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shape. Therefore, quantities like the radius of gyration, which can be obtained
by experimental techniques, are average values. The time average for a
single molecule will normally be identical to the average of a large number of
molecules (of the same DP). The latter is commonly referred to as the
ensemble average.
Figure 43
Figure 11 illustrates the constantly changing shape of flexible polymers
(based on a simplified computer simulation of a DP 500 chain). Each of the
chains has an irregular shape, but on average – for a large number of
molecules – they are indeed spherical. A hint comes from an overlay of the
same 8 molecules (Figure 12). Imagine 1000 chains overlaid.
All linear chains will normally adopt the shape of flexible coils because this
state has the highest entropy. When many proteins and other biopolymers
fold to form very ordered, usually compact structures with well-defined
shapes, this is because of additional forces, manly attractive forces, between
monomers. More about this later.
Figure 44