Silica Units per Particle

Much of the work done with colloidal silica depends on the chemistry of the surface layer of silanol groups, as they are the only part of the particle that is active chemically. Hence it is desirable to have a way to calculate the numbers of active silanols in a sol having a particular size and concentration. The approach shown below is based strictly on a simple geometrical approach. 

The size of the average repeating unit is taken as the volume of a mole of siUca (60 g) divided by its density 2.2 g/cm, divided by Avogadro s number. Expressed in cubic angstroms this volume = 45.3 A.  

TABLE 12.1 Calculated Particle Density Total Vol. silica Calculated 

To simplify things the repeating unit was assumed to have a cubic shape, and the length of a side then is equal to the cube root of 45.3 A = 3.57 A 

The calculation of the particle volume given its diameter (d) is straightforward, Volume = Dividing the particle volume by the volume of one silica unit gives the total number of silica units. Calculating the number of silica units in a particle smaller in diameter by 3.57 A (d-3.57), and substracting the number of silica units in that particle from the previous result gives the number of surface silica units in the particle of diameter (d). 

---