Real polymer size from the ideal chain molecules model in a diffusive Minkowskian spacetime

The universal exponent (νrνr) of the real polymer size (i.e., the excluded volume chain) is derived from constraining the ideal coil model (νi=12) to a Minkowski-type diffusive spacetime. The square end-to-end distance was expanded in wavenumber power series, whence the leading contribution is extracted according to previously proposed Lorentz transforms acting in Brownian media. In the end, it turns out νi≃νrsin(1)νi≃νrsin(1), in good agreement with predictions of the phase transition theory for critical phenomena.

Scheme of length contraction (a) and time dilation (b) in the spacetime scaling of the ideal chain within a Brownian relativity approach.Figure optionsDownload as PowerPoint slide