436 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS that the more concentrated the gel and the older it is the more rapid is the build up of structure. Fig. 7 would appear [o indicate that structural build up of these gels takes place in two successive stages, both following first order kinetics. Thus A 1 2.303 K 1 = log A 1--At t A 2 2.303 and K 2 = log A 2--At t (vIn) (ix) where At is the static yield value at time t, A 1 is the maximum yield value of the first stage, A 2 is the maximum yield value of the second stage and K 1 and K 2 are the rate constants for the first and second stages respectively. The first stage lasts only for a very few minutes and even the second stage may be referred to as the "initial recovery period" so that the results do not necessarily reflect the kinetics of the entire build up reaction which may cover a large number of h. DISCUSSION The relationship between the rigidity of a gel and its structure is com- plex. Because gelatin gel strength is destroyed by degradation it has been assumed that it is related to the chain length of the molecule and hence its molecular weight. The resistance to deformation of gelatin gels follows Hooke's law and can be characterised by a shear modulus or modulus of rigidity for small deformations. This resistance to deformation may arise from two sources (13): the entropy decrease accompanying the decreased randomness of chain segments during the deformation and the increase in the internal energy of the system occasioned by the re-ordering of the en- vironment of the random chain segments. To a first approximation the rigidity/gelatin concentration relationship is proportional to the square of the gelatin concentration, but when glycerin is present the rigidity was not proportional to the square of the gelatin concentration and new relationships had to be developed. Basically, an increase in the gelation concentration still caused an increase in rigidity and the higher the proportion of glycerin present in the gel the greater was this increase. The reason for this may be due to a change in the overall polarity of the interspace fluid causing a decrease in the solubility and corresponding increase in the tendency of the gelatin molecule to orientate into the spiral formation associated with coacervation {14). The consider-

SOME APPLICATIONS OF RIGIDITY AND YIELD VALUES 437 able increase in the viscosity of the interspace fluid, especially at high glycerin concentrations may also cause an increased rigidity due to the increased difficulty of movement of the gelatin chains, relative to the fluid, under an applied stress. Whilst the rigidity is obviously a very valuable parameter for rigid gels such as gelatin similar measurements are of little value on materials such as Laponite which become very fluid once the static yield value is exceeded. Measurements of rigidity at forces below this yield point may be made with relatively dilute gels, but far more information about the funda- mental nature and potential uses of the material may be obtained by studying the rheogram. The significant facts obtainable from this curve are the dynamic and static yield values and the plastic viscosity. With materials such as Lapon- ite the dynamic yield value is the energy input necessary to maintain a constant ratio of shear rate to shear stress in a system whose structure has been destroyed by previous shear. The dynamic yield point gives an in- dication of the degree of internal breakdown in the system and at some rate of shear should reach an optimum value indicating that all the bonds between particles have been broken and the dispersed units consist solely of primary particles. The static yield value on the other hand is the minimum force necessary to initiate flow. This value is not absolute, but depends on the previous history of the gel particularly with thixotropic materials since any des- truction of the internal structure of the gel will take time to rebuild. The increase in the static yield value with age may be due to an increase in the inter-particle linkages, possibly due to slow swelling of the individual particles allowing further particle to particle contacts. The two stages of the primary structural recovery suggest that different types of linkage may be formed in each case. As the first stage of the reaction is the fastest it must involve the linkage most likely to occur spontan- eously and produce the strongest network on which the secondary structure forms. Edge to face links, because they are due to electrostatic attraction between negatively charged surfaces and the positively charged edges of the clay particles, will form the primary links whilst the weaker van der Waal's attractive forces of edge to edge and face to face links will form more slowly and these linkages will predominate in the second stage of gel recovery. The large static yield value of Laponite gels allows solids to remain in permanent suspension and its rapid breakdown on shaking allows easy