Partial Molar and Specific Volumes of Polyelectrolytes:  Comparison of Experimental and Predicted Values in Salt-free Solutions

Abstract

The partial molar volume, V̄, and the partial specific volume, ν̄, were estimated for more than 25 polyelectrolyte structures. The materials investigated by density measurements in highly diluted aqueous solutions (c < 10-2 monomol/L) included both synthetic polyelectrolytes and chemically modified natural polymers. Through a detailed analysis, related to the chemical structure and macromolecular parameters, a linear dependence between the copolymer composition and the partial volumes could be identified for diallyldimethylammonium chloride/acrylamide copolymers. Additivity could also be shown for sodium cellulose sulfate having various degrees of substitution. For a homologous series of poly(vinylbenzyltrialkylammonium chloride)s, a linear correlation between the molar mass of the monomer unit and the partial molar volume was obtained. No influence of the degree of polymerization was observed as long as the contour length exceeds the Debye length. The experimental results were used to evaluate the general applicability of the additivity schemes of Durchschlag and Zipper, as well as Gianni and Lepori, to polyelectrolytes. Agreement between experimental and calculated partial volumes strongly depends on the chemical structures. In the case of the synthetic polycations, the deviations are in a similar range for both models though somewhat smaller for the Gianni/Lepori model. The use of the Durchschlag/Zipper model yields much better agreement for the anionic biopolymers with deviations generally less than 3%. The tendency of the empirical models is correct; however, the precision may be improved by regressing of parameters from the experimental results. The new experimental data may also be useful in polyelectrolyte characterization.

Exploring Molecular Insights into Aggregation of Hydrotrope Sodium Cumene Sulfonate in Aqueous Solution: A Molecular Dynamics Simulation Study

“…The apparent and partial molal volumes of SCS for different solutions can be estimated from the density measurements. 26,44 By using eqs 1 and 2, we have calculated apparent molal volume (ϕ v ) and partial molal volume (V̅ 2 ) of SCS from the measured densities of the aqueous SCS solutions (ρ) for different molal concentrations and temperatures.…”

Interactions of hairy latex particles with cationic copolymers

“…Concerning the scattering objects, the scattering length densities ρ, scattering length b [19], and partial volume V [20,21] are given in Table 2, corresponding to the different parts of the covered particles. In the H 2 O/D 2 O mixture ( ρ latex ) 2 = 17.0 × 10 28 m −4 and ( ρ MAPTAC ) 2 = 24.2 × 10 28 m −4 , but their relative proportion is less than 10%.…”

Adsorption of charged macromolecules on oppositely charged porous column materials

“…Density measurements were carried out in water at 20 • C using a Digital Precision Density Meter DMA60/DMA602 (Anton Paar, Graz, Austria). From concentration series, in the range of 2 × 10 −4 to 4 × 10 −3 g/ml, the partial specific volume ν of the polymers was obtained [15] according to Eq. (1): where ρ and ρ 0 are the density of the solution and the solvent, respectively, and c designates the polymer concentration in g/cm 3 .…”

“…The partial molar volume, as a measure of the volume occupied by the molecules in solution, was calculated from the experimentally obtained partial specific volume by multiplying with the appropriate molar mass [15]. In addition, partial molar and specific volumes have been calculated applying the Durchschlag-Zipper (D-Z) procedure [19].…”

“…The Debye length, l D , serves as a measure for the ionic atmosphere though it has to be noted that it is strictly valid only for point-like charges. The calculated Debye lengths summarized in Table 5 consider both the ions present from the polyelectrolyte molecules and the added salt [15,20,21]. Since the salt concentration exceeds the experimental polyelectrolyte concentrations it is obvious that the salt concentration dominates the total ionic strength and, therefore, the Debye length.…”