Theory of the Thermogravimetric Analysis of Silica Gel

 

The Basic Theory

 

During the thermogravimetric analysis of silica gel there is a continual loss of water over a temperature range from 30^oC about 1050^oC. Water can be held on the surface of the silica gel by different interaction forces; by 'dispersive forces' (e.g. physically bound water), 'polar forces' (e.g. hydrogen bonded water), or, by 'chemical forces' (e.g. silanol groups that condense to siloxane bonds with the release of water). As a result of the interaction forces between the adsorbed water and the silica surface, each molecule has a potential energy of adsorption. Furthermore, the silanol groups must acquire sufficient kinetic energy before they can condense to siloxane bonds and generate water. As the temperature is raised, so the kinetic energy of the adsorbed water and silanol groups increases and when the energy is equivalent or greater than the potential energy of adsorption or chemical combination, water will leave the surface in vapor form. Due to the number of different ways that water can be held on the surface of the silica gel, there will be a number of different sources of desorbable water.

 

These different sources might be considered as groups of adsorbed or combined water, within which, the potential energies of adsorption for each water molecule will be similar but not necessarily identical to one another. Conversely, between groups, the mean potential energy of the adsorbed or combined water may be widely different, as the temperature range over which all the water is evolved, is large. The distribution of adsorption energy within a group could take one of many forms.

Figure 28. Diagram Showing Distribution of Site Adsorption Energy

 

However, due to the irregular nature of the silica gel surface, it is likely that the distribution of energy about a mean would be random in nature and, thus, could be appropriately described by a modified error function. Consequently the energy distribution of a particular desorbable species could take the form of the error function curve shown in figure 28. For any given body, its kinetic energy will be proportional to its temperature and, consequently, temperature is employed as the energy scale in the above graph. Thus the error function can be put in the slightly modified form of the standard equation, vis.,

 

where (n_t) is the number of adsorbed or combined water molecules having

                  energy (e_t) at temperature (T), (where, e_t = jT, and (j) is a constant),

         (T_X) is proportional to the mean energy (e_m) (thus, e_m = jT_X)_,

         (T_s) is the standard deviation of the energy distribution.

 and   (A) is a constant.

 

The mass of molecules having energy (e_t) at temperature (T) will be (an_t) where (a) is the weight of one molecule. Thus, the total weight lost from a given group of similarly adsorbed molecules, (m₁), will be given by,

 

                              

 

For (r) different groups, the total mass lost (M) during TGA will be,

 

 

Furthermore, assuming that the temperature is linearly programmed, the total mass lost up to any arbitrary temperature (T), (M_T), will be given by,

 

Providing the correct values for the constants are identified, the above equation will provide a theoretical TGA curve that should be identical to that shown in figure 27.