Measurement of the stress-relaxation modulus in the primary transition region

Difficulties have been encountered in experimentally measuring the stress-relaxation modulus for systems with steep slopes in the primary transition region. The usually applied “factor-of-ten” rule is shown to apply in these cases as well as in cases where the relaxation is slower; with the steep slope, however, the rule offers little help, since the decay in the modulus is so fast that stresses are usually very small at times when direct modulus calculations may be made. A technique is suggested which allows calculation of the modulus in this difficult region. A slow constant strain-rate deformation is followed by a constant strain period. Modulus values for times during the constant strain rate period are calculated using well known relationships. Long-time values are calculated from the definition of the modulus (the factor-of-ten rule being employed) and a recursion relation is developed which is used for modulus calculations during the constant strain period at relatively short times where effects of strain rate are important. Starting values for the recursion relation are long-time moduli which can be calculated directly.     

Dynamic mechanical and crystal-strain measurements on ultrahigh modulus oriented polyoxymethylene: A revised value for the true crystal modulus

Dynamic mechanical measurements on ultrahigh modulus polyoxymethylene have been undertaken over the temperature range ?150 to 20°C. Measurements of the longitudinal crystal modulus have also been made by studying changes in the (009) reflection with load, over a similar range of temperatures. The dynamic Young's modulus at 5 Hz reaches a value at low temperatures of 64.5 GPa for the most highly oriented sample. The crystal modulus at low temperatures is 105 GPa, which is almost twice the previously reported room-temperature value.     

Temperature-jump investigations of the kinetics of hydrogel nanoparticle volume phase transitions.

The dynamics of the deswelling and swelling processes in thermoresponsive poly-N-isopropylacrylamide (pNIPAm) hydrogel nanoparticles have been studied by using time-resolved transmittance measurements, in combination with a nanosecond laser-induced temperature-jump (T-jump) technique. A decrease in the solution transmittance associated with deswelling of the particles has been observed as the solution temperature traverses the volume phase transition temperature of the particles. Upon inducing the T-jump, the deswelling transition only occurs in a small percentage (<10%) of the particle volume, which was found to be a thin periphery layer of the particles. The particle deswelling occurs on the microsecond time scale, and as shown previously, the collapse time can be tuned via adding small amounts of hydrophobic component to the particle shell. In contrast, the reswelling of the particles was thermodynamically controlled by bath equilibration, and only small differences in particle reswelling kinetics were found due to sluggish heat dissipation (millisecond time scale) from the sample cell.     

Characterization of inhomogeneous polyacrylamide hydrogels

The physical and structural properties of acrylamide gels have been characterized by osmotic deswelling, mechanical compression, and x-ray scattering. These properties vary considerably with the concentration of the crosslinking agent bisacrylamide, at fixed total monomers concentration (10% wt/wt water). In particular, changes in the properties appear more prominent at a crosslinking level of about 5-6% (wt bisacrylamide/wt monomers). The compression modulus of as-prepared and swollen gels passes through a maximum at this level of crosslinking. The swelling pressure curves can be separated into osmotic and elastic contributions of the gel network. The elastic part exhibits similar behavior to the compression modulus. The scaling of the osmotic part with the gel concentration varies with the degree of crosslinking, changing from 2.33 to 3.09. This indicates that the solvent power of water decreases with increasing crosslinking level, towards Φ conditions. The scattering patterns from the gels have been analyzed as arising from additive contributions from a homogeneous gel matrix, and embedded heterogeneities having a higher crosslinking density. These heterogeneities become much more prominent at the same level of crosslinking about 5-6%. Hysteresis observed in the sorption/desorption behavior of polyacrylamide gel suggests that further irreversible structural changes may occur at water activities lower than probed by osmotic deswelling. © 1992 John Wiley & Sons, Inc.     

Giant reduction in dynamic modulus of kappa-carrageenan magnetic gels

Effects of magnetization on the complex modulus of kappa-carrageenan magnetic gels have been investigated. The magnetic gel was made of a natural polymer, kappa-carrageenan, and a ferrimagnetic particle, barium ferrite. The complex modulus was measured before and after magnetization of the gel by dynamic viscoelastic measurements with a compressional strain. The gels showed a giant reduction in the storage modulus of approximately 10(7) Pa and also in the loss modulus of approximately 10(6) Pa due to magnetization. The reduction increased with increasing volume fraction of ferrite, and it was nearly independent of the frequency. It was also found that the change in the modulus was nearly independent of the magnetization direction and irradiation time of the magnetic fields to the gel. The magnetic gels demonstrating the giant reduction in the dynamic modulus showed a large nonlinear viscoelastic response. It was observed that the magnetic gel was deformed slightly due to magnetization. The observed giant complex modulus reduction could be attributed to the nonlinear viscoelasticity and deformation caused by magnetization. Magnetism, nonlinear viscoelasticity, and effects of magnetization on the morphological and shape changes were discussed.     

In-situ AFM studies of the phase-transition behavior of single thermoresponsive hydrogel particles

The volume phase transition (VPT) behavior of individual thermally responsive poly(N-isopropylacrylamide-co-acrylic acid) (pNIPAm-co-AAc) hydrogel microparticles was studied by in-situ dynamic mode atomic force microscopy (AFM) and force spectroscopy during heating and cooling cycles. Hydrogel samples were prepared by electrostatic immobilization of microparticles to amine-modified gold surfaces. The AFM studies of particle deswelling were performed by varying the force applied on the particles during imaging as a function of the geometry and material of the AFM probe. Aluminum-coated silicon cantilevers were found to influence substantially the behavior of the particles during the VPT, leading to a significant shape change. Low force impact magnetic excitation of the AFM probe (MAC mode) during dynamic mode measurements resulted in an undisturbed deswelling behavior enabling observation of the expected volume changes of the particles without significant tip-sample interaction. Hence, MAC-mode AFM was determined to be the most suitable technique for in-situ AFM studies on volume and shape changes at single hydrogel particles during VPT. Elasticity measurements performed at single particles at temperatures below and above the VPT revealed a 15-fold increase in the Young's modulus after passing the VPT, indicating the transition from a soft, swollen network to a stiffer, deswollen state.     

Self‐oscillation mechanism of hydrogel coupled with chemical oscillations

A novel gel which undergoes an autonomic and periodical swelling‐deswelling oscillation has been prepared by the copolymerization of N‐isopropylacrylamide (NIPAAm) with ruthenium tris(2,2'‐bipyridine) (Ru(bpy)₃) as a catalyst for the Belousov‐Zhabotinsky (BZ) reaction. In order to enhance the amplitude of swelling‐deswelling oscillations of the gel, we attempted to change the period and amplitude of the redox oscillation by varying the initial concentration of substrates of the BZ reaction. Both period and amplitude of chemical oscillation varied depending on the substrate concentration. This variation led to a change in the swelling‐deswelling oscillation: i.e., the swelling‐deswelling amplitude increased with an increase in the period and amplitude of the redox changes. The change in gel size with ca. 20% to the initial size was obtained as the maximum value. The swelling‐deswelling amplitude of the gel is controllable by changing the initial concentration of substrates or the content of immobilized Ru(bpy)₃ catalyst within the gel.     

The influence of low-temperature crystallization on the tensile elastic modulus of natural rubber

When natural rubber crystallizes at low temperatures, there is an increase in elastic modulus of up to two orders of magnitude. This phenomenon has been studied at various temperatures in the range 0 to ?55°C for samples held at tensile strains of up to 500%. There is an induction period associated with the nucleation of crystallites, before any increase in modulus is observed. The induction period increases with decreasing strain and passes through a minimum with increasing temperature at ?25°C. The growth rate subsequent to nucleation is successfully described in terms of Avrami-type rate relationships. The Avrami rate coefficient is independent of temperature and follows a simple exponential function of strain. The equilibrium extent of the modulus increase has also been studied by means of experiments of up to three months' duration. The equilibrium modulus increases with decreasing temperature—as predicted by Flory's thermodynamic theory.     

Dynamic bulk modulus of various elastomers

The dynamic bulk modulus of elasticity has been measured for 14 different rubbery elastomers: three natural rubbers, five neoprenes, three polyurethanes, and one each of butyl, nitrile, and butadiene types. The measurements ranged in temperature from ?10 to +40°C, at frequencies from 5 to 3000 Hz, but mostly in the range 100–1000 Hz, at 2.5 MPa pressure. Values of the real (storage) part of the modulus fell within 35% of the mean value of 2.9 GPa for all elastomers, whereas loss moduli were a few percent of the storage moduli. Master curves were obtained for two neoprenes, a polyurethane, and a butyl rubber. These were fitted by hyperbolic functions with four adjustable parameters. Effects of room-temperature aging in artificial sea water were also studied. Aging versus time profiles fell into two distinct forms. Natural rubbers were least stable, neoprenes were intermediate, and urethanes proved most stable in bulk modulus.     

多孔聚乙烯醇缩甲醛凝胶力学行为对含水量变化的敏感性

通过成孔剂法制备具有连通孔结构的聚乙烯醇缩甲醛凝胶(PVFM) ,研究其在吸水膨胀脱水收缩过程中力学行为对含水量变化的响应性.实验表明多孔PVFM具有很快的吸水 脱水速度,吸水80s内就可达到最大的平衡膨胀应力,干燥4h内其膨胀应力可降低95 % ;同时还发现多孔PVFM在脱水干燥过程中出现明显的体积回弹和膨胀应力回复现象,而且压缩模量在一定范围内随含水量的减少反而降低,分析表明这些与PVFM的多孔结构、弹性网络的状态有密切关系.     

Determination of the shear modulus of spin-coated lipid multibilayer films by the spontaneous embedment of submicrometer-sized particles

A novel submicrometer particle embedment technique has been used to determine the shear modulus of 1,2-dipalmitoyl-sn-glycero-3-phosphotidylcholine (DPPC) lipid multibilayers. The depth of the spontaneous embedment of polystyrene and silica spherical particles of 200 nm nominal size has been determined from atomic force microscopy measurements on colloidal particles dispersed onto the surfaces of the DPPC multibilayers. The standard JKR model was used to relate the shear modulus of the lipid multibilayer films to the depth of embedment of the particles. The thus-determined modulus of the DPPC is within the range of reported literature values. Gold particles are also considered, and it is found that for the smallest particles (13 nm) complete engulfment by the DPPC multibilayer film takes place.     

Study on elastic modulus of crosslinked polyurethane/organoclay nanocomposites

In this paper, two polyurethane/clay nanocomposite systems with crosslinked structure were synthesized via in situ polymerization of a polyether‐ as well as a polyester‐based prepolymer with methylene‐bis‐ortho‐chloroanilline (MOCA). Two types of modified clays with different organic modifiers were used in order to see the effect of compatibility between polymer matrix and clays on elastic modulus of nanocomposites. The morphology and the dispersion of clay layers in polyurethanes have been characterized by X‐ray diffraction (XRD) and microscopic techniques. The changes of elastic modulus of nanocomposites with clay content were examined and compared with those predicted by some conventional composite models. The results showed a reasonable fitting of experimental and theoretical values only at very low clay contents. As the clay content exceeds 1.5 wt% in this system, a reduction in elastic modulus was experimentally observed due to insufficient dispersion degree of silicate layers throughout the crosslinked matrix. This behavior was not predicted with the conventional composite theories. A new model on the basis of Wu model was then developed in order to predict the reduction of elastic modulus at various clay contents in crosslinked PU matrix. This model fitted reasonably the experimental results. Copyright © 2010 John Wiley & Sons, Ltd.     

Ab initio investigation of the Young's modulus of polyamide‐6

The Young's modulus of the α form of polyamide‐6 has been calculated using the supermolecule model. The crystalline polymer was represented by a single‐chain molecule, divided into a head, body, and tail part. The body of the model contains an even number of polyamide‐6 units (4–16 units) and is representative for a polyamide‐6 chain. The periodicity of the system was not explicitly taken into account, but in a few tests the effect of a linear constraint has been evaluated. An n‐butyl and n‐pentyl group have been used as head and tail, respectively. In a number of additional calculations the length of the head and tail has been varied. For all supermolecule models the equilibrium and elongated structures have been optimized using ab initio Hartree–Fock calculations with a 6‐31G** basis set. From the energy values of the optimized structure a Young's modulus of 334 GPa has been extrapolated for both the unconstrained and linearly constrained models. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Similarity of the relaxation modulus of polydisperse polymers

A similarity rule due to Markovitz is used for the correlation of the relaxation modulus for different polymeric materials. This rule has long been employed implicitly in the empirical shifting rules for the reduction to common curves of viscoelastic data measured on the same polymer over a range of temperatures and concentrations. It is shown here for the rubbery regime of polydisperse polymers that when relaxation moduli are scaled with the steady-state compliance and the time with the mean relaxation time, data for a variety of amorphous polymeric materials tend to plot on a common curve. This suggests that the dimensionless rubber modulus is, to first order, a common function of dimensionless time for materials which include whole polymers and polymer solutions, the effects of temperature and concentration being automatically incorporated into the two scaling parameters. For materials with sufficient polydispersity the correlation appears to be valid over a wide range of the available experimental data. These amorphous materials appear to share only one feature, flexible molecules with broadly distributed molecular weights. For narrowly dispersed polymers the modulus in the terminal zone is also correlated according to the above rule, but the influence of other parameters appears as the transition to the glassy regime is approached. An additional application of the similarity rule allows the relaxation modulus computed from molecular dynamics simulations of idealized polymers to be compared with experimental moduli for real materials even though the characteristic times for these systems differ by more than ten orders of magnitude.     

Effect of additives on swelling of covalent DNA gels

The volumetric response of polymer gels on cosolute addition depends on the interaction of the polymer with the cosolute and can be used as a simple and sensitive way of elucidating these interactions. Here we report on DNA networks, prepared by crosslinking double-stranded DNA with ethylene glycol diglycidyl ether (EGDE); these have been investigated with respect to their swelling in aqueous solution containing different additives, such as metal ions, polyamines, charged proteins, and surfactants. The deswelling on addition of metal ions occurs at lower concentrations with increasing valency of the counterion. The collapse of the gels in the presence of trivalent ions seems to follow the same kind of mechanism as the interaction in solution, but addition of these ions leads to DNA denaturation and formation of single-stranded DNA. Striking features were found in the deswelling of DNA gels by chitosan, spermine, spermidine, lysozyme, poly-l-lysine and poly-l-arginine. Chitosan is the most efficient cosolute of those investigated with respect to DNA gel collapse. The effect of the cationic surfactant tail length on the volume phase transition of DNA gels was studied as a function of surfactant concentration. Cationic surfactants effectively collapsed the gel from the critical aggregation concentration (cac), decreasing with increasing length of the hydrophobic tail. In several cases, the deswelling as a function of cosolute concentration shows a pronounced two-step behavior, which is interpreted in terms of a combination of DNA chain condensation and general osmotic deswelling. The studies included investigations on the state of the DNA chain after deswelling, on the reversibility of the deswelling as well as on the kinetics. With the exception for the trivalent lanthanide ions, it appears that the DNA chain always retains a double-helix conformation; with these metal ions, single-stranded DNA is found. The deswelling appears to be reversible as exemplified by addition of anionic surfactant subsequent to gel collapsed by cationic surfactant and addition of sodium bromide to gels collapsed by a polycation. An investigation of the kinetics shows that an increase in the surfactant tail length gives a pronouncedly slower deswelling kinetics.     

Elastic modulus and thermal conductivity of ultradrawn polyethylene

The axial and transverse Young's modulus and thermal conductivity of gel and single crystal mat polyethylene with draw ratios λ = 1–350 have been measured from 160 to 360 K. The axial Young's modulus increases sharply with increasing λ, whereas the transverse modulus shows a slight decrease. The thermal conductivity exhibits a similar behavior. At λ = 350, the axial Young's modulus and thermal conductivity are, respectively, 20% and three times higher than those of steel. For this ultradrawn material both the magnitude and the temperature dependence of the axial Young's modulus are close to those of polyethylene crystal. The high values of the axial Young's modulus and thermal conductivity arise from the presence of a large percentage (∼85%) of long needle crystals. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3359–3367, 1999     

Elastic modulus of the crystalline phase of poly(cis 1,4-isoprene)

The crystalline elastic modulus of poly(cis 1,4-isoprene) has been measured by x rays and calculated by molecular mechanics. The experimental modulus is E = (2.3 ± 0.3) × 10⁹N m^?2. The calculated modulus is E = (8.8 ± 0.1) × 10⁹N m^?2 for chains in S⁺ cis S^?T conformation and E = (6.1 ± 0.1) × 10⁹N m^?2 for chains in S⁺ cis S+T conformation. The modulus calculated for a statistical structure including both conformation is E = (6.7 ± 0.1) × 10⁹N m^?2. The experimental modulus is thought to be a lower limit because of partial crystallinity of the sample. The chief mechanism of deformation is rotation around single bonds adjacent to the double bond.     

On the predictability of the high-frequency elastic modulus of semicrystalline polymers as function of crystallinity

The relation of the high-frequency elastic moduli of semicrystalline polymers to volume fraction crystallinity is correctly described by the Hashin-Shtrikman theory, without any disposable constants, as a function of the ratio of the modulus of the amorphous to that of the crystalline phase. Hence the (high-frequency) reduced modulus of semicrystalline polymers is largely a function of the temperature T/T_g. The importance of T/T_m for the modulus of the crystalline phase precludes the existence of a single universal reduced modulus versus temperature curve.     

A buckling mechanics approach to elastic modulus determination of glassy polymer films

Column buckling mechanics were examined as a technique to determine the modulus of glassy polymer films that fail at very low strains in tension. As an alternative modulus measurement technique, free‐standing column buckling (FSCB) mechanics were investigated here. Given the film geometries and the critical buckling load, classical relationships can be used to determine the modulus. Several polymeric materials were tested and compared to uniaxial tensile values to determine the robustness and validity of the technique. Film geometries were varied from 4 to 18 mm in width and from 15 to 60 mm in length. The films were compressed in plane until buckling occurred and the critical buckling load was measured for each geometry. The critical buckling load increased as film width increased and decreased as film length increased, while the thickness was held constant for each material. For polyethylene terephthalate films, the elastic modulus was determined to be 3.06 ± 0.58 GPa. This FSCB‐determined modulus was compared to the elastic modulus obtained by tensile testing (3.54 ± 0.2 GPa). The modulus measurement technique presented here has the potential to be used experimentally to determine the elastic modulus of glassy polymer films that perform poorly in tension. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 15–20     

Complex shear modulus of concentrated suspensions of solid spherical particles

Starting from the complex shear modulus equation for a dilute suspension system, three new equations are developed for the complex shear modulus of concentrated suspensions of solid spheres. The continuous phase (matrix) and the dispersed particles are treated as viscoelastic materials in the derivation. Complex shear modulus data on suspensions of spherical glass beads in polymeric liquid were obtained experimentally and compared with the predictions of the proposed equations. The proposed equations describe the experimental data reasonably well.