Hofmeister effects continue to defy all-encompassing theories, and their origin is still a matter of debate. We observed strong Hofmeister effects in Ca 21 /Na 1 exchange on a permanently charged surface over a wide range of ionic strengths. They could not be attributed to dispersion forces, classical induction forces, ionic size, or hydration effects. We demonstrated that another stronger force was active in the ion-surface interactions, and which would create Hofmeister effects in general. The strength of this force was up to 10 4 times that of the classical induction force, and could be comparable to the Coulomb force. Coulomb, dispersion and hydration effects appeared to be interwined to affect the force. The presence of the observed strong non-classical induction force implied that energies of non-valence electrons of ions/atoms at the interface might be heavily underestimated in current theories, and possibly just those underestimated energies of non-valence electrons determined Hofmeister effects.
Hofmeister effects, also known as specific ion effects, were observed over 120 years ago. Even though they are ubiquitous in the physical, chemical and biological literature, their origin is still contested 1-7 and has been recently brought to the forefront of research [8][9][10][11][12][13][14][15][16][17][18][19] . New work in this area may break down barriers between physics and biology 9 . Ionic sizes, hydration, quantum fluctuations (or dispersion forces) 3,4,8 , and surface charges 1,2 are crucial in Hofmeister effects. Nano-scale surfaces and colloidal particles (e.g., DNA, proteins, cells, bacteria, metal oxides, and clay) are usually strongly charged in aqueous solution, and the sign of the charge or the charge number for biological macromolecules will be dependent on pH and ionic strength 20 . In classical theory, the surface charges can set up a strong electric field extending from the surface to several nanometers in solution. Typical surface charge densities and their corresponding electric field strengths include: (1) . For proteins, surface charge density measurements are primarily based on zeta potentials; therefore, they would be equal to the charge density at the shear plane, which is possibly much lower than the charge density at the surface [27][28][29] , especially when considering the strong surface hydration force [30][31][32] . At the shear plane, the charge density could reach 0.02-0.35 C/m 2 [33][34][35] , with an electric field of 10 7 -10 8 V/m. Therefore, it is reasonable to expect electric field strengths .10 8 V/m at protein surfaces in aqueous solutions. However, in those calculations, adsorbed counter-ions near the surface are treated as point charges. If their ionic size were taken into account, then the electric field near the surface would be much greater than 10 8 V/ m. This is because the finite size of counter ions could weaken their screening effect, as compared with point charges.Noah-Vanhoucke and Geissler found that, the persistence of electric field in the space near ...