Polyions, flexible

It is reasonable to consider that the electrostatic repulsion between the fixed line charges on the polyion tends to straighten the flexible vinylic main chain, and... 

The conformation of macro- or polyions has been defined and discussed briefly in Section 4.1.1. The conformation of a polyion is determined by a balance between contractile forces, which depend on conformation free energy, and extension forces, which arise from electrical free energy. The extent of conformational change is determined by several factors. Changes are facilitated by the degree of flexibility of the polyion, and conformational change is greatest at low concentration of polyions. 

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. 

Hesselink23) attempted to calculate adsorption isotherms for flexible polyelectrolytes. He assumed that, when adsorbed on a surface, a flexible polyelectrolyte takes a conformation consisting of one train and one tail. The theoretical treatment of Hoeve et al.4I) (cf. B.3.1) for non-ionic polymers was extended by taking into account the change in electrical free energy that occurs when the polyelectrolyte is brought from the solution onto the interface. The partition function Q for a system of N polyelectrolytes each consisting of n units, in which Na polyions are adsorbed on the surface of area S and Nf(Nf = N - N ) polyions remain in the bulk solution of volume V, is then represented by... 

A decrease of An or Ak upon addition of salt is quite common for flexible polyelectrolytes (see e.g. [56, 57]). It is generally interpreted as being a consequence of the conformational change brought about by the rise of ionic strength. When the coil size is reduced, the optical and electrical polarizability of the polyions is diminished. This leads to the observed drop of electric birefringence. Coiling of the polyion can also lead to an increase of counted-... 

The situation is more favourable for the study of EB in solutions of flexible-chain polyelectrolytes for which the value of K may be higher by several orders of msg-nitude than for molecules bearing no charge This seems plausible since the uncoiling of a flexible-chain polyion by electrostatic repulsion of ionc enic groups increases the persistent length of the chain and the optical and hydrodynamic properties of the molecule approach those of a rigid-chain polymer ... 

In summary, the light-scattering investigations support the results obtained by conductivity measurements that the effective charge density of cylindrical polyelectrolyte brushes is much smaller than for linear flexible polyions. 

The critical pH for bulk phase separation seems to be significantly larger than the pH at which intrapolymer complexes are first formed, and the aggregation of molecular complexes appears as an intermediate process. One may speculate that, near the isoelectric point of the protein (ca. 4.8 for BSA), each polyion chain binds some number of proteins which depends on polymer chain length and flexibility, and also upon protein dimensions. The net charge of this complex, however, remains positive until the pH substantially exceeds the isoelectric point. Under such conditions, intrapolymer complexes may begin to associate. 

FIG. 2 Relaxation times of dynamic modes observed in polyelectrolyte solutions and mixtures over a broad range of experimental conditions 0 diffusion of low molecular weight salt diffusion of polyions or polyion segments in semidilute solutions 3 interaction mode in polyelectrolyte mixtures and diffusion of polyelectrolyte domains (clusters). The data are based mostly on the work on linear flexible polyelectrolytes. Relaxation times correspond to scattering at 90°. See text for more details. 

The chain conformation is determined by the interaction between neighboring segments and the interaction between distant segments along a polymer which, via chain flexibility, are located in each other s vicinity. The former effect determines the local chain stiffness. The latter is referred to as the excluded volume effect and influences the overall conformation. Both types of interaction can be of electrostatic and nonelectrostatic origin. In the absence of excluded volume effects (flexible polyions in a theta state or... 

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]. 

The last comment concerns polyions which are intrinsically rigid (not flexible or semiflexible). In this case, light scattering can provide information on the size and partly also on the shape of the polyions by comparing... 

For the polyion equivalent conductivity, conditions are different. Here an appreciable concentration dependence is expected even in very dilute solutions. This is partly due to the direct dependence of Ap on a, a quantity that may vary with concentration, and partly due to the concentration dependence of the friction coefficient/p. As in the case of polymeric solutes in general, the friction coefficient depends on the polyion chain conformation, which for flexible polyelectrolytes is strongly concentration dependent. Furthermore, the polyion friction coefficient also includes contributions from the fraction (1 — a) of the counterions, which form a kinetic unit with the polyion. The friction coefficient can therefore be written in the form... 

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