TY - JOUR

T1 - Phase transitions in flexible polymeric surfaces

AU - Kantor, Yacov

AU - Nelson, David R.

PY - 1987

Y1 - 1987

N2 - The statistical mechanics of polymerized surfaces with a finite bending rigidity is studied via the Monte Carlo method. The model system consists of a hexagon, L atoms across, excised from a triangular lattice embedded in three-dimensional space. Nearest-neighbor atoms interact via an infinite-square-well potential, while the bending energy is proportional to the (negative) scalar product of unit normals to adjacent triangles. Self-avoiding interactions are not included. The largest hexagon considered (L=19) consists of 271 atoms. Unlike linear polymers or liquid membranes, these surfaces undergo a remarkable finite-temperature crumpling transition, with a diverging specific heat. For small =/kBT, the surface is crumpled, and the radius of gyration Rg grows as lnL. For large we find that the surface remains flat, i.e., RgL. Our results demonstrate the presence of a finite-temperature (second-order) crumpling transition, and provide a lower bound on a related transition in real self-avoiding membranes.

AB - The statistical mechanics of polymerized surfaces with a finite bending rigidity is studied via the Monte Carlo method. The model system consists of a hexagon, L atoms across, excised from a triangular lattice embedded in three-dimensional space. Nearest-neighbor atoms interact via an infinite-square-well potential, while the bending energy is proportional to the (negative) scalar product of unit normals to adjacent triangles. Self-avoiding interactions are not included. The largest hexagon considered (L=19) consists of 271 atoms. Unlike linear polymers or liquid membranes, these surfaces undergo a remarkable finite-temperature crumpling transition, with a diverging specific heat. For small =/kBT, the surface is crumpled, and the radius of gyration Rg grows as lnL. For large we find that the surface remains flat, i.e., RgL. Our results demonstrate the presence of a finite-temperature (second-order) crumpling transition, and provide a lower bound on a related transition in real self-avoiding membranes.

UR - http://www.scopus.com/inward/record.url?scp=5244254078&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.36.4020

DO - 10.1103/PhysRevA.36.4020

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AN - SCOPUS:5244254078

SN - 1050-2947

VL - 36

SP - 4020

EP - 4032

JO - Physical Review A

JF - Physical Review A

IS - 8

ER -