Electrostatic–Elastic Softening and Ultraviolet Instability Driven by Non-DLVO Interactions in Charged Colloidal Crystals

Colloidal crystals permeated by mobile ions exhibit a coupling between electrostatic and elastic degrees of freedom that renormalizes the effective screening length and induces wave-vector-dependent elastic softening. Building on our recently proposed continuum model, we perform a rigorous Gaussian fluctuation analysis to elucidate the stability limits of the homogeneous phase. By integrating out the electrostatic fluctuations, we derive the effective elastic modulus Γ(q) as a function of wave vector q. We show that the long-wavelength modulus Γ(0) remains identically equal to a bare modulus Γ(q→∞), protected by perfect ionic screening. In contrast, the short-wavelength modulus softens as the electrostatic–elastic coupling strength ξ increases, vanishing at a critical value ξ=1. For ξ>1, the fluctuation spectrum exhibits a negative eigenvalue for all wave vectors q larger than a critical (effective screening) wave vector qc, signaling an ultraviolet instability of the uniform phase. In a real colloidal crystal, this divergence is regulated by the discrete lattice cutoff qmax∼π/a, confining the physical instability to a finite band qc<q<qmax. The macroscopic limit q→0 remains unconditionally stable for all ξ. The transition at ξ=1 thus marks the onset of short-wavelength mechanical failure, while macroscopic elastic stiffness remains intact. Our analysis clarifies the proper physical interpretation of the minimal coupling model and provides a consistent picture of how non-DLVO interactions can drive local structural collapse in charged colloidal crystals.