复合型多元醇酯合成反应的热力学分析及动力学研究

doi:10.11949/0438-1157.20230902

摘要/Abstract

摘要：

采用基团贡献法估算了己二酸、2-乙基己醇及三羟甲基丙烷酯化反应体系中各组分的基础热力学数据，探讨了温度对反应焓变、熵变、Gibbs自由能变和平衡常数的影响规律，热力学分析结果表明体系内各反应在所考察的温度范围内均为自发吸热过程，且升高温度有利于反应的正向进行；研究了氧化亚锡催化己二酸与2-乙基己醇以及己二酸单2-乙基己醇酯与三羟甲基丙烷的酯化反应动力学，实验结果表明两步反应均受动力学控制，且在一定的转化率区间内符合二级不可逆反应动力学特征，确定了两步反应的活化能和指前因子，建立的动力学模型能够较准确地描述复合型多元醇酯的合成过程。

关键词: 复合型多元醇酯, 酯化, 热力学性质, 氧化亚锡, 反应动力学

Abstract:

The basic thermodynamic data of each component in the complicated esterification system comprised of adipic acid, 2-ethylhexanol and trimethylolpropane were estimated by using group-contribution method, and the influence of temperature on standard enthalpy change, entropy change, Gibbs free energy change and equilibrium constant of these reactions was also investigated, the thermodynamic analysis results indicated that all the esterification reactions were endothermic and spontaneous processes under the specified temperature condition, increasing temperature is beneficial to promote the positive reaction. The kinetics of the esterification reactions of adipic acid and 2-ethylhexanol and adipic acid mono-2-ethylhexanol ester and trimethylolpropane catalyzed by stannous oxide were studied. The experimental results demonstrated that the two main reactions were both controlled by kinetics and which match the second-order irreversible reaction kinetics characteristics within a certain conversion range, the activation energy and pre-exponential factors of the reactions were determined as well, the established kinetic model can relatively accurately describe the synthesis process of complex polyolester.

Key words: complex polyolester, esterification, thermodynamic properties, stannous oxide, reaction kinetics

中图分类号:

O 623.4

刘宗鹏, 胡少剑, 张宇宁, 马玲, 李磊, 武本成, 朱建华. 复合型多元醇酯合成反应的热力学分析及动力学研究[J]. 化工学报, 2023, 74(11): 4475-4486.

Zongpeng LIU, Shaojian HU, Yuning ZHANG, Ling MA, Lei LI, Bencheng WU, Jianhua ZHU. Thermodynamic analysis and kinetics study on synthesis reaction of complex polyolester[J]. CIESC Journal, 2023, 74(11): 4475-4486.

图/表 12

表1 不同基团贡献法中各基团的热力学贡献值［14］

Table 1 Thermodynamic contribution value of each group in the different methods［14］

Group	Benson method		Ducros method	Rozicka-Domalski method
Group	$Δ f H 298.15, i ⊖ g$ /(kJ·mol^-1)	$S 298.15, i ⊖ g$ /(J·mol^-1·K^-1)	$Δ v H 298.15, k ⊖$ /(kJ·mol^-1)	a_i	b_i/K^-1	c_i/K^-2
C—(C)₄	2.09	-146.96	0.00	-2.9353	1.4255	-0.0853
C—(C)(H)₃	-42.20	127.32	5.65	3.8452	-0.3400	0.1949
C—(C)(O)(H)₂	-33.91	41.03	4.60	1.4596	1.4657	-0.2714
O—(C)(H)	-158.68	121.71	31.80	12.9520	-10.1450	2.6261
O—(CO)(H)	-243.25	102.66	37.87	-27.5870	-0.1649	2.7483
C—(C)₂(H)₂	-20.72	39.44	4.98	2.7972	-0.0550	0.1068
C—(C)(CO)(H)₂	-21.77	40.19	2.97	6.6782	-2.4473	0.4712
CO—(C)(O)	-146.86	20.01	9.83	29.2460	3.4261	-2.8962
C—(C)₃(H)	-7.95	-50.53	3.01	-0.4287	0.9381	0.0029
O—(C)(CO)	-185.48	35.13	8.37	-21.4340	-4.0164	3.0531

表1 不同基团贡献法中各基团的热力学贡献值［14］

Table 1 Thermodynamic contribution value of each group in the different methods［14］

Group	Benson method		Ducros method	Rozicka-Domalski method
Group	$Δ f H 298.15, i ⊖ g$ /(kJ·mol^-1)	$S 298.15, i ⊖ g$ /(J·mol^-1·K^-1)	$Δ v H 298.15, k ⊖$ /(kJ·mol^-1)	a_i	b_i/K^-1	c_i/K^-2
C—(C)₄	2.09	-146.96	0.00	-2.9353	1.4255	-0.0853
C—(C)(H)₃	-42.20	127.32	5.65	3.8452	-0.3400	0.1949
C—(C)(O)(H)₂	-33.91	41.03	4.60	1.4596	1.4657	-0.2714
O—(C)(H)	-158.68	121.71	31.80	12.9520	-10.1450	2.6261
O—(CO)(H)	-243.25	102.66	37.87	-27.5870	-0.1649	2.7483
C—(C)₂(H)₂	-20.72	39.44	4.98	2.7972	-0.0550	0.1068
C—(C)(CO)(H)₂	-21.77	40.19	2.97	6.6782	-2.4473	0.4712
CO—(C)(O)	-146.86	20.01	9.83	29.2460	3.4261	-2.8962
C—(C)₃(H)	-7.95	-50.53	3.01	-0.4287	0.9381	0.0029
O—(C)(CO)	-185.48	35.13	8.37	-21.4340	-4.0164	3.0531

表2 酯化体系中各组分的热力学数据

Table 2 Thermodynamic data of each component in the esterification system

Component	$Δ f H 298.15 ⊖ g$ /(kJ·mol^-1)	$S 298.15 ⊖ g$ /(J·mol^-1·K^-1)	$Δ v H 298.15 ⊖$ /(kJ·mol^-1)	$Δ v S 298.15 ⊖$ /(J·mol^-1·K^-1)	T_b/K
AA	-865.20	398.84	111.30	215.28	615.27
EH	-367.82	512.11	67.99	176.09	488.39
TMP	-638.60	489.75	119.83	203.31	574.37
EHA	-1016.57	721.71	120.63	131.05	656.25
DEHA	-1167.94	1044.57	129.96	133.81	690.37
TMPME	-1438.72	1056.15	179.16	136.44	726.72
TMPDE	-2238.84	1575.34	238.49	142.55	813.02
TMPTE	-3038.96	2104.43	297.82	146.46	873.51
H₂O(g)^[17]	-241.826	188.82	40.64	108.90	373.15

表2 酯化体系中各组分的热力学数据

Table 2 Thermodynamic data of each component in the esterification system

Component	$Δ f H 298.15 ⊖ g$ /(kJ·mol^-1)	$S 298.15 ⊖ g$ /(J·mol^-1·K^-1)	$Δ v H 298.15 ⊖$ /(kJ·mol^-1)	$Δ v S 298.15 ⊖$ /(J·mol^-1·K^-1)	T_b/K
AA	-865.20	398.84	111.30	215.28	615.27
EH	-367.82	512.11	67.99	176.09	488.39
TMP	-638.60	489.75	119.83	203.31	574.37
EHA	-1016.57	721.71	120.63	131.05	656.25
DEHA	-1167.94	1044.57	129.96	133.81	690.37
TMPME	-1438.72	1056.15	179.16	136.44	726.72
TMPDE	-2238.84	1575.34	238.49	142.55	813.02
TMPTE	-3038.96	2104.43	297.82	146.46	873.51
H₂O(g)^[17]	-241.826	188.82	40.64	108.90	373.15

表3 Constantinous-Gani法中各基团的热力学贡献值［15］

Table 3 Thermodynamic contribution value of each group in the Constantinous-Gani method［15］

Group	ΔT_b_i /K
	0.2878
—CH₂O—	1.6249
—OH	3.2152
—COOH	5.8337
—COO—	2.6446
	0.6033
—CH₂—	0.9225
—CH₃	0.8894
—CH₂COO—	3.3950

表4 酯化体系中各组分比热容与温度的关系

Table 4 Correlation of specific heat capacity and temperature of each component in the esterification system

Component	$C p, m ⊖ l = a + b T + c T 2$
Component	a	b×10²	c×10⁴
AA	185.14	12.62	7.15
EH	273.22	-71.84	26.39
TMP	390.28	-207.91	60.53
EHA	401.83	-6.90	14.25
DEHA	618.52	-26.42	21.34
TMPME	735.58	-162.49	55.48
TMPDE	1080.88	-117.06	50.42
TMPTE	1426.19	-71.63	45.37
H₂O(g)^[17]	36.54	-3.48	1.17

表4 酯化体系中各组分比热容与温度的关系

Table 4 Correlation of specific heat capacity and temperature of each component in the esterification system

Component	$C p, m ⊖ l = a + b T + c T 2$
Component	a	b×10²	c×10⁴
AA	185.14	12.62	7.15
EH	273.22	-71.84	26.39
TMP	390.28	-207.91	60.53
EHA	401.83	-6.90	14.25
DEHA	618.52	-26.42	21.34
TMPME	735.58	-162.49	55.48
TMPDE	1080.88	-117.06	50.42
TMPTE	1426.19	-71.63	45.37
H₂O(g)^[17]	36.54	-3.48	1.17

图1 温度对标准反应焓变、熵变、Gibbs自由能变及平衡常数的影响

Fig.1 Effect of temperature on the ΔrHm⊖, ΔrSm⊖, ΔrGm⊖ and K⊖ of esterification reaction

图2 温度对反应平衡转化率及平衡选择性的影响

Fig.2 Effect of temperature on the equilibrium conversion and selectivity of esterification reaction

图3 搅拌速率对第一步反应及第二步反应转化率的影响

Fig.3 Effect of stirring speed on the conversion of the first and second step reaction

图4 不同温度条件下第一步反应及第二步反应转化率随时间的变化

Fig.4 Variation curves of the conversion of the first and second step reaction with time at different temperatures

图5 不同温度条件下第一步反应及第二步反应速率常数的拟合关系

Fig.5 Linear fitting of the first and second step reaction rate constants at different temperatures

表5 不同温度条件下的反应动力学拟合结果

Table 5 Fitting results of reaction kinetic equations at different temperatures

First esterification step (X_A≈0—90%)			Second esterification step (X_C≈0—80%)
T/K	Fitting equation	R²	T/K	Fitting equation	R²
413.15	y=0.0088x-0.0165	0.9923	423.15	y=0.0113x+0.0034	0.9941
423.15	y=0.0198x-0.0337	0.9936	433.15	y=0.0163x+0.1692	0.9923
433.15	y=0.0325x-0.0086	0.9915	443.15	y=0.0220x+0.2462	0.9850
443.15	y=0.0582x+0.1234	0.9885	453.15	y=0.0339x+0.3084	0.9708

图6 第一步反应及第二步反应的lnki 与1/T的拟合关系

Fig.6 Fitting relationship between lnkiand 1/T of the first and second step reaction

表6 两步酯化反应的动力学参数

Table 6 Kinetic parameters of the two esterification steps

First esterification step(X_A≈0—90%)		Second esterification step(X_C≈0—80%)
A₁/(L·mol^-1·min^-1)	7.153×10⁹	A₂/(L·mol^-1·min^-1)	1.869×10⁵
E_a1/(kJ·mol^-1)	93.99	E_a2/(kJ·mol^-1)	58.59

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