Abstract
We propose a scaling equation describing transport properties (diffusion and viscosity) in the solutions of colloidal particles. We apply the equation to 23 different systems including colloids and proteins differing in size (range of diameters: 4 nm to 1 μm), and volume fractions (10(-3)-0.56). In solutions under study colloids/proteins interact via steric, hydrodynamic, van der Waals and/or electrostatic interactions. We implement contribution of those interactions into the scaling law. Finally we use our scaling law together with the literature values of the barrier for nucleation to predict crystal nucleation rates of hard-sphere like colloids. The resulting crystal nucleation rates agree with existing experimental data.
Highlights
Crystallization is ubiquitous in nature and is a standard way to purify chemical substances or determine the structure of proteins
The nucleation rate I 1⁄4 aP where P 1⁄4 exp(ÀDGcrit/kBT) is the probability of formation of the critical nucleus and DGcrit is the height of a barrier for the nucleus formation. a is the kinetic pre-factor de ned as2,5,6 a 1⁄4 6/pf5/3D/s5, where f is the volume fraction, D is the diffusion coefficient of colloidal particles, and s is the particle diameter
The probability P is usually calculated from the classical nucleation theory (CNT), and the precision of computation depends only on the proper choice of the equation of state and the crystal–liquid surface tension
Summary
Crystallization is ubiquitous in nature and is a standard way to purify chemical substances or determine the structure of proteins. We analyse the viscosity for the broad range of volume fractions (10À3–0.56) and on that basis we calculate the mobility of colloidal particles for the most concentrated systems (f > 0.52). Using these data in combination with the literature values of the nucleation barrier, we determine the crystal nucleation rate for hard-sphere colloids which appear in agreement with experimental data.. We have shown that the transport properties of entangled complex uids (e.g. polymer and micellar solutions) are, at the nanoscale, strongly in uenced by the length-scale dependent viscosity.. For example electrostatic repulsion between colloidal particles increases the shear viscosity of their solutions. the rates of diffusion-limited reactions in bio-complex systems (i.e. cell cytoplasm) depend on the ionic strength of the cellular interior. Here we ask: How do the intermolecular interactions in uence f(rp)?
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