Universal scaling of the osmotic pressure for dense, quasi-two-dimensionally confined polymer melts reveals transitions between fractal dimensions

• Published in: The Journal of chemical physics Vol. 160; no. 8
• Main Authors: Hernández Velázquez, J. D., Alas, S. J., Pérez, E., Goicochea, A. Gama
• Format: Journal Article
• Language: English
• Published: United States American Institute of Physics 28.02.2024
• Subjects: Contours; Distribution functions; Fractal geometry; Melts; Monomers; Osmosis; Polymers; Scaling laws
• ISSN: 0021-9606; 1089-7690; 1089-7690
• 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.