A combination of microfluidic and small-angle laser light scattering enables us to map phase diagrams of two polymers with different chain lengths in three solvents at unprecedented speed. Each precisely measured phase diagram leads to a pair of critical temperature (Tc) and volume fraction of polymer (fc), in which fc is scaled to the chain length (N) as fc ~ N-0.37 + 0.01. Accounting for a huge size difference of polymer chain and solvent molecules, an adjustable solvent-to-volume ratio (Rc) is introduced to generate a dimensionless reduced volume fraction y {= f/[f + Rc(1 - f)]}, so that each skewed phase diagram is shifted and symmetrized with a symmetry axis yc = 0.325 + 0.002. After normalization by a solvent and polymer (not chain length) dependent constant y0, all of the measured 17 phase diagrams collapsed into one master curve: |y -yc|/y0 = €0.325 + 0.007N0.152 + 0.004, where € = |T - Tc|/Tc is a reduced temperature. As N → ∞, |y -yc| ~ |f -fc|/fc near the critical point so that our results lead to |f -fc| ~ €0.325 + 0.007N-0.22 + 0.01, where scaling over the chain length is close to -2/9 as predicted by Muthukumar. Hence we have successfully placed the last jigsaw piece, i.e. the chain-length dependence, in the phase diagrams of polymer solutions.

Universal scaling of phase diagrams of polymer solutions

2019 Fall National Meeting

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