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 settlingoccurs in a time frame of 1 hour +.

Typically, sand > 50 μm settles ~ 10 cm min-1 so that with settling rate proportionalto d2 (Stokes’ Law), measurable setting occurs < 1 h at upper colloidal limit.

Define coagulation as process of suspension becoming unstable and subject tosettling 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 compositionof the soil solution.

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

While the motion is random, diffusion occurs if a concentration gradient existsdue to an external force. A diffusion coefficient can be derived when steady-stateexists.

D = kBT / 6πηR

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

If coagulation occurs when two particles collide, the initial rate of coagulationis 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 sizebefore many larger coagulated particles exist, this second order reactionapplies.

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 transmittedthrough the suspension,

I = I0 exp (-AρmP2)

where mP is mass of individual particle.

Or,

ln (I0 / I) = AρmP2

Soil Colloids

Wide variability in these depending on mineral type and transformationsover time –weathering / deformation and adsorption of mineral and organicpolymers 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 sizecalled domains if relatively larger and quasi-crystals if only a few units areincluded.

Formation of quasi-crystals may occurs with Na-saturated smectite in solutionof 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)6

2+ at interlayer positions of opposing siloxane cavities.

Given non-exchangeable K+ at interlayer positions of illite, would coagulatedmasses 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 per quasi-crystal.

Expressing mP = mCN

where mC is the mineral unit mass and N is the number of such unitsper 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 formshould 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 crystalunits per quasi-crystal as composition of montmorillonite changed from Na-saturated to Ca-saturated.

~ 0.3 intensity forCa-saturated form andfairly abrupt increase atENa = 0.15 indicatingdecomposition of quasi-crystal.

Generally consistent withdispersion at ESP = 15 %.

If quasi-crystals exist, Caexists at interlayer positionsand mix of Ca and Na onexterior 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

Suspended particles are acted upon by gravity, which de-stablizes the suspension causing settling. van der Waals force also de-stablizes thesuspension 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 forceat short distances of approach between two particles.

Interaction of the three interparticle forces are described in terms of planarsurfaces approaching one another.

van der Waals force is due to dipole-dipole attraction, and may includepermanent dipoles, a dipole induced by a permanent dipole and mutuallyinduced dipoles arising from short-time interval distributions of electroniccharge that momentarily produce dipoles.

However, discussion focuses on the latter, referred to as van der Waalsdispersion force. While attraction between 2 mutually induced dipolesvaries 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)

where

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 theDerjaguin, Landau, Verwey and Overbeek (DLVO) model for colloidal stability –suspension will be unstable / coagulate if sum is small comparedwith thermal energy of colloidal particles. If particles collide with sufficientenergy to overcome electrostatic repulsion, van der Waals attraction willdominate 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 notespecially 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 shortdistances 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 anaqueous electrolyte solution is determined by the ions with a chargeopposite in sign to that on the colloid and is proportional to an inversepower 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 istaken 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) doesnot consider adsorption of ions on the particle surface. Inner-sphere andouter-sphere complexes change σP and affect properties of the double layer.

Adsorption Effects on Colloidal Stability

Si-tetrahedral surface / siloxane cavity

1.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 ofthe 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 ismethodologically 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 coagulation.

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

Conditions may be such that adsorbed polymers decrease coagulation.