Interfacial structure

As discussed in Sec. 3.2.2, the electrostatic double layer is formed because of the finite potential difference between the two coexistent phases. Charge separation occurs within the electrostatic double layer. Excess ions accumulate near the interface. On the other hand, the composition of the mixture changes within the diffuse interface, which results in a significant change of the solvation energy. Ions will be preferentially distributed in the region of lower solvation energy as discussed in Sec. 3. The interfacial structure is determined by these two effects.

-20 -10 0 10 20 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 N o r m a l i z e d E l e c t r o s t a t i c P o t e n t i a l z(nm) e (a) C o m p o s i t i o n -20 -10 0 10 20 0.004 0.006 0.008 0.010 0.012 c - I o n C o n c e n t r a t i o n ( m o l / L ) z(nm) c + (b)

severalas, that is on the order of 1nm. However, the Debye screening length can vary from nanometer

to micrometer, depending on salt concentration. Fig. 3 shows the structure of the interface for the electrolyte solution with intermediate salt concentration (c∞

α = 0.01 mol/L). From the composition

profile in Fig. 3.3(a), we can see a diffuse interface with the width of 7nm between the two coexisting bulk solutions. The change of the electrostatic potential profile is smoother than the composition profile, which indicates that the electrostatic double layer is significantly wider than the composition interface (C−1_{< κ}−1_).

The concentration of cations and anions, and the total ion concentration (c++c−) are shown

respectively in Figures 3(b) and 3(c), from which we can see the behavior of ion distribution in different regions. Beyond the electrostatic double layer (i.e. |z|> κ−1_{), the concentration of cations}

-20 -10 0 10 20 0.008 0.012 0.016 0.020 -12 -8 -4 0.02000 0.02005 3 6 9 12 15 0.0090 0.0092 3 2' 2 1' c + + c - ( m o l / L ) z(nm) 1 (c)

Figure 3.3: The interfacial structure for the electrolyte solution withc∞

α = 0.01mol/L, (a) profiles

of normalized electrostatic potential and composition, (b) the concentration of cations and anions, and (c) total ion distribution. The inserts in (c) show the excess ion accumulation in regions 2 and 2’. εA= 80,εB= 40. z+=z−= 1,a+= 0.1nm,a−= 0.2nm,as= 0.5nm,χ= 2.2 andT = 400K.

by 1 and 1’ in Fig. 3.3(c)). In the intermediate region that is inside the electrostatic double layer but outside the diffuse interface (κ−1 _{>|z| > C}−1_{), the composition is nearly constant while the}

electrostatic potential changes smoothly. The behavior of the ion distribution in this region (denoted by 2 and 2’ as in Fig. 3.3(c)) is qualitatively the same as the case of the sharp interface. Charge separation becomes more significant as|z|decreases. There are also excess ions accumulating (see the insets of Fig. 3.3(c)) in this region. Within the diffuse interface (|z|< C−1_{), the composition profile}

changes more dramatically than the electrostatic potential profile. Solvation energy is the dominant effect on the ion distribution in this region (denoted by 3 as in Fig. 3.3(c)). The concentration of both cations and anions decreases when entering from region 2, because of the penetration of the solvent molecules with low dielectric constant in the diffuse interface. Similarly, the ion concentration increases when entering from region 2’. To calculate the net change of the ion concentration in region 3 compared to the bulk region, the exact position of the interface is needed. Onuki[22] pointed out that ions are repelled from the diffuse interface by defining the interface position with the Gibbs construction on the composition profile[34]. With the composition profile, cation and anion profiles all different, an unambiguous Gibbs construction is not obviously possible. Nevertheless, the conclusion that ions are slightly depleted in region 3 still stands, which is reflected by the behavior of the interfacial tension as will be discussed in Section 3.4.2.

The length scale of the electrostatic double layer strongly depends on the salt concentration, which leads to differences in the interfacial structure for the concentrated and the dilute electrolyte solution. Fig. 3.4 and Fig. 3.5 show the profiles of electrostatic potential and composition, and

-60 -40 -20 0 20 40 60 0.2 0.4 0.6 0.8 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 c 1 =1mol/L c 1 =0.001mol/L z(nm) e c 1 =1mol/L c 1 =0.001mol/L

Figure 3.4: Profiles of normalized electrostatic potential and composition for c∞

α = 1 mol/L and

c∞

α = 0.001 mol/L.εA= 80,εB = 40. z+=z−= 1,a+= 0.1nm,a−= 0.2nm,as= 0.5nm,χ= 2.2

andT = 400K.

the ion distribution for these two cases (c∞

α = 1 mol/L andc∞α = 0.001 mol/L). For c∞α = 1mol/L,

both the electrostatic double layer and the diffuse interface have a length scale of a few nanometers (κ−1_∼=C−1_{). Regions 2 and 2’ shrink. The charge separation is greatly inhibited as shown in Fig.}

3.5(a). The change of the solvation energy plays the main role in determining the ion distribution, which leads to ions being repelled from the interfacial area. For the case of very dilute electrolyte solution (c∞

α = 0.001mol/L), the electrostatic double layer is about 100 times wider than the diffuse

interface (κ−1_ÀC−1_{). From the view of the electrostatic potential which changes very smoothly,}

the composition profile behaves as a step function. The behavior of ion distribution is similar to the case of sharp interface, seen from the similarity between Figures 3.5(b) and 3.1(a). Excess ions accumulate in the interface area.