Fig. 1: Simulations of two-component multivalent systems reveal a magic-number effect.
From: Rigidity enhances a magic-number effect in polymer phase separation
a–f Snapshots of 2D simulations of a\({{\rm{A}}}_{7}\):\({{\rm{B}}}_{8{\rm{R}}}\), b\({{\rm{A}}}_{8}\):\({{\rm{B}}}_{8{\rm{R}}}\), c\({{\rm{A}}}_{9}\):\({{\rm{B}}}_{8{\rm{R}}}\), d\({{\rm{A}}}_{7}\):\({{\rm{B}}}_{8}\), e\({{\rm{A}}}_{8}\):\({{\rm{B}}}_{8}\), and f\({{\rm{A}}}_{9}\):\({{\rm{B}}}_{8}\) systems, where \({{\rm{A}}}_{n}\)/\({{\rm{B}}}_{n}\) denotes flexible polymers of species \({\rm{A}}\)/\({\rm{B}}\) with valence \(n\), and \({{\rm{B}}}_{8{\rm{R}}}\) denotes rigid \(4\times 2\) rectangles. Parameters: specific bond energy = 10\({k}_{{\rm{B}}}T\), non-specific bond energy = 0.1\({k}_{{\rm{B}}}T\), \({\rm{A}}\):\({\rm{B}}\) monomer ratio = 1, monomer concentration = 0.3. Insets for the magic-number systems in b and e show characteristic fully-bonded dimers composed of one A and one B polymer. g–l Heat maps of average cluster size as functions of total monomer concentration and strength of specific bonds for systems in a–f. The ratio of A:B monomer concentration is equal to one, and the non-specific bond energy = 0.1\({k}_{{\rm{B}}}T\). Red dots indicate parameters of snapshots in a–f. m Average cluster size for \({{\rm{A}}}_{7}\):\({{\rm{B}}}_{8{\rm{R}}}\), \({{\rm{A}}}_{8}\):\({{\rm{B}}}_{8{\rm{R}}}\), \({{\rm{A}}}_{9}\):\({{\rm{B}}}_{8{\rm{R}}}\) systems (solid curves) with specific bond energy 10\({k}_{{\rm{B}}}T\), i.e., horizontal cuts through g–i. n Fraction of polymers in dimers for \({{\rm{A}}}_{7}\):\({{\rm{B}}}_{8{\rm{R}}}\), \({{\rm{A}}}_{8}\):\({{\rm{B}}}_{8{\rm{R}}}\), \({{\rm{A}}}_{9}\):\({{\rm{B}}}_{8{\rm{R}}}\) systems (solid curves) with specific bond energy 10\({k}_{{\rm{B}}}T\). o Average cluster size for \({{\rm{A}}}_{7}\):\({{\rm{B}}}_{8}\), \({{\rm{A}}}_{8}\):\({{\rm{B}}}_{8}\), \({{\rm{A}}}_{9}\):\({{\rm{B}}}_{8}\) systems (solid curves) with specific bond energy 10\({k}_{{\rm{B}}}T\), i.e., horizontal cuts through j–l. p Fraction of polymers in dimers, i.e., one A-polymer and one B-polymer forming specific bonds only with each other, for \({{\rm{A}}}_{7}\):\({{\rm{B}}}_{8}\), \({{\rm{A}}}_{8}\):\({{\rm{B}}}_{8}\), \({{\rm{A}}}_{9}\):\({{\rm{B}}}_{8}\) systems (solid curves) with specific bond energy 10\({k}_{{\rm{B}}}T\). In m–p, dotted curves show results for a zero-interaction-energy null model.
