The Solubility of Gases in Polyethylene: Integral Equation Study of

Joanne L. Budzien, John D. McCoy, John G. Curro, Randall A. LaViolette, and Eric S. Peter- son: The Solubility of Gases in Polyethylene: Integral. Equ...
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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