How it Works
DLVO theory calculates the total interaction energy between two spherical colloidal particles as a function of surface-to-surface separation h. The two contributions are: (1) electrostatic double-layer repulsion V_EDL which decays exponentially with the Debye length κ⁻¹, and (2) van der Waals attraction V_vdW which decays as 1/h at close range.
A colloid is stable when the energy barrier (maximum of V_T) is much greater than thermal energy kT ≈ 4.1 × 10⁻²¹ J at room temperature. Increasing salt concentration compresses the double layer (shorter Debye length), reducing the barrier until coagulation occurs.
V_vdW = −A·a / (12h) [sphere-sphere, Derjaguin approx]
κ⁻¹ = √(ε₀εrkT / 2NAe²I) [Debye length]
V_T = V_EDL + V_vdW
Frequently Asked Questions
What is DLVO theory?
DLVO theory (Derjaguin-Landau-Verwey-Overbeek) describes the forces between charged particles in solution. The total interaction energy V_T = V_EDL + V_vdW is the sum of electrostatic double-layer repulsion and van der Waals attraction.
What is the electrical double layer?
The electrical double layer consists of a charged particle surface and a diffuse cloud of counterions in solution. It produces a repulsive force between particles. The characteristic decay length is the Debye length κ⁻¹, which decreases with increasing salt concentration.
What is the Debye length?
The Debye length κ⁻¹ = √(ε₀εrkT / 2e²NAI) is the characteristic screening length of the electrostatic interaction. At high salt concentration (high ionic strength I), the Debye length shrinks, reducing repulsion and promoting aggregation.
What is the Hamaker constant?
The Hamaker constant A characterizes the strength of van der Waals attraction between particles across a medium. For silica across water A ≈ 0.83×10⁻²⁰ J; for gold A ≈ 40×10⁻²⁰ J. Higher A means stronger attraction and less stable colloid.
What is zeta potential and why does it matter?
Zeta potential is the electric potential at the slipping plane of a particle moving in solution. Colloids with |ζ| > 30 mV are typically stable. As |ζ| decreases (e.g., by adding salt), aggregation becomes likely.
What is the critical coagulation concentration?
The critical coagulation concentration (CCC) is the salt concentration at which the energy barrier disappears and rapid coagulation occurs. The Schulze-Hardy rule states CCC ∝ 1/z⁶, where z is the valence of the counterion.
What is the primary minimum in DLVO energy?
The primary minimum is the deep attractive well at very close approach (less than 1 nm) where van der Waals attraction dominates. Particles that overcome the energy barrier and reach the primary minimum form irreversible aggregates.
What is the secondary minimum?
The secondary minimum is a shallow attractive well at larger separations (several nm) that can trap particles in reversible, loose aggregates called flocs. Unlike primary minimum aggregation, flocculation in the secondary minimum is reversible by gentle agitation.
Beyond DLVO: what else affects colloidal stability?
Beyond DLVO forces, steric stabilization (polymer brushes), depletion forces (non-adsorbing polymers), hydration forces (water structuring near hydrophilic surfaces), and hydrophobic attraction all affect colloidal stability.
How is colloidal stability measured experimentally?
Dynamic light scattering (DLS) tracks particle size over time to detect aggregation. Electrophoresis measures zeta potential. Turbidity measurements monitor sedimentation. Critical coagulation concentration is found by titrating salt and measuring aggregation onset.