Thermodynamics of Ion-Containing Polymer Blends and Block Copolymers

Abstract

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...

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

“…By examining the c eff for several lithium salts with different anions in PEO-PS block copolymers, Wanakule et al found a systematic dependence on the radii of the anions, 20 which suggested a role of the Born solvation energy. 22 We have recently developed a theory 23 for ion-containing polymers such as lithium salt-doped PEO-PS that incorporates the Born solvation energy of the anions, together with other effects, such as the tight complexation between the Li + ion and the EO monomers, the altered monomer identity due to the Li + binding, the translational entropy of the anions, and the ion-pair equilibrium between the Li + ions and the anions. By studying the shift in the spinodal of the disordered phase using the random phase approximation, we are able to obtain a c eff in good qualitative agreement with experimental results.…”

Ion Solvation in Liquid Mixtures: Effects of Solvent Reorganization

“…For example, Ref. [4] showed that the dramatic increase in the order-disorder transition temperature of (polyethylene oxide)-b-polystyrene block copolymers upon adding a small amount of lithium salt can be explained on the basis of the preferential solvation energy of the anions. Physically, the tendency of an ion to be preferentially solvated by the more polarizable component in a two-component mixture provides a significant driving force for phase separation [3], as well as differential adsorption between the cation and anion at the interface [5][6][7][8].…”

“…However, recently it has been shown that the solvation energy of the salt ions can significantly affect the phase behavior [3,4] and interfacial properties of liquid mixtures [5][6][7][8]. For example, Ref.…”

“…In Refs. [3][4][5][6]8], the solvation energy is modeled phenomenologically at the linear dielectrics level by a crude Born expression: ÁG Born ¼ ½ðzeÞ 2 =ð8 a 0 Þ ð1=" À 1Þ, where e is the elementary charge, a is the radius of the ion, and z is the valency. The local dielectric constant is taken to be given by a simple composition weighted average " ¼ " A A þ " B B .…”

Effects of dielectric inhomogeneity in polyelectrolyte solutions

“…To highlight the effect of the dielectric response of the polymer backbone, we use the same interaction parameters s ps and s pp for charged and neutral monomers. 17 Similarly, all other simplications in the description of our lattice model are adopted in order to illustrate the most important features arising from the dielectric inhomogeneity with a minimal model.…”