Colloidal Phenomena
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Colloidal Phenomena Colloidal Suspensions Soil Colloids Interparticle Forces, DLVO Model, Schulze-Hardy Rule and CCC Adsorption Effects on Colloidal Stability. Colloidal Suspensions Define colloids as 10 – 0.01 μ m effective diameter. Compare to silt and clay,

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Colloidal Phenomena

Colloidal Suspensions

Soil Colloids

Interparticle Forces, DLVO Model, Schulze-Hardy Rule and CCC

Adsorption Effects on Colloidal Stability

Colloidal Suspensions

Define colloids as 10 – 0.01 μm effective diameter. Compare to silt and clay,

50 – 2 μm and < 2 μm, respectively.

Suspensions are stable (and particles remain dispersed) if negligible settling

occurs in a time frame of 1 hour +.

Typically, sand > 50 μm settles ~ 10 cm min-1 so that with settling rate proportional

to d2 (Stokes’ Law), measurable setting occurs < 1 h at upper colloidal limit.

Define coagulation as process of suspension becoming unstable and subject to

settling under the influence of gravity.

Coagulation that produces high porosity bodies is called flocculation.

Coagulation that produces dense, organized bodies is aggregation.

Both processes affected by surface chemistry, particle geometry and composition

of the soil solution.

Suspended particles exhibit Brownian motion (random) due to thermal energy.

While the motion is random, diffusion occurs if a concentration gradient exists

due to an external force. A diffusion coefficient can be derived when steady-state


D = kBT / 6πηR

where kB is the Boltzmann constant (R / NA), T is oK, η is fluid viscosity and R

is particle radius.

If coagulation occurs when two particles collide, the initial rate of coagulation

is given by

dρ / dt = -8πRDρ2

where ρ is number density of particles. The development by Smoluchoski

considers changes in number density of different sized particles (ρ(R,t) / t)

as coagulation proceeds and is said to be difficult. But for a single size

before many larger coagulated particles exist, this second order reaction


2. A suspension consists of plate-like particles 1 thermal energy.μm x 1 μm x 8 nm with a

mass density of 2.5 x 103 kg m-3. Calculate the half-life for Brownian

coagulation at 25 oC in a suspension whose initial density is 1 kg m-3.

By integration or from Eq. 10.4 using the given value of the rate constant,

t1/2 = 1 / Kρ0 = 1.62 x 1017 s m-3 / ρ0

So calculate ρ0 from total suspended mass and mass / particle,

1 kg m-3 / [2.5 x 10 kg m-3 x (10-6 m)2 x (8 x 10-9 m)] = 5 x 1016 m-3

t1/2 = 1.62 x 1017 s m-3 / 5 x 1016 m-3 = 3 s

which is fast.

The number density, thermal energy.ρ0, may be determined by intensity of light transmitted

through the suspension,

I = I0 exp (-AρmP2)

where mP is mass of individual particle.


ln (I0 / I) = AρmP2

Soil Colloids thermal energy.

Wide variability in these depending on mineral type and transformations

over time –weathering / deformation and adsorption of mineral and organic

polymers on the surface and in interlayer positions.

Therefore might expect coagulated masses to be porous and disorganized.

However, 2:1 minerals tend to organize into microaggregates of varying size

called domains if relatively larger and quasi-crystals if only a few units are


Formation of quasi-crystals may occurs with Na-saturated smectite in solution

of high Na+ concentration or particle density of smectite. It occurs at low

concentration for Ca2-smectite.

Quasi-crystal formation with Ca2+-smectite involves interlayer adsorption of

Ca(H2O)62+ at interlayer positions of opposing siloxane cavities.

Given non-exchangeable K+ at interlayer positions of illite, would coagulated

masses of illite be relatively large or small?

Assuming the weakly adsorbed Li disorganized.+ (recall adsorption Cs+ > … > Li+) is

least capable to produce quasi-crystals, light scattering / absorbance

measurements can be used to determine the relative number of crystal units

per quasi-crystal.

Expressing mP = mCN

where mC is the mineral unit mass and N is the number of such units

per quasi-crystal,

ln (I0 / I) = AρmPmCN

Thus, for the same mass density, ρmP, of suspensions of homo-ionic clays,

the ratio of absorbance given by Mx+-saturated form to Li+-saturated form

should give the number of crystal units per quasi-crystal.

Li+ N = 1.0 Light-scattering data for montmorillonite, two different studies.

Na+ N = 1.2 (1.7)

Cs+ N = 2.9 (3.0)

Mg2+ N = 5.5 (4.3)

Ca2+ N = 6.2 (7.0)

5. The absorbance of two Ca-saturated soil colloidal suspensions was

found to depend on the suspension mass concentration (in kg m-3)

according to

Absorbance = 1.005cS

Absorbance = 1.453cS

where cS is suspension mass density.

What is the inference as to the relative mass of the colloidal particles?

From Absorbance = AρmP2 = AcSmP

ABS1 / ABS2 = 1.005 / 1.453 = mP1 / mP2 or

mP2 = (1.453 / 1.005) mP1

Light-scattering was used to show a transition to higher number of crystal

units per quasi-crystal as composition of montmorillonite changed from Na-

saturated to Ca-saturated.

~ 0.3 intensity for

Ca-saturated form and

fairly abrupt increase at

ENa = 0.15 indicating

decomposition of quasi-


Generally consistent with

dispersion at ESP = 15 %.

If quasi-crystals exist, Ca

exists at interlayer positions

and mix of Ca and Na on

exterior surfaces.

8. Light-scattering data for Mg-Ca montmorillonite shows a linear increase

in I / IMg from 0.55 to 1.0 as EMg increases from 0 to 1. Given that I at

EMg = 0.22 I0 at EMg = 0, what is the ratio of NMg / NCa?

Looking for ABSMg-saturated / ABSCa-saturated = (AcSmCNMg) / (AcSmCNCa)

where it is assumed that mass densities, cS, and unit masses, mC, are

the same.

ABSMg / ABSCa = NMg / NCa

IEMg=1 = (1 / 0.55) x 0.22 I0 and ICa=1 = 0.22 I0

So, ABSMg / ABSCa = -ln (IEMg=1 / I0) / -ln (ICa=1 / I0)

= 0.92 / 1.51

and, NMg = 0.61 NCa

Interparticle Forces, DLVO Model, Shultz-Hardy Rule and CCC linear increase

Suspended particles are acted upon by gravity, which de-stablizes the

suspension causing settling. van der Waals force also de-stablizes the

suspension by tending to coagulation and increased settling.

Electrostatic, charge-charge repulsion tends to stabilize the suspension.

Solvation force acts similarly by impeding action of van der Waals force

at short distances of approach between two particles.

Interaction of the three interparticle forces are described in terms of planar

surfaces approaching one another.

van der Waals force is due to dipole-dipole attraction, and may include

permanent dipoles, a dipole induced by a permanent dipole and mutually

induced dipoles arising from short-time interval distributions of electronic

charge that momentarily produce dipoles.

However, discussion focuses on the latter, referred to as van der Waals

dispersion force. While attraction between 2 mutually induced dipoles

varies as 1 / d6, where d is distance between them.

For multi-dipole, large bodies, the force is stronger and in the form of

potential energy per unit area of the planar surfaces is

VVDW = - A / 12πd2

where d is distance of separation.

Electrostatic repulsion is described by the double-layer model. For the

mid-point between two parallel planar surfaces, repulsion is given by

VELS = (64a2c0RT / κ) exp(-κd)


a = tanh(FΦ(0)/4RT), c0 is bulk concentation and κ = as defined (Chapter 8)

Sum of van der Waals and repulsive energies forms the basis for the

Derjaguin, Landau, Verwey and Overbeek (DLVO) model for colloidal

stability –suspension will be unstable / coagulate if sum is small compared

with thermal energy of colloidal particles. If particles collide with sufficient

energy to overcome electrostatic repulsion, van der Waals attraction will

dominate and the particles will remain together.

At longer distances of separation, a secondary minimum may exist.

While coagulation is associated with it, the coagulated particle is not

especially stable. Although stable with respect to Brownian collisions,

the floccules may be broken up by agitation of the suspension.

One might roughly think of aggregation = primary minimum and

flocculation = secondary minimum.

However, another stabilizing (solvation) force should be considered.

Experimental data have shown deviation from DLVO predictions at short

distances of separation due to energy associated with de-solvating near-

surface ions. Empirically modeled as

VSOL = α / 2π exp(-d / δ)

So, energy per unit area would take the form, considered.


= - A / 12πd2 + (64a2c0RT / κ) exp(-κd) + α / 2π exp(-d / δ)

The critical coagulation concentration considered. ccc for a colloid suspended in an

aqueous electrolyte solution is determined by the ions with a charge

opposite in sign to that on the colloid and is proportional to an inverse

power of the valence of the ions.

Schulze-Hardy Rule

Suspend colloid mass in initial concentrations of electrolyte, c1, c2, …, cN.

The ccc is at one or between a pair of these concentrations.

DLVO model provides a basis for Schulze-Hardy Rule. The ccc is

taken as c0 at which Φ(d) = 0 and Φ(d)´ = 0. If the first is necessary, the

second is consistent and gives a way to eliminate the problem of exp(-κd),

which is a problem because κ includes c0. The result is

ccc = [(3072π / e2) x (a2RT / β3/2A)]2 / Z6

where β = κ2 / c0, which does not include c0 since κ directly depends on c01/2.

See Eq. 10.12.

Compare to Table 10.2 for the ratio ccc(Z = 2) / ccc(Z = 1) = 1/ 26.

The DLVO model has shortcomings, including neglect of the VSOL term.

More importantly, the diffuse double layer model (DLVO component) does

not consider adsorption of ions on the particle surface. Inner-sphere and

outer-sphere complexes change σP and affect properties of the double layer.

  • Adsorption Effects on Colloidal Stability ccc is

  • Si-tetrahedral surface / siloxane cavity

  • Inner-sphere complexation increases Li+ < Na+ < … < Cs+

  • Accounts for greater number of crystal units per particle along sequence

  • Accounts for lower ccc along the sequence. DLVO treats all cations of

  • the same valence as equal. This behavior is not explained by the model.

  • 2. Outer-sphere complexation with M2+

  • Further reduces σP.

  • pH-dependent charge sites

  • 1. When σP = σ0 + σH, suspension will coagulate at PZC as affected by pH,

  • regardless of concentration of ions in solution.

  • 2. When σP = σH, this happens and PZC = PZNPC.

Importance of inner-sphere or outer-sphere complex formation on σP

is apparent in effect of mass concentration, cS, on the ccc.

Increasing cS will cause ccc to increase. This is because the ccc is

methodologically defined –more mass of adsorbent in a set volume of

of an initial concentration of electrolyte results in greater adsorption, thus,

a higher initial concentration (ccc) of electrolyte is needed to cause


Surface-adsorbed polymers

May affect geometry, increasing effective size of particle, and σP. If

coagulation increased by polymer-polymer bridging, ccc is decreased.

Extent to which this occurs depends on solution composition (pH,

electrolyte type and concentration) which affects tertiary structure of

polymer and / or association with other surface-adsorbed polymers.

Conditions may be such that adsorbed polymers decrease coagulation.