Brownian motion of charged colloidal particles surrounded by electric double layers

Schumacher, G. A.; Ven, Theodorus G. M. van de

doi:10.1039/dc9878300075

Cited by 117 publications

(67 citation statements)

References 2 publications

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“…The potential in this boundary condition is the potential just outside the core of the sphere, within the solvent. When the dielectric constant of the core of the sphere is constant, the potential inside the core is identically equal to zero, and therefore plays no role in the boundary condition (18). In the presence of a temperature gradient, however, the potential inside the sphere is non-zero.…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…The velocity v c that the colloidal particle attains on average due to the temperature-gradient induced Electrolyte friction effects are known to be less than 5% as compared to friction of the solvent with the core of the colloidal sphere, both experimentally [18] and theoretically [19], [20]. The friction coefficient γ c is therefore to a good approximation equal to the Stokes friction coefficient γ c = 6πη 0 R of the core, where η 0 is the shear viscosity of the solvent.…”

Section: The Soret Coefficientmentioning

confidence: 99%

“…where in the second equation the boundary condition (18) for the unperturbed potential is used. Furthermore,n is the unit normal on the surface of the colloidal sphere pointing into the solvent.…”

Section: The Electric Force F Elmentioning

confidence: 99%

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Single-particle thermal diffusion of charged colloids: Double-layer theory in a temperature gradient

Dhont

Briels

2008

Eur. Phys. J. E

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The double-layer contribution to the single-particle thermal diffusion coefficient of charged, spherical colloids with arbitrary double-layer thickness is calculated and compared to experiments. The calculation is based on an extension of the Debye-Hückel theory for the double-layer structure that includes a small temperature gradient. There are three forces that constitute the total thermophoretic force on a charged colloidal sphere due to the presence of its double layer : (i) the force F W that results from the temperature dependence of the internal electrostatic energy W of the double layer, (ii) the electric force F el with which the temperature-induced non-spherically symmetric double-layer potential acts on the surface charges of the colloidal sphere and (iii) the solvent-friction force F sol on the surface of the colloidal sphere due to the solvent flow that is induced in the double layer because of its asymmetry. The force F W will be shown to reproduce predictions based on irreversiblethermodynamics considerations. The other two forces F el and F sol depend on the details of the temperature-gradient induced asymmetry of the double-layer structure which can not be included in an irreversible-thermodynamics treatment. Explicit expressions for the thermal diffusion coefficient 1 are derived for arbitrary double-layer thickness, which complement the irreversible-thermodynamics result through the inclusion of the thermophoretic velocity resulting from the electric-and solventfriction force.

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Section: Boundary Conditionsmentioning

confidence: 99%

Section: The Soret Coefficientmentioning

confidence: 99%

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Single-particle thermal diffusion of charged colloids: Double-layer theory in a temperature gradient

Dhont

Briels

2008

Eur. Phys. J. E

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“…The moments of a distribution law f(t) are given by anj (t) = (-1) -EO [7] L (,) = -(tp) + (W)o [8] and SL = (t) -(t)2 = -((t') -(t )2) + SL, [9] where 0 refers to the value in the absence of traps (free-flow electrophoresis value) and tp refers to the escape time of a single trap. Calling V and D (respectively, V0 and D0) the mean velocity and the diffusion coefficient in the presence (or in the absence) of traps and recalling that SL V3 = 2 D L for times long enough for the central limit theorem to apply (11) [11] In both formulas, the first term of the right-hand side corresponds to trapping and predominates if natural diffusion is fast.…”

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confidence: 99%

Free-flow electrophoresis with trapping by a transverse inhomogeneous field.

Ajdari

Prost

1991

Proc. Natl. Acad. Sci. U.S.A.

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We propose an electrophoretic technique combining the use of a series of dielectric traps controlled by an ac electric field and conventional continuous field free-flow electrophoresis. From the theoretical model that we describe, one can expect, for DNA electrophoresis, an improvement of one to two orders of magnitude in the selectivities or experimental durations.The separation of biological macromolecules is a crucial problem in areas such as the pharmaceutical industry and biomolecular engineering. As an important example, human genome mapping requires the separation of large DNA molecules according to their sizes-from a few kilobase pairs (kbp) to a few tens of megabase pairs (Mbp). This is not possible by simple free-flow electrophoresis in aqueous solutions; indeed, electrophoretic mobility is independent of the molecular weight for long chains (1).As an alternative, gel electrophoresis techniques were developed. Although it was soon recognized that continuous field devices have severe limitations (molecules of sizes larger than =50 kbp display the same mobility), pulsed-field methods allow for the separation, over a 1-day period, of DNA molecules of a few megabase pairs (2, 3). More recently (4), attaching a globular protein to one end of the chain has resulted in a spectacular increase in the accuracy of the separation for chains of intermediate size; the mobility decreases exponentially with the molecular weight in certain conditions.However, free-flow electrophoresis can also be used with the addition of selective traps. Confinement effects, for example, could lead to separation (5). Here we propose the use of well-controlled geometries with transverse oscillating electric fields. The large paraelectric susceptibilities of polyelectrolytes lead to trapping phenomena in the strong field areas. The trapping time depends exponentially on the polarizability of the chains, which depends sharply on their length: we therefore expect good selectivity.More precisely, we develop a model that describes the macromolecular drift and diffusion in a periodic structure, calculate the conditions for separation, and propose orders of magnitude considerations that demonstrate the efficiency and the feasibility of the technique.The polyelectrolyte is considered as an undeformable charged object, which means that we neglect any conformational consideration. Its evolution in a force field F(x) is that of a Brownian point particle and is governed by a FokkerPlanck equation:-(x, t) = -div J(x, t) Do J(x, t) = -P(x, t) F(x, t) -Do grad P(x, t), kT [1] where P(x, t) is the probability density of the particle at point x and time t.D' is the coefficient characteristic of Brownian diffusion, which also applies for sedimentation and for all situations where the force field is of nonelectrical origin (6, 7). F is the force acting on the backbone plus counterion system, linked to the average velocity through Einstein's relation: V = D°F/kT. When the force is due to an electric field E, this defines a proportionality coeffici...

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“…This theoretical conclusion was confirmed by the experimental results of Schumacher and Van de Ven. 166 In colloid tracer studies, the double-layer width should always be on the order of 10 nm, and the particle radius will be on the order of 500 nrn, so KR will be on the order of 50, which is large enough that the diffusion coefficient of the particles should not be affected significantly by surface charge. The creeping motion equations in the presence of an electrical field are169…”

Section: 7 Dynamic Forces the Magnitudes Of The Surface Forcesmentioning

confidence: 99%

Transport of synthetic colloids through single saturated fractures: A literature review

Reimus¹

1995

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Brownian motion of charged colloidal particles surrounded by electric double layers

Cited by 117 publications

References 2 publications

Single-particle thermal diffusion of charged colloids: Double-layer theory in a temperature gradient

Single-particle thermal diffusion of charged colloids: Double-layer theory in a temperature gradient

Free-flow electrophoresis with trapping by a transverse inhomogeneous field.

Transport of synthetic colloids through single saturated fractures: A literature review

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