Development of an analytical model for the states of the sandwiched GO–induced pore
This protocol is extracted from research article:
Transport of a graphene nanosheet sandwiched inside cell membranes
Sci Adv, Jun 7, 2019; DOI: 10.1126/sciadv.aaw3192

The detailed deduction can be found in section S2. Briefly, the energy cost of pore formation, ER, is determined from the governing equationER=2πγRKaπa2AmR2+Kaπ2AmR4(1)which originates from the balance of energies of both membrane tension and line tension of the pore. Here, R and γ are the radius and the linear tension of the pore, respectively. Am denotes the membrane area. a is the edge length of the GO. By minimizing Eq. 1, a local energy maximum at smaller R and a local energy minimum at larger R can be identified, and the transition point occurs at Ka0=γAma3272π. When Ka > Ka0, a straightforward calculation of the minimum leads to the relation between the pore area and KaπR2a2=23cos2θ3(2)where θ=arccos (γAmKaa3272π).

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