Try the attached webpage.

https://refractiveindex.info/?shelf=main&book=TiO2&page=Bodurov

Perhaps you will find this useful:

Mergel, D.; Buschendorf, D.; Eggert, S.; Grammes, R.; Samset, B., Density and refractive index of TiO2 films prepared by reactive evaporation. Thin Solid Films 2000, 371, 218-224.

Refractive index (n) was between about 2 and 2.3, depending on density (r) with:

n = 0.28*r + 1.37

with r in grams per cm^3

Dear Oliver,

Thanks a lot for your response. However, I have a rather stupid question to ask. I wonder if refractive index of thin films (possibly strained) would be applicable to nano particles ? Kindly let me know.

Regards

Try the attached webpage.

https://refractiveindex.info/?shelf=main&book=TiO2&page=Bodurov

Hi aditya. Hope u are doing well.

Generally for TiO2 = nearly 2.4

But it can vary from 2.4 (anatase phase) to 2.6 (rutile phase)

REF:

https://refractiveindex.info/?shelf=main&book=TiO2&page=Kischkat

Hello Aditya,

I certainly do not know for sure.  However, the density and refractive index are correlated, so it would help if you knew their density?  Since you say they are amorphous, I would expect a density significantly lower than the usual crystalline polymorphs, and therefore a lower index.

Michal's reference is helpful since it is relevant to nanoparticles, however, if they are crystalline, the index is probably higher than your amorphous nanoparticles (and is indeed in the range of the bulk crystals as mentioned by Robin).

See Fig. 1 of Alderman, O.L.G., et al., Phys. Rev. B, 2014. 90(9): 094204. for comparison of the densities of various forms of TiO2. 

Regards,

Oliver

Article Structure of molten titanium dioxide

For a DLS particle size distribution the optical properties are not required for the most robust intensity distribution where the z-average and polydispersity index should be quoted. See:

http://www.materials-talks.com/blog/2014/01/23/intensity-volume-number-which-size-is-correct/

To convert to volume (never to number) the optical properties would be required for Mie theory. The RI's of crystalline forms (rutile, anatase, brookite) of TiO2 are well-known.  For amorphous forms (with sol-gel we also expect substantial hydration too) then I'd expect the RI's to 'smear' and be lower (no birefringence) than the crystalline forms.  The above-quoted 2.2 to 2.4 seems reasonable to me.  Conduct a (mandatory) robustness test on the utilized optical properties and see if it makes a difference. For small (nano) material it invariably makes little difference. If it does then you should go about measuring the RI. There are links (Gladstone-Dale) between density and RI (as described above). See also:

August 11th 2011 Optical properties of the three forms of titanium dioxide

http://tinyurl.com/pbgf9hj 

The reference from Michael above is excellent.  I almost forgot to mention the the RI is highly wavelength dependent (as the wavelength decreases both the real and the imaginary component of the RI increase) but was assuming the 632.8 mm of the He-Ne laser in the Zetasizer.

The dielectric constant, related to refractive index, ranges from 6 (TiO2 dynamic dielectric constant) to 60 (corresponding to a static dielectric constant). See e.g.

J. L. Movilla, G. Garcia-Belmonte, J. Bisquert, and J. Planelles, Phys. Rev. B 72, 153313 (2005); M. Mikami, S. Nakamura, O. Kitao, and H. Arakawa, Phys. Rev. B 66, 155213 (2002); R. A. Parker, Phys. Rev. 124, 1719 (1961)

To add to my previous answer, Mergel et al. actually cite the data of:

Laube, M.; Rauch, F.; Ottermann, C.; Anderson, O.; Bange, K., Density of thin TiO2 films. Nucl. Instrum. Meth. B 1996, 113, 288-292

and recommend using the fit to their dataset which they state as:

n = 0.35*r + 1.27

with n the refractive index at 550nm, and r in grams per cm^3. However, if I fit the data I obtain a slightly different zero density intercept:

n = 0.35(1)*r + 1.23(4)

with uncertainties in parentheses. Also note that Mergel et al.'s data and relationship with density that I quoted above is for 633 nm.