COLLOIDS, LYOPHOBIC 



Particles 



N 

 No.of Portlcles 

 Per Unit 

 Volume. 



Particle 



Fig. 8. a) Particle size distribution curve for sol and b) nucleation curve obtained there- 

 from. (After Turkevich, Stevenson and Hillier). 



Microscopy. Two methods can be used to 

 examine nucleation by electron microscopy 

 (13) firstly, quenching the nucleation process 

 at different times and directly examining the 

 samples and secondly examination of the 

 particle size distribution curves of the formed 

 sol. In the first method the reaction can be 

 quenched at suitable time intervals either by 

 addition of a suitable reagent to stop the 

 reaction, or by a large dilution to slow the 

 reaction down by several orders of magni- 

 tude. Thus from a direct examination of the 

 samples obtained at different times, particle 

 size distribution curves can be obtained for 

 each sample, and a nucleation curve con- 

 structed. 



,The second method, which is less tediotis 

 than the first, was suggested by Turkevich, 

 Stevenson and Hillier (13) and consists of 

 determining the nucleation curve from the 

 particle size distribution curve of the com- 

 pleted sol. The method is based upon the 

 assumption that the principal cause of spread 

 in particle size of the sol is the spread in time 

 in nuclei formation. Thus particles formed in 

 the early stages of nucleation commence to 

 grow immediately, while nuclei formed later 

 have smaller sizes corresponding to a shorter 

 growing time. In the final sol therefore the 

 particles first formed have the larger size 

 and the size distribution curve can be con- 

 sidered as a distorted image of the nticleation 

 curve. Thus if a particle size distribution 

 curve of the type shown in Fig. 8a is con- 



sidered, particles of diameter Dx may be 

 chosen, which correspond to the diameter at- 

 tained by these particles at a time tx on the 

 nticleation curve (Fig. 8b). Thus at a time 

 tx there are Nt^ particles per unit volume, a 

 number which can be expressed as the frac- 

 tion of the number of particles eventually 

 formed at infinite time, i.e., N{t). The total 

 number of particles formed up to time tx is 

 represented by the area shaded in Fig. 8a or 

 the number of particles with diameter 

 greater than D{tx) is given by. 



NiO = 



niD) dD 



0(tx) 



Tiu'kevich, Stevenson and Hillier (13) 

 found that the growth of gold nuclei was 

 given by an eciuation of the form / = (a — 

 log D)/b, where a was a function of the rate 

 constant and of the time at which an arbi- 

 trarily selected reference particle formed; h 

 was proportional to the rate constant. From 

 independent observations of a and h, nuclea- 

 tion curves w^ere constructed from particle 

 size distribution curves. 



The Growth Process. The formation of 

 a sol involves two processes, formation of 

 nuclei and growth of nuclei. If the formation 

 of nuclei is slow and growth rapid the sol 

 consists of a small number of large particles; 

 if nuclei formation is rapid and growth slow 

 the result is a large number of small parti- 

 cles. When both processes are slow, a broad 

 distribtition of sizes is obtained. In nuclea- 



131 



