PEG/VAc自由基接枝聚合与双烯/单烯ATRP交联聚合的模型研究
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摘要
接枝与交联是高性能或功能化聚合物材料制备的两个重要手段。其模型化研究对揭示聚合机理、优化聚合过程和产物结构设计均十分重要。本文运用矩方法分别对聚乙二醇(PEG)接枝醋酸乙烯酯(VAc)聚合体系和双烯／单烯的原子转移自由基(ATRP)交联聚合体系进行了深入的建模研究。
对于PEG接枝VAc聚合体系，本文推导出了对“长出支链方法”的接枝聚合体系普适的矩方程模型。结合PEG／VAc接枝体系强链转移的特点，写出了针对该接枝体系的矩微分方程组。在模型的基础上定义了包括聚合速率、共聚物分子量、VAc接枝效率和接枝率、PEG的被接枝率等在内的动力学参数的矩表达式。
模型计算了以过氧化-2-乙基己酸叔丁酯(TBPO)引发聚合、PEG：VAc=1：1(wt％)间歇聚合情况下的动力学参数，分析了聚合温度、引发剂浓度、PEG的分子量对聚合速率、接枝共聚物分子量、VAc接枝效率和PEG被接枝率的影响，并与实验结果进行了对比。
模型对各温度、引发剂浓度和PEG分子量下的聚合速率进行了很好的预测。模型计算得到的数均分子量与通过实验测得的VAc接枝效率、PEG接枝率计算得到的分子量数值相当吻合，且不同的反应条件下其数值均随着转化率提高而下降。分析了引发剂浓度、温度、PEG分子量对接枝共聚物分子量的的影响。利用模型和不同温度下接枝产物分子量的实验数据对VAc向PEG链转移常数C_(PEG)进行最小二乘法拟和，得到其Arrhenius表达式为C_(PEG)=0．139exp(-11200／RT)。
计算发现VAc的接枝效率很高，接近于1左右，且基本不受温度、引发剂浓度和PEG分子量的影响。这可以从VAc向PEG转移常数远大于向VAc本身转移常数、体系中PEG的链节浓度远大于VAc的浓度两个方面进行解释。模型同样计算了PEG的被接枝率，分析了引发剂浓度、温度和PEG分子量的影响。通过引入C_(PEG)的表达式，可以对不同温度下的PEG被接枝率进行准确的预测。在不同的PEG分子量下，模型对PEG1000和PEG2000实验结果能进行很好的预测，而对于PEG6000的情况则产生了较大的偏差。文中对此进行了解释。
模型还对不同初始主链PDI下接枝聚合前后未接枝PEG的平均分子量进行了研究，证明长的PEG链具有高的接枝概率。对比了均聚PVAc和接枝PVAc链的聚合度，对比了均聚PVAc链和接枝PVAc链的分子量分布，且讨论了不同PEG分子量下主链上的接枝链数目。此外，结合半连续滴加的反应器模型，将接枝模型进一步应用到半连续聚合体系进行研究，并与实验数据进行了对比。
对于双烯／单烯的ATRP交联聚合反应，应用拟动力学常数的方法，推导出了双烯／单烯ATRP交联聚合的普适矩方程模型。通过选取合适的速率常数，对体系的凝胶点和凝胶点特性进行了计算，并进一步研究了模型中双键的非等活性对交联聚合的影响。
在无分子内成环、等活性假定和交联点无规分布假定的基础上，模型计算了不同的双烯／引发剂摩尔比下的凝胶点转化率、交联总数、交联点密度和基链的重均分子量等，并与Flory、Stockmayer理论进行了比较。
根据ATRP体系的特点，对Flory的双烯／单烯凝胶点转化率表达式进行变换，得到了ATRP中凝胶点转化率的表达式，为(?)。同时，将模型计算结果与文献实验工作进行对比，计算了凝胶点基链上含有的平均交联个数。
通过定义休眠种分布指数DDI和自由基分布指数RDI，对体系中休眠种分布和自由基分布进行了研究。发现在低转化率下DDI就已经大于1，即已存在多活性中心链；而RDI则在凝胶点之前均为1，只有在凝胶点产生突变，趋于无穷大。后者说明，在ATRP体系中单自由基的假定是可以成立的，这是因为在ATRP体系中自由基迅速被休眠，形成休眠种。
研究了速率常数对凝胶点转化率的影响。考察了引发剂休眠平衡速率常数和休眠种平衡常数对凝胶点的影响。发现平衡速率常数对凝胶点的影响不大，主要通过对引发剂完全消耗的转化率以及基链PDI的影响来体现。
通过采取不同的单烯双键、双烯双键和悬挂双键的增长速率常数，研究了双键非等活性对交联过程的影响。发现在单烯、双烯双键等活性条件下，随着悬挂双键活性升高，凝胶点转化率降低，凝胶所需交联总数增加，交联点密度升高。双烯双键活性低于单烯双键时，凝胶点转化率比等活性假定情况下有所升高；而双烯双键活性大于单烯双键时，则凝胶点转化率较等活性假定情况低。非等活性的影响，会导致ρ_bP_w乘积数值变化。在双烯双键与悬挂双键活性相同(即k_(p2)／k_(p3)=1)的情况下，ρ_bP_w乘积均接近于1。
Grafting and cross-linking are two important approaches for preparing novelmacromolecular materials. Modeling such processes is of great benefit for thepolymerization mechanism study and process optimization. In this thesis, themethod of moments was used in modeling the graft polymerization of vinyl acetatefrom polyethylene glycol and the vinyl/divinyl atom transfer radical copolymerizationwith cross-linking.
In the first part of the thesis, a general model for the‘grafting from’method wasdeveloped. A set of ordinary differential equations were derived taking into accountthe severe chain transfer reactions in the PEG/VAc system. Expressions ofpolymerization rate, molecular weight of graft-copolymer, VAc graft efficiency andPEG grafted ratio were derived using the moments.
tert-Butyl peroxy-2-ethyl hexanoate was used as initiator and a weight ratio ofPEG to VAc of 1 was adopted in both simulation and experimentation. Theinfluences of polymerization temperature, initiator concentration and PEG molecularweight on the polymerization rate, copolymer MW, VAc graft efficiency and PEGgrafted ratio were analyzed using the model and were compared the experimentaldata.
The model predicts the polymerization rates at various temperatures, initiatorconcentrations and PEG MWs. The simulated final conversions at high temperaturesare higher that experimental data, and the phenomenon was analyzed. The simulatedMW of graft copolymer fitted well the MW acquired by VAc graft efficiency and PEGgrafted ratio, and its value decreased with conversion at all conditions. The chaintransfer constant of VAc to PEG was estimated by correlating the model withexperimental data using a lest-square method, and the Arrhenius expression was foundto be C_(PEG) = 0.139exp(-11200/RT).
The simulated VAc grafting efficiency was very close to 1, seemingly unaffected by temperature, initiator concentration and PEG MW. This could be explained viatwo aspects: the chain transfer rate constant of VAc to PEG is much higher than that toVAc units, and the concentration of PEG units is also much higher than VAc. ThePEG grafted ratio was also simulated and analyzed at different reaction conditions,and the C_(peg) expression was used. The model results agreed well with at the data ofPEG1000 and PEG 6000 systems, but deviated from PEG 6000. The discrepancywas explained.
Different initial MWDs of PEG were examined using the model and it was fountthat longer PEG chains have higher probability to graft chains. The homo-PVAc andgrafted PVAc were compared using the model and were found to have the samemolecular weight distribution. The number of grafted side chains on backbone wasalso discussed at different PEG MWs. Moreover, the model was combined withsemi-batch reactor model to simulate semi-batch process. The results were alsofavorably compared with experimental data.
In the second part of the thesis, the pseudo kinetic constant method was used inmodeling vinyl/divinyl cross-linking atom transfer radical polymerization. Withappropriate rate constants for the model, gel point and chain properties at gel pointwere calculated, and the effect of unequal reactivity of double bonds on gelation wasstudied.
Based on the assumptions of no cyclization, equal reactivity of double bonds, andrandom distribution of cross-linkages, the gel point, total number of cross-linkages,cross-linking density and MW of primary chain were calculated and compared withFlory-Stockmayer's theory of gelation. The gel point in the vinyl/divinyl system canbe calculated via equation(?), which is derived based on Flory's theorytaking into account of ATRP characteristics. Meanwhile, the results were alsocompared with experimental data reported in literatures, and the averagecross-linkages per primary chains were calculated.
The dormant distribution index and radical distribution index were also definedand calculated. At low conversion the DDI was higher than 1, indicating theexistence of poly-dormant chains. However, the RDI remained 1 prior to the gel point, and increased suddenly at the gel point, approaching infinite. Thus themono-radical assumption is valid in ATRP cross-linking system, and this is becausethe radicals are rapidly deactivated in the ATRP system.
The influence of rate constants on cross-linking was also investigated. Theequilibrium rate constants for both of initiator and polymer chains had slight effect ongel point, and the influence was exerted via the consumption rate of initiator and PDIof primary chains.
Different propagating rate constants for various double bonds were used to studythe effect of unequal reactivity on cross-linking. At the same reactivity ofvinyl/divinyl double bonds, increasing pendant double bond reactivity decreases thegel point, increased the total number of cross-linkages at the gel point, and alsoincreased the cross-linking density. When divinyl bond is less reactive than vinyl,the gel point was later than that of equal reactivity condition; and vice visa. Theunequal reactivity of double bonds makes theρ_bP_w change at the gel point. Whenvinyl/divinyl double bonds have the same reactivity (k_(P2)/k_(P3)=1) , the product ofρ_bP_wis close to 1.
对于PEG接枝VAc聚合体系，本文推导出了对“长出支链方法”的接枝聚合体系普适的矩方程模型。结合PEG／VAc接枝体系强链转移的特点，写出了针对该接枝体系的矩微分方程组。在模型的基础上定义了包括聚合速率、共聚物分子量、VAc接枝效率和接枝率、PEG的被接枝率等在内的动力学参数的矩表达式。
模型计算了以过氧化-2-乙基己酸叔丁酯(TBPO)引发聚合、PEG：VAc=1：1(wt％)间歇聚合情况下的动力学参数，分析了聚合温度、引发剂浓度、PEG的分子量对聚合速率、接枝共聚物分子量、VAc接枝效率和PEG被接枝率的影响，并与实验结果进行了对比。
模型对各温度、引发剂浓度和PEG分子量下的聚合速率进行了很好的预测。模型计算得到的数均分子量与通过实验测得的VAc接枝效率、PEG接枝率计算得到的分子量数值相当吻合，且不同的反应条件下其数值均随着转化率提高而下降。分析了引发剂浓度、温度、PEG分子量对接枝共聚物分子量的的影响。利用模型和不同温度下接枝产物分子量的实验数据对VAc向PEG链转移常数C_(PEG)进行最小二乘法拟和，得到其Arrhenius表达式为C_(PEG)=0．139exp(-11200／RT)。
计算发现VAc的接枝效率很高，接近于1左右，且基本不受温度、引发剂浓度和PEG分子量的影响。这可以从VAc向PEG转移常数远大于向VAc本身转移常数、体系中PEG的链节浓度远大于VAc的浓度两个方面进行解释。模型同样计算了PEG的被接枝率，分析了引发剂浓度、温度和PEG分子量的影响。通过引入C_(PEG)的表达式，可以对不同温度下的PEG被接枝率进行准确的预测。在不同的PEG分子量下，模型对PEG1000和PEG2000实验结果能进行很好的预测，而对于PEG6000的情况则产生了较大的偏差。文中对此进行了解释。
模型还对不同初始主链PDI下接枝聚合前后未接枝PEG的平均分子量进行了研究，证明长的PEG链具有高的接枝概率。对比了均聚PVAc和接枝PVAc链的聚合度，对比了均聚PVAc链和接枝PVAc链的分子量分布，且讨论了不同PEG分子量下主链上的接枝链数目。此外，结合半连续滴加的反应器模型，将接枝模型进一步应用到半连续聚合体系进行研究，并与实验数据进行了对比。
对于双烯／单烯的ATRP交联聚合反应，应用拟动力学常数的方法，推导出了双烯／单烯ATRP交联聚合的普适矩方程模型。通过选取合适的速率常数，对体系的凝胶点和凝胶点特性进行了计算，并进一步研究了模型中双键的非等活性对交联聚合的影响。
在无分子内成环、等活性假定和交联点无规分布假定的基础上，模型计算了不同的双烯／引发剂摩尔比下的凝胶点转化率、交联总数、交联点密度和基链的重均分子量等，并与Flory、Stockmayer理论进行了比较。
根据ATRP体系的特点，对Flory的双烯／单烯凝胶点转化率表达式进行变换，得到了ATRP中凝胶点转化率的表达式，为(?)。同时，将模型计算结果与文献实验工作进行对比，计算了凝胶点基链上含有的平均交联个数。
通过定义休眠种分布指数DDI和自由基分布指数RDI，对体系中休眠种分布和自由基分布进行了研究。发现在低转化率下DDI就已经大于1，即已存在多活性中心链；而RDI则在凝胶点之前均为1，只有在凝胶点产生突变，趋于无穷大。后者说明，在ATRP体系中单自由基的假定是可以成立的，这是因为在ATRP体系中自由基迅速被休眠，形成休眠种。
研究了速率常数对凝胶点转化率的影响。考察了引发剂休眠平衡速率常数和休眠种平衡常数对凝胶点的影响。发现平衡速率常数对凝胶点的影响不大，主要通过对引发剂完全消耗的转化率以及基链PDI的影响来体现。
通过采取不同的单烯双键、双烯双键和悬挂双键的增长速率常数，研究了双键非等活性对交联过程的影响。发现在单烯、双烯双键等活性条件下，随着悬挂双键活性升高，凝胶点转化率降低，凝胶所需交联总数增加，交联点密度升高。双烯双键活性低于单烯双键时，凝胶点转化率比等活性假定情况下有所升高；而双烯双键活性大于单烯双键时，则凝胶点转化率较等活性假定情况低。非等活性的影响，会导致ρ_bP_w乘积数值变化。在双烯双键与悬挂双键活性相同(即k_(p2)／k_(p3)=1)的情况下，ρ_bP_w乘积均接近于1。
Grafting and cross-linking are two important approaches for preparing novelmacromolecular materials. Modeling such processes is of great benefit for thepolymerization mechanism study and process optimization. In this thesis, themethod of moments was used in modeling the graft polymerization of vinyl acetatefrom polyethylene glycol and the vinyl/divinyl atom transfer radical copolymerizationwith cross-linking.
In the first part of the thesis, a general model for the‘grafting from’method wasdeveloped. A set of ordinary differential equations were derived taking into accountthe severe chain transfer reactions in the PEG/VAc system. Expressions ofpolymerization rate, molecular weight of graft-copolymer, VAc graft efficiency andPEG grafted ratio were derived using the moments.
tert-Butyl peroxy-2-ethyl hexanoate was used as initiator and a weight ratio ofPEG to VAc of 1 was adopted in both simulation and experimentation. Theinfluences of polymerization temperature, initiator concentration and PEG molecularweight on the polymerization rate, copolymer MW, VAc graft efficiency and PEGgrafted ratio were analyzed using the model and were compared the experimentaldata.
The model predicts the polymerization rates at various temperatures, initiatorconcentrations and PEG MWs. The simulated final conversions at high temperaturesare higher that experimental data, and the phenomenon was analyzed. The simulatedMW of graft copolymer fitted well the MW acquired by VAc graft efficiency and PEGgrafted ratio, and its value decreased with conversion at all conditions. The chaintransfer constant of VAc to PEG was estimated by correlating the model withexperimental data using a lest-square method, and the Arrhenius expression was foundto be C_(PEG) = 0.139exp(-11200/RT).
The simulated VAc grafting efficiency was very close to 1, seemingly unaffected by temperature, initiator concentration and PEG MW. This could be explained viatwo aspects: the chain transfer rate constant of VAc to PEG is much higher than that toVAc units, and the concentration of PEG units is also much higher than VAc. ThePEG grafted ratio was also simulated and analyzed at different reaction conditions,and the C_(peg) expression was used. The model results agreed well with at the data ofPEG1000 and PEG 6000 systems, but deviated from PEG 6000. The discrepancywas explained.
Different initial MWDs of PEG were examined using the model and it was fountthat longer PEG chains have higher probability to graft chains. The homo-PVAc andgrafted PVAc were compared using the model and were found to have the samemolecular weight distribution. The number of grafted side chains on backbone wasalso discussed at different PEG MWs. Moreover, the model was combined withsemi-batch reactor model to simulate semi-batch process. The results were alsofavorably compared with experimental data.
In the second part of the thesis, the pseudo kinetic constant method was used inmodeling vinyl/divinyl cross-linking atom transfer radical polymerization. Withappropriate rate constants for the model, gel point and chain properties at gel pointwere calculated, and the effect of unequal reactivity of double bonds on gelation wasstudied.
Based on the assumptions of no cyclization, equal reactivity of double bonds, andrandom distribution of cross-linkages, the gel point, total number of cross-linkages,cross-linking density and MW of primary chain were calculated and compared withFlory-Stockmayer's theory of gelation. The gel point in the vinyl/divinyl system canbe calculated via equation(?), which is derived based on Flory's theorytaking into account of ATRP characteristics. Meanwhile, the results were alsocompared with experimental data reported in literatures, and the averagecross-linkages per primary chains were calculated.
The dormant distribution index and radical distribution index were also definedand calculated. At low conversion the DDI was higher than 1, indicating theexistence of poly-dormant chains. However, the RDI remained 1 prior to the gel point, and increased suddenly at the gel point, approaching infinite. Thus themono-radical assumption is valid in ATRP cross-linking system, and this is becausethe radicals are rapidly deactivated in the ATRP system.
The influence of rate constants on cross-linking was also investigated. Theequilibrium rate constants for both of initiator and polymer chains had slight effect ongel point, and the influence was exerted via the consumption rate of initiator and PDIof primary chains.
Different propagating rate constants for various double bonds were used to studythe effect of unequal reactivity on cross-linking. At the same reactivity ofvinyl/divinyl double bonds, increasing pendant double bond reactivity decreases thegel point, increased the total number of cross-linkages at the gel point, and alsoincreased the cross-linking density. When divinyl bond is less reactive than vinyl,the gel point was later than that of equal reactivity condition; and vice visa. Theunequal reactivity of double bonds makes theρ_bP_w change at the gel point. Whenvinyl/divinyl double bonds have the same reactivity (k_(P2)/k_(P3)=1) , the product ofρ_bP_wis close to 1.
引文
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