Polyions rodlike

Ray, J. and Manning, G.S. (1994) An attractive force between two rodlike polyions mediated by the sharing of condensed counterions. Langmuir, 10,2450-2461. 

In a polyelectrolyte, a chain of linked, closely spaced charged groups can exist. The accelerating factor may be related to the charge spacing, the concentration, or the radius of rodlike polyions (141), with variation in activation entropy usually responsible for the rate change. The influences can be explained by electrostatic interactions between the... 

In this section, we discuss the interaction of a counterion and a rodlike segment of a polyion as a function of separation distance r between the two [59], We consider as well the coion-polyion [59] and polyion-polyion pair potentials [57,58]. In the latter case, the two polyions may be identically charged or oppositely charged. For each type of pair, there is a polyion selfenergy of the form of Eq. 1 (for the polyion-polyion pairs the factor P is replaced by 2P). The essential difference from Eq. 1 is that the number of condensed counterions 9 is now a function of the pair separation distance, 9 = 9(r). Similarly, in the transfer free energy Eq. 2, both 9 and the condensed layer partition function Q depend on r. In addition to the self-assem-... 

Figure 4 presents a graph of Q(r) for a pair of identical rodlike polyion segments in parallel with separation distance r. Note the large increase as the two polyions approach through the intermediate range of distances. In a free volume interpretation, the condensed layers expand, providing an increased entropy that would tend to drive an attractive interaction between the poly ions. 

FIG. 4 The partition function of the counterion layer condensed on a pair of identical rodlike polyions in parallel orientation with separation distance r. Debye screening length 30 A (0.01 M NaCl) polyion charge spacing 1.7 A. 

FIG. 8 A calculated cross-section of the cylindrically symmetric distribution of condensed counterions held in common by a pair of identical parallel rodlike polyions when the partition function for the condensed layer is interpreted as a free volume. The numerical scale is in A, and the polyions pierce the page at 15 A. The Debye length equals 30 A, so the theoretically calculated condensed layer lies inside the Debye atmosphere, as required on physical grounds. Polymer charge spacing 1.7 A. 

There is ample experimental evidence that identically charged polymers in the presence of ordinary univalent counterions have a tendency to form loose clusters in solution [65-70], and we have asked whether the attractive polyion-polyion potential discussed in Sec. Ill can stabilize a finite-sized cluster of parallel rodlike polyions without leading to precipitation [71,72]. The theoretical problem is complicated by a failure of pairwise additivity the work of assembling N polyions is not equal to the work of assembling the N(N — l)/2 polyion pairs, each in isolation from the other N 2 polyions. To be sure, the Debye-Htickel interaction term for a cluster (the generalization of Eq. 5 above) takes the form of a pairwise sum over polyions,... 

Yoshida M, Kikuchi K. Metropolis Monte Carlo Brownian dynamics simulation of the ion atmosphere polarization around a rodlike polyion. J Phys Chem 1994 98 10303-10306. 

Experimentally, the molecular weight independence of the HF effect (in polyelectrolyte solutions) has been confirmed many times. Van der Touw and Mandel [64,65] attributed the HF dispersion to polarization of bound counterions along a part of the polyelectrolyte molecule. They introduced a model in which the polyelectrolyte is considered as a nonlinear sequence of rodlike subunits and the counterion polarization along the subunit is supposed to be responsible for the amplitude and the critical frequency of HF relaxation. Both quantities would essentially be independent of the molecular weight of the polyion. In solutions, where interactions between macromolecules are taken into account, the length of the above-mentioned subunit is related to the correlation distance between the macromolecular chains [25,26,92], Counterion polarization perpendicular to the polyion axis is pro-... 

Szabo A, Haleem M, Eden D. Theory of the transient electric birefringence of rodlike polyions coupling of rotational and counterion dynamics. J Phys Chem 1986 85 7472-7479. 

Nishida et al., 2001] that the conformation of polyions at low ionic strength is rodlike, and hence the polyions adopt a simplified mean-field expression for g r) = g r, 9) = exp[- 7(r, 6)lkBT, where the intermolecular potential U r, 6) is a function not only of the interparticle distance, r, but the orientation angle, 6, between the rods. Computation of the intermolecular contribution to the viscosity then proceeds, using Eq. (1.80), via... 

In order to simplify the model we present in Figure 8 the DNA in the double helical B form as a rodlike polyion. If the solvent is NaQ, the compensating counterions of negative phosphate sites are Na" and the coions of the electrolyte are Cl . It is possible to show that a correlation exists between the conformation of the macroion and some characteristic parameters of the electrolyte. ... 

Figure 12 shows the Arrhenius diagram of noise conductivity for DNA solutions under salt-free conditions. We observe a discontinuity at 23 C this effect is not related to the released counterions because this temperature is below the DNA T, This premelting effect is related to the ionic sheath around the rodlike DNA. The Na" counterions in this sheath are less firmly bound to the polyion above the premelting point (23 °C) than they are below that temperature. 

Figure 12 Schematic sketch of a polyelectrolyte chain and the definition of different length scales for the two-state model. L is the length of rodlike polyion and / the cell size (R L). Reproduced with permission from Dobrynin, A. V. Rubinstein, M. Prog. Polym. Sci. 2005,30,1049-1118. Copyright 2005, Elsevier.

To verify the predictions of eqn [69] for the osmotic coefficient, Figure 16 shows a universal plot of the reduced osmotic coefficient yo ° /yR as a function of the normalized polymer concentration cjc. For the rodlike chains, we define the overlap concentration c as monomer concentration in the cylindrical zone 4NI nL ), which is an overlap concentration for rodlike polyions. All points collapse onto the universal curve as predicted by eqn [69] for rodlike polyelectrolyte solutions (see Figure 16(a)). However, the size Re of flexible chains is a function of the polymer concentration because polyelectrolytes contract with increasing polymer concentration. To collapse all points into one universal curve and to take into account the chain contraction in Figure 16(b), the reduced osmotic coefficient yo ° /yR is plotted against the ratio of... 

We first consider results for the hydrophilic polyelectrolyte limit. Figure 8 presents the effect of charge screening (denoted here by electrolyte concentration) on the reduced, end-to-end distance of partially-ionized 100-segment polyelectrolytes. The polymer end-to-end distance provides a measure of excluded volume, or space occupied by the polymer. The maximum of the vertical axis represents the fully-extended, or rodlike conformation of the polyion this conformation is approached for... 

J. Ray and G. S. Manning, Langmuir, 10, 2450 (1994). An Attractive Force between Two Rodlike Polyions Mediated by the Sharing of Condensed Counterions. 

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