Model Kratky-Porod

The last relation shows that a long macromolecule rolls up into a coil at high temperatures. The smaller the elasticity coefficient a is, the more it coils up. Another name for the model of flexible thread is the model of persistence length or the Kratky-Porod model. The quantity a/T is called the persistence length (Birshtein and Ptitsyn 1966). 

The worm-like chain model (sometimes called the Kratky-Porod model) is a special case of the freely rotating chain model for very small values of the bond angle. This is a good model for very stiff polymers, such as double-stranded DNA for which the flexibility is due to fluctuations of the contour of the chain from a straight line rather than to trans-gauche bond rotations. For small values of the bond angle ( < 1), the cos 9 in Eq. (2.23) can be expanded about its value of unity at = 0 ... 

This is called the Kratky-Porod model, and the length (2A) is referred to as the persistence length. 

Equation (8.173) indicates the analogy between the change of (.y) of the Kratky-Porod model and the time evolution of u(i) in rotational Brownian motion both processes are Gaussian with the constraint 1,2 = 1,35 pjqjj gqn (g.i74) it can be shown that for small s... 

We emphasize that these deviations from the Kratky-Porod model that occur for semiflexible polymers both in equilibrium and in their response to stretching forces, were not properly noticed in most of the experiments. However, in analyzing data one normally does not have strictly monodisperse chains, and neither p nor L are independently known both parameters are usually used as adjustable fitting parameters. Because fp depends on d, and is also affected by solvent conditions, and for strongly stretched real chains other effects (related to the local chemical structure of the effective monomeric units) come into play, this failure is not surprising. However, some of the confusion over the actual values of p that... 

In the limit, the conformation of the chain is not zigzag bnt rather a smooth curve in a three-dimensional space, as illustrated in Figure 1.43. This model is called a wormlike chain or a Kratky-Porod model. A continuous... 

It was shown that with increasing internal chain stiffness the effective exponent y for Le — crosses over from a value of one toward two as the internal stiffness of a chain increases. The quadratic dependence of the electrostatic persistence length on the Debye radius for the discrete Kratky Porod model of the polyelectrolyte chain was recently obtained in [65]. It seems that the concept of electrostatic persistence length works better for intrinsically stiff chains rather than for flexible ones. Further computer simulations are required to exactly pinpoint the reason for its failure for weakly charged flexible polyelectrolytes. 

Another name for the model of flexible thread is the model of persistence length or the Kratky-Porod model. The quantity a/T is called the persistence length [12]. 

This is the full expression for the mean square end-to-end distance in the Kratky-Porod model. The limits of small persistence length with respect to... 

Therefore, the Kratky-Porod model reduces to the rod conformation for ip L, and the freely-jointed random-walk conformation for ip <[Pg.33]

When the end-to-end distance of the chain corresponds to its contour length, this macromolecule can be identified with a rod-like chain. Thus, the Kratky-Porod model is appropriate to describe the transition from a rigid rod to a flexible chain. 

Chain with local stiffiiess Kratky-Porod model. 

The simplest model for free (or linker) DNA is the wormlike-chain or Kratky-Porod model [48], It is based on the assumption that changing the contour of a linear chain by bending costs energy. If we describe the contour of length I by introducing the contour parameter s e [0, /], an infinitesimal segment of the contour (arc length) can be expressed in local coordinates by... 

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