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SCIENCE 



[N. S. Vol. XLIV. No. 1138 



system with negative surface tension at the 

 boundary between phases,' instead of it requir- 

 ing work to increase the surface, the system 

 could actually be made to do external work on 

 its surroundings when an increase in surface 

 takes place. In such systems there will ob- 

 viously be a decrease in free energy accom- 

 panying increase in surface and if left to 

 themselves these systems will spontaneously 

 increase their surface either by an increase in 

 the convolutions of the boundary or by disper- 

 sion into smaller particles. Since spontaneous 

 changes can only take place when accompanied 

 by decrease in free energy it is evident then 

 that we have negative surface in the case of all 

 systems which are undergoing a spontaneous 

 increase in surface. 



There are of course, as a matter of fact, an 

 enormous number of systems which undergo 

 spontaneous increase in surface, and hence 

 possess negative surface tension. All of the 

 hydrophyllic colloidal substances, such as gela- 

 tine, agar-agar, lecithin, etc., will spontane- 

 ously disperse when placed in contact with 

 water and hence have negative surface ten- 

 sion. (When lecithin is placed in contact with 

 water the formation of protuberances and con- 

 sequent increase in surface can be observed 

 under the microscope.) Also in the case of 

 hydrophobic colloidal systems it is well known 

 that under proper conditions an increase in 

 the degree of dispersion will take place; thus 

 colloidal solutions of ferric hydroxide increase 

 their dispersion when hydrogen ion is added to 

 the solution, flocculent gold can be dispersed 

 with ammonia, 2 ferric hydroxide which has been 

 precipitated with sodium chloride is redis- 

 persed when the chloride is washed out, 3 and, 

 as shown by Mr. R. J. McKay working in the 

 writer's laboratory, the size of the particles in 

 a colloidal solution of carbon (Higgin's draw- 

 ing ink) depends on the concentration of 

 added sodium chloride, and particles whose 

 size has been increased by addition of sodium 

 chloride grow gradually smaller again on 

 dialysis with pure water. Hence in all these 



2 "Whitney and Blake, J. Amer. Chem. Soc, 26, 

 1,341, 1904. 



3Linder and Picton, J. Chem. Soc, 87, 1,924, 

 1905. 



cases we have experimental evidence of nega- 

 tive surface tension. 



From the foregoing considerations we see 

 that there is positive surface tension in the 

 case of all colloidal solutions in which the size 

 of the dispersoid particles is automatically in- 

 creasing, and negative surface tension in case 

 the size of the particles is decreasing, and that 

 for stable colloidal solutions the surface ten- 

 sion at the boundary between dispersing 

 medium and dispersoid will be zero. Further- 

 more, since in cases where automatic disper- 

 sion is taking place, this continues only until 

 a definite size of particle is reached, we are led 

 to the conclusion that surface tension is in 

 general a function of the size of the particles. 

 A stable colloidal solution is thus one in which 

 the particles have that particular size which 

 has zero surface tension. 



Such ideas as to positive, negative and zero 

 surface tension, and as to the relation between 

 surface tension and size have already ap- 

 peared in the literature. The possibility of ex- 

 plaining automatic colloidal solution and the 

 permanent colloidal state by assuming a nega- 

 tive surface tension between phases which be- 

 comes zero at a definite degree of dispersion 

 was first outlined by Donnan, 4 on the basis of 

 a suggestion of Van'T Hoff; has also been ex- 

 pressed by Perrin, 5 and has been definitely 

 adopted by the present writer on thermody- 

 namic grounds in a presentation of a some- 

 what complete theianodynamic theory of equi- 

 libria of dispersed systems in general and of 

 colloids in particular. 6 



* Donnan, Z. physik. Chem., 37, 735, 1901; 46, 

 197, 1903. It is possible that Donnan has since 

 abandoned this theory as a satisfactory explana- 

 tion of the colloidal state. See Ellis, Z. physik. 

 Chem., 80, 611, 1912. 



s Perrin, J. chim. phys., 3, 92, 1904. "II me 

 semble done que 1 'existence mgme d'un hydrosol 

 force a regarder la tension superficielle comme 

 gtant un fonction du diametre du granule, fonc- 

 tion qui, nulle pour un certain diametre, est posi- 

 tive pour un diametre inferieur, et negative pour 

 un diametre superieur. " In a later paragraph 

 (loc. cit., p. 94) Perrin somewhat modifies this 

 point of view that the surface tension is exactly 

 zero at the degree of dispersion which is stable. 



e J. Am. Chem. Soc, 35, 317, 1913. 



