Gelation in Beversihle Colloidal Systems. 



109 



really more than n + 2 independent variables, so that the hydrogel is 

 not a monovariant system. In an ordinary system the independent 

 variables are the components (n), temperature and pressure. Agar- 

 water, however, is a system with two components, temperature and 

 two pressures. This follows from the fact that the surface which 

 separates the fluid and solid phases is curved. In point of fact the 

 system is most closely represented by a system of two solutions 

 separated by a membrane which is permeable by only one of the com- 

 ponents, for while water will readily pass the siu-face of separation, 

 agar, having the heavy immobile molecule characteristic of such 

 organic bodies, will be almost unable to do so. Hence, if time be con- 

 sidered finite and small, the surface may practically be considered to 

 be permeable by only one component. As Bancroft* points out, in a 

 system of two solutions separated by semipermeable membrane, there 

 are two pressures and there will be ti -f 3 phases in a nonvariant 

 system when n = the number of components. The hydrogel is a 

 system of three phases and, therefore, on this view, to fix the com- 

 position, it would be necessary to fix the temperature and one pres- 

 sure. This relation would probably be true if the curvature of the 

 surface of separation could be fixed. This, however, is not the case, 

 and in order to fix the composition of the phases it would be necessary 

 either to fix the temperature and both pressures, that of the internal 

 as well as of the external phase ; or to fix the temperature, one pressure, 

 and the form of the surface. Practically we can only fix the tempera- 

 ture and the pressure of the external phase. I have succeeded in 

 obtaining two phases separated by a plane surface by cooling a hydro- 

 sol slowly in an electric field. This method may prove suitable if the 

 system is able to recover from the forces operating during its forma- 

 tion. The method of taking known weights of dry agar and water 

 and keeping them at constant pressure and temperature until equili- 

 brium is obtained is simple, but unfortunately there is the fallacy that 

 the dry agar is a preformed system. The structure of the hydrogel 

 irom which it is reproduced is not destroyed by drying, and the system 

 tends to reform itself on the old lines by the filling of the original 

 -capillary spaces. 



To sum up these remarks, we may describe the hydrogel of agar as a 

 system of three phases, a solid, a fluid, and a vapour phase. The equi- 

 librium is determined by the chemical potential of the components in 

 the various phases, by two pressures, and by temperature. Other 

 operating variables are capillary tension and the energy of the surface 

 between the fluid and solid phases. I have made no measurements to 

 determine how soon the system reaches equilibrium, but the analogous 

 system, gelatine and water, attains to a constant melting point twenty- 

 four hours after the formation of the hydrogel. f 



* Loc. cU. f ' Gela'inCse Losungen,' ran der Heide, Miinchen, 1837. 



VOL. LXVI. L 



