Quantifying the elasticity and viscosity of geometrically confined polymer films via thermal wrinkling

We apply thermal wrinkling, which is a surface instability that occurs during thermal annealing of polymer films geometrically confined by a rigid substrate and a flexible superstrate, to study the elasticity and viscosity of chemically crosslinked polymer systems. Specifically, we study the thermal wrinkling of aluminum‐capped polyhydroxystyrene films with different extent of chemical crosslinking and find that that the rate of change of the wrinkling wavelength with annealing time and temperature has unique relationships with the elasticity and viscosity of the polymer network. With the aid of analytical expressions that relate the time‐ and temperature‐dependent evolution of the wrinkle wavelength to the elasticity and viscosity, we are able to quantify the elastic modulus and shear viscosity of geometrically confined polymer thin films as a function of the degree of crosslinking. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Strain-hardening modulus of cross-linked glassy poly(methyl methacrylate)

The strain hardening modulus, defined as the slope of the increasing stress with strain during large strain uniaxial plastic deformation, was extracted from a recently proposed constitutive model for the finite nonlinear viscoelastic deformation of polymer glasses, and compared to previously published experimental compressive true stress versus true strain data of glassy crosslinked poly(methyl methacrylate) (PMMA). The model, which treats strain hardening predominantly as a viscous process, with only a minor elastic contribution, agrees well with the experimentally observed dependence of the strain hardening modulus on strain rate and crosslink density in PMMA, and, in addition, predicts the well-known decrease of the strain hardening modulus in polymer glasses with temperature. General scaling aspects of continuum modeling of strain hardening behavior in polymer materials are also presented. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1464–1472, 2010     

分子动力学模拟浓度和温度对TATB/PCTFE PBX力学性能的影响

为探讨高聚物粘结炸药(Polymer Bonded Explosive, PBX)的力学性能随温度和高聚物浓度而变化的规律, 用分子动力学(MD)方法和compass力场, 对著名高能炸药1,3,5-三氨基-2,4,6-三硝基苯(TATB)与常用高聚物粘结剂聚三氟氯乙烯(PCTFE)所构成的TATB/PCTFE PBX进行模拟计算. 结果表明, 在一定范围内, 随高聚物浓度的增加, PBX的弹性系数和模量减小, 表明其刚性减小、弹性增加; 而随温度的升高, PBX的刚性减小、弹性增强. 还发现PBX的结合能随浓度增高而增大, 随温度升高而减小.     

Kinetics of solvent absorption and permeation through a highly swellable elastomeric network

To model a polymer gel or an elastomer undergoing a large change in volume under the action of a solvent diffusing in or out of it, a theoretical approach based on an elastohydrodynamic point of view is proposed. Drawing a parallel between the polymer network/solvent system of interest and a liquid flowing through a porous medium, the friction between the polymer and the solvent is described phenomenologically. An equation that couples the large elastic deformations undergone by the polymer network and the diffusion process is derived and then solved numerically in various cases. Special emphasis is placed on the influence of the shear elasticity during the diffusion process. During the swelling process, a nonzero shear modulus induces a nonisotropic swelling at the surface that is responsible for the “sigmoidal” shape of the mass uptake of solvent with the square root of time, as well as for the presence of a “front” in the concentration profile when the solvent advances inside the network. In a permeation process, the solvent flux deviates from its linear behavior as soon as a nonnegligible deformation of the membrane is present. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 166–182, 2003     

Determination of the heat resistance of polymer construction materials by the dynamic mechanical method

Russian and foreign standards for the techniques for the determination of the heat resistance of polymer materials are analyzed and the incorrectness of their use for polymer construction materials is shown. The determination of the heat resistance by the low-frequency dynamic mechanical method based on the temperature derivative extrema of the dynamic modulus of elasticity and the dynamic loss modulus under the transition of polymer matrices from the glassy to the highly elastic state is experimentally substantiated for multicomponent polymer compositions with dispersed or fibrous fillers.     

辐射交联顺-1,4-聚丁二烯的网络结构特性和力学性能

本文根据Flory的溶胀理论和橡胶弹性理论,考察了顺-1 4-聚丁二烯辐射交联产物的化学网络和物理缠结网络结构特性及其对固体力学性能的影响。结果表明,交联产物的物理缠结网络密度远远大于化学交联网络密度。随着辐照剂量的增大,化学交联密度增高,物理缠结数下降。探讨了交联、缠结密度与Mooney-Rivlin方程的常数项C_1和C_2的关系。C_1来自化学交联网络的贡献;C_2来自物理缠结的贡献。物理缠结网络主要贡献于交联物体在小形变下的起始弹性模量G_0;化学交联网络则主要贡献于交联物体在大形变下的非线性弹性,即断裂强度(?)_B。     

Numerical simulation of nanoparticle melting inside a matrix

A theoretical model is proposed for describing the melting of a metal nanoparticle embedded into a solid matrix. The model is based on a thermodynamic approach that takes into account matrix elasticity. The melting process is described for gold nanoparticles embedded in a solid matrix whose elastic modulus is varied in a wide range. Both spherical and ellipsoidal particles are considered. It is shown that particle melting temperature can be both higher and lower than the melting point of a bulk sample depending on the interaction intensity of the solid and liquid particle surfaces with the matrix. An increase in the shear modulus of the matrix causes a rise in the nanoparticle melting temperature, with the effect of the matrix elasticity becoming noticeable at some critical shear modulus. The conditions are revealed at which only a surface layer of a nanoparticle, the thickness of which depends on the particle radius and temperature, is melted.     

Interaction of elastic bodies via surface forces. 2. Exponential decay

Our goal is to study theoretically the effect of deformation on the exponentially decaying interaction of two elastic solids separated by a thin liquid film. The deformed shape of the surfaces and the contribution of the elasticity to the total force, i.e., an additional term present between elastic bodies, are calculated from continuum elastic theory via a new asymptotic technique. Both the deformation and the contribution of the elasticity to the force are found to be significant on the length scale over which the surface force acts. The surface deformation is exponentially decaying with a decay length equal to that of the original surface interaction. It is especially important for large and/or rapidly changing force. The contribution of the elasticity is also exponentially decaying, but with half the decay length. Its strength depends on the elastic constants and size of the solids and on the magnitude and gradient of the original surface force. Depending on how the separation is detected, it can appear either as an attractive or as a repulsive contribution to the force. Our results open the possibility of recalculating the measured force to the interaction free energy.     

Elastic modulus profiles in the cross sections of drying alkyd coating films: modelling and experiments

The temporal development of the modulus of elasticity and its profile were studied in water-borne alkyd coatings during the drying process of the coating films. Values of the Young’s moduli of elasticity of free coating films were measured using tensile tests. Since the elastic modulus is related to cross-link density, the values of the moduli give information on the advancement of the drying process. A mathematical model was developed to predict the degree of effective cross-linking and the mechanical behaviour of the drying coating films with different thicknesses. This model is based on trends observed by confocal Raman microspectroscopy, which exhibit the profile of the consumption of double bonds and thus can be used to monitor the development of cross-link density as a function of depth from the film surface. The average values of the Young’s measured moduli were successfully described by the numerical model as a function of drying time.     

Rheology of asphaltene-toluene/water interfaces

The stability of water-in-crude oil emulsions is frequently attributed to a rigid asphaltene film at the water/oil interface. The rheological properties of these films and their relationship to emulsion stability are ill defined. In this study, the interfacial tension, elastic modulus, and viscous modulus were measured using a drop shape analyzer for model oils consisting of asphaltenes dissolved in toluene for concentrations varying from 0.002 to 20 kg/m(3). The effects of oscillation frequency, asphaltene concentration, and interface aging time were examined. The films exhibited viscoelastic behavior. The total modulus increased as the interface aged at all asphaltene concentrations. An attempt was made to model the rheology for the full range of asphaltene concentration. The instantaneous elasticity was modeled with a surface equation of state (SEOS), and the elastic and viscous moduli, with the Lucassen-van den Tempel (LVDT) model. It was found that only the early-time data could be modeled using the SEOS-LVDT approach; that is, the instantaneous, elastic, and viscous moduli of interfaces aged for at most 10 minutes. At longer interface aging times, the SEOS-LVDT approach was invalid, likely because of irreversible adsorption of asphaltenes on the interface and the formation of a network structure.     

Numerical simulation of the tensile modulus of nanoclay-filled polymer composites

A numerical simulation model that incorporates three phases, polymer matrix, interlayer, and clay platelet, was developed to predict the tensile modulus of nanoclay-filled polymer composites. The interlayer was introduced to account for the fact that the mechanical properties of the polymer near the clay surface are different from those of the polymer matrix. The effects of the properties of interlayers, the structure of clay clusters, and platelet distributions upon the modulus of elasticity of the nanocomposites, were studied. The simulation results show that a decrease in the interlayer modulus, as well as an increase in the interlayer thickness, would decrease the modulus of the nanocomposites. Furthermore, it was found that the maximum strain, located in the interlayer near the end of the clay platelet, increases significantly with decreasing interlayer modulus. The effects of the distribution of clay platelets upon composite modulus were interpreted in terms of two parameters, platelet overlap length, and the lateral distance between platelets. Comparison of simulation results with experimental data from the literature has confirmed the reliability of the numerical simulation method used in the present study. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2391–2406, 2004     

Synthesis and mechanical behavior of functionally gradient polyisocyanurate materials based on hydroxy-terminated butadiene rubber

Functionally gradient polyisocyanurate-based structural materials in which the modulus of elasticity could be arbitrarily varied over a continuos range from 3 to 2000 MPa were prepared from hydroxy-terminated butadiene rubber and diphenylmethane diisocyanate. The materials are synthetically obtainable both via bulk polymerization (molding) and as composite materials with fillers of any type, including both highly porous compliant fillers that have no effect on the mechanical properties of the polymer matrix and reinforcing fillers, such as carbon and glass clothes. The trends in the main properties were studied; it was found that, over the entire range of elastic moduli relevant to the glass-to-rubber transition, the materials retain the elastic behavior inherent in polymer glasses, not the viscoelastic behavior characteristic of the transitional region between the glassy and rubbery states.     

半结晶硬弹性聚合物的研究进展

硬弹性材料是结晶或非结晶聚合物在特定的条件下加工而形成的,这类材料表现出高弹性、高模量和突出的低温弹性。文章综述了半结晶硬弹性聚合物的力学性能、形态、结构、弹性机理、制备和应用等。     

Surface Complexation Modeling: II. Strategy for Modeling Polymer and Precipitation Reactions at High Surface Coverage

Three triple-layer model (TLM) surface complexation models that allow for the formation of multinuclear surface complexes or precipitates are compared, based on their ability to simulate cobalt sorption on α-Al₂O₃. These models include: (1) a surface solid solution model, (2) a surface polymer model, and (3) a surface continuum model. The solid solution model accounts for high coverage data by invoking a coprecipitation surface reaction, while the polymer model accomplishes the same task with multinuclear surface complexation reactions. In the continuum model, two polymer reactions and one precipitation reaction are proposed. Modeling results indicate that all of the models work reasonably well at predicting sorption data from moderate to high surface coverage (0.1 to 100%). Because the continuum model is the only one presented which is consistent with spectroscopic data throughout the range of surface coverages examined, this model is suggested as the preferred one for modeling metal ion sorption data. Model predictions of pH-edge and isotherm data are discussed and used in the assessment of the merits of the three TLM models.     

Adsorption of water-soluble polymers with surfactant character. Dilational viscoelasticity

A brief summary of dilational surface viscoelatic properties of spread and adsorbed surfactant polymer films at the air-water interface is reported. The viscoelastic moduli have been measured as a function of frequency and surface pressure. The combination of several techniques, oscillating drop and barrier experiments and electrocapillary waves (ECW), has allowed us to investigate a broad frequency range. The dynamic elasticity epsilon shows a slight change with frequency and a noticeable pressure dependence for both kinds of monolayers. In the spread films, elasticity increases steeply with surface pressure, and reaches a constant value before the polymer begins to dissolve into the bulk. On the other hand, the adsorbed films exhibit a pronounced elasticity maximum, followed by a considerable decay when a loose surface structure is formed. The position of the maximum depends on the polymer chemical composition and molecular weight. The results on the overlapping surface pressure range confirm the dynamic equivalence of spread and adsorbed monolayers. At low surface concentration, the agreement between static and dynamic elasticity is quite satisfactory, but the values diverge considerably at higher surface pressures. The loss modulus omegakappa decreases monotonically with increasing omega, becoming zero (it can even take apparent negative values) for the highest frequencies. The frequency dependence of the elasticity has been well described by the diffusive control model of Lucassen-van den Tempel (LVT). However, its predictions for omegakappa do not coincide with the experimental data. The differences between experimental and theoretical values increase at low frequencies.     

Mechanical properties of polymers containing fillers

The addition of fillers can significantly change the mechanical characteristics of a material. In this paper, a general, mechanistic model is established to determine the moduli, relaxation moduli, break strengths, and break strains for polymer films containing liquid and solid micro fillers. Based on rigorous continuum mechanics principles, this model considers the filler/filler interactions, incorporates the nonlinear synergistic effects of fillers, and provides accurate predictions in comparison with experimental data. The analytical model developed provides information that is not available or extremely difficult to obtain experimentally. The model can be applied to determine the filler/matrix adhesion and filler modulus using measured modulus of a filled polymer film (a filled polymer is a polymer containing fillers). It is found that the compression moduli of polymer films containing liquid fillers differ significantly from the tension moduli, especially when the volume fraction of the filler is high. The difference in compression and tension Young's moduli normalized by the tension Young's modulus is as high as 35%. The relative error in maximum pressure calculation during Hertzian contact caused by using the tension moduli is as high as 48%. The relaxation modulus of a filled polymer film is determined through inverse Laplace transforms of its composite modulus in the s‐space. For a filled polymer film containing liquid phase fillers, a closed form solution for its relaxation modulus has been obtained. It is found that the composite relaxation modulus of the filled polymer is proportional to the relaxation modulus of the matrix polymer multiplied by a factor related to the volume fraction of the liquid filler. The break strength of the filled polymer is found to be proportional to the break strength of the polymer matrix material multiplied by a power function of the modulus ratio of filled polymer to polymer matrix, R. The break strain of the filled polymer is proportional to the break strain of the polymer matrix multiplied by a power function of 1/R. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 155–172, 1999     

The elasticity of alpha-helices

The elasticity of alpha-helices is examined using equilibrium molecular-dynamics simulations. From the statistics of curvatures and twists, we compute the elastic moduli of several representative alpha-helices, both in the presence and absence of aqueous solvent. We discover that the bending modulus (persistence length) of the helices is independent of the amino-acid sequence, although helices in water are slightly softer than in vacuum. The response of the helices under the action of an external force is also computed and compared with continuum mechanics predictions. Within the time scale of our simulation, we show that the properties of alpha-helices are well reproduced by an elastic and isotropic rod. The persistence length (bending modulus) of most alpha-helices in water or vacuum is approximately 100 nm, roughly twice that of DNA.     

Communication: correlation of the instantaneous and the intermediate-time elasticity with the structural relaxation in glassforming systems

The elastic models of the glass transition relate the increasing solidity of the glassforming systems with the huge slowing down of the structural relaxation and the viscous flow. The solidity is quantified in terms of the instantaneous shear modulus G(∞), i.e., the immediate response to a step change in the strain. By molecular-dynamics simulations of a model polymer system, one shows the virtual absence of correlations between the instantaneous elasticity and the structural relaxation. Instead, a well-defined scaling is evidenced by considering the elastic response observed at intermediate times after the initial fast stress relaxation. The scaling regime ranges from sluggish states with virtually pure elastic response on the picosecond time scale up to high-mobility states where fast restructuring events are more apparent.     

Polymer gels and brushes at surfaces

We discuss the adsorption of polymer gels on flat surfaces. Even in cases of complete wetting, where the spreading power S is positive and where an equivalent liquid would spread, the elastic stresses due to the gel deformation upon adsorption oppose spreading. The competition between elasticity characterized by the bulk shear modulus G and capillarity, characterized by the spreading power S, defines a typical length scale 1 = S/G for the deformation in the gel. Macroscopic gels larger than 1 deform only at their edges over a region of size 1. Microscopic gels show a finite deformation despite the elastic stresses. These results can be compared to confined polymer brushes.     

Anisotropic fluctuation model for surfactant-laden liquid-liquid crystal interfaces

A model for thermal fluctuations on surfactant-laden liquid-liquid crystal interfaces is formulated and used to derive the expression of the mean square displacement as a function of four elastic moduli of the interface. The measurable liquid crystal contributions to thermal roughness include the average molecular orientation, the interfacial anchoring modulus, and the bulk elasticity modulus. Surfactant-driven interfacial orientation transitions provide an additional means to extract interfacial elastic moduli parameters in surfactant-laden liquid-liquid crystal interfaces in conjunction with thermal roughness measurements.