2008 TRI/PRINCETON CONFERENCE 257 yet it has the lowest composite stiffness. It is surmised that adhesive failure is the cause of this difference in composite stiffness between cassia gum and the cassia HPTC derivatives. On the other hand, comparison of the composite stiffness values at 50% RH for the cassia HPTC polymers shows the importance of polymer cohesion. The 3.0 meq/g CD polymer has greater adhesion to hair, but its cohesive properties are lower than the 1.8 meq/g CD polymer. It is deduced that the adhesion of the 1.8 meq/g cationic polymer to the hair is suffi cient to with- stand the applied fl exure stress, so the cohesion of the polymer has a signifi cant infl uence on composite stiffness. The composite stiffness of the higher CD polymer is relatively insensitive to humidity in comparison to the lower CD polymer, which loses considerable composite stiffness at 90% RH. As a result, the trend in composite stiffness at 50% RH reverses at 90% RH. Composite stiffness for the 3.0 meq/g cationic polymer is greater than that for the 1.8 meq/g polymer at 90% RH. The observed relationship among charge density, stiffness and humidity indicates the relative contributions of adhesion and cohesion for these polymers. The cationic charge density of cassia HPTC affects the cohesive properties as well as the adhesive properties. The cohesive strength of the polymer decreases with increased charge density, but due to the electrostatic forces between the quaternary groups on the polymer and the negative charges on the hair, the adhesive strength should increase with increased cationic CD. The change in cohesion with charge density has been attributed to steric hin- drance of the quaternary groups, which interferes with the intermolecular hydrogen bond- ing of the polymer chains and causes an increase in free volume or plasticization effect of the polymer. At high humidity, water vapor is absorbed, which affects the polymer properties. If the modulus of the polymer were the only contributing factor to composite stiffness, the stiffness of the lower CD polymer would be expected to drop no lower than the stiffness of the higher CD polymer at 90% RH. This is where the importance of adhesion between the polymer and the hair is apparent. At high humidity, the polymer with higher CD has higher composite stiffness than the polymer with lower charge density. Both the higher and lower CD polymers absorb moisture, which may cause the cohesive properties of the poly- mers to become more similar at high humidity. Thus, the differences in adhesion between the polymers become discernible, as illustrated at 90% RH, where the composite stiffness of the higher CD polymer is higher than the composite stiffness of the lower CD polymer. A custom DMA fi xture has been designed and fabricated to test the above hypothesis. This apparatus allows DMA frequency sweeps to be run at various, controlled relative humidities. The results for cationic cassia at 50% and 90% RH, plotted as tan delta ver- sus frequency, are shown in Figures 7 and 8, respectively. Tan delta is defi ned as the ratio Figure 7. Tan delta versus frequency at 50% relative humidity for cassia hydroxypropyltrimonium chloride polymers.

JOURNAL OF COSMETIC SCIENCE 258 of the loss modulus (E ) to the storage modulus (E ), and it is a measure of the bulk com- pliance of the polymer. Higher tan delta values correspond to softer or more compliant polymers, and conversely, lower tan delta values correspond to stiffer polymers. Tan delta at 50% RH confi rms the tensile data presented earlier the lower cationic CD polymer has higher cohesion than the higher CD polymer. Tan delta at 90% RH confi rms that the cohesive properties of the cassia HPTC polymers become similar at 90% RH. Thus, the differences observed in composite stiffness at 90% RH are due to the differences in adhe- sion. CONCLUSIONS The application of polymer composite science to fi xative-treated hair tresses provides bet- ter understanding by giving insight into the mechanisms that govern performance. The relative contributions of adhesion and cohesion to composite stiffness were demonstrated using cassia and cassia hydroxypropyltrimonium chloride polymers as an example. The importance of adhesion was demonstrated by the low composite stiffness values for cassia relative to its HPTC derivatives. The relative contributions of adhesion and cohesion were shown to depend on environmental conditions for the cationic derivatives in the chosen example. Cohesion was dominant at 50% RH, while adhesion became prominent at 90% RH. ACKNOWLEDGMENTS The authors thank Lubrizol Advanced Materials, Inc. (a wholly owned subsidiary of The Lubrizol Corporation) for permission to publish and Carole Lepilleur for her assistance with this work. REFERENCES (1) S. T. Peters, “Introduction, Composite Basics and Road Map,” in Handbook of Composites, 2nd ed., S. T. Peters, Ed. (Chapman & Hall, London, 1998), pp. 1–4. (2) M. Piggott, Load Bearing Fibre Composites, 2nd ed. (Kluwer Academic Publishers, Boston, 2002), p. 173. Figure 8. Tan delta versus frequency at 90% relative humidity for cassia hydroxypropyltrimonium chloride polymers.