Hernández Velázquez J D, Alas S J, Pérez E, Goicochea A Gama
Tecnológico Nacional de México, Tecnológico de Estudios Superiores de Ecatepec, División de Ingeniería Química y Bioquímica, 55210 Estado de México, Mexico.
Departamento de Ciencias Naturales, Universidad Autónoma Metropolitana Unidad Cuajimalpa, 05300 Ciudad de México, Mexico.
J Chem Phys. 2024 Feb 28;160(8). doi: 10.1063/5.0185634.
A scaling law for the osmotic pressure of quasi-two-dimensional polymer melts as a function of concentration is obtained, which shows fractal characteristics. Structural properties such as the chains' contour length and their inner-monomer pair distribution function display fractal scaling properties as well. These predictions are confirmed with mesoscale numerical simulations. The chains are swollen and highly entangled, yet Flory's exponent is always ν = 1/2. The melt can be considered a fluid of "blobs" whose size becomes renormalized in terms of the contour's length while the fractal dimension df increases monotonically between 5/4 and 2, as the monomer concentration is increased. The semidilute scaling of the pressure is recovered when df = 1. Our results agree with recent experiments and with numerical reports on quasi-2d melts. This work provides a new paradigm to study and interpret thermodynamic and structural data in low-dimensional polymer melts, namely as fractal macromolecular objects.
得到了准二维聚合物熔体渗透压作为浓度函数的标度律，其具有分形特征。诸如链的轮廓长度及其内单体对分布函数等结构性质也显示出分形标度性质。这些预测通过介观数值模拟得到了证实。链是膨胀且高度缠结的，但弗洛里指数始终为ν = 1/2。熔体可被视为“链段”流体，其尺寸根据轮廓长度进行重整化，而分形维数df随着单体浓度的增加在5/4和2之间单调增加。当df = 1时，压力的半稀溶液标度得以恢复。我们的结果与最近关于准二维熔体的实验和数值报告一致。这项工作为研究和解释低维聚合物熔体中的热力学和结构数据提供了一个新的范例，即作为分形大分子对象。
