Self-consistent field theory of polymer-ionic molecule complexation

Nakamura, Issei; Shi, An‐Chang

doi:10.1063/1.3430745

Cited by 7 publications

(6 citation statements)

References 36 publications

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“…To describe the distribution of the Li + ions on the PEO backbone, we employ an Ising-like binding variable for the EO sites; C is ¼ 1 if there is a Li + ion at the s-th binding site of the i-th PEO chain, and 0 if there is not. 30 For the ion pair (EO-Li + -X À ), we also need another binding variable; D is ¼ 1 if there is an EO-Li + -X À , and 0 if there is not.…”

Section: Modelmentioning

confidence: 99%

Salt-doped block copolymers: ion distribution, domain spacing and effective χ parameter

2012

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We develop a self-consistent field theory for salt-doped diblock copolymers, such as polyethylene oxide (PEO)-polystyrene with added lithium salts. We account for the inhomogeneous distribution of Li + ions bound to the ion-dissolving block, the preferential solvation energy of anions in the different block domains, the translational entropy of anions, the ion-pair equilibrium between polymer-bound Li + and anion, and changes in the c parameter due to the bound ions. We show that the preferential solvation energy of anions provides a large driving force for microphase separation. Our theory is able to explain many features observed in experiments, particularly the systematic dependence in the effective c-parameter on the radius of the anions, the observed linear dependence in the effective c on salt concentration, and increase in the domain spacing of the lamellar phase due to the addition of lithium salts. We also examine the relationship between two definitions of the effective c parameter, one based on the domain spacing of the ordered phase and the other based on the structure factor in the disordered phase. We argue that the latter is a more fundamental measure of the effective interaction between the two blocks. We show that the ion distribution and the electrostatic potential profile depend strongly on the dielectric contrast between the two blocks and on the ability of the Li + to redistribute along the backbone of the ion-dissolving block.

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Section: Modelmentioning

confidence: 99%

Salt-doped block copolymers: ion distribution, domain spacing and effective χ parameter

2012

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“…Therefore, we must explicitly treat the distribution of Li þ ions on PEO. This is accomplished by introducing an Ising-like binding variable for the EO-Li þ sites [21]. We must also confront the electrostatics in an inhomogeneous medium with spatially varying dielectric constant and hence spatially varying Born energy [17].…”

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confidence: 99%

Thermodynamics of Ion-Containing Polymer Blends and Block Copolymers

2011

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We develop a theory for the thermodynamics of ion-containing polymer blends and diblock copolymers, taking polyethylene oxide (PEO), polystyrene and lithium salts as an example. We account for the tight binding of Li þ ions to the PEO, the preferential solvation energy of anions in the PEO domain, the translational entropy of anions, and the ion-pair equilibrium between EO-complexed Li þ and anion. Our theory is able to predict many features observed in experiments, particularly the systematic dependence in the effective parameter on the size of the anions. Furthermore, comparison with the observed linear dependence in the effective on salt concentration yields an upper limit for the binding constant of the ion pair. DOI: 10.1103/PhysRevLett.107.198301 PACS numbers: 83.80.Uv, 77.22.Àd, 82.35.Rs, 83.80.Sg There is much current interest in ion-containing polymers as materials for energy applications [1]. Of particular interest for rechargeable battery applications are block copolymers [2][3][4] of an ion-dissolving block, typically polyethylene oxide (PEO), and a nonconducting block such as polystyrene (PS), doped with lithium salts. The lithium ions are complexed with EO groups [5], and together with their counterions, provide the charge carriers [6]. The nonconducting block can be tuned to confer other functions, such as mechanical robustness [3,4,6].Experimentally, the addition of lithium salts has been shown to have significant effects on the order-order and order-disorder transitions in block copolymers [3,7,8]. Among other effects, it is found that the effective parameter characterizing the immiscibility of the two blocks increases linearly with salt concentration [9,10],where is the intrinsic Flory-Huggins parameter for the salt-free system, r is the molar ratio of Li þ ions to EO monomers, and the slope m depends on the anion type. Wanakule et al. [10] found that m decreases with increasing anion radius a. No existing theory describes this behavior. Since the Li þ ions are strongly bound to the EO groups [11], one may consider the PEO with its bound Li þ ions as an effective polyelectrolyte, with the anions acting as the counterions. However, existing theories for diblock copolymers with a charged block and a neutral block [12,13] predict enhanced miscibility between the blocks relative to the uncharged system, opposite to experimental observations; there is also no dependence on the radius of the counterions.The strong binding of Li þ to the EO groups clearly will affect the thermodynamics of PEO-PS diblock copolymers. However, as suggested in Ref.[10] and demonstrated here, a key effect in these ion-containing polymers is the solvation energy of the anions, which has been ignored in all existing theories of ion-containing polymers. An earlier theory developed by one of us [14], taking into account the effects of ion solvation, predicted that adding salts to binary polymer blends can decrease the miscibility between the two polymers. However, that theory assumed the salt ions to be fully dissociated a...

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“…Certainly, the complexation between the polymer and the ionic liquid is of significance to enhance their miscibility. However, we also refer to the mechanism to enhance the miscibility of charged polymers, as demonstrated in previous theoretical studies: ,,,, ion-complexed PEO via hydrogen bonding should behave as charged polymers. In this case, the phase separation between the polymer-complexed ion and its counterion causes an entropic penalty due to electroneutrality and thus tends to be inhibited.…”

Section: Fluctuation Around the Homogeneous Phasementioning

confidence: 98%

Spinodal Decomposition of a Polymer and Ionic Liquid Mixture: Effects of Electrostatic Interactions and Hydrogen Bonds on Phase Instability

Nakamura

2016

Macromolecules

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We studied the spinodal decomposition of a homopolymer and ionic liquid mixture. Our theory accounts for the dielectric contrast and hydrogen bond between the polymer and the ionic liquid and the effect of fluctuations in the local density and electrostatic potential. We attempted to rationalize the observed shift in the critical point and the asymmetry of the observed spinodal curve by applying the selfconsistent field theory and Langmuir adsorption model. The dielectric contrast between the polymer and the ionic liquid produces a shift in the critical point toward polymer-rich regions. The fluctuation effect yields drastic changes in the trend of the phase boundary. We show that both effects are marked by the appearance of inflection points in the spinodal curve. Although hydrogen bonding also yields similar effects, the spinodal curve rather exhibits a double-well structure or relatively flat structure when combined with the solvation energy of ions. Hydrogen bonding, ion solvation, and the fluctuation have equal significance on the magnitude and trend of the spinodal curve. Our theory provides strategies to dissolve low-dielectric polymers in ionic liquids by altering the dielectric constant of ionic liquids and employing hydrogen bonding.

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Self-consistent field theory of polymer-ionic molecule complexation

Cited by 7 publications

References 36 publications

Salt-doped block copolymers: ion distribution, domain spacing and effective χ parameter

Salt-doped block copolymers: ion distribution, domain spacing and effective χ parameter

Thermodynamics of Ion-Containing Polymer Blends and Block Copolymers

Spinodal Decomposition of a Polymer and Ionic Liquid Mixture: Effects of Electrostatic Interactions and Hydrogen Bonds on Phase Instability

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