Association Equilibrium for Cross-Associating Chains in a Good Solvent: Crowding and Other Nonideality Effects

Abstract

Association equilibrium has been studied by molecular dynamics (MD) for mixtures of cross-associating molecules (n-decamer+p-dimer and n-decamer+p-decamer) in a good solvent. Each monomer of n-decamers carries an associative site (n-sticker); each molecule of the second component contains two terminal associative sites (p-stickers). To model the univalent association between the n-sticker and the p-sticker, a technique based on introduction of dummy atoms has been used. We report MD data on the effects of temperature, chain flexibility, and location of the sticker within the chain on the association equilibrium. We find that the presence of nonassociating monomer units of p-chain has a substantial effect on the association equilibrium. This effect is similar to "crowding" in reactive mixtures known to be caused by the presence of inert molecules. Widely used mean field theories of associating chains (e.g., SAFT or Semenov-Rubinstein theory) do not account for the effect of crowding caused by the inert fragments of reactive chains. We introduce simple empirical corrections for crowding that describe association equilibrium in the presence of nonassociating fragment in a chain-like molecule.

Molecular Thermodynamic Modeling of Self-Assembly into Branches and Spatial Networks in Solution

“…Recent molecular dynamics (MD) simulations 7 show that the presence of the inert (nonsticky) monomers of p-chain induces substantial nonideality of the association equilibrium. These simulations have been performed for a mixture of p-decamers, carrying 2 terminal p-stickers each, with n-decamers, carrying 10 n-stickers each, in a nearly athermal solvent.…”

“…f pair free free as 0 pair fn fn as (7) where now K as 0 = ν b exp(E/k B T) and V is the system volume. Equation 7where we redefined K as is even formally exact although the free volumes that enter this equation are unknown functions of the density and composition of the system.…”

“…Apparent association constant vs the mole fraction of monomers (both inert and sticking) that build p-chains in the system n-decamer + p-decamer + nearly athermal solvent at constant fraction of solvent monomers X solv = 0.8, 0.5, and 0.2 (bottom to top curves). Symbols, molecular dynamic simulation; curves, mean-field correction for the effect of crowding, eq taking the excluded volume of stickers equal to (dashed) or 20% less than (solid) the average monomer volume. Values of the apparent constants at X p = 0 (system with no crowding), K as 0 , have been taken from the simulation data.…”

“…Number of n-chains S n ( j ) (A) and p-chains S p ( j ) (B) connected to a “central” n-chain in the cluster vs the number of coordination shell around the central n-chain for different compositions of the mixture n-decamer+p-decamer in an athermal monomeric solvent, T = 406 K. Symbols: molecular dynamic simulation; lines: calculation for the cluster of a Cayley tree topology, eqs and . Numbers indicate the ratio of the number of n-chains to the number of p-chains in the mixture X n : X p (each n-chain carries 10 n-stickers, each p-chain carries 2 terminal stickers).…”

“…Molecular thermodynamic models make it possible to estimate the free energies for a number of systems that contain branching chains, including fluids of sticky spheres, surfactant solutions of wormlike micelles, and mixtures of associative polymers. , An individual microscopic “portrait” of the system is reflected in specific models of these free energies. , In this work we discuss recent advances of molecular thermodynamic models in describing self-assembly in systems with branching chains and give several illustrative examples for these systems. We model transformation of an amphiphilic membrane into a spatial micellar network via the appearance of perforations in a bilayer.…”