Polyelectrolyte Chain

The polyelectrolyte chain is often assumed to be a rigid cylinder (at least locally) with a uniform surface charge distribution [33-36], On the basis of this assumption the non-linearized Poisson-Boltzmann (PB) equation can be used to calculate how the electrostatic potential

[Pg.55]

The linearity of L with N is maintained at the theta point. Relative to Eq. 5, the chains have shrunk by a factor of (a/d),/3 but the linear variation indicates that the chains are still distorted at the theta point and characteristic dimensions do not shrink through a series of decreasing power laws as do free chains [29-31]. Experimentally, Auroy [25] has produced evidence for this linearity even in poor solvents. Pincus [32] has recently applied this type of analysis to tethered polyelectrolyte chains, where the electrostatic interactions can produce even stronger stretching effects than those that have been discussed for good solvents. Tethered polyelectrolytes have also been studied by others [33-35],... 

The ionized forms of polypeptides exhibit many characteristics in common therefore, we have studied them under various conditions. The most interesting observation is the transition of a polyelectrolyte brush found by changing the polyelectrolyte chain density. The brush layers have been prepared by means of the LB film deposition of an amphiphile, 2C18PLGA(48), at pH 10. Mixed monolayers of 2C18PLGA(48) and dioctadecylphos-phoric acid, DOP, were used in order to vary the 2C18PLGA(48) content in the monolayer. 

The transition of the compressibility, and other properties of the polyelectrolyte brnshes, is most likely accounted for in terms of the transition in the binding mode of the connterion to the polyelectrolytes, from the loosely bonnd state to the tightly bound one, which rednces inter- and intrachain repulsive interactions. The following snpports this ac-connt (1) At the critical density, = 0.20 chain/nm, the separation distance between polyelectrolyte chains, d, is 2.4 nm. This distance is close to the snm, 2.6 nm, of the chain diameter, 1.3 nm, and the size of two hydrated connterions, 1.32 nm, indicating that the abrupt... 

In polyelectrolyte solutions, the counterion condensation on linear polyelectrolyte chains is known to occur when the charge density along the chain exceeds the critical value [40]. Our work indicates the existence of a critical value for the separation distance between chains, where the interchain interaction changes drastically, most likely due to the transition in the binding mode of the counterions (see Fig. 13). Many peculiar forms of behavior, which are often interpreted by the cluster formation or the interchain organization of polyelectrolytes, have been reported for high concentrations of aqueous polyelectrolytes... 

FIG. 13 Schematic drawing of possible binding modes of counterions to polyelectrolyte chains. Counterions loosely bind and form a cloud around the polyelectrolyte chains when the interchain distance (d) is greater than 2.4 0.5 nm, while they strongly bind to form nearly neutral polyelectrolytes at smaller distances d < 2.4 0.5 nm). 

Muthukumar, M, Theory of Electrophoretic Mobility of Polyelectrolyte Chains, Macromolec-ular Theory and Simulations 3, 61, 1994. 

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). 

Features of polyelectrolyte adsorption are that both the adsorbance and the thickness can be easily varied by changing the concentration of added salt as well as pH in bulk solution since such changes cause variation of the electrostatic repulsions of polyelectrolyte chains adsorbed, i.e., the excluded volume effect. 

Hesselink attempted to calculate theoretical adsorption isotherms for flexible polyelectrolyte chains using one train and one tail conformation (1) and loop-train conformation (2) as functions of the surface charge, polyion charge density, ionic strength, as well as molecular weight. His theoretical treatment led to extensive conclusions, which can be compared with the relevant experimental data. 

Experimentally the expansion factor as of a polyelectrolyte chain in bulk solution is given as follows (17-19). The a is larger than at. s... 

In many biological systems the biological membrane is a type of surface on which hydrophilic molecules can be attached. Then a microenvironment is created in which the ionic composition can be tuned in a controlled way. Such a fluffy polymer layer is sometimes called a slimy layer. Here we report on the first attempt to generate a realistic slimy layer around the bilayer. This is done by grafting a polyelectrolyte chain on the end of a PC lipid molecule. When doing so, it was found that the density in which one can pack such a polyelectrolyte layer depends on the size of the hydrophobic anchor. For this reason, we used stearoyl Ci8 tails. The results of such a calculation are given in Figure 26. 

Fig. 8 Cryo-TEM image of aqueous PB-P2VPQ micelles showing filament network of polyelectrolyte chain bundles. Scale bar is 50 nm. Reprinted with permission from [15]. Copyright (2004) Springer...

Salt effects in polyelectrolyte block copolymer micelles are particularly pronounced because the polyelectrolyte chains are closely assembled in the micellar shell [217]. The situation is quite reminiscent of tethered polymer brushes, to which polyelectrolyte block copolymer micelles have been compared, as summarized in the review of Forster [15]. The analogy to polyelectrolyte brushes was investigated by Guenoun in the study of the behavior of a free-standing film drawn from a PtBS-PSSNa-solution [218] and by Hari-haran et al., who studied the absorbed layer thickness of PtBS-PSSNa block copolymers onto latex particles [219,220]. When the salt concentration exceeded a certain limit, a weak decrease in the layer thickness with increasing salt concentration was observed. Similar results have been obtained by Tauer et al. on electrosterically stabilized latex particles [221]. 

The electrophoretic mobility p of a polyelectrolyte chain in an infinitely dilute solution containing an added salt at concentration c under a constant external electric field E, as defined through... 

In scenario (c) corresponding to semidilute solutions, polyelectrolyte chains interpenetrate. Under these circumstances, there are three kinds of screening. The electrostatic interaction, excluded volume interaction, and the hydro-dynamic interaction between any two segments of a labeled polyelectrolyte chain are all screened by interpenetrating chains. Each of these three interactions is associated with a screening length, namely, and These screening... 

At the same time Rg of a labeled polyelectrolyte chain is derived to be... 

We consider a system of n polyelectrolyte chains each of N segments, ric counterions, Uy ions of species y from dissolved salt, and solvent molecules in volume 17. The total charge on each poly electrolyte is Q assumed to be proportional to N. 

Provided that the polyelectrolyte chains are much larger than the solvent molecules, the solvent can be treated as a homogeneous isothermal viscous... 

Assuming that the total charge Q of a polyelectrolyte chain is uniformly distributed on the chain backbone so that each segment carries a charge of ezp where e is the electronic charge and by integrating over the positions of counterions, salt ions, and solvent molecules, the potential interaction V between any two segments i and j separated by a distance R,y is taken to be [48]... 

The change t] — rig in shear viscosity of the solvent due to the polyelectrolyte chains is given by... 

For a polyelectrolyte chain that has non-Gaussian statistics, exact analytical expression for B is not feasible. To get some insight, we notice that the static structure factor has the limiting behavior. 

Summarizing, the electrophoretic mobility of a flexible polyelectrolyte chain in infinitely dilute solutions is given by Eq. (156) ... 

This value of kn is actually low by an order of magnitude for dilute suspensions of charged spheres of radius Rg. This is due to the neglect of interchain correlations for c < c in the structure factor used in the derivation of Eqs. (295)-(298). If the repulsive interaction between polyelectrolyte chains dominates, as expected in salt-free solutions, the virial expansion for viscosity may be valid over considerable range of concentrations where the average distance between chains scales as. This virial series may be approxi-... 

By accounting for the coupling between the dynamics of polyelectrolyte chains and their counterions and salt ions and assuming that small ions relax faster than polyelectrolyte chains, we have derived Df to be... 

The Huggins coefficient kn is of order unity for neutral chains and for polyelectrolyte chains at high salt concentrations. In low salt concentrations, the value of kn is expected to be an order of magnitude larger, due to the strong Coulomb repulsion between two polyelectrolyte chains, as seen in the case of colloidal solutions of charged spheres. While it is in principle possible to calculate the leading virial coefficients in Eq. (332) for different salt concentrations, the essential feature of the concentration dependence of t can be approximated by... 

M. Houska, E. Brynda, and K. Bohata, "The Effect of Polyelectrolyte Chain Length on Layer-by-layer Protein/Polyelectrolyte Assembly - an Experimental Study," Journal Of Colloid And Interface Science 213, 140-147 (2004). 

The inner structure of polyelectrolyte multilayer films has been studied by neutron and X-ray reflectivity experiments by intercalating deuterated PSS into a nondeut-erated PSS/PAH assembly [94, 99]. An important lesson from these experiments is that polyelectrolytes in PEMs do not present well-defined layers but are rather interpenetrated or fussy systems. As a consequence, polyelectrolyte chains deposited in an adsorption step are intertwined with those deposited in the three or four previous adsorption cycles. When polyelectrolyte mobility is increased by immersion in NaCl 0.8 M, the interpenetration increases with time as the system evolves towards a fully mixed state in order to maximize its entropy ]100]. From the point of view of redox PEMs, polyelectrolyte interpenetration is advantageous in the sense that two layers of a redox polyelectrolyte can be in electrochemical contact even if they are separated by one or more layers of an electroinactive poly ion. For example, electrical connectivity between a layer of a redox polymer and the electrode is maintained even when separated by up to 2.5 insulating bUayers [67, 101-103]. 

If salt is present in the solution, counterions as well as co-ions do penetrate into the brush, which leads to additional screening of the Coulomb repulsion inside the brush. The amount of this screening, and the stretching of the polyelectrolyte chains, are now also controlled by the bulk salt concentration. Since the additional salt screening weakens the swelling of the brush caused by the counterion osmotic pressure, salt leads to a brush con-... 

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