Polyions conformation

There are two broad kinds of polyion conformation the random coil and the ordered helix. In a helix there are regularly repeated structures along the coil there are none in the case of a random coil. In this book we are concerned with the latter where there are often several conformations with approximately equal free energies and, thus, conformational changes occur readily. 

Conformation depends on the degree of ionization and concentration of the polyion, the type and concentration of the counterion and the interaction between counterion and polyion. Extension is favoured by low concentrations of counterion and polyion. Conformational change is also affected by the extent of the charge on the polyion. As the charge on a polyion increases, the chain uncoils and expands under the influence of repulsive forces. Thus, the neutralization of a polyacid is accompanied by... 

In Eq. (62), the concentration of cations in aqueous solution is symbolized by [M+]. An assumption, explicit in Eq. (62), is that the binding equilibrium does not lead to changes in the polyion conformation [31, 65-73]. The physical content of Eq. (62) is simple, namely, that if a ligand of charge z neutralizes z charges on the polyion, then this process leads to the release of z counterions into the bulk solution [31, 65-73]. 

Figure 3. Schematic of the electrostatically driven layer-by-layer adsorption process. It describes the case of the adsorption of a polyanion to a positively charged substrate (A), followed by washing (B), the adsorption of a polycation (C) and another washing step (D). Multilayer films are prepared by repeating steps (A) through (D) in a cyclic fashion. More complicated film architectures are obtained by using additional adsofption/washing steps and applying more than two polyelectrolytes. Note that the drawing is oversimplified with respect to polyion conformation and interpenetration of adjacent layers. Furthermore, any counterions that might be present in the films were omitted for reasons of clarity.

ION DISTRIBUTION AND POLYION CONFORMATION DISPLAYED BY AMPHIPHILIC POLYACIDS IN AQUEOUS AND ORGANIC MEDIA... 

Fig. 2.4 a Schematic of the film deposition process using slides and beakers. Steps 1 and 3 represent the adsorption of a polyanion and polycation, respectively, and steps 2 and 4 are washing steps. The four steps are the basic buildup sequence for the simplest film architecture (A/ B) . The construction of more complex film architectures requires only additional beakers and a different deposition sequence, b Simplified molecular picture of the first two adsorption steps, depicting film deposition starting with a positively charged substrate. Counterions are omitted for clarity. The polyion conformation and layer interpenetration are an idealization of the surface charge reversal with each adsorption step, c Chemical structures of two t3q>ical polyions, the sodium salt of poly(styrene sulfonate) and poly(allylamine hydrochloride). Reproduced with kind permission of Ref. [32]... 

Comparison to the MC-simulations and theory indicates that the osmotic pressure is most likely governed by intermolecular interactions and not by changes in the polyion conformation. Intermolecular interactions at low concentration correspond to an excluded volume of k at higher concentration compared to the hard-core diameter d. The cross-over concentration, as stated earlier, corresponds to k = d or, equivalently, to = 1. 

In appreciation of the first statement, light scattering investigations of the polyion conformation (and probably any other experimental technique for the investigation of conformational properties) are strictly limited to salt concentrations c > 10 -10 m, as even state-of-the-art instruments do not allow measurements significantly below a few mg/l... 

Random coil conformations can range from the spherical contracted state to the fully extended cylindrical or rod-like form. The conformation adopted depends on the charge on the polyion and the effect of the counterions. When the charge is low the conformation is that of a contracted random coil. As the charge increases the chains extend under the influence of mutually repulsive forces to a rod-like form (Jacobsen, 1962). Thus, as a weak polyelectrolyte acid is neutralized, its conformation changes from that of a compact random coil to an extended chain. For example poly(acrylic acid), degree of polymerization 1000, adopts a spherical form with a radius of 20 nm at low pH. As neutralization proceeds the polyion first extends spherically and then becomes rod-like with a maximum extension of 250 nm (Oosawa, 1971). These pH-dependent conformational changes are important to the chemistry of polyelectrolyte cements. 

Conversely, conformation affects the binding of counterions to polyions (Jacobsen, 1962). In the compact spherical conformation some ionized groups on polymer chains will be inaccessible for ion binding. 

Ion binding is affected by the size and charge of the counterion, the charge and conformation of the polyion, and states of hydration. We will examine these effects in some detail. 

The extent of ion binding depends on a number of characteristics of the polyion degree of dissodation, acid strength, conformation, distribution of ionizable groups and cooperative action between these groups (Wilson Crisp, 1977 Oosawa, 1971 Harris Rice, 1954, 1957). The hydration state of the macromolecule, which is in turn dependent on conformation, also affects ion binding (Begala, 1971). 

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. 

The most important factor determining the sensitivity of the conformation to the concentration of polyions is the change in ion activity or osmotic pressure with conformation. If the activity coeflScient of the counterions is sensitive to conformation then conformational change resulting from concentration changes of polyions becomes large. 

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. 

Under the conditions of screening of electrostatic interactions between polyions, as occurs at high ionic strength (say, / > 0.1 mol dm- ), or in solutions containing neutral (non-ionic) polymers, the excluded volume term is the leading term in the theoretical equation for the second virial coefficient. In this latter type of situation, the sizes and conformation/ architecture of the biopolymer molecules/particles become of substantial importance. 

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... 

The main conclusion drawn from the simulations [170] is that in the presence of monovalent counterions, the charged protein-like copolymers can be soluble, even in a very poor solvent for hydrophobic units. There are three temperature regimes, which are characterized by different spatial organization of polyions and their conformational behavior. 

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