60th Annual Report on Research 2015

Our efforts during the last reporting period focused on two aspects of this problem: (1) a nonperturbative theory for image charges in the double layer structure for weakly charged interfaces; (2) inhomogeneous screening near a dielectric interface.

A nonperturbative theory for image charges in the double layer structure for weakly charged surfaces. We constructed a new theory that includes the effects of image charge interactions in a nonperturbative manner. We described our initial findings in last year's report. The work has been published this year in the Journal of Chemical Physics. The following figure shows the qualitative difference in the concentration profiles for the cations and anions near a positively charged surface.

Figure 1. Ion concentration for a 1:1 electrolyte solution near a dielectric interface. The dielectric constants of the solvent and the plate are respectively e_S=80, e_P=2.5 and charge density s=1e/100nm². The dashed lines are predictions of the PB theory and the solid lines are results of our work.

The markedly different concentration profile predicted by our new theory results in qualitatively new effects not captured by the PB theory.  For example, we find a nonmonotonic dependence of the surface energy on concentration and charge inversion. Our work makes an important contribution to a fundamental problem in the study of colloidal and interfacial phenomena.

Inhomogeneous screening near a dielectric interface. Screening due to the ionic atmosphere around a test charge is one of the most important concepts in the study of charged systems. Screening has profound effects on essentially all properties of biophysical and salt-containing soft matter systems.

In bulk, screening is commonly manifested as an exponential damping of the long-range Coulomb interactions between two test charges. When the ion distribution is nonuniform, as in the vicinity of a charged surface or an interface with dielectric discontinuity, screening also becomes inhomogeneous. The inhomogeneous screening of the fixed surface charge by the mobile ions is accounted for, at the mean-field level, by the Poisson-Boltzmann theory; however, the inhomogeneous screening of the interactions between mobile ions as well as between a mobile ion and its own image charge has not been fully examined.

Figure 2. Non-divergent part of the electrostatic potential generated by a test charge in a 1:1 electrolyte solution near a dielectric interface of lower dielectric constant. The test ion is at 0.15nm from the surface for a) and b) and is at 0.5nm for c) and d). The left figures are results using the bulk screening approximation and the right figures are results from our numerical solution of the full Green function.

The prevalent treatment of screening of interactions between ions and between an ion and its own image in an inhomogeneous system relies on ad hoc approximations, such as the WKB and the bulk screening approximation. Of these two, the bulk approximation is by far the most commonly used. The validity of, and the errors introduced by, these approximate schemes have never been elucidated.

We systematically addressed the effects of inhomogeneous screening for an electrolyte solution near a dielectric interface. The inhomogeneous ion concentration has two consequences for screening: the lower ionic strength near the interface results in less screening on the image force, and the depletion zone has a long-range and accumulative effect on screening, extending the range of the depletion layer; Figure 2 shows the potential generated by a test charge near a neutral dielectric surface. Consequently, the ion distribution is significantly affected. The inhomogeneous screening effect becomes more pronounced in less polar solvent and for ions of higher valency.

The importance of our work is both conceptual and practical. For example, on the conceptual side, our work shows that the image charge near a dielectric discontinuity and its screening is governed by the same equation, whereas the bulk screening approximation treats these two as originating from different physics. On the practical side, it is well known that the Samaras-Onsager theory for surface tension of aqueous electrolyte solution leads to marked downward deviation from experimental data at higher concentrations. This has led many researchers to invoke other effects, such as hydration, dispersion forces, etc. Our work implies (we have not studied the surface tension directly but examined a closely related quantity, the negative adsorption; see Figure 3) that the deviation is primarily a consequence of the use of the bulk screening approximation.

Figure 3. Effects of inhomogeneous screening on the negative adsorption of a 1:1 electrolyte solution at the water/air interface. The dielectric constants of water and air are taken to be 80 and 1 respectively.

Impact on the Personnel

PI: The study of the interfacial properties of salt solutions is a relatively new direction for the PI. The work supported by the ACS-PRF has allowed him to be recognized, within a relatively short period of time, as one of the key researchers in the field. He has been invited to give several invited talks in national professional meetings such as ACS, APS and AIChE meetings, as well as focused meetings such as the American Conference on Theoretical Chemistry.

Graduate Student: The projects in this research have formed an excellent platform for the education and training of the graduate student. Working on resolving some long-standing puzzles and on revising standard textbook knowledge has been tremendously motivating for the student. Critically understanding the existing theories, finding the key missing ingredients in them and ways to improve them, and making predictions based on the new theories, have proved an enriching and rewarding experience for the student. He has given talks in the APS Meeting and the ACS Symposium for Colloid and Interface Science. The leading student supported by the ACS-PRF grant graduated at the end of last year and is now doing postdoctoral studies at MIT. Another graduate student, Bilin Zhuang, who has been supported by an A-STAR scholarship from Singapore, is working on another related project of the proposal and has made some initial progress.