Chemical-Pharmaceutical Academy, Prof. Popova 14, 197022 St. Petersburg, Russia.
J Chem Phys. 2010 Feb 14;132(6):064110. doi: 10.1063/1.3308626.
We discuss a unique system that allows exact analytical investigation of first- and second-order transitions with finite-size effects: mechanical desorption of an ideal lattice polymer chain grafted with one end to a solid substrate with a pulling force applied to the other end. We exploit the analogy with a continuum model and use accurate mapping between the parameters in continuum and lattice descriptions, which leads to a fully analytical partition function as a function of chain length, temperature (or adsorption strength), and pulling force. The adsorption-desorption phase diagram, which gives the critical force as a function of temperature, is nonmonotonic and gives rise to re-entrance. We analyze the chain length dependence of several chain properties (bound fraction, chain extension, and heat capacity) for different cross sections of the phase diagram. Close to the transition a single parameter (the product of the chain length N and the deviation from the transition point) describes all thermodynamic properties. We discuss finite-size effects at the second-order transition (adsorption without force) and at the first-order transition (mechanical desorption). The first-order transition has some unusual features: The heat capacity in the transition region increases anomalously with temperature as a power law, metastable states are completely absent, and instead of a bimodal distribution there is a flat region that becomes more pronounced with increasing chain length. The reason for this anomaly is the absence of an excess surface energy for the boundary between adsorbed and stretched coexisting phases (this boundary is one segment only): The two states strongly fluctuate in the transition point. The relation between mechanical desorption and mechanical unzipping of DNA is discussed.
我们讨论了一种独特的系统，该系统允许对具有有限大小效应的一阶和二阶转变进行精确的分析研究：将理想的格状聚合物链的一端机械解吸到固体基质上，同时在另一端施加拉力。我们利用与连续体模型的类比，并在连续体和格点描述之间使用参数的精确映射，这导致了作为链长、温度（或吸附强度）和拉力的函数的完全解析配分函数。给出作为温度函数的临界力的吸附-解吸相图是非单调的，并导致重入。我们分析了不同相图截面的几个链性质（束缚分数、链延伸和热容）的链长依赖性。在接近转变的情况下，单个参数（链长 N 与转变点的偏差的乘积）描述了所有热力学性质。我们讨论了二阶转变（无拉力吸附）和一阶转变（机械解吸）中的有限大小效应。一阶转变具有一些不寻常的特征：在转变区域，热容随温度呈幂律异常增加，不存在亚稳态，并且没有双峰分布，而是存在一个随着链长增加变得更加明显的平坦区域。这种异常的原因是吸附和拉伸共存相之间的边界（此边界仅为一个片段）不存在多余的表面能：在转变点处，两种状态强烈波动。讨论了机械解吸与 DNA 机械解旋之间的关系。
