The DLVO theory was developed by Boris Derjaguin, Lev Landau, Evert Verwey, and Odoor Overbeek in 1940 to explains the stability of colloidal dispersions by combining the attractive van der Waals forces and repulsive electric double-layer forces. It describes how colloids remain stable or aggregate (flocculate or coagulate) based on the interplay between two primary forces: attractive van der Waals forces and repulsive electrostatic forces due to the electrical double layer around particles. The theory assumes spherical, charged particles in a dilute electrolyte solution.
1. Attractive Forces (Van der Waals Attraction):
- These are long-range attractive forces arising from dipole-dipole interactions, induced dipoles, and London dispersion forces.
- The potential energy for van der Waals attraction (VA) between two spherical particles of radius a separated by a distance h (where h << a) is approximated by the Hamaker equation.
For very small separations (h much smaller than a), the simplified form is:
VA ≈ -(A a/12 h) - This attraction is always present and becomes dominant at short distances, pulling particles together.
2. Repulsive Forces (Electrostatic Double Layer Repulsion
- Colloidal particles often carry surface charges (from ionization, adsorption, etc.), surrounded by an electrical double layer (EDL) of counter-ions in the solution.
- When two particles approach, their EDLs overlap, creating a repulsive force.
- The repulsive potential energy (VR) for weakly overlapping double layers (low surface potential, ψo < 25 mV) is given by:
VR = 2 π εr εo a ψ2o exp(-κ h) - For higher potentials or different conditions, more complex expressions (e.g., involving hyperbolic functions) are used.
- The repulsion decays exponentially with distance and is influenced by electrolyte concentration: higher ionic strength compresses the EDL (increases κ), reducing repulsion.
3. Total Interaction Potential
- The net potential is the sum:
Vtotal = VA + VR - Plotting Vtotal vs. separation distance h yields a characteristic curve:
- Primary minimum: Deep attractive well at very close distances (irreversible aggregation if reached).
- Secondary minimum: Shallow attractive well at larger distances (reversible flocculation).
- Energy barrier: Repulsive maximum between the minima; if > 15-20 kT (thermal energy), the colloid is stable as particles can't surmount it via Brownian motion.
Factors Affecting Stability
- Electrolyte Concentration: Increasing salt concentration screens charges, reducing VR and lowering the energy barrier, promoting coagulation (Schulze-Hardy rule: higher-valence ions are more effective).
- pH: Affects surface charge (ζ-potential); at the isoelectric point (pH where net charge is zero), repulsion vanishes, leading to instability.
- Particle Size and Shape: Larger particles have stronger van der Waals attraction.
- Medium Properties: Dielectric constant and refractive index influence the Hamaker constant.
Limitations and Extensions
- DLVO assumes ideal conditions and neglects other forces like steric repulsion (from polymers), hydration forces, or hydrophobic interactions.
- Extensions include DLVO with steric effects (e.g., for polymer-coated particles) or accounting for non-spherical shapes.
- Experimental validation often uses techniques like atomic force microscopy (AFM) to measure interaction forces or turbidity measurements for aggregation rates.
Applications of DLVO Theory
DLVO provides the theoretical foundation for manipulating colloidal stability in many fields:
- Water and wastewater treatment: Optimizing use of coagulants to destabilize colloids for efficient removal.
- Pharmaceuticals: Stabilizing suspension-based medicines.
- Nanotechnology and materials: Designing stable nanomaterial dispersions, paints, and inks.
- Soil science and environmental remediation: Predicting transport of colloidal contaminants and nanoparticles.
- Food industry: Stabilizing emulsions and suspensions.
- Atmospheric science: Understanding aggregation and removal of aerosols.