Shear creep and recovery of a technical polystyrene

The torsional creep and recoverable bahaviour of a technical polystyrene is reported over seven orders of magnitude of the value of the compliance from 10^–8 to 10^–1 Pa^–1 and over more than seven decades in time. The results for the recoverable compliance J_R (t) reveal a dispersion region seen between the glass transition and the steady-state recoverable compliance J_e. The limiting value of the final dispersion J_e = 4.7 · 10^–4 Pa^–1 indicates a broad molecular-weight distribution. The steady-state recoverable compliance J_e is independent of the temperature. The temperature dependence of the final dispersion was found to be indistinguishable from that of viscous flow. However, this temperature dependence differs significantly from that of the glass-rubber transition. A proposal has been made for the construction of creep compliance and recoverable compliance over an extended time scale.     

Creep recovery behavior of metallocene linear low-density polyethylenes

The rheological behavior of two metallocene linear low-density polyethylenes (mLLDPE) is investigated in shear creep recovery measurements using a magnetic bearing torsional creep apparatus of high accuracy. The two mLLDPE used are homogeneous with respect to the comonomer distribution. The most interesting feature of the two mLLDPE is that their molecular mass distributions are alike. Therefore, as one of the mLLDPE contains long-chain branches, the influence of long-chain branching on the elastic properties of polyethylene melts could be investigated. It was found that long-chain branches increase the elasticity of the melt characterized by the steady-state recoverable compliance. The long-chain branched mLLDPE has a flow activation energy of 45 kJ/mol which is distinctly higher than that of the other mLLDPE. The shear thinning behavior is much more pronounced for the long-chain branched mLLDPE. A discrepancy between the weight average molecular mass M _w calculated from size exclusion chromatography measurements by the universal calibration method and the zero shear viscosities of the two mLLDPE was observed. These observations are discussed with reference to the molecular architecture of the long-chain branched mLLDPE. The rheological properties of the long-chain branched mLLDPE are compared with those of a classical long-chain branched LDPE. It is surprisingly found that the rheological behavior is very much the same for these two products although their molecular mass distributions and presumedly the branching structures differ largely. Received: 15 February 1999 Accepted: 10 June 1999     

On the elastic properties of model suspensions as investigated by creep recovery measurements in shear

 The elastic properties of model suspensions with spherical monodisperse hydrophilic glass spheres that were dispersed in a Newtonian liquid were determined in creep and creep recovery measurements in shear with a magnetic bearing torsional creep rheometer. The creep and creep recovery measurements were performed depending on the applied level of shear stresses ranging from 0.19 Pa to 200 Pa. Since the recoverable creep compliances of the chosen suspending medium (i.e. a low molecular weight polyisobutylene) were far below the lower limit of the resolution of the creep rheometer it can be considered to behave as purely viscous. By applying a large shear stress in the creep tests the investigated suspensions with a volume fraction of Φ _t =0.35 behave as Newtonian liquids, too. For these suspensions no significant recoverable creep compliances could be detected, as well. In contrast to the Newtonian state of suspensions at high shear stresses, where a shear induced ordering of the particles can be expected, a non-Newtonian behaviour arises by applying a very low shear stress in the creep test. In this state large recoverable creep compliances were detected for the suspensions. The magnitude of the recoverable creep compliances of the suspensions exceeded the largest creep compliances of polymer melts that are reported in the literature by more than two decades. From the results obtained by creep recovery measurements with a magnetic bearing torsional creep rheometer it can clearly be concluded that the particle structure present in the chosen model suspension gives rise to a pronounced elasticity. Received: 21 November 2000 Accepted: 12 July 2001     

Influence of molecular structure on rheological properties of polyethylenes

Elastic properties of melts of a long-chain branched low density polyethylene (LDPE) with a broad molecular mass distribution and a short-chain branched linear low-density polyethylene (LLDPE) with a more narrow molecular mass distribution were investigated by creep recovery measurements in shear. The results obtained by means of a magnetic bearing torsional creep apparatus in the linear-viscoelastic region, showed that the steady state recoverable compliance of the LLDPE is greater by a factor of two than that of the LDPE. In the short-time region up to 1000 s, however, the time-dependent recoverable compliance of the LDPE is higher than that of the LLDPE. The retardation times for the LLDPE are considerably longer than for the LDPE. For the LDPE the temperature dependence of the entanglement transition is consistent with that of the terminal zone of the creep compliance. The activation energy of 58 kJ/mole lies in the typical range for long-chain branched polyethylenes. In the case of the LLDPE the creep compliances can be shifted to give a mastercurve with an activation energy of 34 kJ/mole, whereas the recoverable compliances do not follow the time-temperature superposition principle. The molecular characterization using TREF showed that the LLDPE has a bimodal branching structure. In addition to a short-chain branched component, a low percentage of a linear constituent with high molecular mass was found. It is postulated that this linear component forms a dispersed phase in the matrix of the short-chain branched constituent. The resulting interfacial tension could be the reason for the long retardation times, the high steady state recoverable compliance and the fact that the time-temperature superposition principle is not fulfilled in the case of the LLDPE investigated. Received: 1 July 1997 Accepted: 12 November 1997     

The numerical calculation of storage and loss compliance from creep data for linear viscoelastic materials

Summary Numerical formulae are given for calculation of storage and loss compliance from the course of the creep compliance for linear viscoelastic materials. These formulae involve values of the creep compliance at times which are equally spaced on a logarithmic time scale. The ratio between succeeding times corresponds to a factor of two. A method is introduced by which bounds for the relative error of those formulae can be derived. These bounds depend on the value of the damping, tanδ. The calculation of the storage compliance is easier with the lower damping values. This calculation involves the value of the creep compliance at timet ₀=1/ω, and that of its derivative with respect to the logarithm of time in a rather narrow region aroundt ₀. In contrast the calculation of the loss compliance is more difficult with the lower damping values. This calculation involves the value of the derivative of the creep compliance with respect to the logarithm of time in a broad interval aroundt ₀.

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Zusammenfassung Numerische Formeln werden angegeben, die die Berechnung der dynamischen Nachgiebigkeit aus der Kriechkurve erm?glichen. In diesen Formeln treten Werte der Kriechkurve auf, die zu logarithmisch ?quidistanten Zeitpunkten gemessen wurden. Das Verh?ltnis zweier aufeinanderfolgender Zeitpunkte entspricht stets einem Faktor 2. Für alle Formeln werden obere und untere Schranken für den relativen Fehler abgeleitet. Diese Schranken h?ngen vom Werte der D?mpfung (tanδ) ab, die bei der Kreisfrequenzω auftritt, für die die Berechnung erfolgt. Die Berechnung der Speicherkomponente der dynamischen Nachgiebigkeit ist desto leichter, je niedriger der Wert der D?mpfung ist. Zu dieser Berechnung ben?tigt man den Wert der Kriechfunktion zum Zeitpunktt ₀=1/ω und deren logarithmische Zeitableitung in einem ziemlich engen Zeitintervall umt ₀. Die Berechnung der Verlustkomponente der dynamischen Nachgiebigkeit ist desto leichter, je h?her der Wert der D?mpfung ist. Zu dieser Berechnung ben?tigt man den Wert der logarithmischen Zeitableitung der Kriechfunktion in einem breiten Zeitintervall umt ₀.

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Dedicated to Prof. Dr.J. Meixner, Aachen, on the occasion of his 60th birthday.     

Presentation of the creep curves of solid biological materials by a simplified mathematical version of the generalized Kelvin-Voigt model

Published creep equations, derived from the Kelvin-Voigt model with a discrete retardation time spectrum were used to generate data for linear presentation of the creep function. It is shown that 2–3 term creep functions, containing 4–6 constants, could be reduced to an algebraic expression having two constants only. Consequently, entire creep curves of a variety of biological and food materials could be described by a single type of equation in the form of:P (t) = k ₀ + k₁ t + t/(k₂ + k₃t) whereP (t) is the creep parameter (compliance, strain or deformation),k ₀ a constant representing the instantaneous compliance,k ₁ a constant representing the steady-state flow, andk ₂ andk ₃ the characteristic constants of the creep function (t) obtained by regression from the linear relationship oft/ (t) vst.     

The determination of a general time creep compliance relation of linear viscoelastic materials under constant load and its extension to nonlinear viscoelastic behavior for the Burger model

Linear viscoelastic materials yield a creep function which only depends on time if creep experiments are performed under constant stress ₀. In practice, this condition is very difficult to realize, and as a consequence, the experiments are performed under constant force. For small strains the difference between the conditions of constant stress and constant force is negligible. Otherwise, the decrease in cross-section has to be taken into account and leads to increasing stress in the course of time for creep experiments under constant load. The Boltzmann superposition principle is solved under the condition of constant load and for strains . The creep complicance C(t; ₀) defined by the ratio becomes, in principle, dependent on the initial stress ₀. As a consequence, a set of creep compliance curves cannot be approximated with a simple parameter fit. Already the application of the solution on the Burger model yields a creep compliance curve with all three creep ranges. Furthermore, the mathematical structure of the time creep compliance relation of the Burger model allows nonlinear viscoelastic extension via the introduction of the yield strength _max and a nonlinearity parameter n _l . The creep behavior of PBT and PC can be described in the range of long times up to initial stresses ₀, being 75% for PBT and 60% for PC of the yield stress _max with only two or one free fit parameter, respectively.     

Multiscale Creep Compliance of Epoxy Networks at Elevated Temperatures

Epoxy networks are thermoset polymers for which an important structural length scale, molecular weight between crosslinks (M _c), influences physical and mechanical properties. In the present work, creep compliance was measured for three aliphatic epoxy networks of differing M _c using both macroscale torsion and microscale depth-sensing indentation at temperatures of 25 and 55°C. Analytical relations were used to compute creep compliance (J(t)) for each approach; similar results were observed for the two techniques at 25°C, but not at 55°C. Although creep compliance measurement differed at elevated temperatures, there were clear correlations between M _c, glass transition temperature, T _g, and the observed time-dependent mechanical behavior via both techniques at 55°C, but these correlations could not be seen at 25°C. This work demonstrates the capacity of depth-sensing indentation to differentiate among epoxy networks of differing structural configurations via J(t) for small material volumes at elevated temperatures.     

The frequency response function of the creep compliance

Motivated from the need to convert time-dependent rheometry data into complex frequency response functions, this paper studies the frequency response function of the creep compliance that is coined the complex creep function. While for any physically realizable viscoelastic model the Fourier transform of the creep compliance diverges in the classical sense, the paper shows that the complex creep function, in spite of exhibiting strong singularities, it can be constructed with the calculus of generalized functions. The mathematical expressions of the real and imaginary parts of the Fourier transform of the creep compliance of simple rheological networks derived in this paper are shown to be Hilbert pairs; therefore, returning back in the time domain a causal creep compliance. The paper proceeds by showing how a measured creep compliance of any solid-like or fluid-like viscoelastic material can be decomposed into elementary functions with parameters that can be identified from best fit of experimental data. The proposed technique allows for a direct determination of the sufficient parameters needed to approximate an experimentally measured creep compliance and the presented mathematical formulae offers dependable expressions of the corresponding complex-frequency response functions.

     

Influence of long-chain branches in polyethylenes on linear viscoelastic flow properties in shear

 This contribution presents a survey on the influence of long-chain branching on the linear viscoelastic properties zero shear-rate viscosity and steady-state recoverable compliance of polyethylene melts. The materials chosen are linear and slightly long-chain branched metallocene-catalyzed polyethylenes of narrow molecular mass distribution as well as linear and highly long-chain branched polyethylenes of broad molecular mass distribution. The linear viscoelastic flow properties are determined in shear creep and recovery experiments by means of a magnetic bearing torsional creep apparatus. The analysis of the molecular structure of the polyethylenes is performed by a coupled size exclusion chromatography and multi-angle laser light scattering device. Polyethylenes with a slight degree of long-chain branching exhibit a surprisingly high zero shear-rate viscosity in comparison to linear polyethylenes whereas the highly branched polyethylenes have a much lower viscosity compared to linear samples. Slightly branched polyethylenes have got a higher steady-state compliance in comparison to linear products of similar polydispersity, whereas the highly branched polyethylenes of broad molecular mass distribution exhibit a surprisingly low elasticity in comparison to linear polyethylenes of broad molecular mass distribution. In addition sparse levels of long-chain branching cause a different time dependence in comparison to linear polyethylenes. The experimental findings are interpreted by comparison with rheological results from literature on model branched polymers of different molecular topography and chemical composition. Received: 12 July 2001 Accepted: 30 October 2001     

Comparison of different shear rheometers with regard to creep and creep recovery measurements

The performance of two shear rheometers with regard to creep and creep recovery measurements is investigated. The first one is a commercially available stress-controlled rheometer that uses an air bearing, and the second one is a magnetic bearing torsional creep apparatus that was built at the Institute of Polymer Materials in Erlangen. The creep and creep recovery measurements were performed in the linear-viscoelastic regime of two polyethylene melts at a temperature of 150°C. The creep compliances of the polyethylenes measured by both rheometers are in excellent agreement. The recoverable compliances of both polyethylene melts, however, have lower values in the case of the commercial rheometer than in the case of the magnetic bearing rheometer. The experimental parameters of creep recovery experiments and the features of the two bearings that are responsible for the different results of the two rheometers are discussed. The influence of the level of the applied shear stress on the short time behavior is investigated as well as the residual torque of the bearings which influences the long time region of the recoverable compliances. Also addressed are the influence of the momentum of inertia of the rotor and the bearing friction which is different for the two rheometers.     

纳米颗粒增强镍基MEMS器件材料的蠕变性能研究

利用同步辐射LIGA微铸复合工艺,将纳米氧化物增强颗粒复合到微电子机械系统(MEMS)结构材料中。制作了专用夹具,采用微力材料试验机测量了纳米Al2O3颗粒增强镍基复合材料的强度为1GPa;将恒加载速率/载荷法和恒载荷法相结合,利用纳米压痕仪测量了该材料的室温蠕变速率敏感指数m。结果表明,LIGA复合技术得到的纳米颗粒增强镍基复合材料具有较高的强度;MEMS器件材料在室温下会发生蠕变;材料在相同压深下最大载荷不随加载速率而改变,加载段粘弹性和粘塑性变形极少;主要由局部高应力导致压痕蠕变;材料的蠕变速率敏感指数m值为0.004,说明纳米Al2O3颗粒可有效增强基体材料的抗蠕变能力;且不同恒.P/P下获得的m值基本相同,表示此种材料对加载速率不敏感。     

Creep behavior of crack near bi-material interface characterized by integral parameters

Creep behavior of crack in dissimilar materials is studied using steady-state C^* path independent integral and ABAQUS finite element code. The specific geometry involves an edge crack parallel to the interface of a bi-material tensile specimen at high temperature. Under extensive creep, the C^* value for the bi-material specimen can be significantly higher than that for the homogeneous specimen. For small-scale creep material mismatch has little influence on the transient integral designated by C_t. The integral parameters C^* or C_t are shown to depend on the inhomogeneity of the system and cannot characterize the creep behavior of cracks.The approach is extended to creep crack growth in a welded compact tension specimen. Modification factors are introduced for different crack and weld interface geometries.     

Numerical calculation of creep compliance from dynamic data for linear viscoelastic materials

Summary Numerical formulae are given for calculation of creep compliance from the known course of the storage and loss compliance with frequency for linear viscoelastic materials. These formulae involve values of the storage compliance and/or loss compliance at frequencies which are equally spaced on a logarithmic frequency scale. The ratio between successive frequencies corresponds to a factor of two.A method is introduced by which bounds for the relative error of those formulae can be derived. These bounds depend on the value of the damping, tan, at the angular frequency, ₀, at which the calculation is performed. The lower this damping, the easier is the calculation of the creep compliance. This calculation involves either the value of the storage compliance at a frequency ₀ = 1/t, and the values of the loss compliance in a rather narrow frequency region around ₀; or the value of the storage compliance at frequency ₀, the value of the loss compliance at frequency ₀/2, and the derivative of the storage compliance with respect to the logarithm of frequency in a frequency region around ₀.

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Zusammenfassung Numerische Formeln werden gegeben, die die Berechnung der Kriechfunktion aus der dynamischen Nachgiebigkeit ermöglichen. In diesen Formeln treten Werte der Speicher- bzw. Verlustkomponente der dynamischen Nachgiebigkeit auf, die bei logarithmisch äquidistanten Frequenzen gemessen wurden. Das Verhältnis zweier aufeinanderfolgender Frequenzen entspricht stets einem Faktor 2.Für alle Formeln werden obere und untere Schranken für den relativen Fehler abgeleitet. Diese Schranken hängen vom Werte der Dämpfung (tan) ab, die bei der Kreisfrequenz ₀ auftritt, für die die Berechnung erfolgt. Die Berechnung der Kriechfunktion ist desto leichter, je niedriger der Wert der Dämpfung ist. Zu dieser Berechnung benötigt man entweder den Wert der Speicherkomponente der dynamischen Nachgiebigkeit bei der Kreisfrequenz ₀ = 1/t und die Werte der Verlustkomponente der dynamischen Nachgiebigkeit in einem ziemlich engen Frequenzintervall um ₀; oder den Wert der Speicherkomponente bei der Kreisfrequenz ₀, den Wert der Verlustkomponente bei der Kreisfrequenz ₀/2 und den Wert der logarithmischen Frequenzableitung der Speicherkomponente in einem Frequenzintervall um ₀.

     

Relations Between Relaxation Modulus and Creep Compliance in Anisotropic Linear Viscoelasticity

The results obtained previously for scalar and class P completely monotone relaxation moduli are extended to arbitrary anisotropy. It is shown for general anisotropic viscoelastic media that, if the relaxation modulus is a locally integrable completely monotone function, then the creep compliance is a Bernstein function and conversely. The elastic and equilibrium limits of the two material functions are related to each other. The relaxation modulus or its derivative can be singular at 0. A rigorous general formulation of the relaxation spectrum in an anisotropic viscoelastic medium is given. The effect of Newtonian viscosity on creep compliance is examined. Put some makeup on him and lay him to rest. Anonymous     

Das viskoelastische Verhalten von Polyamid-6-Schmelzen

Zusammenfassung Das rheologische Verhalten von Polyamid-6-Schmelzen mit verschiedenen Molekulargewichten wurde mit Hilfe von Kapillarviskosimetern, einem modifizierten Weissenberg-Rheogoniometer, einem Parallelplatten-Kriechrheometer und einem Schwingungsviskosimeter untersucht. An Meßbeispielen wird der Einfluß der Feuchte und der Meßzeit auf das Stabilitätsverhalten der Schmelze diskutiert. Auf Grund ihrer gleichartigen Schulz-Flory-Molekulargewichtsverteilungen läßt sich für die Viskositätsfunktionen bei einer Normierung der Viskositäts- und Schergeschwindigkeits-Skala mit der Nullviskosität eine Masterkurve konstruieren, die nicht nur temperaturinvariant, sondern auch vom Molekulargewicht unabhängig ist. Die Strangaufweitungen und Einlaufdruckverluste bei Düsenströmung können als Funktionen der Schubspannung an der Düsenwand ebenfalls temperatur- und molekulargewichtsinvariant dargestellt werden. Die aus dynamischen Messungen, aus Messungen der reversiblen Scherung und der 1. Normalspannungs-differenz im linearen Fließbereich ermittelten Gleichgewichts-Nachgiebigkeiten stimmen überein. Als Folge des konstanten Verhältnisses von ist die Gleichgewichts-Nachgiebigkeit unabhängig vom Molekulargewicht. Die Temperaturabhängigkeit der Nullviskosität folgt einer Arrhenius-Beziehung mit einer vom Molekulargewicht unabhängigen Aktivierungsenergie vonE ₀ = 60 kJ/Mol.

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Summary The rheological behaviour of nylon 6 melts of different molecular weights was investigated by means of capillary viscometers, a modified Weissenberg rheogoniometer, a sandwich creep apparatus, and an oscillatory viscometer. The influence of moisture content and residence time on the stability behaviour of the melts is demonstrated by measurements. Due to the comparable Schulz-Flory molecular weight distributions of the melts a mastercurve for the viscosity functions can be constructed by normalizing the viscosity and the shear rate by means of the zeroshear viscosity. The mastercurve is not only temperature invariant but also independent of the molecular weight. Temperature and molecular weight invariant plots are also obtained for the extrudate swell and entrance pressure losses as functions of the wall shear stress. Coincident values for the steady-state compliance are determined from oscillatory measurements, the recoverable shear strains, and the primary normal stress differences in the linear range of shear flow. As a consequence of the constant ratio the steady-state compliance is independent of the molecular weight. The temperature dependence of the zeroshear viscosity follows an Arrhenius relation with a constant activation energy ofE ₀ = 60 kJ/Mol.

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Auszugsweise vorgetragen auf dem Wissenschaftlichen Kolloquium zu Ehren von Professor Dr.Paul Schlack am 19. Dezember 1977 in Stuttgart.

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Herrn Professor Dr.Paul Schlack zum 80. Geburtstag gewidmet.

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Mit 16 Abbildungen     

The creep behavior of ideally atactic and commercial polymethylmethacrylate

Summary The shear creep behavior of polymethylmethacrylate, PMMA, samples has been studied in the neighborhood of and above their glass temperatures. One of the materials studied was ideally atactic with equal numbers of random isotactic and syndiotactic placements, while the other was a commercial or conventional PMMA which was about 76% syndiotactic. The glass temperatures,T _g , were found to be 106 and 117 °C respectively. Evacuation above the glass temperature for several weeks was necessary before reproducible creep compliance,J (t), curves could be obtained. It is believed that absorbed water plasticized the polar materials and its removal led to the shifting of theJ (t) curves to longer times. For both materials apparently successful temperature reduction was found to be possible within the temperature range of our investigations, i.e. up to 200 °C. Retardation spectra were calculated from the reduced curves and are compared. The temperature dependences, as described by the time scale shift factors,a _T , were similar when allowance is made for the different glass temperature. Botha _T curves could not be fitted to theWilliams, Landel, andFerry, WLF, free volume expression. These are the first examples of such a deviation for amorphous high polymers. It is proposed that the primary softening dispersion has two distinctly different groups of viscoelastic mechanisms contributing to it. On this basis the primary dispersion was decomposed into the two contributions. Both of the resulting temperature dependences were satisfactorily fitted to the WLF equation. Differences in the retardation spectra are noted. The glassy compliance of the commercial PMMA appears to be about twice that of the atactic PMMA.Data on commercial PMMA is incorporated in a thesis which has been submitted in partial fulfillment of the requirements for the degree of Master of Science in Materials Engineering, University of Pittsburgh, 1970.With 12 figures and 1 table     

Compliance of actin filament networks measured by particle-tracking microrheology and diffusing wave spectroscopy

We monitor the time-dependent shear compliance of a solution of semi-flexible polymers, using diffusing wave spectroscopy (DWS) and video-enhanced single-particle-tracking (SPT) microrheology. These two techniques use the small thermally excited motion of probing microspheres to interrogate the local properties of polymer solutions. The solutions consist of networks of actin filaments which are long semi-flexible polymers. We establish a relationship between the mean square displacement (MSD) of microspheres imbedded in the solution and the time-dependent creep compliance of the solution, <Δr ²(t)>=(k _B T/πa)J(t). Here, J(t) is the creep compliance, <Δr ²(t)> is the mean-square displacement, and a is the radius of the microsphere chosen to be larger than the mesh size of the polymer network. DWS allows us to measure mean square displacements with microsecond temporal resolution and Ångström spatial resolution. At short times, the mean square displacement of a 0.96μm diameter sphere in a concentrated actin solution displays sub-diffusion. <Δr ²(t)>∝t ^{, with a characteristic exponent =0.78±0.05, which reflects the finite rigidity of actin. At long times, the MSD reaches a plateau, with a magnitude that decreases with concentration. The creep compliance is shown to be a weak function of polymer concentration and scales as J _p ∝c –1.2±0.3. This exponent is correctly described by a recent model describing the viscoelasticity of semi-flexible polymer solutions. The DWS and video-enhanced SPT measurements of the compliance plateau agree quantitatively with compliance measured independently using classical mechanical rheometry for a viscous oil and for a solution of flexible polymers. This paper extends the use of DWS and single-particle-tracking to probe the local mechanical properties of polymer networks, shows for the first time the proportionality between mean square displacement and local creep compliance, and therefore presents a new, direct way to extract the viscoelastic properties of polymer systems and complex fluids.}     

Heat-induced gelation of globular proteins. Part 5. Creep behaviour of β-lactoglobulin gels

 Creep and recovery experiments have been used to investigate the behaviour of heat set protein gels exemplified by those prepared from β-lactoglobulin (β-Lg). Some initial experiments were also performed on heat set BSA gels to establish appropriate experimental conditions. The latter illustrated the importance of a well-controlled thermal regime and the use of an appropriate solvent trap. Results from the concentration dependence of compliance for β-Lg were in good agreement with previously published results for the long time extrapolated storage modulus, G ^′ _∞ we introduced previously, especially considering the necessarily different experimental conditions. The exponent of creep and recovery phase viscosity vs concentration was extremely high, ∼30, but reflects the nature of such gelling systems close to their critical concentration. In this respect, the behaviour of the creep phase viscosity was in qualitative agreement with our recently postulated viscosity vs concentration state diagram for a gelling system. Received: 12 July 2001 Accepted: 29 October 2001