesized in microemulsions: (a) anionic, (b) nonionic, (c) cat-ionic surfactant system, high magnification (5.00K ×); (d) anionic, (e) nonionic, (f) cationic surfactant system, low magnification (10.00K ×).…”
Poly(p-phenylene) (PPP), electrosynthesized in
different microemulsions by the oxidation of benzene in
the form of a uniform and adherent film on Pt surfaces is characterized
with a view to understanding the
role of different types (anionic, nonionic, cationic) of surfactants.
The scanning electron microscopy results
reveal distinct morphological changes in the films synthesized with
cationic, nonionic, and anionic surfactant
systems. The evidence from X-ray photoelectron spectroscopy
investigations indicates the incorporation
of the sulfur species in the film for the case of cationic surfactant
while the anionic and nonionic surfactant
systems do not show a sulfur signal. IR investigations of the
polymer films show a small degree of cross-linked structure with a long backbone containing aromatic rings
irrespective of the surfactant whereas
13C cross polarization magic angle spinning NMR (solid
state) data support the 1,4 substitution (linkage)
in the monomer unit in PPP. Differential thermal
analysis/thermalgravimetric analysis indicates a higher
thermal stability of PPP due to a longer polymer backbone deposited
from the anionic surfactant system.
The cyclic voltamograms of the films indicate a progressive change
in the redox behavior, which correlates
well with the relative stability of the intermediate species with a
change in surfactant system.
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