First-passage behavior of the random-barrier model

Area of Science:

• Physics
• Physical Chemistry
• Chemical Kinetics

Background:

• Diffusion processes are fundamental in many scientific fields.
• The random-barrier model describes diffusion with memory effects.
• First-passage time calculations are crucial for understanding reaction dynamics.

Purpose of the Study:

• To calculate first-passage times using the random-barrier model.
• To compare these results with those from a normal diffusion equation.
• To investigate discrepancies and their implications for reaction rates.

Main Methods:

• Utilized the transport equation for the random-barrier model.
• Calculated first-passage times for this model.
• Compared results with a normal diffusion equation employing an effective diffusion coefficient.

Main Results:

• The random-barrier model provides accurate first-passage time calculations.
• The normal diffusion equation can significantly overestimate first-passage times.
• Calculated reaction rate constants can be underestimated when using the normal diffusion equation.

Conclusions:

• The random-barrier model offers a more accurate description of diffusion-influenced processes.
• Overestimation of first-passage times by standard diffusion models can lead to underestimation of reaction rates.
• This finding may explain experimentally observed high rates in diffusion-controlled reactions.