Chain behavior, predicted

Based on a mechanical model in a time-independent flow, de Gennes derivation tries to extrapolate it to a time-dependent chain behavior. His implicit assumptions have been criticised by Bird et al. [55]. More recent calculations extending the de Gennes dumbbell to the bead-spring situation [56] tend, nevertheless, to confirm the existence of a well-characterized CS transition results with up to 100-bead chains show a critical value of the strain rate at scs = 0.5035/iz which is just 7% higher than the value predicted by de Gennes. 

The transition from single- to many-chain behavior already becomes obvious qualitatively from a line shape analysis of the NSE spectra (see Fig. 60) [116]. For dilute solutions (c = 0.05) the line shape parameter (3 is equal to about 0.7 for all Q-values, which is characteristic of the Zimm relaxation. In contrast, in semi-dilute solutions (e.g. c = 0.18), ft-values of 0.7 are only found at larger Q-values, whereas P-values of about 1.0, as predicted for collective diffusion [see Eq. (128)] are obtained at small Q-values. A similar observation was reported by [163]. 

Fig. 64. Single-chain behavior in semi-dilute PDMS/d-chlorbenzene solutions. Line-shape parameter (3 as a function of Q at the concentration c = 0.18 and c = 0.45, indicating the occurance of two crossover effects, as predicted by the concept of incompletely screened hydrodynamic interactions. (----), (---) asymptotic Zimm and Rouse behavior, respectively. (Reprinted with per-...

Garten, C. T., Trabalka, J. R. (1983) Evaluation of models for predicting terrestrial food chain behavior of xenobiotics. Environ. Sci. Technol. 17, 590-595. 

A force field for solid state modeling of fluoropolymers predicted a suitable helical conformation but required further improvement in describing intermole-cular effects. Though victory cannot yet be declared, the derived force fields improve substantially on those previously available. Preliminary molecular dynamics simulations with the interim force field indicate that modeling of PTFE chain behavior can now be done in an all-inclusive manner instead of the piecemeal focus on isolated motions and defects required previously. Further refinement of the force field with a backbone dihedral term capable of reproducing the complex torsional profile of perfluorocarbons has provided a parameterization that promises both qualitative and quantitative modeling of fluoropolymer behavior in the near future. 

During this same period, the equilibrium stress-strain properties of well characterized cross-linked networks were being studied intensively. More complex responses than the neo-Hookean behavior predicted by kinetic theory were observed. Among other possibilities it was speculated that, in some unspecified way, chain entanglements might be a contributing factor. 

Other cases of deviation from the behavior predicted within the framework of the free-volume concept have been reported 65 66. We have already mentioned Kanig s conclusion about the dependence of/g on chain flexibility45 and our own conclusion46,47 that it depends on packing density. In connection with this it is worth discussing whether there is really any dependence of the fractional free-volume at Tg on the molecular parameters of chains. 

Thermotropic mesomorphism in linear polymers had been considered theoretically prior to 1975 (see reference 3 for leading references). However, in 1975, de Gennes explicitly considered linear polymers having alternating rigid mesogenic groups and flexible spacers in the polymeric main chain. He predicted possible nematic behavior for such polymers. 

The constant value of up to a = 2 suggests that the chains are deforming far less than the junctions. These results follow neither the i = a (parallel) nor the R = (perpendicular) prediction but rather support Benoit et al. (94) that affine chain behavior is not followed. 

Polymers with a star-like topology have attracted interest for many years. The rheological behavior in the melt and in solution of starpolymers differs from the behavior of linear polymers [172]. Polystyrene starpolymers with selectively deuterated core or corona chains were investigated by SANS and it was found that the chains are more stretched within the core (or close to the branching point), while the outer parts of the chains follow the single chain behavior of linear polymers [173]. This result confirmed theoretical predictions by Daoud and Cotton [174] and Birshtein et al. [175]. A similar behavior was found for the chain conformations in star-like block copolymer ionomer micelles, which were studied by SANS, too [176]. 

The evolution of the polarizability per unit cell(a22 ) with respect to the chain-length (up to 20 carbon atoms) is depicted in the figure. A change of slope is easily identified in each curve, it corresponds to the limit beyond which the parabolic behavior predicted by the free-electron theory(a, L starts to break down to reach a saturation regime in the fimit of large n. Moreover, the shape of the curves noticeably depends upon the alternation degree. 

In the part devoted to neutral polymers, we mentioned that semiflexible and stiff chains do not obey the behavior predicted by the Kuhn model. Restricted flexibility of the chain can be caused by the presence of stiff units with multiple bonds or bulky pendant groups, but it can be a result of external conditions or stimuli. In the preceding part, it was explained in detail that repulsive interactions together with entropic forces increase the stiffness of PE chains. Hence, a sudden pH change can be used as a stimulus affecting the stiffness of annealed PE chains. The properties of semiflexible polymers are usually treated at the level of the wormlike chain (WLC) model developed by Kratky and Porod [31]. The persistence length, /p, is an important parameter strongly related to the WLC model and has been used as the most common characteristic of chain flexibility—in both theoretical and experimental studies. It is used to describe orientational correlations between successive bond vectors in a polymer chain in terms of the normalized orientation correlation function, C(s) = (r,.r,+j). For the WRC model, this function decays exponentially ... 

Gaussian thread limit for N—For many physical problems (e.g., polymer solutions and melts, liquid-vapor equilibria, and thermal polymer blends and block copolymers), the Gaussian thread model has been shown to be reliable in the sense that it is qualitatively consistent with many aspects of the behavior predicted by numerical PRISM for more realistic semiflexible, nonzero thickness chain models. However, there are classes of physical problems where this is not the case. The athermal stiffness blend in certain regions of parameter space is one case, both in... 

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