Dielectric relaxation molecular weight

The accessibility of chitin, mono-O-acetylchitin, and di-O-acetylchitin to lysozyme, as determined by the weight loss as a function of time, has been found to increase in the order chitin < mono-O-acetylchitin < di-O-acetylchitin [120]. The molecular motion and dielectric relaxation behavior of chitin and 0-acetyl-, 0-butyryl-, 0-hexanoyl and 0-decanoylchitin have been studied [121,122]. Chitin and 0-acetylchitin showed only one peak in the plot of the temperature dependence of the loss permittivity, whereas those derivatives having longer 0-acyl groups showed two peaks. 

Master curves are important since they give directly the response to be expected at other times at that temperature. In addition, such curves are required to calculate the distribution of relaxation times as discussed earlier. Master curves can be made from stress relaxation data, dynamic mechanical data, or creep data (and, though less straightforwardly, from constant-strain-rate data and from dielectric response data). Figure 9 shows master curves for the compliance of poly(n. v-isoprene) of different molecular weights. The master curves were constructed from creep curves such as those shown in Figure 10 (32). The reference temperature 7, for the... 

When a chain has lost the memory of its initial state, rubbery flow sets in. The associated characteristic relaxation time is displayed in Fig. 1.3 in terms of the normal mode (polyisoprene displays an electric dipole moment in the direction of the chain) and thus dielectric spectroscopy is able to measure the relaxation of the end-to-end vector of a given chain. The rubbery flow passes over to liquid flow, which is characterized by the translational diffusion coefficient of the chain. Depending on the molecular weight, the characteristic length scales from the motion of a single bond to the overall chain diffusion may cover about three orders of magnitude, while the associated time scales easily may be stretched over ten or more orders. 

Wada et al. (120) studied dielectrically the normal transition of two PBLA samples in m-cresol and observed that the higher-molecular-weight sample exhibited a secondary dispersion at frequencies above the region which could be associated with orientation polarization of the polypeptide. Their contribution will be discussed in the next section, in which such a dispersion is attributed to a relaxational alternation of helix and random-coil units. 

Dielectric measurements are carried out on PPOA and PPODG. The dielectric spectrum of PPOA in the bulk presents a prominent glass-rubber relaxation followed by a subglass absorption. The low-molecular-weight compound only exhibits a prominent glass-liquid absorption followed by a diffuse and weak subglass relaxation. This behaviour cannot be explained in terms of only intramolecular interactions, and therefore intermolecular interactions must play an important role in this process. 

The effects of coupling of the DTO and RB units in not only one- but also three-dimensional arrays are discussed below and molecular weight trends illustrated. A fundamental connection between relaxation times and normal mode frequencies, shown to hold in all dimensions, allows the rapid derivation of the common viscoelastic and dielectric response functions from a knowledge of the appropriate lattice vibration spectra. It is found that the time and frequency dispersion behavior is much sharper when the oscillator elements are established in three-dimensional quasi-lattices as in the case of organic glasses. 

The effective correlation times for an approximately isotropic motion, tr, ranged from 40.3 ps in methanol to 100.7 ps in acetic acid for 5a, and from 61.6 ps to 180.1 ps for 5b in the same solvents. Neither solvent viscosity nor dielectric constant bore any direct relationship to the correlation times found from the overall motion, and attempts to correlate relaxation data with parameters (other than dielectric constant) that reflect solvent polarity, such as Kosover Z-values, Win-stein y-values, and the like, were unsuccessful.90 Based on the maximum allowed error of 13% in the tr values derived from the propagation of the experimental error in the measured T, values, the rate of the overall motion for either 5a or 5b in these solvents followed the order methanol N,N-dimethylformamide d2o < pyridine < dimethyl sulfoxide. This sequence appears to reflect both the solvent viscosity and the molecular weight of the solvated species. On this basis, and assuming that each hydroxyl group is hydrogen-bonded to two molecules of the solvent,137 the molecular weights of the solvated species are as follows in methanol 256, N,N-dimethylformamide 364, water 144, pyridine 496, and dimethyl sulfoxide 312. 

A frequency dependence of complex dielectric permittivity of polar polymer reveals two sets or two branches of relaxation processes (Adachi and Kotaka 1993), which correspond to the two branches of conformational relaxation, described in Section 4.2.4. The available empirical data on the molecular-weight dependencies are consistent with formulae (4.41) and (4.42). It was revealed for undiluted polyisoprene and poly(d, /-lactic acid) that the terminal (slow) dielectric relaxation time depends strongly on molecular weight of polymers (Adachi and Kotaka 1993 Ren et al. 2003). Two relaxation branches were discovered for i.s-polyisoprene melts in experiments by Imanishi et al. (1988) and Fodor and Hill (1994). The fast relaxation times do not depend on the length of the macromolecule, while the slow relaxation times do. For the latter, Imanishi et al. (1988) have found... 

Dielectric spectroscopy was also used by the same group in order to study the local and global dynamics of the PI arm of the same miktoarm star samples [89]. Measurements were confined to the ordered state, where the dynamics of the PI chain tethered on PS cylinders were observed in different environments since in the SIB case the faster moving PB chains are tethered in the same point as the PI arm. The distribution of segmental relaxation times were broader for SI2 than SIB. The effect was less pronounced at higher temperatures. The PI normal mode time was found to be slower in SIB, when compared to SI2 although both arms had the same molecular weight. Additionally, the normal mode relaxation time distributions of the PI chains tethered to PS cylinders in the miktoarm samples were narrower than in P(S-h-I) systems of lamellar structure. 

The first mention of the a(x) dependence was in experimental work [265], The dielectric relaxation data of water in mixtures of seven water-soluble polymers was presented there. It was found that in all these solutions, relaxation of water obeys the CC law, while the bulk water exhibits the well-known Debye-like pattern [270,271], Another observation was that a is dependent not only on the concentration of solute but also on the hydrophilic (or hydrophobic) properties of the polymer. The seven polymers were poly(vinylpyrrolidone) (PVP weight average molecular weight (MW) = 10,000), poly (ethylene glycol) (PEG MW = 8000), poly(ethylene imine) (PEI MW = 500,000), poly(acrylic acid) (PAA MW = 5000), poly(vinyl methyl ether) (PVME MW = 90,000), poly(allylamine) (PA1A MW = 10,000), and poly(vinyl alcohol) (PVA MW = 77,000). These polymers were mixed with different ratios (up to 50% of polymer in solution) to water and measured at a constant room temperature (25°C) [265]. 

The curve for insulin is unusual in that the observed relaxation time is shorter than would be calculated for an anhydrous sphere of molecular weight 36.OOO. At the time when these observations were made in 1939, no explanation of this phenomenon was available. However, it is now known — see the discussion on page 134 — that insulin under certain conditions dissociates into smaller units of molecular weight 12.000 and there is evidence that in the solution of 80% propylene glycol in which the dielectric measurements were made, the insulin molecule actually dissociates into units of the smaller size. 

Figure 18. Dielectric loss data of poly(propylene glycol) (PPG-4000, molecular weight 4000 Da) at various combinations of temperature and pressure as indicated to demonstrate the invariance of the dispersion of the a-relaxation at constant a-loss peak frequency v or equivalently at constant a-relaxation time ra.

Figure 14. Relaxation rate of segmental, normal, and confinement-induced mode versus inverse temperature for a thin PIP film of 45 nm and different molecular weights, as indicated. Inset The corresponding raw data, i.e. dielectric loss s" vs. temperature at 96 Hz for the same thickness and same molecular weights.

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