Substrate concentration dependence of the diffusion-controlled steady-state rate constant.

Area of Science:

• Physical Chemistry
• Chemical Kinetics
• Statistical Mechanics

Background:

• The Smoluchowski approach models diffusion-controlled reactions but typically assumes non-interacting particles.
• Interactions like osmotic pressure and hydrodynamic forces significantly affect reaction rates in real systems.
• Accurate modeling of these interactions is crucial for understanding complex chemical processes.

Purpose of the Study:

• To generalize the Smoluchowski equation for diffusion-controlled reactions to include interacting substrate particles.
• To develop an analytical expression for the diffusion-limited steady-state rate constant considering nonideal particle behavior.
• To provide a new experimental method for determining the second virial coefficient (B2*) of interacting macromolecules.

Main Methods:

• Incorporated osmotic pressure and hydrodynamic interactions into the Smoluchowski equation using a local-density approximation.
• Solved the linearized, time-independent equation with absorbing boundary conditions.
• Performed comparisons with Brownian dynamics simulations for hard sphere and Yukawa interactions.

Main Results:

• Derived an analytical expression for the diffusion-limited steady-state rate constant at low substrate concentrations.
• The expression is in terms of an effective second virial coefficient (B2*).
• Excellent agreement was found between the analytical model and simulations for densities up to B2*rho0 ≈ 0.4.

Conclusions:

• The generalized Smoluchowski approach accurately accounts for particle interactions in diffusion-controlled reactions.
• The study validates the effective second virial coefficient (B2*) as a key parameter.
• This work presents a novel experimental technique to measure B2* of macromolecules via diffusion-controlled reaction rates.