Free Energy Trajectory for Escape of a Single Chain from a Diblock Copolymer Micelle

Seeger, Sarah C.; Dorfman, Kevin D.; Lodge, Timothy P.

doi:10.1021/acsmacrolett.1c00508

Cited by 5 publications

(29 citation statements)

References 45 publications

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“…Solving for f gives f ∼ r − r normalc N core b false( normalΔ a false) 1 / 2 To determine the value of the free energy at some value of r , we substitute eq into eq , which gives a free energy that is linear in r – r c and independent of N core , F k normalB T ≅ r − r normalc b false( normalΔ a false) 1 / 2 The free energy will keep increasing until it is more favorable to extract the entire core block into the solvent rather than stretch further. Assuming that the core block is wetted by the solvent, the maximum in the free energy is F barrier k normalB T ≅ N core normalΔ a and the free energy barrier is linear with both N core and Δ a , as seen in previous work . The corresponding location r * of the chain junction at the maximum in the free energy is obtained by equating eqs and : ( r * − r c ) ∼ N core b false( normalΔ a false) 1 / 2 The key prediction of this model is already e...…”

Section: Modelmentioning

confidence: 89%

“…To create the micelles, 81000 beads including 35 chains of A x B 8 and one chain of A y B 8 ( x and y = 4, 6, 8, 12) were initialized randomly in a cubic box with side 30; periodic boundary conditions were applied. , To initialize the simulation, a harmonic biasing potential was applied to the core blocks to prepare a single micelle of aggregation number Q = 36, as was used in previous work for an A 4 B 8 system . The biasing potential is removed, and the micelle is allowed to relax for t ≈ 10 5 steps prior to the production run.…”

Section: Simulation Methodologymentioning

confidence: 99%

“…41,42 To initialize the simulation, a harmonic biasing potential was applied to the core blocks to prepare a single micelle of aggregation number Q = 36, as was used in previous work for an A 4 B 8 system. 38 The biasing potential is removed, and the micelle is allowed to relax for t ≈ 10 5 steps prior to the production run. Importantly, the choice Δa = 25 effectively halts chain exchange in this system, such that the micelle is stable and no chains leave this micelle prior to the umbrella sampling procedure.…”

Section: ■ Simulation Methodologymentioning

confidence: 99%

“…In Figure c, the position of the transition state was recorded for a range of values of DPD excess interaction energy Δ a from previous work . Contrary to the model, which predicts the position of the transition state to vary linearly with (Δ a ) 1/2 , the dependence on Δ a appears to be weakly nonmonotonic in the range of values tested.…”

Section: Modelmentioning

confidence: 99%

“…Recently, 38 we have shown that the full free energy profile of chain expulsion can be computed by combining dissipative particle dynamics simulations (DPD) 39−47 with an umbrella sampling technique. 48 A similar approach has been applied to surfactant systems to access the free energy barrier for expulsion.…”

Section: ■ Introductionmentioning

confidence: 99%

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Mechanism of Escape of a Single Chain from a Diblock Copolymer Micelle

2022

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We investigate the dependence of the free energy trajectory for chain expulsion from a diblock copolymer micelle in a selective solvent on core chain length through dissipative particle dynamics simulations and umbrella sampling. The free energy barrier scales linearly with the core block length of the expelled tracer chain for N core = 4−12, consistent with experiments. The simulations further reveal that the core chain undergoes a "hyperstretching" mechanism near the transition state, where the core block partially stretches through the corona to allow monomers further from the chain junction to remain shielded in the micelle core. As the junction extends past the transition state, it becomes more favorable for the chain to be fully expelled, and the monomer furthest from the junction exits the micelle core, allowing the core block to escape from the micelle and collapse upon entering the solvent. We propose a simple model to describe this process of chain expulsion, which provides an effective description of the simulation results.

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Section: Modelmentioning

confidence: 89%

Section: Simulation Methodologymentioning

confidence: 99%

Section: ■ Simulation Methodologymentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

Section: ■ Introductionmentioning

confidence: 99%

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Mechanism of Escape of a Single Chain from a Diblock Copolymer Micelle

2022

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Effect of Changing Interfacial Tension on Fragmentation Kinetics of Block Copolymer Micelles

Gupta

Lodge

2023

Macromolecules

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Micelle fragmentation, one of the key mechanisms responsible for equilibration of kinetically trapped micelles, is investigated for block copolymer micelles in ionic liquids (ILs). In particular, the role of driving force for micelle fragmentation is studied by altering the solvent quality after micelle preparation, amounting to a jump in interfacial tension γ between solvent and the micelle core. Direct dissolution of a 1,2-polybutadiene-b-poly(ethylene oxide) (PB-b-PEO) copolymer (M n = 17.5 kDa and f PEO = 0.38) in the ionic liquid [C2mim][TFSI] results in large micelles with average size ⟨R h⟩o ≈ 68 nm and dispersity Đ ≈ 1.27. The solution of the as-prepared micelles is then diluted by the careful addition of a second ionic liquid [C10mim][TFSI] having lower γ with the micelle core, such that the micelles remain unaffected. The γ and hence the quality of the solvent mixture were controlled by the degree of dilution. The choice of the second solvent is based on the measurement of γ for a series of [Cxmim][TFSI] ILs with 1-2-polybutadiene homopolymer, carried out using a pendant drop test. Diluting the micelles by adding another ionic liquid with lower γ tends to decrease the equilibrium micelle size, which, in turn, enhances the driving force for fragmentation of the bigger as-prepared micelles, represented by increase in the ratio of aggregation numbers Q/Q eq. Subjecting the diluted micellar solution to temperature-jump to 170 °C followed by thermal annealing leads to fragmentation of the as-prepared micelles to attain a near-equilibrium state. The micelles are characterized using an in situ dynamic light scattering (DLS) technique to observe the time evolution of average micelle size, from which the relaxation time is obtained. Additionally, small-angle X-ray scattering (SAXS) and cryogenic transmission electron microscopy (TEM) measurements were carried out to obtain the micelle core size and distribution in the micellar solutions before and after fragmentation. The enhancement in the driving force achieved by controlling the amount of low γ solvent resulted in faster fragmentation; the characteristic fragmentation time decreases monotonically on increasing the size ratio Q/Q eq from 1.2 to 5.

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Role of Distance from Equilibrium in the Fragmentation Kinetics of Block Copolymer Micelles

2023

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The fragmentation kinetics of 1,2-polybutadiene-bpoly(ethylene oxide) (M n = 17.2 kDa and f PEO = 0.38) block copolymer micelles have been examined with an emphasis on elucidating the role of driving force for micellar fragmentation, represented by the aggregation number ratio Q/Q eq . Large micelles with size Q > Q eq were formed in an ionic liquid [C 2 mim][TFSI] by the direct dissolution method. A broad range of Q/Q eq was then obtained by altering the solvent quality after micelle formation by addition of a second solvent, selected from a series of imidazoliumbased ionic liquids [C x mim][TFSI] with x = 2, 4, 6, 8, 10, and 12. In order to quantify the change in solvent quality by dilution, the interfacial tension γ between the different ionic liquids and 1,2polybutadiene homopolymer was determined using the pendant drop method. Micelles in a solution diluted with a second ionic liquid with x ≥ 2 were equilibrated by high-temperature annealing at 170 °C, during which in situ dynamic light-scattering measurements were made to follow the decay of average micelle size with time. Micelles were further characterized using small-angle X-ray scattering and cryogenic transmission electron microscopy to obtain micelle core size distributions. Q eq and γ were found to exhibit a power-law correlation, Q eq ∼ γ 6/5 , in accordance with the scaling prediction for star-like micelles. The reduction in γ on dilution with a lower γ solvent (x > 2) results in a smaller equilibrium micelle size, enabling access to a higher Q/Q eq , in the range from 1.1 to 5. The rate of fragmentation was found to increase significantly with an increase in Q/Q eq , thus the greater thermodynamic driving force leads to a systematic acceleration of fragmentation kinetics. The detailed mechanism by which micelles with Q ≫ Q eq achieve Q eq remains to be elucidated; the data suggest that it is not a sequential process but concerted.

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Free Energy Trajectory for Escape of a Single Chain from a Diblock Copolymer Micelle

Cited by 5 publications

References 45 publications

Mechanism of Escape of a Single Chain from a Diblock Copolymer Micelle

Mechanism of Escape of a Single Chain from a Diblock Copolymer Micelle

Effect of Changing Interfacial Tension on Fragmentation Kinetics of Block Copolymer Micelles

Role of Distance from Equilibrium in the Fragmentation Kinetics of Block Copolymer Micelles

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