Identification of a polymer growth process with an equilibrium multicritical collapse phase transition: The meeting point of swollen, collapsed, and crystalline polymers
Identification of a polymer growth process with an equilibrium multicritical collapse phase transition: The meeting point of swollen, collapsed, and crystalline polymers
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DOI：
10.1103/physreve.82.031103
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发表时间：
2010-09-01
影响因子：
2.4
通讯作者：
Prellberg, Thomas
中科院分区：
文献类型：
--
作者：
Doukas, Jason;Owczarek, Aleksander L.;Prellberg, Thomas
我们研究了聚合物在三角形晶格上的生长过程，其中产生的构型是自避免的轨迹。我们表明，这个过程的标度行为是类似的正方形晶格上的类似过程。然而，虽然正方形晶格过程映射到该晶格上的正则相互作用自避免轨迹（ISAT）模型的崩溃转变，但三角形晶格模型上的过程并不映射到正则平衡模型。另一方面，我们表明，崩溃过渡的规范ISAT模型上的三角晶格的行为方式让人想起的θ点的相互作用的自我回避行走（ISAW）模型，这是标准的聚合物崩溃模型。这意味着一个不寻常的晶格依赖性的ISAT崩溃过渡在两个维度。通过研究一个扩展的ISAT模型，我们证明了增长过程映射到一个更大的参数空间中的多临界点。在这个扩展的参数空间中，坍缩相变可以是θ点式（二阶）或一阶，这两个是由一个多临界点分开。增长过程映射的正是这一多临界点。此外，我们提供的证据表明，除了高温气体膨胀的聚合物相（线圈）和低温液滴样塌陷相（小球），也有一个最大密度的晶体状相（晶体）在低温下依赖于参数值。多临界点是这三个阶段的交汇点。我们的假设相图解决了看似不同的行为的ISAW和ISAT模型在两个维度，以及行为的轨迹生长过程中的奥秘。
We have investigated a polymer growth process on the triangular lattice where the configurations produced are self-avoiding trails. We show that the scaling behavior of this process is similar to the analogous process on the square lattice. However, while the square lattice process maps to the collapse transition of the canonical interacting self-avoiding trail (ISAT) model on that lattice, the process on the triangular lattice model does not map to the canonical equilibrium model. On the other hand, we show that the collapse transition of the canonical ISAT model on the triangular lattice behaves in a way reminiscent of the theta point of the interacting self-avoiding walk (ISAW) model, which is the standard model of polymer collapse. This implies an unusual lattice dependency of the ISAT collapse transition in two dimensions. By studying an extended ISAT model, we demonstrate that the growth process maps to a multicritical point in a larger parameter space. In this extended parameter space the collapse phase transition may be either theta-point-like (second order) or first order, and these two are separated by a multicritical point. It is this multicritical point to which the growth process maps. Furthermore, we provide evidence that in addition to the high-temperature gaslike swollen polymer phase (coil) and the low-temperature liquid-drop-like collapse phase (globule) there is also a maximally dense crystal-like phase (crystal) at low temperatures dependent on the parameter values. The multicritical point is the meeting point of these three phases. Our hypothesized phase diagram resolves the mystery of the seemingly differing behaviors of the ISAW and ISAT models in two dimensions as well as the behavior of the trail growth process.