Poly characteristic ratio

For poly(methylene), an exclusion distance (hard sphere diameter) of 2.00 A was used to prevent overlap of methylene residues. The calculation reproduced the accepted theoretical and experimental characteristic ratios (mean square unperturbed end-to-end distance relative to that for a freely jointed gaussian chain with the same number of segments) of 5.9. This wps for zero angular bias and a trans/gauche energy separation of 2.09 kJ mol". ... 

Figure 5 is an ORTEP computer plot of the first 50 backbone carbons in a typical chain. Only the fluorine atoms of the sidechains are shown. The various hard sphere exclusions conspire dramatically to keep the fluorines well separated and the chain highly extended even without introducing any external perturbations. The characteristic ratio from the computer calculations is about 11.6 from data for poly(p-chlorostyrene), CR = I l.l, poly(p-bromostyrene), CR = 12.3, and poly(styrene), CR = 10.3 (all in toluene at 30°C), we expect the experimental value for the fluoro-polymer to be in the range of 10 to 12. 

The intrinsic viscosity of poly(L-proline) is studied as a function of molecular weight and temperature In five commonly used solvents water, trifluoroethanol, acetic acid, propionic acid, and benzyl alcohol. The characteristic ratio is 14 in water and 18-20 in the organic solvents at 303 K, and d (in 0) / d T is negative. The theoretical rotational potential function obtained by Hopfinger and Walton for u-prolyl-L-prolyl-t-prolyl-t-proline J. Macromol. Scl. Phys. 1969, 3, 171 correctly predicts the characteristic ratio at 303 K but predicts the wrong sign for tfiln < >0) IdT. 

The characteristic ratios of poly(pro-gly), poly(hyp-gly), poly(gly-gly-pro-gly), poly(gly-gly-hyp-gly), and poly(pro-ale) are determined in water, The results confirm the main features of the theoretical conformational maps derived by Rory and coworkers for glycine followed by either l-proline or a nonproline residue. Small adjustments, well within the uncertainty described by Schimme and Rory, are suggested In the conformational map for L-proline followed by glycine. The constants for the Lennard-Jones functions of Scheraga and coworkers, as used by Madison and Scheliman, produce a conformational map for L-proline followed by a nonproline residue which is in somewhat poorer agreement with experiment. The two sets of modified constants introduced by Madison and Scheliman fall to predict the conformational properties of these sequential copolypeptides. 

N 054 "Calculation of the Characteristic Ratio of Randomly Coiled Poly(L-proline)"... 

Allowing for rotation about the Ca—C bond (/.e., variation of ijr) and for some degree of freedom about the peptide bond [i.e., small variation of ro), the characteristic ratios of the form / (crs) and form II [trans) poly(L-proline) chain are calculated by a Monte Carlo method in which the conformational energies are used as weighting factors. The Monte Carlo method enabled short-range interactions (beyond those involved in a single residue) to be taken into account. 

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... 

Figure 2. Generalized characteristic ratio C q) plotted vs. qjn for three typical polymers polyethylene (PE) at 400 K [11, 21], atactic polystyrene (PS) at 300 K. [14], and poly(dimethyl-siloxane) (PDMS) at 350 K [15],...

TABLE 5. Degree of polymerization (N) and characteristic ratio (C, ) for poly(silylenes) from light scattering measurements91... 

RNA and DNA are poly anions at pH 7. The pk of the phosphate OH group is close to 1. DNA is a double helix in which a large purine base is always paired with a small pyrimidine base. Only AT and CG pairs occur. AT and GC pairing are favored by optimal hydrogen bonds, which connect the base pairs in the hydrophobic center (Fig. 8.2.5a). Monomeric AT and GC bases do not pair in water but they do pair in organic solvents. The double helices are destroyed reversibly (they melt ) if the hydrogen bonds are thermally disrupted at temperatures between 70 and 80°C. In UV spectra one then observes a loss of intensity of the bands around 270 nm and a small short-wavelength shift. Each DNA has a characteristic ratio (G+C) (A+T), called the coefficient of specifity, which varies... 

The characteristic ratio of the poly(methylene) chain, which might be considered to be the simplest polymer molecule, as a function of chain length is shown in Fig. 4.4 for the simple models considered thus far. All save the simple freely jointed chain display end effects, manifest by an increase in Ci with chain length at small n, which will not be considered further. In what follows, only the asymptotic limit of the characteristic ratio for 00 (Coo) will be discussed. The values of for the freely jointed chain, the freely rotating chain and the chain with independent bond rotational potentials increase in value from 1 through 2 to ca 3-5. The latter value is, however, only ca one-half of the experimentally determined value of Coo=6-9 for poly(methylene). This serious discrepancy points to the fact that the bond rotational potentials are definitely not independent, i.e. the conformation of bond i depends upon the conformations of bonds (/—I) and (/-i-1). 

Fig. 4.4. Plots of the characteristic ratio of poly(methylene) at 140 °C as a function of the number of bonds using different theoretical models (1) the freely jointed chain (2) the rotating chain (3) independent bond rotational (4) interdependmt bond rotational potentials (after Flory, 1969).

Also apparent from Fig. 17.5 is the close agreement between the 272 bond poly(oxyethylene) and the 4 000 bond random flight chains when plotted on the reduced distance scale. As the characteristic ratios C of these two chains are quite different (4 vy 1, respectively), the results suggest that the molecular structure of the chain does not drastically influence the segment density vs distance curves plotted in this reduced fashion. This conclusion requires further confirmation. 

Poly(dlmethyl siloxane) 4 0 Kx determined with bulk and solution equilibrates characteristic ratio measured. Calculations with RIS models. [83]... 

The characteristic ratio, C, is much smaller (1.08) for the ABA chains in the large micelles than in the small aggregates formed at weak segregation [34], since most of the chains form loops. Loops appear to be dominant in the micelle formed in A,Ai-dimethyl acetamide by a large triblock copolymer with polystyrene as the soluble internal block and poly(tert-butylstyrene) as the insoluble terminal blocks [26]. 

Linear polyacrylamides in solution adopt nearly random coil configurations that are partially permeable (draining) to solvent. The coils are unassociated in dilute solution. The average shape of the isolated coils has been described as an ellipsoidal or bean-shaped structure (58). The individual chains are quite flexible, as is common with most vinyl polymers. This is indicated from several parameters shown in Table 2, such as the persistence length, steric hindrance parameter (a), and characteristic ratio (Cco)- The persistence length of 1.52 nm for poly(acrylamide) in water is quite similar to the average intrinsic (bare) persistence length ( 1.4 nm) of many vinyl polymers (59). 

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