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...

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.

Using field-theoretic techniques, we study the solvation of salt ions in liquid mixtures, accounting for the permanent and induced dipole moments, as well as the molecular volume of the species. With no adjustable parameters, we predict solvation energies in both single-component liquids and binary liquid mixtures that are in excellent agreement with experimental data. Our study shows that the solvation energy of an ion is largely determined by the local response of the permanent and induced dipoles, as well as the local solvent composition in the case of mixtures, and does not simply correlate with the bulk dielectric constant. In particular, we show that, in a binary mixture, it is possible for the component with the lower bulk dielectric constant but larger molecular polarizability to be enriched near the ion. DOI: 10.1103/PhysRevLett.109.257802 PACS numbers: 77.84.Nh, 31.15.xr, 31.70.Dk, 78.20.Ci Salt ions are essential in biology, colloidal science, electrochemistry, and many other areas of science and engineering. For example, protein stability and solubility are well known to be significantly affected by the addition of salts [1]. In the energy arena, there is much current interest in lithium salt-doped polymers as new battery materials [2].The effects of salt ions on the properties of soft matter can often be understood in terms of translational entropy and electrostatic screening. 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. [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].While a very large body of theoretical literature exists for ion solvation in single-component liquids for comprehensive reviews and Ref. [14] for recent developments of ion force fields for solvation.), we are not aware of any theory that predicts the composition dependence of ion solvation in liquid mixtures. 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 . The Born model has the virtue of being simple and intuitive in capturing the essential qualitative physics of solvation. However, quantitatively, the Born expression is known to be a poor description of the solva...

We study the microphase separation of block copolymer electrolytes containing lithium salts. Taking poly(ethylene oxide)-b-polystyrene (PEO-b-PS) as an example, we show that in the presence of lithium salts the disordered-to-lamellar phase transition becomes first-order even at the level of mean-field theory, with a moderate range of temperature in which both the disordered and lamellar phases coexist, and different salt concentration in the coexisting phases. The coexistence arises from the different partitioning of the salt ions between the disordered phase and the lamellar phase, driven primarily by the solvation energy of anions. A striking consequence of the coexistence is that heating a lamellar phase into the coexistence region leads to increased order in the remaining lamellar phase.

Recent work by Teran et al 1 demonstrated a correlation between the ionic conductivity and morphology in block copolymer salt mixtures. Their worked revealed a discontinuous increase in ionic conductivity as the sample transitioned from ordered lamellae to a disordered morphology. This work sought to gain insight into the ion transport behavior within coexistence window of the ODT. The temperature dependent ionic conductivity values of the three SEO(1.7-1.4)/LiTFI(r=0.075) samples measured in this study are shown in Figure S1, where the coexistence window determined through SAXS is highlighted in yellow. All three samples demonstrate a discontinuous increase in ionic conductivity between the ordered lamellar and disordered phases present at low and high temperatures, respectively. The ionic conductivity within the coexistence temperature window is unremarkable and monotonically increases from the lower lamellar phase conductivity to the higher disordered phase conductivity.