We have the same instrument in our lab. I would advice not to use it and to explain it let me give a brief insight about the instrument. The way it measures the size of nanoparticle is by amount of scattering of the incident light. If we have to compare 2 nanoparticle of different sizes, the bigger sized nanoparticle will scatter the light more than the smaller sized one. In the actual measurement there will be some scattering of the incident laser light from the cuvette material as well. The polystyrene cuvettes are already calibrated and will give you an accurate nanoparticle size measurement. If the quartz cuvette is used instead of polystyrene one, then the scattering will be different from the polystyrene ones and you will end up getting either higher particle size and lower particle size. The only thing you would be able to tell is which nanoparticle is bigger or smaller. However, if you could find a quartz based cuvette in their library that will give a better result.
If your quartz cuvette is clean it should present no problems whatsoever. Just make sure each side of the cuvette is clean, since the scattering angle analyzed is usually perpendicular to the incident laser beam. Plastic cuvettes are convenient as they are inexpensive and disposable.
The size is measured, not by the amount of light scattered, but by measuring intensity fluctuations in the scattered light, calculating an auto-correlation function of these scattered intensities, and measuring the dynamical decay constant of this function. This decay constant is used to measure q^2D where D is the particle self-diffusion coefficient of the particle(s) you are studying and the scattering vector q, containing laser wavelength and sin(theta) information [sin(theta)=1 for 90 degree scattering].
The self-diffusion coefficient, D, is used to calculate particle diameter, using the Stokes-Einstein equation, solvent viscosity, and temperature.
We have routinely used quartz and glass cuvettes for DLS/QELSS measurements. There should be no issue. With respect to plastic cuvettes, I recall an occasion many years ago in which either the solvent or the coolant for the bath dissolved part of the cell. This was an incredible mess to clean up, because something coated some of the windows.
Yes, most standard quartz cuvettes should be just fine. Only potential issue is when the cuvette is black in parts to minimize background. Here is what to keep in mind:
For a 90 degree system [Zetasizer Nano ZS90, Zetasizer Nano S90, Zetasizer microV] the fluorescence cuvette must be totally clear for at minimum 3 sides of the cuvette, in order to not block the light on the way into the cuvette, one the way out of the cuvette, and on the path from the scattering volume to the detector (at 90 degrees).
For a backscattering 173 degree system (Zetasizer Nano ZS, ZSP, S) the optical path much be clear at least for two opposite windows of the four sides, the front and the back window. The 'line of detection' must pass through the cuvette window about 3mm next to the laser beam, so the front window should be about >5mm wide.
So for cuvettes with 4 clear windows, there should not be any issues, keeping in mind that the laser goes through the cuvette about ~9mm from the bottom [the "z-height"]. In essence, if you can measure a sample then it should be fine. If the beam is blocked you would not be able to get any scattering intensity and thus cannot use that cuvette. The picture of the flow cell may be intuitive for clarification.