784 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Table I Factors Which Can Influence Primary Single Fiber Properties Other Single Fiber Properties Treatment Effects Primary Single Fiber Property Static Friction (Fs) x Kinetic Friction (Fu) x Stiffness (S) x Static Charge (E) x x Hair Fiber Curvature (C) Weight (W) x Diameter (4) (D) x Luster (I) Color (H) x x x (2) x (2) x x x x x x x x x x (3) X X X X X X X X X X X (t) (t) (t) X X X X X X X X X X X X X X X X X X X X X X X X X X (I) Only excessive treatment, and wet properties affected first. (2) Elastic and yield properties influence friction. (16) (3) Cohesion is considered as one part of F• in this report. (4) Cross-sectional areas. manageability, luster and feel or handle. Most of these terms are extremely complex to analyze since generally each depends of several physical properties of a fiber assembly which are interrelated. For example, stiffness on a fiber assembly includes contributions from the number of entanglements, and from kinetic and static friction as well as from the actual stiffness of the fibers. This principle holds for most properties of fiber assemblies. By contrast, certain "primary" properties of single fibers are isolatable, i.e., can be measured independently of each other, and they directly influence the properties of an assembly of hair. Thus it occurred to us that most of the complex terms that are used by consumers for describing hair behavior might be approximated by algebraic expressions combining single fiber properties, such as: static friction (Fs) , kinetic friction (Fk) , stiffness (S), static charge (E), curvature (C), weight (W) and diameter or cross-sectional area (D). Certain nonchemical treatments that are applied to the fiber surface nonuniformly, e.g., hair sprays, will produce small changes in the fiber weight but not in the fiber diameter, thus we include fiber weight as a separate term. Table I lists other fiber properties or characteristics and several cosmetic treatment effects. The primary fiber properties relate to these other characteristics and to the prior history including treatments to the fibers. In this manuscript, five assessments of a consumer's hair (combing ease, style retention,

HAIR ASSEMBLY CHARACTERISTICS 785 Table II Effect of Changes in Primary Single Fiber Properties on Changes in Assembly Properties Increase in Subjective Hair Property A Fu AFs AE AW AD AS AC + combing -N + style retention + n + flyaway 0 ñ body limpness + n + manageability - N -N -N 0 +n +n -N +N 0 -n 0 -n ñN -n +N -n 0 -n -n +N 0 -n +N +N +N +N -N -n 0 -n ñN F• = Kinetic Friction Fs = Static Friction E = Static Charge W = Weight of Fiber D = Diameter (cross-sectional area) S -- Stiffness C = Hair Fiber Curvature ñ = Effect may improve or detract (see text) N = Very important to subjective property 0 = No influence flyaway, body and manageability) are described in terms of the primary single fiber properties (Fk, Fs, S, E, C, W and D) which could "change" in a specific treatment, Table II. Considering changes in place of abso!ute values permits us to neglect properties that undergo no change during treatment, e.g., density of hair population on the scalp and fiber length. We also assume no change in hair style. Furthermore, values of the primary properties are representative of the "average hair fiber" of the assembly under consideration. For simplification, it is assumed that cohesion is a part of static friction. If this simplification proves unsatisfactory, then separate terms will have to be used. Hair fiber curvature is proportional to the number of crooks and bends of the fiber and may be estimated by the decrease in length and it may be neglected when considering changes produced by products other than permanent waves, straighteners or setting aids. For example, an initial state of the assembly (K) is described in (eq 1) as a function Of the appropriate primary properties which may undergo change in a specific treatment on a specific head. f(L, Fk, S, E) (1) A change in the assembly propertylis defined in (eq 2) as a linear combination of changes in the single fiber properties. Changes in single fiber properties are considered as "after treatment" minus "before treatment," e.g., AS ----- S^fter Treatment -- S•fo•e Treatment, which results in a positive change in the assembly property as indicating an increase by treatment. + AK -, N•AF u + n•AF, -- N2AS -- n2AE (2) Multiplying constants that are capitalized (N) indicate that specific primary property to be of greater importance, in our judgment, than those preceded by small letter multiplying factors (n). Initial uses of the system are anticipated to be directional, providing approaches for