The Origins of Surface and Interfacial Tension

The Molecular Origin of Surface Tension

Imbalance of intermolecular forces exists at the liquid-air interface

la= the surface tension that exists at the liquid-air interface

Surface Tensions of Pure Liquids at 293 K

Substance / (10-3 N/m)

Acetone 23.7

Benzene 28.8

CarbonTetrachloride 27.0

Methylene Iodide 50.8

Water 72.8

Methanol 22.6

n-Hexane 18.4

Alternative Explanation of Surface TensionSuppose we have a thin liquid film

suspended on a wire loop as follows

liquid film

expanded liquid film

dx

dA

f = force needed to move wire

dw = dG = dA

l = length of wire

Measurement of Surface TensionEarly measurements – even pure liquids has

been described as a ‘comedy of errors’Today – possible to routinely measure the

surface tension of liquids and solutions to an accuracy of + 0.05 mN/m

Capillary Action

The tendency of liquids to rise up in narrow tubes - capillary action.

Due to the phenomenon of surface tension.

The Complication of Contact Angles

The balance of forces that results in a contact angle, c.

The contact angle gives information on the ‘wettability’ of a surface.

Capillary RiseThe pressure exerted

by a column of liquid is balanced by the hydrostatic pressure.

This gives us one of the best ways to measure the surface tension of pure liquids and solutions. r2

gh

ghr2

The Wilhelmy Plate Method

a) detachment

b) static

The Du Nüoy Ring MethodMeasure the force required to pull the

ring from the surface of the liquid or an interface by suspending the ring from one arm of a sensitive balance

Water

F

R

The Correction FactorThe correction factor takes into account of the

small droplets that are pulled up by the ring when it detaches from the surface

Drop Weight/Drop Volume Method

A stream of liquid (e.g., H2O) falls slowly from the tip of a glass tube as drops

Drop Weight MethodThe drop weight is found by

Counting the number of drops for a specified liquid volume passing through the tip;

Weighing a counted number of drops

Vg= mg = 2rgA correction factor - F

r/v1/3

Sessile Drop MethodThe surface tension of a liquid may be

obtained from the shape and size of a sessile drop resting on a horizontal surface

e

Surface

Sessile Drop

h

Sessile Drop Method (Cont’d)Three techniques for obtaining the surface

tension from the image of the sessile dropMeasure the height of the top of a large sessile

drop above its maximum diameter.Estimate the shape factor of the drop from the

coordinates of the drop profile.Fit the drop profile to ones that are generated

theoretically.

Drop ProfilesThe sessile drop method may also be used to

obtain the value of the equilibrium contact angle.

Contact angle, e < 90°

e

The Maximum Bubble Pressure Method

The maximum pressure required to force a bubble through a tube is related to the surface tension of the liquid.

gas stream

b

l

The Bubble Pressure Technique The maximum bubble pressure is related to

the surface tension of the liquid as followsP = g l + 2 / b

= the density difference between the liquid and the vapour

b = radius of curvature at the apex of the bubblel = hydrostatic height to the bottom of the bubbleg = 9.807 m / s2

The Differential Maximum Bubble Pressure Method

Two probes of different diameters. A differential pressure is generated, P.

b2

gas stream

b1

z2z1

t

The Differential Bubble Pressure Equations The maximum bubble pressure is related to

the surface tension of the liquid as followsP = g z1 + 2 / b1 - g z2 + 2 / b2

= the density difference between the liquid and the vapour of the first bubble

= the density difference between the liquid and the vapour of the second bubble

z1 = the distance from the tip to the bottom, of the first bubble

z2 = the distance from the tip to the bottom, of the second bubble

Methods of Measuring Surface Tension

Method Pure Liquids Solutions

WilhelmyPlate

quick andeasy tooperate

Good, suitablewhen ageingoccurs

Du Nuöy Ring Satisfactory n/a

Sessile Drop Very Good Good whensurfaceageing occurs

Drop Weight Suitable Poor whensurfaceageing occurs

CapillaryHeight

Very Good n/a if

Bubblepressure

Very Good Good whenageing occurs

Molecular Contributions to an Oil-water Interfacial Tension

= Oil = water

Oil Phase

Water Phase

oil

water

oil x dwater)1/2

oil x dwater)1/2

The Work of Adhesion Energy required to reversibly pull apart

to form unit surface areas of each of the two substances.

1221 adhW

12

1

2

1

1

Wcoh 2 1

The Work of Cohesion Defined in terms of the energy required to

reversibly separate a column of a pure liquid to form two (2) new unit surface areas of the liquid.

The Definition of the Surface ExcessTo obtain a clearer meaning of the surface

excess, let’s consider the following system.

z

Ci

zo

-

+

CJ(1)

CJ(2)

The Spreading CoefficientSubstance (usually liquid) already in contact

with another liquid (or solid) spreads increases the interfacial contact between the

first and second liquid (or the liquid and the solid)

decreases the liquid-vapour interfacial area

Three Cases of Spreading Place a drop of oil on a clean water surfaceDefine the spreading coefficient

Water

Airwa

ow

oa

Oil

)( oawowa wodA

dG-= S

S = -dG

dAwo

W Wwo oo

The spreading coefficient (to be defined later) is indicative of the difference in the adhesive forces between liquid 1 and liquid 2 (or the solid), and the cohesive forces that exist in liquid 1

S > 0, spreading occurs spontaneously

S < 0, formation of oil lenses on surface

Water

Airwa

owoa

Oil

Water

Air ow oa Oil

e

A third possibility is the a monolayer spreads until spreading is not favourable; excess oil is left in equilibrium with the spread monolayer

Water

Airoa

ow

oaOil

oa wowo

Wetting Ability and Contact AnglesWetting - the displacement of a fluid (e.G.,

A gas or a liquid) from one surface by another fluid

Wetting agent - a surfactant which promotes wetting

Three types of wetting Spreading wetting Immersional wetting Adhesional wetting

Spreading WettingLiquid already in contact with another liquid (or

solid) wets the surface of the second component (liquid or solid) by spreading across the surface of the second component

Using the spreading coefficient defined earlier, we find that the liquid spreads spontaneously over the surface when S > 0

S = -dG

dAwo

wa wo oa( )

Solid

Air sl la Liquid

Solid SurfacesConsider the case of a liquid drop placed

on a solid surface (non-spreading)

For a liquid drop making a contact angle with the solid surface

Solid

Air

sl Liquid

sa

la

e

sa sl la Cos e

Cos = sa sl

la

e

A spreading drop e < 90°

e

Solid Surfaces/Different Contact AnglesExamine the following two surfaces.

A drop with a contact angle << 90

e

The Derivation of Young’s Equation

la

sa

lse

change in the liquid-solid interfacial area = dA

dA

e

change in the solid-air interfacial area = - dA

change in the liquid-air interfacial area = dA Cos e

Young’s EquationFor a liquid (as a drop or at at the surface

of a capillary) making a contact angle c with the solid surface

claslsa Cos

= Cosla

slsac

Adhesional WettingThe ability of the liquid to wet the solid will

be dependent on its ability to ‘stick’ to the solid

liquid droplets

Solid Surface

la

droplets adhering to solid surface

sl

• from the Young Equation

WG

AAA

sa la sl

sa sl la Cos e

W CosA la e ( )1

• Note: the solid is completely wetted if e = 0; it is partially wetted for finite values of e.

Immersional WettingImmerse a solid substance in a pure

liquid or solutionarea of the solid-air interface decreasesinterfacial contact between solid and

liquid is increased

solid particle

Water

sa

immersedsolid particle

sl

Work required to immerse the solid in the liquid Examine the difference ion the solid-air

‘surface tension’ and the solid-liquid interfacial tension

slsaI

I AG

W

Applying young’s equation

elaI

I CosAG

W

If sa > sl, spontaneous wetting while if sa < sl, work must be done to wet the surface

Wadh wetG S Cos eq eq

adh > coh < 0 spont. 1 0 adh < coh < 0 non-spont. 0 90 adh < coh > 0 non-spont. -1 180

Degrees of Liquid-solid Interaction

Surfactants What is a surfactant?

Surface active agent

Headgroup Tail

Heads or Tails? Headgroup – hydrophilic functional group(s)Tail – hydrocarbon or fluorocarbon chain Typical headgroups (charged or uncharged)

SulfateSulfonateTrimethylammoniumEthylene oxidecarboxybetaine

Properties of Surfactant MoleculesAggregate at various interfaces due to the

hydrophobic effectAir-water interfaceOil-water interface

Form aggregates in solution called micelles at a specific concentration of surfactant called the critical micelle concentration (the cmc)Micellar aggregates are known as association

colloids

Applications of SurfactantsSurfactants are an integral part of

everyday life; they are formulated into a wide variety of consumer products ShampoosDish detergentsLaundry detergentsConditionersFabric softenersDiapersContact lens cleaners

Applications of Surfactants (Cont’d)Surfactants are also widely used in

industry due to their ability to lower surface and interfacial tensions and act as wetting agents and detergents Heavy and tertiary oil recoveryOre flotationDry cleaning Pesticide and herbicide applicationsWater repellency

Interfacial Properties of Surfactant MoleculesSurfactants – used in a large number of

applications due to their ability to lower the surface and interfacial tension

Gibbs energy change to create a surface of area dA

dG = dA

Using the Gibbs adsorption equation for a 1:1 ionic surfactant

surfsurf

2RTlnC d

d

Where surf = nsurf /

A

log Csurf

dyne/cm

cmc

Plot of vs. Log Csurf for Sodium Dodecylsulfate at 298.2 K

Surfactants and Detergents Detergency - the theory and practice of

soil removal from solid surfaces by chemical means

Early detergentsAncient Egypt - boiled animal fat and wood

ashes to make soap

Past thirty years Made significant progress in our understanding

of detergency on a molecular level