Article Cite This: Chem. Mater. 2018, 30, 5041−5049
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Increased Storage through Heterogeneous Doping Chia-Chin Chen and Joachim Maier* Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany
Chem. Mater. 2018.30:5041-5049. Downloaded from pubs.acs.org by UNIV OF SUSSEX on 08/15/18. For personal use only.
S Supporting Information *
ABSTRACT: We investigate the storage behavior of composites of mixed conductors and insulating phases which are surface-active. Here, extra storage is achieved by specific adsorption. For a master example, we refer to experiments on dispersions of Al2O3 in Ag2Se. Quantitative modeling is applied, suggesting double-layer storage of the heterointerface with silver ions adsorbed on the Al2O3 side and electrons on the Ag2Se side, whereas underpotential deposition of Ag may occur at large coverage.
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INTRODUCTION Mass storage (e.g., of Li) in solids is the key feature of modern energy storage technologies.1,2 Apart from homogeneous storage in which both ions (e.g., Li+) and electrons (e−) are accommodated in the bulk phase,3 heterogeneous storage at interfaces between an ion-storing phase and an electron-storing phase have been reported (job-sharing storage).4−11 Such a mechanism can offer a perceptible capacity in negative as well as positive nanocomposite electrodes.12 In a typically electroactive material that incorporates both Li+ and e− and thus is a mixed conductor, interfacial storage will occur in parallel with bulk storage but at usually different voltages.12−14 Here, we set out the possibility of introducing an interfacial storage component by creating interfaces with insulating second phases (e.g., in a dispersion) that are only electroactive via surface interactions. Composites of insulating second phases, typically Al2O3, SiO2, etc., have been explored in the context of heterogeneous electrolytes referring to dispersions in weak solid electrolytes.15−19 The oldest example is LiI:Al2O3 in which the Li+ conductivity is significantly increased.20 Later studies mostly on Ag-halides:Al2O3 have clarified the picture and led to the explanation of this phenomenon in the framework of heterogeneous electrolyte theory: silver ions are adsorbed and the counter carriers in the space charge zones (i.e., silver vacancies) are responsible for the conductivity enhancement.21 Also, adsorption of anions in PbF2:SiO222 or in composite soft matter electrolytes23,24 have been exploited where anion vacancies or mobile cations carry the current. The generalized treatment of this phenomenon has to analyze the ionic and electronic defect concentrations as a function of the component potential25 (hence, e.g., of Li or Ag activity). This dependency is mirrored in concomitant variations of the electronic concentration and thus also in the varied stoichiometry. The latter is equivalent to mass storage even though the stoichiometric variations are very small if the electronic carriers are in minority. Substantial stoichiometric effects are expected−and this forms the bridge to the job-sharing © 2018 American Chemical Society
storage mechanismif the electronic carrier concentration is substantial. Petuskey26 in an early paper, which has not received adequate attention, investigated the stoichiometry of Ag2S:Al2O3 by a coulometric titration cell, the thermodynamic equivalent of a battery charge/discharge. The Ag2S:Al2O3 composite showed an extended apparent homogeneity range when compared to Ag2S. Petuskey explained the behavior by a stabilization (adsorption) of either Ag or S at the alumina interface in the form of approximately a monolayer. In this contribution we refer to Ag2Se:Al2O3 and analyze the results quantitatively in the light of a recently developed thermodynamic framework.27 The experiments of ref 26 are also included in the discussion. In contrast to Ag2S, Ag2Se has the peculiarity that electronic disorder is in the majority,28 and thus ΔμAg ≅ ΔμAg+, that is, changes in the chemical potential of silver (μAg) are governed by the changes in the chemical potential of the silver ions (μAg+). Apart from the mechanistic interpretation and the fundamental significance, the results are discussed in view of a possible application of heterogeneous doping (i.e., admixing of a surface-active second phase) for battery purposes.
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EXPERIMENTAL DETAILS For the preparation of Ag2Se, Ag (Sigma-Aldrich, 99.9%) and Se (Sigma-Aldrich, 99.99%) were mixed in stoichiometric amounts. The obtained mixture was heated at 105 °C for 2 h and then 240 °C for 48 h, followed by slow cooling. The heat treatment was carried out under Ar atmosphere. The Ag2Se:Al2O3 composites were prepared by admixing Al2O3 nanoparticles (Sigma-Aldrich, 0, regime 3). (b) For Ag2Se:Al2O3 schematic shows that Ag deficiency is realized by VAg composite (3 vol % Al2O3, 70 °C), a significant extension of the homogeneity range is observed with the same voltage window. Unlike (a), the measured nonstoichiometry (δm) is an overall quantity that comprises bulk and interfacial contributions. The bottom x-axis gives δm relative to the value at the contact with Ag (at E = 0, δm = δAg m ). For comparison, the curve for the pure Ag2Se according to Figure 2a is shown as well. The zero point of the top x-axis indicates the zero point of bulk phase. As shown in the schematic, the bulk shows a transition from Ag deficiency (regime 1) to Ag excess (regime 3) while the adsorbed Ag on Al2O3 surfaces (Ag•ad + e′, indicated by the red bar between Ag2Se and Al2O3) prevails over the bulk contributions in all shown situations. The overall silver content δm thus remains positive over the whole potential range. The nonstoichiometry value is calculated based on the total amount of Ag2Se.
Figure 3. (a) Stoichiometry increase due to interfacial storage as a function of Al2O3 volume fraction. The relative bulk values (δ∞ − δAg ∞ ) and the corresponding values for the composite (δm − δAg m ) are obtained in Figure 2a,b. The initial slope characterizes the proportional increase at low Al2O3 fraction. (b) The slope obtained from the initial linearity in Figure 3a (cf. eq 6) plotted as a function of potential. At high potential, the linearity reflects the constant local capacitance at interfaces.
consistent with ref 33 (3.4 × 10−11 at 75 °C) but higher than ref 28 (5.76 × 10−12 at 80 °C). We do not know the exact reason for the difference (note that a residual doping content would shift the inflection point but not pronouncedly the prefactor of eq 3).3 Probably the results for KF in ref 28 are more reliable in view of the significantly longer annealing times used there. This point is however not important for the following evaluation.
Let us now consider the Ag2Se:Al2O3 composites. Figure 3 shows the effect of the Al2O3 volume fraction (φAl2O3) on the extension of the homogeneity range due to adsorption. The effect linearly increases with φAl2O3 and then saturates at 3%. The initial linearity reflects the interfacial behavior as here the interfacial area increases proportionally, and the flattening at high φAl2O3 is a natural consequence of not all Al2O3 particles being contacted by Ag2Se (large portion of Al2O3:Al2O3 5044
DOI: 10.1021/acs.chemmater.8b01288 Chem. Mater. 2018, 30, 5041−5049
Article
Chemistry of Materials
material into different parts, the unperturbed part with contribution (1 − φint)δ∞ and the adjoining interfacial part with the contribution φintδint, whereby δint is the local nonstoichiometry of the interfacial zone (in the single-layer model used here it is the outmost Ag2Se unit cell (the width of which we denote as l) to which we attribute the adsorption effects on the alumina side). As φint ≪ 1, both approaches are similarly straightforward. Assuming the Al2O3 particle surface to fully contribute to the heterointerface area, we can express φint in terms of the volume fraction of Al2O3 (φAl2O3) as φint = φAl2O3α[(l × Al2O3 particle surface area)/(Al2O3 particle volume)] = φAl2O3α(3l/r). Here, the parameter r represents the Al2O3 particle radius. As the Al2O3 particles may all stay in contact with Ag2Se but are not embedded in it, we have to correct the formula by a correction factor α (≤1) that is constant for a given preparation and will correct for Al2O3 agglomerations, that is,
boundaries due to aggregation). As here also severe kinetic problems occur, the treatment of which is complex and out of the scope of this paper, we will restrict ourselves to the thermodynamics of silver storage at low φAl2O3. Though the linearity suggests ideal contact behavior of Al2O3 with Ag2Se, we notice agglomeration of the Al2O3 particles even at low volume fractions (Figure 1d). Figure 4a depicts the defect chemical situation in the space charge zone at the interface under concern. The concentration
φint = φ Al O
2 3
The linearity observed in Figure 3a for
small φAl2O3 suggests that α ≅ constant with respect to φAl2O3 in that range (similar morphology). (As also mentioned, the Ag2Se grain size becomes smaller as φAl2O3 increases, suggesting that the Ag2Se surfaces are rather fully contacted by Al2O3 particles. So we can formulate an upper limit for φint by assessing the interface area from the surface area of the Ag2Se particles by φint = α′(1 − φAl2O3)(3l/r′), where r′ is the radius of the covered Ag2Se particles (particle aggregation) and the geometry factor α′ (≤1) takes account of noncontacted area that even exists for a densely populated surface). As already mentioned, the composition axis following from coulometric titrations is defined up to a constant, which is different for any experimental run (see also Figure 2b). We abbreviate these primary experimental values by Δ. We follow ref 26 and express our results as stoichiometry values relative to the value at E = 0, that is, where phase equilibrium with macroscopic silver is established (upper index Ag). Then in the subtraction of the experimental curves, the different constants disappear:
Figure 4. Equilibrium picture for the contact of Ag2Se with Al2O3. (a) The situation illustrated refers to Ag deficiency. Since Ag2Se is mainly electronically disordered, the concentration variations of electron and hole in the bulk phase are negligible, i.e., [e′]∞ ≈ [h•]∞ while the variations of ionic defects in the bulk are more pronounced. The position “s” indicates the site where silver is adsorbed. The general treatment of Ag storage/removal in such system highlights the significance of unifying bulk and interfacial storage. (b) Schematic of homogeneous neutral Ag adsorption and (c) heterogeneous dissociative Ag adsorption (job-sharing storage).
profiles are typically described by the Gouy−Chapman model,34 which is applicable when the Debye length (≡λD) exceeds the lattice constant. If λD is close to the lattice constant or smaller, a monolayer model is to be preferred.27 For Ag2Se, the λD value is calculated to range from 5 Å to 1.5 nm, equivalent to 1 to 3 layers (see Supporting Information 1). Considering the uncertainty of the dielectric constant and for the purpose of simplicity, we will, in the following, use the monolayer model. The readers who are interested in Gouy−Chapman corrections are referred to Supporting Information 2. In a dispersion (in which Al2O3 admixture results in an overall composition Ag2+δmSe) the measured (overall) stoichiometric variation, termed δm, is composed of a bulk and a boundary contribution δm = δ∞ + Δδm
( αr3l ).
Ag Ag B ≡ (Δcomposite − Δcomposite ) − (Δpure − Δpure )
≅ (δm − δmAg) − (δ∞ − δ∞Ag) Ag ) ≅ φint(δint − δint
(5)
where the superscript Ag represents the nonstoichiometry at E = 0. This explains why at the Ag-rich sidethough the titration curves for the composite and pure Ag2Se look identical thereeven the greatest but constant discrepancy between composite and pure may occur (as evidenced below), δint reaches a maximum value but δint − δAg int = 0. Equation 5 shows that the interfacial contribution φint(δint − δAg int) is simply the difference between the measured value (δm − δAg m ) and the bulk value (δ∞ − δAg ∞ ). This allows us to further evaluate the results obtained with different volume fractions (Figure 3a) (In Figure 3a this parameter B is plotted as a function of the volume fraction). For small φAl2O3, one recognizes a proportionality, indicating ideal access to the Al2O3 particles. The slope is given by
(4)
To emphasize again, δm refers to the overall Ag−Se ratio in the composite, that is, represents the sum of the bulk value (δ∞) and the excess value of the boundary (Δδm). The boundary contribution Δδm can be related to the local boundary excess contribution Δδ via Δδm = φintΔδ, whereby φint denotes the volume fraction of interfaces in the dispersion. (Here and in the following: φα = (volume of region α)/(total volume of composite).) Instead of splitting the nonstoichiometry into bulk background and excess contribution, one can also split the
3l ∂B Ag ) ≅ α(δint − δint r ∂φ Al O 2 3
(6)
For α = 1, the (δint − δAg int) value referring to the relative local nonstoichiometry at the interface is about −0.3 at 240 mV if 5045
DOI: 10.1021/acs.chemmater.8b01288 Chem. Mater. 2018, 30, 5041−5049
Article
Chemistry of Materials Table 1. Comparison of Different Ag Storage Mechanisms without Interactionsa bulk
incorporation
Ag ⇄ Ag+Ag2Se + e−Ag2Se
interface
neutral Ag adsorption (Figure 4b)
Ag ⇄ AgAl2O3
dissociative Ag adsorption (Figure 4c)
− Ag ⇄ Ag+Al2O3 + eAg 2Se
y i F (E − E*)zzz δ∞ = 2 KF sinhjjj− { k RT m X = K aAg mMax − m
eq 3 eq 8
yz F 2sm m jij zz e RTεε0 = K #a jj zz Ag jm m − Max { k 2
eq 10
m = [Ag]s or [Ag•]s. mMax = [Ag]s,Max or [Ag•]s,Max.
a
Figure 5. Fitting experimental data with different models, where m − mMax is the interfacial contributions extracted by subtracting the bulk F 2s . RTεε0 −2
contribution from the overall nonstoichiometry. (a) Ag2Se:Al2O3 (3 vol % Al2O3) at 70 °C, where the parameter γ stands for −6
(6.98 vol % Al2O3) at 158 °C. Experimental data are extracted from ref 26. Parameters: mMax = 3.3 × 10 details are given in Supporting Information 3.
taking l ≈ 6 Å35 and r = 5 nm. A lower α-value implies a larger difference (δint − δAg int). As the unit cell contains four Ag2Se units, a variation of δint by 0.3 from high to low voltage is consistent with our assumption. Moreover, the variation of the slope (cf. eq 6) with the voltage (Figure 3b) allows us to ∂δ extract the local capacitance int directly. The linearity at ∂E
Ag
(≅2 nm ), ε = 10.46−48 More
Ag
e
Ag
e
(9)
This relation follows from the qualitatively invariance of the electrochemical potentials of ions and electrons (cf. μ̃Ag+ and μ̃e− Figure 4a). Note that Δϕ stands for the electrical potential difference between position s and 0. Thus, the last term in eq 9 reflects the electric penalty that is to be paid by the charge separation which (in the second scenario) is overcompensated by the standard potential μ0e−(0) ≪ μ0e−(s) (free energy gain in accommodating e− at 0 instead of s). With neglect of interaction effects, the occupancy of ions at site s in Figure 4c (denoting as [Ag·]s) can be described by a Langmuir-type relation. Such relation may also approximately apply for electrons in the first layer.39,40 If we, for the sake of simplicity, assume the same number of maximum sites/states for both carriers and express Δϕ in terms of the adsorbed ion at position s, eq 9 can be rewritten with the heterogeneous adsorption constant K# as well as the length of the charge separation s and the dielectric constant εε0 as5,27
μAg = ∼ μ Ag + (x) + ∼ μe− (x) = μ Ag + (∞) + μe− (∞) (7)
The latter formulation is most adequate if both Ag+ and e− and thus neutral Ag is accommodated in the adsorption layer (homogeneous Ag adsorption, cf. Figure 4b, Table 1).37,38 Then the area-specific Ag concentration ([Ag]s) on the Al2O3 surface is expected to simply follow a Langmuir-type relation with aAg as silver activity and the mass action constant Kx as proportionality factor [Ag]s = K xaAg [Ag]s,Max − [Ag]s
(b) Ag2S:Al2O3
where [Ag]s,Max is the maximum adsorbed surface concentration. For simplicity, here we ignore interaction effects, which typically become nontrivial at high [Ag]s. The second scenario shown in Figure 4c refers to the situation that only the ions are adsorbed, and the positive layer is compensated by the electrons in Ag2Se (cf. job-sharing storage, Table 1) and then we better refer to μe−(0) in the form of μ =∼ μ + (s) + ∼ μ − (0) = μ + (s) + μ − (0) + F Δϕ
higher voltages indicates a constant capacitance. The obtained capacitance is −10 V−1, equivalent to 1 Ag per 100 mV related to the unit cell composition in the linear E vs (δm − δAg m) regime (cf. Figure 2b). The cell potential is determined by μAg which is positionally invariant in the measuring electrode but different from the reference electrode (typically silver metal).36 With use of the coordinate values ∞, 0, and s to indicate bulk position, position in the outmost layer adjacent to the alumina surface, and position in the surface layer, respectively (cf. Figure 4a), we can formulate for this quantity
= μ Ag + (0) + μe− (0) = μ Ag + (s) + μe− (s)
mol m
−2
ij yz 2 • [Ag •]s jj zz e(F s[Ag ]s )/(RTεε0) = K #a jj Ag • • z z [ ] − [ ] Ag Ag s,Max s{ k 2
(10)
To address both scenarios, we use later the term m (see also Table 1), which is short for either [Ag]s (scenario 1) or [Ag•]s (scenario 2).
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DOI: 10.1021/acs.chemmater.8b01288 Chem. Mater. 2018, 30, 5041−5049
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Chemistry of Materials
In spite of the points that remain to be clarified, this study clearly demonstrates that admixing of surface-active particles can lead to a distinct extension of the homogeneity range. Should such an addition be useful in terms of specific energy, one has to refer to very fine particles that provide high interfacial areas. Moreover, the second phase (i.e., Al2O3 in this study) should be of low weight in order to not introduce much dead weight. A more elegant approach is to fabricate layer-bylayer heterostructures.43,44 In term of rate capability, job-sharing composites are expected to be advantageous over the materials described here if diffusion is rate-determining.12,45 It remains to be studied whether the considered composites can be helpful as far as charge transfer or wiring aspects are concerned. At any rate, the consideration of the relevance of heterogeneous doping on storage is of basic interest for storage research, as it describes a novel storage mechanism and opens a novel degree of freedom.
In the following we will investigate the two interfacial models summarized in Table 1 for interpreting the experimental results. The first model that simply assumes a Langmuir type of a neutral Ag deposition provides a qualitatively reasonable fit (blue curve in Figure 5a). A less good, but qualitatively still satisfactory, fit is obtained for the double-layer model which includes the configurational effects but ignores any repulsion interactions (green curve), providing a very small s value (
