二维囊泡的热力学行为
Thermodynamic behaviour of two-dimensional vesicles revisited
摘要：
我们研究了加压自避免环聚合物在两个维度上使用蒙特卡罗模拟，缩放参数和Flory型理论，通过模型概括模型Leibler，Singh和Fisher [Phys. Rev. Lett.第59卷，1989（1987）]。我们证明了在非零标度压力$\tilde{p}$，其中$\tilde{p} = Np/4π$，与单体的数量$N \rightarrow \infty$和压力$p \rightarrow 0$，保持$\tilde{p}$恒定，在一类这样的模型的热力学相变的存在。这种转变是由键能驱动的，可以是连续的或不连续的。它可以被解释为一种形状转变，其中环状聚合物在临界压力以上呈规则的N边形，其边随着压力平滑地缩放，而在该临界压力以下保持无刻面。在一般情况下，我们认为，过渡是由一个尖锐的交叉取代。然而，在所有这些模型中，对于所有正$p$，该区域与$N^2$成比例，与早期的比例理论一致。
英文摘要：
We study pressurised self-avoiding ring polymers in two dimensions using Monte Carlo simulations, scaling arguments and Flory-type theories, through models which generalise the model of Leibler, Singh and Fisher [Phys. Rev. Lett. Vol. 59, 1989 (1987)]. We demonstrate the existence of a thermodynamic phase transition at a non-zero scaled pressure $\tilde{p}$, where $\tilde{p} = Np/4π$, with the number of monomers $N \rightarrow \infty$ and the pressure $p \rightarrow 0$, keeping $\tilde{p}$ constant, in a class of such models. This transition is driven by bond energetics and can be either continuous or discontinuous. It can be interpreted as a shape transition in which the ring polymer takes the shape, above the critical pressure, of a regular N-gon whose sides scale smoothly with pressure, while staying unfaceted below this critical pressure. In the general case, we argue that the transition is replaced by a sharp crossover. The area, however, scales with $N^2$ for all positive $p$ in all such models, consistent with earlier scaling theories.
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