The vacuum stresses between a metal half-space and a metal sphere were recently measured at room temperature, in the 0.6-6 &mgr;m range, with an estimated accuracy of 5%. In the interpretation it was assumed that the accuracy was not good enough for observing any thermal effects. We claim that thermal effects are important in this separation range and back up this claim with numerical calculations of the Casimir force at zero temperature and at 300 K, based on tabulated optical data of gold, copper, and aluminum. The effects of dissipation and temperature are investigated and we demonstrate the importance of considering these two corrections together.
The classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of colloids, and corresponding theories of electrolytes, are unable to explain ion specific forces between colloidal particles quantitatively. The same is true generally, for surfactant aggregates, lipids, proteins, for zeta and membrane potentials and in adsorption phenomena. Even with fitting parameters the theory is not predictive. The classical theories of interactions begin with continuum solvent electrostatic (double layer) forces. Extensions to include surface hydration are taken care of with concepts like inner and outer Helmholtz planes, and "dressed" ion sizes. The opposing quantum mechanical attractive forces (variously termed van der Waals, Hamaker, Lifshitz, dispersion, nonelectrostatic forces) are treated separately from electrostatic forces. The ansatz that separates electrostatic and quantum forces can be shown to be thermodynamically inconsistent. Hofmeister or specific ion effects usually show up above ≈10(-2) molar salt. Parameters to accommodate these in terms of hydration and ion size had to be invoked, specific to each case. Ionic dispersion forces, between ions and solvent, for ion-ion and ion-surface interactions are not explicit in classical theories that use "effective" potentials. It can be shown that the missing ionic quantum fluctuation forces have a large role to play in specific ion effects, and in hydration. In a consistent predictive theory they have to be included at the same level as the nonlinear electrostatic forces that form the skeletal framework of standard theory. This poses a challenge. The challenges go further than academic theory and have implications for the interpretation and meaning of concepts like pH, buffers and membrane potentials, and for their experimental interpretation. In this article we overview recent quantitative developments in our evolving understanding of the theoretical origins of specific ion, or Hofmeister effects. These are demonstrated through an analysis that incorporates nonelectrostatic ion-surface and ion-ion dispersion interactions. This is based on ab initio ionic polarisabilities, and finite ion sizes quantified through recent ab initio work. We underline the central role of ionic polarisabilities and of ion size in the nonelectrostatic interactions that involve ions, solvent molecules and interfaces. Examples of mechanisms through which they operate are discussed in detail. An ab initio hydration model that accounts for polarisabilities of the tightly held hydration shell of "cosmotropic" ions is introduced. It is shown how Hofmeister effects depend on an interplay between specific surface chemistry, surface charge density, pH, buffer, and counterion with polarisabilities and ion size. We also discuss how the most recent theories on surface hydration combined with hydrated nonelectrostatic potentials may predict experimental zeta potentials and hydration forces.
The classical Derjaguin-Landau-Verwey-Overbeek theory that underpins colloid and surface science is shown to be flawed, especially at biological salt concentrations. This is in part because the dispersion forces acting on the ions are ignored. When these are included properly very different results are obtained. These results have substantial implications for biological and for ordinary colloid systems at moderate salt concentrations.
The surface tension of ionic solutions shows marked specific ion effects not explained by existing theories. The effects are here accounted for by invoking a dispersion force between ions and the air−water interface. The measurements can be explained with reasonable values for the dispersion potential.
The surface tension of electrolyte solutions shows marked specific ion effects. We here show an important role for both ionic solvation energies and ionic dispersion potentials in determining this ion specific surface tension of salt solutions. The ion self-free energy changes when an ion moves from bulk solution into the interfacial region, with its decreasing water density profile. We will show that the solvation energies of different ions correlate very well with the surface tension of salt solutions. Inclusion of this distance-dependent self-free energy contribution brings qualitative agreement with experiments and the right Hofmeister series. This is so not only for surface tension changes but also for measured surface potentials. The inclusion of ionic dispersion interaction potentials further improves the agreement with experiments. We discuss how further progress in the theory of the surface tension of salts can be achieved.
The points of zero charge/potential of proteins depend not only on pH but also on how they are measured. They depend also on background salt solution type and concentration. The protein isoelectric point (IEP) is determined by electrokinetical measurements, whereas the isoionic point (IIP) is determined by potentiometric titrations. Here we use potentiometric titration and zeta potential (ζ) measurements at different NaCl concentrations to study systematically the effect of ionic strength on the IEP and IIP of bovine serum albumin (BSA) aqueous solutions. It is found that high ionic strengths produce a shift of both points toward lower (IEP) and higher (IIP) pH values. This result was already reported more than 60 years ago. At that time, the only available theory was the purely electrostatic Debye-Hückel theory. It was not able to predict the opposite trends of IIP and IEP with ionic strength increase. Here, we extend that theory to admit both electrostatic and nonelectrostatic (NES) dispersion interactions. The use of a modified Poisson-Boltzmann equation for a simple model system (a charge regulated spherical colloidal particle in NaCl salt solutions), that includes these ion specific interactions, allows us to explain the opposite trends observed for isoelectric point (zero zeta potential) and isoionic point (zero protein charge) of BSA. At higher concentrations, an excess of the anion (with stronger NES interactions than the cation) is adsorbed at the surface due to an attractive ionic NES potential. This makes the potential relatively more negative. Consequently, the IEP is pushed toward lower pH. But the charge regulation condition means that the surface charge becomes relatively more positive as the surface potential becomes more negative. Consequently, the IIP (measuring charge) shifts toward higher pH as concentration increases, in the opposite direction from the IEP (measuring potential).
Protein solubility studies below the isoelectric point exhibit a direct Hofmeister series at high salt concentrations and an inverse Hofmeister series at low salt concentrations. The efficiencies of different anions measured by salt concentrations needed to effect precipitation at fixed cations are the usual Hofmeister series (Cl(-) > NO(3)(-) > Br(-) > ClO(4)(-) > I(-) > SCN(-)). The sequence is reversed at low concentrations. This has been known for over a century. Reversal of the Hofmeister series is not peculiar to proteins. Its origin poses a key test for any theoretical model. Such specific ion effects in the cloud points of lysozyme suspensions have recently been revisited. Here, a model for lysozymes is considered that takes into account forces acting on ions that are missing from classical theory. It is shown that both direct and reverse Hofmeister effects can be predicted quantitatively. The attractive/repulsive force between two protein molecules was calculated. To do this, a modification of Poisson-Boltzmann theory is used that accounts for the effects of ion polarizabilities and ion sizes obtained from ab initio calculations. At low salt concentrations, the adsorption of the more polarizable anions is enhanced by ion-surface dispersion interactions. The increased adsorption screens the protein surface charge, thus reducing the surface forces to give an inverse Hofmeister series. At high concentrations, enhanced adsorption of the more polarizable counterions (anions) leads to an effective reversal in surface charge. Consequently, an increase in co-ion (cations) adsorption occurs, resulting in an increase in surface forces. It will be demonstrated that among the different contributions determining the predicted specific ion effect the entropic term due to anions is the main responsible for the Hofmeister sequence at low salt concentrations. Conversely, the entropic term due to cations determines the Hofmeister sequence at high salt concentrations. This behavior is a remarkable example of the charge-reversal phenomenon.
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