On the comparisons between dissipative particle dynamics simulations and self-consistent field calculations of diblock copolymer microphase separation

Abstract

To highlight the importance of quantitative and parameter-fitting-free comparisons among different models/methods, we revisited the comparisons made by Groot and Madden [J. Chem. Phys. 108, 8713 (1998)] and Chen et al. [J. Chem. Phys. 122, 104907 (2005)] between their dissipative particle dynamics (DPD) simulations of the DPD model and the self-consistent field (SCF) calculations of the "standard" model done by Matsen and Bates [Macromolecules 29, 1091 (1996)] for diblock copolymer (DBC) A-B melts. The small values of the invariant degree of polymerization used in the DPD simulations do not justify the use of the fluctuation theory of Fredrickson and Helfand [J. Chem. Phys. 87, 697 (1987)] by Groot and Madden, and their fitting between the DPD interaction parameters and the Flory-Huggins χ parameter in the "standard" model also has no rigorous basis. Even with their use of the fluctuation theory and the parameter-fitting, we do not find the "quantitative match" for the order-disorder transition of symmetric DBC claimed by Groot and Madden. For lamellar and cylindrical structures, we find that the system fluctuations/correlations decrease the bulk period and greatly suppress the large depletion of the total segmental density at the A-B interfaces as well as its oscillations in A- and B-domains predicted by our SCF calculations of the DPD model. At all values of the A-block volume fractions in the copolymer f (which are integer multiples of 0.1), our SCF calculations give the same sequence of phase transitions with varying χN as the "standard" model, where N denotes the number of segments on each DBC chain. All phase boundaries, however, are shifted to higher χN due to the finite interaction range in the DPD model, except at f = 0.1 (and 0.9), where χN at the transition between the disordered phase and the spheres arranged on a body-centered cubic lattice is lower due to N = 10 in the DPD model. Finally, in 11 of the total 20 cases (f-χN combinations) studied in the DPD simulations, a morphology different from the SCF prediction was obtained due to the differences between these two methods.

Fluctuation/correlation effects in symmetric diblock copolymers: On the order-disorder transition

“…43 In fact, the equivalence of our model system to that used by Groot and Madden in their DPD simulations of DBC microphase separation 39 is explicitly shown in our recent work, Ref. 40.…”

“…N = 10 and σ/a = 2/ √ 3 ≈ 1.15 were used in the DPD simulations by Groot and Madden,39,40 which are followed here. N = 20 is used (at σ/a = 2/ √ 3 and 0.3) to examine the effects of chain discretization; larger N-values make the simulations more expensive to do.…”

Self-assembly in Solutions of Amphiphilic Homopolymers: Computer Modeling and Analytical Theory

“…The Flory–Huggins parameter χ αβ of interaction in DPD is determined by the difference between repulsion parameter a αβ of different components and repulsion parameter of similar beads ( a αα or a ββ ) with prefactor χ 0 : χ αβ ≈ χ 0 ( a αβ – a αα ). ,, The prefactor χ 0 depends on density ρ, and for ρ = 3, it could be approximately set as χ 0 ≈ 0.3. The Flory–Huggins parameter χ HP of H and P beads interaction is positive and quite large: χ HP = 7.5.…”

Developing Local Order Parameters for Order–Disorder Transitions From Particles to Block Copolymers: Methodological Framework

“…From a computational perspective, disorder-to-lamellar and disorder-to-cylinder transitions have been studied using various techniques such as field-theoretic simulations, , on-lattice − and off-lattice − Monte Carlo simulations, dissipative particle dynamics, − and molecular dynamics. , While the results from these computational studies do provide an insight into the mechanism of ordering, a quantitative description of the specific kinetic pathway for disorder–order transitions is still lacking. Carilli et al attempted to fill this gap for the disorder-to-lamellar transition using the renormalized Landau–Brazovskii model and estimated the free energy barriers and critical nucleus size for the transition.…”