Article pubs.acs.org/accounts
Mechanically Tunable, Readily Processable Ion Gels by Self-Assembly of Block Copolymers in Ionic Liquids Timothy P. Lodge*,† and Takeshi Ueki‡ †
Department of Chemistry and Department of Chemical Engineering & Materials Science, University of Minnesota, 207 Pleasant St SE, Minneapolis, Minnesota 55455, United States ‡ National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan CONSPECTUS: Room temperature ionic liquids are of great interest for many advanced applications, due to the combination of attractive physical properties with essentially unlimited tunability of chemical structure. High chemical and thermal stability, favorable ionic conductivity, and complete nonvolatility are just some of the most important physical characteristics that make ionic liquids promising candidates for emerging technologies. Examples include separation membranes, actuators, polymer gel electrolytes, supercapacitors, ion batteries, fuel cell membranes, sensors, printable plastic electronics, and flexible displays. However, in these and other applications, it is essential to solidify the ionic liquid, while retaining the liquid state properties of interest. A broadly applicable solidification strategy relies on gelation by addition of suitable triblock copolymers with the ABA architecture, producing ion gels or ionogels. In this paradigm, the A end blocks are immiscible with the ionic liquid, and consequently selfassemble into micellar cores, while some fraction of the well-solvated B midblocks bridge between micelles, forming a percolating network. The chemical structures of the A and B repeat units, the molar mass of the blocks, and the concentration of the copolymer in the ionic liquid are all independently tunable to attain desired property combinations. In particular, the modulus of the resulting ion gel can be readily varied between 100 Pa and 1 MPa, with little sacrifice of the transport properties of the ionic liquid, such as ionic conductivity or gas diffusivity. Suitable A blocks can impart thermoreversible gelation (with solidification either on heating or cooling) or even photoreversible gelation. By virtue of the nonvolatility of ionic liquids, a wide range of processing strategies can be employed directly to prepare ion gels in thin or thick film forms, including solvent casting, spin coating, aerosol jet printing, photopatterning, and transfer printing. For higher modulus ion gels it is even possible to employ a manual “cut and stick” strategy for easy device fabrication. Ion gels prepared from common triblock copolymers, for example, with A = polystyrene and B = poly(ethylene oxide) or poly(methyl methacrylate), in imidazolium based ionic liquids provide exceptional performance in membranes for separating CO2 from N2 or CH4. The same materials also are the best available gate dielectrics for printed plastic electronics, because their high capacitance endows organic transistors with milliamp output currents for sub-1 V applied bias, with switching speeds that can go well beyond 100 kHz, while being amenable to large area roll-to-roll printing. Incorporation of well-designed electroluminescent (e.g., Ru(bpy)3-based) or electrochromic (e.g., viologen-based) moieties into ion gels held between transparent electrodes yields flexible color displays operating with sub-1 V dc inputs.
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INTRODUCTION
A gel is a polymer network swollen with a significant amount of solvent. There are various routes to introducing a polymer network in an IL, including in situ polymerization of dissolved monomer and cross-linker,3 hydrogen-bonding supramolecular systems,4,5 and others.6−11 However, the self-assembly of ABA triblock copolymers, where the A end blocks are insoluble but the B midblock is well-solvated, is a particularly versatile and general approach. Beyond a modest concentration c (typically a few percent), the A blocks associate into micellar cross-links,12 and the B blocks provide bridging connections between micelles, forming a percolating network. The chemical identity and length of the A and B blocks (Figure 1), the copolymer
Ionic liquids, or room temperature molten salts, are attracting considerable attention by virtue of a wide range of appealing physical and chemical properties, including nonvolatility, high thermal and electrochemical stability, exquisitely tunable solvation, and favorable ionic conductivity. Consequently they are promising candidates for a plethora of applications, including separations, plastic electronics, fuel cell and battery membranes, and greener chemical transformations.1 In many cases, it is necessary to immobilize the ionic liquid (IL), while retaining the other desirable attributes. To this end, we have pioneered the general strategy of combining ILs with appropriately designed triblock copolymers to obtain functional soft solids termed ion gels.2 © 2016 American Chemical Society
Received: June 21, 2016 Published: October 5, 2016 2107
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Accounts of Chemical Research concentration c, and the IL cation and anion structures are all independently tunable.
Figure 1. Structures of blocks for various ABA and ABC triblock polymers discussed in the text. PIL = polymerized ionic liquid; EA = poly(ethyl acrylate); N = poly(N-isopropylacrylamide); M = poly(methyl methacrylate); O = poly(ethylene oxide); P = poly(ethylenealt-propylene); S = polystyrene.
Figure 2. Linear viscoelastic properties of SOS/[BMIM][PF6] samples for the indicated concentrations, at 10 °C; Mn = 34 000 and f PS = 0.28. Reproduced with permission from ref 14. Copyright 2007 American Chemical Society.
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Our efforts have been directed at chemically straightforward routes to readily processable ion gels. Often, two attributes of a given system act in apparent opposition, for example, achieving both high modulus and high ionic conductivity simultaneously, and thus to optimize a given gel we need a quantitative understanding of how molecular attributes of the ingredients influence the final properties. We have studied a series of gels in which the monomer identity, composition, molar mass, and concentration of the polymer were tuned. The resulting viscoelastic moduli and ionic conductivity were characterized to establish the design rules for achieving given property combinations. Once the ion gel composition has been selected, the next challenge is to establish facile processing routes to enable device fabrication. We have demonstrated how to make gels that can be applied as liquids at elevated temperatures and simply cooled to solidify in situ, photopatterned, printed with 25 μm spatial resolution, transfer printed and manually cut to shape and installed. These strategies depend on careful modulation of both mechanical strength and end-block chemistry. Finally, the performance of ion gels in three distinct applications (gate dielectrics in plastic electronics; electroluminescent and electrochromic displays; gas separation membranes) has been explored for the first time and shown to be exceptional.
TUNABLE MECHANICAL PROPERTIES The modulus of an ion gel is dictated by the concentration and molecular weight (M) of the copolymer. From the theory of rubber elasticity, the shear modulus can be approximated as G′ ≅ νkBT
(1)
where ν is the number density of elastically effective strands. For an ABA gel, ν can in turn be estimated as cNav (2) M where γ is the fraction of midblocks that bridge between micelles (as opposed to looping back). From eq 2, it is evident that G′ will increase with c and decrease with M. As an estimate, with a low M ≈ 10 000 and high c ≈ 0.5 g/mL, eqs 1 and 2 anticipate a maximum modulus of 1 MPa, comparable to a rubber band; it is straightforward to achieve lower values, down to tens of pascals. Enhanced moduli can be obtained if the midblock length exceeds the molecular weight between entanglements, in which case ν is redefined as the number density of entanglement strands. Figure 3 illustrates the dependence of the modulus on c and midblock M, for the system polystyrene-b-poly(ethyl acrylate)-b-polystyrene (SEAS).15 The modulus increases monotonically with c and ν≅γ
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ION GELS USING ABA TRIBLOCK COPOLYMERS Gelation is most conveniently characterized by rheological measurements, and particularly the frequency (ω) dependent linear viscoelastic moduli, G′ and G″, representing the elastic and viscous responses at low strain amplitudes, respectively.13 We have shown that the negligible vapor pressure of the IL facilitates sample preparation using a volatile cosolvent and enables rheological measurements well above 200 °C. The viscoelastic response for our first reported copolymer-based ion gel (polystyrene-b-poly(ethylene oxide)-b-polystyrene (SOS) triblock in the common IL butylmethylimidazolium phosphorus hexafluoride [BMI][PF6]) is shown in Figure 2.14 At 1% polymer, the sample is a free-flowing liquid, containing “flowerlike” micelles (G″ ≫ G′); at 10%, the system solidified, with a modulus (G′ ≫ G″) near 1 kPa; 4% corresponds to the critical gel point, with G′ ≈ G″ ≈ ω0.5.
Figure 3. Shear modulus vs c for SEAS gels in [EMI][TFSI] with various midblock molecular weights at 30 °C. Reproduced with permission from ref 15. Copyright 2015 American Chemical Society. 2108
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Accounts of Chemical Research with decreasing midblock M at fixed c, consistent with eqs 1 and 2; in fact, for all but the highest M sample, the agreement with the simple theory is within a factor of 2. We developed the SEAS system in order to marry the favorable attributes of our earlier SMS- and SOS-based ion gels. In particular, SOS provides higher conductivity than SMS, due to the lower glass transition Tg of the middle block, but suffers from water uptake over time; SEAS also has a low Tg but is not hygroscopic. The modulus describes the linear (Hooke’s law) response, but in some applications, it is desirable to improve the large strain response. One way to accomplish this is to introduce chemical cross-links within the physically associated micelles. We copolymerized 4-vinyl benzyl chloride into the styrene end blocks, followed by reaction with NaN3 to install azide functionalities.16 The latter groups can be cross-linked by thermal or UV stimulus, releasing only N2 as a byproduct. The resulting effect on the stress−strain response is shown in Figure 4; we achieved a doubling of the strain-to-break, and the
polymer increases Tg of the conducting phase and can reduce D by orders of magnitude as c increases. For this reason, when higher conductivity gels are desired, a low Tg midblock (PEO or PEA) is preferable to a high Tg midblock (PMMA, see Figure 1).19 This analysis applies to all transport coefficients, including σ. However, in this particular case; the midblock can play an additional role, by either promoting or suppressing ion pairing.20
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THERMALLY AND OPTICALLY REVERSIBLE ION GELS The physical associations that form the micellar cross-links open the door to reversibility, enabling direct processing in the liquid state, with subsequent solidification on cooling or advanced processing techniques such as photopatterning. The most direct way to impart thermoreversibility is to select A blocks that undergo liquid−liquid phase separation in the IL. An excellent example is PNIPAm (“N”, Figure 1), which has been reported to exhibit an upper critical solution temperature (UCST) phase diagram in imidazolium-based ILs.21−23 We demonstrated that NON triblocks form gels at low temperature but are free-flowing liquids above a gelation temperature (Tgel).24,25 A particularly attractive feature of imidazolium-based ILs is that phase boundaries (and therefore Tgel) can be readily tuned over many tens of degrees, as we have shown simply by blending cations with different alkyl substituents (e.g., ethyl and butyl methylimidazolium).26,27 In an extension of this idea,28 we developed an ABC triblock terpolymer, “PON”, in which block “P” is the insoluble poly(ethylene-alt-propylene), which forms PEP-core micelles at all temperatures.29 On cooling, the N blocks associate to form ion gels, just as an NON analog (see Figure 5). However, the “preorganization” afforded by the PEP
Figure 4. Stress−strain relationships for ion gels with 10 wt % SOS before (dashed lines) and after chemical cross-linking (solid lines) measured at 40 °C. Inset photo is an ion gel sample on the rheometer extensional fixture. Reproduced with permission from ref 16. Copyright 2013 American Chemical Society.
toughness (area under the stress−strain curve) went up by a factor of 5, after cross-linking. As we expected, the cross-linking reaction has no effect on the ionic conductivity, σ, since the chemical transformation is confined within the micellar cores.
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ION TRANSPORT IN ION GELS It is of central importance to understand how the presence of the polymer network affects the transport of ions (or other small molecules) in an ion gel. The translational diffusivity of an individual ion, D, will be reduced from its value in the pure solvent, D0, by two separate effects. The first concerns the “obstacles” represented by the micellar cross-links.17 We have shown this effect to be quite modest, as can be anticipated from the Mackie−Meares “obstruction” model: ⎛ 1 − ϕ ⎞2 D ≅⎜ ⎟ D0 ⎝ 1 + ϕ ⎠
Figure 5. Dynamic temperature sweeps of 1 wt % PON in [EMI][TFSI], at a cooling/heating rate of 1 °C/min and ω = 10 rad/s. Reproduced with permission from ref 29. Copyright 2016 American Chemical Society.
(3)
micelles enables gelation at c ≈ 1%, far superior to the equivalent NON. Thus, even at low polymer loadings, the PEPcore micelles adopt a liquid-like packing, with the N blocks preconcentrated in the interstitial space. Several polymers have been reported to exhibit lower critical solution temperature (LCST) phase diagrams,30−34 thereby providing ion gels that form on heating; examples of suitable LCST end blocks include poly(benzyl methacrylate),35,36 poly(phenylethyl methacrylate),37 and poly(n-butyl methacrylate).26
where ϕ is the obstacle volume fraction. Even for high concentrations, c ≈ 0.5 g/mL, with a total volume fraction of insoluble block fA = 0.2, eq 3 anticipates only halving of the mobility. The second contribution depends on the concentration and identity of the midblock, and particularly its Tg. Because ILs are glass-formers, the temperature dependence of transport coefficients is very strong, following the Vogel− Fulcher form. We have shown that addition of a high Tg 18
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Accounts of Chemical Research Watanabe and co-workers have pioneered the development of optically reversible micellization38 and ion gel systems.39 The enabling concept is to incorporate a photochromic moiety into the thermally sensitive block, such that Tgel depends on the photostate.40 In one example from our recent collaboration, the NON framework was elaborated by including 10 mol % of an azobenzene methacrylate monomer statistically into the N blocks.39 The photoexcited cis form is significantly more polar than the ground state trans isomer, resulting in a shift of about 15 °C in the equivalent UCST phase boundary. UV illumination at a bistable temperature intermediate between Tgel(cis) and Tgel(trans) can dissolve the gel, while visible light drives formation of trans and reassembly of the cross-links (Figure 6). We have also extended the same approach to achieve photohealing of ion gels.41
Figure 7. Flexible drive circuit and integrated electrochromic (EC) pixel based on printed p-type electrolyte-gated transistors, capacitors, and resistors. Printed circuit with a 2 mm × 2 mm EC display pixel on a flexible PET substrate. The entire circuit consists of 23 EGTs, 12 capacitors, 20 resistors, and nine crossovers. Reproduced with permission from ref 44. Copyright 2013 American Chemical Society.
SOS ion gel sufficiently short; for PS with M ≈ 3000 g/mol, some solubility in [EMI][TFSI] is achieved near 100 °C. An even simpler means of preparing and transferring ion gels is the “cut-and-stick” method illustrated in Figure 8.47 In place of an ABA triblock, we used a commercially available copolymer of vinylidene fluoride and hexafluoropropylene (P(VDF-co-HFP). The cross-links are provided by VDF crystallites, but the polymer can readily absorb up to 80% IL. The resulting gel modulus, approximately 1 MPa, is more than sufficient to allow direct cutting and handling. As a further example of processing strategies, we used photopatterning to chemically cross-link the micelles, using the azide-functional PS end blocks discussed in the context of Figure 4, followed by washing to remove the un-cross-linked regions.48 The initial film can be applied by any facile lowresolution approach, before illumination through a suitable mask.
Figure 6. Reversible sol−gel transition of 20% (N-azo)-O-(N-azo) copolymer (20 wt %) in [BMIM][PF6] by alternately switching between UV and visible-light irradiation at 53 °C. Reproduced with permission from ref 39. Copyright 2015 Wiley.
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PROCESSING AND PATTERNING The thermoreversible ion gels exemplified above enable liquid state processing at elevated temperatures, with solidification below a tunable Tgel. However, because ILs are typically about 100 times more viscous than common solvents, the resulting fluid may be too viscous for some processing protocols. This difficulty may be circumvented with a volatile cosolvent, thereby enabling standard solution casting and spin-coating approaches. A major application that we have explored for ion gels is as gate dielectrics in plastic electronics.42 To this end, large area printing of ion gels is essential. In collaboration with the Frisbie group, we have demonstrated that aerosol jet printing enables rapid preparation of printed circuits on plastic substrates, with 25 μm features.43,44 A particularly attractive feature of this method is its tolerance of a wide range of “ink” viscosity, in contrast to traditional inkjet printing.45 A functional circuit completely prepared in this way is shown in Figure 7.44 We have also demonstrated that ion gels can be prepared by transfer printing onto various substrates, using a polydimethylsiloxane (PDMS) stamp, with feature resolution down to 10 μm. An interesting aspect of this process is the need to achieve conformal contact of the ion gel with the receiving surface.46 To this end, end blocks that are close to dissolution are preferred, so that local rearrangements of the micellar network are possible when brought into contact with the receiving substrate. We achieved this by making the end blocks of an
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ION GELS AS HIGH CAPACITANCE GATE DIELECTRICS FOR PLASTIC ELECTRONICS Ion gels offer exceptional performance as gate dielectrics in organic field effect transistors (OFETs) (Figure 9a).49−51 One key OFET metric is to deliver large current (1 mA) upon application of a low gate voltage (1 V). The drain current is proportional not only to carrier mobility, determined primarily by the semiconductor, but also to carrier density, dictated largely by the gate dielectric capacitance (C). We have shown that C for SOS and SMS ion gels is about10 μF/cm2, orders of magnitude larger than commonly employed materials such as SiO2. The excellent performance of an OFET with an ion gel gate dielectric is illustrated in Figure 9b. This high C can be mostly attributed to the formation of very thin electrical double layers (EDL) at the gate/gel and gel/semiconductor interfaces. Application of the Helmholtz equation (C ≈ ε/d) and assuming a d = 1 nm thick layer yields an estimated C ≈ 10 μF/cm2, in broad agreement with our experiments. Ion gels also offer much higher switching speeds (>100 kHz) than other common polymer electrolytes such as PEO/LiClO4. The RC time constant for EDL formation can be estimated, using σ and the gel thickness to determine R;52 the microsecond regime 2110
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Figure 8. (a) Structures of the copolymer and the ionic liquid; (b) Optical images of the free-standing ion gel containg 20% P(VDF-HFP) and 80% [EMI][TFSI]. Ion gel films were prepared by spin coating (upper left, ∼10 mm thick) or by solvent casting (lower left and right, ∼0.6 mm thick). Reproduced with permission from ref 47. Copyright 2012 Wiley.
Figure 10. (top) Electrochemiluminescent ion gel consisting of SMS, [EMIM][TFSI], and Ru(bpy)32+, driven by an applied ac voltage (60 Hz, peak-to-peak VPP = 3.6 V). Reproduced with permission from ref 59. Copyright 2014 American Chemical Society. (bottom) Electrochromic ion gels consisting of P(VDF-HFP), [BMIM][TFSI], ferrocene, and three different methyl viologen derivatives, bleached (at 0.00 V) and colored (at −0.70 V). Reproduced with permission from ref 62. Copyright 2016 American Chemical Society.
Figure 9. (a) Cartoon of an OFET device with a p-type semiconductor; (b) performance of a poly(3-hexylthiophene) OFET with an SMS/[EMI][TFSI] ion gel as gate dielectric. Reproduced with permission from ref 46. Copyright 2013 American Chemical Society.
requires a thickness below 1 μm. It should be noted that the detailed gating mechanism is likely more complicated and remains a topic of current interest. If the ions penetrate into the semiconductor, as appears to be the case for polymeric semiconductors such as poly(3-hexylthiophene), then the ion gel acts as an electrochemical rather than an EDL capacitor, with implications for the maximum switching speed.53 Our demonstration of the ability of ILs and ion gels to deliver exceptional C with little experimental complexity has sparked interest within the community in other gating applications,54 for example, in oxides, chalcogenides, and magnetic materials.55,56
which occurred when the oxidized and reduced species interdiffused and reacted, producing the luminescent excited state species Ru(bpy)32+,*. To achieve a more versatile dcdriven EL ion gel, we introduced a co-reactant (“fuel”), tetraammonium oxalate (Figure 11).60 In this case, the strong reductant CO2•− is formed by oxidation near the anode and participates in generating Ru(bpy)32+,* by a “co-reactant” pathway (see Figure 11c). We achieved electrochromism using equivalent SMS/[EMI][TFSI] ion gels but with methyl viologen (MV) as the chromophore.61 Ferrocene was added to complete the redox reaction, because its redox potential matches well with MV. The EC gel was inserted between two ITO-coated glass slides or plastic sheets to make a simple two-terminal EC device that changed color upon application of 0.7 V. The coloration efficiency was high, and the device exhibited good operational stability over 24 h even in air. To achieve different colors beyond the characteristic deep blue of MV2+, we prepared pcyanophenyl viologen dication (CN-PV2+) for green, and ptrifluoromethylphenyl viologen dication (CF3-PV2+) for red (see Figure 10).62 In this case, we reverted to the commercially available P(VDF-co-HFP) with [BMI][TFSI] or [BMI][BF4] to prepare the devices by the “cut-and-stick” approach. Overall, these results demonstrate that sub-1 V, flexible EC devices based on ion gels can be simply prepared, and are thus attractive components for printed electronics.
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LUMINESCENT AND ELECTROCHROMIC ION GELS Ion gels are inherently solid polymer electrolytes, but with high σ. As such they are candidates for a variety of electrochemical devices (ECD), such as inexpensive flexible displays.57,58 We have accordingly developed ion gels that display either electrochemiluminescence (EL) or electrochromism (EC). Figure 10 illustrates examples of both. In the EL case, the chromophore was Ru(bpy)32+ in an SMS/[EMIM][TFSI] ion gel. We sandwiched a thin layer of gel between two electrodes and applied an ac voltage.59 As the polarity switched, the chromophore was alternately reduced and oxidized by one electron. The primary “annihilation” pathway for EL was the recombination reaction Ru(bpy)31 + + Ru(bpy)33 + → Ru(bpy)32+, * + Ru(bpy)32 + 2111
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Figure 11. Mechanistic steps for electrochemiluminescence in the presence of oxalate co-reactant. Reproduced with permission from ref 60. Copyright 2014 American Chemical Society.
Figure 12. Robeson plot of permselectivity for CO2 over N2, versus CO2 permeability, for reported polymeric membranes. Star represents the approximate performance of SOS, SMS, and SPILS ion gels.
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SUMMARY We have shown that self-assembly of ABA triblock copolymers in an ionic liquid is a simple and extremely versatile strategy to prepare soft solids that retain the liquid state functionality of ionic liquids. Tuning of the block molecular weight and copolymer concentration allows ready control over the modulus and ionic conductivity of the resulting material. Thermoreversible and photoreversible gelation was accessed by appropriate design of the A block chemistry. Ion gel-based devices were processed via a wide variety of straightforward protocols, including solvent casting, spin coating, aerosol jet printing, photopatterning, transfer stamping, and “cut-andstick” manipulation. The application space for ion gels is huge and growing, including printed plastic electronics, electrochromic and electroluminescent displays, gas separation membranes, actuators,69 supercapacitors, and sensors. There is also great promise for biocompatible and biorenewable systems.70−73
GAS SEPARATION PERFORMANCE A fascinating property of certain ILs is a significant solubility preference for CO2 over other gases. For example, [EMIM][BF4] has been reported to dissolve CO2 25 (89) times more than CH4 (N2).63 This presents the intriguing possibility of inexpensive membrane-based separation and sequestration of CO2. Commercial gas separation membranes rely on subtle differences in free volume in glassy polymers. The separation is kinetically based and encounters an inevitable compromise between permselectivity and throughput: any structural improvement that enhances the mobility difference between two gases tends to reduce the absolute mobility of both.64 An IL-based membrane could circumvent this bottleneck by offering a thermodynamically based separation. The first challenge is to immobilize the IL while retaining its favorable selectivity and permeability, conferring sufficient mechanical strength for a thin layer membrane.65 Ion gels are a straightforward means to this end.66−68 We have shown that the SOS and SMS gels utilized successfully as gate dielectrics also confer excellent gas separation performance (at least at modest pressure drops). A standard representation of separation performance is the “Robeson plot”, in which permselectivity for a given gas pair is plotted against permeability of the more permeable gas. In such a plot, it is desirable to be as far to the upper right as possible, and Robeson drew (empirically) a straight line with a negative slope representing the current state of the art, “Robeson’s upper bound”. An example for CO2/N2 is shown in Figure 12, where the red points represent published values for polymer membranes, collected by Robeson.64 The star indicates the approximate performance we achieved with the SOS and SMS ion gels, plus a SPILS ion gel whose structure is given in Figure 1.66,67 We designed this polymerized ionic liquid (PIL) midblock to anchor the cation into the polymer network; at large pressure drops, this should suppress leakage of the ionic liquid. Furthermore, chemical cross-linking, as discussed in the context of Figure 4, could be a straightforward route to meeting the extra mechanical demands of gas separation applications.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported in part by the National Science Foundation through Award DMR-1206459, by the Air Force Office of Scientific Research under Grant FA9550-12-1-0067, and in part by Grants-in-Aid for Scientific Research No. 26620164 and No. 15H05495 (T.U.) from the Ministry of Education, Culture, Sports, Science and Technology of Japan. Selected measurements were carried out in the Characterization Facility, University of Minnesota, which has received capital equipment funding from the NSF through the UMN MRSEC program, under Award DMR-1420013. Collaborations and discussions with M. Watanabe, C. D. Frisbie, Y. Kitazawa, Y. He, B. Tang, S. Zhang, K.-H. Lee, J.-H. Choi, H.-C. Moon, and Y. Gu are gratefully acknowledged. 2112
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