Transient lateral contraction ratio of polymers in creep and relaxation

Summary Simultaneous measurements of the longitudinal extension and the lateral contraction strains in tension specimens made from a pure epoxy polymer by using the differential moiré method yielded the extension creep compliance and relaxation modulus master curves along the whole viscoelastic spectrum of the material. Moreover, they provided the lateral contraction ratio curves in creep and relaxation. Both pairs of curves determine completely the viscoelastic behavior of the polymeric substances. It was shown that the transient lateral contraction ratio functions are monotonically increasing functions with time and temperature and the creep function is lagging in time with respect to the corresponding relaxation function.

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Zusammenfassung Gleichzeitige Messungen von L?ngsdehnung und Querkontraktion wurden an reinen Epoxydharzen durchgeführt, indem die Differential-Moiré-Methode angewendet wird, die Kriechverhalten und Relaxations-Master-Kurven über das ganze viskoelastische Spektrum des Materials liefert. Darüber hinaus ergibt sich das Querkontraktionsverh?ltnis für Kriechen und Relaxation. Beide Kurvenpaare bestimmen vollkommen das viskoelastische Verhalten polymerer Substanzen. Es l?\t sich zeigen, da\ die Querkontraktions-funktionen monoton wachsende Funktionen mit Zeit und Temperatur sind und da\ die Kriechfunktion hinsichtlich der entsprechenden Relaxationsfunktion verz?gert verl?uft.

     

Contribution of relaxation processes to adhesive-joint strength of viscoelastic polymers

Relaxation processes accompany all stages of the lifetime of viscoelastic pressure-sensitive polymer adhesives, which can form strong adhesive joints with substrates of various chemical natures under application of a slight external pressure to the adhesive film for a few seconds. This review deals with comparison of the adhesion and relaxation properties of a number of typical pressure-sensitive adhesives based on polyisobutylene, butyl rubber, styrene-isoprene-styrene triblock copolymers, alkyl acrylate copolymers, and silicone adhesives as well as pressure-sensitive adhesives based on blends of high-molecular-mass polyvinylpyrrolidone with oligomeric poly(ethylene glycol). Within all three stages of the lifetime of adhesive joints (under adhesive-bond-forming pressure, upon withdrawal of contact pressure in the course of relaxation of the adhesive material, and under the force detaching an adhesive film from the substrate surface), the strength of adhesive joints has been shown to be controlled by large-scale relaxation processes, which are characterized by long relaxation times in the range 150–800 s. All examined pressure-sensitive adhesives can be arbitrarily divided into two groups. The first group is composed of fluid adhesives that relax comparatively fast and exhibit no residual (unrelaxed) stress. The second group includes elastic adhesives capable storing mechanical energy in the course of deformation that are characterized by appreciably longer relaxation times and display residual stress after relaxation. Conditions of adhesive debonding (e.g., strain amplitude and deformation velocity) significantly affect the relaxation process.     

A discrete complex compliance spectra model of the nonlinear viscoelastic creep and recovery of microcellular polymers

The present work reports a discrete stress‐dependent, complex compliance spectra method that may be used to predict the mechanical response of nonlinear viscoelastic polymers during creep and recovery processes. The method is based on the observation that the real and imaginary parts of a discrete complex compliance frequency spectra obtained from creep and recovery measurements are smooth, easily fit functions of stress. The new method is applied to a set of microcellular polycarbonate materials with differing relative density. The nonlinear viscoelastic characteristics of a microcellular polycarbonate material system are very sensitive to relative density and therefore, this material system is a particularly difficult modeling challenge. However, the present model was able to exhibit excellent quantitative agreement with the basis creep and recovery measurements at all experimental stress levels for each of the experimental relative density material types. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 691–697, 2000     

Thermal,viscoelastic, and mechanical properties of DCPD-containing polymers

The thermal, viscoelastic, and mechanical properties of cured dicyclopentadiene (DCPD)-containing polymers prepared from novel DCPD-modified unsaturated epoxypolyesters and styrene were evaluated. This was accomplished using thermogravimetric analysis, differential scanning calorimetry, dynamic mechanical analysis, three-point bending test, and Brinell’s hardness. The thermal, viscoelastic, and mechanical properties of DCPD-containing polymers were strongly dependent on chemical structure. The cross-linking density (υ _e) of obtained networks increased with increasing content of carbon–carbon double bonds in the poly(ester) structure. In addition, the introduction of DCPD rings into the poly(ester) structure increased the rigidity of the molecular backbone. It resulted in obtaining polymers which showed great improvement in mechanical properties including remarkably higher storage modulus ( E_{20 ^°\textC}^￠ E_{{20\,{}^{\circ}{\text{C}}}}^{'} ), flexural modulus at bending (E _mod), hardness, lower extension at maximum force (ε-F _max), as well as higher thermal stability. These good properties make these materials highly promising as potential candidates for structural applications.     

Measurement of viscoelastic properties for polymers by nanoindentation

A new method has been proposed and verified to measure the viscoelastic properties of polymers by nanoindentation tests. With the mechanical response of load–displacement curves at different loading rates, the parameters of creep compliance and relaxation modulus are calculated through the viscoelastic contact model. Dynamic thermomechanical analysis (DMA) tests are conducted to compare the results by the proposed technique. The results show that the correlation coefficients between DMA tests and the new method are above 0.9 in the entire range, which verified the feasibility of the method. The loading curves fitted by the model are identical to the experimental curves within the discrete points and so it shows that this technique is more suitable for general linear viscoelastic materials. Numerical creep tests are carried out to examine the effectiveness of the proposed method by input the Prony series calculated by the three-element Maxwell model and the viscoelastic contact model. The good agreement shows that the proposed technique can be applied in practice.     

Relative rates of creep and relaxation in shear,elongation, and isotropic compression

The relative rates of relaxation and creep in shear, elongation, and isotropic compression are discussed in terms of the theory of linear viscoelasticity. Exact expressions are given for the creep rates; for the relaxation rates approximations are found which are useful in the glassy range where the amount of relaxation is small. Among the results of interest is the relation: valid if d In B/d In t is less than d In J/d In t as is intuitively expected and experimentally found. Here J(t), E(t), and B(t) are the shear, tensile, and bulk creep compliances, respectively. For polymers in the rubbery and flow regions, (d In J/d In t)/(d In D/d In t) is very close to 1(usually within 0.01%); in the glassy region, it is unlikely to be greater than 1.2.     

Dielectric relaxation analysis of cellulose oligomers and polymers in dependency on their chain length

For all cellulose‐like oligo‐ and polyglucans, beginning with the dimer cellobiose, a broad relaxation process at low temperatures is observed using the dielectric relaxation spectroscopy method. This relaxation has its molecular origin in orientational motions of the sugar rings via the glucosidic linkages. We investigated the dynamics of this main chain motion for β(1‐4) oligoglucans with 2, 3, 4, or 5 anhydroglucose units (AGUs), as well as for β(1‐4) polyglucans having a degree of polymerization molecular weight averages (DP_w) of 23, 37, 50, and 140 up to 3000. As a result we found that the activation energy (E_a) of the segmental chain motion has the lowest value (32 ± 1 kJ/mol) for cellobiose, followed by passing through a maximum for a DP between 7 and 15 with E_a = 51 ± 1 kJ/mol. Subsequently, the activation energy is decreased at a value around 44.8 ± 1.2 kJ/mol for chains containing more than 100 AGUs. Obviously, from a distinctly molecular dimension (DP_w ～ 100) the mean number of AGUs that take part in the local chain motions and cross‐correlation between the motions of neighboring AGUs are nearly the same and the chain length has no influence on the segmental motion. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2491–2500, 2001     

Dielectric relaxation analysis of starch oligomers and polymers with respect to their chain length

Starch belongs to the polyglucan group. This type of polysaccharide shows a broad β-relaxation process in dielectric spectra at low temperatures, which has its molecular origin in orientational motions of sugar rings via glucosidic linkages. This chain dynamic was investigated for α(1,4)-linked starch oligomers with well-defined chain lengths of 2, 3, 4, 6, and 7 anhydroglucose units (AGUs) and for α(1,4)-polyglucans with average degrees of polymerization of 5, 10, 56, 70, and so forth (up to 3000; calculated from the mean molecular weight). The activation energy (E_a) of the segmental chain motion was lowest for dimeric maltose (E_a = 49.4 ± 1.3 kJ/mol), and this was followed by passage through a maximum at a degree of polymerization of 6 (E_a = 60.8 ± 1.8 kJ/mol). Subsequently, E_a leveled off at a value of about 52 ± 1.5 kJ/mol for chains containing more than 100 repeating units. The results were compared with the values of cellulose-like oligomers and polymers bearing a β(1,4)-linkage. Interestingly, the shape of the E_a dependency on the chain length of the molecules was qualitatively the same for both systems, whereas quantitatively the starch-like substances generally showed higher E_a values. Additionally, and for comparison, three cyclodextrins were measured by dielectric relaxation spectroscopy. The ringlike molecules, with 6, 7, and 8 α(1,4)-linked AGUs, showed moderately different types of dielectric spectra. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 188–197, 2004     

Mechanical and viscoelastic properties of confined amorphous polymers

Confinement of polymers to nanoscale dimensions can dramatically impact their physical properties. Substantial efforts have focused on the glass transition temperature (T_g) of polymers confined to thin films, but their mechanical properties are less studied despite their technological importance. In this review, challenges with mechanical measurements of polymer thin films are discussed along with novel metrologies that provide insight into their mechanical properties. A comparison of experimental measurements, simulations and theory provide several general conclusions about the mechanical properties under confinement. Confinement impacts the elastic modulus, rubbery compliance and viscosity of polystyrene, the archetypal polymer for confinement, but the confinement effect appears to depend on the measurement technique. This effect may be due to the details of averaging of gradients in properties that are dependent on the measurement details. Routes to minimize confinement effects are addressed. Despite progress in the measurements of mechanical properties of polymer thin films, there remain unresolved questions about the impact of confinement, which we highlight at the end of this review. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 9–30     

Correlations between the viscoelastic behavior of pyrene-labeled associative polymers and the associations of their fluorescent hydrophobes

The viscoelastic behavior of a series of three pyrene-labeled hydrophobically modified alkali swellable emulsion copolymers (Py-HASEs) was investigated. All Py-HASEs thickened the aqueous solutions with viscosities orders of magnitude larger than that of a HASE control which displayed no pyrene hydrophobe. This fact demonstrated that the pyrene molecule is a good hydrophobe for associative thickeners such as HASEs. The Py-HASE solutions exhibited shear thinning, whose magnitude was found to increase with increasing pyrene content. A large shear-thinning effect indicates that a large fraction of the elastically active cross-links has been severed. Fluorescence measurements on the Py-HASEs confirmed that the smaller the pyrene content of the Py-HASE, the more intermolecular associations it formed, in agreement with the results obtained by rheology. Above the overlap concentration of the polymers, the zero-shear viscosity of the Py-HASE solutions increased steeply with increasing polymer concentration. The onset concentration where viscosity increases matches the onset concentration where intermolecular associations are being formed, as probed by fluorescence. Oscillatory rheological measurements were carried out to determine the terminal relaxation time, Td, and the storage modulus at the infinite time limit, G0, of the Py-HASE network. G0 was found to increase with decreasing pyrene contents, indicating that Py-HASEs with lower pyrene contents exhibited a higher density of elastically active chains. This result is in agreement with the trends obtained by the fluorescence and steady-state rheology measurements. A model is suggested that accounts for the fluorescence and rheology results.     

Chain entanglement and viscoelastic properties of molten polymers

Linear low-density polyethylenes (LLDPES) and polypropylene (PP) have been recovered from solutions of varying initial polymer concentration. Melts of these polymers show significant reductions in viscosity and elasticity, and the effects are attributed to changes in the entanglement density of the polymer. Measurements of entanglement densities have been attempted from experimental values of the apparent zero-shear melt viscosity. These indicate that solution treatments in trichlorobenzene at 135°C reduce the entanglement density more effectively in PP than in LLDPE. In all cases the observed effects are reversible by annealing at elevated temperatures. Analytic data point to entanglement changes as the true origin of changes in viscoelastic properties, since solution treatments produce no changes in molecular weights and weight distributions, and the samples tested are free of solvent residues.     

On the viscoelastic fracture criteria for polymers: experiments and analysis

Creep deformation and fracture tests on two polymeric materials were performed at various temperatures and strain rates. The data obtained were analyzed and used to test four viscoelastic fracture criteria, based on different theoretical approaches. No definitive conclusion could be reached as to the identification of an appropriate invariant fracture parameter.     

Combined constant strain rate and stress relaxation test for linear viscoelastic studies

The strain history of the combined test is formed by a constant strain rate during the period 0 <t < t₁ followed by a constant strain for t > t₁. This test includes as limiting cases the relaxation test (t₁ → 0), the constant strain rate or stress growth experiment (t₁ → ∞), and the stress relaxation after cessation of constant strain rate flow (t₁ sufficiently large). The constant t₁ can be chosen arbitrarily such that the test conditions of the combined test can be adjusted according to the problem investigated and to the capability of the testing device. From this, practical advantages follow for linear viscoelastic studies of polymeric solids and liquids, e.g., the zero shear viscosity η₀ for unstable polymer melts can be determined at least approximately. In order to obtain linear viscoelastic material functions from the measured stress record, a simple procedure is given which avoids the difficulties with the “factor-of-10 rule” for short relaxation times.     

Effect of the molecular mobility of epoxy amine crosslinked polymers on their relaxation and physicomechanical characteristics

The results on molecular mobility in epoxy amine crosslinked polymers at segmental (α process) and local (β process) levels are analyzed. The effect of intrachain and interchain rigidities on the above processes is considered, where the intrachain rigidity is measured with the use of flexibilizing agents and the interchain rigidity is dependent on the intermolecular-interaction intensity, which is governed by the introduction of plasticizing agents. Both modes of molecular mobility in the crosslinked polymers show a cooperative character that controls the dissipation energy of the corresponding relaxation process. The correlation between the above processes and the elastic, strength, and relaxation characteristics of the epoxy amine crosslinked polymers is studied. Molecular mobility is shown to exert an inverse effect on the relaxation and dissipative characteristics of the network polymers.     

A viscoelastic description of the glass transition-conversion relationship for reactive polymers

The glass transition temperature,T _g is a sensitive and practical parameter for following cure of reactive thermosetting systems. A new equation was developed for predicting theT _g -conversion relationship based on the Dillman-Seferis viscoelastic compliance model. It assumes that the changes inT _g are primarily due to changes in relaxation time as chain extension and crosslinking reduce the mobility of a polymer network. Such information is essential in combining kinetic and viscoelastic measurements, which monitor transformations of thermosets during cure. The equation derived from the viscoelastic model was shown to be applicable for a variety of experimental data. The success of the methodology was further demonstrated by comparing well-established relations, such as the Fox equation and the Di-Benedetto equation, to predictions made possible by adjusting two viscoelastic model parameters. Finally, the fitting power of the proposed equation was shown by fitting published epoxy data from the literature as well as experimental data on a relatively new resin system such as dicyanates used as a model in this study.Der GlasumwandlungspunktT _g ist eine empfindliche und praktische Grö\e zum Verfolgen der AushÄrtung reaktiver Duroplaste. Basierend auf dem viskoelastischen Steifigkeitsmodell von Dillman-Seferis wurde eine neue Gleichung zur Vorhersage der Beziehung zwischenT _g und Konversion entwickelt. Dabei wird angenommen, da\ die Änderung vonT _g in erster Linie durch eine Änderung der Relaxationszeit bedingt ist, da KettenverlÄngerung und Vernetzung die Beweglichkeit des Polymergefüges herabsetzen. Bei einer Kombination von kinetischen und viskoelastischen Messungen, mit denen die Umwandlungen wÄhrend des AushÄrtens von Duroplasten verfolgt werden können, ist diese Erkenntnis von gro\er Bedeutung. Die auf der Basis des viskoelastischen Modelles erhaltene Gleichung ist für eine gro\e Breite von experimentellen Daten anwendbar. Den Erfolg dieser Methodik zeigt weiterhin ein Vergleich bewÄhrter Beziehungen, wie z.B. der Foxschen Gleichung und der Gleichung von DiBenedetto, mit Aussagen, die durch Anpassung zweier viskoelastischer Parameter ermöglicht wurden. Die StÄrke der vorgeschlagenen Gleichung wird letztlich durch Anpassen von Epoxy-Daten aus der Literatur sowie von experimentellen Daten eines relativ neuen und in dieser Untersuchung als Modell benutzten Harzsystemes gezeigt.     

Surface diffusion and relaxation of partially adsorbed polymers

We studied by lattice simulation the surface diffusion and relaxation of isolated, self‐avoiding polymers partially adsorbed onto a flat surface. The key parameters describing the system are the number of segments in the chain, N, the adsorption energy of a segment, expressed as a dimensionless surface temperature T_s, and the segmental friction factor on the surface relative to that in the bulk, ζ_s/ζ_b. The simulation data indicate Rouse scaling of the surface diffusion coefficient, D_∥, and in‐plane relaxation time, τ, versus N for all values of T_s and ζ_s/ζ_b studied. A simple application of the Rouse model to a partially adsorbed chain, which ignores fluctuations in adsorbed trains, yields a formula for D_∥ with the correct N‐scaling. It can account for the effects of T_s when ζ_s/ζ_b is finite (≲10), but it fails when ζ_s/ζ_b diverges, predicting no surface diffusion at all, whereas simulations indicate finite surface mobilities facilitated by a caterpillar‐like motion. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1146–1154, 2000     

Structural relaxation of glass-forming polymers based on an equation for configurational entropy, 4. Structural relaxation in styrene-acrylonitrile copolymer

The structural relaxation process in styrene-acrylonitrile copolymer has been characterized by means of differential scanning calorimetry (DSC) experiments. The results in the form of heat capacity, c_p(T), curves are analyzed using a model for the evolution of the configurational entropy during the process recently proposed by the authors.^11,12 The model simulation allows one to determine the enthalpy (or entropy) structural relaxation times and the β parameter of the Kohlrausch-Williams-Watts equation characterizing the width of the distribution of relaxation times. This material parameters are compared with their analogues determined from the dielectric and dynamic-mechanical relaxation processes. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2201–2217, 1997