Figure 1

(a) Schematic depiction of a chain conformation in the solvent lattice. Solvent cells occupy a two-dimensional square lattice while the chain of monomers (the self-avoiding random walk) is comprised of a sequence of nodes placed at interstitial sites in the square lattice (black circles). Hydrophobicity is modeled by the requirement that sites adjacent to each monomer be in the vapor $\left(S=+1\right)$ state, shown in white in the figure. Cells occupied by liquid $\left(S=-1\right)$ are colored gray. The parameters are $J=1$, $H=0$, and $ϵ=-1$. (b) Example of a collapsed configuration at a temperature $T<{\theta }_s$, the collapse temperature in the presence of the solvent. (c) Configuration at the collapse temperature $T={\theta }_s\simeq 2$ and (d) an extended coil configuration at $T⪢{\theta }_s$.Reuse & Permissions

Figure 2

Dimensionless potential of mean force $\beta W\left(r\right)$ acting on two solute particles a distance $r$ apart in units of the lattice spacing $a$, with $J=1$ and $H=0$, and a range of temperatures both below and above the collapse transition. Insets show the magnetization $m$ and the specific heat of the solvent $C_s$ obtained from numerical simulation for the same values of the parameters. The order-disorder transition of the solvent is $T_c^{\left(s\right)}\simeq 2.269$. Given the definition of $W\left(r\right)$ and the stepwise attractive force between two solutes [Eq. (2)], the surface tension between a solute-rich region and a pure solvent region is of the order of $ϵe^{-\beta W\left(a\right)}$. The graph above shows that the surface tension decreases with increasing temperature, as expected.Reuse & Permissions

Figure 3

(a) Radius of gyration ${⟨R_g^2⟩}^{1/2}$ and (b) its derivative $⟨R_g^{\prime }⟩$ as a function of temperature for a SARW of length $L=20$. Shown are our results for no solvent and for three magnetic field amplitudes $H=\left\{0,-0.01,-0.1\right\}$, with $J=1$ and $ϵ=-1$. Other statistical measures of chain conformation (end to end distance, its derivative, and fluctuations in chain energy) show similar qualitative features and are not shown. The chain is in a globular collapsed state at low temperature and in an extended coil state at high temperature.Reuse & Permissions

Figure 4

Circularly averaged radial distribution function of the solvent $g\left(r-r_{\text{cm}}\right)$ for a chain length $L=20$ with $ϵ=-1$ and $J=1$, (a) $H=-0.01$, and (b) $H=-0.1$. The characteristic size of the vapor domain $R_c$ is determined by the zero crossing of the correlation function. As shown in Fig. 3, the chain in a field $H=-0.01$ exhibits a sharp collapse, but the chain at $H=-0.1$ does not. Inset show the effective vapor radius $R_c$ as a function of the radius of gyration ${⟨R_g^2⟩}^{1/2}$. The radius $R_c$ scales linearly with ${⟨R_g^2⟩}^{1/2}$, indicating, in this model, the correlation between the growth of the vapor domain and the motion of the SARW that both creates the vapor domain and is effectively constrained to remain within it.Reuse & Permissions