Excluded volume shielding

Despite their distinct advantages, on-line SPE and column-switching proce-dures do not always represent ideal separation techniques. In many cases, only a small number of samples can be analyzed before contamination of the precolumn by proteins occurs. Alternative techniques that prevent the adsorption of macromolecules onto column packings and allow direct injection of sample extracts are those based on use of specific LC columns. Shielded hydrophobic phase (27), small pore reversed-phase (28), and internal surface reversed-phase (29, 30) columns can be used to elute proteins in the excluded volumes, allowing small... 

But a double bond located inside a large branched macromolecule also has less probability of reacting than one located at the periphery this is called the shielding effect. For this reason, spatial correlations due to excluded volume can also decrease the apparent reactivity of pendant double bonds. 

When account is taken of the excluded volume effects, one has also to take into account the possible effect of the shielding of the inner segments of the macromolecular coil, the latter effect being the greater the longer the macromolecule, so that the expression for the anisotropy coefficient, which has to be covariant in relation to subdivisions into subchain, assumes the form... 

For such moderately longer alkyl chains (i.e., n = 4 and 8), due to the low degree of van der Waals interactions possible between the attached intermediate length alkyl chains, there may be an excluded volume for the folded alkyl chains to be relatively more mobile, disordered, and "liquid-like than the self-assembling,crys-tal-like n 18 case. Therefore, there may be a shielding effect of the folded chains... 

Figure 4.18. The polymer chain contracts with an increasing concentration becanse of shielding of excluded volume. The radius of gyration decreases in a power of monomer density p with an exponent of -1/8.

At the upper limit of the semidilute regime, there will be little distinction between the good solvent and the theta solvent, as the excluded volume is shielded... 

In the semidilute solution, the hydrodynamic interactions are shielded over the distance beyond the correlation length, just as the excluded volume is shielded. We can therefore approximate the dynamics of the test chain by a Rouse model, although the motion is constrained to the space within the tube. In the Rouse model, the chain as a whole receives the friction of N, where is the friction coefficient per bead. When the motion is limited to the curvilinear path of the primitive chain, the friction is the same. Because the test chain makes a Rouse motion within the tube, only the motion along the tube survives over time, leading to the translation of the primitive chain along its own contour. The one-dimensional diffusion coefficient for the motion of the primitive chain is called the curvilinear diffusion coefficient. It is therefore equal to Dq of the Rouse chain (Eq. 3.160) and given by... 

Olaj and Zifferer [229] have performed Monte Carlo simulations in which they placed 300 polymer chains in a lattice, considering excluded volume effects. From the obtained configurations they evaluated the shielding factor which describes how severely the presence of a polymer coil retards the termination of its own radical compared to small (unshielded) radicals. For chains of unequal size Olaj and Zifferer showed that the geometric mean model provided a reasonable mathematical description of their results, although the harmonic mean model. 

Interactions between parts of the chain separated by more than 5 chain segments are neglected as long-distance excluded-volume interactions are effectively shielded for the mean chain. 

A useful qualitative way of looking at the question of what is, as well as addressing many other problems in semi-dilute systems, is in terms of bloos, a term introduced by de Gennes. Let us regard the bonded units, expected to be within distance of each other, as a blob. The number of monomers in a blob, g, is given by the distance-number relation of excluded volume theory, since these units are not shielded from excluded volume forces ... 

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