Polyelectrolytes rodlike

More than half a century ago, Bawden and Pirie [77] found that aqueous solutions of tobacco mosaic virus (TMV), a charged rodlike virus, formed a liquid crystal phase at as very low a concentration as 2%. To explain such remarkable liquid crystallinity was one of the central themes in the famous 1949 paper of Onsager [2], However, systematic experimental studies on the phase behavior in stiff polyelectrolyte solutions have begun only recently. At present, phase equilibrium data on aqueous solutions qualified for quantitative discussion are available for four stiff polyelectrolytes, TMV, DNA, xanthan (a double helical polysaccharide), and fd-virus. 

Figure 1 shows the results obtained by Francois and Skoulios (27) on the conductivity of various liquid crystalline phases in the binary systems water-sodium lauryl sulfate and water-potassium laurate at 50 °C. As might be expected, the water-continuous normal hexagonal phase has the highest conductivity among the liquid crystals while the lamellar phase with its bimolecular leaflets of surfactant has the lowest conductivity. Francois (28) has presented data on the conductivity of the hexagonal phases of other soaps. She has also discussed the mechanism of ion transport in the hexagonal phase and its similarity to ion transport in aqueous solutions of rodlike polyelectrolytes. 

The monomer-monomer correlation functions of flexible polyelectrolytes exhibit qualitatively the same behavior as those for rod-like molecules. The conformational changes, however, result in more pronounced and shifted peaks. From Fig. 8 we deduce a shift of the peaks of flexible chains to larger distances compared to those of rod-like chains. This is a consequence of a smaller overlap between flexible chains compared to the one between rodlike molecules. Naturally, the effect is most pronounced for densities larger than the overlap densities. The increased peak intensity corresponds to a more pronounced order in the system of flexible chains, and is a result of the more compact structure of a polymer coil. (The structural properties of flexible polyelectrolytes without medium-induced potential have been studied in [48].)... 

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... 

Bacquet, R. and P. Rossky. (1984). Ionic Atmosphere of Rodlike Polyelectrolytes. A Hypemetted Chain Study. J. Phys. Chem. 88 2660. 

Nishio, T., and Minakata, A. Effects of ion size and valence on ion distribution in mixed counterion systems of a rodlike polyelectrolyte solution. 2. mixed-valence counterion systems. Journal of Physical Chemistry B, 2003, 107, No. 32, p. 8140-8145. 

Blaul, J., Wittemann, M., Ballauff, M., and Rehahn, M. Osmotic coefficient of a synthetic rodlike polyelectrolyte in salt-free solution as a test of the Poisson-Boltzmann cell model. Journal of Physical Chemistry B, 2000,104, No. 30, p. 7077-7081. 

Figure 1 Chemical structure of the rodlike polyelectrolyte used for the ASAXS-study discussed here [19, 27].

Rodlike polyelectrolytes have been known for a long time. Biological polymers such as DNA [4-8] and xanthane [9-12], or colloidal systems like the ferredoxin virus [13, 14] and the tobacco mosaic virus (TMV) [15, 16], may be the most prominent examples. However, there were also publications on some synthetic rods in the early 1990s when we started our program. Poly(p-phenylene-benzobisoxazoles) and poly(p-phenylene-benzobisthia-zoles) may serve as examples [17-20]. Nevertheless, new rodlike polyelec-... 

SAXS and osmometry, on the other hand, allow the conclusion that the Poisson-Boltzmann cell model gives a quite realistic description of counterion condensation in rodlike macromolecules. However, prior to a final evaluation, a more profound analysis is required. Here, it will be of particular importance to consider polyelectrolytes with substantially lower charge densities also. Unfortunately, but in accordance with expectations, all polyelectrolytes containing phenylene moieties without charged side groups, such as 20-22, proved to be insoluble in water (Scheme 4). 

In addition to the research work presented so far, in the 1990s many other activities were directed towards the synthesis of rodlike polyelectrolytes. Some important examples will be referred to in the following. Regarding cationic polyelectrolytes in particular, Reynolds et al. described the synthesis of water-soluble PPPs such as 29 [28]. These polymers were analyzed with regard to their potential application as luminescent materials [29]. Similar polymers were reported by Swager et al. in 2000 [30]. Here, poly(p-phenyl-ene ethynylenes) 30 were investigated as active components for chemosen-sors (Scheme 7). 

Scheme 7 Rodlike polyelectrolytes developed by other research groups...

PPPs such as 32 [35, 36]. Here, also, a direct in-aqua synthesis was applied. Simultaneously, Wegner et al. developed precursor syntheses of sulfonated PPPs such as 33 and 34 [37-42]. Due to their long aliphatic side chains, these latter polymers form well-defined cylindrical micelles in solution. They are of considerable current interest because they allow more to be learned about the association behavior of rodlike polyelectrolytes consisting of hydrophilic and hydrophobic sub-units. In this context, the studies represent an important supplement for the studies performed in our groups. 

Podgornik R, Parsegian V. Charge-fluctuation forces between rodlike polyelectrolytes pairwise summability reexamined. Phys Rev Letters 1998 80 1560-1563. 

A complementary approach is to fix the conformation of the chain and to focus on a detailed description of the counterion distribution. Usually polyelectrolytes stretch due to the electrostatic repulsion of their charged groups. Moreover, many important polyelectrolytes have a large intrinsic stiffness (e.g., DNA, actin filaments, or microtubules). Therefore a rodlike conformation is an obvious first choice see Figure 2. The remaining problem of charged rods immersed into solution is much easier but is still far from being exactly solvable. 

Lyubartsev AP, Tang JX, Janmey PA, Nordenskiold L. Electrostatically induced polyelectrolyte association of rodlike virus particles. Phys. Rev. Lett. 1998 81 5465. 

Guilleaume B, Blaul J, Wittemann M, Rehahn M, Ballauff M. Investigations of rodlike polyelectrolytes in solution by small-angle x-ray scattering. J. Phys. Cond. Matt., 2000 A245 12. 

Shklovskii BI. Wigner crystal model of counterion induced bundle formation of rodlike polyelectrolytes. Phys. Rev. Lett. 1999 82 3268-3271. 

Another striking experimental feature is that the attractions do not appear to lead to macroscopic phase separation. In this sense, the counterion-mediated attraction between the chains appears to have a different character from ordinary attractions that lead simply to phase separation at sufficiently high concentrations. Instead, the chains tend to form dense bundles of a fairly well-defined thickness [8,11]. The precise morphology of the bundles appears to depend sensitively on the persistence length of the polyelectrolyte, the chain length, and the concentration. In the case of dilute DNA, the bundles tend to be toroidal or rod-shaped. Other stiff polyelectrolytes tend to form rodlike bundles or networks of bundles. In each case, however, there is a well-defined cross-sectional thickness for the bundles. We will concentrate on the question of why there is a characteristic cross-sectional bundle diameter, rather than on the specific morphology of the bundles. 

F. J. Solis and M. O. de la Cruz. Attractive interactions between rodlike polyelectrolytes polarization, crystallization, and packing. Physical Review E 60 4496-4499 (1999). 

B. Y. Ha and A. J. Liu. Effect of non-pairwise-additive interactions on bundles of rodlike polyelectrolytes. Physical Review Letters 81 1011-1014 (1998). 

Figure 12 shows polymer concentration cP dependence of the anisotropy of the electrical polarizability Aa of a 64/128 base-pair DNA fragment. Aa increases on dilution of polymer concentration. Experimentally, Aa is determined via measurement of the Kerr constant of the polyelectrolyte solutions, and in the case of rodlike polyelectrolytes both quantities are proportional to each other. It has been observed that the Kerr constant of polyelectrolytes in salt-free aqueous solutions increases on dilution [46,47], This behavior of the Kerr constant is one of the characteristic properties of polyelectrolytes in salt-free aqueous solutions whose reproduction we have succeeded in by computer simulation. The figure also indicates that Aa is... 

McTague JP, Gibbs JH. Electric polarization of solutions of rodlike polyelectrolytes. J Chem Phys 1966 44 4295-4301. 

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-... 

Theoretical predictions for a quadratic increase of the induced dipole moment in the presence of divalent counterions in comparison to that in the presence of monovalent counterions have been made [71,84,97,99]. An increase of the polarizability with increasing counterion valence is also predicted by Monte Carlo simulation, applied in the investigation of rodlike polyelectrolytes in solution [100]. Experimentally, however, the degree of DNA orientation has been found only slightly higher (ca. 5%) in the presence of divalent counterions than in monovalent solutions [96]. This means, according to the authors of Ref. 96, that the increased repulsion between divalent counterions counterbalances the expected increase in polarizability because of the increased charge fluctuation. 

Sokerov S, Weill G. Polarized fluorescence in an electric field comparison with the other electro-optical effects for rodlike fragments of DNA and the problem of the saturation of the induced moment in polyelectrolytes. Biophys Chem 1979 10 161-171. 

Cametti C, Di Biasio A. Counterion residence time and counterion radial diffusion in rodlike polyelectrolyte solutions. Macromolecules 1987 20 1579-1581. 

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