非均匀温度场明胶物理凝胶化转变过程数值模拟
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摘要
随着科学技术的发展,凝胶材料在人们日常生活中的应用越来越广泛,已受到越来越多的重视。其中,聚合物物理凝胶是凝胶材料中的一大类,具有溶胶—凝胶和凝胶—溶胶可逆转变的优良特性。基于此特性,聚合物物理凝胶通常用作智能材料实现某一方面的功能,这是与通常用作结构材料的化学凝胶相比较的一个巨大不同。因此,不论从当今科技发展前进的方向,还是从人们日常生活的需要看,聚合物物理凝胶已成为一种非常前沿与重要的材料,具有巨大的科研与实际应用价值。
明胶凝胶是聚合物物理凝胶中的一种。当温度低于平衡溶解温度时,明胶溶胶中的无规线团分子会互相缠绕形成三螺旋结构,并以此为交联点把明胶分子链连接成三维网状结构。三螺旋的浓度达到一定值,明胶溶胶即变成凝胶。当温度高于平衡溶解温度时,三螺旋结构便会溶解,凝胶又会重新变为溶胶。基于此优良的可逆转变特性,明胶被广泛应用于药物控释缓释、生物组织工程、照相感光、食品、化妆品和日用品等行业中。
研究者们对明胶物理凝胶开展了大量的研究工作,包括：凝胶化机理、凝胶化动力学、凝胶化过程中交联结构和宏观性能的分析等。由于明胶是热的不良导体,在明胶物理凝胶化过程中,低的导热系数必然会导致明胶内部产生非均匀的温度场,最终造成转变过程中明胶结构和性能的非均匀性。尤其当明胶产品体积比较大时,这种情况更为明显。明胶结构和性能的非均匀性将直接影响明胶的使用。例如,作为药物载体,明胶凝胶不均匀的交联密度会影响药物释放速率的稳定性；作为生物组织支架,明胶凝胶不均匀的力学性能会影响支架的强度和寿命。由于目前的实验手段在时空间尺度上测量动态凝胶化过程中明胶的结构与性能存在很大困难,因此本文采用计算机模拟的方法来研究这个问题。
本文采用有限元方法,模拟研究复杂温度场下明胶物理凝胶的唯象凝胶化演变行为,分析凝胶化过程中明胶交联结构与宏观性能的演变规律,揭示由非均匀温度场引发的不同位置节点上凝胶结构与性能的差异,并探究材料配方和工艺条件对凝胶结构与性能的影响。
主要工作与结论如下：
(1)根据明胶线团—螺旋转变动力学方程,确定了三螺旋转化率的动力学模型,按照向后差分的方法,构建了三螺旋转化率的数值计算式；把每一个三螺旋结构看成是一个交联点,提出了交联密度增量的概念,构建了全量交联密度的数值计算式；引入三螺旋长度分布密度函数的概念来描述三螺旋的长度分布；定义了数均三螺旋长度、重均三螺旋长度和三螺旋长度多分散指数。
(2)推导出明胶比旋光度与三螺旋转化率的关系式；建立了在凝胶点时三螺旋转化率与明胶初始浓度的关系,并根据三螺旋转化率判断凝胶点；根据动态标度理论,计算明胶凝胶点前的零剪切黏度、凝胶点后的平衡剪切模量和储能剪切模量。
(3)详述了明胶凝胶化温度场的离散、插值函数计算、单元变分、总体合成及边界条件的有限元分析过程,忽略明胶线团—螺旋转变中的微弱放热,获得了非稳态温度场的有限元计算方程。
(4)阐述了考虑温度场非均匀分布与变化的明胶物理凝胶化转变场的有限元模拟方法及具体步骤,说明了若干关键技术与关键数值的处理,如凝胶化区域的离散方法与准则、传热边界条件的选取、凝胶化温度的选取、等压比热容与导热系数等热物理性能参数的计算和确定、性能计算中流变指数和指前因子的确定等。自主开发了明胶冷致物理凝胶化转变过程的有限元模拟程序。
(5)将数值模拟结果与相同凝胶化条件下的实验结果进行了对比,结果表明,两者的三螺旋转化率和储能剪切模量非常相近,验证了数值模拟程序的正确性。使用模拟程序,分析了一个内含型芯的矩形明胶试样凝胶化转变的二维问题,该模型的边界条件虽然是恒定作用的,但由边界向模型体内传输形成的温度场是不均匀的。通过对结构参数和性能参数的演化模拟,发现了既有科学价值又有实用指导意义的结果。基于模拟结果提出了改变材料配方和工艺条件的设计措施。
With the development of science and technology, gels have been widely used in people's daily life, and are paid more and more attentions by researchers. Polymer physical gel is a major class of gel material, which has good sol-gel and gel-sol reversible transition property. Due to this special property, polymer physical gels are commonly used as smart materials to achieve certain functions, which are different from polymer chemical gels that are used as structural materials. Whether from the aspect of the development direction of modern science and technology, or from the aspect of the need in people's daily life, polymer physical gels have become very advanced and important materials, and have great scientific and practical application values.
Gelatin gel is one kind of polymer physical gel. When the temperature of gelatin is reduced below the equilibrium melting temperature, the gelatin molecule coils will wrap each other to form triple helix structure. These helices act as the crosslinks and connect the molecules to form three-dimensional network structure. When the concentration of triple helices reaches a certain value, the gelatin gel is formed. When the gelatin temperature is increased above the equilibrium melting temperature, the helices will melt again, and the gel will transform into the sol. Attributed to the good features of reversible transition, gelatin is widely used in controlled drug release, biological tissue engineering, photographic, food and cosmetic industries.
Plenty of studies on the gelatin physical gel have been carried out by researchers, which include gelation mechanisms, gelation kinetics, analysis on the crosslinked structure and macroscopic performance during the gelation process. In the gelation process of gelatin, the low thermal conductivity of gelatin can lead to the uneven and unstable temperature field, which further results in the structural and performance inhomogeneities, especially when the gelatin is large. The structural and performance inhomogeneities of gelatin will directly affect its application. E.g., as a drug carrier, a gelatin gel with nonuniform crosslinking degree can adjust the rate of drug release. As a biological tissue scaffold, the inhomogeneity of the mechanical property of gelatin can affect the strength and life of the scaffold. The dynamic gelation process makes it difficult to measure the structural and performance parameters in time and space scales in experiments. Hence, the computer simulations are used to analyze the gelation processes of gelatin.
In this dissertation, the study on gelation processes of gelatin under complicated temperature field is carried out by finite element method. The evolution characters of crosslinked structure and macroscopic performance during the gelation processes are analyzed. The differences of gel structure and performance on different nodes caused by uneven temperature field are revealed, and the effects of material formulation and processing conditions on gel structure and performance are discussed.
The main works and conclusions are as follows.
(1) The coil-helix transition kinetic model of gelatin under complicated temperature field is rebuilt on the basis of the kinetic equations. The numerical calculation equations of reverted helix fraction are constructed on the basis of backwards difference method. Each triple helix is considered as a crosslink, the definition of crosslinking density increment is presented, and the numerical calculated equation of the total crosslinking density is constructed. A length distribution density function is introduced to describe the continuous distribution of the triple helix length. The number average helix length, weight average helix length and helix polydispersity index are defined during the calculation.
(2) The numerical relationship equations between the specific optical rotation of gelatin and the reverted helix fraction are deduced. The relationship equation between the reverted helix fraction and the initial concentration of gelatin at the gel point is constructed, and the reverted helix fraction value can be used as the criterion to judge the gel point. The viscosity before the gel point, the equilibrium shear modulus and storage shear modulus beyond the gel point are calculated on the basis of dynamic scaling theory.
(3) The finite element analytic processes of the discreteness of temperature field, calculation of interpolation function, element variation, total synthesis and boundary conditions are described in detail. The finite element calculated equations of uneven temperature field are obtained regardless of the weak exothermic.
(4) The finite element simulation method and specific steps of gelatin physical gelation field are expounded by considering the uneven temperature field. The handling of some key technologies and values are explained, e.g., the discrete methods and rules of gelation fields, selection of heat transfer boundary conditions, selection of gelation temperature, the calculation and determination of thermal physical parameters such as the isopiestic specific heat capacity and thermal conductivity, the determination of rheological indexes and prefactors during the calculation on the performance parameters. The finite element simulation programs of thermal induced gelatin physical gelation processes are developed.
(5) The comparisons between the simulation results and the experimental ones under the same gelation conditions show that the values of reverted helix fraction and storage shear modulus of the two kinds of results are very similar, the simulation programs are proved to be correct. A two-dimensional model of a rectangular gelatin with a rectangular core inside is analyzed by the simulation program. Although the boundary conditions are constant, the temperature field formed by the heat transfer is uneven. The simulation results on the evolution of the structural and performance parameters have both scientific and practical significance. The design of changing material formula and processing conditions is suggested on the basis of the simulation results.
明胶凝胶是聚合物物理凝胶中的一种。当温度低于平衡溶解温度时,明胶溶胶中的无规线团分子会互相缠绕形成三螺旋结构,并以此为交联点把明胶分子链连接成三维网状结构。三螺旋的浓度达到一定值,明胶溶胶即变成凝胶。当温度高于平衡溶解温度时,三螺旋结构便会溶解,凝胶又会重新变为溶胶。基于此优良的可逆转变特性,明胶被广泛应用于药物控释缓释、生物组织工程、照相感光、食品、化妆品和日用品等行业中。
研究者们对明胶物理凝胶开展了大量的研究工作,包括：凝胶化机理、凝胶化动力学、凝胶化过程中交联结构和宏观性能的分析等。由于明胶是热的不良导体,在明胶物理凝胶化过程中,低的导热系数必然会导致明胶内部产生非均匀的温度场,最终造成转变过程中明胶结构和性能的非均匀性。尤其当明胶产品体积比较大时,这种情况更为明显。明胶结构和性能的非均匀性将直接影响明胶的使用。例如,作为药物载体,明胶凝胶不均匀的交联密度会影响药物释放速率的稳定性；作为生物组织支架,明胶凝胶不均匀的力学性能会影响支架的强度和寿命。由于目前的实验手段在时空间尺度上测量动态凝胶化过程中明胶的结构与性能存在很大困难,因此本文采用计算机模拟的方法来研究这个问题。
本文采用有限元方法,模拟研究复杂温度场下明胶物理凝胶的唯象凝胶化演变行为,分析凝胶化过程中明胶交联结构与宏观性能的演变规律,揭示由非均匀温度场引发的不同位置节点上凝胶结构与性能的差异,并探究材料配方和工艺条件对凝胶结构与性能的影响。
主要工作与结论如下：
(1)根据明胶线团—螺旋转变动力学方程,确定了三螺旋转化率的动力学模型,按照向后差分的方法,构建了三螺旋转化率的数值计算式；把每一个三螺旋结构看成是一个交联点,提出了交联密度增量的概念,构建了全量交联密度的数值计算式；引入三螺旋长度分布密度函数的概念来描述三螺旋的长度分布；定义了数均三螺旋长度、重均三螺旋长度和三螺旋长度多分散指数。
(2)推导出明胶比旋光度与三螺旋转化率的关系式；建立了在凝胶点时三螺旋转化率与明胶初始浓度的关系,并根据三螺旋转化率判断凝胶点；根据动态标度理论,计算明胶凝胶点前的零剪切黏度、凝胶点后的平衡剪切模量和储能剪切模量。
(3)详述了明胶凝胶化温度场的离散、插值函数计算、单元变分、总体合成及边界条件的有限元分析过程,忽略明胶线团—螺旋转变中的微弱放热,获得了非稳态温度场的有限元计算方程。
(4)阐述了考虑温度场非均匀分布与变化的明胶物理凝胶化转变场的有限元模拟方法及具体步骤,说明了若干关键技术与关键数值的处理,如凝胶化区域的离散方法与准则、传热边界条件的选取、凝胶化温度的选取、等压比热容与导热系数等热物理性能参数的计算和确定、性能计算中流变指数和指前因子的确定等。自主开发了明胶冷致物理凝胶化转变过程的有限元模拟程序。
(5)将数值模拟结果与相同凝胶化条件下的实验结果进行了对比,结果表明,两者的三螺旋转化率和储能剪切模量非常相近,验证了数值模拟程序的正确性。使用模拟程序,分析了一个内含型芯的矩形明胶试样凝胶化转变的二维问题,该模型的边界条件虽然是恒定作用的,但由边界向模型体内传输形成的温度场是不均匀的。通过对结构参数和性能参数的演化模拟,发现了既有科学价值又有实用指导意义的结果。基于模拟结果提出了改变材料配方和工艺条件的设计措施。
With the development of science and technology, gels have been widely used in people's daily life, and are paid more and more attentions by researchers. Polymer physical gel is a major class of gel material, which has good sol-gel and gel-sol reversible transition property. Due to this special property, polymer physical gels are commonly used as smart materials to achieve certain functions, which are different from polymer chemical gels that are used as structural materials. Whether from the aspect of the development direction of modern science and technology, or from the aspect of the need in people's daily life, polymer physical gels have become very advanced and important materials, and have great scientific and practical application values.
Gelatin gel is one kind of polymer physical gel. When the temperature of gelatin is reduced below the equilibrium melting temperature, the gelatin molecule coils will wrap each other to form triple helix structure. These helices act as the crosslinks and connect the molecules to form three-dimensional network structure. When the concentration of triple helices reaches a certain value, the gelatin gel is formed. When the gelatin temperature is increased above the equilibrium melting temperature, the helices will melt again, and the gel will transform into the sol. Attributed to the good features of reversible transition, gelatin is widely used in controlled drug release, biological tissue engineering, photographic, food and cosmetic industries.
Plenty of studies on the gelatin physical gel have been carried out by researchers, which include gelation mechanisms, gelation kinetics, analysis on the crosslinked structure and macroscopic performance during the gelation process. In the gelation process of gelatin, the low thermal conductivity of gelatin can lead to the uneven and unstable temperature field, which further results in the structural and performance inhomogeneities, especially when the gelatin is large. The structural and performance inhomogeneities of gelatin will directly affect its application. E.g., as a drug carrier, a gelatin gel with nonuniform crosslinking degree can adjust the rate of drug release. As a biological tissue scaffold, the inhomogeneity of the mechanical property of gelatin can affect the strength and life of the scaffold. The dynamic gelation process makes it difficult to measure the structural and performance parameters in time and space scales in experiments. Hence, the computer simulations are used to analyze the gelation processes of gelatin.
In this dissertation, the study on gelation processes of gelatin under complicated temperature field is carried out by finite element method. The evolution characters of crosslinked structure and macroscopic performance during the gelation processes are analyzed. The differences of gel structure and performance on different nodes caused by uneven temperature field are revealed, and the effects of material formulation and processing conditions on gel structure and performance are discussed.
The main works and conclusions are as follows.
(1) The coil-helix transition kinetic model of gelatin under complicated temperature field is rebuilt on the basis of the kinetic equations. The numerical calculation equations of reverted helix fraction are constructed on the basis of backwards difference method. Each triple helix is considered as a crosslink, the definition of crosslinking density increment is presented, and the numerical calculated equation of the total crosslinking density is constructed. A length distribution density function is introduced to describe the continuous distribution of the triple helix length. The number average helix length, weight average helix length and helix polydispersity index are defined during the calculation.
(2) The numerical relationship equations between the specific optical rotation of gelatin and the reverted helix fraction are deduced. The relationship equation between the reverted helix fraction and the initial concentration of gelatin at the gel point is constructed, and the reverted helix fraction value can be used as the criterion to judge the gel point. The viscosity before the gel point, the equilibrium shear modulus and storage shear modulus beyond the gel point are calculated on the basis of dynamic scaling theory.
(3) The finite element analytic processes of the discreteness of temperature field, calculation of interpolation function, element variation, total synthesis and boundary conditions are described in detail. The finite element calculated equations of uneven temperature field are obtained regardless of the weak exothermic.
(4) The finite element simulation method and specific steps of gelatin physical gelation field are expounded by considering the uneven temperature field. The handling of some key technologies and values are explained, e.g., the discrete methods and rules of gelation fields, selection of heat transfer boundary conditions, selection of gelation temperature, the calculation and determination of thermal physical parameters such as the isopiestic specific heat capacity and thermal conductivity, the determination of rheological indexes and prefactors during the calculation on the performance parameters. The finite element simulation programs of thermal induced gelatin physical gelation processes are developed.
(5) The comparisons between the simulation results and the experimental ones under the same gelation conditions show that the values of reverted helix fraction and storage shear modulus of the two kinds of results are very similar, the simulation programs are proved to be correct. A two-dimensional model of a rectangular gelatin with a rectangular core inside is analyzed by the simulation program. Although the boundary conditions are constant, the temperature field formed by the heat transfer is uneven. The simulation results on the evolution of the structural and performance parameters have both scientific and practical significance. The design of changing material formula and processing conditions is suggested on the basis of the simulation results.
引文
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