Persistence length, description

This result may be compared with Eq. (9.7), from which it follows that the persistence length is equal to half the length of a statistical chain element or Kuhn length ap = i A. This representation of the wormlike chain is of particular importance for the description of stiff polymers. 

The OxDNA model provides a good representation of the DNA thermodynamics, while also providing an accurate description of the structural and mechanical properties of dsDNA B-DNA and ssDNA. Moreover, the ssDNA correctly describes the formation of hairpins or other ssDNA secondary structures through the stacking interactions of the intra-strand sites. This model accurately reproduces the persistence lengths of the ssDNA and dsDNA and... 

Statistical properties of an unperturbed HW chain in equilibrium are determined with five parameters chain length L, ao,l3o,Ko, and tq (the latter four characterize U s) of the chain). This should be contrasted to the fact that only two parameters L and q are needed for the description of these properties of an unperturbed wormlike chain. In adapting the HW chain to actual polymers, the shift factor Ml(= M/L), instead of L, may be chosen as a parameter since M can be determined experimentally. Thanks to eq 2.10 the stiffness parameter (2A) may be used for ao. For HW chains we have no equation corresponding to eq 2.2. Hence (2A) may not be equated to q according to eq 2.14. It should be noted that the persistence length q is the concept associated only with wormlike chains. The Poisson ratio ao of the HW chain is expressed in terms of o and j3o as... 

The variations of S(0 and N(0 versus time are usually presented as log-log plots. The z and w values give a quantitative description of the flocculation processes under the conditions of the space dimension d, the biopolymer persistence length or rigidity /p, biopolymer size 4 and particle/biopolymer concentration ratio r. Hence z(d, /p, k, x) and w(d, /p, 4, x) values can be calculated for various systems [80], and comparison between experiments and computer models to isolate the key parameters controlling both structure and kinetics is possible upon parameterization of the model with experimental data. 

The power law exponent fell between the values of 0.5 observed for a 0 solvent and 0.6 for a thermodynamically good one, confirming the above description of tetrahydrofiiran as a moderately good solvent. Poly(3-hexylthiophene) macromolecules exist as isolated flexible-coil chains in a dilute solution with a persistent length of 2.4 0.3 nm. 

When one fits the Hory-Huggins theory to experiment [7], nontrivial dependence of Hory-Huggins interaction parameters on temperature and volume fractions also result, but might have other reasons than those noted above in particular, it is important to take into account the disparity between size and shape of effective monomers in a blend, and also the effects of variable chain stiffness and persistence length [25, 26]). To some extent, such effects can be accounted for by the lattice cluster theories [27-30], but the latter still invokes the mean-field approximations, with the shortcomings noted above. In the present article, we shall focus on another aspect that becomes important for the equation of state for polymer materials containing solvent pressure is an important control parameter, and for a sufficiently accurate description of the equation of state it clearly does not suffice to treat the solvent molecules as vacant sites of a lattice model. In most cases it would be better to use completely different starting points in terms of off-lattice models. 

Finally, some rather recent devdopments must be noted. Several years ago, Yamakawa and co-workers [25-27] developed the wormlike continuous cylinder model. This approach models the polymer as a continuous cylinder of hydrodynamic diameter d, contour length L, and persistence length q (or Kuhn length / ). The axis of the cylinder conforms to wormlike chain statistics. More recently, Yamakawa and co-workers [28] have developed the helical wormlike chain model. This is a more complicated and detailed model, which requires a total of five chain parameters to be evaluated as compared to only two, q and L, for the wormlike chain model and three for a wormlike cylinder. Conversely, the helical wormlike chain model allows a more rigorous description of properties, and especially of local dynamics of semi-flexible chains. In large part due to the complexity of this model, it has not yet gained widespread use among experimentalists. Yamakawa and co-workers [29-31] have interpreted experimental data for several polymers in terms of this model. 

In the concentrated and marginal regimes of fig 5,3 a mean-field description, which neglects any spatial fluctuations, is appropriate. In these regimes, the solution is homogeneous and there is no chain-length dependence. Neither does the persistence p of the chains play a role since the Floiy-Huggins expressions do not contain the chain flexibility. This is so because the flexibility is assumed to be the same in the solution and in the reference state, so that p cancels in the entropy difference between the two states. 

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