Pasinetti P M, Ramirez-Pastor A J, Vogel E E
Departamento de Física, Instituto de Física Aplicada (INFAP), Universidad Nacional de San Luis - CONICET, Ejército de Los Andes 950, D5700HHW San Luis, Argentina.
Departamento de Física, Universidad de La Frontera, Casilla 54-D, Temuco 481180, Chile.
Phys Rev E. 2023 Jun;107(6-1):064126. doi: 10.1103/PhysRevE.107.064126.
Combining Monte Carlo simulations and thermodynamic integration method, we study the configurational entropy per site of straight rigid rods of length k (k-mers) adsorbed on three-dimensional (3D) simple cubic lattices. The process is monitored by following the dependence of the lattice coverage θ on the chemical potential μ (adsorption isotherm). Then, we perform the integration of μ(θ) over θ to calculate the configurational entropy per site of the adsorbed phase s(k,θ) as a function of the coverage. Based on the behavior of the function s(k,θ), different phase diagrams are obtained according to the k values: k≤4, disordered phase; k=5,6, disordered and layered-disordered phases; and k≥7, disordered, nematic and layered-disordered phases. In the limit of θ→1 (full coverage), the configurational entropy per site is determined for values of k ranging between 2 and 8. For k≥6, MC data coincide (within the statistical uncertainty) with recent analytical predictions [D. Dhar and R. Rajesh, Phys. Rev. E 103, 042130 (2021)2470-004510.1103/PhysRevE.103.042130] for very large rods. This finding represents the first numerical validation of the expression obtained by Dhar and Rajesh for d-dimensional lattices with d>2. In addition, for k≥5, the values of s(k,θ→1) for simple cubic lattices are coincident with those values reported in [P. M. Pasinetti et al., Phys. Rev. E 104, 054136 (2021)2470-004510.1103/PhysRevE.104.054136] for two-dimensional (2D) square lattices. This is consistent with the picture that at high densities and k≥5, the layered-disordered phase is formed on the lattice. Under these conditions, the system breaks to 2D layers, and the adsorbed phase becomes essentially 2D. The 2D behavior of the fully covered lattice reinforces the conjecture that the large-k behavior of entropy per site is superuniversal, and holds on d-dimensional hypercubical lattices for all d≥2.
结合蒙特卡罗模拟和热力学积分方法，我们研究了长度为(k)（(k)聚体）的直刚性棒吸附在三维（3D）简单立方晶格上时每个位点的构型熵。通过跟踪晶格覆盖率(\theta)对化学势(\mu)的依赖性（吸附等温线）来监测该过程。然后，我们对(\mu(\theta))在(\theta)上进行积分，以计算吸附相每个位点的构型熵(s(k,\theta))作为覆盖率的函数。根据函数(s(k,\theta))的行为，根据(k)值获得不同的相图：(k\leq4)，无序相；(k = 5,6)，无序和层状无序相；(k\geq7)，无序、向列相和层状无序相。在(\theta\rightarrow1)（完全覆盖）的极限情况下，确定了(k)在(2)到(8)之间时每个位点的构型熵。对于(k\geq6)，蒙特卡罗数据（在统计不确定性范围内）与最近对非常大的棒的分析预测[D. Dhar和R. Rajesh，《物理评论E》103，042130（2021）2470 - 004510.1103/PhysRevE.103.042130]一致。这一发现代表了对Dhar和Rajesh为(d>2)的(d)维晶格获得的表达式的首次数值验证。此外，对于(k\geq5)，简单立方晶格的(s(k,\theta\rightarrow1))值与[P. M. Pasinetti等人，《物理评论E》104，054136（2021）2470 - 004510.1103/PhysRevE.104.054136]中报道的二维（2D）正方形晶格的值一致。这与在高密度且(k\geq5)时在晶格上形成层状无序相的图景一致。在这些条件下，系统分解为二维层，吸附相基本上变为二维。完全覆盖晶格的二维行为强化了这样的推测，即每个位点熵的大(k)行为是超通用的，并且对于所有(d\geq2)的(d)维超立方晶格都成立。
