Flexible coil macromolecules solutions

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 ... 

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 ... 

Usually, dilute polymer solutions are isotropic systems, i.e. macromolecular chains can exist in these solutions independently of each other with a random distribution of orientations of the long axes of coils. The solutions of flexible-chain polymers remain isotropic when the solution concentration increases whereas in concentrated solutions of macromolecules of limited flexibility the chains can no longer be oriented arbitrarily and some direction of preferential orientations of macromolecular axes appears, i.e. the mutual orientations of the axes of neighboring molecules are correlated. This means that... 

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. 

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. 

The power law exponent fell between the values of 0.5 observed for a 0 solvent and 0.6 for a thermodynamically good one, confirming the above description of tetrahydrofiiran as a moderately good solvent. Poly(3-hexylthiophene) macromolecules exist as isolated flexible-coil chains in a dilute solution with a persistent length of 2.4 0.3 nm. 

A desirable property of non-ionic xerogellants is their natural insensitivity to the presence of ionic solutes in the fluid being absorbed. Unlike polyelectrolytes, non-ionics can gel as much urine as pure water. A critical impediment to the effective utilization of the poly(ethylene-oxide) xerogellants in disposable diapers is the soft, almost flowable, nature of the gel. Even fully hydrated, the polyether macromolecule is a flexible coil. This flexible structure is manifested as weakness of the highly swollen gels. Increasing the crosslink density stiffens the gel but reduces swellability. 

The rheological behaviour of polymeric solutions is strongly influenced by the conformation of the polymer. In principle one has to deal with three different conformations, namely (1) random coil polymers (2) semi-flexible rod-like macromolecules and (2) rigid rods. It is easily understood that the hydrody-namically effective volume increases in the sequence mentioned, i.e. molecules with an equal degree of polymerisation exhibit drastically larger viscosities in a rod-like conformation than as statistical coil molecules. An experimental parameter, easily determined, for the conformation of a polymer is the exponent a of the Mark-Houwink relationship [25,26]. In the case of coiled polymers a is between 0.5 and 0.9,semi-flexible rods exhibit values between 1 and 1.3, whereas for an ideal rod the intrinsic viscosity is found to be proportional to M2. 

The transitions of the coil-globule type were considered not only in the usual space, but also in the space of monomeric units orientation, where such transition is equivalent to the nematic liquid crystal ordering [60,61]. Such an approach using the formalism developed by I.M. Lifshitz has led to the creation of the theory of liquid crystal ordering in the solutions of semi-flexible macromolecules [62,63]. 

It should be noted that, due to the difficulty of perfect mutual packing of two flexible polymer chains, the complex structure is imperfect and, along with complexed parts, there may exist imperfect ones such as loops. Mutual screening of hydrophilic parts of the interacting macromolecules leads to strong hydrophobization of the polymer complex in aqueous solution and its coiling up into a compact structure. 

Most synthetic polymers in which the monomer units are connected via single bonds have rather flexible chains. The bond torsion energy is relatively small and the units can rotate around their bonds [14,30,31]. Each molecule can adopt a large number of energetically equivalent conformations and the resulting molecular geometry is that of a statistical coil, approximately described by a Gaussian density distribution. This coil conformation is the characteristic secondary structure of macromolecules in solution and in the melt. It is entropically favoured because of its... 

Chain rigidity can cause partial ordering of the macromolecules. While flexible macromolecules yield amorphous solutions and melts in which the individual coils interpenetrate each other, semiflexible macromolecular systems order in nematic domains [43],... 

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