Polyelectrolyte chain stiffness

Cooper, C.L., et al. Effects of polyelectrolyte chain stiffness, charge mobility, and charge sequences on binding to proteins and micelles. Biomacromolecules 7(4), 1025-1035 (2006)... 

The conformations adopted by polyelectrolytes under different conditions in aqueous solution have been the subject of much study. It is known, for example, that at low charge densities or at high ionic strengths polyelectrolytes have more or less randomly coiled conformations. As neutralization proceeds, with concomitant increase in charge density, so the polyelectrolyte chain uncoils due to electrostatic repulsion. Eventually at full neutralization such molecules have conformations that are essentially rod-like (Kitano et al., 1980). This rod-like conformation for poly(acrylic acid) neutralized with sodium hydroxide in aqueous solution is not due to an increase in stiffness of the polymer, but to an increase in the so-called excluded volume, i.e. that region around an individual polymer molecule that cannot be entered by another molecule. The excluded volume itself increases due to an increase in electrostatic charge density (Kitano et al., 1980). 

The analysis described above is useful for modelling colligative properties but does not address polyelectrolyte conformations. Polyelectrolyte conformations in dilute solution have been calculated using the worm-like chain model [103,104], Here, the polymer conformation is characterized by a persistence length (a measure of the local chain stiffness) [96]. One consequence of the... 

In pure polyelectrolyte solutions a decreasing polyelectrolyte concentration cp is followed by an increase of the Debye length 1D and an increase in chain stiffness. Applying scaling concepts [109] and considering an electrostatic contribution to the persistence length Lp [110-113] various concentration regimes could be identified for polyelectrolyte solutions. Odijk derived different critical con-... 

The molecular characterization of polyelectrolytes in general, and of DADMAC polymers in particular is complicated for several reasons. First, in aqueous solution the individual properties of the macromolecules are dominated by Coulom-bic interactions. Therefore, the resulting polyelectrolyte effects have to be suppressed through the addition of low molecular electrolyte, such as NaCl. The increase of the ionic strength results in a decrease of the chain stiffness of the polyelectrolyte molecules (see Sect. 5). The chains then revert to the coil dimensions of neutral macromolecules in dilute solutions. However, problems may still arise, particularly since the mode of action of these effects is quite different in various characterization methods [27]. 

Ha, B. Y., and Thirumalai, D. (2003). Bending rigidity of stiff polyelectrolyte chains A single chain and a bundle of multichains. Macromolecules 36, 9658—9666. 

Theories of conformations of polyelectrolytes fall into two groups. In the first group [32-34] the chain is assumed to be a flexible chain and the consequence of electrostatic interaction is calculated. In the second category [35-42], the chain is assumed to be a stiff chain and calculations are performed to obtain the effect of the electrostatic interaction between charges on the chain backbone. To date, there is no satisfactory theory in the literature to describe the electrostatic effect on conformations of polyelectrolyte chains with arbitrary intrinsic stiffness. In the following we briefly outline the developments for both groups of theories. 

Fig. 9. The segment concentration distribution between plates at a small distance for various stiffnesses of the polyelectrolyte chains. D=ll A, and the other parameter values used in the calculation are as for Fig. 8. (1) a =4...

The stiffness of the chains, represented by the term Hi) in Eq. (2), together with the electrical and van der Waals interactions determine the conformation of the polyelectrolyte chains and hence their charge and segment concentration distributions in solution. The chains become more extended with increasing stiffness. As a result, at short distances, the force between plates is repulsive for... 

Maurstad, G., Danielsen, S., and Stokke, B.T. (2003). Analysis of compacted semiflexible polyanions visualized by atomic force microscopy Influence of chain stiffness on the morphologies of polyelectrolyte complexes. J. Chem. B, 107(32) 8172-8180. 

Borochov N, Eisenberg H. Stiff (DNA) and flexible (NaPSS) polyelectrolyte chain expansion at very low salt concentration. Macromolecules 1994 27 1440-1445. 

In the absence of a cooperative conformational transition, for many polysaccharide polyelectrolytes a linear dependence of [rj] upon I Ms observed, with the slope diminishing with the charge density associated to the polysaccharide chain (Figure 12.2.13). A theory has been presented for an estimation of the relative stiffness of the molecular chains by Smidsrod and Haug, which is based on the Fixman s theory and Mark-Houwink equation. The chain stiffness parameter is estimated from the normalized slope B of [r ] vs. the inverse square root of the ionic strength ... 

Table 4.2 Equilibrated conformations from Monte Carlo simulations of complexes composed of a semi-flexible polyelectroly te and a single colloidal particle as a function of the solution ionic strength I and polyelectrolyte intrinsic rigidity k ng- By increasing the chain stiffness, solenoid conformations are progressively achieved at the particle surface, whereas an increase in ionic strength leads to the desorption of the polyelectrolyte.

Kayitmazer, A. B., Seyrec, E., Dubin, P. L., and Staggemeier, B. A. 2003. Influence of chain stiffness on the interaction of polyelectrolytes with oppositely charged micelles and proteins. J. Phys. Chem. B. 107 8158-8165. 

Narambuena CF, Leiva EPM, Chavez-Paez M et al (2010) Effect of chain stiffness on the morphology of polyelectrolyte complexes. A Monte Carlo simulation study. Polymer 51 3293-3302... 

Thus, for lower salt concentrations, a semiflexible polyelectrolyte chain is fully stretched. Note that eqn [117c] is correct only for suffidentiy stiff polyelectrolyte chains with the bare persistence length lp°>b/up (see Section 1.05.3.1). 

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. 

Fig. 2 Conformations of semiflexible polyelectrolyte chains adsorbed on a spherical colloidal particle for various salt concentrations C and stiffness iang (from [95]). With increasing stiffness, the adsorbed polyelectrolyte undergoes conformational changes from tennis ball-like patterns to solenoid-like structures. The adsorption threshold depends on salt concentration and polyelectrolyte stiffness. More details of the underlying Monte Carlo simulations are provided in Ref. [95]...

Experimentally, a large number of similar studies on the influence of chain stiffness, colloid charge density, and salt concentration have been performed [43, 44, 121-138]. Some theoretical trends regarding the effect of surface curvature and salt concentration on critical adsorption and polyelectrolyte-colloid complexation are supported by experimental observations. These studies, however, also revealed a number of discrepancies and additional physical parameters to be taken into account, as compared with the outcomes of theoretical studies and computer simulations. 

An example of the way the incorporation of a charged monomer in a copolymer chain affects the copolymer behavior, in terms of polyelectrolyte behavior and chain stiffness, is presented in the following [47]. 

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