Gaussian chains conformational distribution

Ideal behaviour for chain conformation is represented by a Gaussian distribution W(r) of end-to-end distances. Excluded volume effects give a much different end distance distribution function. Figure 1, with the biggest differences operating on chains which happen to have their chain ends in proximity (4). 

Gaussian segment distribution for PUMA. Since the presence of the naphthalene groups could perturb the average chain conformation,... 

In order to decide whether cellulose molecules have an extended or a folded-chain conformation in the native cell-wall, Muggli and co-workers (see also. Ref. 10) devised an interesting experiment based on determination of the molecular-weight distribution in ramie microfibrils before and after they had been cut into 2-ju.m sections. As shown in Fig. 14, should the molecules have an extended conformation, many of the molecular chains would be cut in a random fashion (Gaussian distribution), resulting in substantial diminution in the molecular weight. On the other hand, in the folded conformation, a few macromolecules would be cut, but the rest would retain their... 

For the non-Gaussian case, the distribution in angle of the individual chain segments is calculated first. Then, the probability of a given conformation is determined. Finally, the most probable distribution is derived by differentiation, as in the Gaussian case. 

On the other hand, according to the Boltzmann relationship and the Gaussian distribution of chain conformations, the conformational entropy loss is proportional to kT(RIRof. The total conformation entropy loss of the single coil is thus scaled as... 

Fig. 4.15a. Similar to Flory s mean-field treatment, each blob has the volume repulsive energy kTd (Nlg)IR//, and the overall volume repulsive energy kTcf NI gf IRii. On the other hand, the entropic elasticity of chain conformations formed by blobs still follows the Gaussian distribution, as kTR// l(d Nlg). In the thermody-...

A Gaussian chain is self-similar. This means that, for example, a chain of 2N units has the same conformational distribution as an N-chain if (i) we make every other unit of the 2N-chain invisible and (ii) shrink all position vectors of this... 

Random-flight Chain Conformations Are Described by the Gaussian Distribution Function... 

Equation (32.15) gives you the relative numbers of all JV-mer chain conformations that begin at the origin of the x-axis and end at x. The Gaussian distribution has a peak at x = 0, implying that most of the chains have about as many -H steps as - steps, as we noted in Chapter 4. 

The second entropic contribution, Asp conf accounts for a decrease in entropy which follows from a change in the chain conformations. The Gaussian conformational distribution found in the homogeneous phase cannot be maintained in the microphase-separated state. Formation of a layer structure leads, for steric reasons, necessarily to a chain stretching which in turn results in a loss in entropy. For a qualitative description we employ the previous Eq. (2.93)... 

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