Long-range correlations, geometrical structure, and transport properties of macromolecular solutions. The equivalence of configurational statistics and geometrodynamics of large molecules.
A special theory of Brownian relativity was previously proposed to describe the universal picture arising in ideal polymer solutions. In brief, it redefines a Gaussian macromolecule in a 4-dimensional diffusive spacetime, establishing a (weak) Lorentz-Poincaré invariance between liquid and polymer Einstein's laws for Brownian movement. Here, aimed at inquiring into the effect of correlations, we deepen the extension of the special theory to a general formulation. The previous statistical equivalence, for dynamic trajectories of liquid molecules and static configurations of macromolecules, and rather obvious in uncorrelated systems, is enlarged by a more general principle of equivalence, for configurational statistics and geometrodynamics. Accordingly, the three geodesic motion, continuity, and field equations could be rewritten, and a number of scaling behaviors were recovered in a spacetime endowed with general static isotropic metric (i.e., for equilibrium polymer solutions). We also dealt with universality in the volume fraction and, unexpectedly, found that a hyperscaling relation of the form, (average size) x (diffusivity) x (viscosity)1/2 ~f(N0, phi0) is fulfilled in several regimes, both in the chain monomer number (N) and polymer volume fraction (phi). Entangled macromolecular dynamics was treated as a geodesic light deflection, entaglements acting in close analogy to the field generated by a spherically symmetric mass source, where length fluctuations of the chain primitive path behave as azimuth fluctuations of its shape. Finally, the general transformation rule for translational and diffusive frames gives a coordinate gauge invariance, suggesting a widened Lorentz-Poincaré symmetry for Brownian statistics. We expect this approach to find effective applications to solutions of arbitrarily large molecules displaying a variety of structures, where the effect of geometry is more explicit and significant in itself (e.g., surfactants, lipids, proteins).
Mezzasalma
Stefano A
SA
Department of Biophysics, Biochemistry and Macromolecular Chemistry, Trieste University, Via Giorgieri 1, 34127, Trieste, Italy.
D046911:Macromolecular Substances / Q000737:chemistry*; D044367:Phase Transition; D011108:Polymers / Q000737:chemistry*; D012996:Solutions / Q000737:chemistry; D013499:Surface Properties; D013816:Thermodynamics
D046911:Macromolecular Substances; D011108:Polymers; D012996:Solutions