Ind. Eng. Chem. Res. 1993,32, 3128-3134
3128
Synthesis of Polymer Electrolytes with High Ion Conductivity Using Experimental Design of Multicomponent Polymer Systems Martin J. Schneider,'.+ Clemens Elster,i Rolf Mulhaupt2.t Josef HonerkampP Roland Nolte,l Volker Wittwer,l and Konstantin Ledjeffl Institut fur Makromolekulare Chemie der Universitat Freiburg, Stefan-Meierstr. 31, Hermann Staudinger Haus, 0-79104 Freiburg im Breisgau, Federal Republic of Germany; Freiburger Materialforschungszentrum, Stefan-Meier-Str. 31 A, 0-79104 Freiburg im Breisgau, Federal Republic of Germany; Fakultat fur Physik der 79104 Freiburg im Breisgau, Federal Republic of Germany; Universitat Freiburg, Hermann-Herder-Str. 3, 0and Fraunhofer-Institut fur Solare Energiesysteme, Oltmannstr. 22, 0-79100 Freiburg im Breisgau, Federal Republic of Germany
Transparent and opaque solid polymer electrolytes with high lithium ion conductivity were synthesized using various photocurable acrylates and methacrylates in combination with low molecular weight poly(ethy1ene oxides) (PEO)and LiC104. The methods of experimental design and optimization were applied to identify the optimum composition range of acrylic monomers, PEO, and LiC104. The highest ion conductivities were found to be 8.5 X 10-6 Q-l cm-l for multiphase and 3.7 X 106 Q4 cm-1 for single-phase multicomponent systems a t 25 "C. The polymer electrolytes are used for electrochromic "smart window" applications. 1. Introduction Research in the field of polymer electrolytes dates back to the original work of Fenton et al. (19731, Wright (19751, and Armand et al. (1979). They found that poly(ethy1ene oxide) is able to dissolve salts with low lattice energies and measured the ion conductivities of such polymer electrolytes. In the synthesis of new polymers, the use of ethylene oxide units and other Lewis bases containing 0, N, and S has led to a wide variety of polymer electrolytes (see MacCallum and Vincent (1987) and Ido and Imachi (1989)). Most of the applications of the polymer electrolytes, e.g., high-energy-densityelectrochemicalbatteries and electrochromic windows with adjustable transmission or reflection (electrochromic "smart windows"), require high ion conductivities; see, for instance, Deroo (1990) and Kobayachi et al. (1987). For the production of electrochromic smart windows, it is advantageous to use liquid acrylic monomers, because these monomers can fill the gap between the electrochromic layers and are polymerized subsequently by UV irradiation. In addition to difunctional oligo(ethy1ene oxide) dimethacrylate (abbreviated PE0400DMA), with nine ethylene oxide units corresponding to a number-average molecular weight of 400 g/mol, monofunctional acrylates and methacrylates have been used. The structures of these monomers are summarized in Table I. Ethyltriethylene glycol monomethacrylate (ETMA) represents a reactive plasticizer which can be copolymerized to produce graft copolymers with pendant triethylene glycol segments. As additional comonomers, hydroxyethyl acrylate (HEA), hydroxyethyl methacrylate (HEMA), NJV-dimethylaminoethyl acrylate (DMAEA), NJV-dimethylaminoethyl methacrylate (DMAEMA), and Nfl-dimethylaminopropyl methacrylamide (DMAPMA) have been used in order to vary the polarities of the polymer backbones and to compare acrylates with methacrylates. Oligomeric dihydroxy-terminated ethylene oxide polymers of 200, 400, and 600 g/molnumber-average molecular weight have been + Institut ftir Makromolekulare Chemie der Universitat Freiburg. t Freiburger Materialforschungszentrum. 1 Fakulut far Physik der Universiat Freiburg. 1 Fraunhofer-Institut fijr Solare Energiesysteme.
used as nonreactive, high boiling point plasticizers. All formulations investigated contain lithium perchlorate (LiC104) as a salt because of its attractive combination of low lattice energy and high electrochemical stability. To initiate photo-cross-linking reactions of the plasticized mixture of mono- and difunctional acrylate and methacrylate monomers, l-(4-isopropylphenyl)-2-hydroxy-2methylpropan-1-one has been used as the photoinitiator. In practice, a large number of formulation experiments are required to empirically find the optimum concentrations of 11components, i.e., seven monomers, three oligo(ethylene oxide) plasticizers, and the LiC104 salt. Therefore, tools from the theory of experimental design and optimization have been introduced to guide and minimize formulation experiments for the development of polymer electrolytes with high ion conductivity, which are suitable for smart window applications. In section 2 of this paper, the synthesis of the photocurable polymer electrolyte films and the measurement technique are described. In section 3, the theory of experimental design is introduced. Section 4 contains the procedures and results, and section 5 closes with the conclusions of this work. 2. Experimental Section 2.1. Chemicals. The monomers (Table I) were supplied by Rohm; the photoinitiator (1-(4-isopropylphenyl)-2hydroxy-2-methylpropan-1-one) Darocur 1116 was supplied by Ciba; and the dihydroxy-terminated oligo(ethylene oxides) (PEO 200, 400, and 600), ethanol, and LiC104 were supplied by Aldrich. The acrylic monomers were used without further purification. The PEO were dried under vacuum at 90 "C for 8 h. LiC104 was dried under vacuum at 160 "C for 4 h. The ethanol had previouslybeen stored over a molecular sieve. All subsequent manipulations of these materials were carried out in a nitrogen atmosphere. The LiC104 was dissolved in ethanol (0.5 g/mL). 2.2. Synthesis of the Polymer Electrolyte Films. The monomers, the PEO, and the solution of LiC104 (see Tables 11,111,and VI) were mixed with the photoinitiator Darocur 1116 (10 pL/g of the mixture). The ethanol was removed under reduced pressure at 303 K. The mixture
0888-588519312632-3128$04.00/0 0 1993 American Chemical Society
Ind. Eng. Chem. Res., Vol. 32, No. 12,1993 3129 Table I. Monomer Structures
Table 111. First 70 Experimental Runs* ~~
monomer
abbreviation
CH~(CHS)CO~(PEO~~~)-~~C(CHB)=CH* PE0400DMA C H ~ ( C H S ) C O ~ - ( C H ~ C H ~ O ) ~ - C H ~ C HETMA ~ CH~(CHI)CO~-CH~CH~OH CH~HCO~H~CHZOH CH~(CHS)CO~-CH~CH~N(CH& CH~HCO~H~CHZN(CH~)~
HEMA HEA DMAEMA DMAEA CH+~(CH~)CONH-CH~CH~CH~N(CH~)Z DMAPMA
Table 11. Abbreviations and Variations of the Components component PE0200 PE0400 PE0600 PE0400DMA HEMA HEA DMAEA DMAPMA DMAEMA LiClOh ETMA
class plasticizer plasticizer plasticizer monomer monomer monomer monomer monomer monomer salt monomer
abbrev.
lower limit, wt %
2 0
upper limit, wt % 40 40 40 98 96 96 96 96 96 40 96
was stored between two parallel glass plates coated with polyethylene. The polymerization reaction was initiated by UV irradiation (Xenon lamp 1500W) for 30min. Films of approximately 270-pm thickness were obtained, which were dried afterward under vacuum at 60 "C for 5 days. 2.3. ConductivityMeasurements. The conductivity of the polymer electrolytes was determined by AC impedance measurements over a frequency range from 1Hz to 100 kHz, using a Schlumberger 1255 HF frequency response analyzer coupled to a Schlumberger 1286 electrochemical interface and a personal computer. Two parallel symmetrical plane electrodes of platinum, with a surface area of 1.0 cm2, were used in the electrochemical cell. The values of conductivity given in this paper correspond to a temperature of 25 "C.
3. Experimental Design The amount of information gained from experiments, e.g., the certainty of conclusions drawn from the obtained data, depends on the design of these experiments. Hence, the efficiency of experiments can be maximized by appropriate planning. This concept shall be described briefly in the following. Let y be some quantity depending on the settings of the ...,xn + 3, i.e., y = y ( 3 ) and assume a relation variables XI, for y in terms of 3 and known functions CY = 1, ...,p ) :
va,
for instance n
y(3)= a
+Caaxa a=l
In order to estimate the unknown coefficients {ua,CY = 1, ...,p},a number of experiments, say N , may be performed, and the coefficients will be determined by least squares, i.e., by minimizing
run XI x2 x 3 1 0 0 4 0 2 0 0 0 3 0 020 4 4 0 0 0 5 20 0 20 6 0 0 0 7 0 0 0 8 0 40 0 9 4 0 0 0 10 0 0 0 11 0 4 0 0 12 0 0 0 13 0 0 0 14 0 0 0 15 40 0 0 16 0 0 0 17 0 0 0 18 0 0 0 19 0 0 0 20 0 0 0 21 0 0 0 22 0 0 20 23 0 4 0 0 24 40 0 0 25 20 0 20 26 0 40 0 27 0 20 20 28 0 0 0 29 0 0 40 3040 0 0 31 0 0 0 32 0 0 0 33 0 0 0 34 0 0 0 35 0 0 0 36 0 0 40 37 0 20 20 38 0 40 0 39 0 0 0 40 20 0 0 41 0 0 0 42 0 0 0 43 0 0 0 44 0 2 0 0 45 0 0 0 46 20 20 0 47 018 0 48 0 0 0 49 0 0 0 50 0 0 4 0 51 20 0 0 52 0 0 0 53 0 40 0 54 0 0 0 55 0 0 40 56 0 0 0 57 0 4 0 0 58 0 0 0 59 0 0 0 60 0 0 0 61 0 0 40 62 0 0 0 63 20 20 0 64 0 0 40 65 0 0 0 66 40 0 0 67 0 0 0 68 40 0 0 69 5 5 5 70 0 18 0
x4
2 2 2 58 15
xs
X6
x7
XS
xs
0 0 0 5 6 0 0 0 0 047 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 49 0 0 049 0 5 0 13 0 0 40 5 0 0 0 0 5 3 49 0 049 0 0 5 8 0 0 0 0 0 2 0 47 0 0 0 2 0 0 0 96 0 5 0 0 0 0 93 2 0 56 0 0 0 2 0 0 0 47 0 49 0 49 0 0 0 2 0 58 0 0 0 2 0 096 0 0 2 0 0 0 47 49 2 49 47 0 0 0 2 0 0 38 0 0 2 0 0 056 0 2 0 0 56 0 0 50 0 0 0 0 0 2 0 56 0 0 0 15 0 0 0 0 0 49 0 0 0 0 0 58 0 0 0 0 0 2 0 0 056 0 5 0 0 0 55 0 9 8 0 0 0 0 0 2 0 49 0 0 47 2 58 0 0 0 0 2 0 0 47 0 0 5 0 13 0 0 40 5 0 0 49 0 0 15 0 0 0 0 0 2 47 0 0 0 0 2 38 0 0 0 0 60 0 0 0 0 0 2 49 0 0 47 0 2 0 0 5 8 0 0 2 038 0 0 0 49 49 0 0 0 0 2 0 0 48 0 0 2 0 0 0 0 0 5 0 0 0 0 55 2 0 47 0 49 0 256 0 0 0 0 2 0 0 0 0 0 49 0 0 0 0 49 2 0 0 56 0 0 2 0 49 47 0 0 2 0 56 0 0 0 2 47 0 49 0 0 256 0 0 0 0 2 49 0 0 0 47 2 0 0 49 47 0 18 0 0 40 0 40 15 0 0 0 0 0 5 0 0 0 0 0 10 0 0 0 0 0 2 0 0 56 0 0 2 96 0 0 0 0 15 0 0 0 0 0 2 096 0 0 0 2 56 0 0 0 0 10 10 10 10 10 10 10 0 0 0 0 0
~
210 XII
S
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 40 2 2 2 40 2 2 10 2 10 2 2 2 40 2
8 6 5 7 2 3 9 4 3 7 8 5 10 10 5 9 8 4 4 10 9 5 6 2 7 5 2 8 7 2 10 8 8 10 2 4 2 2 9 6 9 10 4 9 10 2 5 6 10 6 3 9 2 6 5 8 4 10 9 6 2 8
2
40 2 2
2 2 2 40 4 0 2 4 0 4 0 2 10 2 40 2 2 10 2 2 2 2 2 2 2 2
2 2 40 2 2 2
10 2 2
15 2
logC 0 -7.36 4 9 -9.07 7 6 -7.3 0 -4.6 43 -4.46 9 6 -7.39 0-12 0 -5.61 0 -4.99 0 -7.9 0 -4.8 49 -7.79 0 -12.7 0 -11.2 0 -5.32 49 -9.93 0 -8.76 0 -7.04 0 -8.24 0 -12.7 0 -9.22 0 -7.8 0 -6.98 0 -4.93 0 -4.92 0 -5.67 35 -4.97 49 -7.64 0 -4.83 0 -6.65 0 -7.21 0 -7.63 0 -10.53 0 -7.39 49 -7.43 0 -6.36 4 -5.11 43 -4.71 49 -9.95 0 -6.97 0 -8.3 0 -10.7 0 -6.89 0 -6.6 0 -12.7 0 -5.25 7 8 -6.96 0 -8.44 0 -10.7 0 -6.65 68 -5.27 0 -10.27 0 -5.33 0 -9.01 0 -5.89 0 -10.96 0 -6.43 0 -12.1 0 -10.4 0 -9.01 43 -4.89 55 -8.64 48 -4.36 0 -5.45 0 -11.7 35 -4.38 0 -8.23 0 -5.98 10 -8.26 70 -6.96
1 2 10 2 7 5 9 4
The rows contain the concentrations in w t % of the components
XI,
...,x l l together with the logarithm of the obtained conductivity
(3)
C and the corresponding solidity S. The solidity was estimated on a scale of 0 (pasty) to 10 (solid).
with respect to the {ua,CY = 1,...,p } . yp denotes the value for the i-th measurement and Zi the corresponding settings of the variables. Denoting by X the N X p design matrix:
{Xi: = fj(fi), j = 1, ...,p ; i = 1, ...,N) and by P.the N X 1 vector of observations, the p x 1 vector of estimated coefficientsB defined by the minimum of (3)maybe written
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Ind. Eng. Chem. Res., Vol. 32, No. 12, 1993
as 6 = (XTX)-lXTjI"
(4)
where XT stands for the transpose of X. Experimental data are always contaminated by measurement errors, or, more precisely, the experimental data {yu(Zi),i = 1, ...,N) represent N random variables { Y(Zi), I = 1, ...,N) which are the sum of the true valuesy(2i) and random variables vi:
Y(Q = y(zi)
+ vi,
i = 1, ...,N
(5)
We shall assume that the N random variables {vi, i = 1, ...,N) are independently distributed with zero mean and equal variance a2 independent of the chosen {Zi, i = 1, ..., N). The measurement errors will lead to uncertainties in the estimated coefficients21 as represented by the variancecovariance matrix cov(a,,ag) = a2(XTX)-' (6) Note that this variance-covariance matrix is essentially determined by the location of the measurements {Zi, i = 1, ..., N), i.e., the chosen design. Various (optimality) criteria have been proposed in order to measure the quality of a chosen design. Of these, a very important one is the determinant criterion: A design {Zi, i = 1, ...,N) is called d-optimal if it maximizes the determinant of the information matrix XTX. An important property of d-optimality is that in the case of normally and independently distributed measurement errors (with zero mean and common variance) a d-optimal design leads to a minimum confidence region for the estimated coefficients 21 among all possible designs (consisting of N trials). Apart from variance optimal designs like d-optimal designs, there are also a number of classical designs for response surface modeling. However, in contrast to d-optimal designs classical designs are restricted by the number of possible trials N , and they assume a specific experimental region for the variables XI, ...,x,, like a cube or a regular simplex. Thus, d-optimal designs are more flexible in the type of experimental situation that they can accommodate. For further reading on experimental design, see, for instance, Dodge et al. (19881, Cornel1 (19811, and Box et al. (1987).
Applications and Results 4.1. Modeling Conductivity. Multicomponent polymer electrolytes are composed of photocurable acrylic monomers as summarized in Table I, low molecular weight PEO (PE0200, 400, 600), and LiC104. Altogether 11 components were chosen, and each component contributes to the conductivity of the polymer. The mixture of the substances may show special effects with regard to the conductivity. In order to detect such effects, a model for the conductivity is introduced. Because the ion conductivity C itself typically varies over several decades, its logarithm was modeled. The conductivity depends only on the concentrations of the components. A quadratic model was assumed to be adequate, i.e. 4.
10
10
10
Xll
= 100 wt % - Exa a=l
where the (xi, i = 1, ..., 11) denote the concentrations of
Table IV. Analysis of Variance (ANOVA) of the First Model Set Up for the Conductivity sourceof degrees sumof mean variation of freedom squares squares Pratio significance total 69 379.1 regression 47 378.6 8.1 335.4 0.0 residual 22 0.53 0.02
the different components. Details are given in Table 11. A preliminary test showed that, for high concentrations of plasticizers such as 40 w t 5% and low concentrations of PE0400DMA less than 2 w t %, the obtained polymer electrolytes were soft pasty materials. Thus, we had to introduce constraints on variations of the individual concentrations. More specifically, we restricted the concentration of the plasticizers to less than 40 wt % and the concentration of PE0400DMA to more than 2 w t %. Furthermore, the overall concentrations of monomers should be greater than 40 w t % ,and the concentration of LiC104 was varied between 2 and 40 wt %. Hence, we added the constraints 3
Owt%5~xi
