Optical quantification of interfacial charge states

1. An apparatus for probing an interface via second harmonic generation (SHG) spectroscopy, the apparatus comprising:

(a) a sample cell comprising a noncentrosymmetric material having a selected orientation angle with respect to a reference axis;

(b) optics configured to illuminate an interface formed between the noncentrosymmetric material and a different material, or formed between two different materials and disposed over the noncentrosymmetric material, with light having a frequency ω under conditions to generate a second harmonic generation (SHG) signal having frequency 2ω;

(c) a detector configured to detect the SHG signal, the SHG signal comprising a bulk second harmonic signal from the noncentrosymmetric material and an interfacial second harmonic signal from the interface; and

(d) a device comprising a processor and a computer-readable medium operably coupled to the processor, the computer-readable medium having computer-readable instructions stored thereon that, when executed by the processor, cause the apparatus to

illuminate the interface to generate the SHG signal; and

detect the SHG signal.

2. The apparatus of claim 1 , the computer-readable medium further having computer-readable instructions stored thereon that, when executed by the processor, cause the device to associate the detected SHG signal with an interfacial charge at the interface.

3. The apparatus of claim 2 , wherein associating the detected SHG signal with the interfacial charge is carried out by comparing the detected SHG signal to a SHG signal generated from a reference interface formed between the noncentrosymmetric material and a reference material at the selected orientation angle.

4. The apparatus of claim 3 , wherein the noncentrosymmetric material is α-quartz and the reference material comprises water.

5. The apparatus of claim 4 , wherein the selected orientation angle is 30°.

6. The apparatus of claim 1 , the computer-readable medium further having computer-readable instructions stored thereon that, when executed by the processor, cause the apparatus to repeat the illumination and detection steps at a second, different orientation angle.

7. The apparatus of claim 1 , wherein the sample cell is configured to provide an external reflection geometry.

8. The apparatus of claim 1 , wherein the noncentrosymmetric material is α-quartz.

9. The apparatus of claim 1 , wherein the noncentrosymmetric material is provided as a substrate composed entirely of the noncentrosymmetric material.

10. The apparatus of claim 1 , wherein the noncentrosymmetric material is provided as a film on a supporting substrate.

11. The apparatus of claim 10 , wherein the supporting substrate comprises a centrosymmetric material.

12. The apparatus of claim 1 , wherein the different material, or one of the two different materials, comprises water.

13. The apparatus of claim 1 , wherein the interface is the interface formed between the two different materials.

14. The apparatus of claim 13 , wherein one of the two different materials comprises water.

15. The apparatus of claim 13 wherein one of the two different materials is a film formed on the noncentrosymmetric material.

16. The apparatus of claim 15 , wherein the other of the two different materials comprises water.