Collapse Transition in Random Copolymer Solutions

Abstract

We present dynamic Monte Carlo lattice simulations of the coil to globule collapse of single chains of a copolymer comprising monomer units, m and c, wherein there is a net attractive interaction between c-units. As the copolymer is cooled, the solvent quality becomes poorer, and the size of the chain decreases, driven by the net m-m and c-c attractions. The strong c-c attraction increases the overall solvophobicity of the chain relative to a homopolymer and, therefore, copolymers collapse more abruptly and at a higher effective temperature relative to homopolymers. We compare copolymers with homopolymers by rescaling collapse data to the same θ values to account for the effect of overall solvophobicity. This comparison shows that the behavior of copolymers and the corresponding homopolymers is identical as the chain size reduces from high temperatures to the θ value. Beyond θ, copolymers with c-content < ∼50% collapse more abruptly than either homopolymer, after accounting for the difference in overall solvophobicity. Collapse of copolymers containing higher c-content is dominated entirely by the c-c attractions, and these chains behave qualitatively like homopolymers with a higher effective solvophobicity. Analysis of the chain structure during collapse provides a structural reason for the qualitative change in copolymer collapse at low c-content. When such copolymers are cooled below θ, the c-units rapidly aggregate to form an isotropic, compact core surrounded by an anisotropic solvated shell of m-units. The shell densifies as the copolymer is further cooled, but remains anisotropic for the finite chain sizes investigated.

Pathway to copolymer collapse in dilute solution: Uniform versus random distribution of comonomers

“…The radius of gyration of the chain and the c-c pair correlation function, g͑r͒, are calculated as described in our earlier work. 25 In this work, we examine copolymer chains of size N = 128 containing 12.5% c-units with =20 ͑we also state our findings for = 10, 50; N = 512; and 25% c-units͒. We have previously shown 25 that a random copolymer with this composition exhibits copolymerness, viz., in such chains, a microphase-separated c-unit-core m-unit-shell intermediate forms as the chain collapses abruptly between the state ͑B 0 Ϸ 0.02, the B range where ͗R g 2 ͘ϳN͒ and collapse ͑B Ͼ 0.1͒.…”

“…25 In this work, we examine copolymer chains of size N = 128 containing 12.5% c-units with =20 ͑we also state our findings for = 10, 50; N = 512; and 25% c-units͒. We have previously shown 25 that a random copolymer with this composition exhibits copolymerness, viz., in such chains, a microphase-separated c-unit-core m-unit-shell intermediate forms as the chain collapses abruptly between the state ͑B 0 Ϸ 0.02, the B range where ͗R g 2 ͘ϳN͒ and collapse ͑B Ͼ 0.1͒. As mentioned above, copolymer chains containing a large fraction of sticky c-units ͑greater than 50%͒ do not show copolymerness and collapse by crumpling locally rather than via a core-shell intermediate.…”

“…The simulation scheme and the microrelaxation moves used in our MC algorithm are as described previously, 4,25 where we ensure that there is no bond crossing, and that the excluded volume criterion is satisfied. The energy for a chain depends on the number of contacts between dissimilar units and the change in energy for a single MC move is ⌬E = 1 2 ͚ ␣ ␤ ⌬N ␣␤ B ␣␤ , where ␣ , ␤ ͕m , c , s͖, and ⌬N ␣␤ represents the net change in nearest neighbor contacts between ␣ and ␤.…”

“…We have recently reported 25 dynamic Monte Carlo simulations of the collapse of flexible, nearly random copolymers and have demonstrated that in these copolymers, collapse happens via aggregation of c-units, and that the fraction of c-units dictates collapse behavior. Collapse of chains containing a high c-unit fraction ͑greater than about 50%͒ is qualitatively identical to a homopolymer with a higher effective solvophobicity.…”

Polymer crystallization in the presence of “sticky” additives

“…We employ a microrelaxation algorithm, viz., a combination of single site bond fluctuation and slithering diffusion to move the chain units along the lattice sites with periodic boundary conditions. 27,30 Specifically, our algorithm randomly ͓random number generator, MT19937 ͑Ref. 31͔͒ selects a vacant site and attempts to move a monomer or additive from one of the nearest neighboring sites to this vacant site.…”