Entropic Colloidal Interactions in Concentrated DNA Solutions

Abstract

We explore the entropic interactions between a pair of micron-sized colloidal spheres in DNA solutions. By confining the particles in a line-scanned optical tweezer, we directly measured the functional form of the interaction potential with sub- kBT resolution in samples where the spheres and the polymer coils were of comparable size. The potential is well described by the Asakura-Oosawa depletion model even in the semidilute regime where DNA coils overlap strongly. Its range and depth increase with increasing concentration in a manner consistent with a crossover from a dilute solution of Gaussian coils to the weakly fluctuating semidilute regime dominated by two-point collisions which is unique to semiflexible polymers. [S0031-9007(98)07491-2] Colloidal suspensions and polymer solutions are two classic soft materials that have been the focus of decades of study, and yet their properties when mixed together are still only poorly understood. These colloid-polymer mixtures exhibit a rich phase behavior which is not only of fundamental interest [1 ‐ 10] but also of relevance to systems as diverse as motor oils and frozen desserts. The structural and dynamical properties of these complex fluids ultimately depend on the microscopic interactions between the suspension constituents. We present the first direct measurement of the functional form of the depletion interaction between two colloidal spheres in a nonadsorbing polymer background. Our measurements probe the variations in depth and range of the potential as a function of polymer concentration, spanning the dilute region where individual coils are noninteracting to the semidilute regime where they become entangled. Unlike other force measurements [3,5], our experiments probe a previously unexplored regime where colloid and polymer sizes are comparable. We find that the traditional hard-sphere depletion potential [8,9] for dilute solutions still applies and that it can be extended into the entangled region by rescaling the effective size of the polymer coils. We obtain quantitative measurements of the polymers’ osmotic pressure and correlation length above and below the overlap concentration. A dilute polymer solution can be modeled as an ideal gas of hard spheres [8] with a mean size given by the radius of gyration of the individual polymer coils. Unlike hard spheres, polymers in solution can interpenetrate, significantly reducing any effects due to liquid structure. The experimental situation is depicted in Fig. 1(a). The centers of the polymer “spheres” are excluded from a region of thickness Rg surrounding the colloidal particles. When the “depletion zones” surrounding the two spheres overlap, the total volume accessible to the polymer increases, leading to a gain in the system entropy. This produces an attractive interaction between the two spheres.