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,
Interparticle Forces, DLVO Model, Schulze-Hardy Rule and CCC
Adsorption Effects on Colloidal Stability
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 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, 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
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+ (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
Expressing mP = mCN
where mC is the mineral unit mass and N is the number of such units
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 = 1.0Light-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)
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
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
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
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,
Φ(d) = VVDW + VELS + VSOL
= - A / 12πd2 + (64a2c0RT / κ) exp(-κd) + α / 2π exp(-d / δ)
The critical coagulation concentration 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.
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.
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
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.