Ind. Eng. Chem. Res. 1999, 38, 1415-1419
1415
Application of Experimental Design to the Conductivity Optimization for Waterborne Polyurethane Electrolytes Ten-Chin Wen* and Yeong-Jyh Wang Department of Chemical Engineering, National Cheng Kung University, Tainan 701, Taiwan
The optimization of conductivity for waterborne polyurethane (WPU) electrolytes and liquid electrolytes was studied by using response surface methodology (RSM) coupled with central composition design (CCD). Alternating current impedance and differential scanning calorimeter experiments were performed to obtain the ionic conductivities and thermal properties of WPU electrolytes, respectively. By means of RSM and CCD, the effect of lithium perchlorate (LiClO4) concentration and ratio of propylene carbonate (PC) to ethylene carbonate on conductivity for WPU electrolytes has been systematically investigated. Through this methodology, an empirical equation of conductivity for WPU electrolytes is obtained via regression analysis to be plotted as contour diagrams, facilitating the straight examination of experimental results. The contour plots show that the maximum conductivity (ca. 0.22 mS cm-1) can be obtained at a LiClO4 concentration of 0.9 M and a PC content of 37.5%. To confirm this optimum, three additional experiments were performed and the average conductivity at room temperature is 0.282 mS cm-1. Introduction Since the discovery that a number of polymersolvent-salt systems exhibit considerable conductivity, much research effort has been directed to find the optimal combination of polymer, solvent, and salt (Tobishima et al., 1984, 1990; Tobishima and Okada, 1985). The technical interest in these materials is that they can be used as solid polymer electrolytes (SPEs) in lithium batteries. Polyacrylonitrile (PAN) containing a plasticizer and a lithium salt (Abraham and Alamgir, 1993) was reported to possess a rather high ionic conductivity at room temperature. Normally, polymer electrolytes containing a plasticizer and a lithium salt are called mixed-phase or gel electrolyte (Wang et al., 1996). In our previous study (Cheng and Wen, 1998a), PEG- polyethylene glycol-based waterborne polyurethane (WPU) was used as the matrix in a gel electrolyte, which exhibited the best conductivity at room temperature of ∼10-3 S‚cm-1. Ethylene carbonate (EC) and propylene carbonate (PC) are attractive solvents for a high dielectric constant in the development of lithium batteries. Physical properties of EC and PC are listed in Table 1. The donor number (DN) is a parameter to measure the solvation power of the solvent toward Li+ (Tobishima and Okada, 1985). DN values are useful in determining the solvent environment around the deposited Li. In comparison to PC, EC has many desirable properties as an electrolyte solvent. For example, EC has a higher dielectric constant and lower viscosity than PC. These characteristics seem to be effective for the ionic dissociation of the salt and easy ion migration. However, the EC alone solvent has a shortcoming for practical use; it has a high melting point (36.4 °C). It is expected that this shortcoming can be improved by mixing cosolvent PC and * To whom correspondence should be addressed. Tel.: 8866-2757575, ext. 62656. Fax: 886-6-2344496. E-mail: tcwen@ mail.ncku.edu.tw.
EC. Tobishima and Yamaji (1983) reported the effectiveness of adding EC in improving ionic conductivity and Li cycling efficiency for EC/PC electrolyte system. Some fundamental studies have been reported on a binary cosolvent (Werblan et al., 1994; Srivastava and Samant, 1995; Salomon and Plichta, 1983; Matsuda et al., 1981). The interaction between salt and solvent is another important factor in developing electrolytes for lithium batteries. Tobishima et al. (1984) reported that ionic conductivity and Li cycling efficiency of LiClO4 in an EC/PC mixed system were higher than LiCF3SO3 or LiBF4. In our laboratory, we have successfully developed a series of WPU materials as SPEs for lithium batteries (Cheng and Wen, 1998b). Because of the different physical properties (see Table 1), most commercial electrolytes used the mixture of more than two solvents. In this work, EC and PC with the addition of LiClO4 in WPU films were used to study the optimization. Therefore, response surface methodology (RSM) coupled with central composition design (CCD) (Li et al., 1996; Box et al., 1978) was employed in planning the experiments for studying the effects of solvent composition and salt concentration on ionic conductivity. The data of experiments were subjected to regression analysis to determine the conditions required for the optimum ionic conductivity. Experimental Section Materials. PEG (Mw ) 2000, Showa Chemical Co.), used as a soft segment, was dried at 75 °C in a vacuum oven for 72 h; isophorone diisocyanate (IPDI) (Lancaster Chemical Co.) and dimethylol propionic acid (DMPA) (Aldrich Co.), used as the hard segment, were vacuumdried at 80 °C for 24 h. EC and PC (Merck Co.) were distilled at low pressure and stored over 3 Å molecular sieves before use. Acetone (Tedia Co.) and N-methyl-2pyrrolidinone (NMP) (Aldrich Co.) were immersed in 4 Å molecular sieves for more than a week before use. Di-
10.1021/ie980304i CCC: $18.00 © 1999 American Chemical Society Published on Web 03/13/1999
1416 Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 Table 1. Physical Propertiesa for PC and EC solvent ethylene carbonate (EC) propylene carbonate (PC)
η (cP, 40 °C)
(25 °C)
DN
Vs (Å3, 25 °C)
1.9
95.3
16.4
110.4
2.3
64.4
15.1
140.5
mp (°C, 760 Torr)
bp (°C, 760 Torr)
36.4
238
-49
241
References 11-14. Note: η, viscosity; , dielectric constant; DN, donor number; Vs, molecular volume; mp, melting point; bp, boiling point. a
n-butyltin(IV) dilaurate (DBTDL) (Wako Co.), ethylenediamine (EDA) (Merck Co.), butane sultone (BS) (Aldrich Co.), lithium hydroxide (LiOH) (Merck Co.) and LiClO4 (Aldrich Co.), were used without further treatment. Preparations of WPU Dispersion. WPU was prepared through our modified acetone process with NCO/ OH ) 1.5 (Yang et al., 1995, 1997). The solution of PEG and DMPA was added to the reactor and heated to 50 °C. IPDI and the catalyst DBTDL were then added to the mixture and reacted at 85 °C under a nitrogen atmosphere for 6 h. The final NCO-terminated polyurethane (PU) prepolymer were added to a suitable amount of acetone. LiOH, as the neutralizing agent, and an ethylenediamine-based chain extender bearing sulfonate groups in aqueous solution (see ref 15, neutralized with LiOH) were added immediately to the freshly prepared NCO-terminated PU prepolymer solution. The resulting mixture was then heated at the phase-inversion temperature of 50 °C, yielding PU anionmers in acetone. The stoichiometric ratio of LiOH to COOH was 1.0. Doubly distilled water was added to the neutralizing PU anionmer solutions at an agitation rate and water addition rate of 200 rpm and 2.0 mL/min, respectively. An aqueous dispersion of ≈30 wt % solids was obtained upon removal of acetone by rotary vacuum evaporation. Sample Preparation and Measurement. The films from the solvent evaporation method were obtained by casting the WPU dispersion solution on a Teflon disk, followed by drying at 45 °C for 2 days. The films were then removed and put into a glovebox for cell assembly. The impedance analysis of the electrolytes was performed using the CMS300 EIS system (Gamry Instrument, Inc., Warminster, PA) with a SR810 DSP lock-in amplifier (Stanford Research System, Inc., Sunnyvale, CA) under an oscillation potential of 10 mV from 100 kHz to 100 Hz. The WPU electrolytes were sandwiched by two stainless steel blocking electrodes for the conductivity test. Thermal analysis of WPU electrolytes was carried out by using a differential scanning calorimeter (DSC) (Du Pont, New Castle, DE) with a temperature range from -10 to 100 °C and at a heating rate of 10 °C/min. RSM-CCD. Response surface methodology (Box et al., 1978) is used to investigate a minimum/maximum for a specific response. It consists of a regression analysis which is performed on the data. Preceding the analysis, the experiments must be designed; that is, the explanatory variables must be selected and valued to be used during the actual experimentation. The experimental design for estimating the coefficient in a quadratic model is mostly employed as central composite design (denoted as CCD). CCD consists of the 2k vertices and 2k vertices of a k-dimensional “cube” and “octahedron”, respectively, as well as n0 center point replicates. In this study, k is assigned as 2 and consequently, 2k ) 4; 2k ) 4; n0 ) 3. Accordingly, these are 11 experiments from CCD (see Table 3) in this study.
Table 2. Variables in Original and Coded Unit for CCD variables in original unit variables in coded unit, X1, X2
PC content (wt %)
LiClO4 concentration (M)
-x2 -1 0 +1 +x2
14.64 25 50 75 85.36
0.29 0.5 1 1.5 1.71
Table 3. Design Matrix and Experimental Data from CCD for the Quadratic Form Fit
run
variables in coded unit X1 X2
1 2 3 4 5 6 7 8 9 10 11
+1 -1 +1 -1 0 0 0 -x2 +x2 0 0
a
σa of WPU electrolytes (mS‚cm-1) at 25 °C
σa of liquid electrolytes (mS‚cm-1) at 25 °C
0.0298 0.1065 0.1295 0.2474 0.2636 0.2710 0.2691 0.2098 0.0317 0.0732 0.0358
5.092 5.953 4.157 5.949 5.585 5.594 5.604 6.999 4.562 4.676 4.221
-1 -1 +1 +1 0 0 0 0 0 +x2 -x2
Conductivity.
Results and Discussion AC Impedance. AC (alternating current) impedance of WPU electrolytes with 50% (w/o) 1 M LiClO4 in EC and PC sandwiched between stainless steel (SS) electrodes was performed to obtain the Nyquist plots with an equivalent circuit as shown in Figure 1. The profiles show a straight line in a high-frequency region and could be simulated by an equivalent circuit of chargetransfer resistance (Rct) and double-layer capacitor (Cd) parallel to each other and bulk resistance (Rb) in series. The mathematics for impedance (Z) of this equivalent circuit can be expressed as
(
Z ) Rb +
Rct
)(
1 + (RctωCd)2
-
Rct2ωCd
)
1 + (RctωCd)2
j (1)
where ω is the angular frequency and j represents the imaginary part of Z. From the denominator, 1 + (RctωCd)2 in eq 1, the order of magnitude of this dimensionless group, RctωCd, in comparison to unity is very important to the analysis of a physical system. According to the engineering viewpoint, there are two extreme cases: (1) when RctωCd . 1, then Z f Rb, while (2) when RctωCd , 1, then Z f Rb + Rct. In this study, since the charge-transfer reaction is extremely difficult to obtain under oscillation potential due to SS electrodes, RctCd is too large to have the arc for locating Rb + Rct. The straight line represents the response of a Cd parallel to a large Rct. Thus, with
Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 1417
Figure 3. DSC thermograms of WPU electrolytes. WPU films containing 50% (w/o) electrolytes of 1 M LiClO4 in (1) EC, (2) EC + PC (1:1), and (3) PC. Figure 1. Nyquist plot of SS/WPU electrolytes/SS at 25 °C. WPU films containing 50% (w/o) electrolytes of 1 M LiClO4 in (1) EC and (2) PC. Films thickness: (1) 150 µm and (2) 170 µm. Electrode area: 0.785 cm2. Frequency range: 100 kHz∼100 Hz.
Figure 2. Arrhenius plots of conductivity for WPU electrolytes. WPU films containing 50% (w/o) electrolytes of 1 M LiClO4 in (1) PC and (2) EC.
increasing ω, the straight line intercepts the real axis to locate Rb. For presenting data by the conductivity (σ) value, Rb obtained from impedance studies is transferred by using σ ) (1/Rb)(l/A), where l and A represent the film thickness and surface area of an electrode, respectively. The Arrhenius plots of conductivity for WPU electrolytes were drawn in Figure 2. It is clear that the conductivity of a WPU electrolyte containing 50% (w/o) 1 M LiClO4 in PC obeys Arrhenius law and exhibits a straight line (line 1). This implies that the conductive environment of Li+ in this WPU electrolyte is liquidlike and remains unchanged in the investigated temperature region. As for the WPU electrolyte containing 50% (w/o) 1 M LiClO4 in EC, its Arrhenius plot shows a two-segmental
line (line 2) separated by a transition of ≈25 °C. This result might be inferred that a certain process occurred in the WPU electrolyte at ≈25 °C. At temperatures > 25 °C, the WPU electrolyte with EC has the higher conductivity than that with PC. It can be reasonably explained that EC possessing the higher dielectric constant can dissociate more LiClO4 (cf. PC). At temperatures < 25 °C, the conductivity of the WPU electrolyte with EC becomes very sensitive to temperature, and its conductivity is lower than that with PC. This might be attributed to the melting temperature (Tm) of EC (see DSC results). It is clear that, in our investigated WPU electrolytes, EC is not suitable to be used alone for ambient temperature service in lithium batteries. DSC. To confirm the above results, WPU electrolytes with LiClO4 in (1) EC, (2) EC + PC (1:1), and (3) PC were subjected to thermal analysis using DSC at the heating rate of 10 °C/min and the results are shown in Figure 3. There is an endothermic peak on curve 1 between 15 and 40 °C, and no peaks were found on curves 2 and 3, being attributed to the different Tm of EC (ca. 36 °C) and PC (ca. -49 °C), respectively. Meanwhile, Tm of the cosolvent of EC and PC (1:1) should be much lower than the ambient temperature. It is because commercial electrolytes are usually employed with the cosolvent of EC with the other solvent. Consequently, the optimization of cosolvent and salt is interesting to many researchers. RSM-CCD. RSM (Li et al., 1996) is a powerful tool used to study the optimization of PC, EC, and LiClO4 for the conductivity of WPU electrolytes and the pure liquid electrolytes. Accordingly, CCD experiments were performed. Design variables in a code unit and original unit are listed in Table 2, and the design matrix with the corresponding results are listed in Table 3. To quantitatively elucidate the effects of these two variables, the conductivity of WPU electrolytes in Table 3 was subjected to regression analysis. The analysis generated the following equation:
σ ) 0.2679 - 0.0558X1 + 0.0367X2 - 0.0634X12 0.0965X22 - 0.0103X1X2 (2) where the X1 and X2 terms respectively represent PC content and LiClO4 concentration in a coded unit. The
1418 Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 Table 4. Analysis of Variance for Fit Conductivity of WPU Electrolytes from CCD at 25 °C source model error total R2 ) 0.9219
degree of freedoms
sum of square
mean square
5 5 10
0.0963 0.0082 0.1045
0.0193 0.0016
F 11.802
analysis of variance is presented in Table 4. The test statistics, F and R2, are defined:
F)
MSR , MSE
R2 )
SSR SST
where MSR is the mean square of regression, obtained by dividing the sum of squares of regression by the degree of freedom. MSE is the mean squares of error from the analysis of variance. If the calculated value of F is greater than that in the F table at a specified probability level (i.e., F(P-1,ν,1-R)), then a “statistically significant” regression model is obtained, where ν is the degree of freedom of error and P is the number of parameters. F(P-1,ν,1-R) is the F value at the R probability level. The multiple correlation coefficient, R2, defined as R2 ) SSR/SST, where the SSR and SST terms respectively represent the sum of squares of regression and sum of squares of the total, gives an indication of the regression model fit. R2 is the correlation coefficient, with a value close to 1, meaning a perfect fit to the experimental data. The multiple correlation coefficient, R2, for the conductivity of WPU electrolytes is equal to 0.92, and the regression model is considered an accurate representation of the experimental data. Now, to clarify the role of WPU film in conductivity, experiments by CCD for liquid electrolytes were performed. The design matrix and results for liquid electrolytes are also shown in Table 3. Again, the conductivity data of liquid electrolytes were subjected to regression analysis and generated the following equation:
Figure 4. Constant conductivity of WPU electrolytes contour lines against PC content and LiClO4 concentration. (Note: bottom X1 and left X2 coordinates are arbitrary level values as used in Table 2.)
σ ) 5.5943 - 0.7625X1 - 0.0370X2 + 0.1365X12 0.5297X22 - 0.2328X1X2 (3) R2
with a value close to 1 indicates that this regression model is statistically significant. Contour Plots. To facilitate a straightforward examination of the conductivity of WPU electrolytes on PC content and LiClO4 concentration, the contour plots (Figure 4) were constructed by using eq 2. The maximum conductivity (ca. 0.22 mS‚cm-1) was in the region of 25∼75% PC and 0.75∼1.1 M LiClO4. The horizontal oval shape in the maximum region suggests that the effect of PC content on conductivity is not obvious. In contrast to PC content, the LiClO4 concentration has a great influence on conductivity in the maximum region. Consequently, the maximum conductivity of WPU electrolytes occurs at approximately 37.5% PC and 0.9 M LiClO4. Figure 5 shows the contour plots (solid lines) of liquid electrolytes, which were constructed by eq 3 while the dashed lines from Figure 4 were used for comparisons. Note that contour plots are parabolic in LiClO4 concentration and the maximum conductivity occurs at ≈1.0 M, almost the same as the WPU electrolytes. This result implies that the effect of polymer chains on conductivity is not obvious for the variable of LiClO4 concentration.
Figure 5. Constant conductivity of liquid electrolytes (solid line) and WPU electrolytes (dashed line) contour lines against PC content and LiClO4 concentration. (Note: bottom X1 and left X2 coordinates are arbitrary level values as used in Table 2.)
In both WPU and liquid electrolytes, the increase in the LiClO4 concentration from 0.25 to 1.75 M renders an increase in the Li+ ion and a decrease in the degree of ionic dissociation of LiClO4 at each composition of the mixtures. The increase in the Li+ ion provides an increase in conductivity while the decrease in the degree of ionic dissociation gives an increase in viscosity due to the association of Li+ and ClO4- to form a solventseparated ion pair (Prabhu et al., 1993), resulting in a decrease in conductivity. According to the above assertions, the optimum LiClO4 concentration exists in ≈0.9 and 1 M, respectively, for WPU and liquid electrolytes to achieve the maximum conductivity. The slight discrepancy in the LiClO4 concentration might result from the complicated interactions among polymer chains, solvent, and salt. The maximum conductivity for liquid electrolytes occurs at ≈10% PC, approximating whole EC, while for WPU electrolytes, the maximum at ≈37.5% PC in the binary EC + PC cosolvent was observed. This difference
Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 1419 Table 5. Confirmation Experiments for Conductivity of WPU Electrolytes at Optimum Conditions electrolyte composition LiClO4 concentration (M)
PC content (%)
1M 1M 0.9 Mb
100 0 37.5
a
σa (mS‚cm-1) for WPU electrolytes at 25 °C 1 2 3 0.068 0.125 0.275
0.063 0.122 0.287
0.060 0.118 0.283
Conductivity. b At optimum conditions.
might be explained by the fact that a certain amount of PC in polymer chains plays a role in opening a channel for the migration of the ion complex. From the molecular structure, an extra CH3- side chain of PC renders the more complicated interaction between the polymer chain and the solvent molecular (cf. EC). However, an electrolyte with the higher dielectric constant (sufficient degree of ionic dissociation) solvent (e.g., EC) contains the higher ionic concentration. Accordingly, the conductivity of liquid electrolytes in the EC richer region is higher than that in the PC richer region. To understand the solvation tendency of Li+ in the cosolvent of EC and PC, the DN value was used to explain our experimental results (Burger, 1983). In Table 1, the DN value of EC (16.4) is considerably higher than that of PC (15.1). Therefore, the Li+ solvation tendency of EC is stronger than that of PC. Therefore, the conductivity of liquid electrolytes decreases with increasing PC content. The discrepancy of the maximum conductivity between liquid and WPU electrolytes is reasonably attributed to the differences between ion-solvent and ion-solventpolymer interactions. Confirmation Experiments. To confirm the validity of the statistical experimental strategies, three additional experiments based on the above optimum condition (0.9 M LiClO4 in a cosolvent of 37.5% PC and 62.5% EC) were carried out. The repeated conductivities of WPU electrolytes for this optimum and pure EC as well as PC were listed in Table 5. These reproducibly high-conductivity values (0.275, 0.287, and 0.283) for WPU electrolytes at the optimum condition validate that RSM coupled with CCD is a useful method for optimization. In addition, the other two experiments for 1 M LiClO4 in pure EC and PC have much lower conductivities than the maximum one (Table 5).
Conclusion RSM via CCD experiments and regression analysis to obtain an empirical model for plotting contour diagrams is validated as a good optimization tool in searching for the maximum conductivity for WPU electrolytes or liquid electrolytes. The optimum condition of conductivity occurs in the region of 0.9 M LiClO4 and 37.5% PC and 1 M LiClO4 and almost whole EC, for WPU and liquid electrolytes, respectively. The maximum conductivity of WPU electrolytes can be located from contour plots as ≈0.22 mS‚cm-1 at room temperature. The confirmation experiments for WPU electrolytes shows 0.282 mS‚cm-1 for average maximum conductivity.
Acknowledgment The financial support for this work by the Nation Science Council of the Republic of China under contract NSC 87-2214-E-006-026 is gratefully acknowledged. Literature Cited Abraham, K. M.; Alamgir, M. Ambient-Temperature Rechargeable Polymer-Electrolyte Batteries. J. Power Sources 1993, 43, 195. Box, G. E. P.; Hunter, W. G.; Hunter, J. S. Statistics for Experiment; John Wiley & Sons: New York, 1978. Burger, K. Solvation Ionic and Complex Formation Reactions in Non-Aqueous Solvents. Elsevier Scientific Publishing Co.: New York, 1983. Cheng, T. T.; Wen, T. C. Novel Waterborne Polyurethane Based Electrolytes for Lithium Batteriess(II) The Effect of Adding LiCF3SO3-PC. Solid State Ionics. 1998a, 106, 161. Cheng, T. T.; Wen, T. C. Novel Waterborne Polyurethane Based Electrolytes for Lithium Batteriess(IV) The Influence of DMPA/ PEG Ratios on Conductivity. J. Chin. Inst. Chem. Eng. 1998b, 29, 327. Li, Y. J.; Chang, C. C.; Wen, T. C. Application of Statistical Experimental Strategies to H2O2 Production on Au/Graphite in Alkaline Solution. Ind. Eng. Chem. Res. 1996, 35, 4767. Matsuda, Y.; Nakashima, H.; Morita, M.; Takasu, Y. Behavior of Some Ions in Mixed Organic Electrolytes of High Energy Density Batteries. J. Electrochem. Soc. 1981, 128, 2552. Prabhu, P. V. S. S.; Kumar, T. P.; Namboodiri, P. N. N.; Gangadharan, R. Conductivity and Viscosity Studies of Ethylene Carbonate Based Solutions Containing Lithium Perchlorate. J. Appl. Electrochem. 1993, 23, 151. Salomon, M.; Plichta, E. Conductivity and ion association of 1:1 Electrolytes in Mixed Aprotic Solvents. Electrochim. Acta 1983, 28, 1681. Srivastava, A. K.; Samant, R. A. Some Conductance and Potentiometric Studies in 20 mass % Propylene Carbonate + Ethylene Carbonate: Application of Hydrogen and Quinhydrone Electrodes. J. Electroanal. Chem. 1995, 380, 29. Tobishima, S. I.; Yamaji, A. Ethylene Carbonate-Propylene Carbonate Mixed Electrolytes for Lithium Batteries. Electrochim. Acta 1983, 28, 267. Tobishima, S. I.; Okada, T. Lithium Cycling Effiency and Conductivity for High Dielectric Solvent/Low Viscosity Solvent Mixed System. Electrochim. Acta 1985, 30, 1715. Tobishima, S. I.; Yamaki, J. I.; Okada, T. Ethylene Carbonate/ Ether Mixed Solvents Electrolyte for Lithium Batteries. Electrochim. Acta 1984, 29, 1471. Tobishima, S. I.; Arakawa, M.; Yamaki, J. Ethylene Carbonate/ Linear-Structured Solvent Mixed Electrolyte System for HighRate Secondary Lithium Batteries. Electrochim. Acta 1990, 35, 383. Wang, Z.; Huang, B.; Huang, H.; Xue, R.; Chen, L.; Wang, F. A Vibrational Spectroscopic Study on the Interaction between Lithium Salt and Ethylene Carbonate Plasticizer for PANBased Electrolytes. J. Electrochem. Soc. 1996, 143, 1510. Werblan, L.; Balkowska, A.; Warycha, S.; Romiszowski, P.; Cai, W. D. Conductivity of Dilute and Concentrated LiAsF6 Solutions in Acetonitrile + Ethylene Carbonate and Ethylene Carbonate + Propylene Carbonate Mixtures. Some Thermodynamic Properties of Pure Acetonitrile + Ethylene Carbonate Mixtures. J. Electroanal. Chem. 1994, 374, 141. Yang, C. H.; Lin, S. M.; Wen, T. C. Application of Statistical Experimental Strategies to the Process Optimization of Waterborne Polyurethane. Polym. Eng. Sci. 1995, 8, 722. Yang, C. H.; Li, Y. J.; Wen, T. C. A Mixture Design Approach to PEG-PPG-PTMG Ternary Polyol-Based Waterborne Polyurethanes. Ind. Eng. Chem. Res. 1997, 36, 1614.
Received for review May 18, 1998 Revised manuscript received January 7, 1999 Accepted January 18, 1999 IE980304I
