1. Colloidal Phenomena Colloidal Suspensions Soil Colloids Interparticle Forces, DLVO Model, Schulze-Hardy Rule and CCC Adsorption Effects on Colloidal Stability

2. 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 d 2 (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.

3. 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 exists. D = k B T / 6πηR where k B is the Boltzmann constant (R / N A ), T is o K, 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 = -8πRDρ 2 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 applies.

4. 2. A suspension consists of plate-like particles 1 μm x 1 μm x 8 nm with a mass density of 2.5 x 10 3 kg m -3. Calculate the half-life for Brownian coagulation at 25 o C 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, t 1/2 = 1 / Kρ 0 = 1.62 x 10 17 s m -3 / ρ 0 So calculate ρ 0 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 10 16 m -3 t 1/2 = 1.62 x 10 17 s m -3 / 5 x 10 16 m -3 = 3 s which is fast.

5. The number density, ρ 0, may be determined by intensity of light transmitted through the suspension, I = I 0 exp (-Aρm P 2 ) where m P is mass of individual particle. Or, ln (I 0 / I) = Aρm P 2

6. Soil Colloids 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.

7. 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 included. 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 Ca 2 -smectite. Quasi-crystal formation with Ca 2+ -smectite involves interlayer adsorption of Ca(H 2 O) 6 2+ 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?

8. 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 m P = m C N where m C is the mineral unit mass and N is the number of such units per quasi-crystal, ln (I 0 / I) = Aρm P m C N Thus, for the same mass density, ρm P, of suspensions of homo-ionic clays, the ratio of absorbance given by M x+ -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) Mg 2+ N = 5.5 (4.3) Ca 2+ N = 6.2 (7.0)

9. 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 = 1.005c S Absorbance = 1.453c S where c S is suspension mass density. What is the inference as to the relative mass of the colloidal particles? From Absorbance = Aρm P 2 = Ac S m P ABS 1 / ABS 2 = 1.005 / 1.453 = m P1 / m P2 or m P2 = (1.453 / 1.005) m P1

10. 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 E Na = 0.15 indicating decomposition of quasi- crystal. 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.

11. 8. Light-scattering data for Mg-Ca montmorillonite shows a linear increase in I / I Mg from 0.55 to 1.0 as E Mg increases from 0 to 1. Given that I at E Mg = 0.22 I 0 at E Mg = 0, what is the ratio of N Mg / N Ca ? Looking for ABS Mg-saturated / ABS Ca-saturated = (Ac S m C N Mg ) / (Ac S m C N Ca ) where it is assumed that mass densities, c S, and unit masses, m C, are the same. ABS Mg / ABS Ca = N Mg / N Ca I EMg=1 = (1 / 0.55) x 0.22 I 0 and I Ca=1 = 0.22 I 0 So, ABS Mg / ABS Ca = -ln (I EMg=1 / I 0 ) / -ln (I Ca=1 / I 0 ) = 0.92 / 1.51 and, N Mg = 0.61 N Ca

12. 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.

13. However, discussion focuses on the latter, referred to as van der Waals dispersion force. While attraction between 2 mutually induced dipoles varies as 1 / d 6, 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 V VDW = - A / 12πd 2 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 V ELS = (64a 2 c 0 RT / κ) exp(-κd) where a = tanh(FΦ(0)/4RT), c 0 is bulk concentation and κ = as defined (Chapter 8)

14. 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.

15. 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.

16. 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 V SOL = α / 2π exp(-d / δ)

17. So, energy per unit area would take the form, Φ(d) = V VDW + V ELS + V SOL = - A / 12πd 2 + (64a 2 c 0 RT / κ) exp(-κd) + α / 2π exp(-d / δ)

18. 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. Schulze-Hardy Rule Suspend colloid mass in initial concentrations of electrolyte, c 1, c 2, …, c N. The ccc is at one or between a pair of these concentrations.

19. DLVO model provides a basis for Schulze-Hardy Rule. The ccc is taken as c 0 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 c 0. The result is ccc = [(3072π / e 2 ) x (a 2 RT / β 3/2 A)] 2 / Z 6 where β = κ 2 / c 0, which does not include c 0 since κ directly depends on c 0 1/2. See Eq. 10.12. Compare to Table 10.2 for the ratio ccc(Z = 2) / ccc(Z = 1) = 1/ 2 6. The DLVO model has shortcomings, including neglect of the V SOL 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 σ P and affect properties of the double layer.

20. 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 of the same valence as equal. This behavior is not explained by the model. 2. Outer-sphere complexation with M 2+ Further reduces σ P. pH-dependent charge sites 1.When σ P = σ 0 + σ H, suspension will coagulate at PZC as affected by pH, regardless of concentration of ions in solution. 2. When σ P = σ H, this happens and PZC = PZNPC.

21. Importance of inner-sphere or outer-sphere complex formation on σ P is apparent in effect of mass concentration, c S, on the ccc. Increasing c S 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 coagulation. Surface-adsorbed polymers May affect geometry, increasing effective size of particle, and σ P. 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.