Charge Melting of Liposome Colloidal Crystals

Abstract

Recently we measured the charge dependence of electrostatic interparticle repulsions in liposome colloidal crystals (Cohen, Wei & Ou-Yang, ms. in preparation). The liposomes were made from binary mixtures of charged and neutral phospholipids at various ratios. The shear modulus (rigidity) of each liposome suspension in deionized water was measured by laser-tweezer methods. As a function of increasing liposome charge, suspension rigidity first increased, peaked at ∼20% charged-lipid content, then decreased, becoming watery near 100% charged lipids. By analogy to colloidal-crystal “shear melting,” we call this phenomenon “charge melting.” The effect was calculated quantitatively by use of the Wigner-Seitz (WS) model, which requires solving the electrostatics problem of a radially symmetric charged sphere and its counterions in an electroneutral spherical WS shell whose radius R is determined by the liposome concentration. Electroneutrality means the entire H+ screening cloud surrounding each liposome is compressed into its WS cell. The compression creates an osmotic pressure related to the electrostatic potential ψ(R) at the WS-cell surface. The osmotic pressure is a measure of the interparticle interaction strength, which is what stiffens the sample. “Melting” as a function of particle charge Z arises because electroneutrality requires (a) as Z increases, so does the number of counterions, which increases osmotic pressure and ψ(R). This effect is linear in Z. (b) More counterions also cause more screening of Z, which decreases ψ(R) and osmotic pressure. This effect is exponential in Z, so it ultimately dominates. We solve the WS electrostatics problem analytically in the Debye-Hückel approximation and numerically with the full Poisson-Boltzmann equation. The problem must be solved self-consistently for a closed system with no reservoir, a counterion-only electrolyte, surface H+ binding with charge regulation, and zero electric fields at the WS-cell surface and liposome center.