Dear Abdullah

I think in creasing the porosity the refractive index decrease because of the the surface of pore being partially saturated by the adsorbed O

Hello Mr. M.H. Abdullah,

It is very clear, it is all to do with the light and how it gets refracted froom a surface. If you have more uniform surface better it is for RI. The voids and porosities absorb/refract/diffract the light in various directions thereby decreasing the RI.

You will find our following paper exactly discusses these issues along with the TiO2 thickness, on the RI. Paper is attached below.

Hope you find this answer useful and interesting.

best wishes

R.Shabadi

I wonder, tend to think that reflective properties do depend on porosity, refractive index of the material not. Measureability is another question, i.e. apparent refractive index might change, the real RI not?

The measured refractive index is determined by the sum of all the materials in a composite film. In the case of a porous film, some percentage of the material is air. Thus the observed refractive index for a 90% dense film (with the balance as air) would be 0.9 x refractive index of TiO2 + 0.1 x refractive index of air. Reflective properties are different however and would be influenced by the surface roughness on the scale of the wavelength of the light.

[A]Both THEORETICAL and EMPIRICAL analyses show that a denser material generally tends to have a larger refractive index* because the applied electric field induces a greater number of electric dipoles which changes the relation among refractive index, mass density, molecular polarizability and molecular weight .

[I]Theoretically:

R= (n-1) ^2+k^2/ (n+1) ^2+k^2. ------ [i].

Here R is reflectivity and n is refractive index and k is the extinction coefficient.

R+A+T=1 --------- [ii] and

k= α. λ/4π ----- [iii]

α. (optical absorption coefficient) = 2.303A/t--- (b) – [iv].

A is absorbance and t is thickness .

As the quantities like A,T, α and k change with density ,the n is expected to change.

[II]Empirically:

[a]In general, the refractive index of a glass increases with its density. However, there does not exist an overall linear relation between the refractive index and the density for all silicate and borosilicate glasses. A relatively high refractive index and low density can be obtained with glasses containing light metal oxides such as as Li2Oand MgO, while the opposite trend is observed with glasses containing PbO and BaO .

[c] For gases, n is proportional to the density of the gas as long as the chemical composition does not change. This means that it is also proportional to the pressure and inversely proportional to the temperature for ideal gases.

[B] As the porocity of TiO2 decreases density,its refractive index is expected to decrease as the porocity increases

* Many oils (olive oil) and ethyl alcohol are examples of liquids which are more refractive, but less dense, than water, contrary to the general correlation between density and refractive index( A reverse trend).

Porosity does not changes the density of Titania bulk material, i.e. it does not change the material refractive index.

Dear Dr. M.H. Abdullah,

Though I have not even the slightest intention of challenging your excellence/scholarship in the field( I have never been associated with the reseach in this field, yet I had been the teaching the field during my teaching career from where I had retired over a decade before), yet I humbly put forth my point of view irrespective of the consequences of even proving wrong. I had always been of the opinion that in an academic discussion, no one loses; both win.

Now first an argument:

IRRESPECTIVE OF THE NATURE OF THE SOLID,POROCITY CHANGES THE PACKING FRACTION AND THE LATTICE OCCUPANCY. BOTH THESE FACTORS ARE RELATED TO THE % OF EMPTY SPACE AND THUS THE DENSITY.

Now three references to

The first gives relation between POROCITY ,BULK DENSITY AND SKELTAL DENSITY OF TiO2

[A]“ Studies on Porous Monolithic Materials Prepared by Soln.- Gel Process

By

George Hasegawa

Page116[Table-8.3]

Porocity% (65,42,39)

Bull density(1.28,2.23,2.57)

Skeltal density(3.63,3.88,4.17).

[B] Journal of Physics D: Applied Physics Volume 33 Number 21

Q Fan et al 2000 J. Phys. D: Appl. Phys. 33 2683

[C]Journal of Electrochemical Societry 2005),152(7)F71-F74.

The answer to this question hinges on one fact- whether porocity changes density of TiO2. I have,humbly, put forth the argument( rightly or wrongly) that the density of TiO2 should chage with porocity and have sited some data from a standard book( Reference-I in my previous answer). I will appreciate if the answerees look into this reference to decide its authenticity. If this reference is of some worth , then the density of TiO2 changes with porocity and so should be its refractive index. Even if proved wrong, this man entering the 8th decade of his life (and belonging to an old school of thought) will have the satisfaction to have learnt some more from the my young RG colleagues even at this ripe age.Awaiting.

Reference:

Journal of The Electrochemical Society 2005;152(7) :F71-F74

Two points to note:

[1] The following is relation between density and refractive index of a TiO2 thin film observed anatase (ρ = 3.84 g/cm^3)

ρ = n(film)-0.91933/0.42751

[ II] Relation between porocity and density inTiO2----- See Table-2 of the reference.