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Structure, Dynamic Properties, and Phase Transitions of Tethered Membranes
Author(s) -
Popova Hristina,
Milchev Andrey
Publication year - 2009
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.2008.04067.x
Subject(s) - radius of gyration , scaling , tensor (intrinsic definition) , membrane , eigenvalues and eigenvectors , phase transition , monte carlo method , exponent , inertia , gyration , critical exponent , physics , relaxation (psychology) , statistical physics , radius , moment of inertia , chemistry , condensed matter physics , mathematics , classical mechanics , geometry , quantum mechanics , nuclear magnetic resonance , statistics , psychology , social psychology , biochemistry , linguistics , philosophy , computer security , computer science , polymer
A coarse‐grained model of a self‐avoiding tethered membrane with hexagonal coordination, embedded in three‐dimensional space, is studied by means of extensive Monte Carlo computer simulations. The simulations are performed at various temperatures for membranes with linear size 5 ≤ L ≤ 30. We find that the membrane undergoes several folding transitions from a high‐temperature flat phase to multiple‐folded structure as the temperature is steadily decreased. Using a suitable order parameter and finite size scaling analysis, these phase transitions are shown to be of first order. The equilibrium shape of the membranes is analyzed by calculating the eigenvalues λ 2 max ≥λ 2 med ≥λ 2 min of the inertia tensor. We present a systematic finite size scaling analysis of the radius of gyration and the eigenvalues of the inertia tensor at different phases of the observed folding transitions. In the high temperature flat phase, the radius of gyration R g grows with the linear size of the membrane L as R g ∝ L ν , where the exponent ν≈ 1.0. The eigenvalues of the inertia tensor scale as whereby the roughness exponent ν min ≈ 0.7. We also find that the Rouse relaxation time τ R of a self‐avoiding membrane scales as τ R ∝ L 2ν+2 , in good agreement with the theoretical predictions.