Macromolecules 1998, 31, 8653-8654
8653
CORRECTIONS
Joanne L. Budzien, John D. McCoy, John G. Curro, Randall A. LaViolette, and Eric S. Peterson: The Solubility of Gases in Polyethylene: Integral Equation Study of Standard Molecular Models. Volume 31, Number 19, September 22, 1998, p 6669. In the attractive component of the WCA decomposition of the potential defined by eq 2.9b, the cutoff was inadvertently programmed to be at σAB rather than the stipulated 21/6σAB. Correcting the WCA calculation changes a number of tables and figures: the corrected ones (Tables 1, 6, and 7 and Figures 2 and 3) are presented here. Table 1. Potential Parameters and Solubility Coefficient Ratio SPRISM/SMD (%) for Comparison with the Molecular Dynamics Study Reported by van der Vegt et al.11
gases
σ (Å)
(K)
N2 Ar O2 CH4 CH2
3.70 3.40 3.50 3.73 3.93
95 120 110 150 47
SPRISM/ SMD(BH)
SPRISM/ SMD(WCA)
SPRISM/ SMD(av of BH and WCA)
59 ( 7 50 ( 5 57 ( 6 63 ( 8
130 ( 10 88 ( 9 120 ( 10 152 ( 9
95 69 88 107
Table 6. Comparison of Solubility with Experimental Data5 as SPRISM/Sexp (%)a gas Tc(K)
a. NERD CH2 Potential8 N2 Ar O2 CH4 Kr Xe CO2 C2H6 126 150.8 154.8 191 209.4 289.4 304 305.42
HCB WCA av 2HCB BH BAH WCA av BAH BH VHCB WCA av VHCB BH MS WCA av MS BH
175 142 109 178 148 118 158 130 101 220 183 146
169 142 115 159 136 112 185 155 124 161 142 122
gas Tc(K)
N2 126
b. TRaPPE CH2 Potential9 Ar O2 CH4 Kr Xe 150.8 154.8 191 209.4 289.4
CO2 304
C2H6 305.4
2HCB WCA av 2HCB BH BAH WCA av BAH BH VHCB WCA av VHCB BH MS WCA av MS BH
172 121 69 176 127 77 155 111 66 218 158 98
173 127 80 162 121 79 185 137 88 159 124 89
109 66 22 362 237 111 112 75 38 342 231 119
169 113 56 255 150 45 165 99 33
148 127 105
155 129 103 172 142 112
142 106 70
155 114 72 172 126 80
122 97 72 103 81 59 91 70 49 199 161 123
125 85 45 99 68 37 90 60 29 206 143 79
158 127 95 126 100 74 237 186 134 180 142 103
159 112 64 127 88 49 240 165 89 181 125 68
113 83 53 136 106 75 130 97 64 221 162 102
133 81 29 146 97 47 140 89 38 239 150 60
106 75 43 319 244 169 106 85 63 331 256 180
157 123 89 206 143 79 153 109 65
a The first letters indicate the gas parameters with 2HCB ) second virial coefficient of Hirschfelder, Curtiss, and Bird,4 BAH ) Ben-Amotz and Herschbach,17 VHCB ) viscosity of Hirschfelder, Curtiss, and Bird,4 and MS ) Matyushov and Schmid.18 The final letters indicate the method of potential decomposition with BH ) Barker-Henderson, and WCA ) Weeks-Chandler-Anderson. Average refers to the arithmetic mean of the WCA and BH values for that gas.
Table 7. Best Fit for Each Gas (Notation Same as Table 6) with Experimental5 Values of S in Units of (cm3(STP)/cm3/cm Hg). a. NERD CH2 Potential8 SPRISM/ Tc (K) Sexp (%)
WCA gas sets
N2 Ar O2 CH4 Kr Xe CO2
126 150.8 154.8 191 209.4 289.4 304
158 159 148 103 126 113 106
C2H6
305.4
153
VHCB BAH 2HCB BAH BAH 2HCB 2HCB, VHCB VHCB
gas
b. TRaPPE CH2 gas
Tc (K)
SPRISM/ Sexp (%)
N2 Ar O2 CH4 Kr Xe CO2 C2H6
126 150.8 154.8 191 209.4 289.4 304 305.4
155 159 142 99 127 133 109 165
SPRISM/ BH Sexp (%) gas sets
experi -mental
101 112 103 123 103 102 65
VHCB BAH VHCB MS MS MS VHCB
9.05E-04 2.13E-03 1.96E-03 4.67E-03 6.41E-03 2.75E-02 1.30E-02
89
2HCB
2.72E-02
Potential9
WCA gas sets
SPRISM/ Sexp (%)
BH gas sets
experimental
VHCB MS 2HCB BAH BAH 2HCB 2HCB VHCB
98 89 80 79 89 60 111 56
MS MS MS MS VHCB MS BAH 2HCB
9.05E-04 2.13E-03 1.96E-03 4.67E-03 6.41E-03 2.75E-02 1.30E-02 2.72E-02
c. Best Set for Each Potential when Averaging WCA and BH
gas
Tc (K)
SPRISM/Sexp (%) NERD
N2 Ar O2 CH4 Kr Xe CO2 C2H6
126 150.8 154.8 191 209.4 289.4 304 305.4
130 136 127 97 100 97 85 109
av gas sets NERD
SPRISM/Sexp (%) TRaPPe
av gas sets TRaPPe
VHCB BAH 2HCB 2HCB BAH VHCB VHCB VHCB
111 121 106 85 88,112 97 75 99
VHCB BAH 2HCB 2HCB BAH, 2HCB BAH VHCB VHCB
Figure 2. Solubility predictions for the best fit gases for the NERD potential.8 The crossed squares are for amorphous polyethylene,5 the triangles for the WCA separation, and the diamonds for the BH separation. See Table 7a for the best fit values and gas set.
8654 Corrections
Macromolecules, Vol. 31, No. 24, 1998
The conclusions of the study are also slightly changed. From the comparison with simulation, it appears that an average of the results of the WCA and BH separations works best. From the comparison to the alkane extrapolation, it is less clear what separation or combination works best in most cases. By judiciously selection of the gas from among the gas sets for a CH2 parameter set with a given separation, the agreement is within 50% and is often much better. The results of the WCA decomposition are still fairly insensitive to the differences between the two CH2 potentials while the BH decomposition can lead to large differences in the predicted solubilities. Figure 3. Solubility predictions for the best fit gases for the TRaPPE9 potential. The crossed squares are for amorphous polyethylene,5 the triangles for the WCA separation, and the diamonds for the BH separation. See Table 7b for the best fit values and gas set.
MA9819900 10.1021/ma9819900 Published on Web 11/07/1998
