The effective hydrodynamic radius of single DNA-grafted colloids as measured by fast Brownian motion analysis Olaf Ueberschär * , Carolin Wagner, Tim Stangner, Christof Gutsche, Friedrich Kremer Institut für Experimentelle Physik I, Universität Leipzig, Linnéstraße 5, 04103 Leipzig, Germany article info Article history: Received 26 November 2010 Received in revised form 31 January 2011 Accepted 1 February 2011 Keywords: Colloidal polymer brush Polyelectrolyte brush height scaling Brownian motion analysis abstract Optical tweezers accomplished with fast position detection enable one to carry out Brownian motion analysis of single DNA-grafted (grafting density: w1000 molecules per particle, molecular weight: 4000 bp) colloids in media of varying NaCl concentration. By that the effective hydrodynamic radius of the colloid under study is determined and found to be strongly dependent on the conformation of the grafted DNA chains. Our results compare well both with recent measurements of the pair interaction potential between DNA-grafted colloids (Kegler et al. Phys Rev Lett 2008; 100:118302) and with microfluidic studies (Gutsche et al. Microfluid Nanofluid 2006; 2:381-386). The observed scaling of the brush height with the ion concentration is in full accord with the theoretical predictions by Pincus, Zhulina, Birshtein and Borisov. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Polymer layers that are grafted to microsphere surfaces, so- called colloidal polymer brushes, are of great interest in several fields of current material science. The radius of the used beads usually ranges from 0.5 mm to 2 mm. Colloidal polymer brushes show intriguing macroscopic properties that emerge from their unique microscopic surface structure and the characteristics of its interaction with the surrounding fluid. The scientific and techno- logical application of these properties comprises, for instance, the improvement of colloidal stability [1], the preparation of biode- gradable lubricants [2] as well as basic research on microscopic and molecular friction. Detailed studies of the physical properties of such polymer- grafted surfaces have been carried out by means of experimental [3e19], analytical [20e27] and numerical approaches [2,28e30]. The previously employed experimental methods include dynamic light scattering, small-angle neutron and X-ray scattering as well as cryogenic transmission electron microscopy [4]. In essence, all these studies show that the interaction of the polymer layer with the surrounding fluid, especially under shear flow, plays a key role in the understanding of the physical properties of the surface. The influ- ence of the shear flow on polymer brushes has been thoroughly discussed for steady-state conditions [11,32]. It has been revealed therein that the polymer brushes significantly attenuate the surrounding shear flow by viscous drag. The fluid flow is affected in such a way that it stagnates at a certain finite height, the so-called stagnation height, above the surface. These “lift up” and “no slip” properties of the polymer layer are of eminent relevance for the (micro-)rheology of the grafted surface. In analogy, polymer-grafted colloids show a hydrodynamic radius that is significantly increased with respect to the blank colloid [32], both under shear flow and thermal equilibrium conditions. In recent experimental studies, polyelectrolytes are often used for surface grafting [19,31e35]. Polyelectrolytes, such as DNA molecules, are polymer macromolecules whose monomers carry ionizable functional groups, which dissociate in polar solvents, such as water. This property is characterized by the degree of ionization a. If the latter is independent of the pH value, the polymers are referred to as quenched polyelectrolytes. If, however, the degree of ionization depends on the pH value of the surrounding fluid, the polymers are called annealed polyelectrolytes [7,9,10,36]. On the basis of these properties, polyelectrolytes that are grafted, for instance, to colloids show different spatial conformations. These conformational states are classified as “pancake”, “mushroom” and “brush” regimes. Depending on the grafting density s (number of macromolecules per area unit of the surface) and the degree of ionization a, always one of these three conformations is adopted [37]. Theoretical treatises of polymer brushes are commonly based on the work by Pincus [20], Zhulina, Borisov and Birshtein [21,23,24]. They found scaling laws for the height of polyelectrolyte brushes with respect to different salt concentrations of the * Corresponding author. Permanent address. Institut für Experimentelle Physik I, Fakultät für Physik und Geowissenschaften, Universität Leipzig, Linnéstraße 5, 04103 Leipzig, Germany. Tel.: þ49 341 9732718; fax: þ49 341 9732599. E-mail address: ueberschaer@physik.uni-leipzig.de (O. Ueberschär). Contents lists available at ScienceDirect Polymer journal homepage: www.elsevier.com/locate/polymer 0032-3861/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymer.2011.02.001 Polymer 52 (2011) 1829e1836