Molecular Mass Dependence of Interfacial Tension in Complex Coacervation

The interfacial tension of coacervates, the liquidlike phase composed of oppositely charged polymers that coexists at equilibrium with a supernatant, forms the basis for multiple technologies. Here we present a comprehensive set of experiments and molecular dynamics simulations to probe the effect of molecular mass on interfacial tension $\gamma$, far from the critical point, and derive $\gamma ={\gamma }_{\infty }(1-h/N)$, where $N$ is the degree of polymerization, ${\gamma }_{\infty }$ is the infinite molecular mass limit, and $h$ is a constant that physically corresponds to the number of monomers of one chain within the coacervate correlation volume.

Figure 1

Interfacial tension as a function of the degree of polymerization for the experimental system of PAA and qPDMAEMA, as well as molecular dynamics of coarse-grained polymers in a theta solvent both with and without salt. In all cases, the functional form for the data is $\gamma ={\gamma }_{\infty }(1-h/N)$. For the experimental data, ${\gamma }_{\infty }=999.6\pm 3.5\mu \mathrm{N}/\mathrm{m}$, $h=56.97\pm 0.11$, and $N^{*}$ is used for the degree of polymerization (see Table 1). Uncertainty in the fit represents standard error.

Figure 2

Polymer concentration in the coacervate phase both with and without salt, as well as salt concentration in both phases as a function of the degree of polymerization for coarse-grained polymers in a theta solvent. Most error bars are smaller than the symbol size.

Figure 3

Interfacial profiles normalized to infinite molecular mass for three cases: theoretically for a theta solvent with the random phase approximation expression for electrostatics (with $Nw{\varphi }_{\infty }^2$ of 2, 5, 10, 20, 100, 1000, and infinity), simulations without and with salt for $N$ ranging from 20 to 120 in increments of 20.