Dependence for Polyelectrolytes

The intrinsic viscosity can be empirically determined via the Fuoss equation 

9 Determination of Molar Mass and Molar Mass Distributions 

The Intrinsic Viscosity and the Molar Mass of Rigid Molecules 

Unsolvated Spheres. The intrinsic viscosity [rj], according to Equation (9-123), depends on both the molar mass and the hydrodynamic volume, and the latter can also be a function of the molar mass. Unsolvated spheres present the simplest case. These spheres can be defined by their type and a density that is independent of its environment and equal to the density of the dry material. The mass nimoi of an individual molecule is related to its hydrodynamic volume via mmol = Vhpi, or with the molar mass Mi via Mi = Ni nimox = N Vhpi. Equation (9-123) therefore changes, for unsolvated spheres, to 

the intrinsic viscosity of solvated spheres depends on the partial specific volume V2 of the solute, the specific volume vi of water, and the mass ratio r = mP/mi (degree of solvation) of both components in the interior of the sphere. Therefore, it is not possible to calculate the molar mass of a solvated sphere from the intrinsic viscosity alone. The intrinsic viscosities of spherical protein molecules are low, and for equal degrees of hydration are independent of the molar mass (Table 9-6). Admittedly, the proteins included in Table 9-6 are not perfectly spherical, since their coefficients of friction / are somewhat larger than those expected for a perfect sphere, o. 

The effect is explained in the following manner With decrease in polyelectrolyte concentration, the degree of ionization increases. In the 

9 Determination of Molecular Weight, Molecular-Weight Distribution 

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In the following paper, the possibility of equilibration of the primarily adsorbed portions of polymer was analyzed [20]. The surface coupling constant (k0) was introduced to characterize the polymer-surface interaction. The constant k0 includes an electrostatic interaction term, thus being k0 > 1 for polyelectrolytes and k0 1 for neutral polymers. It was found that, theoretically, the adsorption characteristics do not depend on the equilibration processes for k0 > 1. In contrast, for neutral polymers (k0 < 1), the difference between the equilibrium and non-equilibrium modes could be considerable. As more polymer is adsorbed, excluded-volume effects will swell out the loops of the adsorbate, so that the mutual reorientation of the polymer chains occurs. 

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... 

We have now looked at two models for the second virial coefficient of uncharged colloidal solutes. In Section 3.5b we see that B depends on the magnitude of the particle charge for polyelectrolyte solutes. 

Pig. 1. Dependence of the swelling parameter, a, on the quality of solvent, x, for polyelectrolyte (/), intermediate (2) and isoelectric (3) networks swelling in a salt-free one-component solvent... 

Fig. 2. Dependence of the swelling parameter, a, on the quality of solvent, x, for polyelectrolyte networks (m = 86, a, = a = 11) swollen in solutions of lo w-molecular-weight salt of concentrations n,a3 = 0 (/), 0.001 (2), 0.004 (. ), 0.01 (4). The dashed line corresponds to an electroneutrai network. Reproduced from Ref. [27]...

Figure 11 shows the dependences of o on for polyelectrolyte networks swollen in the solution of incompatible polymer (yNp > 0). In this case, the network always deswells linear polymers do not penetrate inside the network... 

As can be seen from the Figs. 2 and 3, the character of dependencies doesn t qualitatively differ for polyelectrolytes of different nature. The quantitative characteristics such as the time of establishment of surface potential magnitude and its values are different. 

FIG. 6 Typical dependencies of the swelling ratio a of a single polyelectrolyte molecule on the salt concentration ns for good (A) and poor (B) solvent. Dashed lines show the corresponding dependencies for electroneutral macroion t/3 = 0). 

All of the observations made for random ionomer nonaqueous (polar) solutions parallel those for polyelectrolyte aqueous solutions the difference is only quantity, not the quality. These include upturn in a viscosity curve, negative angular dependence at low concentration and positive dependence at higher concentration in Zimm plots, appearance of two modes in dynamic scattering, and a drop in conductance. 

A different approach is to vary a parameter to which the saturated adsorbed amount T is expected to respond significantly, e.g., temperature or solvent quality. For polyelectrolytes such an approach is quite natural, because T depends on salt concentration (ionic strength) and quite often also on pH. Hence, cycling these parameters should reveal the extent of reversibility. 

As typically observed for polyelectrolytes, a large proportion of small co-ions and counterions is held within the domain of the macro-ion. Activity measurements made with ion-specific electrodes have shown that 66% of the Na" " ions of sodium heparinate are bound to the polyanionic chain. Binding of Na" " by heparin was also studied by Na-n.m.r. spectroscopy. Ion-activity data have been interpreted in the framework of the Manning theory, providing intercharge distances ranging from 0.24 to 0.47 nm, depending on the heparin preparation and the experimental conditions (see Ref. 7, and references cited therein). 

Both forces act into opposite directions the osmotic force tries to stretch the chain into the continuous phase, whereas the elastic force pulls the chain back to the interface. Setting Pci = Posm shows that AP a This is a much lower electrolyte dependence than in the case of low-molecular-weight ionic stabilizers where an exponential dependence of Vim is predicted (cf. equations (8.20)). Note, this scaling behavior of AR with Cl is the same as for polyelectrolyte chains in solution [2]. Regarding colloid stability, this means that polyelectrolyte-decorated droplets/particles possess an extraordinary electrolyte stability when compared to low-molecular-weight ionic stabilizers. Indeed, the Pincus brush behaviour (AP oc was experimen-... 

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