Entropic interactions in suspensions of semiflexible rods: Short-range effects of flexibility

Abstract

We compute the entropic interactions between two colloidal spheres immersed in a dilute suspension of semi-flexible rods. Our model treats the semi-flexible rod as a bent rod at fixed angle, set by the rod contour and persistence lengths. The entropic forces arising from this additional rotational degree of freedom are captured quantitatively by the model, and account for observations at short range in a recent experiment. Global fits to the interaction potential data suggest the persistence length of fd-virus is about two to three times smaller than the commonly used value of 2.2 µm.PACS numbers: 82.70. Dd, 87.15.La Colloidal dispersions exhibit a fascinating range of equilibrium and non-equilibrium structures, and they have important impact on our daily lives [1]. The interactions between suspension constituents determines the stability of the dispersion against flocculation, and the phase behavior of the colloid. Quantitative models and measurements of these interactions test our basic understanding about these systems, and enable experimenters to better control suspension behaviors and properties. In this paper we focus on a particular class of entropic interaction, exploring the forces between spheres in a suspension of rodlike particles. This system class has produced a variety of interesting phases [2,3,4], and has stimulated several theoretical models [5,6,7,8,9] and a measurement [10] of the rod-induced depletion interaction.The depletion attraction between two spheres immersed in a dilute suspension of thin rods of length, L c , was first considered by Asakara and Oosawa [11]. Their most important physical insight was that rods in suspension gain both translational and rotational entropy when the sphere surfaces come within L c of one another. Subsequent theories computed the attraction more accurately within the Derjaguin approximation [6,7] and beyond [5]. However, in many practical scenarios the rods are not rigid, and current theories do not account for the flexibility of the rods. Indeed, flexibility effects can be important as evidenced by a recent interaction measurement [10] of micron diameter spheres in suspensions of fd-virus; in this case systematic deviations between experiment and "rigid-rod" theories were found at short-range, and were suggested to arise as a result of the flexibility of the fd-virus. Flexible or bent rods have an additional degree of freedom: the rotation about their central axis. As the spheres get closer, this degree of freedom is depleted, the system entropy increases, and the sphere interactions become even more attractive.A quantitative model for this observation is still lacking, and indeed a complete theory of semi-flexible rods near surfaces remains a difficult task. In this paper, we introduce a simple model to compute the depletion potential between two spheres in a dilute solution of semiflexible rods. We use the model to quantitatively explain the experiments of Ref. [10]. The model accounts for the entropic effects of flexibility at short-range, and provi...

Single M13 bacteriophage tethering and stretching

“…The fluctuating rod limit of the WLC was equipped with an elastic chain stretching term and then used to model optical tweezers stretching data. The extracted mean l p (1,265 nm) supports recent predictions that filamentous bacteriophage l p may be shorter than previously thought (16). Additionally, the two expected contour lengths (at full length and g9p-H 6 plasmid length) and a mean K near 2,200 pN, approximately double that of dsDNA, were obtained.…”

“…Specifically, deviations between depletion attraction measurements and ''rigid-rod'' theories were resolved when rod flexibility was introduced in the model. From this analysis, persistence lengths two to three times smaller than 2.2 m, the commonly cited value obtained from dynamic light scattering of bacteriophage solutions, were suggested (16). Furthermore, spontaneous nano-ring formation was readily observed when M13 remote and proximal tips were functionalized with hexahistidines (H 6 ) and divalent cations, respectively (17).…”

Simulation and theory of fluid–fluid interfaces in binary mixtures of hard spheres and hard rods

“…For small needle-to-sphere size ratios this was shown to be an accurate description and, using a theory for the effective onecomponent fluid of spheres, purely entropy-induced wetting of the hard wall was found [16]. Rod-induced depletion forces have been experimentally measured and were found to compare well with theoretical predictions [17][18][19]. Non-vanishing interactions between rods further enrich phase behaviour [20] and correlations between spheres [21].…”

Depletion interaction mediated by polydisperse rods

“…However, Lau et al published experimental data for the sphere/sphere interaction mediated by the rod-like fd-virus [8] and compared these to numerical results, which were calculated with Yaman's algorithm. In this paper, both the experimental and the numerical data show a pronounced upturn at small separation distances.…”

“…Although rod-like particles are expected to be much more effective depletants than spherical particles or polymers, there have been only a few experimental studies in which depletion potentials were measured directly. Yodh and coworkers have thoroughly studied the depletion potential induced by bacteriophage fd-virus [7,8] by optical tweezer experiments. The potential between flat glass wall and a latex bead in solutions of boehmite rods was measured with Total Internal Reflection Microscopy (TIRM) by Helden et al [9,10].…”