Figure 1

(a) Schematic illustration of the examined system—the part inside the enclosing rectangle. A much larger system can be thought, where a force produces the pressure needed to confine the polymer. (b) Simulation snapshots of the model system with $N=800$ and $\beta \sigma a^2=0.4$. From a low pressure ($\beta p{a}^3=0.04$), the confined (C) conformation changes continuously to a more profound, localized state at the transition pressure, $\beta p^{*}{a}^3=0.42$. The conformation then jumps to a strongly confined (SC) state, where the polymer is almost flattened out. The length scales are labeled in units of $a$. The size of monomers and the discretization density of the membrane shape in (b) have been reduced for visualization clarity.Reuse & Permissions

Figure 2

Discretization scheme of the curve describing the membrane shape.Reuse & Permissions

Figure 3

Phase boundaries between the strongly confined state (upper right region) and the confined state (lower left region) for various values of $\beta \sigma a^2$. Symbols are the transition points determined by the Monte Carlo simulation, and lines are the estimated boundary. A first-order transition occurs when the system crosses the boundary line.Reuse & Permissions

Figure 4

Monte Carlo simulation data with $N=1600$ as a function of $\beta p{a}^3$ for $\beta \sigma a^2=0.1$ (open symbols) and $\beta \sigma a^2=6.4$ (closed symbols): (a) the energy components in the system. Increasing the surface tension, $\beta \sigma a^2$, minimizes the energy gap between the states. (b) The system volume, $\langle V\rangle /a^3$, increases after the jump from the confined state to the strongly confined state. The estimated error bars are smaller than the size of the symbols plotted in (a) and (b).Reuse & Permissions

Figure 5

Ratios of the polymer's gyration dimensions along (a) the $z$ axis and (b) in $xy$ plane, defined in Eqs. (5) and (6). All closed symbols correspond to $N=1600$ and open symbols correspond to $N=800$. (c) The system volume as a function of $N$ at $\beta \sigma a^2=0.4$ for various $\beta p{a}^3$. As the pressure rises, $V$ becomes proportional to $N$. In (a), (b), and (c), the estimated error bars are smaller than the size of the symbols plotted.Reuse & Permissions

Figure 6

(a) The aspect ratio, $\langle w/h\rangle$, and (b) the open surface area not in contact with the membrane, $\pi \langle w^2\rangle /4a^2$, measured from the Monte Carlo simulation, as functions of $\beta p{a}^3$ for $N=1600$ (filled symbols), $N=800$ (open symbols), and various $\beta \sigma a^2$ specified in (b). To compare the simulation data with the scaling prediction in the confined state, the horizontal axes in (c) and (d) are rescaled according to Eqs. (12) and (13); factors of $\beta$ and $a$ are set to 1 in these plots for simplicity. The estimated error bars are smaller than the size of the symbols plotted in all figures.Reuse & Permissions