There IS a relationship between T1 and correlation time which in turn is dependent on MW and viscosity. However, this method will only given you a rough estimate.

The relationship between rotational correlation time and T1 is given by the Bloembergen, Purcell and Pound equation (BPP) see (http://en.citizendium.org/wiki/Nmr*spectroscopy#NMR*spectroscopy:*Observable*parameters).

The correlation time can be estimated from knowledge of MW and viscosity as follows:

assuming a spherical shape the radius of hydration rh = ((MW)^0.44)/1.5

Use this radius to calculate volume of hydration Vh.

According to the stokes-einstein relation the rotational diffusion coefficient Dr = kT/(6Vh*viscosity)

Since rotational correlation time = 1/(6Dr)

rotational correlation time = Vh*viscosity/(kT)

k=Boltzmann constant and T=Temperature

References:

Cantor and Schimmel : Biophysical Chemistry

M.Goldman : Quantum description of high-resolution NMR in liquids.