Fig. 2.

Optimal conformations of tubes subject to compaction. In our simulations, we considered a discretized representation with N segments separated by a distance b = Δ/2, where Δ is the tube radius. The continuum limit is obtained when b ≪ Δ—we have verified that our results are substantially the same on reducing the value of b down to Δ/3. The conformations are obtained by using metropolis Monte Carlo simulations by annealing or by long simulations at constant temperature. The simulations are performed with standard pivot and crank-shaft move sets (25). For systems of multiple chains, the tubes are placed inside a hard-wall cubic box of side of 40Δ—we verified that the walls of the box did not influence the conformations shown. (a–e) Conformations of single solvophobic tubes (c = 0) of various lengths and for different solvent molecule radius R that maximize the buried area (Eq. 8). (a) N = 20 and R = 0.1Δ. (b) N = 20 and R = 0.2Δ. (c) N = 30 and R = 0.1Δ. (d) N = 40 and R = 0.1Δ. (e) N = 50 and R = 0.2Δ. (f–h) Optimal conformations of multiple solvophobic tubes (c = 0) of length N = 20 and for R = 0.1Δ obtained in long simulations at constant temperatures. (f) Two tubes at a low temperature. (g) Three tubes at a low temperature. (h) Four tubes at an intermediate temperature. (i–l) Conformations of mixed solvophobicity tubes (c = 5) that minimize the energy (Eq. 9). R = Δ/2 for all cases. (i) A single helix of length N = 30 and θ₁ = 15° obtained by slow annealing (one obtains the same conformation for θ₁ = 30° or 45°). (j) A stack of four helices of length N = 15 and θ₁ = 45° obtained by slow annealing. (k and l) Two views of a planar sheet arrangement of five chains of length N = 15 and θ₁ = 30° obtained in a constant temperature simulation run at T = 0.4.