Unified View on the Mean-Field Order of Coil–Globule Transition

Yang, Delian; Wang, Qiang

doi:10.1021/mz400457h

Cited by 20 publications

(31 citation statements)

References 13 publications

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“…2(b) also shows that, compared to the case of N = 40, a larger chain length of N = 80 moves the binodal curve towards smaller χ . This trend is qualitatively consistent with the Flory-type mean-field theory of CGT of a ungrafted chain in an explicit solvent, 29 which predicts χ c ≈ 0.656 for N = 40 and 0.608 for N = 80.…”

Section: Cgt and Phase Diagrams From Lscf Calculationssupporting

confidence: 87%

“…19, their results for a mushroom show that it exhibits the "type I" phase behavior. The analysis performed in our recent work 29 is therefore also applicable to one-mushroom systems. In addition, Milik and Orszagh 8,9 performed MC simulations to study CGT of a grafted chain obeying the self-avoiding walk (SAW) on a diamond lattice, and found continuous variation of the chain dimension with monomer-monomer interaction (i.e., the solvent quality).…”

Section: Introductionmentioning

confidence: 99%

“…14 In that case, it is well known that the mean-field theory predicts ODT to be a second-order phase transition, 16 and that the system fluctuations stabilize the disordered phase and change ODT to a weak first-order phase transition. 17 In the case of CGT of a ungrafted chain, a Flory-type 18 mean-field theory, which is similar to but simpler than SCF theory, is commonly used; [19][20][21][22][23][24][25][26] the transition order predicted by this or SCF 27,28 theory, however, has been controversial until our very recent work, 29 where we clarified that CGT, at the mean-field level, can be either a first-order transition, a critical point, or a crossover for finite N (referred to as the "type I" behavior), and only in the limit of N → ∞ becomes a second-order transition with respect to the solvent quality characterized by either the second virial coefficient (also known as the excluded-volume parameter) v, 24, 27 the Flory-Huggins interaction parameter χ , or the temperature. 29 The phase behavior of a mushroom, on the other hand, has rarely been reported in the literature.…”

Section: Introductionmentioning

confidence: 99%

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Structural and phase transitions of one and two polymer mushrooms in poor solvent

Yang

Wang

2014

The Journal of Chemical Physics

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Using the recently proposed fast lattice Monte Carlo (FLMC) simulations and the corresponding lattice self-consistent field (LSCF) calculations based on the same model system, where multiple occupancy of lattice sites is allowed [Q. Wang, Soft Matter 5, 4564 (2009); Q. Wang, Soft Matter 5, 6206 (2010)], we studied the coil-globule transition (CGT) of one-mushroom systems and the fused-separated transition (FST) of two-mushroom systems, where a polymer mushroom is formed by a group of n homopolymer chains each of N segments end-grafted at the same point onto a flat substrate and immersed in a poor solvent. With our soft potential that allows complete particle overlapping, LSCF theory neglecting the system fluctuations/correlations becomes exact in the limit of n → ∞, and FLMC results approach LSCF predictions with increasing n. Using LSCF calculations, we systematically constructed the phase diagrams of one- and two-mushroom systems. A second-order symmetric-asymmetric transition (SAT) was found in the globule state of one-mushroom systems, where the rotational symmetry around the substrate normal passing through the grafting point is broken in each individual configuration but preserved by the degeneracy of different orientations of these asymmetric configurations. Three different states were also found in two-mushroom systems: separated coils, separated globules, and fused globule. We further studied the coupling between FST in two-mushroom systems and CGT and SAT of each mushroom. Finally, direct comparisons between our simulation and theoretical results, without any parameter-fitting, unambiguously and quantitatively revealed the fluctuation/correlation effects on these phase transitions.

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Section: Cgt and Phase Diagrams From Lscf Calculationssupporting

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Structural and phase transitions of one and two polymer mushrooms in poor solvent

Yang

Wang

2014

The Journal of Chemical Physics

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“…Depending on the format of the free energy, slightly different forms for the swelling can be derived. [31][32][33][34] The result of eqn (9) is that the swelling of polymers is a non-trivial function of the degree of polymerization. In Fig.…”

Section: Discussionmentioning

confidence: 99%

The pH-responsive behaviour of poly(acrylic acid) in aqueous solution is dependent on molar mass

et al. 2016

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Fluorescence spectroscopy on a series of aqueous solutions of poly(acrylic acid) containing a luminescent label showed that polymers with molar mass, Mn < 16.5 kDa did not exhibit a pH responsive conformational change, which is typical of higher molar mass poly(acrylic acid). Below this molar mass, polymers remained in an extended conformation, regardless of pH. Above this molar mass, a pH-dependent conformational change was observed. Diffusion-ordered nuclear magnetic resonance spectroscopy confirmed that low molar mass polymers did not undergo a conformational transition, although large molar mass polymers did exhibit pH-dependent diffusion.

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“…70,71 The second term −3 ln(α) is a term that resists chain compression, first deduced by Flory and used by several subsequent authors. [72][73][74][75] We also note that the expression for the interaction energy Eq. (3.9) is an improvement upon typical scaling estimates of the Coulomb energy.…”

Section: Self-consistent Calculation Of Flexible Chain Structurementioning

confidence: 99%

Electrostatic correlations and the polyelectrolyte self energy

Shen

Wang

2017

The Journal of Chemical Physics

154

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We address the effects of chain connectivity on electrostatic fluctuations in polyelectrolyte solutions using a field-theoretic, renormalized Gaussian fluctuation (RGF) theory. As in simple electrolyte solutions (Z.-G. Wang, Phys. Rev. E. 81, 021501 (2010)), the RGF provides a unified theory for electrostatic fluctuations, accounting for both dielectric and charge correlation effects in terms of the self-energy. Unlike simple ions, the polyelectrolyte self energy depends intimately on the chain conformation, and our theory naturally provides a self-consistent determination of the response of intramolecular chain structure to polyelectrolyte and salt concentrations. The theory captures the expected scaling behavior of chain size from the dilute to semidilute regimes; by properly accounting for chain structure the theory provides improved estimates of the self energy in dilute solution and correctly predicts the eventual N -independence of the critical temperature and concentration of salt-free solutions of flexible polyelectrolytes. We show that the self energy can be interpreted in terms of an infinite-dilution energy µ el m,0 and a finite concentration correlation correction µ corr which tends to cancel out the former with increasing concentration.

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Unified View on the Mean-Field Order of Coil–Globule Transition

Cited by 20 publications

References 13 publications

Structural and phase transitions of one and two polymer mushrooms in poor solvent

Structural and phase transitions of one and two polymer mushrooms in poor solvent

The pH-responsive behaviour of poly(acrylic acid) in aqueous solution is dependent on molar mass

Electrostatic correlations and the polyelectrolyte self energy

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