Spread Lipid Films on Liquid Surfaces (Langmuir–Blodgett Films) - Surface and Colloid Chemistry: Principles and Applications - page 81

{Tangential force per centimeter of surface} = η s × (rate of strain) (4.5)

and is thus expressed in units of (m t −1 )(surface poises), whereas bulk viscosity, η, is
in units of poise (m −1 l t −1 ). The relationship between these two kinds of viscosity is

η s = η/ d (4.6)

where d is the thickness of the “surface phase,” approximately 10 −7 cm (= 10 Å = 10 −9
m = nm) for many films. That the magnitude of η s is of the order of 0.001 − 1 surface
poise implies that, over the thickness of the monolayer, the surface viscosity is about
10 4 −10 7 poises. This has been compared to the viscosity of butter. The η s is given in
surface poise (gram per second or kilogram per second).
It is easily realized that, if a monolayer is moving along the surface under the
influence of a gradient of surface pressure, it will carry some of the underlying water
with it. In other words, there is no slippage between the monolayer molecules and the
adjacent water molecules. The thickness of such regions has been reported to be of
the order of 0.003 cm. It has also been asserted that the thickness would be expected
to increase as the magnitude of η s increases. However, analogous to the bulk phase,
the concept of free volume of fluids should be also considered in these films.
Monolayers of long-chain alcohols exhibit η s approximately 20 times larger
than those of the corresponding fatty acids. This difference may explain some data
reported on the effect of temperature on monolayers of these molecules (Birdi, 1989).
If the monolayer is flowing along the surface under the influence of π, it carries with
it some underlying water. This transport is a consequence of the lack of slippage
between the monolayer and the bulk liquid adjacent to it. For a monolayer of oleic
acid moving at between 1 and 5 cm/s, the direct measurement gives the thickness
of the entrained water as approximately 0.003 cm. If the bulk viscosity increases,
the thickness of the aqueous layer also increases in direct proportion. Conversely, if
the liquid is moving at C, it carries the surface film molecules along with it, giving
rise to compression at E, and the backspreading pressure tends to move from E to D.
The interfacial water molecules are thus of importance and give rise to these surface
phenomena. Accordingly, as mentioned elsewhere, the role of interfacial water needs
to be considered in all surface phenomena.
It is also obvious that many such films will exhibit complex viscoelastic behavior,
the same as found in bulk phases. The flow behavior then can be treated in terms of
viscous and elastic components.
Further, the equilibrium elasticity of a monolayer film is related to the compress-
ibility of the monolayer (analogous to bulk compressibility) by

C s = −1/ A (d A /d Π) (4.7)

where A is the area per molecule of the film. The surface compressional modulus, K s
(= 1/C s ), is the reciprocal of C s .
Since there is no change in surface tension with a change in the rate of a pure liq-
uid surface (i.e., d A /d Π = infinity), the elasticity is zero. The interfacial dilational
viscosity, k s , is defined as