Macroion effect

Tipping, E., Backes, C.A. and Hurley, M.A. (1988) The complexation of protons, aluminium and calcium by aquatic humic substances a model incorporating binding-site heterogeneity and macroionic effects. Water Res., 22(5), 597-611. 

The parameter n reflects the measure of deviation of the system from the behavior of the monomeric acid where n = 1, i.e., it characterizes the degree of interaction between the neighboring functional groups of the macroion. The value of n depends on the structure of the polyelectrolyte and the nature of the counterion pK = pK0 — log (1 — a)/a is the negative decadic logarithm of the effective dissociation constant of the carboxylic CP depending on a. 

The combined effects of electroneutrality and the Donnan equilibrium permits us to evaluate the distribution of simple ions across a semipermeable membrane. If electrodes reversible to either the M+ or the X ions were introduced to both sides of the membrane, there would be no potential difference between them the system is at equilibrium and the ion activity is the same in both compartments. However, if calomel reference electrodes are also introduced into each compartment in addition to the reversible electrodes, then a potential difference will be observed between the two reference electrodes. This potential, called the membrane potential, reflects the fact that the membrane must be polarized because of the macroions on one side. It might be noted that polarized membranes abound in living systems, but the polarization there is thought to be primarily due to differences in ionic mobilities for different solutes rather than the sort of mechanism that we have been discussing. We return to a more detailed discussion of the electrochemistry of colloidal systems in Chapter 11. 

How are we to understand this odd result The answer is easy when we remember that osmotic pressure counts solute particles. The macroion cannot pass through the semiperme-able membrane. In the absence of added salt, its counterions will not pass through the membrane either since the electroneutrality of the solution must be maintained. Therefore the equilibrium pressure is that associated with z + 1) particles. Failure to consider the presence of the counterions will lead to the interpretation of a low molecular weight for the colloid. As we already saw, the presence of increasing amounts of salt leads to a leveling off of the ion concentrations on the two sides of the membrane. The effect of the charge on the macroion is essentially swamped out with increasing electrolyte. 

The cell model is a commonly used way of reducing the complicated many-body problem of a polyelectrolyte solution to an effective one-particle theory [24-30]. The idea depicted in Fig. 1 is to partition the solution into subvolumes, each containing only a single macroion together with its counterions. Since each sub-volume is electrically neutral, the electric field will on average vanish on the cell surface. By virtue of this construction different sub-volumes are electrostatically decoupled to a first approximation. Hence, the partition function is factorized and the problem is reduced to a singleparticle problem, namely the treatment of one sub-volume, called cell . Its shape should reflect the symmetry of the polyelectrolyte. Reviews of the basic concepts can be found in [24-26]. 

An important effect not taken into account by the various models discussed in Sect. 2 is the specific interactions of the counterions with the macroion. It is well-known that counterions may even be complexated by macroions and these effects have been discussed abundantly in the early literature in the field [24]. From the above discussion it now becomes clear that these effects must be traced back to specific effects which are not related to the electrostatic interaction of counterions and macroions. Hence, hydrophobic interactions related to subtle changes in the hydratation shell of the counterions could be responsible for this small but significant discrepancy of the electrostatic theory and experiment. Further studies using the PPP-polyelectrolytes will serve for a quantitative understanding of these effects which are outside of the scope of the present review. 

The electrical effect of the highly charged macroion is screened by addition of simple electrolytes of high concentrations. This causes conformational changes, and a decrease of the repulsive forces between two polyions may eventually lead to a salting-out effect (see -> DLVO theory). When a polyacid is partially neutralized by addition of abase, the pH of the solution can be calculated as follows (titration curve)... 

If it is assumed that the final effective charge at the macroion surface of a polypeptide or protein can be represented by Zq, where Z is the magnitude of the charge, q is the sign of the charge, r is the protein radius [calculated71 from the relationship r = (0.81 Mr1/3), then... 

Preliminary inspection of Equation 2.16 reveals that the Gibbs pair potential leads to repulsion at small interplate separations and attraction at large distances. Because it is U°n and not 17 F that is the appropriate pair potential for describing the effective interaction between the mth and nth macroions in solution under isobaric conditions, the different analytic properties of and U, have profound implications for colloid science. 

To make things simpler, let us abbreviate the effective thermodynamic pair potential by V and the separation between the macroions m and n, Xmn, by X. Let us also assume that the macroions m and n have the same charge Z. Then, abbreviating the constant (4 ne2 e) by b, we have... 

The situation illustrated in Figure 4. la has by now become familiar. It depicts a gel composed of a parallel stack of plate macroions with a well-defined interplate spacing (in the colloidal range 10 to 100 nm) in equilibrium with a supernatant fluid. Let us think of the boundary of the gel as an effective membrane enclosing the macroions, transforming the picture into Figure 4.1b. This chapter is concerned with the calculation of the distribution of salt between the gel (I) and supernatant fluid (II) in the two-phase region of colloid stability. 

FIGURE 4.1 Schematic illustration of the phenomenon (a) a swollen n-butylammonium vermiculite gel and (b) the components present in the two phases, the gel (I) and supernatant fluid (II). The dotted line represents an effective membrane enclosing the plate macroions Pn. The symbols M+, X , and S stand for univalent counterions (n-butylammonium ions), univalent co-ions (chloride ions) and solvent (water) molecules, respectively. 

So, what are we to make of the story that emerges from Chapters 1 to 8 The central result that emerged from Chapter 8 is that in a model clay system, the naked clay particle (of a thickness of about 10 A) is covered by two ordered layers of water molecules on each side, followed by a layer of counterions and another layer of partially ordered water molecules, to produce a dressed clay particle of a thickness of about 35 A. Within this dressed macroion, short-range molecular forces are dominant. We can interpret these as giving rise to an effective clay plate thickness of about 35 A in a swollen clay. 

We can rule out the possibility that the effect is due to the n-butylammonium ions. An electron micrograph of the supernatant fluid, taken under the same freeze-fracture conditions, was completely featureless. This is consistent with the thermodynamic behavior of simple n-butylammonium salt solutions their enthalpy of solution is nearly equal to zero [8] and their partial molar volumes are nearly independent of concentration [9], implying that there are no special ion-solvent effects in the system. The necessary conclusion is that the cooling rate used in our experiments, of the order of 103 K/sec, was too low to prevent a major reorganization of the microstructure. This could have serious repercussions for data taken from electron microscopy studies of biological systems, which are necessarily aqueous macroionic systems. 

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