Surface and Interface Chemistry

Liquid/gas Interface

Valentim M. B. Nunes

Engineering Unit of IPT

2014

From a technological standpoint, the heterogeneous processes involve surfaces: precipitation, diffusion, flocculation, detergents effects, etc.

The concept of phase and interface:

Phase

Phase

Interface, Few molecular layers

Surface Tension

Molecular explanation: imbalance in Intermolecular forces that exists on the surface.

Gas

Liquid

R 0

R = 0

Surface molecule is "pulled" to the interior

Molecule inside the liquid is subject to Intermolecular forces, but the resultant is null.

To increase the surface area is necessary to perform work against the intermolecular forces of liquid. The work required to change the surface area of an infinitesimal quantity dσ is given by:

ddwThe coefficient is the surface tension (SI units: J.m-2 or N.m-1). At constant pressure and temperature dw = dG , then:

Tpd

dG

,

Liquids with greater Intermolecular forces are those that presents larger surface tensions.

/mN.m-1 (T = 293 K)

Isopentane 13.72

Ethyl ether 17.10

Hexane 18.43

Ethyl bromide 24.16

Benzene 28.86

Carbon tetrachloride 26.66

Water 72.75

Mercury 472.0

There is no fundamental distinction between surfaces and interfaces, although it is customary to designate the boundary between two phases in which one of them is gaseous as surface, and between two non-gaseous phases as an interface.

At the interface between two liquid's there is again an imbalance in intermolecular forces in the interior and along the interface. Intermolecular forces responsible for surface or interfacial tension include London dispersion forces (Universal), hydrogen bonds and metallic bond.

Interfacial tension: contact angle

The imbalance of intermolecular forces on the liquid/gas interface and solid/gas interface are always bigger than between condensed phases, then interfacial tensions for two liquids or between solid and liquid systems are always smaller than the biggest of the surface tensions.

The work of adhesion between two phases α and β is expressed by the equation of Dupré:

At a solid/liquid interface it comes:

W

SLLSSLW

Consider the following system:

solid

liquid

GasF

F’F’’

F – surface tension of liquid, L

F’ – interfacial tension, SL

F’’- surface tension of solid, S

- contact angle

Condition of equilibria (Young’s equation):

cosLSLS

And we obtain the Young-Dupré equation:

cos1 LSLW

Since WLL is 2 L :

2

cos1 LLSL WW

= 0 S = L WSL = WLL Liquid completely wets the solid

0 < < /2 S > SL WLL/2<WSL<WLL Liquid partially wets the solid

/2< < S < SL 0 < WSL < WLL/2 Solid is difficulty wet by the liquid

= SL = L WSL = 0 Liquid does not wet the solid

As a consequence of surface tension there is a difference of pressure through any curved surface; consider a drop of liquid ~ Spherically:

z

Pe

Pi a

r

cosra

The existence of surface tension prevents the liquid to spread across the surface. The outside pressure (Pe) will be lower than the internal pressure (Pi). At equilibrium, the resultant of the forces that are due to the difference in pressure, Pi-Pe, will be equal to the forces due to ϒ, along the zz axis (spherical symmetry)

22

2

1 2cos2

aPPR

r

aaR

ei

rPPP ei

2

This is the Laplace equation

For non spherically surfaces (two curvature radii):

21

112

rrP

Laplace's equation shows that the pressure inside a curved surface (concave side of the interface) is greater than the pressure outside (drops, bubbles,......)

Vapor pressure of a pressurized liquid

dpVgd

dPVld

gl

gm

m

,)(

)(

)()(

Pressure of liquid is increased in dP, then dp represents the change of vapor pressure..

PVp

pRT

dPVdpp

RT

dPVdpp

RT

m

Pp

p m

p

p

m

*ln

1 *

**

RT

PVm

epp

*This equation shows that the vapor pressure increases when the pressure exerted over an condensed phase increases!

rP

2

RTr

Vepp m2

*

Kelvin’s equation

Vapor pressure of water drops with 10-3 mm to 10-6 mm is 1.001 to 2.95 times the vapor pressure of the water "flat"!, preventing condensation, and favoring the formation of clouds

The surface tension of most liquids decreases with increasing temperature, being fairly low near the critical point (except for liquid Cu and Fe!)

Eötvos equation: )(3/2cL TTkV

Ramsay and Shields: k 2.1 for normal liquids (benzene, carbon tetrachloride, S2C, etc…)

Katayama:

Guggenheim:

cGL T

Tk 13

2

constant 3

11

GL

Capillarity

The tendency of fluids to climb in a capillary tube is a consequence of surface tension and is called capillarity or capillary rise.

rhg

hgp

2

R

2r

rR

Rr

0

cos

2

hgr

cos2

grh