3.3 DLVO theory

DLVO theory explains colloidal stability by combining attractive van der Waals forces and repulsive electrostatic double layer forces. It predicts particle interactions based on separation distance, revealing energy minima and maxima that determine aggregation behavior.

The theory assumes smooth, spherical particles in a uniform medium, but real systems often deviate. Non-DLVO forces and system complexities can limit its accuracy, leading to extended models that incorporate additional interactions for better predictions.

Origins of DLVO theory

• Developed in the 1940s by Derjaguin, Landau, Verwey, and Overbeek to explain the stability of colloidal systems
• Combines the effects of attractive van der Waals forces and repulsive electrostatic double layer forces to determine the net interaction between colloidal particles
• Provides a theoretical framework for understanding the stability and aggregation behavior of colloidal dispersions based on the balance of these forces

Assumptions in DLVO theory

• Colloidal particles are treated as smooth, spherical, and uniformly charged surfaces
• The medium is considered a continuum with a uniform dielectric constant
• Ionic species in the medium are treated as point charges and their concentration is assumed to follow the Boltzmann distribution
• Van der Waals forces are assumed to be additive and non-retarded
• The electric double layer is described by the Gouy-Chapman model, assuming a diffuse distribution of counterions

Interaction forces

Van der Waals forces

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• Attractive forces that arise from instantaneous dipole-induced dipole interactions between atoms or molecules
• Depend on the material properties of the particles (Hamaker constant) and the medium
• Decay with increasing separation distance between particles according to an inverse power law ($F_{vdW} \propto 1/r^6$)
• Contribute to the overall attractive interaction between colloidal particles

Electrostatic double layer forces

• Repulsive forces that originate from the overlap of electrical double layers surrounding charged colloidal particles
• Arise due to the accumulation of counterions near the particle surface to maintain electroneutrality
• Depend on the surface potential (or charge) of the particles and the ionic strength of the medium
• Decay exponentially with increasing separation distance according to the Debye length ($\kappa^{-1}$)
  • Debye length characterizes the thickness of the electrical double layer
  • Influenced by the ionic strength of the medium (higher ionic strength leads to a thinner double layer)

Potential energy vs separation distance

Primary minimum

• Represents a deep potential energy well at close separation distances where van der Waals attraction dominates
• Particles that fall into the primary minimum are considered irreversibly aggregated or coagulated
• Occurs when the particle surfaces come into direct contact (separation distance $\approx$ 0)

Primary maximum

• Represents an energy barrier that particles must overcome to reach the primary minimum and aggregate
• Arises from the repulsive electrostatic double layer forces that become significant at intermediate separation distances
• The height of the primary maximum determines the stability of the colloidal system against aggregation
  • Higher primary maximum implies greater stability and resistance to aggregation

Secondary minimum

• Represents a shallow potential energy well at larger separation distances where a balance between van der Waals attraction and double layer repulsion is achieved
• Particles trapped in the secondary minimum are considered reversibly aggregated or flocculated
• The depth of the secondary minimum depends on the relative strengths of the attractive and repulsive forces
  • Deeper secondary minimum implies a more stable flocculated state

Implications for colloid stability

Aggregation in primary minimum

• Occurs when the attractive van der Waals forces overcome the repulsive double layer forces, leading to irreversible coagulation
• Results in the formation of compact, dense aggregates with particles in direct contact
• Typically requires a significant reduction in the repulsive barrier (primary maximum) through changes in solution conditions (pH, ionic strength)
• Coagulated systems are difficult to redisperse due to the strong attractive interactions

Aggregation in secondary minimum

• Occurs when particles are trapped in the shallow potential energy well at larger separation distances
• Results in the formation of loosely bound, open flocs with particles separated by a thin liquid film
• Flocculated systems can be easily redispersed by applying shear or changing solution conditions
• Flocculation is often reversible and can be controlled by adjusting the balance between attractive and repulsive forces

Limitations of DLVO theory

Non-DLVO forces

• DLVO theory only considers van der Waals and electrostatic double layer forces, but other interactions can also influence colloidal stability
• Examples of non-DLVO forces include:
  • Hydration forces: Short-range repulsive forces due to the hydration of particle surfaces
  • Steric forces: Repulsive forces arising from the presence of adsorbed polymers or surfactants on particle surfaces
  • Hydrophobic interactions: Attractive forces between hydrophobic surfaces in aqueous media
• Neglecting these forces can lead to discrepancies between DLVO predictions and experimental observations

Assumptions vs real systems

• DLVO theory relies on several simplifying assumptions that may not hold true for all colloidal systems
• Real colloidal particles are often non-spherical, polydisperse, and have surface heterogeneities or roughness
• The medium may have a non-uniform dielectric constant or contain specific ion effects that are not accounted for in the theory
• The assumption of pairwise additivity of van der Waals forces may break down at short separation distances or for highly concentrated systems
• These deviations from the ideal assumptions can result in limitations in the quantitative prediction of colloidal stability using DLVO theory

Extensions of DLVO theory

• Various modifications and extensions of DLVO theory have been proposed to address its limitations and incorporate additional interactions
• Examples of extended DLVO theories include:
  • Extended DLVO (XDLVO) theory: Incorporates short-range interactions such as hydration forces and steric forces
  • Charge regulation models: Account for the variation of surface charge with changes in solution conditions (pH, ionic strength)
  • Non-linear Poisson-Boltzmann equation: Considers the finite size of ions and ion-ion correlations in the electrical double layer
  • Van der Waals force retardation: Includes the effect of electromagnetic retardation on van der Waals forces at larger separation distances
• These extensions aim to provide a more comprehensive and accurate description of colloidal interactions and stability in complex systems