pH敏感凝胶平衡溶胀的有限元研究

1943年Flory提出第一个凝胶溶胀理论以来,凝胶溶胀理论的发展极大地促进了凝胶科学的发展．在诸多凝胶溶胀理论中,Flory-Rehner凝胶溶胀理论是最为经典的理论之一,成功地预测了聚合物胶体的诸多溶胀变形特性．但该模型是基于一种最为简单的自由连接链模型,存在精度较差的局限．因此,本文采用能够表征网络缠结拓扑等微观结构影响的弹性自由能模型,即由Edwards-Vilgis提出的Slip-Link模型,构造自由能模型并形成pH敏感凝胶的平衡溶胀理论,并基于Abaqus有限元分析了微观结构及几何限制作用对pH敏感凝胶力学行为的影响．分析结果可为微流体控制阀的设计提供参考．     

非饱和介电凝胶的力学性能及力电失稳行为研究

力-电耦合场作用下,介电凝胶的体积、形状会发生相应的变化,在智能传感器与促动器等领域具有广阔的应用前景．浸入溶液中,介电凝胶将吸收溶液而溶胀．当外界溶液的量足够多时,介电凝胶将吸收足量的溶液而达到饱和状态;但如果外界溶液的量较小,没有足够的溶液可被吸收时,介电凝胶将处于非饱和状态．基于介电凝胶大变形与极化理论,对非饱和介电凝胶在等双轴应力与电场耦合作用下的力学行为及力电失稳现象进行研究．结果表明,饱和度越低介电凝胶的刚性越大,材料越硬;预应力技术可以提高介电凝胶的力电稳定性,预应力越大,力电失稳出现时的临界电压值越高．     

基于Slip-Link模型的凝胶大变形与扩散耦合瞬态问题分析

长链聚合物通过化学键,范德华力等相互作用交联构成的弹性体吸收溶剂后形成聚合物凝胶.聚合物凝胶的溶胀变形过程是溶剂在凝胶网络内的扩散、迁移与凝胶网络变形耦合作用的结果.通常,研究凝胶的扩散-变形耦合问题是基于经典的Flory-Rehner自由能模型进行的,然而该自由能函数由于忽略了凝胶网络链段相互缠绕引起的物理交联对凝胶弹性网络自由能的影响,在计算大变形与扩散耦合问题时误差较大.本文基于Edwards-Vilgis slip-link弹性模型和Flory-Huggins混合理论构建能反映聚合物网络链缠结拓扑限制作用的凝胶自由能函数,并结合凝胶的运动方程和扩散方程,得到能够反映链段缠结影响的凝胶大变形与扩散耦合瞬态方程,并基于此研究网络缠结对凝胶在受压状态下变形梯度和凝胶内溶剂的名义浓度的影响.     

弹性/粘塑性线性硬化模型及有限元算法

1.粘塑性力学的本构方程粘塑性力学的近日研究说明它不仅可用于解决那种对变形率敏感的材料的力学问题,例如材料在高速载荷作用下的时滞现象问题,而且还适用于解决一般塑性力学、应力松弛、蠕变等问题.按照文的定义:弹性-粘塑性,材料在其弹性及塑性阶段均出现粘滞现象;弹性/粘塑性,材料仅在其塑     

双层球壳结构准静态线性化学弹性问题的位移势函数解

本文研究了各向同性固体的化学-力学耦合问题,在传统化学弹性理论描述的扩散-变形耦合关系基础上,进一步考虑了化学反应与固体变形的相互作用关系,发展了等温状态下固体-扩散-反应-变形耦合的线性化学弹性理论,拓展了化学弹性力学的应用范围．该理论能够同时描述固体内介质扩散和固体与介质之间化学反应两个不同时间尺度的化学过程,并给出由此引起的弹性范围内的应变和应力．为应用该模型求解具体化学弹性问题,本文通过构造扩散-反应位移势函数来获得位移特解形式,再与齐次Lamé方程通解叠加获得完整解;针对反应控制问题,引入化学弹性准静态假设,将反应-扩散-变形全耦合的瞬态过程分解为两个可解耦的相继过程,从而获得相应位移解．基于此解法,本文获得了反应控制的双层球壳结构化学弹性问题的解析解,并分析了化学反应、几何结构和弹性模量对应力分布的影响．     

考虑微观变形特征的水凝胶均匀和非均匀溶胀分析及其影响参数研究

本文给出考虑微观变形的水凝胶溶胀的分析模型,该模型假设构成聚合物网络的单链受到由于周围链的作用而产生类似圆管状的约束,并且认为每个单链变形与网络变形之间存在非仿射关系.利用该模型分析了凝胶在自由溶胀情形,预拉伸凝胶单一方向溶胀情形以及具有刚性核的球形凝胶溶胀至平衡状态情形的变形特征.研究表明,对于自由溶胀的均匀变形情形...     

功能梯度球形水凝胶的化学力学耦合分析

作为一种新型智能材料,水凝胶具有特殊的化学力学耦合性能.采用功能梯度形式可使得水凝胶具有更好的适应性和可调控性.本研究中假设交联密度沿径向按幂函数规律变化,并基于水凝胶的大变形多场耦合一般理论,采用Flory-Huggins自由能函数,建立了功能梯度球形水凝胶在球对称情形的控制方程,并开展了功能梯度球形水凝胶在给定内压和化学势情行的非均匀大变形溶胀行为的理论研究.计算结果表明,不同梯度指数的球形水凝胶的内压、内孔半径曲线和内压、内表面径向伸长率曲线均呈现出一段稳定区间和另一段不稳定区间,说明内压超出某临界值会发生失稳并导致水凝胶的最终破坏.内压的临界值随梯度指数的增大而增大.研究表明,功能梯度球形水凝胶的材料参数(梯度指数、亲疏水特性、交联密度和溶剂分子的体积)和环境化学势对水凝胶溶胀行为具有重要的影响.在给定内表面压力的情况下,功能梯度球形水凝胶内表面的径向位移随梯度指数的改变接近为线性变化,而随其他参数的影响都呈现出明显的非线性.本研究有助于实现水凝胶智能结构和器件在复杂条件下的精准调控.}      

超弹性材料的不稳定性问题

超弹性材料是一类性能独特、不可替代且有广泛工程应用的高分子材料,对其独特的材料不稳定性问题的研究极大地推动了连续介质力学有限变形理论和超弹性理论的发展.综述了超弹性材料中的材料不稳定性问题的研究成果和最新进展,包括Rivlin立方块问题、薄壁球壳和薄壁圆筒的内压膨胀问题、圆柱的扭转问题、块体的表面不稳定性问题、空穴的生成、增长和闭合问题等.阐述了这类材料中各类非线性不稳定性问题的特点、问题的求解、主要结果及今后进一步的研究方向等.      

功能梯度球形水凝胶的化学力学耦合分析

作为一种新型智能材料,水凝胶具有特殊的化学力学耦合性能.采用功能梯度形式可使得水凝胶具有更好的适应性和可调控性.本研究中假设交联密度沿径向按幂函数规律变化,并基于水凝胶的大变形多场耦合一般理论,采用Flory-Huggins自由能函数,建立了功能梯度球形水凝胶在球对称情形的控制方程,并开展了功能梯度球形水凝胶在给定内压和化学势情行的非均匀大变形溶胀行为的理论研究.计算结果表明,不同梯度指数的球形水凝胶的内压–内孔半径曲线和内压–内表面径向伸长率曲线均呈现出一段稳定区间和另一段不稳定区间,说明内压超出某临界值会发生失稳并导致水凝胶的最终破坏.内压的临界值随梯度指数的增大而增大.研究表明,功能梯度球形水凝胶的材料参数(梯度指数、亲疏水特性、交联密度和溶剂分子的体积)和环境化学势对水凝胶溶胀行为具有重要的影响.在给定内表面压力的情况下,功能梯度球形水凝胶内表面的径向位移随梯度指数的改变接近为线性变化,而随其他参数的影响都呈现出明显的非线性.本研究有助于实现水凝胶智能结构和器件在复杂条件下的精准调控.     

化学腐蚀后砂岩三轴压缩力学特性及其能量机制的试验研究

为研究不同化学溶液对砂岩力学性质及能量特征的影响,采用不同的水化学溶液对砂岩试样进行腐蚀,利用WDT-1500多功能材料试验机对化学腐蚀后饱和状态与自然状态的试样进行常规三轴压缩试验。试验结果表明:化学腐蚀后砂岩试样的强度及其抗变形能力呈现不同程度的劣化;化学腐蚀后砂岩试样的峰值应变小于相同围压下自然状态试样的峰值应变,与单轴压缩条件下不同,这可能是由于围压和化学溶液共同作用的结果;砂岩试样的似软化系数与围压之间呈现负相关性,同时,其降低速率随着围压的增加而降低。砂岩试样峰值前吸收的能量绝大部分是以可释放弹性应变能Ue形式储存下来的,而化学腐蚀后砂岩试样以Ue形式储存下来的能量占其总吸收应变能的百分比却有所下降;同时,围压与试样的可释放应变能/应变能比值之间呈负相关性,而与耗散能/应变能比值存在正相关性;岩石脆性指标修正值呈现不同程度的增加,试样的脆性减弱延性增强,即塑性变形增加,塑性变形与耗散能之间具有很好的线性特征。溶液的pH值、浓度和化学成分对砂岩试样峰值处各部分应变能的影响显著。     

Equilibrium swelling and electrochemistry of polyampholytic pH-sensitive hydrogel

Immersed in an ionic solution, a network of polyampholytic polyelectrolyte imbibes the solution and swells, resulting in a polyampholytic pH-sensitive hydrogel, which can respond to changes in the surrounding environmental pH. The presence of fixed charges and mobile ions due to the dissociation of ionizable acidic and basic groups may give rise to a region called the electrical double layer of a thickness scaled by the Debye length. Owing to the existence of the electrical double layer, when the size of a polyampholytic pH-sensitive hydrogels is comparable to, or smaller than, the Debye length, the behavior of the gel may deviate from that of the gel of a large size. To account of the size effects, this paper develops a field theory for polyampholytic pH-sensitive hydrogels by coupling large deformation of the network, the dissociation of the functional groups and the migration of the ions and the solvent. The theory is then applied to explore the influence of pH, salt concentration, geometric constraint and the effects of the electrical double layer on swelling properties by analyzing a thin layer of a polyampholytic pH-sensitive hydrogel immersed in a solution.     

A nonlinear,transient finite element method for coupled solvent diffusion and large deformation of hydrogels

Hydrogels are capable of coupled mass transport and large deformation in response to external stimuli. In this paper, a nonlinear, transient finite element formulation is presented for initial boundary value problems associated with swelling and deformation of hydrogels, based on a nonlinear continuum theory that is consistent with classical theory of linear poroelasticity. A mixed finite element method is implemented with implicit time integration. The incompressible or nearly incompressible behavior at the initial stage imposes a constraint to the finite element discretization in order to satisfy the Ladyzhenskaya–Babuska–Brezzi (LBB) condition for stability of the mixed method, similar to linear poroelasticity as well as incompressible elasticity and Stokes flow; failure to choose an appropriate discretization would result in locking and numerical oscillations in transient analysis. To demonstrate the numerical method, two problems of practical interests are considered: constrained swelling and flat-punch indentation of hydrogel layers. Constrained swelling may lead to instantaneous surface instability for a soft hydrogel in a good solvent, which can be regulated by assuming a stiff surface layer. Indentation relaxation of hydrogels is simulated beyond the linear regime under plane strain conditions, in comparison with two elastic limits for the instantaneous and equilibrium states. The effects of Poisson’s ratio and loading rate are discussed. It is concluded that the present finite element method is robust and can be extended to study other transient phenomena in hydrogels.     

Transient analysis of temperature-sensitive neutral hydrogels

A model for transient deformation of neutral hydrogels that takes into account conservation of momentum, energy and mass for the solid polymer and fluid phase is derived, nondimensionalized and analyzed. Slow- and fast-response hydrogels are studied for three cases based on the response of (i) a spherical hydrogel, (ii) a constrained hydrogel slab to a step change in temperature, and (iii) the deformation in a temperature gradient. Model predictions for case (i) are shown to agree well with experiments for swelling and shrinking. For case (ii), solvent can be seen entering at the sides and flowing into the interior and towards the corners, such that the corners undergo a faster deformation than the sides. Immersed in a temperature gradient, case (iii), the hydrogel undergoes a bending motion and reaches a curved equilibrium shape, similar to the bending motion of polyelectrolyte hydrogels subjected to an external electric field. The benefit of the scale analysis conducted here, to predict correctly, prior to numerical computations, important characteristics such as stress, osmotic pressure and deformation times, is also highlighted.     

Swelling-induced ?nite bending of functionally graded p H-responsive hydrogels: a semi-analytical method

Recently, pH-sensitive hydrogels have been utilized in the diverse applications including sensors, switches, and actuators. In order to have continuous stress and deformation ?elds, a new semi-analytical approach is developed to predict the swelling induced?nite bending for a functionally graded(FG) layer composed of a pH-sensitive hydrogel,in which the cross-link density is continuously distributed along the thickness direction under the plane strain condition. Without considering the intermediary virtual reference,the initial state is mapped into the deformed con?guration in a circular shape by utilizing a total deformation gradient tensor stemming from the inhomogeneous swelling of an FG layer in response to the variation of the pH value of the solvent. To enlighten the capability of the presented analytical method, the ?nite element method(FEM) is used to verify the accuracy of the analytical results in some case studies. The perfect agreement con-?rms the accuracy of the presented method. Due to the applicability of FG pH-sensitive hydrogels, some design factors such as the semi-angle, the bending curvature, the aspect ratio, and the distributions of deformation and stress ?elds are studied. Furthermore, the tangential free-stress axes are illustrated in deformed con?guration.     

Computational analysis of smart soft hydrogels subjected to pH-electrical coupled stimuli: Effects of initial geometry

A chemo-electro-mechanical formulation, referred to as the multi-effect-coupling pH-stimulus (MECpH) model, is presented in this paper for the analysis of the effects of the initial geometrical size on the responsive behavior of pH-sensitive hydrogels subject to the coupled stimuli of environmental solution pH and externally applied electric voltage. The model is composed of coupled nonlinear partial differential equations, and it accounts for the diffusion of ionic species, distributive electric potential and large mechanical deformation. In addition, the correlation between the diffusive hydrogen ion within the hydrogel and charge groups fixed to the polymeric network chains is incorporated quantitatively into this MECpH model. For the simulation of the response characteristics of the smart hydrogel, we solve the one-dimensional steady-state problem using the Hermite–Cloud meshless technique. For the MECpH model, the present numerical simulations were compared with experimental data available from literature to validate the accuracy and robustness of the model, and good agreement was observed. Several parameter studies were then carried out in the analysis of the hydrogel swelling when immersed in solution, and it was observed that the initial geometrical size has significant influence on the volume variations of these pH-responsive hydrogels.     

Mechanics and chemical thermodynamics of phase transition in temperature-sensitive hydrogels

This paper uses the thermodynamic data of aqueous solutions of uncrosslinked poly(N-isopropylacrylamide) (PNIPAM) to study the phase transition of PNIPAM hydrogels. At a low temperature, uncrosslinked PNIPAM can be dissolved in water and form a homogenous liquid solution. When the temperature is increased, the solution separates into two liquid phases with different concentrations of the polymer. Covalently crosslinked PNIPAM, however, does not dissolve in water, but can imbibe water and form a hydrogel. When the temperature is changed, the hydrogel undergoes a phase transition: the amount of water in the hydrogel in equilibrium changes with temperature discontinuously. While the aqueous solution is a liquid and cannot sustain any nonhydrostatic stress in equilibrium, the hydrogel is a solid and can sustain nonhydrostatic stress in equilibrium. The nonhydrostatic stress can markedly affect various aspects of the phase transition in the hydrogel. We adopt the Flory-Rehner model, and show that the interaction parameter as a function of temperature and concentration obtained from the PNIPAM-water solution can be used to analyze diverse phenomena associated with the phase transition of the PNIPAM hydrogel. We analyze free swelling, uniaxially and biaxially constrained swelling of a hydrogel, swelling of a core-shell structure, and coexistent phases in a rod. The analysis is related to available experimental observations. Also outlined is a general theory of coexistent phases undergoing inhomogeneous deformation.     

Experimental techniques for mechanical characterization of hydrogels at the microscale

Hydrogel actuators in microfluidic devices must endure the forces of aqueous flow, the constraint of device walls, and the restoring force of elastic membranes. In order to assess the capabilities of hydrogels, three experimental techniques for determining the uniaxial tensile properties and functional swelling properties of microscale hydrogel structures have been developed. Tensile tests were conducted to determine Young's modulus and Poisson's ratio at varying degrees of swelling equilibrium. Force response tests were performed to determine the force exerted by cylindrical hydrogel structures on compression platens held at fixed displacement. Particle image velocimetry, a method originally developed to measure velocity fields in fluid flows, was adapted to investigate the deformation rates at various times within hydrogel structures during volumetric swelling. The techniques and sample fabrication methods outlined are applicable to a variety of hydrogel chemistries.     

Swell-induced surface instability of confined hydrogel layers on substrates

In response to external stimuli, polymeric hydrogels can change volume and shape dramatically. Experimental studies have observed a variety of instability patterns of hydrogels, due to swelling or shrinking, many of which have not been well understood. The present paper considers swell-induced surface instability of a hydrogel layer on a rigid substrate. Based on a recently developed theoretical framework for neutral polymeric gels, a linear perturbation analysis is performed to predict the critical condition for the onset of the surface instability. Using a nonlinear finite element method, numerical simulations are presented to show the swelling process, with the evolution of initial surface perturbations followed by the formation of crease-like surface patterns. In contrast to previously suggested critical conditions for surface creasing, the present study suggests a material-specific condition that predicts a range of critical swelling ratios from about 2.5 to 3.4 and quantitatively relates the critical condition to material properties of the hydrogel system. A stability diagram is constructed with two distinct regions for stable and unstable hydrogels depending on two dimensionless material parameters.