Flexible coil macromolecules

In dilute solution BBB behaves as a flexible coil macromolecule, perhaps with relatively free rotation about the single bond connecting the long, inflexible, nearly planar, repeat units. 

Finally, when studying dilute solutions of high-molecular-weight flexible coil macromolecules, an additional contribution to the spectral dispersion of the scattered light can arise from the dynamic behavior of the low frequency, long wavelength internal vibrational motions of the chains (70). Additional Lorentzian spectral components (or exponential components of the correlation function) arise through this mechanism characterized by halfwidth (time constant) ... 

Corresponding theoretical analysis of concentration dependence of Dt in solutions of flexible coil macromolecules have been carried out exclusively using the classical theory embodied in Equation 37 and have also turned out to be very sensitive to details of the particular model. The original treatment of Pyun and Fixman (75) based on a model of soft interpenetrable spheres of uniform segment density has been most commonly applied to these data. Their result is ... 

From a microscopic standpoint, the molecules in the films are restricted in three-dimensional space between two walls having different characters one is the silicon wafer surface (hard wall) and the other is the air-polymer surface (soft wall). The polyimide films form the LOA during the solvent evaporation process. Moreover, aromatic polyimides possess intrinsically larger differences in the refi active indices along and perpendicular to the molecular chain directions than flexible coil macromolecules. On the other hand, the film thickness in this study are at least one to several orders of magnitude greater than the molecular size. The LOA may thus not... 

Wolff C. On non Newtonian intrinsic viscosity of flexible coil macromolecules. 23e Intern. Congress lUPAC/ Boston 1971. Macromolecular preprints, Vol. 1, p. 23-27... 

It appears, then, that the mechanical degradation process is intimately connected with the molecular structure of the macromolecule and the resulting fluid rheology that arises from this structure. For a flexible coil macromolecule, such as HPAM or polyethylene oxide, the polymer solutions are known to display viscoelastic behaviour (see Chapter 3) and thus a liquid relaxation time, may be defined as the time for the fluid to respond to the changing flow field in the porous medium. It may be computed from several possible models (Rouse, 1953 Warner, 1972 Durst et al, 1982 Haas and Durst, 1982 Bird et al. 1987). The finite extendible non-linear elastic (FENE) (Warner, 1972 Bird et al, 1987a Haas and Durst, 1982 Durst et al, 1982) dumbbell model of the polymer molecule may be used to find the relaxation time, tg, as it is known that this model provides a good description of HPAM flow in porous media (Durst et al, 1982 Haas and Durst, 1982) the expression for fe is ... 

R. Pecora. Spectral distribution of light scattered from flexible-coil macromolecules. /. Chem. Phys., 49 (1968), 1032-1035. 

First approaches at modeling the viscoelasticity of polymer solutions on the basis of a molecular theory can be traced back to Rouse [33], who derived the so-called bead-spring model for flexible coiled polymers. It is assumed that the macromolecules can be treated as threads consisting of N beads freely jointed by (N-l) springs. Furthermore, it is considered that the solution is ideally dilute, so that intermolecular interactions can be neglected. 

In order to estimate whether the true molar masses of the dendronized polymers are larger or smaller than the GPC molar masses reported in Table 1, it is useful to recall that the separation in a GPC experiment is based on the hydro-dynamic volume (Vn) of macromolecules. For flexible coils, Vn depends on the chain length (i. e. contour length) L = MxbxMo1 according to... 

Mucus is a network of linear, flexible, and random-coil macromolecules. 

Particles which are too small to show a series of maxima and minima in the angular variation of scattered light are frequently studied by measuring the dissymmetry of scattering (usually defined as the ratio of the light scattered at 45° to that scattered at 135°). The dissymmetry of scattering is a measure of the extent of the particles compared with A. If the molecular or particle size is known, it can be related to the axial ratio of rod-like particles or the coiling of flexible linear macromolecules. 

The GPC-viscometry with universal calibration provides the unique opportunity to measure the intrinsic viscosity as a function of molecular weight (viscosity law, log [17] (it versus log M) across the polymer distribution (curves 3 and 4 in Fig. 1). This dependence is an important source of information about the macromolecule architecture and conformations in a dilute solution. Thus, the Mark-Houwink equation usually describes this law for linear polymers log[i7] = ogK+ a log M (see the entry Mark-Houwink Relationship). The value of the exponent a is affected by the macromolecule conformations Flexible coils have the values between 0.5 and 0.8, the higher values are typical for stiff anisotropic ( rod -like) molecules, and much lower (even negative) values are associated with dense spherical conformations. 

Equations (1.28) to (1.30) do not apply to flexible chain molecules, which are not rigid and can exhibit fluctuations in conformation. Here, one approach is to ignore shape anisometry and to make the assumption v = 2.5 in Eq. (1.30). This enables determination of an impermeable sphere-equivalent hydrodynamic volume for flexible chain macromolecules from [ ], provided that M is known. As noted above, the Mark-Houwink-Sakurada equation [Eq. (1.23)] is often used to relate [ j] to M when dealing with flexible coils. 

Coil macromolecules tend, however, to occur in the form of ellipsoids (cf. Section 4.4.3). With ellipsoid-shaped coils, Rs corresponds to the major rotational axis of the ellipsoid. For such coils, a simple empirical relationship between the shielding factor and the quantity e has been found when the coils are flexible [e.g., in the case of poly(styrene)]. The relationship is = 3. The effect of the solvent on the coil expansion is described by e [cf. Equation (9-158)]. Thus, Equation (9-159) becomes... 

The discussion of the chain statistics permits one, thus, to have a more quantitative description of a flexible, linear macromolecule. The random coil of a sufficiently long molecule can be compared in mass-density and randomness to an ideal gas at atmospheric pressure. The elastic compression and expansion of gases are caused by changes in entropy. It will be shown below that corresponding behavior exists for the extension and contraction of random-coil macromolecules (entropy or rubber elasticity, see Sect. 5.6.5). Combining many random coils into a... 

Houwink Relationship, p. 1429). The value of the exponent a is affected by the macromolecule conformations Flexible coils have the values between 0.5 and 0.8, the higher values are typical for stiff anisotropic ( rod -like) molecules, and much lower (even negative) values are associated with dense spherical conformations. 

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