Ionic Behavior in Highly Concentrated Aqueous Solutions Nanoconfined between Discretely Charged Silicon Surfaces

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1 Ionic Behavior in Highly Concentrated Aqueous Solutions Nanoconfined between Discretely Charged Silicon Surfaces Yinghua Qiu, Jian Ma and Yunfei Chen* Jiangsu Key Laboratory for Design and Manufacture of Micro-Nano Biomedical Instruments, School of Mechanical Engineering, Southeast University, Nanjing, , China *Corresponding author: Tel: Fax:

2 Table S1. Numbers of the water molecules and ions in the MD systems with 1.0M NaCl and different surface charge densities. Surface charge density (C/m 2 ) number of water molecules number of Na + ions number of Cl ions Case Case Table S2. Numbers of the water molecules and ions in the MD systems with C/m 2 and different concentrations. Concentration (M) number of water molecules number of Na + ions number of Cl ions Table S3. Numbers of the water molecules and ions in the MD systems with C/m 2 in 4.0M NaCl but different channel widths. channel width (nm) number of water molecules number of Na + ions number of Cl ions

3 Table S4. LJ potential parameters in the equation U( r) ε ( σ rij ) ( σ rij ) = 4 [ / / ] without consideration of the interaction involving hydrogen atoms. Atom pair σ(å) ε (kj mol -1 ) O-O O-Na O-Cl O-Si Na + -Na Na + -Cl Na + -Si Cl - -Cl Cl - -Si

4 (a) (b) Fig. S1. (a)snapshot of the local structures for Na + ions in inner and outer layers from the MD simulation with surface charge density C/m 2 in 1 M NaCl solution at 3.0 nm separation between the surfaces. The gray and red dashed lines show the outer and inner Helmholtz layer, respectively. (b) Red circle shows the ions in inner Helmholtz layer.

5 Fig. S2. Snapshot of the local structures for Na + ions in inner and outer layers from the MD simulation with surface charge density C/m 2 in 1 M NaCl solution at 3.0 nm separation between the surfaces. The red circles show two Na + ions accumulate near one surface charge.

6 Fig. S3. MD simulation results of ion density profiles and charge distribution perpendicular to the surface with charge density from C/m 2 to 0.3 C/m 2 in 0.5 M CaCl 2 solution at 3.0 nm separation between the surfaces. (a). Ca 2+ ion profiles (b). Cl ion profiles (c). Integrated Charge distributions. (d) The most

7 inverted charges at each interface with different surface charge density from 0.075C/m 2 to 0.3C/m 2.The corresponding charge distributions are shown in Fig 2(a), (b), (c), and (e). Fig. S4 Coulomb coupling constant at charged surfaces with different surface charge densities. (Ref. 1) Fig. S5 Normalized peak values for Na + and Cl - ions in different concentration solutions. The peak values in 0.2 M NaCl solution were set as 1.

8 Fig. S6 Repulsive pressure between two silicon surfaces in NaCl solutions with different concentrations (a), separations (b) and time (c). During the simulation, the pressure was calculated each ps. Each point in (a) and (b) was average over 1ns.

9 Fig. S7 Ion concentration distributions in the normal direction of the same charged surfaces but immersed in differently concentrated NaCl solution. The inset is the ion concentration profiles in the center of the nanospace. The surface charge density is 0.3C/m 2. Fig. S8 Debye lengths in monovalent aqueous solutions with different concentrations.

Fig. S9 Ion distributions in the nanoconfined spaces with surface separation from 3.0 to 0.85 nm. The surface charge density in the five cases was the same as 0.15 C/m 2.

10 Fig. S9 Ion distributions in the nanoconfined spaces with surface separation from 3.0 to 0.85 nm. The surface charge density in the five cases was the same as 0.15 C/m 2. In the figure of different cases, the y axis has the same range. Fig. S10 Integrated charge distributions in different nanochannels with the same charged surfaces but different confinements in 4.0 M NaCl solution. The surface charge density is 0.15 C/m 2.

11 Fig. S11 Radial distribution function g ( r) Na + O in 1.0 M NaCl solution. The surface charge density is 0.15 C/m 2 and channel height is 3.0 nm. Fig. S12 Coordination number distributions in different nanochannels with the same charged surfaces but different confinements in 4.0 M NaCl solution. The surface charge density is 0.15 C/m 2. Reference:

12 1. Grosberg, A. Y.; Nguyen, T. T.; Shklovskii, B. I., Colloquium: The Physics of Charge Inversion in Chemical and Biological Systems. Rev. Mod. Phys. 2002, 74,

The change in free energy on transferring an ion from a medium of low dielectric constantε1 to one of high dielectric constant ε2:

The change in free energy on transferring an ion from a medium of low dielectric constantε1 to one of high dielectric constant ε2: The Born Energy of an Ion The free energy density of an electric field E arising from a charge is ½(ε 0 ε E 2 ) per unit volume Integrating the energy density of an ion over all of space = Born energy: