2. Stages in the Formation of a Collodal Particle

3. The Colloidal Particle is an Unstable Species
Thermo dynamics tells us that any particle with high specific surface area will have an associated high surface energy.
If we imagine the work needed to increase the surface of a particle by a small increment d then the work is the product of the force resisting increase in area times the distance it moves.
All material exhibits a resistance which we define as the surface tension X. Then the increment of the work dw is Xd, i.e. dw =X d

4. = Entropy + Surface Creation + pressure/volume
A more rigorous argument is that work of surface creation is additional to pressure/volume work and if we examine Helmhotz function relating the change of state of a system to entropy, p-v work and surface creation, we can express this as follows:
Helmholtz function:
= Entropy + Surface Creation pressure/volume   
dA = -S dT – pdV + X d
 dA is the Helmholtz function
 S is entropy
 T is Temperature
 P/v is pressure/volume

5. All systems try to lower dA thus a system attempts to lower its internal energy and increase entropy or disorder.
The additional term in the expression shown above indicates the desire to decrease surface energy.
With the Gibbs free energy function we are often more interested in changes at constant pressure and not constant volume
For our purposes, the Helmholtz is preferred because it considers changes in a system at constant temperature and volume and more appropriate to consider the work to increase surface area of a particle.

6. From this, it should be apparent that the colloidal state should not exist at all yet experience tell otherwise.
The Stability of a colloid is therefore a very kinetic one.
The particles are trying to collaspe and move towards one another and coalesce to reduce surface energy.

7. Imagine two spherical particles 200 nm diameter.
Their volumes are 4/3 R13 = R3 and surface areas are 4R2 = 12.57R2
For the basis of a simple unit of square area in nm we would then have:
Volumes, V1 = x 106 and areas = x 104
The total surface area of the two sphere is = x 104
If we dissolve the two sphere into one larger sphere we need to calculate its new diameter.
 Therefore 4/3 R23 = R23 = 2 x V1 = 2 x x 106
 Therefore R2 = and the new area of that sphere is 19.9 x 104

8. Another way of looking at it is the ratio of area to volume, V/A:
Thus area of the single combine sphere is much smaller than two separate spheres for the same volume.
Another way of looking at it is the ratio of area to volume, V/A:
(4R2) / (4/3 R3) = 3/R
therefore A/V as R goes to zero goes to infinity
This then provides a strong driving force for the particles to combine.

9. Mechanism of Combining
Particles when they pass close enough, will experience a force of attraction know as van der Waals force. And differ from electrostatic forces.
Electrostatic

10. van der Waal Forces
Unlike electrostatic forces which vary with 1/r2 van der Waal forces obey a higher power law, 1/r6
Permanent Dipole
Dipole Induced in a Non-Polar Molecule by a Permanent Dipole
Resonant Induction of dipoles

11. van der Waal Forces
Permanent Dipoles
Van der Waal forces arise because of the permanent or induced polarization in adjacent atoms or molecules even though the normal valence requirements are satisfied.

12. Permanent Dipoles
Molecules with permanent dipoles can orient in such a way a to produce attractive forces.
Attractive orientations correspond to a lower energy state than repulsive ones; hence, in a fluid the net average orientations cause attraction.

13. Dipole Induced in a Non-Polar Molecule by a Permanent Dipole
Here the electron cloud around the non polar molecule is distorted and forms an induced dipole.

14. Resonant Induction of Dipoles
If the electron cloud in one molecule resonate, it can induce a dipole in an adjacent electron cloud leading to attraction.
This induced dipole – dipole interaction is sometimes called london attraction or dispersion force.

15. Molecules with permanent dipoles can orient in such a way a to produce attractive forces.
Attractive orientations correspond to a lower energy state than repulsive ones; hence, in a fluid the net average orientation cause attraction.
The total attractive force is between molecules is cause by the sum of all three mechanism above.
This augument has only considered dipoles but molecules exist with more complex electron distributions such as quadrupoles and higher.
There are many more interactions but all lead to a depence on 1/r6.

16. Why do Colloids Exist at All?
Example:
Basis: 1cm3 of cube of material with Area = 6 cm3
Divide this into many 100 nm cubes
The area increases now to 6000,000 cm3
Divide this into many 10 nm cubes
Thus, any effects connected with colloids are going to be surface dominated.

17. The are Other Forces that Oppose the Long Range Effects
It possible for a particle to develop a protective film at its surfaceby reacting with the solvent.
Example:
A platinum sols will react in water to form Pt-(OH)3. This forms a protective layer around the particle
Emulsification of fat by soap is another example
The adsorption of surface active molecules (neutral or ionic).
This can lead to kinetic stablization due to electrical charge on the particle surface and its surrounding ions in solution.
Electrical Double Layer ( we will discuss in more detail later )

18. Stages in the Formation of a Collodal Particle

19. Sequence of Events leading to Uniform spheres
(A_C) Time elaspe
over 6 hrs at
90 degrees
(D)
Aging 48 hrs

20. Oswald Ripening
Ostwald ripening Derives from the mechanism driving small particles to combine.
It is the process by which larger particles (or, for emulsions, droplets) grow at the expense of smaller ones due to the higher solubility of the smaller particles and to molecular diffusion through the continuous phase.
Initial formed aggregates restructure through disolution-reprecipitation to form larger, more stable particles, thereby consuming the small primary particles.

21. Continued:
On prolonged heat treatment, the precipitates coarsen to decrease the interfacial free energy between the precipitate and the matrix.
During Oswald ripening the volume fraction Vf of precipitates remains constant and the diameter of the precipitates increases.
The final product of Oswald Ripening is indistinguishable from the structure of a nucleation and growth process

22. S = S0 exp[(2slVm)/(RgTr)]
Continued:
The fate of primary nanoparticles depends on their size, as well as on T and pH of the solution
The Solubility, S, of a particle is related to its radius, r, by the Oswald-Freundlich equation:
S = S0 exp[(2slVm)/(RgTr)]
Where So is the solubility of a flat plat, sl is the solid-liquid interfacial energy, Vm is the molar volume of the solid phase, Rg is the ideal gas constant, and T is the temperature.

23. Continued:
The effect of size on solubility is most important for nanoparticles with smallest diameters.
Nanoparticles of silica less than 5 nm will tend to dissolve and reprecipitate on larger particles
This process of particle growth will raise the average particle diameter from 5 to 10 at pH > 7
At low pH growth will be negligible for particles larger than 2 to 4 nm.
The final particle size increases with temperature and pressure, as both increase the solubility

24. Continued:
Since the condensation reation is exothermic, each Si atom tries to surrounds itself with four siloxane (i.e. Si-O-Si ) bonds
For nanoparticles less than 5 nm, more than 50% of the Si atoms are on the surface, so they must have one or more silanol ( i.e. Si-OH) bonds
The interiors can be regarded as dense SIO2

25. Solubility with Radius of Curvature

26. Silica Sol Gel Reaction
Silica particles were precipitated from solution of:
1.7 M tetraethly orthosilica,
1.3 M amomonia,
and 2.0 M H2O in ethanol at 25oC
SEM pictures of this reaction was taken with time

27. Hydrolysis and Condensation Reaction of TEOS

28. Model of Silica Particle Growth
Cubic octasilic acids
Cyclic trisilicic
Oxygen
hydrogen
Silica not shown
C and D colloidal particles formed by momoners to form
closed rings until covered with a layer of silanol groups

29. Polymerization Behavior of Silica

30. The effect of Salt on Silica Particle Formation and Growth
With salt presence aggregation, precipitation or gelation can occur at pH< 7 or pH 7 to 10.
In the absence of salt, no chaining or aggregation occur, because the particles are mutually repulsive.
The addition of salt reduces the thickness of the electrical double layer at a given pH, dramatically reducing the gel times.

31. Ripening of Silica Particles
Bar = 100 nm
Grids taken 2,8, 30 and 120 minutes apart after initial reaction.
No salt present.

32. Continued:
The effect of size on solubility is most important for nanoparticles with smallest diameters.
Nanoparticles of silica less than 5 nm will tend to dissolve and reprecipitate on larger particles
This process of particle growth will raise the average particle diameter from 5 to 10 at pH > 7
At low pH growth will be negligible for particles larger than 2 to 4 nm.
The final particle size increases with temperature and pressure, as both increase the solubility

33. Silica Solubility vs its Particle Diameter
Particles formed at 80 to 100oC, pH 8
Particles formed at 25 to 50oC, pH 2.2

34. pH Dependence of the Reaction
The polymerization process may be divided into three domains: pH2, pH2 to 7, and >pH 7
pH 2 is a boundary as the point of zero charge and the isoelectric point ( zero mobility) both fall the range of pH 1-3
Ph 7 is a boundary because silica solubility and dissolution rates are maximized at or above pH7 and because above this the particles are so ionized that particle growth occurs with aggregation or gelation

35. Silica Polymerization, pH 2 to 6
Since the gel time decreases steadily between pH 2 and ~pH 6, it is generally assumed that above the isoelectric point the condensation rate is proportional to [OH-]

36. Effect of pH on Silica/H20 System

37. Polymerization Behavior of Silica

38. Silica Solubility vs pH & T

39. Solubility with Radius of Curvature

42. Necking Effects in aging Aggregates

43. Sequence of Events leading to Uniform spheres
(A_C) Time elaspe
over 6 hrs at
90 degrees
(D)
Aging 48 hrs

44. Growth by Aggregating Spheres
Silica from reacting TEOS

45. Silica Growth by Sweeping and Aggregation

46. Aggregate Particle