Introduction

Ionization processes in aqueous solutions have long been a point of central interest to physical chemistry. Much progress has been made in recent years in understanding the charging properties of such different entities as small molecules, polyelectrolytes and various kinds of interfaces [1].

In this context, silica and silicate glass surfaces immersed in water are known to acquire a negative surface charge density, primarily through the dissociation of terminal silanol groups. The degree of dissociation and thus the surface charge density results from an equilibrium between counterions at the glass surface and free ions in the bulk electrolyte. Experimentally, this type of equilibrium and its dependence on the solution conditions can be studied by potentiometric acid-base titrations on colloidal dispersions of non-porous silica particles [2]. This technique actually measures the volume concentration of protons transferred between the surfaces and the solution. In order for the surfaces to accommodate a sufficient amount of charge, the electrostatic interaction between the surface sites must be screened at least partially by added salt ions, and/or the available surface area must be large.

These constraints can be relaxed to some degree by resorting to alternative techniques like microelectrophoresis [3,4], streaming potential measurements [5], conductometry [6] and electroacoustic methods [7,8]. All of these methods, however, rely heavily on approximate models for electrostatic or hydrodynamic processes in the interfacial region, introducing uncertainties that are difficult to estimate. We are not aware of any way to measure directly the surface charge of silica in a solution of very low ionic strength.

Theoretical studies of low ionic strength solutions typically deal with dense colloidal and macroionic systems and consider the regime of ``no salt'', ``low salt'', or ``counterions only''. Here the defining assumption is that the overall ionic strength is due predominantly to the particles or macroions and the compensating counterions in solution, whereas the concentration of any additional ions is negligible. For colloidal dispersions this assumption is again legitimate if the specific surface area carrying the colloidal charge is large.

A series of recent experiments has spurred interest in the charge on glass and silica surfaces of low specific area in pure water, i.e. systems for which the usual picture of the ``no salt'' regime does not apply. For example, interaction measurements using digital video microscopy and optical trapping suggest that highly charged latex spheres may experience an anomalous long-ranged attraction when confined by charged glass walls [9,10,11,12], contrary to the predictions of Poisson-Boltzmann theory [13,14,15]. In one particular case [12], the attraction appears to result from a hydrodynamic interaction driven by the spheres' electrostatic repulsion from a nearby wall [16]. This explanation hinges on the heretofore untested assumption that the glass wall carries an effective charge density of $-2000 \pm 200~e/\mu {\rm m}^2 \xspace$, where $e$ is the elementary charge. Such hydrodynamic coupling does not seem to explain the like-charge attractions measured for spheres confined between two charged glass walls [9,10,11], since the proposed effect is strongly suppressed by the second wall. How the walls' charge influence colloidal electrostatic interactions is not yet resolved, in part because of open questions regarding the charging state of the glass. We recently reported that the pair interaction of silica spheres remains monotonically repulsive even in the presence of a single glass wall [17]. The spheres' effective surface charge density of $- 700 \pm 150~e/\mu {\rm m}^2 \xspace$ extracted from these measurements is considerably smaller than the value posited in Ref. [16] for a compact glass surface.

Because a silica surface's charge density depends on the local chemical environment, it necessarily varies with proximity to other charge-carrying surfaces. The interpretation of typical particle deposition experiments [18] and force measurements by atomic force microscopy (AFM) [19,20] or total internal reflection microscopy (TIRM) [21] for example, is complicated by the fact that the charge densities of the substrate and the probe are a function of their separation, a phenomenon known as ``charge regulation'' [22,23,24]. Since local properties of the enclosed solution rather than bulk properties determine the charging state, a naive use of charging data from bulk measurements can lead to errors.

In the following section we discuss how the experimentally supported 1-pK Basic Stern Model [25,26] for silica surfaces may be used to calculate the elusive charge of glass plates and strongly diluted silica particles in deionized water. In the remainder of this paper we take advantage of a recently proposed theoretical treatment of charge regulation [27,28] to discuss the the charge of a silica-like surface in close proximity to a second anionic surface, which will be chosen, in view of the most common applications, as either of the same type or of constant charge (like sulfate latex) or of carboxylic nature (like carboxyl latex and many biological surfaces).