1. On the analytical solutions for the Poisson-Boltzmann problem
in 1D case

2. Old good theory
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3. Onsager-Manning-Oosawa results
Self-consistent solution for PBE for the linear charge density of the polyelectrolyte: l=e/b
assume two (or) one salt(s) : n1 and n2
Main scales: Bjerrum length
Debye length
temperature: b=1/(kT)
Unitless

4. Onsager-Manning-Oosawa results
Self-consistent solution for PBE for the linear charge density
The solution of non-linear equation
Near-zone solution maintains the free polyelectrolyte surface charge density boundary condition for the electric field
Far-zone solutions follow Debye-Hueckel model (linearized PBE)
Depending on the linear charge parameter (parts of the critical linear charge, Manning charge) the solutions are drastically different

5. Onsager-Manning-Oosawa results
Self-consistent solution for PBE for the linear charge density
Connection problem
Near-zone and Far-zone solutions

6. Onsager-Manning-Oosawa results
Self-consistent solution for PBE for the linear charge density
Connection problem
Near-zone and Far-zone solutions

7. Onsager-Manning-Oosawa results
Self-consistent solution for PBE for the linear charge density
Connection problem
Near-zone and Far-zone solutions

8. Onsager-Manning-Oosawa results
Self-consistent solution for PBE for the linear charge density
Connection problem
Near-zone and Far-zone solutions

10. New stuff
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11. Tight-binding results
Self-consistent solution for the charge density of semiconductor [7,0] zigzag NT under DNA wrap perturbation

12. Tight-binding results
Self-consistent solution for the charge density of semiconductor [7,0] zigzag NT under DNA wrap perturbation

13. Tight-binding results
Self-consistent solution for the charge density of semiconductor [7,0] zigzag NT under DNA wrap perturbation