a) 12 7 0 10 FADING OF ART FICI .... HAIR COLOR 419 20 JO 40 50 lrr,adlation 1ime (Hr:&) 60 b) frer 8 hrs irradiafon Irradia1ed through quartz Irradiated through filter blocking UV light "igun: 7. Total color loss for white hair, dyed with medium auburn dye (a) and irradiated through a quartz filter and a filter completely absorbing UV light (b). away, and% protection would be reduced m zero). In summary, the present data confirm the previous suggestion that blocking UV light can ·ignificantly limit artifici, I hair­ color fading. THEORETI 'AL AND EXPERIMENTAL ANAI.YSIS OF PHOH R TECTION B UVA AND fJVB PHOT HlTER, The tht:oretical extent of phoroprotection by a formulation, containing phow-absorbers 'nd evenly disnjbuted on h, ir, can b� assessed by calcula1ting the percentage of UV lighr it absorbs. It can be shown that the attemntinn of li :i-ht, at a given wavelength, b, a multi-component photofilter , ystem is given by 1:he foJlowing: relationship, which is a modification of Beer's equation: wh. re / /"Ii.) is the ab, orbanc of _pho ofil t r i at wavelength A, l s(A) i the intensity of solar radiation, ep1.) is the molar extinction coefficient of )homfilter i at wavelen , h (A.), m i is the amoun of formulation deposited on hair (gig hair), C is i:he concentm -ion of a photofilter in a formulation (% w/w), J\ is the specific surface area of hair assumed to be 800 (cm2/g), p is the densiry of a dry formulation (assumed to be approximately 1 g/cm3 ), and /W u •i is th molecular weight of an i-�h photofil r. Equation 4 can be used to calculate the fraction of light absorbed at each wavel.ength by a given quantity of absorber on the hair. The total percentage of absorbed UV radiation can be determined by integrating (numerically) equation 4 over th wavelength range 29-0-400 nm. For calculations, values for the solar irradiation on the surface of the earth between ?90 mm and 400 nm were taken from the literature (19). figure 8 shows rhe _percentage of attenuated UVB and UV A light (290�/400 nm) as a function of the

420 JOURNAL OF COSMETIC SCIENCE 9()-.-------------------------------------, 80 -----------------------------1 Avobenzone -a 70+---------------=�-==----------------I CD .cl 0 60+--------------::-.,,,,::.-----------------------1 u, .cl !50-t-------------------------------------1 .c en ���--��-----------�--������-----I ::I Benz-4 :30+--��-----�----:::--o,::::_--------:�---=---------=-:-:-=----------1 ::, · · · · · · · · · -;;e 20+-------.,-----------:::aJll"'l-,::__--:::a.,..=----=--..-----,,------!!..•__.!•:........:.._•_•_._._.---=--:-:-----,=-:--::--:--I CmalTIQOpmpyl Trineth'JI 10 0 0 10 mg absorber/gm hair Amin.Cl 20 30 Figure 8. Calculated proponion of attenuated UVB and UV A light (290--400 nm) as a function of the amount of photo-absorber deposited on the surface of hair. amount of UV photo-absorbers deposited on the hair. The data show that UVB absorbers such as dimethylpabaimidopropyl laurdimonium tosylate, cinnamidopropyl ammonium chloride, and octyl methoxy cinnamate absorb less than 25% of the total UV radiation. This is because UVB (290-320 nm) constitutes only about 9% of the total solar radiation in the UV range. As might be expected, the compounds with a greater UV A absorbance (benzophenone-3, benzophenone-4, and butyl methoxydibenzoylmethane) absorb a greater percentage of the radiation between 290 mm and 400 nm. It has to be stressed that the theoretical assessment of the performance of various photofilters pre­ sented in Figure 8 assumes that they are characterized by perfect photostability. Such an assumption is justified in the case of materials such as benzophenone-3 and benzophe­ none-4. For butyl methoxydibenzoylmethane, which is very unstable under irradiation, the results of the calculation probably overestimate the capacity of this compound to absorb UV light under practical usage conditions. In a series of experiments, tresses of natural white hair dyed with a medium auburn dye were treated with leave-in aqueous or ethanol solutions of benzophenone-3 and benzo­ phenone-4, respectively. Figure 9 presents a gradual decrease in L1E as a function of the concentration of benzophenone-3 after 16 hours of irradiation and two shampooings. Figure 10 is a plot of percent color protection (calculated according to equation 3 from the experimental data) for both benzophenone-3 and benzophnone-4 as a function of the calculated extent of UV attenuation (calculated from spectroscopic data by using equa­ tion 4) by a given treatment. Extrapolation of the linear least-square fit to the data points suggests 72% color protection for 100% UV attenuation. This is in reasonable agree­ ment with the 63% protection observed in an experiment in which glass filters were employed to completely eliminate UV radiation (Figure 7), but it has to be kept in mind