(Color online) Inverse of Flory parameter (proportional to temperature at fixed nonbonded attraction energy) and volume fraction at the critical point as functions of association constant , with and without ring formation, from theory.
(Color online) Coexistence curves from theory showing phase separation of equilibrium polymer systems (chain only: solid black curves; : dotted red curves) as a function of inverse Flory parameter for labeled association constants . The lines of critical points are also shown; for chain-only system, the line terminates at , , while for ring-containing system, the line terminates at , .
(Color online) Grand canonical Monte Carlo (GCMC) simulation results (symbols) and fits to data for chain-only simulations. Circles: ; squares, ; diamonds, . Solid curve (violet): ; dash curve (blue): ; dot-dash curve (black): ; dot-dot-dash curve (green): ; dotted curve (red): . Fit parameters are given in Table I. The gray horizontal lines indicate coexistence boundaries calculated from fits.
(Color online) Mean number of square-well interactions per monomer at (open symbols) and (filled symbols). Circles (black): ; squares (blue), ; diamonds (green), . X’s are ring-containing simulations at .
(Color online) Coexistence curves derived from simulation data. The symbols represent phase boundaries at different as in Fig. 3. The open circles/dotted curve represents system with .
(Color online) Mean square radius of gyration vs chain contour length under dilute conditions . The black curve, to guide the eye, is .
(Color online) Length distribution of chains under dilute conditions. Symbols are as in Fig. 6; the dashed black line gives ideal exponential distribution.
(Color online) Chain growth vs concentration from MC simulations. The dashed curves are from Eq. (10). Open circles: ; filled circles, ; squares, ; diamonds, ; upright triangles, ; left-facing triangles, .
(Color online) Fraction of monomers in rings and mean ring size in containing system at . The symbols indicate square-well depth as in Fig. 8. The curves are from equilibrium distributions based on free energy of Eq. (8).
Ratio of ring to chain concentration vs aggregate size (a) and mean square radius of gyration (b) of rings with no attractions (open circles) and (filled diamonds) at . The straight lines in (a) indicate power law scaling for reference: (solid) and (dashed). The curves in (b) show mean square radius of gyration of chains, scaled by 0.55.
Mean chain-only and all-aggregate contour lengths in containing system at . The symbols indicate square-well depth as in Fig. 8. The solid curves are from equilibrium distributions based on free energy of Eq. (8), while the dashed curve is growth law for ideal chain-only system from Eq. (10), shown for comparison.
(Color online) Comparison of isotherms in systems with only chains (filled circles, solid curves) and (open circles, dashed/dotted curves), at . The horizontal lines indicate phase coexistence boundaries calculated from fits with parameters given in Table I.
Parameters for nonideal contribution to vs fit: . For interpolation purposes, the formulas and were used.
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