Coils expanded chains

Staudinger showed that the intrinsic viscosity or LVN of a solution ([tj]) is related to the molecular weight of the polymer. The present form of this relationship was developed by Mark-Houwink (and is known as the Mark Houwink equation), in which the proportionality constant K is characteristic of the polymer and solvent, and the exponential a is a function of the shape of the polymer in a solution. For theta solvents, the value of a is 0.5. This value, which is actually a measure of the interaction of the solvent and polymer, increases as the coil expands, and the value is between 1.8 and 2.0 for rigid polymer chains extended to their full contour length and zero for spheres. When a is 1.0, the Mark Houwink equation (3.26) becomes the Staudinger viscosity equation. 

The interactions between solvent and polymer depend not only on the nature of the polymer and type of solvent but also on the temperature. Increasing temperature usually favors solvation of the macromolecule by the solvent (the coil expands further and a becomes larger), while with decreasing temperature the association of like species, i.e., between segments of the polymer chains and between solvent molecules, is preferred. In principle, for a given polymer there is a temperature for every solvent at which the two sets of forces (solvation and association) are equally strong this is designated the theta temperature. At this temperature the dissolved polymer exists in solution in the form of a nonexpanded coil, i.e., the exponent a has the value 0.5. This situation is found for numerous polymers e.g., the theta temperature is 34 °C for polystyrene in cyclohexane, and 14 °C for polyisobutylene in benzene. 

The exponent a is a measure of the interaction of the solvent and polymer. It is a function of the shape of the polymer coil in a solution, and usually has a value between 0.5 (for a randomly coiled polymer in a 0 solvent) and 0.8 (when the polymer coils expand in good solvents). The a value is 0 for spheres, about 1 for semicoils, and is between 1.8 and 2.0 for a rigid polymer chain extended to its full contour length. The proportionality constant K is characteristic of the polymer and solvent. The constants K and a are the intercept and slope, respectively, of a plot of log [ 7] versus log Af of a series of fractionated polymer samples. Viscosity average molecular weights he between those of the corresponding... 

A number of studies have considered the nature of the PAn conformation in solution as an effect of solvent/dopant/oxidation state. As described in Chapter 5, the PAn can form either tight coils or expanded chains depending on the nature of the solvent used. This behavior is typical of polymers in either poor or good solvents, but has a significant impact on the electrical properties of conjugated polymers, as described in Chapter 5 for PAn. 

Anilkumar, P., Jayakannan, M., 2007. Single-molecular-s tem-based selective micellar templates for polyaniline nanomaterials control of shape, size, solid state ordering, and expanded chain to coil like conformation. Macromolecules 40,7311-7319. 

In dilute solutions, the single polymer coil expands in the athermal solvent. In a good solvent, the coil will expand more significantly. In contrast, in a poor solvent, the chain units and the solvent undergo a phase separatiOTi under a proper thermodynamic condition. Consequently, the single chain will collapse drastically into a condensed sphere. Therefore, the internal concentration reaches... 

With flexible macromolecules, the coil expands with increasing temperature, probably because solvation increases with temperature. The expansion occurs, however, only up to a limiting value that is given by the skeletal parameters and the optimum degree of solvation. At still higher temperatures, the flexibility of the chain increases because of a decrease... 

A swollen coil (expanded by excluded-volume interactions) is a fractal. The size of any internal chain segment (blob) of g rmits (N < g < N) is g . The mean number of rmits in a sphere of radius r around any unit is Nr for b < r < R, that is, the chain fractal dimension is df= 1/v. The pair correlation function (cf. eqn [18]) of a swollen chain is... 

A number of studies have considered the nature of the polyaniline conformation in solution- effect of solvent/dopant/oxidation state. As described in Chapter 5, the polyaniline can form either tight coils or expanded chains. 

What is especially significant about Eq. (9.68) is the observation that the coil expansion factor a definitely increases with M for good solvents, meaning that-all other things being equal longer polymer chains expand above their 0 dimensions more than shorter chains. Even though the dependence of a on... 

Two extreme types of polyanions can be distinguished. In the first, the main chain is flexible and can assume a large number of different conformations so that the overall shape of the ion depends on the solvent. In some solvents (called bad ), they are rolled up to form a relatively rigid random coil , while in others ( good ) the coil is more or less expanded. This type includes most synthetic polyelectrolytes such as the following acids ... 

M molar mass), where I and III are the tricritical or -regions. Here, the chain molecules exhibit an unperturbed random coil confirmation. In contrast, I and II are the critical or good solvent regimes, which are characterized by structural fluctuations in direction of an expanded coil conformation. According to the underlying concept of critical phenomena, the phase boundaries have to be considered as a continuous crossover and not as discontinuous transitions. 

V, is the molar volume of polymer or solvent, as appropriate, and the concentration is in mass per unit volume. It can be seen from Equation (2.42) that the interaction term changes with the square of the polymer concentration but more importantly for our discussion is the implications of the value of x- When x = 0.5 we are left with the van t Hoff expression which describes the osmotic pressure of an ideal polymer solution. A sol vent/temperature condition that yields this result is known as the 0-condition. For example, the 0-temperature for poly(styrene) in cyclohexane is 311.5 K. At this temperature, the poly(styrene) molecule is at its closest to a random coil configuration because its conformation is unperturbed by specific solvent effects. If x is greater than 0.5 we have a poor solvent for our polymer and the coil will collapse. At x values less than 0.5 we have the polymer in a good solvent and the conformation will be expanded in order to pack as many solvent molecules around each chain segment as possible. A 0-condition is often used when determining the molecular weight of a polymer by measurement of the concentration dependence of viscosity, for example, but solution polymers are invariably used in better than 0-conditions. 

Polymer reactivity can also be affected by the conformation of polymer chains [Imanishi, 1979 Overberger et al., 1973 Overberger and Morimoto, 1971 Pshezetsky et al., 1968], Whether the polymer chain exists in a tight or expanded coil can influence the accessibility of polymer functional groups and the local concentration of a small-molecule reactant. 

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