INDEX

INTERFACES, COLLOIDS AND GELS *

Course Outline *

1. Nature and Relevance of Colloids *

2. Colloid Stability *

2.1 Creating surfaces *

2.2 Interparticle Forces *

2.2.1 Intermolecular Forces and Attraction *

2.2.2 Attraction between an atom and a slab *

2.2.3 Attraction between two colloidal particles *

2.3 Diffuse Electrical Double Layers *

2.3.1 Gouy-Chapman Electrical Double Layer Model *

2.3.2 Double Layer Overlap *

2.4 Total Potential Energy of Interaction: DLVO Theory *

2.5 Schulze-Hardy Rule *

2.6 Other Factors affecting Colloidal Stability *

2.6.1 Steric Stabilisation due to adsorbed polymer *

2.6.2 Depletion Flocculation *

2.6.3 Bridging Flocculation *

2.7 Summary *

3. Preparation Methods *

3.1 Dispersion methods: *

3.2 Condensation methods *

4. Clays, the Swelling of Clays and Direct Measurement of Repulsive Forces *

4.1 Crystal Structure of Clay Minerals *

4.2 Clay Swelling *

4.3 Direct Measurement of Forces Between Surfaces. *

5 Association Colloids *

5.1 Influencing Factors on C.M.C. *

5.2 Thermodynamics of Micelle Formation *

6 Liquid Surfaces and Films at Liquid Interfaces *

6.1 Pure Liquid Surface *

6.2 The Gibbs Adsorption Isotherm and Surface Tension of Solutions *

6.3 Spread Films on Liquid Substrates *

6.4 Experimental Study of Spread Films *

6.5 Monolayer States *

6.5.1 Gaseous Film *

6.5.2 Liquid Expanded State *

6.5.3 Liquid Condensed State *

6.5.4 Solid Film *

6.6 Surface Waves on Liquid Surfaces *

 

 

Course Outline

Nature and relevance of colloidal state; classification and examples; reasons for stability; lyophilic and lyophobic colloids. Gouy-Chapman electrical double layer theory; Poisson-Boltzmann equation; interaction of electrical double layers; DLVO theory for stability of colloids. Preparation methods. Properties.

Clay minerals; clay swelling as an example of electrical double layer properties.

Association colloids; micelles; critical micelle concentration; thermodynamic of micelle formation.

Adsorbed and spread films at liquid-air interfaces; surface pressure; surface pressure isotherms; organisation of adsorbed and spread films.

 

INTERFACES, COLLOIDS AND GELS

 

1. Nature and Relevance of Colloids

Colloids are an important class of materials, intermediate between bulk and molecularly dispersed systems.

 

Definition of a colloid

Colloidal systems consist of a disperse phase distributed uniformly in a finely-divided state in a dispersion medium (the continuous phase).

What do we mean by finely-divided?

At least one of the dimensions of the dispersed phase lies between 10 Å (1 nm) and 10 000 Å (1 m m).

Consequently:

e.g. compare the surface areas of a 1cm cube – 6 cm2 with that available when the cube is broke into smaller cubes of 0.5 m m dimensions (= (1/5´ 10-5)3´ 6´ 2.5´ 10-9cm2) = 1.2´ 105 cm2.

Colloidal systems are widespread in their occurrence and have biological and technological significance.

 

Colloidal Systems

Disperse Phase

Dispersion Medium

Class

Example

Liquid

Gas

Liquid Aerosol

Fog, mist, aerosol sprays

Solid

Gas

Solid Aerosol

Industrial smoke

Gas

Liquid

Foam

Fire-extinguisher, foam, froths

Liquid

Liquid

Emulsion

Milk, butter, mayonnaise, some creams

Solid

Liquid

Sol, Colloidal Suspension

Inorganic colloids, e.g. silver halides

Gas

Solid

Solid Foam

Insulating foam, expanded polymers

Liquid

Solid

Solid Emulsion

Ice cream

Solid

Solid

Solid Suspension

Stained glass, pigmented polymers, pearl

Micelles

Liquid

Association Colloids

Soap, detergents in water

Polymers

Liquid

Gels

Jellies, glue

Biocolloids

 

 

 

Corpuscles

Serum

 

Blood

Hydroxy-apatite

Collagen

 

Bone

Protein structures, thin films of lethecin, etc.

 

Muscle, cell membranes

 

 

NB. Association colloids are formed by surface-active molecules aggregating together to form micelles.

Usually, a clear distinction can be made between the dispersed phase and the dispersion medium. Network colloids are an exception. In these, both phases consist of interpenetrating networks on the colloidal scale. Gels are a typical example.

In foams, it is the thickness of the dispersion medium film that has colloidal dimensions.

 

 

2. Colloid Stability

A key question is what factors affect the stability of colloidal dispersions?

For example, under certain conditions, the colloidal particles will aggregate together to form the condensed phase.

The aggregation process is called:

  1. Coagulation: aggregate (known as the coagulum) is densely packed and the process is irreversible.
  2. Flocculation: aggregate (known as a floc) is packed more loosely and the process can be reversible.

 

To understand why colloidal dispersions can either be stable, or unstable, we need to consider:

(i) the effect of the large surface area to volume ratio,

(ii) the forces operating between the colloidal particles.

 

 

2.1 Creating surfaces

Consider a column of material with a cross sectional area, A, clearly split to form two fresh surfaces of total cross sectional area 2A and moved apart in a vacuum to infinite separation in a reversible process.

Molecules in the column have attractive forces between them, otherwise they would not be in a condensed state.

\ in splitting the column, work has to be done against these attractive forces. This work, DW, is equal to the increase in Gibbs free energy, DG.

D G µ area of surface created (in this instance, 2A), since the greater the area created, the more intermolecular forces that have to be overcome.

Hence:

The proportionality, g , is known as the surface tension, or interfacial tension.

 

Consequently, it is clear that producing colloidal particles from a bulk material requires work, e.g. we have to grind a bulk material up in order to produce a fine powder. So how can colloidal dispersions remain stable? Why don't the colloidal particles spontaneously aggregate to form bulk material?

 

If a colloidal dispersion is stable, there must be an energy barrier to overcome in order to form the bulk phase; i.e. the system is metastable, and the system is under kinetic rather than thermodynamic control.

But what is the nature of this energy barrier?

To understand this further, we need to consider the nature of intermolecular forces that exist between molecules, and then the interparticle forces that exist between colloid particles.

 

2.2 Interparticle Forces

The forces between colloidal particles will be the sum of the forces that exist between molecules.

 

2.2.1 Intermolecular Forces and Attraction

Molecules without permanent dipoles are attracted to each other by van der Waals forces (also known as London dispersion forces). The electron distribution in an atom fluctuates continuously and these fluctuations make the molecule an instantaneous dipole, which induces a dipole in neighbouring molecules and hence they attract each other.

In a hydrogen atom (single e in 1s orbital) the instantaneous dipole moment is;

p1 = a0e

a0 = Bohr radius of ground state orbital
e = electron charge

Consider the potential energy between particles, (this is easier than considering the forces between particles, since force is a vector property involving direction, whereas potential energy is a scalar property).

A positive potential energy results from a repulsive force.

A negative potential energy results from an attractive force.

The potential energy of attractive interaction between the two hydrogen dipoles is:

(2.1)

a = polarisability, e 0 = permitivitty of free space, r is separation, C6 is a +ve constant.

When atoms (or particles) are so close that the electron clouds interact with each other – we have Born repulsion which prevents too close an approach. This combination of attraction and repulsion between atoms is summarised in the Lennard-Jones 6-12 potential:

 

Lennard-Jones 6-12 Potential

 

 

C6 and C12 are +ve constants.

Also written as:

e = depth of potential well, r0 = value of r at which V(r) = 0,
re = value of r at the well minimum = 21/6r0.

 

2.2.2 Attraction between an atom and a slab

 

In general:

We need to sum the potential over all atoms in the slab:

i.e. (2.2)

where n is the number of atoms in the slab.

We can do this by integrating over all the atoms in a small volume of slab of depth, dz and thickness, dR.

The no. of atoms in a small volume, dV = r ' x volume of small slab element = r ' 2p R dR dz

where: r ' = density. This gives:

Then, since:

(2.3)

Note that the potential energy falls off much more slowly (1/D3) than atom-atom interactions (1/D6).

 

2.2.3 Attraction between two colloidal particles

Treating the two particles as infinitely large flat plates, then the attraction per unit surface area becomes (by integrating 2.3 with respect to D from D = D to Ą ):

(2.4)

Where A is the Hamaker constant. A is determined by C6 and r ' of the material forming the particle and the nature of the intervening material. Note, the potential energy falls off much more slowly (1/D2).

For two spherical particles of equal radius a, a distance H apart between centres, the attractive potential becomes:

(2.5)

When a fluid fills the intervening space, the attractive force is reduced (but does not become zero) and hence the reduction in Gibbs free energy on aggregation is not so large. In this more typical case, we use the composite Hamaker Constant, AC, instead of A. AC is given by:

AC = (A111/2 - A221/2)2 (2.6)

where: A11 is the Hamaker constant of the disperse material and A22 is the Hamaker constant of the intervening medium (the dispersion medium).

Values of A and AC are ~ 10-20 J.

Assumptions in Hamaker theory

  1. Pairwise additivity of interactions: i.e. assumes the total interaction is just the sum of the interaction between pairs of molecules. However, the neighbouring molecules will moderate the interaction between any molecule pair.
  2. Interaction between fluctuating dipoles is instantaneous. The electromagnetic wave set up by the moving electrons travels at a finite rate, c. When the wave reaches a neighbouring molecule that is greater than ~ 10 nm away, the original electronic state of the molecule might have changed.

Þ interaction between the molecules will be reduced.

Þ interaction between particles falls off more rapidly if the particles are further than ~ 10 nm apart; e.g. for 2 plates, the interaction is µ D-3 instead of D-2, when D ~ 10 nm or more. This is known as the retardation effect.

The alternative Lifshitz theory tries to address these assumptions.

However, the main results of the Hamaker theory still follow, i.e.:

the attractive potential energy between colloid particles falls off far more slowly than the attractive potential energy between molecules.

So why don't all colloidal particles coagulate under the influence of this attractive potential? There must be a repulsive potential, of similar long range order, present.

 

2.3 Diffuse Electrical Double Layers

Colloids dispersed in water usually carry an electrical charge due to:

  1. Surface group ionisation: controlled by the pH of the dispersion medium.
  2. Differential solubility of ions: e.g. silver iodide crystals are sparingly soluble in water and silver ions dissolve preferentially to leave a negatively charged surface.
  3. Isomorphous replacement: e.g. in kaolinite, Si4+ is replaced by Al3+ to give negative charges.
  4. Charged crystal surface: Fracturing crystals can reveal surfaces with differing properties.
  5. Specific ion adsorption: Surfactant ions may be specifically adsorbed.

 

Helmholtz first development a model for the electrical double layer in the 1850s for the charge on a metal surface. This charge was balanced by an equal charge in the liquid phase.

Subsequently it was appreciated that thermal motion of the charges in the dispersion medium would distribute the charges in some manner over a spatial region near the surface.

The model of the electrical double layer in these circumstances is the Gouy-Chapman model.

 

2.3.1 Gouy-Chapman Electrical Double Layer Model

A flat surface is considered. The charge on that surface influences the ion distribution in nearby layers of the electrolyte. The electrostatic potential, y , and the volume charge density, r , which is the excess of charges of one type over the other, are related by the Poisson equation:

(2.7)

e r = relative permitivitty (dielectric constant) of electrolyte.

The ion distribution in the charged surface region is determined by (i) temperature and (ii) the energy required, wi, to bring the ion from an infinite distance away (where y = 0) to the region where the electrostatic potential is y . This distribution is given by a Boltzmann equation:

(2.8)

ni0 = no of ions of type i per unit volume of bulk solution.

wi = ziey , the energy expended in bringing an ion from an infinite distance from the surface to a point where the potential is y .

zi = valency of ion species i.

 

The volume charge density at y is:

Thus the combination of this with the Poisson equation gives the Poisson-Boltzmann equation:

(2.9)

When kBT >> (|ziey |), the exponential can be expanded and only the first two terms retained. This is called the Debye-Hückel approximation.

exp(x) =1 + x + x2/2! + x3/3! + x4/4! + …, hence:

but (preservation of electroneutrality)

\

i.e.

Þ y = y 0exp (-k x) (2.10)

y 0 is the potential at the plate surface, k is the Debye-Hückel parameter; it has units of (length)-1.

1/k is the distance at which the potential, y , has dropped to (1/e) of its value at the solid surface, y 0, and this distance is called the double layer thickness or Debye length.

(2.11)

F = Faraday’s constant = eNA = 96.485 x 103 C mol-1;

, the ionic strength of the electrolyte; ci = concn in mol dm-3.

for an aqueous phase at 25 ° C.

As the concentration of ions increases, the double layer thickness decreases.

If the Debye-Hückel approximation is not valid (i.e. kBT is not >> |ziey |), then for z:z symmetrical electrolytes i.e |zi| = |z+| = |-z-| = z, Equation 2.9 can be written as:

 

 

Trig relations: ,

 

\

or (2.12)

 

This can be solved to give:

(2.13)

Case 1. Potential, y 0, is low

For very low potentials, then tanh(x) ~ x, so 2.13 reduces to equation 2.10:

y = y 0exp (-k x) (2.10)

 

Case 2. Far from a plate of high potential, y 0

Far out in the double layer, where the potential, y , is low, using tanh(x) ~ x gives:

Then if y 0 is high, tanh(x) ~1 and we have:

(2.14)

Comparing equations 2.10 and 2.14, we see that far from a flat plate of high potential, the potential seems to have arisen from a plate of potential 4kBT/ze, irrespective of the actual y 0 value.

 

2.3.2 Double Layer Overlap

For mathematical simplification, consider this situation applied to flat plates. Assume that the electrical potential between the two plates is additive and that overlap is small enough to have constant charge between the plates.

The mean excess osmotic pressure, , developed between the plates is

where: p p = osmotic pressure between plates, p bulk = osmotic pressure in bulk dispersion.

Osmotic pressure, p , is given by: , where n = number of ions per unit volume. Hence, at the mid-point between the plates, we have:

where: (n++n-)m = number of positive and negative ions at the mid-point between plates.

\

(2.15)

If the electrical potential at the mid-point between the plates is small, we can use just the first two terms in the series expansion of cosh(x) = 1+x2/2! + x4/4! + .. to give:

(2.16)

At the mid-point between the plates, , and using equation 2.14 for y , then:

where: D = distance between plates.

\ (2.17)

The repulsive potential energy per unit area due to the overlap of the flat plate electrical double layers, VR, is the work done when the plates are brought closer to each other from an infinite separation. The opposition to this closer movement is provided by . Hence:

(2.18)

Since k = (2 e2 n0 z2/e 0 e r kBT )1/2 for a symmetric electrolyte, as the concentration of ions increases, the repulsion due to double layer overlap decreases.


Overlap of Ionic Double Layers

 

Increased ionic concentration leads to:

 

 

2.4 Total Potential Energy of Interaction: DLVO Theory

DLVO theory (named after Deryagin, Landau, Verwey and Overbeek) states that the expressions for the attractive potential energy, VA, (Equation 2.4) and repulsive potential energy, VR, (Equation 2.18) can be combined to give the total interaction energy function, VT, i.e.:

(2.19)

The form of equation 2.19 is such that the van der Waals attraction always dominates at both small and large separations. In between, however, the behaviour depends critically upon the ionic strength, I, and hence the electrolyte concentration, of the dispersion.

Curve 1: Low I values: primary minimum and maximum Þ stable colloidal dispersion.

Curve 2: Intermediate I values: primary minimum, primary maximum and secondary minimum Þ colloidal dispersions can be stable or unstable.

Curve 3: High I values: only primary minimum Þ unstable colloidal dispersion.

 

The concentration of electrolyte at which coagulation becomes rapid is the critical coagulation concentration (c.c.c.). The condition for rapid coagulation can be considered to be that the primary maximum in the total potential energy curve is tangential to the x-axis, i.e.

Þ

and

These two equations are satisfied if k D=2. This gives the concentration of ions, n0(c.c.c.) at the critical coagulation concentration as:

(2.20)

Hence as the valency of counter ion increases from 1 to 3 we expect the c.c.c values to be in the ratio of 1:2-6: 3-6: (1:0.0156: 0.0014).

2.5 Schulze-Hardy Rule

The Schulze-Hardy rule, which has been known since the end of the nineteenth century, states that c.c.c values are determined by the counter ion valency.

 

As2 S3 sol -ve charged

Fe(OH)3 sol +ve charged

Electrolyte Valency

c.c.c. / millimole dm-3

c.c.c. / millimole dm-3

Mono

LiCl

58

NaCl

9.25

NaCl

51

1/2BaCl2

9.65

 

KNO3

50

KNO3

12

Di

MgCl2

0.72

K2SO4

0.205

 

MgSO4

0.81

MgSO4

0.22

 

ZnCl2

0.69

K2Cr2O7

0.195

Tri

AlCl3

0.093

 

 

 

1/2Al2(SO4)3

0.096

 

 

 

Cl(NO3)3

0.080

 

 

Note the following.

  1. Similar electrolytes have similar c.c.c. values.
  2. Effectiveness of the electrolyte in coagulating the dispersion increases when multivalent ions are contained.
  3. Counter ion valency is the important factor in determining c.c.c.

 For the As2 S3 sol, the c.c.c. values above are in the ratio 1:0.015: 0.0018, as the counter ion valency increases from 1 to 3. This is in excellent agreement with the DLVO theory which states that the ratios should be 1:2-6: 3-6 (1:0.0156: 0.0014).

 

Colloids can be broadly divided into two classes.

Lyophilic (solvent loving)

Lyophobic, (solvent hating)

 

2.6 Other Factors affecting Colloidal Stability

Effect of polymers (very long chain molecules).

 

2.6.1 Steric Stabilisation due to adsorbed polymer

Þ steric stabilisation.

The steric potential, Vs, may be considered to arise mainly from two contributions:

  1. Entropic term (always repulsive) due to loss of conformational entropy of polymer chains as they overlap one another.
  2. Enthalpic term. Depends upon extent to which polymer segments prefer to be next to solvent compared to themselves (depends on Flory-Huggins parameter which you will encounter next year in Prof. Richard's Polymer Course).

The ideal polymer for steric stabilisation is a diblock copolymer, AB.

  • One component (A) adsorbs strongly onto the colloidal particles.
  • The other component (B) likes to be immersed in solvent (maximises d ).

Alternatively the polymer can be chemically grafted onto the colloidal surface.

 

Advantages of Steric over Charge Stabilisation

Steric Stabilisation

Charge Stabilisation

Insensitive to electrolyte

Coagulates on addition of electrolyte

Effective in both aqueous & non-aqueous dispersions

Effective mainly in aqueous dispersions

Effective at high and low colloid concentrations

Ineffective at high colloid concentrations

Reversible flocculation possible

Coagulation usually irreversible

Can reserve the term flocculation for colloidal particles in the presence of polymers.

2.6.2 Depletion Flocculation

\ a polymer concentration gradient, and hence an osmotic pressure, exists.

Solvent between the colloidal particles then tends to diffuse out to reduce the concentration gradient, causing the colloidal particles to aggregate.

This is known as depletion flocculation.

 

2.6.3 Bridging Flocculation

A high molecular weight (i.e. very long chain) polymer is present in a very small amount (i.e. p.p.m.) and adsorbs onto the colloidal particles.

The two ends of the polymer may adsorb onto different colloidal particles and then draw them together, leading to bridging flocculation.

This flocculation mechanism can be highly effective; e.g. in water purification, addition of a few p.p.m. of a high molecular weight polyacrylamide results in the flocculation of any remaining particulate matter.

 

2.7 Summary

The use of polymers in colloidal dispersions to either stabilise (steric stabilisation) or flocculate (bridging or depletion) colloidal dispersions is now widespread. There is much interest in producing so-called 'smart' colloids, which are system-responsive colloids that are reversibly flocculating depending upon the conditions, i.e. temperature, pH, dispersion medium etc.

 

 

3. Preparation Methods

Two broad methods of preparing colloids:

  1. breaking down bulk matter into colloidal dimensions known as dispersion methods and
  2. building up molecular aggregates to colloidal sizes known as condensation methods.

 

3.1 Dispersion methods:

Comminution, emulsification, suspension and aerosol methods

 

3.2 Condensation methods

Includes precipitation processes, vapour condensation and chemical reaction to produce an insoluble colloidal dispersion.

Examples of the latter include the oxidation of thiosulphate under acid conditions to produce colloidal sulphur:

and the reaction of silver nitrate with alkali halides to produce silver halide sols.

In forming lyophobic colloids, a stabilising mechanism, e.g. charge or steric, must operate so that the colloid particles remain dispersed.

To produce a colloidal dispersion by condensation, the supply of molecules must run out whilst the particles are in the colloidal size range.

This is achieved by:

  1. having dilute solutions
  2. ensuring that a very large number of nuclei are formed in as short a time as
    possible.

Consider the precipitation process more fully:

nA(aq) ® An(s)

The creation of surfaces/interfaces requires work.

 

Hence these nuclei are unstable relative to larger aggregates, and they will tend to dissociate before they can grow to larger sizes.

(shown by Gibbs Thomson equation)

This will be true for all nuclei up to a certain critical size, r*. Nuclei with this size, r*, are termed critical nuclei.

 

Consequently, an energy barrier exists to the formation of the new phase.

So how does the new phase form?

In any thermodynamic system, statistical fluctuations about the normal state occur.

Þ new phase will be able to form provided a positive free energy fluctuation occurs that is equal to, or larger than, the magnitude of this energy barrier, D Gbarrier.

This process is known as nucleation.

After the nucleation process, growth of the critical nuclei to colloidal (and more typically macroscopic) sizes occurs.

Colloidal dispersions can sometimes be made monodisperse, i.e. the distribution in particle size is very small.

E.g. if the supersaturation is achieved rapidly (i.e. reaction producing insoluble material is fast, or the system is suddenly cooled) then the rate at which critical nuclei are formed (termed the nucleation rate) is also fast.

The fast nucleation rate means material is used up rapidly, so the concentration then quickly drops.

 

New nuclei can only form

during time t .

No nuclei can then be produced (supersaturation is too low) and the nuclei then grow to colloidal dimensions at all the same rate

Þ colloidal particles have very similar sizes.

Inorganic colloids, and polymer latexes produced by polymerisation of monomers in emulsions, can be monodisperse.

 

 

4. Clays, the Swelling of Clays and Direct Measurement of Repulsive Forces

Clays are soils where the particles have a radius less than ~2 m m. The term clay mineral refers to a specific group of silicate minerals. In terms of tonnage, clays are second only to oil in use. Clay minerals are used in the ceramic industry to make bricks, china and pottery. Clays are extensively used as fillers in paper, paint, polymers etc.

The essential feature of clay minerals is the existence of extensive sheets of silicon bonded with oxygen combined with flat sheets of metal (usually Al or Mg) oxides. Layered crystals are formed. This basic structure is exhibited by talc, pyrophyllite and kaolinite. The first two can be modified to produce vermiculite, mica and montmorillonite.

 

4.1 Crystal Structure of Clay Minerals

Basic structure

Silica layer: Oxygen atoms are arranged tetrahedrally around a central silicon, the bonds between Si and O being equally ionic and covalent in character. These tetrahedra link together to form hexagonal rings that repeat in two dimensions forming a sheet.

Alumina layer: Aluminium and oxygen (and hydroxyl) form octahedra with the Al at the centre, and the octahedra link together to form a sheet.

In kaolinite, the alumina octahedra are on top of the silica tetrahedra, with the apical oxygens from the silica layer being shared between both layers.

Kaolinite crystals:

>Al-OH ® >Al+ + OH- .

This process is readily reversed at high pH.

Kaolinite is called a 1:1 non-swelling clay; 1 silica layer to 1 alumina layer; double sheets do not separate from each other under normal circumstances.

There are two forms of clay minerals of the 2 to 1 type (2 silica sheets to 1 of alumina or magnesia).

Pyrophyllite - alumina central layer

Talc - magnesia central layer

Only van der Waals forces between basal oxygen planes hold the successive tri-layers together and hence pyrophyllite and talc can easily be cleaved along these planes.

Replacement of Ľ of the Si atoms by Al atoms in pyrophillite results in the formation of muscovite mica.

Montmorillonite is obtained when one in six of the Al atoms in pyrophillite is replaced by Mg2+.

Vermiculite is derived from talc by replacing 1/6 of the tetrahedral silicons by aluminium. The balancing cation is often magnesium.

 

4.2 Clay Swelling

The swelling of clay minerals by water clearly has important implications in civil engineering and in the manufacture of ceramic products.

In montmorillonite and vermiculite, the sheets are held together by the alternating layers of bridging cations (Na+, K+ or Ca2+). In the presence of water these ions dissociate and a double layer repulsion is generated between the triple sheets.

Empirical relation between the thickness of the water interlayer, dw /nm, and the concentration, c, of monovalent electrolyte solution in which the clay mineral is immersed:

(4.1)

and which is valid for 0.01 < c/mol dm-3 < 0.25.

 

4.3 Direct Measurement of Forces Between Surfaces.

The ability to cleave mica to produce atomically smooth surfaces allows the measurement of forces between surfaces using the surface force balance first developed by Tabor but subsequently improved by Israelachvili.

Mica, silver coated on one surface, is stuck to transparent quartz discs which have a half-cylindrical cross section. The half cylinders are mounted in a surface force balance apparatus so that they have a crossed cylinder configuration.

 

 

 

White light is passed through the cylinder attached to the leaf spring, multiply reflected between the silvered cylinders and then collected by the spectrometer. Only certain wavelengths (i.e. fringes of equal chromatic order) are transmitted, and the shift in wavelength of these fringes gives the change in separation of the two cylinders.

The lower cylinder can be accurately translated to the upper cylinder by the micrometers. If the fringe orders indicate that the distance travelled is less than that imparted by the micrometers, then the leaf spring has bent this distance differential due to repulsive forces.

Since the spring constant is known the repulsive force can be calculated.

When immersed in water, the potassium counter ions at the mica surface dissociate to form a diffuse double layer and the interaction between these can be accurately measured.

At large separations the data follows the curve for the constant potential case, at closer distances the constant charge calculations, are more appropriate. But the overall decay of the repulsion potential is exponential as predicted by theory. If the two cylinders approach each other sufficiently closely, they jump into adhesive contact due to the attractive van der Waals forces.

 

 

5 Association Colloids

Certain amphiphilic molecules (i.e. molecules which have both a hydrophillic region and a hydrophobic region), exhibit a sharp change in the behaviour of certain properties when this property is plotted as a function of concentration

 

The process can be understood as follows:

At low concentrations these molecules dissolve in water and form a true solution but with an excess of the molecules at the air-water interface. This enables the non-polar tail to avoid contact with the water whilst the polar head group remains in contact. Consequently, these materials are known as surfactants (i.e. they are surface-active).

 

Schematic diagram of surfactant molecule

 

As the concentration increases the interface becomes packed with surfactant until a complete monolayer is formed.

 

At this fairly distinct concentration, the c.m.c., further addition of surfactant causes them to aggregate into micelles. Micelles are association colloids.

In water the micelle structure can be schematically drawn as:

Surfactants which display this behaviour include ionic (anionic, cationic) and non-ionic molecules.

Surfactant

Name

Headgroup

c.m.c./mol dm-3

Anionic

C12H25OSO3Na

Sodium dodecyl sulphate

-OSO3-

8.1×10-3

Cationic +

C10H21N(CH3)3Br

Decyl trimethyl ammonium

Bromide

6.8×10-2

Non-ionic

Rn(O CH2CH2)mOH

Polyethylene oxides

-(O CH2CH2)mOH

8.7×10-5

(for m=6; n=12)

Soap molecules (sodium or potassium salts of organic acids) are well-known example of surfactants, e.g. sodium stearate, , potassium oleate, .

 

Analysis of the thermodynamics of micellisation shows that it is accompanied by an increase in the entropy of the system; this increase is the major contributor to the negative D Go. This phenomenon is rationalised in the following way.

Below the c.m.c., the hydrocarbon tail constitutes a cavity in the water structure, this cavity is lined by water molecules which differ in their organisation from that of the bulk water. The water becomes more ‘structured’. Furthermore, the hydrocarbon tail is less free to move in the solvated molecule because of the surrounding water.

On micelle formation, the bulk structure of water is restored and the entropy of the water increases. In the micelle core, which is essentially liquid hydrocarbon, there is greater freedom for movement and so the entropy associated with the hydrocarbon tails also increases.

The head groups are little affected by micellisation since they are surrounded by water molecules at all stages of the process. However, interactions between headgroups (within the same micelle) will determine the size and shape of the micelle. These interactions will result in some of the hydrocarbon core being exposed to water because the surface cannot be covered by a close-packed arrangement of polar head groups.

 

5.1 Influencing Factors on C.M.C.

Head group and chain length

Log (c.m.c.) = b0-b1mc (5.1)

mc = no of carbon atoms in hydrocarbon chain, b0 and b1 are constants for particular surfactants.

 

b0

b1

Na Carboxylates

2.41

0.341

K Carboxylates

1.92

0.29

Alkyl ammonium chlorides

1.25

0.265

Note the head group influences b0 and b1.

Branching, double bonds in the hydrocarbon increase the c.m.c.

 

Counter ion

Changing the valency of the counter ion has a strong influence on the c.m.c. in the same way as they influence the critical coagulation concentration.

 

Temperature and Pressure

For ionic surfactants below a certain temperature, known as the Krafft point, the surfactant comes out of solution and there are no micelles present.

For non-ionics increasing the temperature causes the formation of large aggregates which separate out as a distinct phase at the cloud point. This is attributed to the reduction in hydrogen bonding solvation between head groups and water.

 

Organic Molecules

Organic molecules can influence c.m.c. behaviour markedly and in ionic surfactants may frequently be present as impurities. Sodium dodecyl sulphate often contains dodecanol as a hydrolysis product.

The micellar phenomenon of solubilisation is very important, whereby lipophiles are apparently solubilised in water by the addition of surfactants.

Þ detergent action of surfactants.

Dirt on clothing is a mixture of soil and oil, on dishes it is denatured proteins, fats and sugars. The surfactant adsorbs on to the exposed surfaces and the shearing action of the washing process lifts the dirt from the surface, the fresh dirt surfaces become covered in surfactant that then disperses the dirt in the aqueous phase. Other additives in the detergent adsorb on to the clean surface to block redeposition of dirt.

 

5.2 Thermodynamics of Micelle Formation

The size of micelles in the c.m.c. region is typically uniform, i.e. the micelles are generally quite monodisperse. Consequently, some insight into the micellation process can be obtained by using a simple closed association model, in which the following simplified process is assumed to occur:

The equilibrium constant is for this process is:

where: xn = mole fraction of micelles, x1 = mole fraction of monomer.

The standard Gibbs free energy change of formation of one mol of micelles is then:

The free energy of formation per mole of surfactants is:

At the c.m.c., n is large (typically > 50) and xn ~ x1, therefore the first term on the LHS is small. Therefore:

 

How do we expect D Go(n) to vary with n?

Consequently, D Go(n) must have a more complicated variation with n.

 

Consider the micellation process. A possible mechanism for micelle formation is:

  1. Formation of a micelle eliminates hydrocarbon-water interactions and increases hydrocarbon/hydrocarbon interactions; the latter is a maximum on completion of the structure.
  2. As the micelle increases in size it becomes increasingly difficult to insert hydrocarbon tails.
  3. Growth is accompanied by packing of head groups on the surface and repulsions become increasingly important.

Þ three contributions to the expression for D Go(n), i.e.:

(5.2)

...........1.............2..............3

  1. Decrease in free energy from replacement of hydrocarbon-water interactions by hydrocarbon-hydrocarbon interactions.
  2. Excess free energy from surface.
  3. Contribution due to increasing head group interactions.

The form of equation 5.2 then gives the desired property that at a distinct surfactant concentration (i.e. the c.m.c.), the concentration of micelles rapidly rises from ~0 to x1, the monomer concentration.

 

 

6 Liquid Surfaces and Films at Liquid Interfaces

 

6.1 Pure Liquid Surface

Liquids exhibit properties that imply there is a surface ‘skin’ that has properties differing from the bulk liquid. This surface ‘skin’ is provided by the surface tension, g . If the surface area changes by dA then the reversible work done is g dA. At constant p and T, this work is the increase in Gibbs free energy of the system, i.e.:

Hence: (6.1)

i.e. g is the surface free energy per unit area, Gs.

 

6.2 The Gibbs Adsorption Isotherm and Surface Tension of Solutions

Consider two bulk phases, a and b , separated by an interfacial region. In Gibbs treatment, the bulk phases are considered uniform in composition up to some (Gibbs) dividing surface, S, between them.

 

The properties of the entire system then include the properties of each bulk phase, a and b , and that of the Gibbs dividing surface; properties of the latter are given the superscript s .

 

 

For instance, the surface energy, Us , ascribed to the Gibbs surface is:

where: U = total energy of system. Us represents the extra energy in the system due to the presence of the interface.

Similarly, nis represents the extra amount of species i in the system due to the presence of the interface. nis can be +ve (adsorption at the interface) or -ve (depletion at the interface) and is given by:

( 6.2)

where: ni = total number of species i in the system.

 

Consider a small change in energy, dUs , of the interfacial region.

From the 1st law of thermodynamics: dU = dq + dw. dq = TdS, and dw consists of the chemical work due to composition changes, S m idnis , and the mechanical work done in extending the surface, g dA. Hence:

(6.3)

Integrating gives:

 

Differentiating this with complete generality:

(6.4)

 

Comparison of equations 6.3 and 6.4 shows that:

(6.5)

 

This is the Gibbs adsorption equation.

 

At constant T, this reduces to:

(6.6)

where G i= ni/A and is known as the surface excess concentration (units of G i are moles per unit area).

 

At constant T and for a two component solution (solvent 1 and solute 2):

 

The dividing surface, S, is placed so that G1 = 0 (i.e. no adsorption of the solvent at the surface) and thus:

but . In addition, if the solution is sufficiently dilute, the activity, a, can be replaced by the concentration, c.

\

\

or (6.7)

 

This is the Gibbs adsorption isotherm.

 

Thus if dg /dc is negative we have an excess of the solute at the surface or interface ( is positive).

If dg /dc is positive we have a depletion of solute from the surface ( is negative).

 

 

For simple electrolytes (e.g. NaCl, KCl) an increase in surface tension with salt concentration is observed, \ is negative. In contrast, simple organic molecules typically show a lowering of the surface tension with concentration, indicating that is positive and that preferential adsorption of the molecules occurs at the air-water interface.

Surfactants exhibit a rapid fall in surface tension with concentration until the c.m.c. is reached, whereafter the surface tension is constant. Hence, (as expected) is positive and an excess of surfactant occurs at the interface.

 

 

 

6.3 Spread Films on Liquid Substrates

The surface excess of surfactants is sufficiently large to produce a monomolecular layer of surfactant at the interface, such layers are called monolayers. These monolayers exert a surface pressure, p .

mN m-1 (6.8)

where: g 0 = surface tension of pure solvent (for water, g 0 = 72 mNm-1), and g = surface tension of the surfactant solution. p represents the surface tension lowering that results from replacing solvent molecules with surfactant molecules at the surface.

 

An interpretation of this surface pressure is that the adsorbed, essentially insoluble, surfactant molecules cannot pass through a barrier that separates them from a surface of pure solvent. The adsorbed molecules bombard this barrier and thus analogous to gas molecules bombarding container walls, a pressure is generated.

Surfactants that are placed on a liquid surface can spread to occupy all the available area by forming monolayers. Molecules forming monolayers have amphiphilic characteristics, i.e. they have hydrophilic and hydrophobic regions. Typical examples include the long hydrocarbon tail and polar/ionic headgroup surfactants we discussed previously, and also some polymers, proteins and lipids.

The spreading behaviour of insoluble/sparingly soluble amphiphilic materials has been known since ancient times. ‘Spreading oil on troubled water’ was recorded by Pliny the elder. Moreover, in 1765 Benjamin Franklin spread known volumes of oils onto Clapham common pond, and by measuring the surface areas covered by the films, he estimated that the films were ~ 2.5 nm thick (i.e. a monolayer thick). Langmuir devised the surface film balance to measure the surface pressure of such spread films directly.

 

6.4 Experimental Study of Spread Films

Spread films are generally investigated using a Langmuir film balance, comprising a trough with moveable barriers and a surface pressure sensor. A dilute solution of the surfactant in a volatile solvent (typically CHCl3) is prepared. A few drops of this solution (~40m l) are deposited on the liquid surface between the barriers. The volatile solvent spreads and evaporates, leaving just the surfactant molecules at the liquid surface. The surfactant film is compressed by moving the barriers inwards, and the surface pressure, p , is measured continuously as the surface area available to the surfactant decreases. p can be measured to an accuracy of ~ 0.01 N m-1.

6.5 Monolayer States

Monolayers are typically characterised as gaseous, liquid expanded, liquid condensed or solid; however other 'liquid' states can also occur and may be considered as 2D analogues of smectic liquid crystal phases. Different monolayer states represent different degrees of film molecule freedom and order. The particular state occurring at a given T and p depends upon the magnitude of the intermolecular forces present. Ionic surfactants often produce gaseous and expanded monolayer states, due to repulsion between the charged headgroups. In contrast, surfactants with polar headgroups and long hydrocarbon tails (e.g. octadecanoic acid) produce more condensed states. Increased tailgroup length favours more condensed states.

Transitions between monolayer states are shown on the p -A curve by a gradient discontinuity. A plateau region in the p -A curve illustrates a first order transition. From the temperature variation of this plateau, a latent enthalpy can be determined by using a 2D analogue of the Clausius equation (). A sharp gradient change without a plateau, represents a higher order transition.

 

A typical p -A isotherm is shown below.

 

 

6.5.1 Gaseous Film

The area per molecule, A is large compared to the molecular area and the films are highly compressible, and have a low viscosity. In principle, all materials that spread can exhibit this behaviour if a sufficiently large area is available.

If the solution is dilute, then the surfactant molecules do not interact with one another appreciably and the surface pressure lowering, p , can be considered to be proportional to the bulk surfactant concentration, c.

i.e. p = bc (6.9)

where: b is a constant. From the Gibbs adsorption isotherm:

but:

\

Since the surfactant is only very sparingly soluble, c is small and the surface excess is effectively the surface molar concentration. Hence: . Then:

p A = kT (6.10)

This equation of state is the 2D analogue of the ideal gas equation. A more realistic expression, which takes into account the finite size of the film headgroups and the interactions between surfactant molecules is:

(6.11)

where c' is a constant.

 

6.5.2 Liquid Expanded State

In this state, the monolayer tailgroups begin to interact with one another and can be considered to be in a random, liquid-like arrangement. The molecular areas at which these films occur are typically 2 to 3 times the molecular cross-section, A0. The molecules are thought to adopt a variety of arrangements on the surface ranging from completely flat as for the gaseous case, to perpendicularly oriented as in the solid state. An equation of state for this phase has been proposed:

(6.12)

where: p 0 = surface tension of the "liquid" hydrocarbon tails. This state is usually observed for long chain molecules with a polar group (acids, alcohols, amides, nitriles).

 

6.5.3 Liquid Condensed State

The monolayer is semi-solid with water squeezed out from between the hydrophillic heads; appreciable tailgroup interactions occur. This state is the 2D analogue of a liquid crystalline phase, i.e. there is some degree of orientational order. On compression, more water is squeezed out and a solid film is obtained.

 

 

6.5.4 Solid Film

This state is the 2D analogue of a crystalline solid. The surfactant molecules are ordered and close-packed, and the film has low compressibility and high viscosity. Carboxylic acids at sufficiently low temperature or with sufficiently long hydrocarbon tail exhibit this behaviour. Surface pressure isotherms tend to be linear with a limiting area, A0, that reflects the cross-sectional area of the surfactant molecule (e.g. for carboxylic acids this area ~ 20.5Å-2).

Upon further compression, these films can collapse, with film molecules being forced out of the monolayer, resulting in multilayer (often trilayer) structures. The collapse point is shown by a sudden fall in p .

The surface pressures of the films appear to be small, but an analogy with 3D can be made by noting:

Thus for p = 10 mN m-1 and thickness ~ 20Å, p = 10´ 10-3/(20×10-10) ~ 5×106 N m-2 i.e. ~ 50 bar. Hence at ‘high’ surface pressures ~30 mN m-1, the compressive effect on the molecules in the film may be equivalent to ~ 100-1000 bar.

 

6.6 Surface Waves on Liquid Surfaces

The surface of a liquid is subjected to continuous thermal fluctuations which can be described as a wave-like motion of the surface that is collectively described as capillary waves. These capillary waves have a small amplitude ~ 5Å at most and wavelengths of ~ 10-100s m m. The waves on a pure liquid are damped by the viscosity of the fluid and their frequency is proportional to the surface tension. If a surface film is present, the capillary waves perturb the film. Capillary waves scatter light efficiently and this is used to observe the capillary waves and evaluate the transverse and dilational parameters.