306 Langmuir, Vol. 3, No. 2, 1987

.......

.......

C,

Figure 3. Schematic illustration of the mterfad density of solute i relative to the solvents.

phases A and B. In Figure 2, a picture of how the con- centrations vary across the interfacial region is illustrated schematically on an enlarged scale. The dividing planes are drawn so that eq 11 and 12 are satisfied simultaneously; that is, the area shaded with vertical strokes is equal to the area shaded with horizontal strokes for each solvent. It is understood, therefore, that the interfacial density of solute i relative to the solvents, riH, corresponds to its interfacial excess number of moles per unit area repre- sented by the area shaded with cross strokes in Figure 3. For an extensive quantity Y of the system, the corre- sponding interfacial excess quantity per unit area with reference to the dividing planes, yH. can be defined in an analogous manner:

YH = y/,, - p , , A - p . H y B (13)

Letters

where yA and yB are the quantities per unit volume in the phases A and B, respectively.

Finally it is necessary to make sure that the interfacial excess thermodynamic quantities defined above are iden- tical with those defined by Hansen. According to Hansen? the specific surface excess quantities $, r,, and 9 are given by the expressions

rs = v/o - @/a - AB/. (14)

r, = n , / a - (A*/&," - (xB/u)c,B (15)

and

ys = Y / . - (AA/a),,A - ( X B / u ) y B

r, = rz = o (17) Supposing that components 1 and 2 are the solvents, comparison of eq 14-17 with eq 2,3, and 11-13 leads us to the conclusion that the quantities $, r,, and ys are the same BS the quantities r", r,H, and yH, respectively, because the relations

(16)

where XA and AB are chosen so that

A A / ~ = 1A.H (18)

x B i o = 1B.H (19)

and

hold for the system shown in Figure 1. Therefore, we can conclude that the geometric formalism based on the specification of two dividing planes is identical with the Hansen convention.

PAUL BILOEN, 1939-1986

It is with much sadness that we report the death of a member of the Langmuir Advisory Board, Paul Biloen, on Oct. 28, 1986, at the age of 47.

Paul will be missed aa a researcher in the field of catalysis, a member of the Langmuir family, and a warm human being. Born in Holland at the outbreak of World War 11, his philosophy of life was tempered by his experiences as a child caught up in the Holocaust. After completing his studies in chemistry and chemical engineering a t the University of Amsterdam, culminating in a doctoral thesis with Professor G. Jan Hoytink, Biloen joined the research staff of the Koninklyke/Shell Laboratories in 1968, where he remained until 1982. From 1976 to 1982, he was Head of the Physical Chemistry and Heterogeneous Catalysis section of Shell Laboratories. His contributions to his chosen field were recognized in 1982 with an appointment BS Professor of Chemical and Petroleum Engineering at the University of Pittsburgh, where he remained until his death.

He is survived by his wife Ansje and his two sons David, 18, and Peter, 16.