Coil Molecules in Solution

To obtain some idea of the structure of macromolecules covalently bound to the surface of a solid, we may compare the space requirement of the macromolecule as a random coiled molecule in solution with that on the surface. For this purpose, the root-mean-square end-to-end distance in the relevant solvent is obtained from the molecular weight of the macromolecule and hence the largest cross section, of the molecule in this solvent may be calculated. 

One thing that is apparent at the outset is that polymer molecules in solution are very different species from the rigid spheres upon which the Einstein theory is based. On the other hand, we saw in the last chapter that the random coil contributes an excluded volume to the second virial coefficient that is at least... 

The typical shape of most polymer molecules in solution is the random coil. This is due to the relative ease of rotation around the bonds of the molecule and the resulting large number of possible conformations that the molecule can adopt. We should note in passing that where rotation is relatively hindered, the polymer may not adopt a random coil conformation until higher temperatures. 

According to the interpretation given above, the intrinsic viscosity is considered to be proportional to the ratio of the effective volume of the molecule in solution divided by its molecular weight. In particular (see Eq. 23), this effective volume is represented as being proportional to the cube of a linear dimension of the randomly coiled polymer chain,... 

Size exclusion chromatography (which is also known as gel permeation chromatography) is based on the premise that a polymer molecule in solution adopts a random coil configuration, which encompasses a volume (known as its hydrodynamic volume) that is proportional to its molecular weight. We fractionate polymers according to their hydrodynamic volumes to generate a molecular weight distribution plot. 

The solution properties of dendrigraft polybutadienes are, as in the previous cases discussed, consistent with a hard sphere morphology. The intrinsic viscosity of arborescent-poly(butadienes) levels off for the G1 and G2 polymers. Additionally, the ratio of the radius of gyration in solution (Rg) to the hydrodynamic radius (Rb) of the molecules decreases from RJRb = 1.4 to 0.8 from G1 to G2. For linear polymer chains with a coiled conformation in solution, a ratio RJRb = 1.48-1.50 is expected. For rigid spheres, in comparison, a limiting value RJRb = 0.775 is predicted. 

It is now useful to consider how we may define the concentration of polymers in solution. Dilute solutions are ones in which the polymer molecules have space to move independently of each other, i.e. the volume available to a molecule is in excess of the excluded volume of that molecule. Once the concentration reaches a value where there are too many molecules in solution for this to be possible, the solution is considered to be semi-dilute.8 The concentration at which this occurs is denoted by c. For convenience c is defined as the concentration when the volumes of the coils just occupy the total volume of the system, i.e. 

In practice, the emission anisotropy of luminescent molecules in solution is considered to be proportional to the viscosity of the medium, except in the case where structural reasons arise, for instance helix-coil transition, cross-linking in polymer systems etc... (18-21). Therefore, if there is only the effect in viscosity, the mobility of the marker must be higher in the case of the compact complex system which have a very low viscosity. 

The peculiarity of this expression, however, is that it does not make sense for dilute solutions of Gaussian coil molecules. In fact, the free-draining case is characterized by the limit of infinetely smaE friction coefficient . For this case, the contributions of the chain molecules to the viscosity of the solution becomes zero. 

If a polymer molecule in solution behaves as a random coil, its average end-to-end distance is proportional to the square root of its extended chain length (see page 25) - i.e. proportional to Ai 5, where Mr is the relative molecular mass. The average solvated volume of the polymer molecule is, therefore, proportional to M 5 and, since the unsolvated volume is proportional to A/r, the average solvation factor is proportional to (i.e. Af 5). The intrinsic viscosity of... 

Three different viewpoints on the humic substances structural conformation are actually reported in the literature. One suggests that HS are macromolecular and assume random coil conformations in solution (Swift, 1999) a second proposes that HS are molecular associations of relatively small molecules held together by weak interaction forces, thus forming a supramolecular structure (Piccolo and Conte, 1999) a third considers that HS are in solution as micelles or pseudomicellar structures (Wershaw, 1999). Viewpoints two and three could be broadly considered to be under the same umbrella (Clapp and Hayes, 1999). 

Apart from this excluded volume effect, coil size in solutions is affected by interaction between a coil and a solvent. Solvent molecules penetrate... 

If one traces a longer stretch of a DNA molecule in solution, a clear divergence from linearity becomes evident. Thermally induced structural fluctuations allow a bending of DNA, which is why long DNA molecules are described as a random coil. This bending of the DNA occurs in molecules with a length of more than ca. 200 bp. 

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