Electrostatic persistence length

If the chain is uniformly charged, consideration (Odijk 1977, Skolnick and Fixman 1977) of electrostatic repulsion within the Debye-Huckel approximation leads to an additional term for Ub/ksT, which is proportional to 0 /2L. Therefore, the coefficient of the additional contribution can be identified as a persistence length, 

---

Complicated theories of ionic gel swelling [99, 113, 114] must inevitably take into account the real electrostatic interactions, the finite extensibility of chains, as well as the electrostatic persistence length effect. Their application is most advisable in the case of strongly charged hydrogels [114]. 

The viscosity of xanthan solutions is also distinct from that of flexible polyelectrolyte solutions which generally shows a strong Cs dependence [141]. In this connection, we refer to Sho et al. [142] and Liu et al. [143], who measured the intrinsic viscosity and radius of gyration of Na salt xanthan at infinite dilution which were quite insensitive to Cs ( > 0.005 mol/1). Their finding can be attributed to the xanthan double helix which is so stiff that its conformation is hardly perturbed by the intramolecular electrostatic interactions. In fact, it has been shown that the electrostatic persistence length contributes only 10% to the total persistence length even at as low a Cs as 0.005 mol/1 [142]. Therefore, the difference in viscosity behavior between xanthan and flexible polyelectrolyte... 

The alternative method [46] of analyzing the data is based on the treatment by Odijk and Houwaart [36] of the excluded volume effect on the electrostatic stiffening of semi flexible chains. The total persistence length lt of a stiff polyelectrolyte is the sum of the intrinsic persistence length lp=hl2 and the electrostatic persistence length le,... 

Fig. 5 Electrostatic persistence length of a flexible polyelectrolyte chain as function of k/v b for the Bjerrum lengths lB/b=0.1, 0.5, 1.0 (bottom to top). The chain length is N=1000. The slopes of the straight lines are -1 and -2, respectively...

This equation tells us that, since is proportional to the molar salt concentration (see, for example, [3.5.7]), the electrostatic persistence length (or chain stiffness) decreases Inversely proportionally with Increasing salt concentration. In fig. 5.5 we present, as an experimental example, the salt dependence of for DNA, as measured by several techniques. For comparison, the theoretical dependence based on [5.2.24] is also shown. 

In the case of intrinsically rigid polyelectrolytes, such as DNA, experimental results [67] show that electrostatic persistence length calculated from the data shows no unique power law dependence on cs. Compared to the OSF theory [60,61], a much better agreement with these data was achieved later by the calculation of Le via numerical solution of the Poisson-Boltzmann equation for a toroidal polyion geometry [59,62], These calculations showed that the exponent ft in the scaling Rg cs p varies from -1 to -1/4 upon increase of cs. A breakdown of the OSF theory for flexible chains (unless Le /.p) was indicated by taking into account fluctuations in the chain configuration [63]. 

Skolnick J, Fixman M. Electrostatic persistence length of a wormlike polyelectrolyte. Macromolecules 1977 10 944-948. 

Fenley, M. O. Manning, G. S. Olson, K. W. Electrostatic persistence length of a smoothly bending polyion computed by numerical counterion condensation theory. J. Phys. Chem. 1992 96 3963—3969. 

Fig. 2 Snapshots of Monte Carlo simulations of a polyelectrolyte chain of N = 100 monomers of size b, taken as the unit length. In all simulations the bare persistence length is fixed at to/b =, and the screening length and the charge interactions are tuned such that the electrostatic persistence length (f osf) is constant and fosp/h = 100, see Eq. (18). The parameters used are (a) k jb = and t Lb(o = (b) K fb = n/200 and b o = 2 (c) K lb = /m and b o = 1A and (d) K jb = V3200 and = 1 /8. Noticeably, the weakly charged chains crumple...

The electrostatic persistence length, first derived by Odijk and independently by... 

It is valid only for polymer conformations that do not deviate too much from the rodlike reference state. The electrostatic persistence length gives a sizable contribution to the effective persistence length only for osF > fo- This is equivalent to the condition... 

The electrostatic persistence length is visualized in Fig. 3, in which we present snapshots of Monte-Carlo simulations of a charged chain consisting of 100 monomers of size b. The bare persistence length was fixed at fo = h, and the charge-interaction parameter was chosen to be = 2,... 

Combining Eqs. (18) and (20) gives the effective electrostatic persistence length for a string of electrostatic blobs. 

In solution, we have considered the scaling behavior of a single PE (Sect. 2.7.3.1). The importance of the electrostatic persistence length was stressed. The Manning condensation of counterions leads to a reduction of the effective linear charge density (Sect. 2.7.3.1.1). Excluded volume effects are typically less important than for neutral polymers (Sect. 2.7.3.1.2). Dilute PE solutions are typically dominated by the behavior of the counterions. So is the large osmotic pressure of dilute PE solutions due to the entropic contribution of the counterions (Sect. 2.7.3.2). Semidilute PE solutions can be described by the RPA, which in particular yields the characteristic peak of the structure factor. 

To model the first of these effects the OSF approach splits Zp into two contributions, one assigned from the equivalent neutral chain, defining the bare or intrinsic persistence length Zo, and one defined by electrostatic interactions, defining the electrostatic persistence length U,... 

Figure 18 Schematic representation of the conformation of a polyelectrolyte chain for calculation of the OSF electrostatic persistence length. Reproduced with permission from Dobrynin, A. V. Rubinstein, M. Prog. Polym. Sci. 2005,30,1049-1118. " Copyright 2005, Elsevier.

---