Polymer electrolytes—Some principles, cautions, and new practices

Accepted Manuscript Title: Polymer electrolytes- some principles, cautions, and new practices Author: C. Austen Angell PII: DOI: Reference:

S0013-4686(17)31536-0 http://dx.doi.org/doi:10.1016/j.electacta.2017.07.118 EA 29935

To appear in:

Electrochimica Acta

Received date: Revised date: Accepted date:

23-3-2017 17-7-2017 20-7-2017

Please cite this article as: C.Austen Angell, Polymer electrolytessome principles, cautions, and new practices, Electrochimica Actahttp://dx.doi.org/10.1016/j.electacta.2017.07.118 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Review article Polymer electrolytes- some principles, cautions, and new practices. C. Austen Angell, School of Molecular Sciences, Arizona State University, Tempe, AZ 85287-1604 Abstract We give a short review of the basics of ionic dynamics in simple ionic liquids and their solutions (liquid fragility, conductivity-viscosity relations, limiting high conductivity, decoupling of conductivity from viscosity, conductivity maxima in solutions, and ionicity), and then summarize how these conceptual underpinnings must change when the ionic liquid becomes an ionic polymer or salt-in- polymer solution - the field of polymer electrolytes. We discuss the generation of rubbery plateaus, segmental relaxation and its control of thermodynamics, ionicity, and gelation), and revisit some of the key equations needed to provide quantitative accounts of the observed behavior. Finally we describe two alternative approaches to preparing flexible solid electrolytes, both higher-dimensional and one of them allinorganic.

Keywords: Simple ionic liquid electrolytes; Polymer electrolytes; gelelectrolytes; g-MOF electrolytes

1. Introduction The field of polymer electrolytes is commonly thought of as (i) the study of ionic transport in materials made of chain polymers acting as electrolyte solvents, or alternatively (ii) the study of polymers that are polyionic and ion-conducting themselves - in either case providing tough flexible ion transporting materials. More recently the advantages of using chain polymers to support gel structures, within which a higher-conducting solution component can be supported, has been found successful. Indeed, it is now incorporated in the current lithium ion battery electrolyte technology. Here, in this short review, we revisit1 some of the key ideas and the equations that quantify them before giving a brief account of two novel sorts of polymer + electrolyte materials, one a gel polymer that is all inorganic in character and might easily be developed as a general vehicle for ionic-conducting membranes, and the other a glassy (or rubbery) metal-organic framework that enhances the ionicity of occluded electrolyte solutions.

2. Phenomenology and equations The non-Arrhenius character of the equations describing the temperature dependence of the conductivity of the various classes of polymer electrolytes is

1

familiar to everyone, but some the factors that control the degree of departure of conductivity from Arrhenius law are often paid inadequate attention, then leading to some confusion in the description and understanding of what is observed. This makes for an unfavorable comparison with the understanding available for simple ionic liquids and concentrated aqueous solutions that have a longer history. In the latter systems it is generally possible to explore a wider temperature range than is commonly studied for polymer electrolytes. It is known from these that at sufficiently high temperatures, the Arrhenius character of the transport processes is restored. However this high temperature range is usually not available for study with polymer solvents because of decomposition and we will not be directly dealing with it in the following discussion. For the simpler systems, the three-parameter relations that describe the temperature dependences of viscosity and conductivity within the non-Arrhenius domain are: 

 = oexp(-B/[T-T0]) and

(1a)

 = oexp(B/[T-T0]))

(1b)

(where the T0 and B parameters are material specific). T0 is usually the same for both the viscosity  and the specific conductivity , and the o value should common to all "well-behaved" systems (see Figure 4 of ref.2). It is close to the value of 10-5 Pa.s. that is associated with a structural relaxation time (see below) of 10-14 s - an inverse quasi-lattice vibration time. It is common for systems with small values of the ratio B/T0 (liquids that deviate very greatly from simple Arrhenius behavior) to require two sets of Eq. (1) parameters to fit data that cover the whole range from high temperatures down to the low temperature limit for measurable flow (at the glass transition temperature, Tg)3. For less deviant liquids, a single set is usually sufficient. In most of the polymer electrolyte literature, Eqs. 1 are referred to as the VTF equation named after three early and independent promoters of the equation (1) form (Vogel, Tammann, and Fulcher). The idiosyncrasy of this acronym will be commented on in section 2.5. More important to note is the modification of equations 1 now in common usage, in which the parameter B is replaced by DT0, leading to2 

 = oexp(-DT0/[T-T0]) = oexp(-D/[T/T0-1]

(2)

The advantage of this seemingly trivial modification is that the parameter D now describes the characteristic deviation of the system from the Arrhenius law (small D, large deviation) or the so-called "fragility" of the liquid2. The fragility parameter then also quantifies how rapidly the viscosity decreases (and the corresponding 2

conductivity increases) as temperature rises above the glass transition temperature. It varies greatly among different liquids and can be as important as the glass transition temperature in determining which of a group of different ionic liquids will have the highest fluidity, and hence highest conductivity, at ambient temperature (see Figures 4 and 7 of ref. 4) Let us comment further on the relaxation time mentioned above in order to establish at an early stage what should be the theoretical upper limit on dc conductivity. The characteristic time for response to shear stress, may be obtained from Maxwell's famous relation in which the liquid-like property, viscosity , is ratioed to the solid-like property, shear modulus, (measured at so-called infinite frequency G∞) thus    /G∞ (3) The "universal" pre-exponent o then corresponds to a universal relaxation time o which is a quasilattice vibration time (time between successive attempts to breach the barrier opposing molecular or ionic rearrangements). For conductivity, the relevant vibration time can be measured directly (as its inverse) by far IR spectroscopy5,6 to detect the rattling frequency of the main conducting species in the cage of its neighbors. For sodium ions in oxide glasses it corresponds to a limiting ionic conductivity of approximately 10 Scm-1. 5,6 While the values of T0 are typically found to be the same for conductivity and viscosity of simple fully ionic systems, the B parameters of Eqs. (1) (and so also the D values of Eq. (2)), are nearly always different, being a little smaller for the conductivity than for the viscosity (see, for instance, Figure 7 of ref.7 for ionic liquids, and Figure 6 of ref. 8 on the Ca(NO3)2-H2O system in which B for equivalent conductance is about 10% smaller than for viscosity, and D for equivalent conductance is actually independent of composition over the entire range up to molten hydrate compositions). In these "well-behaved" systems, the value of T0, which corresponds to the temperature at which the viscosity would diverge, always lies below the value of the glass transition temperature Tg where Tg is determined as the temperature at which the heat capacity jumps from a glass-like to a liquid-like value. Tg , which marks where the system emerges from the non-ergodic glassy state to become a supercooled liquid, is usually close to the temperature where the viscosity reaches 1012 Pa.s. By contrast, with polymer electrolytes none of the above simple and physical correspondences holds up, though the three parameter equation may continue to give a satisfactory account of the data. The data usually do not extend over the number of decades for which the simpler liquids are routinely studied. Here we quickly review the factors that lead to the discrepancies, and the sort of equations that are needed to restore physical meaning to the parameters of the data fittings. 2.2 Viscosity, polymer chain length, glass transition and the rubbery domain Firstly, note that the number 16-17 which is the number of orders of magnitude of viscosity change between the standard Tg and infinite temperature) is the most common value of the parameter C1 in the famous Williams-Landel-Ferry

3

WLF equation9 for the temperature shift factor of polymer viscosity - and that this is not accidental10. The WLF equation was developed to deal with the following problem. For viscosity, if the polymer molecular weight is more than that characteristic of an oligomer, then the pre-exponent will be larger than that corresponding to any quasilattice vibration time, and is proportional to the number of monomers in the polymer chain i.e. to the polymer solvent molecular weight , to the first power. For the polypropylene glycol (PPG) solvents that have been much used in salt-in polymer studies because of their resistance to crystallization, the value of Tg (-75ºC) barely changes with increasing molecular weight so the only effect of increasing chain length comes from the pre-exponent. Thus the equation for viscosity of a short (N=5-200)) chain polymer solvent should be given simply by: 





= oNexp(-DT0/[T-T0])

(4)

(though it is frequently written with Mw the molecular weight , in place of N). Above about 200 monomers (depending on the particular polymer) the flow mechanism changes to reptation11 and the pre-exponent increases as N3.6 where N is the number of monomers in the polymer chain. The variation of viscosity with temperature for the case of PPG is shown in Arrhenius plot form for different molecular weights, in Figure 1(a). Although the range of molecular weights is limited, the parameterization of the curves by their fits to Eq. (1) allows one to see that viscosities of the different molecular weight liquids will reach those of the arrested (non-flowing) state, 1012 Pa.s, at temperatures that are progressively above the temperature 198K characteristic of their common glass transition temperatures. The glass transition temperature in polymers, as manifested by onset of heat capacity (or compressibility) "jump" when configurational degrees of freedom are accessed, occurs when the segmental relaxation time reaches 100s for upscans at the "standard" rate, 20K/min. Equivalently, it is where the bulk modulus (inverse of isothermal compressibility) begins its sudden decrease to the liquid-like value. Thus the polymers with large numbers of repeat units (high molecular weight) become non-flowing while thermodynamically they are still liquid. The transition to the non-flowing state is not detectable by normal thermodynamic means, only by onset of a non-zero but very small shear modulus. The state of the system between this temperature and the glass transition temperature is denoted as "rubbery". The range of temperatures above which the viscosity exceeds 1012 Pa.s and the "real" Tg clearly must become much larger than in Fig 1 (a) as the molecular weight is increased into the tens of thousands (as qualitatively indicated by the dashed curve and low temperature extension added to Fig. 1(a)). For the majority of polymers, Tg itself (and hence T0 also) changes with N (up to about N=200 in the case of polystyrene) complicating the molecular weight dependence of viscosity. Above N≈ 200 the Tg dependence on N flattens out and the behavior simplifies again. Figure 1(b) shows, qualitatively, the consequence of increasing the polymer molecular weight on the shear modulus, when measured on the same time scale as used for the ordinary glass transition (100-200s) for a 4

polymer of intermediate chain length. The glass transition, at which the major change in G occurs, corresponds to the glass-to-rubber transition because, although the segmental motions can freely occur, the liquid-like flow can only occur when the temperature has risen high enough to overcome the extra viscosity contribution due to the factor N in the pre-exponent. Thus within this range, and because of the residual small G∞ value, the system in this range will distort elastically under shear stress and then return to the original shape when the stress is removed, provided no time is allowed for irreversible relaxation. This implies the behavior of a rubber and so the domain of small but finite G∞ is called a rubbery plateau14. This is a very important range for polymer gel electrolytes. With sufficiently high molecular weight polymer solvents, the end of the rubbery plateau is not reached before there is polymer pyrolysis. To avoid dealing with such effects in studying the thermal behavior of polymer liquids it is common to turn to an expression that eliminates the N factor in Eq. (4). This is what is achieved by using the famous Williams-Landel-Ferry equation9. An immediate consequence of the viscosity behavior due to Eq. 1 is that any attempt to determine the ionicity of a salt-in polymer solution, by means of the Walden plot (log conductance vs log fluidity), that is so commonly used to classify ionicities of ionic liquids and simple molecular solutions, will fail. This will be demonstrated later. 2.3 Conductivity Associated with the final statement of the preceding section is the wellrecognized fact that the ionic conductivity is controlled not by the measured viscosity as in simple or ideal ionic liquids, but by the local viscosity (commonly discussed in terms of the segmental relaxation time9,14). This is the same relaxation time that controls the glass transition where the major decrease in shear modulus seen in Figure 1(b), occurs. Thus the conductivity will retain the form that it had for the simple liquids except for depending on a concentration term c related to how many moles of ions are contained in a one ml cube of the solution. At the limit of high concentration when the polymer is the minority component and is just enough to give the solution a rubbery or gel consistency, we have the "polymer-in-salt" condition15,16 on which considerable research has been expended in search of superionic polymer electrolytes. Thus the conductivity will be described by the equation 



 = oc exp(-DT0/[T-T0])

(5)

where the charge concentration term, c, will dominate at low salt concentrations while at high concentration the ionic mobility term, which responds to the T0 value (that rises with charge concentration), will dominate. This leads to the occurrence of a maximum value for the isothermal conductivity. The maximum seems to occur at about 0.5-1.0 molar for univalent salt components at ambient temperature regardless of what sort of system is under study. An exception is the case of aqueous solutions of 1:1 electrolytes, where the maximum occurs at higher concentrations, 5

about 4M, for reasons that are not clear. An example is shown in Figure 217 Systems that can be studied over the whole concentration range (0-100% salt) abound when the salts in the system are stable liquids at ambient temperature (i.e. ionic liquids with organic cations)16 and the "polymer-in-salt" domain can be freely examined. Unfortunately, when the salts have alkali metal cations it is difficult to find either pure salts or alkali salt mixtures that remain in the liquid state at ambient temperatures. A possible answer to this problem might seem to lie in using a mixture of salts, in which one salt has alkali cations and the other salt has organic cations, as the salt component. Unfortunately such salt mixtures seem to have a special problem due to the trapping of the alkali cations by a shell of anions which causes the mixture to have an ambient temperature conductivity that can be as much as an order of magnitude below the value expected from additivity at 25ºC18 2.4. Ionicity Finally, with many, if not most, salt-in-polymer electrolytes there is a problem with the ability of the polymer to fully dissociate the added salt. The effective dielectric constants are simply not large enough (> 50). This requires the addition of an extra term  ( 0 < <1.0) in the conductivity equation, to account for the extent of dissociation, thus  = ocexp(-DT0/[T-T0]

(5)

The problem that arises here is that  is temperature-dependent, decreasing with increasing temperature (disconcertingly) and even leading to salt precipitation above some characteristic temperature, depending on the salt dissolved and its concentration. A consequence is that the measured conductivity does not then increase as rapidly with increasing temperature as in a fully ionic solution. This leads to a curvature in the high temperature data that would not be there if the salt were fully dissociated. A naive application of Eq. (5) then might, and often does, result in the conclusion that the value of T0 for the system is much higher than correct data analysis (using low temperature data) would show, and indeed T0 has been reported to be (unphysically) higher than Tg in some cases in consequence of this effect. 2.5 Alternative viscosity equations Before leaving this section on data handling it should be mentioned that Eq. (1a) (and its derivatives), which predict some sort of phase transition at T0 (T0< Tg) , is not the only equation that fits the data with precision. Amongst a number of rival expressions there is one that we particularly should note, because it has been extensively tested in non-electrolyte systems over very wide ranges of data and been shown to be at least as adequate as Eq. (1) and in some cases better. It also does not require that there be any singularity below Tg. This is the transcendental (double exponential) equation, which has been derived in semi-empirical fashion by

6

different groups. It is best known from the work of Mauro et al.19 who derived the following form, Eq. (6), (now known as the MYEGA equation, for all its authors) K  C  y  y0 exp  exp    …………………………………………..(6)  T  T

(where y is a viscosity or a relaxation time), by incorporating constraint counting considerations within a two-state model into the Adam-Gibbs equation for relaxation times20. They carried out a detailed comparison of data-fitting ability with the VFT and Avramov-Milchek21 equations and found it superior. As Mauro and coauthors noted, Eq. (6) was actually proposed as an empirical fitting equation in 1932 by Waterton22, but then was largely ignored, perhaps because of the simpler form of the VFT equation and perhaps also for the lack of theoretical justification for this form. A similar double-exponential form was developed by Bressel and Angell8 in 1972 from a bond lattice model for the liquid thermodynamics and one assumption (see also Angell and Rao 1972, Eq. (12)23). They found that their equation described their precise conductivity data just as well as did the VTF equation, and noted that, except for y0, the parameters then had thermodynamic significance. Most recently, detailed comparisons of the VTF equation and MYEGA equations have been carried out over 16 orders of magnitude of precise dielectric relaxation time data on molecular liquids and plastic crystals, by Lunkenheimer et al.24 Differences between their precisions of fitting were only found at the extremes of high temperature and low temperature, with VFT seeming better at high temperatures and MYEGA slightly better at low temperatures. An example of the data fitting is shown in Figure 4. Finally we point out that the VTF designation of Eq. (1) is formally an idiosyncratic representation of the normally strictly calendar order convention for independent author contributions. The idiosyncrasy seems to have been deliberately introduced in 1970 by Moynihan, Angell and coworkers25 out of irritation with the convention, when it was clear that the latest author, Tammann, was the only one of the three (Vogel26, Fulcher27 and Tammann28) who recognized the significance of the equation that was being used to describe the data. Vogel, whose equation had a 4 year lead over the others, never studied a supercooled liquid or made a glass! The idiosyncracy appears to have been unwittingly carried forward by subsequent authors describing non-aqueous electrolyte solutions and now permeates the electrochemical literature. The formally correct designation is VFT as used in the Lunkenheimer article. To conclude this section we stress that it is important to be able to assess the ionicity of solutions of interest before attempting to fit their temperature dependences with any of the transport equations we have mentioned. For simple ionic liquids, the Walden plot offers a direct means of deciding whether the liquids under study are fully ionic or not. Figure 5(a) offers a good example of how well the data for four related ionic liquids conform to the ideal Walden line.29 By contrast,

7

when alkali metal salts are dissolved in polymer solvents, and the conductivity and viscosity treated in the same way, an initially confusing pattern results - for which an interpretation is easily provided. In Figure 5(b) the data for Na triflate in PPO425 - an oligomer of ~10 repeat units, at salt content (Na+: -O- = 1:16) (filled triangles) fall far below the ideal line because the dielectric constant is low (3.5) and the Na triflate in it acts like a weak electrolyte. (The diamond is for LiCl, 1M in water, used as the calibration point, and solid squares are for the molten hydrate LiCl.4H2O, which exemplifies almost ideal behavior). The open triangles are for the Na triflate at the same concentration, but now in a polymer PPO4000, a chain nearly 10 times as long. The data would suggest that the salt is suddenly fully dissociated, but that is quite wrong. It is because of the chainlength factor N for the viscosity (see Eq. (4)) decreasing the fluidity at any temperature by an order of magnitude, i.e. a manifestation of the polymer effect that is key to the whole idea of polymerelectrolytes. If a high molecular weight polymer were used, and the same procedure followed, the Walden plot would lie far to the left of the ideal line, in a domain called "superionic" for non-polymer systems. For the more strongly dissociating salt NaSCN, solutions near the conductivity maximum appear slightly superionic because of a weak polymer effect on the viscosity. Thus, if one wants to assess "ionicity" in a salt-in-polymer system, it has to be done in a quite different, more time-consuming way, usually based on the NernstEinstein equation, by comparing conductivity obtained by direct measurement with conductivities calculated from diffusivities30,31. We do not go into this here.

3. Optimizing the "solidity" of the polymer + salt system for high ambient conductivity. In seeking to optimize the joint conditions of solidity of the electrolyte, the mechanical robustness of the electrolyte, and the conductivity of the electrolyte (assuming it will first-of-all be chosen to be electrochemically stable), we briefly consider several options that are available. They are distinguished by the length scales of their relevant structures and the number of mechanically relevant components of the structure, as described in the following: 3.1 "True" decoupling. "True decoupling" refers to the decoupling of the ionic component, cation or anion, from the control by the segmental relaxation of the polyme-salt complex. Here we recognize that it has so far proven impossible to obtain room temperature ionic conductivity, either in an (unplasticized) salt-in-polymer electrolyte or in an anionic polymer, that is greater than10-4 Scm-1. This can be otherwise stated by saying that, while the separation of time scales of conductivity from viscosity is the essence of the polymer electrolyte concept, all efforts to significantly decouple the ionic motion from the segmental motion in an unplasticized or ungelled polymer electrolyte have so far not succeeded. The criterion for success here is the ratio of the structural (segmental) relaxation time s (which has the value 100s at the calorimetric glass transition temperature and can be followed to higher

8

temperatures using ultrasonic and Brillouin scattering techniques), to the conductivity relaxation time, , defined by the relation  = e0s/dc 32. This latter is the analog of the (earlier-discussed) Maxwell relation, Eq. (3), for the shear relaxation time of viscous liquids32. Unless we count the intermediate case of liquidcrystal polymer solvents as examples, there are as yet no clear cases of the sort of decoupling of ionic motion from the structure that are routinely obtained in superionic glassy or crystalline electrolytes, where  can be as much as 12 orders of magnitude shorter than s6. The reasons for this failure, despite decades of effort, are not clear. Somehow the flexibility of the polymer matrix, that is its mechanically desirable property, seems incompatible with the existence of the sort of ion-conducting channels that permit independent motion by small cations (or anions like F- in some cases) in favorable crystal and glass matrices. The failure has led to the development of nominally solid systems in which the polymer is dilute and entangled or otherwise obligated to remain open while the normal liquid solution state in its interstices carries out the ionic conductivity function, almost unimpeded by the presence of the polymer. 3.2. Confining the liquid electrolyte or electrolyte solution in a

polymer matrix: how to do it.

3.2.1. 1D gels by entanglement of dissolved high molecular weight chain polymers. This strategy has been highly developed and, to the author's understanding, is currently the strategy employed in lithium battery technology. We are not in a position to add to it. Emphasis has been on developing "tough" gels, extensions factors of 10-20 and self-healing being possible with ionic crosslinking33 or mixed polymers. Due to the organic solvents employed, fire hazards remain. 3.2.2. 2D and 3D gels by self-assembly Higher dimensional gels, that self-assemble in the presence of the electrolyte or electrolyte solution to be confined, constitute another and distinct line of research. We describe two types of process that can be used to this end. acids.

3.2.2.1. 3-dimensional SiO2 gels that form by hydrolysis of silico-phosphate

This is a method utilized recently to produce an all-inorganic flexible solid fuel cell membrane that provided remarkably good performance in a H2/O2 fuel cell34. It was obtained by hydrolysis of an initially anhydrous, highly disordered, compound Si(OPO3H)4 obtained as the product of reaction between SiCl4 and pure phosphoric acid, H3PO4 . This semi-solid acid dissolves completely in water, rather than precipitating hydrated silica and, on slow dehydration in a vacuum oven, yields

9

a translucent gel which, as structural studies using normal and also solid state NMR show, contains H3PO4 sequestered in a nanoporous silica network34. The conductivity of the gel ("SiPOHgel") is the same as that of pure H3PO4 which means it is as high as that of fully hydrated Nafion, and accordingly is largely due to decoupled proton motion of the general Grotthus type. In contrast to Nafion, SiPOHgel can sustain working temperatures of 150ºC over long periods. In a 24 hour constant current test, at 50 mAcm-2, no decrease in cell potential could be detected34. The gel has a stiff rubbery behavior but rather low tensile modulus. Although it can be used as a standalone membrane, fuel cell performance (open circuit voltage and maximum power) is better if the gel is prepared in the presence of a completely immersed silica wool support. Polarization curves with maximum current density over 1 Acm-2 and power curves with maximum above 200 mWcm-2 obtained using this 2mm thick membrane34 are shown in Figure 6 which includes a graphic of the proposed structure. 3.2.2.2. 3-dimension nanoporous metal-organic frameworks (g-MOFs) that selfassemble with occluded ionic solutions, and promote ionicity. One of the most active fields of structural chemistry of the last two decades has been that of "reticular chemistry" in which structures of interest are produced by the reaction within solutions that contain the basic building blocks of the soughtafter structures35. To a large extent, these structures, which may be of great elegance, are empty of matter, containing cages of dimension 1.5-4.0nm. ("empty" crystals). The crystals are usually slow to form, so the product is commonly a powder. There are some 500 known structures providing examples of nearly all the known network symmetries. The practical interests are manifold e.g. the potential for separation or storage of gases, for instance methane and even hydrogen. Glassy versions of these "empty" networks had been sought for some time, with little success. Recently, glassy materials of certain less stable MOF compositions (e.g. ZIF-4) have been made by fusion36, or pressure-induced amorphization37, of the crystalline precursor, but only at the expense of the interesting nanoporosity aspect of their structures. In our own investigations, an alternative (and constructive rather than destructive) approach to the formation of nets whose ground state is a nanoporous glass, has been explored38. In particular, using "activation" techniques developed in the foremost MOF lab at UC Berkeley, the generation of monolithic nanoporous glassy structures, with 330 m2/g accessible interior surface, and 33% open space, has been demonstrated39. In forerunner experiments to the above,40 these nets have been formed with the pores filled with an LiTFSI electrolyte solution of the same solvent, m-cresol, that dissolves the initial powdery product39, and the conductivity has been measured and compared with the conductivity of the free cresol solutions themselves - with the interesting results shown in Figure 7. m-Cresol is not a good solvent for electrolyte salts, having a dielectric constant of only 11.8 and Tg of -75ºC. 10

The effect of this combination is manifested both by the low conductivity and its temperature dependence which, for two concentrations, shows the typical flattening out at high temperatures (open symbols) known for low ionicity solutions. Interestingly, for the same solution sequestered in the polymer net, the conductivity is not only higher but also shows the temperature dependence of a strong electrolyte. Evidently the net is promoting ionic dissociation perhaps because of the high internal surface. This aspect of the new materials deserves much further study. The nets discussed above have been made by linking tetrahedral network centers ("nodes") using rigid "struts", such as bisphenol-A. If producing large internal surface is not the primary objective, then flexible struts such as PEO 600 can be used in which case a flexible gel-like material is obtained, in which various solutions can be supported and high conductivities demonstrated. The parameter space of such materials is very broad and there is much to be investigated. In either of the latter two cases, section 3.2.2), it should be possible to carry out a liquid exchange process between the membrane as formed and an alternative liquid electrolyte that would have higher intrinsic conductivity and electrochemical stability.

4. Conclusions Although some non-polymeric systems (e.g. concentrated aqueous sulfuric acid) closely approach the theoretical high conductivity limit for non-electronic conducting materials, to date it seems that, in systems with high concentration of chain polymers, ionic mobility is constrained by the much slower segmental relaxations of polymer systems so that conductivities lie four orders of magnitude lower, at best. Decoupling of ion motion from the solid matrix, which is achieved in many crystals and glasses, seems very difficult to achieve at ambient temperatures. The successful route to high conductivities seems to be one in which the polymer offers a flexible support to an occluded liquid phase. Examples in which such gel structure can be all-inorganic, or nano-porous are briefly described. Acknowledgements. The experimental portions of this work were supported by (a) DOD Army Research Office, under Grant no. W911NF-07-1-0423 for the synthesis and fuel cell work, and to W911NF-11-1-0263 for the structural analysis. and (b) for the later work on nanoporous nets, by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Vehicle Technologies of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231, Subcontract No. 6920968 under the Batteries for Advanced Transportation Technologies (BATT) Program.

11

References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Angell, C. A., Imrie, C. T. & Ingram, M. D. From simple electrolyte solutions through polymer electrolytes to superionic rubbers: Some fundamental considerations. Polymer Internat. 47, 9-15 (1998). Angell, C. A. Formation of Glasses from Liquids and Biopolymers. Science 267, 1924-1935 (1995). Stickel, F., Fischer, E. W. & Richert, R. Dynamics of glass-forming liquids. I. Temperature-derivative analysis of dielectric relaxation data. J. Chem. Phys. 102, 6251 (1995). Xu, W., Cooper, E. I. & Angell, C. A. Ionic liquids: Ion mobilities, glass temperatures, and fragilities. J. Phys. Chem. B 107, 6170-6178 (2003). Liu, C.-L. & Angell, C. A. Near and far-infrared absorption of alkali borate glasses and the limit of superionic conductivity. J. Chem. Phys. 93, 7378-7386 (1990). Angell, C. A. Dynamic processes in ionic glasses. Chemical Reviews 90, 523542:DOI: 510.1021/cr00101a00006 (1990). Fannin, A. A. et al. Properties of 1,3-Dialkylimldazolium Chloride-Aluminum Chloride Ionic Liquids. 2. Phase Transitions, Densities, Electrical Conductivities, and Viscosities. . J. Phys. Chem. 88, 2614-2621 (1984). Angell, C. A. & Bressel, R. D. Fluidity and Conductance in Aqueous Electrolyte Solutions. An Approach from the Glassy State and High-Concentration Limit. I.Ca(NO3)2 Solutions. J. Phys. Chem. 76, 3244-3253 (1972). Williams, M., Landel, R. F. & Ferry, J. D. J. Am. Chem. Soc. 77, 3701 (1995). Angell, C. A. Why C1 = 16-17 in the WLF equation is physical - and the fragility of polymers. Polymer 38, 6261-6266 (1997). de Gennes, P. G. J. Chem. Phys. 55, 572 (1972). Wang, C. H., Fytas, G., Lilge, D. & Dorfmuller, T. Laser Light Beating Spectroscopic Studies of Dynamics in Bulk Polymers: Poly(propy1ene glycol). Macromolecules 14, 1363-1370 (1981). Angell, C. A., Clarke, J. H. R. & Woodcock, L. V. Interaction Potentials and Glass Formation: A Survey of Computer Experiments, . Adv. Chem. Phys. 48, 397-453 (1981). Ward, I. M. & Headley, D. W. Introduction to properties of solid polymers, John Wiley, Chichester, 1993. Angell, C. A., Liu, C. & Sanchez, E. Rubbery solid electrolytes with dominant cation transport and high ambient conductivity. Nature 362, 137 (1993). Watanabe, M., Yamada, S.-I., Sanui, K. & Ogata, N. J. Chem. Soc. Chem. Commun., 929-931 (1993). Xue, R.-J. & Angell, C. A. High Ionic Conductivity in PEO.PPO Block Polymer + Salt Solutions. Solid State Ionics 25, 223-230 (1987). Tucker, T. G. & Angell, C. A. Approaches to, and Problems with, Ionic Liquid Electrolytes for Alkali Metal Electrochemical Devices: The Case of LowMelting Chloroaluminate Binary Solutions. J. Electrochem. Soc. 161, H796H802 DOI: 0013-4651/2014/0161(0012)/H0011/0016/ (2014).

12

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

Mauro, J. C., Yue, Y.-Z., Ellison, A. J., Gupta, P. K. & Allana, D. C. Viscosity of glass-forming liquids. Proc. Nat. Acad. Sci. 106, 19780–19784 (2009). Adam, G. & Gibbs, J. H. On the Temperature Dependence of Cooperative Relaxation Properties in Glass‐Forming Liquids. J. Chem. Phys. 43, 139 -146 (1965). Avramov, I. & Milchev, A. Effect of Disorder on Diffusion and Viscosity in Condensed Systems. J. Non.-Cryst. Solids 104, 253-260 (1988). Waterton, S. C. The viscosity-temperature relationship and some inferences on the nature of molten and plastic glass. J. Soc. Glass Technology 16, 244-249 (1932). Angell, C. A. & Rao, K. J. Configurational Excitations in Condensed Matter, and Bond Lattice Model for Liquid-Glass Transition. Journal of Chemical Physics 57, 470-& (1972). Lunkenheimer, P., Kastner, S., Köhler, M. & Loidl, A. Temperature development of glassy -relaxation dynamics determined by broadband dielectric spectroscopy. Phys. Rev. E (2010). Moynihan, C. T., Bressel, R. D. & Angell, C. A. Conductivity and Dielectric Relaxation in Concentrated Aqueous Lithium Chloride Solutions. J. Chem. Phys. 55, 4414 (1971). Vogel, H. Physik. Z. 22, 645 (1921). Fulcher, G. S., J . Amer. Ceram. Soc. 8, 339 (1925). Tammann, G. & Hesse, W. Z. Inorg. Allgem. Chem. 156, 245 (1926). Pan, Y. F. et al. Physical and Transport Properties of N(Tf)2-Based RTILs: Application to the Diffusion of Tris(2,2_-bipyridyl)ruthenium(II) J. Electrochem. Soc. 158, F1-F9 (2011). Ueno, K., Tokuda, H. & Watanabe, M. Ionicity in ionic liquids: correlation with ionic structure and physicochemical properties Phys. Chem. Chem. Phys. 12, 1649-1658 DOI: 1610.1039/b921462n (2010). Stoimenovski, J., Izgorodina, E. I. & MacFarlane, D. R. Ionicity and proton transfer in protic ionic liquids. Phys. Chem. Chem. Phys. 12, 10341-10347 (2010). Macedo, P. B., Moynihan, C. T. & Bose, R. Phys. Chem. Glasses 13, 171 (1972). Sun, J.-Y. et al. Highly stretchable and tough hydrogels. Nature 489, 133-136 (2012). Ansari, Y. et al. A flexible all-inorganic fuel cell membrane with conductivity above Nafion, and durable operation at 150ºC. J. Power Sources 303, 142149 (2016). Yaghi, O. M., O'Keeffe, M. & Ockwig, N. W. et al. Reticular synthesis and the design of new materials. Nature 423, 705-714 (2003). Bennett, T. D. et al. Hybrid glasses from strong and fragile metal-organic framework liquids. Nature Commun., DOI: 10.1038/ncomms9079 (2015). Chapman, K. W., Halder, G. J. & Chupas, P. J., Pressure-Induced Amorphization and Porosity Modification in a Metal−Organic Framework. J. Am. Chem. Soc. 131, 17546–17547 (2009). Angell, C. A. DOE-BATT program second quarterly report (2012).

13

39 40

Zhao, Y., Lee, S.-Y., Becknell, M., Yaghi, O. M. & Angell, C. A. Nanoporous transparent MOF glasses with accessible internal surface. J. Am. Chem. Soc. 138, 10818-10821 (2016). Lee, S.-Y. & Angell, C. A. Conductivity of glassy MOF networks containing conducting ions or solutions (to be published).

14

es (a)

(b)

Figure 1. (a) Arrhenius plots of the viscosity of PPG polymers of molecular weights 425, 1025, 2025, and 4000 together with their extensions to lower temperatures approaching the common T g of -75ºC implied by common values of the parameters Bh and T0 found by Wang et al. in ref. 12. The difference between the temperature for viscosity of 1012 Pa.s and Tg defines the rubbery domain in which the the liquid has a finite shear modulus but liquid-like thermodynamics (b) Shear modulus vs temperature schematic for a medium molecular weight chain polymer solvent, showing the distinction between the glass-rubber transition (Tg) and rubber-liquid transition (TRL) due to the chain length factor in Eq. (4). Each is measured on the same time scale, which is established by the heating rate. TRL will be much more spread out in temperature than is the shear modulus at Tg due to the same temperature shift effect that smears out the glass transition in computer simulation studies of simple liquids13 (adapted from ref. 1 with permission)

15

Figure 2. Conductivity maxima in salt- in-chain polymer solutions, (PEO-PPO block polymer, 25 +31 mers, with LiI as salt ). Comparison is made with aqueous solutions. Arrows on polymer solution data are for conductivity maxima predicted by a simple but inadequate model17 not discussed here.

16

Figure 3. Glass temperature and Eq. (5) fitted T0 values, for a LiI in PEO-PPO (56mer di-block) chain polymer solutions: (constrained fit). Reproduced from ref. 17 with permission

17

Figure 4. Fitting of dielectric relaxation time data on a selection of glassforming liquids and plastic crystals by the MYEGA and VFT equations. (after Lunkenheimer et al. 24 by permission)

18

(a)

(b)

Figure 5(a). Walden plots for four simple ionic liquids, derivatives of dimethylimidazolium tetrachloroaluminate, (after Pan et al, ref. 29 by permission). (b) Walden plot for Natriflate in low and medium molecular weight PPO, showing how polymer effect on viscosity can disguise low ionicity of salt in Polymer solution (see text for details) (from ref.1, by permission)

19

Figure 6. Polarization and power curves for H3PO4 nano-permeating a 3D open network SiO2 gel, cartooned on the LHS.

20

Figure 7. Ionic conductivities of solutions of LiTFSI in m-cresol both inside (filled symbols) and outside (open sybols) the nanoporous 3D g-MOF net.

21