塑料包装材料中迁移物扩散系数的分子动力学研究
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摘要
塑料食品包装材料中化学物迁移对食品安全的影响引起了人们的广泛关注。迁移物从塑料食品包装材料进入食品的过程可分为三个不同但内部相关的阶段：在聚合物中的扩散,在聚合物-食品界面上的溶解和在食品内的分散,分别对应于“扩散”、“溶解”和“分散”。对上述三阶段建立合理的假设,基于Fick第二定律求解便得到迁移数学模型。迁移数学模型中有一重要参数——扩散系数决定了迁移的动力学过程,数学模型的关键问题是求取迁移物在聚合物中扩散时的扩散系数。
为此,本文首先深入分析了扩散系数的影响因素：聚合物特性、迁移物特性、温度、聚合物与食品溶剂间的相互作用等,以聚烯烃为例深入分析了四种常见的扩散系数估测模型预测值与实验值间的差异,以非聚烯烃为例深入分析了Brandsch模型的适用性。介绍了扩散系数的迁移测试方法——与溶剂接触法和无溶剂接触法,无溶剂接触法的思想与采用分子动力学模拟获取扩散系数的思想相一致。
实验测试扩散系数非常困难,经验估算公式又存在参数难以确定等问题,都缺乏对聚合物微观结构和扩散机理的本质认识。近年来基于经典力学的分子动力学模拟已经成为研究聚合物材料结构及其扩散机理的工具。因此,本文概述了分子动力学发展历程、动力学原理、技术细节、分子力场等动力学基本理论,对小分子在聚合物中扩散的动力学模拟从扩散机理、影响因素和定量描述三个方面进行了总结,为随后的动力学模拟奠定基础。
通过构建不同的无定型聚合物模型考察了低聚物在高分子母体中扩散的影响因素,动力学模拟结果表明模拟体系的分子数越多,动力学平衡所需的时间呈几何级数增加。高分子链长增加导致低聚物在高分子母体中的扩散系数降低。低聚物浓度对其扩散系数没有显著影响,不同浓度间扩散系数的微弱差异可能由系数时系统误差引起。随聚合度增加,低聚物在高分子母体中的扩散系数迅速降低。
通过对Limonene分子在PP-H、PP-B、PP-R中扩散的动力学模拟,发现PP-R中均方位移值高于PP-B、PP-H,扩散系数随PP-H、PP-B、PP-R的顺序增加。采用Connolly表面计算了探针原子半径rp=0.9A、1.1 A、1.28 A、2.09 A时PP-H、PP-B、PP-R中可被探针原子访问自由体积,随着迁移分子半径增加聚合物基体中可被迁移分子访问的自由体积越来越少,PP-R元胞模型中可被探针分子访问的自由体积比PP-H、PP-B元胞模型不仅数量上多而且连成的自由体积区域面积大,这解释了迁移物在PP-R中的扩散系数大于迁移物在PP-H、PP-B中的扩散系数的原因。通过观察Limonene分子在PP-H、PP-B、PP-R元胞模型中的运动和扩散轨迹发现,跳跃扩散机理并不适合于解释Limonene分子在聚丙烯中的扩散行为。在相当长的模拟时间内Limonene分子在聚合物基体中作缓慢地蠕动,而不是跳跃。Limonene分子在PP-R和PP-B中扩散轨迹范围非常宽,说明Limonene分子在PP-R和PP-B中比PP-H中运动更活跃,这也与扩散系数的计算结果相吻合。
通过对13种迁移物分子在聚对苯二甲酸乙二酯中扩散的动力学模拟,发现动力学模拟得到的扩散系数与实验值很接近,模拟得到的活化能与实验活化能具有很好的一致性。采用Connolly表面方法定量计算PET-迁移物分子模型中的自由体积总量、自由体积分数和自由体积形态。利用球形探测原子方法计算自由体积分数时,探测原子半径rp对自由体积分数计算结果影响很大。随着rp增大时,自由体积分数迅速减小。随温度增加,模型中可容纳迁移物分子的自由体积增加。温度增加导致聚合物链段活性增强,链段活性越强连接自由体积空穴间的通道变化越快,很多较小的自由体积空穴有可能连接在一起而形成一个较大的空穴,恰好能够容纳迁移物分子,从而有利于迁移物分子在聚合物基体中扩散。观察迁移物在聚合物中的扩散轨迹,发现第一类分子在元胞模型中的扩散轨迹分布范围非常宽,分子在元胞模型中的运动非常活跃。第三类分子在元胞模型中的扩散轨迹密密麻麻地重叠在一起,分子在元胞模型中运动能力有限。第三类分子在元胞模型中的扩散轨迹介于第一类和第二类之间,轨迹分布范围宽,仍有部分重叠。这说明迁移物分子在元胞中的扩散轨迹强烈地依赖于分子形状和分子体积(分子质量),与扩散系数计算表现出的规律性相一致。
Migration from plastic food packaging materials into food initiates widespread concern of the consumers on food safety. Migration process can be divided to three different but interrelated stages:diffuse through polymers, dissolve at the interface between polymer and food, and disperse into food bulk, respectively corresponding to "diffusion, dissolution and dispersion" Given some reasonable assumptions on such above three stages, the migration mathematics models based on Fick's second law can be obtained. There has one key model parameter for most of migration mathematics models, diffusion coefficient, which decides the migration dynamic process. The most important question for the migration mathematics models is to obtain the diffusion coefficients of migrant in polymer during the migration process.
The paper first analyzes in detail the influence factors of diffusion coefficients, such as the properties of polymer, the properties of migrants, temperature, interaction between polymer and food, et al. Then, the paper take the polyolefins as examples to analyze the difference of diffusion coefficients between experimental values and the values predicted by four kinds of diffusion estimation models, and take non-polyolefins as examples to discuss the applicability of Brandsch model which is one of diffusion estimation models. Besides, the paper reviews the migration test method of diffusion coefficients, such as contact with solvent and without solvent. The principle design of method without solvent is consistent with the idea of the method to obtain diffusion coefficients by molecular dynamics simulations.
It is very difficult for experimental test methods to obtain diffusion coefficients while it is hard to determine the model parameters for diffusion models. Not only the experimental test methods but also the diffusion estimation models are all lack of the intrinsic acknowledge about the microcosmic structures and diffusion mechanisms. In recent years molecular dynamics simulation based on Newton's classical mechanics have been the tools to study the polymer material structures as well as its diffusion mechanisms. The paper reviews the basic theories of molecular dynamics methods, such as the development history, principle, technical details and molecular force-fileds. The application of molecular dynamics simulations on small molecules diffusion in polymer are summarized from three respects-diffusion mechanisms, influences factors and quantitative description.
Molecular dynamics simulations are used to study diffusion of oligmers in amorphous poly(methyl methacrylate). A number of amorphous models with periodic boundary conditions are generated by changing the chains length of PMMA, polymerization degree and contents of oligomers. The results of molecular dynamics simulations show that the simulations time to reach dynamics equilibrium increases exponentially when the number of molecules in the systems increases. The diffusion coefficients reduce with the increase of polymer chains. The contents of oligomer do not significantly affect the diffusion coefficients and the weak discrepancy may be result from the system errors. The diffusion coefficients reduce rapidly with the increase of polymerization degree.
Taking limonene as the model migrant, the diffusion properties of three types of polypropylene materials are studied by using molecular dynamics method. The diffusion coefficients of limonene through PP-H, PP-B and PP-R are evaluated from the limiting slope of the mean square displacements as a function of time. The diffusion coefficient of Limonene in PP-H at 313K is 3.39×10-9cm2/s, which is consist with the values of the literature reports 2.1×10-9cm2/s. The free volume in polymer matrix plays vital roles in diffusion of low molecular-weight through polymer materials. A Connolly surface is calculated to define the free volume. The results suggest that the accessible free volume reduces with the probe radius increase. Another phenomenon can be observed that not only the amount of accessible free volume in PP-R cell model is larger than that of PP-H and PP-B, but also the free volume combines a piece of area. That can also explain why the diffusion coefficients of limonene in PP-R are higher than that of PP-H and PP-B. The movement of limonene molecules through PP-H, PP-B and PP-R cell model at different simulation time suggest that hopping diffusion mechanism is not suitable to explain the diffusion of limonene in polypropylene. For a long time limonene molecules slowly squirm in the polymer simulation cell rather than jump. The movement trajectories of limonene molecules in PP-R have very wide range and reveal that the movements of limonene in PP-R are more active. That is consistent with the calculated diffusion coefficients.
The diffusion coefficients of 13 kinds of small molecules with molecular weights ranging from 32 to 339 g/mol in amorphous PET are calculated based on molecular dynamics simulation. By comparison of diffusion coefficients simulated by MD simulation techniques, predicted by Brandsch model and by experiments, the accuracy of Brandsch model and MD simulation techniques for estimation of diffusion coefficients of migrants in PET is evaluated. The activation energy is calculated by Arrhenius equation which characterizes the relationship between diffusion coefficient and temperature. It is shown that the MD simulation yields acceptable activation energy. Connolly surface method is used to calculate the amount, fraction and morphology of free volume. The results show that the fraction of free volume reduces rapidly with the increase of the probe radius. The temperature leads to the increase of mobility of polymer chains, furthermore induces the fast change of channel between free volume cavities in polymer matrix. Some small free volume cavities conjoin together and form the larger cavities which exactly accommodate migrant molecules. Thus, it facilitates the diffusion of migrant molecules in polymer matrix. The diffusion trajectories suggest that the molecules in first class move actively, but the molecules in class third class move limitedly and the movement mobility of molecules in second class is between that of first class and third class.
The study suggests that MD simulation may be a useful approach to calculate the diffusion coefficients and understand the polymer structure and diffusion mechanism.
为此,本文首先深入分析了扩散系数的影响因素：聚合物特性、迁移物特性、温度、聚合物与食品溶剂间的相互作用等,以聚烯烃为例深入分析了四种常见的扩散系数估测模型预测值与实验值间的差异,以非聚烯烃为例深入分析了Brandsch模型的适用性。介绍了扩散系数的迁移测试方法——与溶剂接触法和无溶剂接触法,无溶剂接触法的思想与采用分子动力学模拟获取扩散系数的思想相一致。
实验测试扩散系数非常困难,经验估算公式又存在参数难以确定等问题,都缺乏对聚合物微观结构和扩散机理的本质认识。近年来基于经典力学的分子动力学模拟已经成为研究聚合物材料结构及其扩散机理的工具。因此,本文概述了分子动力学发展历程、动力学原理、技术细节、分子力场等动力学基本理论,对小分子在聚合物中扩散的动力学模拟从扩散机理、影响因素和定量描述三个方面进行了总结,为随后的动力学模拟奠定基础。
通过构建不同的无定型聚合物模型考察了低聚物在高分子母体中扩散的影响因素,动力学模拟结果表明模拟体系的分子数越多,动力学平衡所需的时间呈几何级数增加。高分子链长增加导致低聚物在高分子母体中的扩散系数降低。低聚物浓度对其扩散系数没有显著影响,不同浓度间扩散系数的微弱差异可能由系数时系统误差引起。随聚合度增加,低聚物在高分子母体中的扩散系数迅速降低。
通过对Limonene分子在PP-H、PP-B、PP-R中扩散的动力学模拟,发现PP-R中均方位移值高于PP-B、PP-H,扩散系数随PP-H、PP-B、PP-R的顺序增加。采用Connolly表面计算了探针原子半径rp=0.9A、1.1 A、1.28 A、2.09 A时PP-H、PP-B、PP-R中可被探针原子访问自由体积,随着迁移分子半径增加聚合物基体中可被迁移分子访问的自由体积越来越少,PP-R元胞模型中可被探针分子访问的自由体积比PP-H、PP-B元胞模型不仅数量上多而且连成的自由体积区域面积大,这解释了迁移物在PP-R中的扩散系数大于迁移物在PP-H、PP-B中的扩散系数的原因。通过观察Limonene分子在PP-H、PP-B、PP-R元胞模型中的运动和扩散轨迹发现,跳跃扩散机理并不适合于解释Limonene分子在聚丙烯中的扩散行为。在相当长的模拟时间内Limonene分子在聚合物基体中作缓慢地蠕动,而不是跳跃。Limonene分子在PP-R和PP-B中扩散轨迹范围非常宽,说明Limonene分子在PP-R和PP-B中比PP-H中运动更活跃,这也与扩散系数的计算结果相吻合。
通过对13种迁移物分子在聚对苯二甲酸乙二酯中扩散的动力学模拟,发现动力学模拟得到的扩散系数与实验值很接近,模拟得到的活化能与实验活化能具有很好的一致性。采用Connolly表面方法定量计算PET-迁移物分子模型中的自由体积总量、自由体积分数和自由体积形态。利用球形探测原子方法计算自由体积分数时,探测原子半径rp对自由体积分数计算结果影响很大。随着rp增大时,自由体积分数迅速减小。随温度增加,模型中可容纳迁移物分子的自由体积增加。温度增加导致聚合物链段活性增强,链段活性越强连接自由体积空穴间的通道变化越快,很多较小的自由体积空穴有可能连接在一起而形成一个较大的空穴,恰好能够容纳迁移物分子,从而有利于迁移物分子在聚合物基体中扩散。观察迁移物在聚合物中的扩散轨迹,发现第一类分子在元胞模型中的扩散轨迹分布范围非常宽,分子在元胞模型中的运动非常活跃。第三类分子在元胞模型中的扩散轨迹密密麻麻地重叠在一起,分子在元胞模型中运动能力有限。第三类分子在元胞模型中的扩散轨迹介于第一类和第二类之间,轨迹分布范围宽,仍有部分重叠。这说明迁移物分子在元胞中的扩散轨迹强烈地依赖于分子形状和分子体积(分子质量),与扩散系数计算表现出的规律性相一致。
Migration from plastic food packaging materials into food initiates widespread concern of the consumers on food safety. Migration process can be divided to three different but interrelated stages:diffuse through polymers, dissolve at the interface between polymer and food, and disperse into food bulk, respectively corresponding to "diffusion, dissolution and dispersion" Given some reasonable assumptions on such above three stages, the migration mathematics models based on Fick's second law can be obtained. There has one key model parameter for most of migration mathematics models, diffusion coefficient, which decides the migration dynamic process. The most important question for the migration mathematics models is to obtain the diffusion coefficients of migrant in polymer during the migration process.
The paper first analyzes in detail the influence factors of diffusion coefficients, such as the properties of polymer, the properties of migrants, temperature, interaction between polymer and food, et al. Then, the paper take the polyolefins as examples to analyze the difference of diffusion coefficients between experimental values and the values predicted by four kinds of diffusion estimation models, and take non-polyolefins as examples to discuss the applicability of Brandsch model which is one of diffusion estimation models. Besides, the paper reviews the migration test method of diffusion coefficients, such as contact with solvent and without solvent. The principle design of method without solvent is consistent with the idea of the method to obtain diffusion coefficients by molecular dynamics simulations.
It is very difficult for experimental test methods to obtain diffusion coefficients while it is hard to determine the model parameters for diffusion models. Not only the experimental test methods but also the diffusion estimation models are all lack of the intrinsic acknowledge about the microcosmic structures and diffusion mechanisms. In recent years molecular dynamics simulation based on Newton's classical mechanics have been the tools to study the polymer material structures as well as its diffusion mechanisms. The paper reviews the basic theories of molecular dynamics methods, such as the development history, principle, technical details and molecular force-fileds. The application of molecular dynamics simulations on small molecules diffusion in polymer are summarized from three respects-diffusion mechanisms, influences factors and quantitative description.
Molecular dynamics simulations are used to study diffusion of oligmers in amorphous poly(methyl methacrylate). A number of amorphous models with periodic boundary conditions are generated by changing the chains length of PMMA, polymerization degree and contents of oligomers. The results of molecular dynamics simulations show that the simulations time to reach dynamics equilibrium increases exponentially when the number of molecules in the systems increases. The diffusion coefficients reduce with the increase of polymer chains. The contents of oligomer do not significantly affect the diffusion coefficients and the weak discrepancy may be result from the system errors. The diffusion coefficients reduce rapidly with the increase of polymerization degree.
Taking limonene as the model migrant, the diffusion properties of three types of polypropylene materials are studied by using molecular dynamics method. The diffusion coefficients of limonene through PP-H, PP-B and PP-R are evaluated from the limiting slope of the mean square displacements as a function of time. The diffusion coefficient of Limonene in PP-H at 313K is 3.39×10-9cm2/s, which is consist with the values of the literature reports 2.1×10-9cm2/s. The free volume in polymer matrix plays vital roles in diffusion of low molecular-weight through polymer materials. A Connolly surface is calculated to define the free volume. The results suggest that the accessible free volume reduces with the probe radius increase. Another phenomenon can be observed that not only the amount of accessible free volume in PP-R cell model is larger than that of PP-H and PP-B, but also the free volume combines a piece of area. That can also explain why the diffusion coefficients of limonene in PP-R are higher than that of PP-H and PP-B. The movement of limonene molecules through PP-H, PP-B and PP-R cell model at different simulation time suggest that hopping diffusion mechanism is not suitable to explain the diffusion of limonene in polypropylene. For a long time limonene molecules slowly squirm in the polymer simulation cell rather than jump. The movement trajectories of limonene molecules in PP-R have very wide range and reveal that the movements of limonene in PP-R are more active. That is consistent with the calculated diffusion coefficients.
The diffusion coefficients of 13 kinds of small molecules with molecular weights ranging from 32 to 339 g/mol in amorphous PET are calculated based on molecular dynamics simulation. By comparison of diffusion coefficients simulated by MD simulation techniques, predicted by Brandsch model and by experiments, the accuracy of Brandsch model and MD simulation techniques for estimation of diffusion coefficients of migrants in PET is evaluated. The activation energy is calculated by Arrhenius equation which characterizes the relationship between diffusion coefficient and temperature. It is shown that the MD simulation yields acceptable activation energy. Connolly surface method is used to calculate the amount, fraction and morphology of free volume. The results show that the fraction of free volume reduces rapidly with the increase of the probe radius. The temperature leads to the increase of mobility of polymer chains, furthermore induces the fast change of channel between free volume cavities in polymer matrix. Some small free volume cavities conjoin together and form the larger cavities which exactly accommodate migrant molecules. Thus, it facilitates the diffusion of migrant molecules in polymer matrix. The diffusion trajectories suggest that the molecules in first class move actively, but the molecules in class third class move limitedly and the movement mobility of molecules in second class is between that of first class and third class.
The study suggests that MD simulation may be a useful approach to calculate the diffusion coefficients and understand the polymer structure and diffusion mechanism.
引文
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