Irregularity of Polymer Domain Boundaries in Two-Dimensional Polymer Solution

Polymer chains composing a polymer solution in strict two dimensions (2D) are characterized with irregular domain boundaries, whose fractal dimension (D-partial derivative) varies with the area fraction of the solution and the solvent quality. Our analysis of numerical simulations of polymer solutions finds that D-partial derivative in good solvents changes nonmonotonically from D-partial derivative = 4/3 in dilute phase to D-partial derivative = 5/ 4 in dense phase, maximizing to D-partial derivative approximate to 3/2 at a crossover area fraction phi cr approximate to 0.2, whereas for polymers in Theta solvents D-partial derivative remains constant at D-partial derivative = 4/ 3 from dilute to semidilute phase. Using polymer physics arguments, we rationalize these values, and show that the maximum irregularity of D-partial derivative approximate to 3/2 is due to "fjord"-like corrugations formed along the domain boundaries which also maximize at the same crossover area fraction. Our finding of D-partial derivative approximate to 3/ 2 is, in fact, in perfect agreement with the upper bound for the fractal dimension of the external perimeter of 2D random curves at scaling limit, which is predicted by the Schramm-Loewner evolution (SLE).