Unrestricted join

It is appropriate to consider first a hypothetical chain consisting of linkages of length I joined in linear sequence without any restrictions whatever on the angles between successive bonds. Thus, for the case to be discussed d may assume all values from 0 to tt with equal probability and 0 is likewise unrestricted. Only the bond length is fixed. Of... 

The simplest model of this type is called the freely jointed chain, and is illustrated in Figure 2.21. In it, the skeletal bonds are joined end to end, but are completely unrestricted in direction. This is clearly a situation not found in a real polymer (bond angles in real polymers are relatively fixed). It is also assumed that the chains have zero cross-sectional area, that is that the chains are unperturbed by excluded-volume effects. These effects arise because atoms of a chain exclude from the space they take up all other atoms from all other chains. They are related to excluded-volume effects occurring even in systems as simple as real gases. The expression for the mean-square end-to-end distance of such an idealized chain is particularly simple ... 

Additional theoretical approaches include the biellipsoidal model calculations of Bendler et ai 2 i-2 9 which the A and B chains are modelled as smooth ellipsoidal density clouds. The method is to generate an unrestricted (i.e. intersecting) random walk for each block and use this to obtain a Gaussian ellipsoidal density distribution for the two blocks. These two clouds are joined at their chain ends and then allowed to pivot around the bonding point. In order to obtain the orientation, a particular configuration is Boltzmann weighted by a mean field potential given by iS = AA+ BB+ AB Where... 

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