Hydrodynamic Size and Charge of Polyelectrolyte Complexes ² Ute Bo1 hme and Ulrich Scheler* Leibniz Institute of Polymer Research Dresden, Hohe Strasse 6, D-01069 Dresden, Germany ReceiVed: January 24, 2007; In Final Form: April 27, 2007 Polyelectrolyte complexes have a wide range of applications for surface modification and flocculation and sorption of organic molecules from solutions. As an example, complexes between poly(diallyl dimethyl ammonium chloride) and poly(styrene sulfonate) have been investigated by diffusion and electrophoresis NMR. The formation of primary or soluble complexes is monitored. The hydrodynamic size is characterized by the hydrodynamic radius, calculated from the diffusion coefficient determined by pulsed field gradient NMR. In the combination with electrophoresis NMR, the effective charge of the molecules and complexes is determined. The hydrodynamic size of the primary complex is smaller than that of the pure polyelectrolyte of the larger molecular weight, in the present case poly(styrene sulfonate), in solution, since charges are compensated by the oppositely charged polyelectrolyte and hence the repelling forces diminish. The effective charge of the complexes is drastically reduced. Introduction Electrostatic interaction plays an important role in the formation of complexes from molecules in aqueous solution and the binding of ligands to proteins. 1 Complexes of oppositely charged polyelectrolytes may act as a model system for such studies. However, most synthetic polyelectrolytes have ad- ditional conformational degrees of freedom, mostly missing for proteins. Polyelectrolytes in solution adopt a much more extended conformation than uncharged polymers in a good solvent. If the ionic strength of the solution is increased, this repelling force becomes weaker, this effect is even stronger for bivalent salts at the same ionic strength. 2 In addition, polyelec- trolyte complexes and polyelectrolyte complex nanoparticles offer a much wider range of application conditions than the pure polyelectrolytes; they are more tolerant against changes in pH and ionic strength for flocculation 3 and sorption. 4 Polyelectrolyte complex nanoparticles are formed from primary or soluble polyelectrolyte complexes. 5,6 These primary complexes are the subject of the present study. The hydrodynamic size is conveniently probed by diffusion measurements using pulsed field gradient (PFG) NMR. 7 Com- pared to dynamic light scattering PFG NMR has distinct advantages: it is applicable to small molecules and in salt-free solution as well. The detection of NMR spectra in each experiments permits the data analysis for each species, that is resolved by its respective chemical shift in a mixture separately. 8 There is a sufficiently large range of conditions in which both light scattering and NMR are applicable as well permitting an effective comparison. 9 From the diffusion coefficient the hydrodynamic radius R h is calculated by the Stokes-Einstein equation given in eq 1: 10 with k B Boltzmanns constant, η the solvent viscosity, and T the sample temperature. The effective charge on small molecules, polymers or complexes is derived from a combination of diffusion and electrophoresis NMR. In the electrophoresis NMR experiment, a constant electrophoretic drift velocity is the result of the force balance between the force of the electric field on all the charges on the molecule and the hydrodynamic friction, which is derived from the diffusion coefficient using Einsteins formula. 11 The electrophoretic mobility is measured in the electrophoresis NMR experiment, where the NMR experiment again offers the possibility to assign the species that is moving especially in mixtures. 12,13,14 From the electrophoretic mobility and the diffusion coefficient, the effective charge of the molecule or complex is calculated assuming a steady state resulting from the force balance between the force of electric field acting on the effective charges and the hydrodynamic friction according to eq 2: with D being the diffusion coefficient, μ the electro- phoretic mobility, k B Boltzmanns constant, and T the sample temperature. On the time scale of the PFG-NMR experiment of tens of milliseconds, in many situations, only a population-weighted average between free and bound states is observed, which has to be taken into account. Experimental Poly(diallyl dimethyl ammonium chloride) (PDADMAC) with a molecular weight of 5 kg/mol, has been provided by W. Jaeger, Golm. Synthesis and characterization are specified elsewhere. 15,16 Poly(styrene sulfonate) (PSS, for GPC, M w ) 77kg/mol) has been purchased from Fluka. Both chemicals have been dried under vacuum and used without further treatment. Samples were prepared from stock solutions in D 2 O (99.95%, Deutero GmbH). Deuterated water has been used to minimize the residual proton signals of the solvent and thus to improve the measurements of low polyelectrolyte concentration. Different monomer ratios of polyanion to polycation (n - /n + ) have been ² Part of the special issue “International Symposium on Polyelectrolytes (2006)”. * Corresponding author. E-mail: scheler@ipfdd.de. D ) k B T 6πηR h (1) Z ) k B Tμ eD (2) 8348 J. Phys. Chem. B 2007, 111, 8348-8350 10.1021/jp070611e CCC: $37.00 © 2007 American Chemical Society Published on Web 06/13/2007