FUNDAMENTALS OF SURFACE MODES:
¥ COLLOIDS ¥ means ÒglueÓ in Greek ¥ was coined in 1861 by Thomas Graham. ¥ ¥ ¥ ¥ ¥

WHAT IS A COLLOID? usually consists of two phases; one continuous phase in which the other phase is dispersed. Size of particles: larger than the size of molecules and small enough for the dispersed phase to stay suspended for a longer period of time. ¥ No strict boundaries for the size limits.

OFFICIAL DEFINITION
¥ In 1903 Wolfgang Ostwald formulated the official definition of a colloid: ¥ a system containing entities having at least one length scale in between 1nm and 1µm. ¥ For smaller particles there is no distinct boundaries between the phases and the system is considered a solution; ¥ for larger entities the particles will fall to the bottom due to the gravitational force, and the phases are separated.

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MESOSCOPIC PHYSICS
¥ The particle size is in the so-called mesoscopic range in between the macroscopic and microscopic limits.

LARGE INTERFACIAL AREA
¥ One very important quality of the colloids is the large interfacial area between the dispersed and the continuous phases.

WHAT EFFECTS HAS THIS?
¥ This means that interface effects and hence the electromagnetic surface modes, are very important for the properties of the colloids. ¥ It costs energy to create this much surface and the particles would clump together if this isnÕt prevented. ¥ Usually the particles are charged and hence repel each other.
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Four states of matter:
¥ solid, liquid, gas and plasma→16 types. ¥ Eight types of common colloids:
Homogenous Phase Solid Solid Solid Liquid Liquid Liquid Gas Gas Disp. Phase Solid Liquid Gas Solid Liquid Gas Solid Liquid Name Solid Suspension Solid Emulsion Solid Foam Sol Emulsion Foam Aerosol Aerosol Examples ruby glass, composites, ceramics, bone bitumen( asphalt ), opal, pearl expanded polystyrene, isolation foam, pumice ink, paint, blood , tooth paste, mud milk, mayonnaise, cream beer foam, fireext. foam, soap foam smoke, dust mist, fog, clouds, household sprays

COLLOIDS IN INDUSTRY
¥ Colloidal properties are utilized in many branches of industry: ¥ food industry ¥ cosmetic industry ¥ pharmaceutical industry ¥ mining industry ¥ paint industry
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OTHER EXAMPLES
¥ The minerals our bodies absorb from food are in the form of colloids, and much of our body-fluids and -tissues themselves can be regarded as colloids. ¥ The large surface- or interface-area in colloids makes these systems ideal for catalytic applications.
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NEW MATERIAL THAT HAS STARTED BEEING EXPLOITED
¥ Solid foam can have very interesting properties. ¥ One may make foam out of metals, like aluminum, that is much lighter than the pure metal but still keeps the same strength as the pure metal. ¥ This means a tremendous potential for applications.

YET ANOTHER NEW MATERIAL
¥ Aerogels are similar to solid foams. ¥ A gel is a sol, i.e., a solid phase dispersed in a liquid phase, where the solid phase is lyophilic. ¥ A continuous solid network may form. As an example we may choose gelatin. It behaves as an elastic solid or semi-solid rather than a liquid. The particles have lost their mobility.
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¥ It is possible, although tricky, to replace the liquid phase with air without damaging the solid component and keep the open structure. ¥ The result is an aerogel. ¥ These materials are very light, typically a fraction of a percent of the density of the solid phase. ¥ Other names for dried-out gels are zerogels or xerogels. ¥ It is used in space missions to collect interstellar dust.

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¥ have both liquid and solid properties. They can support small static shear like a solid, but can also flow and deform arbitrarily like a liquid. ¥ They can be considered complex fluids or soft matter. They are characterized by soft order, i.e., by microstructures which are both flexible and stable. ¥ There are discussions going on about classifying these substances as a fifth state of matter.

FOAMS

MILK
¥ This colloid consists of more than two components. ¥ Homogeneous phase is a liquid; ¥ Dispersed phase consists of fat droplets and protein particles. The fat dominates the general properties so we can consider the colloid to be an emulsion.
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Fat is hydrophobic.
¥ Raw milk, i.e., the milk that is produced by the cow is not very stable. ¥ Dispersed phase floats towards the surface and collects there as cream and can be skimmed of. ¥ Milk we buy has been treated to become more stable. It has been homogenized which means that the fat droplets have been split up into smaller droplets.

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Whipping cream
¥ can be viewed as concentrated milk. ¥ It is still an emulsion but there is less of the liquid phase than in milk. ¥ It contains approximately 40 % fat.

AIR BUBBLES
¥ When we whip the cream we introduce yet another dispersed component, viz. small air bubbles. ¥ The fat droplets are collected at the surface of the air bubbles; the energy is minimized in this way. ¥ We get a more or less stable foam.
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PHASE INVERSION
¥ If we continue whipping we break the bubbles and the fat now becomes the homogeneous phase with the water as the dispersed phase; ¥ we have a new emulsion where the phases have been inverted.

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BUTTER
¥ The result is butter. ¥ Some of the water has left the material and the fat content is now around 80 %.
Ð Butter is also a colloid where the homogeneous phase is fat and the dispersed phase water.

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¥ If we want to use this butter in preparing a juicy steak for dinner we put it in the frying pan. ¥ The butter, or rather the fat, melts and the water evaporates. When the butter has silenced, i.e., when all water has evaporated it is time to put in the steak. ¥ At this stage the phase separation is complete; the colloid is gone and the fat phase remains.

FRYING A STEAK

THE PROTEINS
¥ We have completely neglected the proteins. ¥ They help stabilize the colloid by forming layers between the water and fat. ¥ The skin on boiled milk is polymerized protein

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STABILITY OF COLLOIDS
¥ Casimir effect sprung out of the study of colloid stability. ¥ Colloids are divided into two classes called lyophobic and lyophilic. ¥ In the first class the dispersed medium avoids or dislikes the solvent ¥ while in the second it prefers or likes the solvent.
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WATER AS SOLVENT
¥ If the solvent is water the classes are called hydrophobic and hydrophilic, respectively.

ORGANIC LIQUID AS SOLVENT
¥ If the solvent is an organic liquid (usually fatty, e.g. oil) the classes are called lipophobic or oleophobic and lipophilic or oleophilic, respectively.

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DISPERSION
¥ A lyophilic colloid can be dispersed by just adding the proper solvent ¥ while in the case of a lyophobic colloids one has to mechanically force the particles to disperse.

LYOPHOBIC COLLOIDS
¥ A lyophobic colloid is never really thermodynamically stable. ¥ Given enough time it will eventually form aggregates. ¥ A highly stable lyophobic colloid may look homogeneous for days, weeks and even months
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EXAMPLES OF THE TWO TYPES
¥ Gelatin is an example of a hydrophilic substance. ¥ Milk is a hydrophobic colloid where a homogenization process is used to break the dispersed particles into smaller pieces and thereby making the colloid more stable.

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BREAKING DOWN PROCESS
¥ The particles in a colloid undergo Brownian motion and collide with each other. ¥ If they come close enough to each other they get stuck due to the van der Waals attraction. ¥ As this process goes on the particles or aggregates of particles get larger and larger until gravitation leads to phase separation. ¥ The aggregates fall to the bottom of the container or float to the top.

PREVENTING PARTICLE AGGREGATION
¥ The formation of aggregates can be prevented or reduced by different mechanisms. ¥ If the solvent is properly chosen the particles become charged and are surrounded by a cloud of opposite charge Ð a so-called double layer is formed. ¥ This leads to a repulsive part of the potential between two particles. We will return to this later.

HYDROPHILIC COLLOIDS
¥ Another effect is responsible for the hindrance of formation of aggregates in hydrophilic colloids. ¥ Water molecules are bound to the surface of the particles and it costs too much energy to remove the water molecules from the polar groups of the particles to let the particles come close enough to bind via the vdW forces. ¥ This repulsive force is called a hydration force.

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SURFACTANTS
¥ One method to increase the colloid stability is to let surfactants or polymers bind to the surface of the particles and thereby prevent particles to come close together. ¥ This leads to a repulsive so-called steric force. ¥ The proteins in milk have this effect.
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THE PARTICLE SIZE
¥ The particles in a colloid, where the homogeneous phase is a liquid or gas, have to have the right size or rather be in a specific range of sizes to keep suspended for a reasonable long time. ¥ If the particles are too big they fall to the bottom due to the gravitational forces.

OUTER SPACE
¥ This is different in the outer space, where we can neglect gravitational effects. ¥ Thus the behavior of colloids is different in a gravitational-free environment or in micro-gravity.

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VARIATION OF PARTICLE SIZE WITH TIME ¥ If the particles clump together they will sooner or later reach a size where they no longer stay suspended and the colloid breaks down.

FLOCCULATION, COAGULATION AND COALESCENCE
¥ If the particles bind weakly to each other the process may be reversible; ¥ this process is called flocculation. ¥ If the process is irreversible it is called coagulation. ¥ In the case of liquid droplets the two droplets usually transform into one, bigger droplet after the coagulation. ¥ This is called coalescence.

POTENTIAL HAS DOUBLE MINIMUM
¥ We will see later that the interaction potential between two particles often has two minima; one weak at large separation and one deep at small separation. ¥ If the temperature is low the particles can bind weakly and reversibly. Increase of the temperature may lead to strong and irreversible binding.

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FLOCCULATION AND COAGULATION IN SAME SYSTEM
¥ Thus flocculation and coagulation can occur in the same system under different circumstances.

OSTWALD RIPENING
¥ We may also have another effect if the particles are slightly soluble in the liquid and in equilibrium with the solution. ¥ In that case larger particles grow at the cost of smaller. The net effect is the same. The particle size increases and destabilizes the colloid. ¥ This is termed Ostwald ripening.

STABILITY OF LYOPHOBIC COLLOIDS
¥ We will now discuss the stability of lyophobic colloids. ¥ Examples of lyophobic colloids are: ¥ a gold sol, ¥ a silver iodide sol, ¥ a quartz suspension (in water or in an organic liquid), and ¥ the emulsions.
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DIFFERENT PARTICLE TYPES
¥ The particles are either rigid particles, amorphous or crystalline, or small droplets. ¥ The stability of these colloids is very sensitive to electrolytes. ¥ As an example of this we may choose milk, where a small amount of citrus acid is enough to destroy the stability and cause coagulation.
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IN CONTRAST TO LYOPHILIC
¥ In general the lyophilic colloids do not show up this sensitivity, although there are exceptions. They are also affected by the electrolyte, but not in the same way.

CHARGING OF THE PARTICLES
¥ The dispersed particles in the lyophobic colloids carry an electric charge typically of the size of hundreds of elementary charges. ¥ Since the colloid is neutral the corresponding opposite charge is in the form of ions in the liquid. ¥ Typically a fraction of the surface atoms of the particle are ionized.
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COUNTER IONS
¥ The counter ions in the liquid are moving around in thermal motion so at least not all are bound to the particle. ¥ They are however not homogeneously distributed throughout the solvent; ¥ they are affected by the fields from the charged particles and preferably stay close to the particles and make up an effective screening of them.

DOUBLE LAYER
¥ If we consider one particle separately it is surrounded by an electric double layer. ¥ One layer of this double layer is made up by the charges in the surface layer of the particle and ¥ the second by the neutralizing ions in the liquid.
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DIFFUSE LAYER
¥ One may to a fairly good approximation treat the surface charge as homogeneously distributed over the surface of the particle. ¥ The concentration of charges in the outer layer decreases with distance from the particle and constitutes a so-called diffuse layer.
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WAYS TO INFLUENCE THE STABILITY
¥ As we shall see this formation of a double layer is very important for the stability of the colloid. ¥ The double layer is sensitive to electrolytes and also temperature. ¥ This means that the stability of the colloid may be manipulated by adding electrolytes or changing the temperature.
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PEPTIZATION
¥ For some colloids the formation and stabilization occur spontaneously when adding the solvent; ¥ for others one needs to add small amounts of specific electrolytes. ¥ The process in which the dispersed phase is broken up in small particles with the formation of a double layer around each is called peptization. ¥ The inverse process is called depeptization.
Flocculation values in millimols/liter for negatively charged sols

ELECTROLYTES
¥ When adding a proper electrolyte the ions in the diffuse layer are sometimes neutralized and the stability is reduced, but this effect is not so common. ¥ The stability is in most situations changed without affecting the ions bound to the particles or the ions of opposite charge in the solution.
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Electrolyte

As2 S3 − sol 58

Au − sol

AgI − sol

HOW MUCH ELECTROLYTE IS NEEDED FOR FLOCCULATION?
¥ For each combination of colloid and electrolyte one may determine how much electrolyte is needed to cause flocculation.

LiCl LiNO3

165 51 24 165 49.5 25 65.5 23 126 0.72 2.53 0.81 0.65 0.41 2.38 0.635 2.33 0.69 0.35 2.20 0.685 2.50 0.64 0.093 0.095 0.096 0.009 0.069 0.080 0.003 0.069 0.013 0.067 2.8 3.15 136

WHAT DETERMINES?
Flocculation values in millimols/liter for positively charged sols Electrolyte NaCl KCl Fe2 O3 − sol 9.25 9.0 9.65 12 14 0.205 0.22 0.195 0.63 0.080 0.053 0.3 60 Al2 O3 − sol 43.5 46

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NaCl NaNO3 KCl KNO3
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K2 SO4

RbNO3 MgCl2 Mg( NO3 )2 MgSO4 CaCl2 Ca( NO3 )2 SrCl2 Sr ( NO3 )2 BaCl2 Ba( NO3 )2 ZnCl2 Zn( NO3 )2 UO2 ( NO3 )2 AlCl3 Al ( NO3 )3
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1

1 2

BaCl2 Ba( NO3 )2

KNO3
1 2

K2 SO4

2 3 4

MgSO4 K2 Cr2 O7 K3 Fe(CN )6 K 4 Fe(CN )6

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Al2 ( SO4 )3

La( NO3 )3 Ce( NO3 )3 Th( NO3 )4

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¥ It turns out that this amount is strongly dependent on the valency of the counter ion, i.e. the ion with opposite charge to that of the particles. ¥ Which the anions and cations are is much less important. ¥ The size of the counter ions has importance, although small; the larger the counter ion the less amount of electrolyte is needed. ¥ Experimental results clearly demonstrate these effects.

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FORMATION OF THE DOUBLE LAYER
¥ There are two types of objects that are most important and will be treated here. ¥ They are objects with flat surfaces and spherical particles. ¥ The charges bound to the surface of the particle is usually treated as a homogeneous surface charge. ¥ We will here consider solid particles.
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The charges in the diffuse layer
¥ We will treat the charges as point charges. ¥ If it wasnÕt for the Brownian motion counter ions would accumulate at the particle surface and completely neutralize the charges of the particle. ¥ In the linear-response approximation the charges are distributed according to the Debye-HŸckel screening. ¥ We will here go beyond the linear response approximation but still treat the atoms and ions in the solvent as point particles.

GOUY AND CHAPMAN THEORY
¥ The potential in the diffuse layer is given by PoissonÕs equation:
∇ 2 Φ = −4πρ / κ ; ρ = ρ+ + ρ− = Z+ en+ + Z− en−

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¥ where Z± are the valencies of the cat- and anions taken with signs. ¥ The charge distributions depend on the potential so these two eqs must be solved simultaneously.

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TEMPERATURE EFFECTS
¥ At zero temperature the counter ions will be collected at the surface of the particle. ¥ This is prevented for finite temperatures due to the thermal motion of the atoms and ions.

ASSUMPTION OF THE GC THEORY:
¥ The theory assumes that the average concentration of the ions at a point in the diffuse layer is determined by the average potential at that point. ¥ The concentration is determined by a Boltzmann factor: ˜ n± = n± e − Z±eβΦ
˜ ¥ where n± are the equilibrium concentrations of the ions far away from the particle, where the potential is zero. 56

IONS OF EQUAL VALENCY
¥ We will now limit the treatment to the case of ions of equal valency type. We let

Z+ = − Z− = Z

¥ Thus we have: ˜ 8πZen ∇2Φ = sinh( ZeβΦ) κ ¥ This is a nonlinear equation for Φ.
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y = ZeβΦ ; y0 = ZeβΦ 0 ;
2 q0 =

New variables:

˜ 8πnZ 2 e 2 β 2 ; ⇒ ∇ 2 y = q0 sinh( y) κ

γ =

e y0 2 − 1 e y0 2 + 1

¥ If y is small this may be linearized with the 2 result: ∇2 y = q0 y
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