Finding wavelength from infrared LED in a photodiode sensor

It's not obvious to me if you want to calibrate your instrument to measure the size of your particles, or to measure the concentration of particles in a volume. I'm assuming you want to measure particle concentration, but most of this applies to either case.

I'm not familiar with the measurement you're describing, but the obvious way to calibrate it is to buy samples of powders of known particle size, disperse them in a known volume, and measure the response of the detector. A web page at the University of Manchester supports this method:

"In practise, theoretical instrument response curves are not used for sizing of particles, rather a series of calibration particles of known size are used to determine the response of the instrument over its full size range. A curve is fitted to these measurements to allow sizing of particles which fall between the calibration points."

If the particles you're measuring are not very tightly distributed in size (say they vary by +/- 50% in diameter), then you probably don't need to worry about the ripples in the Mie scattering curve you showed. Just use an average value of the response over the range of sizes you expect in your sample. To calibrate the instrument you'd need a reference sample with a comparable spread of particle sizes.

Generally with a measurement like this there's so many factors that vary between experiments (maybe the shape of the particles, the amount of turbulence in the sample volume, or other sources of reflected light) that a factory calibration from the instrument vendor isn't likely to be very precise. More likely you'll need to start with a reference measurement in your lab, and then make further measurements relative to that.

The peak sensitivity wavelength of the photodiodes is completely unrelated to the PWM frequency that might be used to modulate the IR signal. The system you have assembled does not use modulated IR and cannot benefit from applying PWM to the emitters.

What you can do is verify that the peak emission from your IR LEDs is close to the wavelength of peak sensitivity for the photodiodes. You could also consider using an IR filter that would block visible light from getting to your photodiodes. They may not be very sensitive to visible light but there is a lot of visible light that competes with your IR signal.