固体推进剂和高分子共混物的微观、介观和宏观多尺度模拟研究
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摘要
随着计算机运算能力的不断提高，计算机模拟在材料设计和开发过程中的作用越来越重要，其可以揭示一些无法或很难从实验获得的微观机理和本质。高分子材料的特性是具有多个时间和空间尺度，到目前为止没有一种单一的模拟方法可以跨越多个时间及空间尺度。本文采用分子动力学（MD）、介观动力学（MesoDyn）、耗散粒子动力学（DPD）和有限元分析方法（FEM）对几种高分子材料的结构与性能进行了研究，主要包括：高分子粘结剂/增塑剂、二元高分子共混物和高分子/粘土纳米复合材料。
固体推进剂和塑性炸药（RBX）的力学性能在很大程度上依赖于配方中高分子粘结剂与增塑剂的相容性。为预测这两种材料的相容性，本文对高分子粘结剂/增塑剂共混物进行了MD和MesoDyn模拟研究，即在COMPASS力场条件下，对端羟基聚丁二烯（HTPB）/癸二酸二辛酯（DOS）和HTPB/硝化甘油（NG）共混物的的密度（ρ）、内聚能密度（CED）、溶度参数（δ）、Flory–Huggins相互作用参数（χ）、玻璃化转变温度（Tg）和力学性能等进行了模拟计算。结果表明通过比较溶度参数差值（Δδ）的大小、分子间径向分布函数g(r)或模拟前后体系密度变化情况均可以推测HTPB/DOS属于相容体系，而HTPB/NG则不然。通过分析温度-体积曲线得到HTPB、HTPB/DOS和HTPB/NG的T_g分别为197.54 K、176.30 K和200.03 K，而HTPB/DOS中只出现一个T_g的情况则进一步表明其为相容体系；另外，通过MD模拟也可以得到共混物的弹性模量（E），体积模量（K）和剪切模量（G），添加DOS增塑剂后使E、K和G显著下降，柔性增强，共混物的力学性能得到有效改善。
将通过MD模拟得到的Δδ转化为MesoDyn模拟的输入参数，然后采用MesoDyn模拟方法对共混体系的介观形貌与动力学演变过程进行了计算。计算所得的等密度图、有序度参数和自由能密度等也可用于判断共混体系的相容性。MD和MesoDyn模拟结果均表明：HTPB/DOS属于相容体系，而HTPB/NG属于不相容体系，其结论与现有实验结果一致。
（2）通过MD、MesoDyn和FEM等模拟计算方法研究了聚丙烯（PP）/尼龙1（1PA11）和聚乳酸（PLA）/聚对苯二甲酸乙二醇酯（PET）共混物的相容性、介观结构和力学性能。分别建立了五个质量比例为10/90、30/70、50/50、70/30和90/10的PP/PA11和PLA/PET共混物。通过MD模拟得到纯物质的δ与文献的实验值比较一致，通过比较模拟得到的χ与临界值χc的大小以及C-C原子对分子间g(r)的大小可以确定在90/10比例下PP/PA11共混具有一定相容性，其它比例下的PP/PA11共混物不相容，而PLA在任意比例下均与PET完全互溶。PP/PA11共混物出现两个T_g，每个值分别对应于各自组分的T_g，而PLA/PET共混物只有一个T_g，通过共混物的玻璃化转变过程也可以证明共混体系的相容与否。
为了进一步探究PP/PA11和PLA/PET共混物的介观结构，将MD模拟的组分间相互作用的χ参数转化为MesoDyn模拟的相互作用参数，采用MesoDyn模拟方法在介观水平研究了共混物的相分离动力学过程，共混物的相容性可以从其介观形态结构得到进一步证实。
将通过MesoDyn模拟得到的周期性模拟盒子中基于网格的两相浓度分布转化为宏观模拟中FEM分析的输入结构，通过FEM分析得到共混体系的力学性能和局部应力分布情况。结果表明：所有的共混物均为各向同性材料，PP/PA11共混物的模量（E，K和G）随PP含量的增加线性降低，PLA/PET共混物的E和G随PLA含量的增加而增加，K随PLA含量的增加而降低，FEM预测的值与实验测试值吻合较好。
（3）通过MD、DPD和FEM等计算模拟方法对PA11/季铵盐（Quat）/蒙脱土（MMT）纳米复合材料的微观分子结构、介观结构和宏观力学性能进行了研究。MD模拟得到的平衡构象表明：Quat分子平铺在MMT上，几乎覆盖了MMT的整个表面，高分子链塌缩在季铵盐分子上，没有直接与MMT表面相接触。Quat与MMT之间存在强烈的相互作用，Quat中的极性基团通过强烈的静电吸引保持在邻近的MMT层上，Quat中的非极性基团通过范德华（vdW）力与高分子链发生作用，Quat与PA11之间的结合能也比较强。
通过将MD模拟得到的非键相互作用能转化为介观模拟中的相互作用参数，采用DPD模拟方法研究了共混物的介观形态结构，DPD模拟得到的介观形貌结构与MD模拟结果一致。将通过DPD模拟得到的介观结构作为宏观模拟中FEM分析的输入结构，采用FEM方法预测了共混物的力学性能。FEM分析结果表明，共混物为各向异性材料，在z方向的模量值与实验值一致，且比垂直与z方向（x和y方向）的低很多。
With the improvement of computational power, computer simulations have played anincreasingly important role in materials modeling and subsequent technology development, asthey can reveal the microscopic pictures of underlying mechanisms that are otherwiseexperimentally inaccessible or difficult to obtain. Polymersarecharacterizedby theirabroadrangeof lengthandtime scales, which, up till now, cannot be encompassed by anysinglemodel or simulation algorithm currently available. In this paper, the moleculardynamics(MD), dissipative particle dynamics (DPD), mesoscopic dynamics (MesoDyn)simulation and the finite element (FEM) methodare employed toinvestigate the relationshipbetween structures and properties in several polymer systems includingpolymerbinder/plasticizer blends, binary polymer/polymer blends and polymer-clay nanocompositessystem.
(1) It has been found that the mechanical properties of solid propellants and plasticbonded explosives (PBX) are largely decided by the compatibility of the polymer binder andplasticizer used in theirs formulation. To predict this compatibility, MD and MesoDynsimulations are conducted in this paper to calculate the density (ρ), cohesive energy density(CED), solubility parameters (δ), the Flory–Huggins interaction parameters,χ, bindingenergies, the glass transition temperature (T_g) and the mechanical properties ofhydroxyl-terminated Polybutadiene (HTPB)/Dioctyl sebacate (DOS) blend and HTPB/nitroglycerine (NG) blend in the COMPASS force field. Then by comparing differentsolubility parameters value (Δδ), the radial distribution functions g(r), or the change in density,it can be all found that HTPB/DOS is a miscibility system while HTPB and NG are not. Inaddition, by analyzing the volume–temperature curve, this paper determines the T_gof HTPB,HTPB/DOS and HTPB/NG, which are 197.54, 176.30 and 200.03 K respectively. The factthat HTPB/DOS has only one glass transition indicates it is a miscible system. Meanwhile,MD simulations can also be used to predict the mechanicalproperties of blends such as tensilemodulus (E), bulk modulus (K) and shear modulus (G) of blends, which will greatly decreasewith the adding of DOS.
In the following process,Δδcalculated through MD simulation serves as the inputparameters of MesoDyn, which is then used to simulate the mesoscale morphologies of blendsand the dynamic evolution process of the system. The obtained isosurface of the density fields,order parameters and free energy density can be further used to predict the compatibility ofthe blend system. The results of both simulations prove that HTPB/DOS is miscibleHTPB/NG is not, which is consistent with the existing experimental observations.
(2) The miscibility, mesoscopic structures and their mechanical properties ofPolypropylene (PP)/Polyamide-11 (PA11) and Polylactide (PLA)/Polyethylene terephthalate(PET) blends are investigated by MD, MesoDyn simulation and FEM method. Five PP/PA11and PLA/PET blends (with the weight ratio at 10/90, 30/70, 50/50, 70/30 and 90/10) areexamined. Theδvalues of pure polymer obtained by using the MD simulation are in goodagreement with the reference data. By comparing the calculatedχwith the critical valuesχcand comparing the different heights of g(r) of the inter-molecular atomic pairs, it can be foundthat PP/PA11 blend is miscible only when its composition is 90/10, while PLA is completelymiscible with PET over the entire composition range. For each PP/PA11 blend system, two T_gcan be detected, each of which indicates the frozen temperature of one component, while onlyone T_gis observed for PLA/PET blends. This also can indicate the miscibility/immiscibility ofstudied blend system.
In order to further study the mesoscopic structures of PP/PA11 and PLA/PET blends, MesoDyn is applied to simulate the phase separation dynamics of the blends at themesoscopic level.χparameters calculated by MD simulation between polymer–polymer areconverted into the interaction MesoDyn parameters. The miscibility/immiscibility is provedby the mesoscopic morphologies of polymer blends.
The distribution of the grid-based concentration density of thetwo phases in the periodicsimulation cell,which are calculated from MesoDyn simulations, are converted into theinputmorphology of FEM method, which is then used to obtain the mechanical propertiesofoverall modulus and local stress distribution.The result indicates that all blends have overallisotropic behavior; in the case of PP/PA11 blends, the increase of PP will lead to the lineardecrease of the modulus (E, G and K), while in the case PLA/PET blends, the increase of PLAwill result in the rise of E and G and the fall of K. which is in consistent with the existingexperimental conclusion.
(3) The atomistic structures, mesoscopic structures and mechanical properties ofPA11/Quat/Montmorillonite (MMT)nanocomposites system are investigated by MD,DPDsimulationand FEM method. The equilibrium conformationsobtained by MD show that theQuat chains are flattenonto the MMT, covering almost the entire surface, and the polymermolecules collapse onto the Quat themselves rather than directly on the MMT surface. Strongfavorableinteractions between MMT and the surfactants exist; the polar groups of the Quat aremaintainedin the proximity of the MMT layer by virtue of a strongelectrostaticattraction.While the apolar groups of the Quat positively interact, mainlyvia vdW forces, withthe polymer chain, and the bindingenergy between PA11 and the Quat is favorable.
The DPDis adopted as the mesoscopic simulation technique,and the interactionparameters of the mesoscopic model areestimated by mapping the corresponding nonbondedinteraction energy values obtainedfrom MD simulations. The predicted structure of polymerblend obtained by DPD is in excellent agreement with MD simulation results. The output ofDPD serves as the input morphology for FEM simulations, which are used to predict theirmechanical properties basedon the simulated morphology.The FEM simulationresults showthe blend has an anisotropic behavior, themodulus along z direction show a good agreement with those of the existing experiments and is lower thanthose perpendiculars to it (xand y).
固体推进剂和塑性炸药（RBX）的力学性能在很大程度上依赖于配方中高分子粘结剂与增塑剂的相容性。为预测这两种材料的相容性，本文对高分子粘结剂/增塑剂共混物进行了MD和MesoDyn模拟研究，即在COMPASS力场条件下，对端羟基聚丁二烯（HTPB）/癸二酸二辛酯（DOS）和HTPB/硝化甘油（NG）共混物的的密度（ρ）、内聚能密度（CED）、溶度参数（δ）、Flory–Huggins相互作用参数（χ）、玻璃化转变温度（Tg）和力学性能等进行了模拟计算。结果表明通过比较溶度参数差值（Δδ）的大小、分子间径向分布函数g(r)或模拟前后体系密度变化情况均可以推测HTPB/DOS属于相容体系，而HTPB/NG则不然。通过分析温度-体积曲线得到HTPB、HTPB/DOS和HTPB/NG的T_g分别为197.54 K、176.30 K和200.03 K，而HTPB/DOS中只出现一个T_g的情况则进一步表明其为相容体系；另外，通过MD模拟也可以得到共混物的弹性模量（E），体积模量（K）和剪切模量（G），添加DOS增塑剂后使E、K和G显著下降，柔性增强，共混物的力学性能得到有效改善。
将通过MD模拟得到的Δδ转化为MesoDyn模拟的输入参数，然后采用MesoDyn模拟方法对共混体系的介观形貌与动力学演变过程进行了计算。计算所得的等密度图、有序度参数和自由能密度等也可用于判断共混体系的相容性。MD和MesoDyn模拟结果均表明：HTPB/DOS属于相容体系，而HTPB/NG属于不相容体系，其结论与现有实验结果一致。
（2）通过MD、MesoDyn和FEM等模拟计算方法研究了聚丙烯（PP）/尼龙1（1PA11）和聚乳酸（PLA）/聚对苯二甲酸乙二醇酯（PET）共混物的相容性、介观结构和力学性能。分别建立了五个质量比例为10/90、30/70、50/50、70/30和90/10的PP/PA11和PLA/PET共混物。通过MD模拟得到纯物质的δ与文献的实验值比较一致，通过比较模拟得到的χ与临界值χc的大小以及C-C原子对分子间g(r)的大小可以确定在90/10比例下PP/PA11共混具有一定相容性，其它比例下的PP/PA11共混物不相容，而PLA在任意比例下均与PET完全互溶。PP/PA11共混物出现两个T_g，每个值分别对应于各自组分的T_g，而PLA/PET共混物只有一个T_g，通过共混物的玻璃化转变过程也可以证明共混体系的相容与否。
为了进一步探究PP/PA11和PLA/PET共混物的介观结构，将MD模拟的组分间相互作用的χ参数转化为MesoDyn模拟的相互作用参数，采用MesoDyn模拟方法在介观水平研究了共混物的相分离动力学过程，共混物的相容性可以从其介观形态结构得到进一步证实。
将通过MesoDyn模拟得到的周期性模拟盒子中基于网格的两相浓度分布转化为宏观模拟中FEM分析的输入结构，通过FEM分析得到共混体系的力学性能和局部应力分布情况。结果表明：所有的共混物均为各向同性材料，PP/PA11共混物的模量（E，K和G）随PP含量的增加线性降低，PLA/PET共混物的E和G随PLA含量的增加而增加，K随PLA含量的增加而降低，FEM预测的值与实验测试值吻合较好。
（3）通过MD、DPD和FEM等计算模拟方法对PA11/季铵盐（Quat）/蒙脱土（MMT）纳米复合材料的微观分子结构、介观结构和宏观力学性能进行了研究。MD模拟得到的平衡构象表明：Quat分子平铺在MMT上，几乎覆盖了MMT的整个表面，高分子链塌缩在季铵盐分子上，没有直接与MMT表面相接触。Quat与MMT之间存在强烈的相互作用，Quat中的极性基团通过强烈的静电吸引保持在邻近的MMT层上，Quat中的非极性基团通过范德华（vdW）力与高分子链发生作用，Quat与PA11之间的结合能也比较强。
通过将MD模拟得到的非键相互作用能转化为介观模拟中的相互作用参数，采用DPD模拟方法研究了共混物的介观形态结构，DPD模拟得到的介观形貌结构与MD模拟结果一致。将通过DPD模拟得到的介观结构作为宏观模拟中FEM分析的输入结构，采用FEM方法预测了共混物的力学性能。FEM分析结果表明，共混物为各向异性材料，在z方向的模量值与实验值一致，且比垂直与z方向（x和y方向）的低很多。
With the improvement of computational power, computer simulations have played anincreasingly important role in materials modeling and subsequent technology development, asthey can reveal the microscopic pictures of underlying mechanisms that are otherwiseexperimentally inaccessible or difficult to obtain. Polymersarecharacterizedby theirabroadrangeof lengthandtime scales, which, up till now, cannot be encompassed by anysinglemodel or simulation algorithm currently available. In this paper, the moleculardynamics(MD), dissipative particle dynamics (DPD), mesoscopic dynamics (MesoDyn)simulation and the finite element (FEM) methodare employed toinvestigate the relationshipbetween structures and properties in several polymer systems includingpolymerbinder/plasticizer blends, binary polymer/polymer blends and polymer-clay nanocompositessystem.
(1) It has been found that the mechanical properties of solid propellants and plasticbonded explosives (PBX) are largely decided by the compatibility of the polymer binder andplasticizer used in theirs formulation. To predict this compatibility, MD and MesoDynsimulations are conducted in this paper to calculate the density (ρ), cohesive energy density(CED), solubility parameters (δ), the Flory–Huggins interaction parameters,χ, bindingenergies, the glass transition temperature (T_g) and the mechanical properties ofhydroxyl-terminated Polybutadiene (HTPB)/Dioctyl sebacate (DOS) blend and HTPB/nitroglycerine (NG) blend in the COMPASS force field. Then by comparing differentsolubility parameters value (Δδ), the radial distribution functions g(r), or the change in density,it can be all found that HTPB/DOS is a miscibility system while HTPB and NG are not. Inaddition, by analyzing the volume–temperature curve, this paper determines the T_gof HTPB,HTPB/DOS and HTPB/NG, which are 197.54, 176.30 and 200.03 K respectively. The factthat HTPB/DOS has only one glass transition indicates it is a miscible system. Meanwhile,MD simulations can also be used to predict the mechanicalproperties of blends such as tensilemodulus (E), bulk modulus (K) and shear modulus (G) of blends, which will greatly decreasewith the adding of DOS.
In the following process,Δδcalculated through MD simulation serves as the inputparameters of MesoDyn, which is then used to simulate the mesoscale morphologies of blendsand the dynamic evolution process of the system. The obtained isosurface of the density fields,order parameters and free energy density can be further used to predict the compatibility ofthe blend system. The results of both simulations prove that HTPB/DOS is miscibleHTPB/NG is not, which is consistent with the existing experimental observations.
(2) The miscibility, mesoscopic structures and their mechanical properties ofPolypropylene (PP)/Polyamide-11 (PA11) and Polylactide (PLA)/Polyethylene terephthalate(PET) blends are investigated by MD, MesoDyn simulation and FEM method. Five PP/PA11and PLA/PET blends (with the weight ratio at 10/90, 30/70, 50/50, 70/30 and 90/10) areexamined. Theδvalues of pure polymer obtained by using the MD simulation are in goodagreement with the reference data. By comparing the calculatedχwith the critical valuesχcand comparing the different heights of g(r) of the inter-molecular atomic pairs, it can be foundthat PP/PA11 blend is miscible only when its composition is 90/10, while PLA is completelymiscible with PET over the entire composition range. For each PP/PA11 blend system, two T_gcan be detected, each of which indicates the frozen temperature of one component, while onlyone T_gis observed for PLA/PET blends. This also can indicate the miscibility/immiscibility ofstudied blend system.
In order to further study the mesoscopic structures of PP/PA11 and PLA/PET blends, MesoDyn is applied to simulate the phase separation dynamics of the blends at themesoscopic level.χparameters calculated by MD simulation between polymer–polymer areconverted into the interaction MesoDyn parameters. The miscibility/immiscibility is provedby the mesoscopic morphologies of polymer blends.
The distribution of the grid-based concentration density of thetwo phases in the periodicsimulation cell,which are calculated from MesoDyn simulations, are converted into theinputmorphology of FEM method, which is then used to obtain the mechanical propertiesofoverall modulus and local stress distribution.The result indicates that all blends have overallisotropic behavior; in the case of PP/PA11 blends, the increase of PP will lead to the lineardecrease of the modulus (E, G and K), while in the case PLA/PET blends, the increase of PLAwill result in the rise of E and G and the fall of K. which is in consistent with the existingexperimental conclusion.
(3) The atomistic structures, mesoscopic structures and mechanical properties ofPA11/Quat/Montmorillonite (MMT)nanocomposites system are investigated by MD,DPDsimulationand FEM method. The equilibrium conformationsobtained by MD show that theQuat chains are flattenonto the MMT, covering almost the entire surface, and the polymermolecules collapse onto the Quat themselves rather than directly on the MMT surface. Strongfavorableinteractions between MMT and the surfactants exist; the polar groups of the Quat aremaintainedin the proximity of the MMT layer by virtue of a strongelectrostaticattraction.While the apolar groups of the Quat positively interact, mainlyvia vdW forces, withthe polymer chain, and the bindingenergy between PA11 and the Quat is favorable.
The DPDis adopted as the mesoscopic simulation technique,and the interactionparameters of the mesoscopic model areestimated by mapping the corresponding nonbondedinteraction energy values obtainedfrom MD simulations. The predicted structure of polymerblend obtained by DPD is in excellent agreement with MD simulation results. The output ofDPD serves as the input morphology for FEM simulations, which are used to predict theirmechanical properties basedon the simulated morphology.The FEM simulationresults showthe blend has an anisotropic behavior, themodulus along z direction show a good agreement with those of the existing experiments and is lower thanthose perpendiculars to it (xand y).
引文
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