Studies on the Calculation of Lennard-Jones Parameters for Intermediates in Hydrocarbon Combustion†

doi:10.7503/cjcu20150647

Abstract

Abstract:

Lennard-Jones(L-J) parameters were used in combustion modeling as transport parameters and in pressure-dependent rate-coefficient calculations as collision rate parameters. However, there are no reported values for most of the radical intermediates in hydrocarbon combustion. In this work, a new group contribution formula was proposed and group contribution values of 40 groups for intermediates in the combustion of hydrocarbons were fitted from critical properties of 250 species, including 185 stable species with experimental critical property values and 65 radical species with calculated critical property values and these group contribution values were used to estimate critical properties for new species. 30 hydrocarbon compounds with available experimental properties were chosen to validate the accuracy of the model, the average absolute deviation of T_C and P_Cwere 8.52% and 16.83%, respectively, showing an agreement with experimental data. This model can predict critical properties for macromolecular and radical species. According to the empirical relations between critical properties and L-J parameters, L-J parameters of hydrocarbon combustion intermediates were estimated. It was shown that the predicted values for 46 compounds with available reported data were in good agreement with the reported values and the average absolute deviation of T_C and P_C were 9.88% and 9.96%, respectively. The L-J parameters of alkane radical ^·C₆H₁₃, alkene radical ^·C₅H₉ and alkyne radical ^·C₅H₇ isomers were compared. L-J parameters of ^·C₆H₁₃ and similar compound C₆H₁₄ were also compared and the results showed that there were obvious differences of the L-J parameters between isomers or between similar compounds. In addition, L-J parameters for 114 hydrocarbon radicals, for which L-J parameters had not been reported yet, were predicted. These data are important in the combustion modeling of hydrocarbons and pressure-dependent rate-coefficient calculations for elementary reactions in hydrocarbon combustion.

Key words: Lennard-Jones parameter, Critical property, Group contribution method, Radical group, Intermediate in hydrocarbon combustion

CLC Number:

O643

TrendMD:

SUN Yanjin, YAO Qian, LI Zerong, LI Juanqin, LI Xiangyuan. Studies on the Calculation of Lennard-Jones Parameters for Intermediates in Hydrocarbon Combustion^†[J]. Chem. J. Chinese Universities, 2016, 37(2): 328.

Figures/Tables 2

Table 1 Definition of groups and fitted values of the group contribution to TC and PC

Species	Number	Group	10⁶T_C/P_C	10³T_C/ $P C$	Species	Number	Group	10⁶T_C/P_C	10³T_C/ $P C$
Non-ring group	1	—CH₃	1.0669	0.4851	Ring group	22		0.2339	0.1860
	2	—CH₂—	0.9790	0.5102		23		0.3711	0.0993
	3		0.9326	0.3908		24	=CH—	0.7422	0.4339
	4		0.4717	0.2441		25		1.3077	0.6686
	5	=CH₂	0.6415	0.3522		26	—O—	-0.4668	-0.0339
	6	=CH—	1.1409	0.4822		27		2.1643	1.1678
	7		0.8527	0.3710		28	—OH(phenol)	0.7718	0.6183
	8	=C=	0.5468	0.5325	Radical group	29	^·CH₃	-1.0323	0.0811
	9	—C≡≡	1.2396	0.3852		30	^·CH₂	-0.8409	0.2765
	10	HC≡≡	-0.1855	0.2419		31	^·CH	0.7747	0.5529
	11	—OH	0.3563	0.4339		32	^·C	0.9119	0.4926
	12	—O—	0.2605	0.1320		33	≡≡C^·	-0.7037	0.2686
	13	=O	-0.9652	-0.1043		34	=HC^·	-0.6070	0.3487
	14		0.1678	0.4273		35	=C^·	0.6208	0.5910
	15	—CHO	2.3755	1.1621		36	O^·	-0.7550	0.3522
	16	—COOH	4.3198	2.3013		37	O=C^·	0.0829	0.8423
	17	—COO—	1.6955	0.9372		38	^·CHO	-1.8110	0.8822
	18	HCOO—	1.4962	0.8203		39	^·C₆H₅	4.2142	2.2259
	19	C₆H₅—	3.9931	2.3327		40	=C^·	0.8863	0.3299
	20	C₁₀H₇—	6.9539	4.1225	RMSD			0.0919	0.0956
Ring group	21	—CH₂—	0.9257	0.4760	$r 2 *$			0.9232	0.9582

Table 1 Definition of groups and fitted values of the group contribution to TC and PC

Species	Number	Group	10⁶T_C/P_C	10³T_C/ $P C$	Species	Number	Group	10⁶T_C/P_C	10³T_C/ $P C$
Non-ring group	1	—CH₃	1.0669	0.4851	Ring group	22		0.2339	0.1860
	2	—CH₂—	0.9790	0.5102		23		0.3711	0.0993
	3		0.9326	0.3908		24	=CH—	0.7422	0.4339
	4		0.4717	0.2441		25		1.3077	0.6686
	5	=CH₂	0.6415	0.3522		26	—O—	-0.4668	-0.0339
	6	=CH—	1.1409	0.4822		27		2.1643	1.1678
	7		0.8527	0.3710		28	—OH(phenol)	0.7718	0.6183
	8	=C=	0.5468	0.5325	Radical group	29	^·CH₃	-1.0323	0.0811
	9	—C≡≡	1.2396	0.3852		30	^·CH₂	-0.8409	0.2765
	10	HC≡≡	-0.1855	0.2419		31	^·CH	0.7747	0.5529
	11	—OH	0.3563	0.4339		32	^·C	0.9119	0.4926
	12	—O—	0.2605	0.1320		33	≡≡C^·	-0.7037	0.2686
	13	=O	-0.9652	-0.1043		34	=HC^·	-0.6070	0.3487
	14		0.1678	0.4273		35	=C^·	0.6208	0.5910
	15	—CHO	2.3755	1.1621		36	O^·	-0.7550	0.3522
	16	—COOH	4.3198	2.3013		37	O=C^·	0.0829	0.8423
	17	—COO—	1.6955	0.9372		38	^·CHO	-1.8110	0.8822
	18	HCOO—	1.4962	0.8203		39	^·C₆H₅	4.2142	2.2259
	19	C₆H₅—	3.9931	2.3327		40	=C^·	0.8863	0.3299
	20	C₁₀H₇—	6.9539	4.1225	RMSD			0.0919	0.0956
Ring group	21	—CH₂—	0.9257	0.4760	$r 2 *$			0.9232	0.9582

Table 2 L-J parameters for isomers and similar compounds

Radical group	Isomer	T_C/K	10^-6P_C/Pa	(ε/ $k B cal$ )/K	σ^cal/nm
^·C₆H₁₃	^·CH₂(CH₂)₄CH₃	700.304	5.976	539.234	0.5567
	C $H 3 ·$ CH(CH₂)₃CH₃	597.035	3.902	459.717	0.6084
	CH₃C $H 2 ·$ CH(CH₂)₂CH₃	597.035	3.902	459.717	0.6084
	CH₃(^·CH₂)CH(CH₂)₂CH₃	651.717	5.523	501.822	0.5579
	(CH₃ $) 2 ·$ C(CH₂)₂CH₃	557.011	3.520	428.899	0.6153
	(CH₃)₂CH^·CHCH₂CH₃	558.345	3.626	429.925	0.6097
	(CH₃)₂CHC $H 2 ·$ CHCH₃	558.345	3.626	429.925	0.6097
	(CH₃)₂CH(CH₂ $) 2 ·$ CH₂	651.717	5.523	501.822	0.5579
	^·CH₂(CH₃)CHCH(CH₃)₂	604.806	5.091	465.701	0.5592
	(CH₃ $) 2 ·$ CCH(CH₃)₂	520.208	3.267	400.560	0.6166
	^·CH₂(CH₃)₂CCH₂CH₃	638.886	5.757	491.942	0.5466
	(CH₃)₃C^·CHCH₃	547.811	3.764	421.815	0.5983
	(CH₃)₃CC $H 2 ·$ CH₂	638.886	5.757	491.942	0.5466
	CH₃(CH₂)₄CH₃(hexane)	568.90	3.606	438.054	0.6146
^·C₅H₉	^·CH=CH(CH₂)₂CH₃	618.809	5.815	476.483	0.5390
	CH₂ C(CH₂)₂CH₃	580.316	4.836	446.843	0.5611
	CH₂=CH^·CH₂CH₃	533.871	4.229	411.081	0.5706
	CH₂=CH(CH₂ $) 2 ·$ CH₂	621.829	6.541	478.808	0.5192
	^·CH₂CH=CHCH₂CH₃	525.958	3.851	404.988	0.5858
	C $H 3 ·$ C=CHCH₂CH₃	555.762	4.217	427.937	0.5789
	CH₃CH=CH^·CHCH₃	512.549	3.702	394.663	0.5885
	CH₃CH=CHC $H 2 ·$ CH₂	594.755	5.657	457.961	0.5369
	^·CH=CHCH(CH₃)₂	570.013	5.319	438.910	0.5403
	CH₂ CCH(CH₃)₂	536.128	4.438	412.818	0.5623
	CH₂=CH^·(CH₃)₂	493.234	3.770	379.790	0.5775
	CH₂=CHCH^·CH₂(CH₃)	569.527	5.947	438.536	0.5204
	^·CH=C(CH₃)CH₂CH₃	596.348	5.797	459.188	0.5330
	CH₂=C(^·CH₂)CH₂CH₃	596.869	6.501	459.589	0.5132
	CH₂=C(CH₃)^·CHCH₃	514.157	4.206	395.901	0.5646
	CH₂=C(CH₃)C $H 2 ·$ CH₂	596.869	6.501	459.589	0.5132
	^·CH₂CH=C(CH₃)₂	571.847	5.627	440.322	0.5308
	C $H 3 ·$ C=C(CH₃)₂	536.983	4.206	413.477	0.5728
	CH₃CH=C^·CH₂(CH₃)	571.847	5.627	440.322	0.5308
^·C₅H₇	^·C≡≡C(CH₂)₂CH₃	563.845	5.297	434.161	0.5391
	CH≡≡C^·CHCH₂CH₃	539.748	4.812	415.606	0.5486
	CH≡≡C(CH₂ $) 2 ·$ CH₂	629.295	7.530	484.557	4.973
	^·C≡≡CCH(CH₃)₂	516.954	4.823	398.054	0.5404
	CH≡≡C^·C(CH₃)₂	487.025	5.158	375.009	0.5180
	CH≡≡CCH(^·CH₂)CH₃	539.748	4.812	415.606	0.5486
	^·CH₂C≡≡CCH₂CH₃	517.853	4.765	398.747	0.5428
	CH₃C≡≡C^·CHCH₃	444.182	3.786	342.020	0.5569
	CH₃C≡≡CC $H 2 ·$ CH₂	517.853	4.765	398.747	0.5428

Table 2 L-J parameters for isomers and similar compounds

Radical group	Isomer	T_C/K	10^-6P_C/Pa	(ε/ $k B cal$ )/K	σ^cal/nm
^·C₆H₁₃	^·CH₂(CH₂)₄CH₃	700.304	5.976	539.234	0.5567
	C $H 3 ·$ CH(CH₂)₃CH₃	597.035	3.902	459.717	0.6084
	CH₃C $H 2 ·$ CH(CH₂)₂CH₃	597.035	3.902	459.717	0.6084
	CH₃(^·CH₂)CH(CH₂)₂CH₃	651.717	5.523	501.822	0.5579
	(CH₃ $) 2 ·$ C(CH₂)₂CH₃	557.011	3.520	428.899	0.6153
	(CH₃)₂CH^·CHCH₂CH₃	558.345	3.626	429.925	0.6097
	(CH₃)₂CHC $H 2 ·$ CHCH₃	558.345	3.626	429.925	0.6097
	(CH₃)₂CH(CH₂ $) 2 ·$ CH₂	651.717	5.523	501.822	0.5579
	^·CH₂(CH₃)CHCH(CH₃)₂	604.806	5.091	465.701	0.5592
	(CH₃ $) 2 ·$ CCH(CH₃)₂	520.208	3.267	400.560	0.6166
	^·CH₂(CH₃)₂CCH₂CH₃	638.886	5.757	491.942	0.5466
	(CH₃)₃C^·CHCH₃	547.811	3.764	421.815	0.5983
	(CH₃)₃CC $H 2 ·$ CH₂	638.886	5.757	491.942	0.5466
	CH₃(CH₂)₄CH₃(hexane)	568.90	3.606	438.054	0.6146
^·C₅H₉	^·CH=CH(CH₂)₂CH₃	618.809	5.815	476.483	0.5390
	CH₂ C(CH₂)₂CH₃	580.316	4.836	446.843	0.5611
	CH₂=CH^·CH₂CH₃	533.871	4.229	411.081	0.5706
	CH₂=CH(CH₂ $) 2 ·$ CH₂	621.829	6.541	478.808	0.5192
	^·CH₂CH=CHCH₂CH₃	525.958	3.851	404.988	0.5858
	C $H 3 ·$ C=CHCH₂CH₃	555.762	4.217	427.937	0.5789
	CH₃CH=CH^·CHCH₃	512.549	3.702	394.663	0.5885
	CH₃CH=CHC $H 2 ·$ CH₂	594.755	5.657	457.961	0.5369
	^·CH=CHCH(CH₃)₂	570.013	5.319	438.910	0.5403
	CH₂ CCH(CH₃)₂	536.128	4.438	412.818	0.5623
	CH₂=CH^·(CH₃)₂	493.234	3.770	379.790	0.5775
	CH₂=CHCH^·CH₂(CH₃)	569.527	5.947	438.536	0.5204
	^·CH=C(CH₃)CH₂CH₃	596.348	5.797	459.188	0.5330
	CH₂=C(^·CH₂)CH₂CH₃	596.869	6.501	459.589	0.5132
	CH₂=C(CH₃)^·CHCH₃	514.157	4.206	395.901	0.5646
	CH₂=C(CH₃)C $H 2 ·$ CH₂	596.869	6.501	459.589	0.5132
	^·CH₂CH=C(CH₃)₂	571.847	5.627	440.322	0.5308
	C $H 3 ·$ C=C(CH₃)₂	536.983	4.206	413.477	0.5728
	CH₃CH=C^·CH₂(CH₃)	571.847	5.627	440.322	0.5308
^·C₅H₇	^·C≡≡C(CH₂)₂CH₃	563.845	5.297	434.161	0.5391
	CH≡≡C^·CHCH₂CH₃	539.748	4.812	415.606	0.5486
	CH≡≡C(CH₂ $) 2 ·$ CH₂	629.295	7.530	484.557	4.973
	^·C≡≡CCH(CH₃)₂	516.954	4.823	398.054	0.5404
	CH≡≡C^·C(CH₃)₂	487.025	5.158	375.009	0.5180
	CH≡≡CCH(^·CH₂)CH₃	539.748	4.812	415.606	0.5486
	^·CH₂C≡≡CCH₂CH₃	517.853	4.765	398.747	0.5428
	CH₃C≡≡C^·CHCH₃	444.182	3.786	342.020	0.5569
	CH₃C≡≡CC $H 2 ·$ CH₂	517.853	4.765	398.747	0.5428

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