Liquid–Polymer Contact Electrification: Modeling the Dependence of Surface Charges and ξ-Potential on pH and Added-Salt Concentration

Abstract

Here, a mathematical model is presented, which accounts for the dependence of the surface electrical charge density (σ) on pH and the concentration of added salts (C s), generated when a water drop rolls or slides on the surface of a hydrophobic polymer, a process known as liquid–polymer contact electrification (LPCE). The same model was successfully applied to fit the isotherms of ξ-potential as a function of pH, reported in the literature by other authors for water–poly­(tetrafluoroethylene) (PTFE) interfaces. Hence, the dependence of σ and ξ on pH was described using the same concept: acid–base equilibria at the water–polymer interface. Equilibrium constants were estimated by fitting experimental isotherms. The experimental results and the model are consistent with a number of 10–100 acid–base sites/μm2. The model predicts the increase of |σ| and |ξ| with pH in the range of 2–10 and the existence of a zero-charge point at pHzcp ≅ 3 for PTFE (independent of C s). Excellent fits were obtained with K a/K b ∼ 9 × 107, where K a and K b are the respective acid and base equilibrium constants. On the other hand, the observed decrease in |σ| and |ξ| with C s at fixed pH is quantitatively described by introducing an activity factor associated with the quenching of water activity by the salt ions at the polymer–water interface, with quenching constant K q. Additionally, the quenching predicts a decrease in |σ| and |ξ| at extreme pH, where I > (1/K q) (I: ionic strength), in agreement with literature reports.

Ion Concentration Influences the Charge Transfer Due to a Water–Air Contact Line Moving over a Hydrophobic Surface: Charge Measurements and Theoretical Models

“…This is in contrast to a solution of HCl (green squares), which for the smallest concentrations does not alter the charge transfer to within the experimental uncertainty, but beyond 5 μM gives rise to a strong decrease. Moreover, it is found that for HCl concentrations in the range 0.1–1 mM, the charge transfer changes sign and becomes negative, as was also reported in refs and . This reversal of charge transfer can also be seen from the green curve in Figure a.…”

“…It also explains the observed increase in charge transfer for increasing pH up to 10, as well as the decrease in charge transfer with salt concentration. However, the theory presented in ref does not naturally explain why dissolved salts give rise to the same increase in charge transfer for small concentrations as is observed in Figure . In the current work, it is shown that by some modifications of the theory of ref , clarifying the various contributions to charge transfer, one may construct a chemical equilibrium theory which explains all the features mentioned earlier.…”

“…The surface-active protons denoted false( normalH + false) normals are released near the polymer surface. This reaction can be written as P normals normalp + normalH 2 normalO ⇆ false( P normals normalp normalO normalH − false) normals + false( normalH + false) normals , goodbreak0em3em⁣ K normala = a false( normalH + false) normals .25em · .25em θ false( P normals normalp normalO normalH − false) normals a normalH 2 normalO .25em · .25em θ P normals normalp Here, K a is a dimensionless equilibrium constant following the description in ref , a normalH 2 normalO is the water activity, …”

“…The quenching is described by a factor γ p = a f /( a f + a b ), where a f is the activity of free water and a b is the activity of water bound by ions. If one assumes that the sum of free and bound water molecules is constant and that the reaction between salt and water to create bound water is associated with an equilibrium constant K qp , then γ p = 1/(1 + K qp c ), where c is the concentration . This equation for γ p must be included to account for the effective number of ions participating in the charge transfer and will be used in the modeling.…”

“…The influence of the ion concentration plays a role when liquid–solid interfaces charge up in the presence of flow. − Measurements of the zeta potential at different salt concentrations demonstrate that for polytetrafluoroethylene (PTFE), the isoelectric point occurs for a pH about 3. , X-ray photoelectron spectroscopy indicates that surface contaminations are unlikely to be the source of the proton release from the inert PTFE-particle surfaces, although the expected limit of detection is too uncertain to allow conclusive evidence thereof . Recent measurements using different types of measurements on different liquid motion systems appear to indicate that the charge transfer increases with the ion concentration for very dilute solutions but decreases with the ion concentration above 0.1–1 mM. − However, at the same time, it is also known that some acids lead to a monotonic decay of charge transfer, and even reversal of charge, when the pH decreases. ,,, Some of these effects are well explained by an acid-base chemical equilibrium theory given in ref . For example, the theory of ref explains very well why the charge transfer decreases with increasing concentration of acid, corresponding to a gradual decrease in pH, and the occurrence of an isoelectric point where the charge transfer is zero.…”