Conformational transitions of single polymer adsorption in poor solvent: Wetting transition due to molecular confinement induced line tension

We report a theory capable of describing conformational transitions for single polymer adsorption in a poor solvent. We show that an additional molecular confinement effect near the contact line can act exactly like line tension, playing a critical role in the behavior of an absorbed polymer chain. Using this theory, distinct conformational states: desorbed globule (DG), surface attached cap (SAC), and adsorbed lens (AL), can be vividly revealed, resembling the drying-wetting transition of a nanodroplet. But the transitions between these states can behave rather differently from those in the usual wetting transitions. The DG-SAC transition is discrete, occurring at the adsorption threshold when the globule size at the desorbed state is equal to the adsorption blob. The SAC-AL transition is smooth for finite chain lengths, but can change to discontinuous in the infinite chain limit, characterized by the different end-to-end exponent 3/8 and the unique crossover exponent 1/4. Distinctive critical exponents near this transition are also determined, indicating that it is an additional universality class of phase transitions. This work also sheds light on nanodrop spreading, wherein the important role played by line tension might simply be a manifestation of the local molecular confinement near the contact line.

Figure 1

Distinct conformational states: DG (desorbed globule), SAC (surface absorbed cap), and AL (absorbed lens), can exist for adsorption of a single polymer chain in a poor solvent, depending on the reduced temperature τ and the adsorption strength $\delta$. The DG-SAC transition (blue line) is discrete. The SAC-AL transition is continuous. However, it can become discontinuous in the thermodynamic limit ($N\to \infty$) as the crossover region (enclosed by dotted pink lines) shrinks toward the transition boundary (pink line) as the chain size $N\to \infty$.

Figure 2

Apparent contact angle $\theta$ as a function of $\tau$ and $\delta$ for various values of the chain size $N$ (a)–(f). As $N$ is increased, the DG zone shrinks (a)–(c), whereas the SAC-AL transition is getting sharper (d)–(f). Solid line away from the ${180}^{\circ }$ plateau is the SAC-AL transition point $\delta =2\tau$, with the crossover zone indicated by dashed lines. (g) plots $\theta$ vs $\delta$ at $\tau =0.05$, showing that the SAC-AC transition can become discontinuous at $\delta =2\tau =0.1$ when $N$ becomes sufficiently large.

Figure 3

$R_{\parallel }(\varepsilon =0)\propto N^{3/8}$, as confirmed by the result that all the curves with different values of $N$ cross at $\varepsilon =0$. For $\varepsilon <0$ and $\varepsilon >0, R_{\parallel }$ scales as $N^{1/3}$ and $N^{1/2}$, respectively (see the insets). $\tau =0.2$.

Figure 4

(a) Surface susceptibility $\chi$ against $\delta -2\tau (\equiv \varepsilon \delta )$ at $\tau =0.1$, showing an apparent jump for a sufficiently large $N$. Inset shows collapse of the curves on plotting $\chi$ against $\varepsilon N^{1/4}$. Distinctive critical exponents for the fraction of absorbed monomers $z, \chi$, and the heat capacity $C$ can be obtained by plotting them against $t\equiv (T_{\mathrm{w}}-T)/T_{\mathrm{w}}$ in the small-$t$ regime. In (b) and (c), $\tau =0.4$. In (d), $\delta =0.4$.