Nonideal polymer chains and theta solvents in .NET Integrating Data Matrix in .NET Nonideal polymer chains and theta solvents

3.5 Nonideal polymer chains and theta solvents use none none creation todraw none for none Microsoft Official Website In the above analysis of ran none none dom chains, the only intersegment interactions that were considered were constraints on bond angles. Two additional kinds of interaction are also important. They strongly influence the conformations available to a molecule, but the mathematical treatment is much more difficult.

The first of these is attractive interactions such as hydrogen bonds and hydrophobic forces ( 2), which pull distant segments together and tend to make a chain more compact. The second is steric repulsion (also discussed in 2), which prevents two segments from occupying the same space at the same time. This is referred to as the excluded volume effect, and tends to work against the attractive forces to spread a chain out.

Exact mathematical solutions to models with these interactions have not been found. This makes the random-coil model especially important as a reference point. From this perspective random-coil.

CONFORMATIONS OF MACROMOLECULES models are referred to as id none for none eal chains, and the more realistic but approximate models that incorporate attractive and excluded volume interactions are referred to as nonideal chains. For the excluded volume effect a number of approximate treatments indicate that the rms end-to-end distance is proportional to a fractional power of the number of segments..

q R N2 / N  (3:25). For an ideal chain  1/2 ( none none Section 3.3). The theories for the excluded volume effect give values somewhat greater than 1/2;  3/ 5 is typical.

A theory by De Gennes (1972) gave  0.5975. These theoretical results make the reasonable point that when a polymer is not allowed to overlap onto itself it will spread out further; the ends will on average be separated by a greater distance.

Thus, the excluded volume effect tends to increase the effective size of the molecule relative to that expected for an ideal chain. The set of all configurations available to a chain subject to excluded volume is necessarily a subset of the configurations available to the corresponding ideal chain. Excluded volume reduces the total number of configurations, and this means that the randomcoil model overestimates the configurational entropy of a polymer.

If we consider an ideal chain strung out randomly on a cubic lattice (recall the final comments about the rotational isomer model in Section 3.3), the number of possible configurations would be 6N. This follows because each site has six neighboring sites, so that each new segment can be added in six ways.

Computers have been used to count the number of nonoverlapping configurations of a chain on a cubic lattice, and the result was empirically fitted by the expression N1/ 64.68N (Chan and Dill, 1991; Camacho and Thirumalai, 1993). Dividing 6N by this expression indicates that the ideal chain model on a cubic lattice overestimates the true number of configurations by a factor of 1.

28N/N1/ 6. We could easily improve the random-coil model by realizing that the value six, the number of ways to add a new segment to a lattice, must include at least one site already occupied. Subtracting this one site is clearly an improvement, and this leaves five ways to add a new segment.

There are then 5N configurations, and this simple improvement of the random-coil model overcounts by a factor of 1.07N/N1/ 6. Attractive interactions between segments have the opposite effect.

They tend to draw the segments together and make the molecule more compact. They thus oppose the spreading out effect of excluded volume interactions. This depends strongly on the choice of solvent.

If the polymer segments are weakly soluble, then the segments will clump together to reduce the unfavorable interactions with the solvent. On the other hand, a good solvent will make the chain more extended. A solvent can be chosen to make intersegment attractions counteract the excluded volume repulsions.

If the right balance is found,.
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