Theoretical study on the polymer translocation into an attractive sphere.

Area of Science:

• Polymer physics
• Statistical mechanics
• Soft matter physics

Background:

• Polymer translocation is crucial in biological processes and nanotechnology.
• Understanding polymer behavior in confined environments is essential for designing nanoscale devices.
• Previous models often simplify the complex interactions during translocation.

Purpose of the Study:

• To develop a non-sampling model for calculating polymer translocation free energy into an attractive sphere.
• To investigate the interplay between confinement and polymer-sphere attraction on translocation dynamics.
• To analyze the scaling relationship of critical sphere radius with polymer length.

Main Methods:

• Combining the blob method with lattice-based approximation for free energy calculation.
• Utilizing the Fokker-Planck equation to determine translocation time from the free energy profile.
• Analyzing the distinct uncrowded and crowded stages of translocation.

Main Results:

• A competition exists between sphere confinement (increasing time) and polymer-sphere attraction (decreasing time).
• These opposing effects balance at a specific polymer-sphere attraction strength, dependent on sphere size, polymer length, and driving force.
• A critical sphere radius (R*) exhibits a scaling relation with polymer length (N) as R* ~ N^β.

Conclusions:

• The developed model effectively simulates the translocation of 3D self-avoiding polymers into spherical confinement.
• The findings provide insights into the factors governing polymer dynamics in confined geometries.
• The study establishes a framework for predicting translocation behavior under competing forces.