ELECTRON MICROSCOPY 



tioii the number of particles formed as a 

 f miction of time is studied, whereas in the 

 case of growth the rate of increase in the size 

 of the particle with time is the important 

 factor; strictly, in order to study growth the 

 number of nuclei should be kept constant. 

 One method of maintaining this condition in 

 practice is to add nuclei to a slightly super- 

 saturated solution of the growing species. 



The growth process which appears to have 

 been investigated in most detail by electron 

 microscopy is that of colloidal gold. Turke- 

 vich, Stevenson and Hillier (13) took ad- 

 vantage of the fact that in a slightly acid 

 solution of chlorauric acid and hydroxyla- 

 mine hydrochloride, in a very clean closed 

 vessel, colloidal gold was not produced until 

 a sufficient number of nuclei were intro- 

 duced. Thus when the growth medium was 

 inoculated with nuclei, the chlorauric acid 

 was reduced by the hydroxylamine and the 

 metallic gold was deposited only on the 

 nuclei; hence the nuclei increased in size but 

 not in number. The mean diameter of the 

 resulting particles, Dg , was shown to be 

 given by 



D, = Dn 



, 3/M„ -f Mc, 



M„ 



where Dn was equal to the mean diameter of 

 the nuclei and Mn and Mce were the respec- 

 tive masses of the metallic gold in the nuclei 

 and ionic gold in the growth medium. 



From an examination of the particle size 

 distribution curves obtained from the ki- 

 netics of citrate reduction determined chem- 

 ically, it was found that the growth law was 

 of the form 



dt 



= kD 



where k was a constant dependent on tem- 

 perature and reagent concentration but not 

 on particle size. 



The growth of gold particles in monodis- 

 perse gold sols produced by the action of 

 sodium citrate on chlorauric acid has also 



been studied by Takiyama (15) using elec- 

 tron microscopy. The size of a particle at a 

 time t (minutes) was expressed by the mole 

 number of one particle, x (mole), as calcu- 

 lated from the mean particle diameter D by 

 the relation, 



X = 4/37r(D/2)'p/M 



where p and M are the density and molecular 

 weight of gold, respectively. It was found 

 that the rate of growth was expressed by the 

 equation, 



— = A;x2/3(x„ — x) , 

 at 



where x and Xoa are the mole numbers of the 

 particles at a time t and after completion of 

 growth; k was a rate constant. It was found 

 that the growth process was autocatalytic 

 with respect to the surface of the gold parti- 

 cles. 



The Ageing Process. A lyophobic sol is 

 never stable in the thermodynamic sense 

 and is always proceeding in the direction 

 which involves a decrease in the surface free 

 energy of the solid-liquid interface. Thus 

 there is always present a tendency for the 

 total surface area of the sol to decrease, until 

 a pseudo-stable equilibrium is reached; at 

 this stage the sol consists of dispersed pri- 

 mary particles. The process of change from 

 the initial sol, which may consist of a large 

 number of small particles, to the final "sta- 

 ble" sol which may consist of a small number 

 of large particles is termed ageing; the dis- 

 solving of smaller particles accompanied by 

 growth of larger ones is sometimes termed 

 Ostwald ripening (Fig. 9). The rate of ageing 

 may be slow or fast, according to the condi- 

 tions and the material employed. In the case 

 of barium sulfate, for example, the ageing 

 process even at room temperature is rapid 

 and large crystals are formed ; it is difficult to 

 prepare a very stable finely dispersed sol. On 

 the other hand, in the case of silver iodide, 

 sols of finely dispersed particles can be pre- 

 pared which are stable for several years. The 



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