The Theory of Membrane Equilibria.

Donnan, F. G.

doi:10.1021/cr60001a003

Cited by 705 publications

(415 citation statements)

References 7 publications

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“…This leads to an imbalance in the osmotic pressure across the membrane. The equilibrium between the suspension and the salt reservoir is referred to as Donnan equilibrium [42,43,44]. The effective average salt concentration n s in the suspension is not the same as the reservoir salt concentration c s , but is a function of the physical parameters of the system and can be calculated, e.g., in the PB cell model [45,46,47].…”

Section: Simulation Techniquementioning

confidence: 99%

Many-body interactions and the melting of colloidal crystals

Dobnikar

Chen

Rzehak

et al. 2003

The Journal of Chemical Physics

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We study the melting behavior of charged colloidal crystals, using a simulation technique that combines a continuous mean-field Poisson-Boltzmann description for the microscopic electrolyte ions with a Brownian-dynamics simulation for the mesoscopic colloids. This technique ensures that many-body interactions between the colloids are fully taken into account, and thus allows us to investigate how many-body interactions affect the solid-liquid phase behavior of charged colloids.Using the Lindemann criterion, we determine the melting line in a phase-diagram spanned by the colloidal charge and the salt concentration. We compare our results to predictions based on the established description of colloidal suspensions in terms of pairwise additive Yukawa potentials, and find good agreement at high-salt, but not at low-salt concentration. Analyzing the effective pairinteraction between two colloids in a crystalline environment, we demonstrate that the difference in the melting behavior observed at low salt is due to many-body interactions. If the salt concentration is high, we find configuration-independent pair-forces of perfect Yukawa form with effective charges and screening constants that are in good agreement with well-established theories. At low added salt, however, the pair-forces are Yukawa-like only at short distances with effective parameters that depend on the analyzed colloidal configuration. At larger distances, in contrast, the pair-forces decay to zero much faster than they would following a Yukawa force law. This is explained with a screening effect of the macroions. Based on these findings, we suggest a simple model potential for colloids in suspension which has the form of a Yukawa potential, truncated after the first coordination shell of a colloid in a crystal. Using this potential in a one-component simulation, we find a melting line that shows good agreement with the one derived from the full PoissonBoltzmann-Brownian-dynamics simulation.2

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Section: Simulation Techniquementioning

confidence: 99%

Many-body interactions and the melting of colloidal crystals

Dobnikar

Chen

Rzehak

et al. 2003

The Journal of Chemical Physics

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“…This equilibrium between the suspension and the salt reservoir is referred to as a Donnan equilibrium. 83,84,9,85 Like in the previous subsections we will consider only the case of monovalent counterions and symmetric monovalent (1:1) salt.…”

Section: In Contact With An Infinite Salt Reservoir (Semi-grand-canonmentioning

confidence: 99%

Where the linearized Poisson–Boltzmann cell model fails: Spurious phase separation in charged colloidal suspensions

Tamashiro

Schiessel

2003

The Journal of Chemical Physics

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We perform a linearization of the Poisson-Boltzmann (PB) density functional for spherical WignerSeitz cells that yields Debye-Hückel-like equations agreeing asymptotically with the PB results in the weak-coupling (high-temperature) limit. Both the canonical (fixed number of microions) as well as the semi-grand-canonical (in contact with an infinite salt reservoir) cases are considered and discussed in a unified linearized framework. In the canonical case, for sufficiently large colloidal charges the linearized theory predicts the occurrence of a thermodynamical instability with an associated phase separation of the homogeneous suspension into dilute (gas) and dense (liquid) phases. In the semi-grand-canonical case it is predicted that the isothermal compressibility and the osmotic-pressure difference between the colloidal suspension and the salt reservoir become negative in the low-temperature, high-surface charge or infinite-dilution (of polyions) limits. As already pointed out in the literature for the latter case, these features are in disagreement with the exact nonlinear PB solution inside a Wigner-Seitz cell and are thus artifacts of the linearization. By using explicitly gauge-invariant forms of the electrostatic potential we show that these artifacts, although thermodynamically consistent with quadratic expansions of the nonlinear functional and osmotic pressure, may be traced back to the non-fulfillment of the underlying assumptions of the linearization.

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“…[2] defines the concentration work and the second term defines the electrical work required to move a charged ion between phases of different electrical potential, E N . In a Gibbs-Donnan equilibrium system (2,3), formed when an impermeant charged material is present on one side of a water-permeant rigid membrane, the ratios of all the permeant ion concentrations conform to the Nernst potential defined in Eq. [1].…”

Section: Introductionmentioning

confidence: 99%

The Energetics of Ion Distribution: The Origin of the Resting Electric Potential of Cells

Veech¹,

Kashiwaya²,

Gates³

et al. 2002

IUBMB Life

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SummaryThe relation between the energies of ion movement and ATP hydrolysis is unknown in tissues with widely varying electric potentials. Consequently, we measured the concentration of the nine major inorganic ions in the extra-and intracellular phases in heart, liver, and red cells with resting electrical potentials, E N , of −86, −28, and −6 mV, respectively, under six different physiological conditions. We calculated the Nernst electric potential and the energy of ion movement between the phases. We found that the energy of ATP hydrolysis was essentially constant, between −54 and −58 kJ/mol, in all tissues and conditions. In contrast, as E N decreased, the energies of the Na + and K + gradients decreased, with slopes approximating their valence. The difference between the energies of Na + and K + gradients remained constant at 17 kJ/mol, which is approximately one third of the energy of ATP hydrolysis, demonstrating near-equilibrium of the Na + /K + ATPase in all tissues under all conditions. All cations, except K + , were pumped out of cells and all anions, except Cl − in liver and red cell, were pumped into cells. We conclude that the energy of ATP was expressed in Na + /K + ATPase and its linked inorganic ion transporters to create a Gibbs-Donnan near-equilibrium system, an inherent part of which was the electric potential.

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The Theory of Membrane Equilibria.

Cited by 705 publications

References 7 publications

Many-body interactions and the melting of colloidal crystals

Many-body interactions and the melting of colloidal crystals

Where the linearized Poisson–Boltzmann cell model fails: Spurious phase separation in charged colloidal suspensions

The Energetics of Ion Distribution: The Origin of the Resting Electric Potential of Cells

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