Nonlinear stress relaxation of a styrene–butadiene random copolymer

The isothermal uniaxial stress relaxation response in the vicinity of the glass-to-rubber transition has been measured for a lightly crosslinked poly(styrene–butadiene) random copolymer, 85% styrene by weight. The volume change during stress relaxation was determined by measuring the time-dependent lateral contraction of the specimen with a Hall-effect proximity detector. The specimen exhibited an instantaneous dilation upon application of the strain and a subsequent time-dependent volume decrease. The stress relaxation behavior and the associated volume relaxation were determined for a variety of strains and temperatures in both the linear and nonlinear viscoelastic regime. As the applied strain was increased the isothermal tensile modulus decreased and the shape of the log(modulus) vs. log(time) curve was altered. At equal levels of strain the tensile modulus exhibited increasing deviations from the linear viscoelastic response as the temperature was decreased. The maximum difference between the nonlinear tensile modulus and the linear viscoelastic response was observed at short times. Subsequently, the nonlinear tensile modulus began to approach the linear viscoelastic modulus with increasing time. Both the instantaneous dilation and the magnitude of the time-dependent part of the volume change increased as the level of applied strain was increased and/or as the temperature was decreased. The observed nonlinearity in the tensile stress relaxation response has been quantitively related to the experimentally measured volume relaxation with a free-volume model.     

单向应力条件下松弛时间率相关的非线性粘弹性本构模型

基于单向拉伸实验研究和内变量理论 ,提出了一种新的简单的一维非线性粘弹性本构关系 .对两种粘弹性材料 ,即高密度聚乙烯和聚丙烯进行了不同加载速率作用下的拉伸实验研究 ,实验结果表明 ,两种材料的应力应变关系与加载速率相关 ;对材料的应力应变实验数据进行拟合发现 ,材料的松弛时间具有很强的应变率相关性 ,当应变率发生数量级变化时 ,材料的松弛时间也发生数量级的变化 .采用内变量理论 ,导出了在单轴应力条件下松弛时间率相关的非线性粘弹性本构关系的迭代形式 ,并给出其收敛条件 .当采取一次迭代形式时 ,本构关系退化为松弛时间率相关的Maxwell模型 .数值拟合的结果表明 ,一次迭代形式的本构关系就可以很好地拟合和预测实验结果 .     

应变调控单层氧化锌能带结构的第一性原理研究

采用基于密度泛函理论的第一性原理计算对单层ZnO薄膜能带结构的应变调控进行了研究.计算结果表明:沿着之字形方向的压缩应变和扶椅形方向的拉伸应变对薄膜带隙的调控都是线性的,而且带隙调控的范围最大;相反地,在沿着之字形方向的拉伸应变和扶椅形方向的压缩应变的调控下,带隙则呈现出非线性的变化.对于双轴应变的拉伸与压缩,带隙的变化都是非线性的.这种通过不同的应变加载方式来实现对带隙不同程度的调控,对ZnO薄膜在光学和催化等领域的应用具有重要的指导意义.     

Nonlinear viscoelastic behavior of styrene‐[ethylene‐(ethylene‐propylene)]‐styrene block copolymer

Studies on the nonlinear viscoelastic behavior of styrene‐[ethylene‐(ethylene‐propylene)]‐styrene block copolymer (SEEPS) were carried out. The nonlinear viscoelastic region was determined through dynamic strain sweep test, and the critical shear strain (γ_c) of transition from linear viscoelastic region to nonlinear viscoealstic region was obtained. The relaxation time and modulus corresponding to the characteristic relaxation modes were also acquired through simulating the linear relaxation modulus curves using Maxwell model, and the damping functions were evaluated. Meanwhile, it is found that the nonlinear relaxation modulus obtained at relatively low shear strains follows the strain–time separation principle, and the damping function of SEEPS can be fit to Laun double exponential model well. Moreover, the successive start‐up of shear behavior, the steady shear behavior, and the relaxation behavior after steady shear were investigated, respectively. The results showed that Wagner model, derived from the K‐BKZ (Kearsley‐Bernstein, Kearsley, Zapas) constitutive equation, could simulate the experiment data well, and in addition, experiment data under the lower shear rates are almost identical with the fitting data, but there exists some deviation for data under considerable high shear rates. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1309–1319, 2006     

聚乙烯熔体的离散松弛时间谱与熔融指数的关系

该文通过动态线性小振幅剪切震荡实验所得的聚乙烯熔体储能模量Ｇ′（ω）和耗能模量Ｇ″（ω）数据,采用最小二乘法线性回归、正则法和非线性回归法分别计算得到离散松弛时间谱,比较三种方法得到结果的差别,讨论计算参数、温度和材料对离散松驰时间谱影响．     

Nonlinear stress relaxation of an entangled linear polystyrene in single step‐strain flow: A quantitative theoretical investigation

The nonlinear stress relaxation of a nearly monodisperse, moderately entangled polystyrene solution (i.e., roughly seven entanglements per chain at equilibrium) in single step‐strain flow is investigated quantitatively by a detailed comparison of an existing set of experimental data with a simulation based on the tube model. The proposed simulation enables the effects of primary nonlinear relaxation mechanisms other than chain retraction to be identified more clearly and investigated individually. Two peculiar nonlinear relaxation behaviors are observed in this experiment. One is concerned with an apparent enhancement in the stress relaxation at short times, and the other is responsible for a seeming slowdown of the stress relaxation at long times. These findings are discussed within the tube model, in view of the effects of convective constraint release, partial strand extension, and nonaffine deformation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1281–1293, 2003     

Electrostatic relaxation and hydrodynamic interactions for self-diffusion of ions in electrolyte solutions

The concentration dependence of self-diffusion of ions in solutions at large concentrations has remained an interesting yet unsolved problem. Here we develop a self-consistent microscopic approach based on the ideas of mode-coupling theory. It allows us to calculate both contributions which influence the friction of a moving ion: the ion atmosphere relaxation and hydrodynamic interactions. The resulting theory provides an excellent agreement with known experimental results over a wide concentration range. Interestingly, the mode-coupling self-consistent calculation of friction reveal a nonlinear coupling between the hydrodynamic interactions and the ion atmosphere relaxation which enhances ion diffusion by reducing friction, particularly at intermediate ion concentrations. This rather striking result has its origin in the similar time scales of the relaxation of the ion atmosphere relaxation and the hydrodynamic term, which are essentially given by the Debye relaxation time. The results are also in agreement with computer simulations, with and without hydrodynamic interactions.     

Dielectric relaxation studies of aqueous N,N-dimethylformamide using a picosecond time domain technique

The dielectric relaxation studies of N,N-dimethylformamide at thirteen concentration in aqueous solutions have been carried out using a time domain reflectometry technique in the frequency range 10 MHz to 10 GHz. The dielectric parameters and excess dielectric properties have also been determined from 5 to 40°C. The Luzar theory was applied to compute the cross correlation terms for the mixture. It adequately reproduces the experimental values of the static dielectric constants. The Bruggeman model for the nonlinear case has been fitted to the dielectric data for mixtures.     

Strain and temperature accelerated relaxation in polycarbonate

The nonlinear viscoelastic behavior of glassy polymers and its relationship to ductile yielding is studied by single- and double-step stress relaxation experiments. In the latter case a small stress relaxation step is superimposed on a specimen at an elevated state of temperature or strain. The results show that the changes in the relaxation behaviors in the two cases closely parallel each other. The relaxation behavior at strains near yield closely approximates that at low strain but near Tg. The small strain relaxation response can be described well by a Kohlrausch-Williams-Watts (KWW) type function. The interpretation of these data in terms of a coupling model which includes the KWW form is discussed.     

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     

Solvation dynamics by coherence period resolved transient grating

We report a third-order nonlinear time-domain method, coherence period (τ) resolved transient grating (TRTG), that gives accurate solvation dynamics free from population relaxation in a short data acquisition time. The validity of TRTG is established by theory and experiment. The TRTG signal is shown to follow the transition frequency correlation function by an analytic expression based on the response function theory for delta function pulses and by model numerical calculations including finite pulse durations. TRTG is demonstrated for two cyanine dyes IR144 and IR125 in methanol by using a diffractive-optics based four wave mixing apparatus. Solvation dynamics in methanol obtained from the TRTG are consistent with those reported previously confirming the validity of TRTG.     

Molecular rheology of concentrated polymer systems. I

The primitive chain model of Doi and Edwards is generalized to include the short-time relaxation process. Stress relaxation after a sudden imposition of strain is studied in detail. It is shown that in the linear region (small strain) stress relaxation occurs in two steps, the relaxation of chain segments between the fixed entanglement points, and the relaxation of the entanglement points, in accordance with the conventional picture, whereas in the nonlinear region (large strain) there appears a new relaxation process between the above two. The characteristic time of this process is the Rouse relaxation time which the entire chain would have if there were no entanglements, and increases with the square of the molecular weight. This result is consistent with experimental observations.     

Nonlinear viscoelasticity of sorbitan tristearate monolayers at liquid/gas interface

The interfacial rheology of sorbitan tristearate monolayers formed at the liquid/air interface reveal a distinct nonlinear viscoelastic behavior under oscillatory shear usually observed in many 3D metastable complex fluids with large structural relaxation times. At large strain amplitudes (gamma), the storage modulus (G') decreases monotonically whereas the loss modulus (G') exhibits a peak above a critical strain amplitude before it decreases at higher strain amplitudes. The power law decay exponents of G' and G' are in the ratio 2:1. The peak in G' is absent at high temperatures and low concentration of sorbitan tristearate. Strain-rate frequency sweep measurements on the monolayers do indicate a strain-rate dependence on the structural relaxation time. The present study on sorbitan tristearate monolayers clearly indicates that the nonlinear viscoelastic behavior in 2D Langmuir monolayers is more general and exhibits many of the features observed in 3D complex fluids.     

Short‐time stretch relaxation of entangled polymer solutions investigated using full Rouse model predictions

We conduct a systematical investigation into the short‐time stretch relaxation behavior (i.e., shorter than the Rouse time but sufficiently longer than the glassy time) of entangled polymer liquid in single‐step strain flows, on the basis of theory/data comparisons for a broad series of type‐A entangled polymer solutions. First, within existing normal‐mode formulations, the Rouse model predictions on a full‐chain stretch relaxation in single‐step strain flows are derived for a popular 1‐D model proposed within the Doi–Edwards tube model, as well as for the original 3‐D model for nonentangled systems. In addition, an existing formula for the aforementioned 1‐D model that, however, rested upon a consistent‐averaging or the so‐called uniform‐chain‐stretch approximation is simultaneously examined. Subsequently, the previously derived formulas on chain stretch relaxation are directly incorporated into a reliable mean‐field tube model that utilizes the linear relaxation spectrum and the Rouse time constant consistently determined from linear viscoelastic data. It is found that the predictions of the 1‐D model differ substantially from that of the original 3‐D model at short times. Theory/data comparisons further indicate that the 1‐D model without approximations seems able to describe fairly well the nonlinear relaxation data under investigation. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1199–1211, 2006     

Longitudinal NLO properties of C2H2, HCCF,and C2F2: Electron correlation and vibration effects

Electron correlation and vibration effects on longitudinal nonlinear optical properties of acetylene (C₂H₂), fluoroacetylene (HCCF), and difluoroacetylene (C₂F₂) have been studied using various quantum chemistry methods, including the second‐order perturbation theory (MP2); coupled cluster approach with singles, doubles (CCSD), and noniterative triples (CCSD(T)); and density functional methods (B3LYP and B98). Evaluation of the static and dynamic vibration (nuclear relaxation) contributions was based on the finite field relaxation method. Particular attention has been devoted to the assessment of the electron correlation effects on the nuclear relaxation contributions to the molecular properties. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Stress-dependent dynamic compliance spectra approach to the nonlinear viscoelastic response of polymers

The present work reports a discrete, stress-dependent dynamic compliance spectra method which may be used to predict the mechanical response of nonlinear viscoelastic polymers during strain-defined processes. The method is based on the observation that the real and complex parts of the discrete dynamic compliance frequency components obtained from creep measurements are smooth, easily fit functions of stress. Comparisons between experimental measurements and model calculations show that the model exhibits excellent quantitative agreement with the basis creep measurements at all experimental stress levels. The model exhibits good quantitative agreement with stress relaxation measurements at moderate levels of applied strain. However, the model underestimates the experimental stress relaxation at an applied strain of 3.26%. The stress relaxation error appears to be a real material effect resulting from the different strain character of creep and stress relaxation tests. The model provides a good quantitative agreement with experimental constant strain rate measurements up to approximately 4% strain, after which the model underestimates the experimental flow stress. This effect is explained by the time dependence of the stress-activated configurational changes necessary for large strains in glassy polymers. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2301–2309, 1998     

Network models of concentrated polymer solutions derived from the yamamoto network theory

Several choices of the functions describing the creation and destruction processes of entanglement junctions in the Yamamoto network theory of concentrated polymer solutions have been examined. These choices are simple functions of the extension of the network segments bridging the entanglement points and it is demonstrated that the moments of the distribution function describing the network conformation can be solved for analytically. This has been done for a wide range of two-dimensional flows, both for the steady state and transient start-up and relaxation problems. The macroscopic stress tensor and flow birefringence are calculated and a variety of nonlinear effects are predicted and discussed.     

Internal water molecules and magnetic relaxation in agarose gels

Agarose gels have long been known to produce exceptionally large enhancements of the water 1H and 2H magnetic relaxation rates. The molecular basis for this effect has not been clearly established, despite its potential importance for a wide range of applications of agarose gels, including their use as biological tissue models in magnetic resonance imaging. To resolve this issue, we have measured the 2H magnetic relaxation dispersion profile from agarose gels over more than 4 frequency decades. We find a very large dispersion, which, at neutral pH, is produced entirely by internal water molecules, exchanging with bulk water on the time scale 10(-8)-10(-6) s. The most long-lived of these dominate the dispersion and give rise to a temperature maximum in the low-frequency relaxation rate. At acidic pH, there is also a low-frequency contribution from hydroxyl deuterons exchanging on a time scale of 10(-4) s. Our analysis of the dispersion profiles is based on a nonperturbative relaxation theory that remains valid outside the conventional motional-narrowing regime. The results of this analysis suggest that the internal water molecules responsible for the dispersion are located in the central cavity of the agarose double helix, as previously proposed on the basis of fiber diffraction data. The magnetic relaxation mechanism invoked here, where spin relaxation is induced directly by molecular exchange, also provides a molecular basis for understanding the water 1H relaxation behavior that governs the intrinsic magnetic resonance image contrast in biological tissue.     

Dynamics of hydrogen bond complexes in polymer melts

The dynamics of hydrogen bond complex formation between functional groups which are attached to a polymer chain, is studied in the molten state. The concentration of complexes in the thermodynamic equilibrium is distorted by the application of a large oscillatory strain in the nonlinear viscoelastic regime. The relaxation back to the thermodynamic equilibrium is studied as a function of the temperature in the linear viscoelastic regime. From the mechanical response the kinetic analysis can be performed using a modified Doi-Edwards theory. Using the equilibrium constants obtained from IR-spectroscopy, the rate constants for complex formation and decomplexation are obtained. The temperature dependence is equivalent to the temperature dependence of the zero shear viscosity which implies that complex formation is a diffusion-controlled process.     

Comparison of optical and mechanical limits of linear relaxation behavior in glassy polycarbonate

The decay in birefringence of glassy polycarbonate held at constant extension has been studied at 23°C, in the time-scale range 10–10³ sec, up to about 6% strain. The results show that, under these conditions, the birefringence can be validly expressed as a linear hereditary integral of the strain history up to a relatively high strain level which is about 3.4% for an experimental time-scale of 100 sec. Comparison with previously obtained data on the stress relaxation behavior of the same polymer shows that, other factors remaining constant, mechanical relaxation is linear only up to about 1.1% strain. The earlier onset of mechanical nonlinearity is discussed and it is suggested that the mechanical relaxation spectrum is richer than the optical spectrum in relatively long relaxation times, corresponding to relatively slow molecular motions. It is further suggested that these slow molecular motions are accelerated first as the polymer is extended beyond the limit of linear viscoelastic behavior. The observed nonidentity between strain limits for linear mechanical and linear optical behavior is discussed in the light of current practices in photomechanical stress analysis.