Disjoining pressure of an electrolyte film confined between semipermeable membranes

Partial osmotic pressures of ions in electrolyte solutions and the Gibbs-Guggenheim uncertainty principle

The concept of the partial osmotic pressure of ions in an electrolyte solution is critically examined. In principle these can be defined by introducing a solvent-permeable wall and measuring the force per unit area which can certainly be attributed to individual ions. Here I demonstrate that although the total wall force balances the bulk osmotic pressure as required by mechanical equilibrium, the individual partial osmotic pressures are extrathermodynamic quantities dependent on the electrical structure at the wall, and as such they resemble attempts to define individual ion activity coefficients. The limiting case where the wall is a barrier to only one species of ion is also considered, and with ions on both sides the classic Gibbs-Donnan membrane equilibrium is recovered, thus providing a unifying treatment. The analysis can be extended to illustrate how the electrical state of the bulk is affected by the nature of the walls and the container handling history, thus supporting the "Gibbs-Guggenheim uncertainty principle," namely the notion that the electrical state is unmeasurable and usually accidentally determined. Since this uncertainty is conferred also onto individual ion activities, it has implications for the current (2002) IUPAC definition of pH.

Electrostatics and Interactions of an Ionizable Silica Nanoparticle Approaching a Plasma Membrane

The surface charge of the plasma membrane (PM) and the large salt content of the extracellular space ensure a significant role of the electrostatic effect dictating the interaction between the PM and an approaching nanoparticle (NP). In this article, we theoretically study the case of an ionizable silica NP approaching the PM. We witness that the surface charge of the silica NP, dictated by the surface ionization of the silica in the electrostatic environment created by the PM surface charge and the extracellular ion concentration, decreases as it approaches the PM. In other words, a silica NP is more negative away from the PM than in close proximity to the PM. Accordingly, we witness a significantly lower repulsion between the PM and NP favoring the approach and the interactions of the silica NP with the PM. Additionally, the presence of the silica NP in the vicinity of the PM induces a large nonisopotentiality, even across a fully permeable PM. We anticipate that these findings will be critically important in the better design of the widely used silica NPs for targeted drug and gene deliveries.

Effect of Plasma Membrane Semipermeability in Making the Membrane Electric Double Layer Capacitances Significant

Electric double layers (or EDLs) formed at the membrane-electrolyte interface (MEI) and membrane-cytosol interface (MCI) of a charged lipid bilayer plasma membrane develop finitely large capacitances. However, these EDL capacitances are often much larger than the intrinsic capacitance of the membrane, and all of these capacitances are in series. Consequently, the effect of these EDL capacitances in dictating the overall membrane-EDL effective capacitance C_eff becomes negligible. In this paper, we challenge this conventional notion pertaining to the membrane-EDL capacitances. We demonstrate that, on the basis of the system parameters, the EDL capacitance for both the permeable and semipermeable membranes can be small enough to influence C_eff. For the semipermeable membranes, however, this lowering of the EDL capacitance can be much larger, ensuring a reduction of C_eff by more than 20-25%. Furthermore, for the semipermeable membranes, the reduction in C_eff is witnessed over a much larger range of system parameters. We attribute such an occurrence to the highly nonintuitive electrostatic potential distribution associated with the recently discovered phenomena of charge-inversion-like electrostatics and the attainment of a positive zeta potential at the MCI for charged semipermeable membranes. We anticipate that our findings will impact the quantification and the identification of a large number of biophysical phenomena that are probed by measuring the plasma membrane capacitance.

Electric double layer electrostatics of lipid-bilayer-encapsulated nanoparticles: Toward a better understanding of protocell electrostatics

Lipid-bilayer-encapsulated nanoparticles (LBLENPs) or NP-supported LBL systems, such as protocells (which are lipid bilayer encapsulated mesoporous silica nanoparticles or MSNPs) have received extensive attention for applications like targeted drug and gene deliveries, multimodal diagnostics, characterization of membrane-geometry sensitive molecules, etc. Very often electrostatic-mediated interactions have been hypothesized to play key roles in the functioning of these LBLENPs. Despite that, very little has been done to theoretically quantify the fundamental electric double layer (EDL) electrostatics of such LBLENPs. In this study, we develop an EDL theory to describe the electrostatics of such LBLENPs. We show that the electrostatics is a manifestation of the charged/dielectric nature of the NP, LBL structure and charging, and the ionic environment in which the LBLENPs are present. We also establish that for certain conditions of charging of the NP one witnesses a most remarkable charge inversion like electrostatics within the LBL membrane or the NP itself. We anticipate that our findings will provide an extremely useful platform for better understanding the fabrication and functioning of such LBLENPs and discuss examples where our theory can be useful.

Electrostatic interactions and electro-osmotic properties of semipermeable surfaces

We consider two charged semipermeable membranes which bound bulk electrolyte solutions and are separated by a thin film of salt-free liquid. Small ions permeate into the gap, which leads to a steric charge separation in the system. To quantify the problem, we define an effective surface charge density of an imaginary impermeable surface, which mimics an actual semipermeable membrane and greatly simplifies the analysis. The effective charge depends on separation, generally differs from the real one, and could even be of the opposite sign. From the exact and asymptotic solutions of the nonlinear Poisson-Boltzmann equation, we obtain the distribution of the potential and of ions in the system. We then derive explicit formulae for the disjoining pressure in the gap and electro-osmotic velocity and show that both are controlled by the effective surface charge.