Incipient behaviour of gelatin gels

The present work describes isothermal (25°C) gelation measurements for gelatin gels over a range of concentrations. Methods for the estimation of the gel time are discussed, and data compared with two recent models. The isothermal time growth of modulus is also investigated, and the superposition of such data discussed. For concentrations close to the critical gel concentration C ₀ there are significant deviations in the latter case. These may be related to the approach to the biphasic region of the phase diagram suggested by other workers.     

Elongational rheology of polyethylene melts — temporary network constitutive laws

The uniaxial elongational properties of various polyethylenes have been evaluated using an elongational rheometer and a melt-strength apparatus. It is possible to derive the data obtained in elongation from the distribution of relaxation times obtained from oscillatory shearing measurements (linear viscoelasticity), using a Wagner constitutive equation. The effects of the molecular parameters of the samples have been studied, in particular the effect of polydispersity on the shape of the damping function.     

A model for the effect of physical ageing on the stress relaxation behavior of high density polyethylene

The stress relaxation behavior of high density polyethylene (HDPE) can be affected by ageing processes; e.g., with increasing storage time at a low temperature following a quench from a high temperature (close to the melting point) the relaxation curves change shape. More specifically, the stress level approached after very long loading times in a stress relaxation experiment increases with the ageing time. Here this stress level is denoted the internal stress _i. Struik has pointed out that physical ageing may also occur in semicrystalline polymers like HDPE. The physical ageing should then be associated with that part of the amorphous phase which is closest to the surfaces of the crystallites. This part of the amorphous phase of HDPE can be assumed to have a restricted mobility at room temperature and may have a partially glassy character. In this paper a model for explaining the increase in _i for HDPE with increasing ageing time is proposed and discussed. It is based on the separation of the amorphous phase into two parts as suggested by Struik. The glassy part of the amorphous phase ages in a way similar to that of an entirely amorphous polymer quenched to a temperature below its glass transition, while the more rubbery phase is assumed not to undergo any physical ageing.     

In situ technique for monitoring the gelation of UV curable polymers

Ultraviolet-radiation-cured cross-linked systems are used extensively in optoelectronic applications. We describe a new in situ technique for doing controlled curing of photosensitive materials and monitoring the gelation through dynamic theological measurements. In this method, a sample placed between quartz windows of a modified parallel plate fixture of a Rheometrics Mechanical Spectrometer is radiated from a collimated UV source using a liquid light guide and a mirror. By varying the sample exposure to UV radiation, the degree of cross-linking can be precisely controlled to observe the material behavior in the pre, post, and critical gel state. Time-dependent measurements on urethane based materials show the gelation behavior to have an induction period with no change in dynamic moduli (G, G), followed by their sharp increase as the materials develop a network structure. The critical gel point is characterized by a power-law dependence of the dynamic moduli on frequency. The gelation kinetics scales with sample thickness and radiation intensity, the scaling factor in both cases being the critical gelation time. The rheological measurements correlate with differential photocalorimetric studies.     

Correlation between interfacial interactions and internal stresses in filled high density polyethylene

The stress relaxation and the creep behaviour of high density polyethylene (HDPE) filled with glass fibres, clay (plate-like particles) or CaCO₃ (particles with irregular shape) were measured in uniaxial extension at room temperature. It was observed that the addition of filler increased the internal stress level, as evaluated from stress relaxation data. This increase was larger than the corresponding increase in the (short-term) elastic modulus. This behaviour may be attributed to a reduced macromolecular mobility in the matrix material close to the filler surface, i.e. to formation of an interphase region in the HDPE-matrix. From the internal stress values, the thickness of this interphase region around each filler particle was estimated, assuming a uniform coverage of the particles. It was suggested that the amount of matrix material with reduced mobility (or the thickness of the interphase region) reflected the degree of adhesion between the filler and HDPE. The change in the internal stress level due to the incorporation of different fillers, which were surface treated in some cases, was also consistent with the observed creep behaviour.     

Determination of discrete relaxation and retardation time spectra from dynamic mechanical data

A powerful but still easy to use technique is proposed for the processing and analysis of dynamic mechanical data. The experimentally determined dynamic moduli,G() andG(), are converted into a discrete relaxation modulusG(t) and a discrete creep complianceJ(t). The discrete spectra are valid in a time window which corresponds to the frequency window of the input data. A nonlinear regression simultaneously adjust the parametersg _i , _i ,i = 1,2, N, of the discrete spectrum to obtain a best fit ofG, G, and it was found to be essential that bothg _i and _i are freely adjustable. The number of relaxation times,N, adjusts during the iterative calculations depending on the needs for avoiding ill-posedness and for improved fit. The solution is insensitive to the choice of initial valuesg _i,0, _i,0,N ₀. The numerical program was calibrated with the gel equation which gives analytical expressions both in the time and the frequency domain. The sensitivity of the solution was tested with model data which, by definition, are free of experimental error. From the relaxation time spectrum, a corresponding discrete set of parametersJ ₀,, J _d,i and _i of the creep complianceJ(t) can then readily be calculated using the Laplace transform.This paper is dedicated to Professor Hanswalter Giesekus on the occasion of his retirement as Editor of Rheologica Acta.     

The evolution of linear viscoelasticity during the vulcanization of polyethylene

The evolution of linear viscoelasticity during the vulcanization of polyethylene is studied through the gel point. The material in the vicinity of the gel point is described by two scaling laws: one characterizes the viscoelasticity at the critical point and a second characterizes the evolution of viscoelasticity near the gel point. Time Resolved Mechanical Spectroscopy is used to observe both scaling phenomena. The material at the gel point displays power law relaxation over five decades of time with a power-law relaxation exponent equal to 0.32. This study conforms with previous findings that this exponent is composition-dependent. The longest relaxation time diverges in the vicinity of the gel point as _max |p _c - p| ^–1/, and we find = 0.2. This result conforms with previous reports that this exponent may be independent of composition. The Arrhenius flow activation energy for this material undergoes three-fold changes during crosslinking up to the gel point. A single-adjustable-parameter stretched-exponential-power law relaxation function is an inadequate representation of crosslinked materials over any significant range of extent of the reaction up to the gel point.     

Rheological properties of lightly crosslinked carboxy copolymers in aqueous solutions

The rheological properties of a series of lightly crosslinked carboxy copolymers in aqueous solutions have been evaluated in steady shear and dynamic oscillatory modes. Viscosity profiles and the behavior of storage modulus are related to the chemical composition of the copolymers and their crosslinking density. A maximum in viscosity and in storage modulus which depends on the type of crosslinking agent used is explained by a combination of a chain entanglement mechanism and a closely-packed spheres model. The recovery of viscosity and storage modulus after shearing is very fast and is related to the very fast rearrangement of the microgel structure as a function of time.     

Evaluation of the dynamic-mechanical properties of solids from a cooperative model for stress relaxation

For many solid materials the stress relaxation process obeys the universal relationF = – (d/d lnt)_max = (0.1 ± 0.01) ( ₀ — _i ), regardless of the structure of the material. Here denotes the stress,t the time, ₀ the initial stress of the experiment and _i the internal stress. A cooperative model accounting for the similarity in relaxation behaviour between different materials was developed earlier. Since this model has a spectral character, the concepts of linear viscoelasticity are used here to evaluate the corresponding prediction of the dynamic mechanical properties, i.e. the frequency dependence of the storageE () and lossE () moduli. Useful numerical approximations ofE () andE () are also evaluated. It is noted that the universal relation in stress relaxation had a counterpart in the frequency dependence ofE (). The theoretical prediction of the loss factor for high-density polyethylene is compared with experimental results. The agreement is good.     

Measurements of slip at the wall during flow of high-density polyethylene through a rectangular conduit

A hot-film probe has been used to measure slip of high-density polyethylene flowing through a conduit with a rectangular cross section. A transition from no slip to a stick-slip condition has been observed and associated with irregular extrudate shape. Appreciable extrudate roughness was initiated at the same flow rate as that at which the relationship between Nusselt number and Péclet number for heat transfer from the probe departed from the behavior expected for a no-slip condition at the conduit wall. A ₁ constant defined by eq. (A3) - C dimensionless group used in eq. (7) - C _p heat capacity - D constant in eq. (13) - f u _s/u - f _lin defined by eq. (A6) - G storage modulus - G loss modulus - k thermal conductivity - L length of hot film in thex-direction - L _eff effective length of large probe found from eq. (A3) - Nu _L Nusselt number, defined for a lengthL by eq. (2) - (Nu _L)₀ value ofNu _L atPe = 0 (eq. (A 1)) - Pe Péclet number,uL/ - Pe ₀ Péclet number in slip flow, eq. (6) - Pe ₁ Péclet number in shear flow, eq. (4) - q _L average heat flux over hot film of lengthL - R _i resistances defined by figure 8 - R _AB correlation coefficient defined by eq. (14) for signalsA andB - T temperature - T _s temperature of probe surface - T ambient temperature - T T _s –T - u average velocity - u _s slip velocity - V _b voltage indicated in figure 8 - W probe dimension (figure 6) - x distance in flow direction (figure 1) - y distance perpendicular to flow direction (figure 1) - thermal diffusivity,k/C _p - wall shear rate - _5% thickness of lubricating layer during probe calibration for introduction of an error no greater than 5%; see Appendix I - ^* complex viscosity - density - time - _c critical shear stress, eq. (13) - _w wall shear stress - frequency characterizing extrudate distortion (figures 12 and 13), or frequency of oscillation during rheometric characterization (figures 18–20) - * quantity obtained from normalized Nusselt number, eq. (A1), or complex viscosity ^* - A actual (small) probe (see Appendix I) - M model (large) probe (see Appendix I)     

Effect of secondary zone dimensions on melt fracture manifestations of high density polyethylene

An experimental study was performed on melt fracture phenomena in extrusion of high density polyethylene. The purpose of the work was to study the sensitivity of melt fracture driven roughness to the size of recirculation zones, viz. secondary zones. The experimental apparatus consists of a right angle die and a hypodermic needle used as a capillary. The position of the needle relative to the die was adjusted using a special fixture. The roughness of the extrudate was studied as a function of penetration depth. A developed procedure provides a comparison between profile lengths of extruded strands. The computed mean, median, and mode values for roughness were presented as a function of capillary position. A qualitative analysis was conducted for the force oscillations during extrusion with a separate set of dies, equipped with the fixed capillaries of identical lengths and different depths of penetration. It was observed that the oscillatory pattern is sensitive to the sizes of the secondary zones. This qualitative observation supports the conclusions from the quantitative analysis that the roughness of the extrudate can be controlled through an adjustment of the secondary zone sizes.Partly presented at the 58th Annual Meeting of the Society of Rheology, Tulsa, Oklahoma, October 20–23, 1986     

Temperature and concentration dependent viscosity and gelation temperature of ABA triblock copolymer solutions

In solutions of ABA-triblock copolymers in a poor solvent for A thermoreversible gelation can occur. A three-dimensional dynamic network may form and, given the polymer and the solvent, its structure will depend on temperature and polymer mass fraction. The zero-shear rate viscosity of solutions of the triblock-copolymer polystyrene-polyisoprene-polystyrene in n-tetradecane was measured as a function of temperature and polymer mass fraction, and analyzed; the polystyrene blocks contained about 100 monomers, the polyisoprene blocks about 2000 monomers. Empirically, in the viscosity at constant mass fraction plotted versus inverse temperature, two contributions could be discerned; one contribution dominating at high and the other one dominating at low temperatures. In a comparison with theory, the contribution dominating at low temperatures was identified with the Lodge transient network viscosity; some questions remain to be answered, however. An earlier proposal for defining the gelation temperature T _gel is specified for the systems considered, and leads to a gelation curve; T _gel as a function of polymer mass fraction.Mathematical symbols {} functional dependence; e.g., f{x} means f is a function of x - p _log logarithm to the base number p; e.g., ¹⁰log is the common logarithm - exp exponential function with base number e - sin trigonometric sine function - lim limit operation - – in integral sign: Cauchy Principal Value of integral, e.g., - derivative to x - partial derivative to x Latin symbols dimensionless constant - b constant with dimension of absolute temperature - constant with dimension of absolute temperature - B dimensionless constant - c mass fraction - dimensionless constant - constant with dimension of absolute temperature - d ^* dimensionless constant - D{0} constant with dimension of absolute temperature - e base number of natural (or Naperian) logarithm - g distribution function of inverse relaxation times - G relaxation strength relaxation function - h distribution function of relaxation times reaction constant enthalpy of a molecule - H Heaviside unit step function - i complex number defined by i ² = –1 - j{0} constant with dimension of viscosity - j index number - k Boltzmann's constant - k _H Huggins' coefficient - m mass of a molecule - n number - N number - p index number - s entropy of a molecule - t time - T absolute temperature Greek symbols as index: type of polymer molecule - as index: type of polymer molecule - shear as index: type of polymer molecule - shear rate - small variation; e.g. T is a small variation in T relative deviation Dirac delta distribution as index: type of polymer molecule - difference; e.g. is a difference in chemical potential - constant with dimension of absolute temperature - (complex) viscosity - constant with dimension of viscosity - [] intrinsic viscosity number - inverse of relaxation time - chemical potential - number pi; circle circumference divided by its diameter - mass per unit volume - relaxation time shear stress - angular frequency     

Evaluation of the extent of the gel particle grafting of impact polystyrene

High Impact Polystyrene (HIPS) consists of a glassy polystyrene matrix and a rubber-like particle phase (gel phase). The extent of grafting of the gel phase is known to be an important parameter in the fracture toughness of the material. [1]. A simple quantitative model is developed in this paper to determine the extent of gel-particle grafting from the observed shifts in the glass transition temperature of the gel phase of three commercial types of HIPS.Although the increase in interfacial [2] and gel-particle grafting accounts for an increase in the energy absorbed before fracture at low strain rates, above a certain amount of grafting the material becomes embrittled at high strain rates. The adhesion factor A of mesophase models [3, 19], considered between the main phases of the material, was found to correlate with the observed impact behaviour.     

Finite shear strain behavior of a crosslinking polydimethylsiloxane near its gel point

A power law distribution of relaxation times, large normal stress differences, and physical rupture of molecular network strands dominate the shear behavior of polymers at the gel point (critical gels). This is shown in a series of well-defined experiments with increasing magnitude of shear on a model-network polymer system consisting of a linear, telechelic, vinyl-terminated poly-dimethylsiloxane (PDMS) and a four-functional siloxane crosslinker. Stable samples were prepared by stopping the crosslinking reaction at different extents of reaction in the vicinity of the gel point (GP). The Gel Equation has been shown to be valid up to strains of about 2 when using a finite strain tensor. Larger strains have been found to disrupt the network structure of the crosslinking polymer, and introduce a mechanical delay to the gel point. A sample that was crosslinked beyond the gel point (p>p _c ) can be reduced from the solid state to a critical gel, or even to a viscoelastic liquid, depending on the magnitude of shear strain. As a consequence, the relaxation exponent of a critical gel created under the influence of shear is less than that of a quiescently crosslinked critical gel.     

A study of swelling and collapse in polyelectrolyte gels

Swelling and collapse of a polyelectrolyte are shown to be the result of a delicate balance of three thermodynamic forces, viz. osmotic pressure, polymer elasticity, and van der Waals attraction. The behaviour of the polyelectrolyte gel is studied under isotropic pressure and under uniaxial and biaxial loading.     

Evolution of the rheological properties during the reactive processing of thermoplastic/thermoset epoxy

The melt state reaction, or fusion process of bisphenol-A and the diglycidyl ether of bisphenol-A can produce both linear phenoxy backbone chains and crosslinked network structures. The linear chains can be thought of as thermoplastic polymer, while the crosslinked molecular matrix is a thermoset; therefore, this resin system can be termed a thermoplastic/thermoset epoxy.Rheological analysis has been performed on this system to determine the occurrence of the crossover of the storage and loss moduli during the reaction using three techniques: isothermal cure, interval frequency sweep, and interval stress relaxation.Determination of the activation energy of the reaction by consideration of the conventional gel-point determination prove unsatisfactory as compared to that which is determined by FTIR. An alternative technique is presented which yields a value in good agreement with that obtained by following epoxide consumption. The thermoplastic/thermoset nature of this material leads to the deviation from traditional thermoset cure behavior.     

Zum Einfluß von Füllstoffen auf das rheologische Verhalten von hochmolekularen Polyethylenschmelzen

Zusammenfassung Zur Sichtbarmachung der Strömungsvorgänge im Bereich der konvergenten Strömung vor einer Kapillaren wurde ein Verfahren entwickelt, das die Eigenschaften bestimmter teilkristalliner Polymere bei der Kristallisation unter Scherung bzw. aus einer vorgescherten Schmelze nutzt. Diese zeigen im erstarrten Zustand sogenannte Fließlinien, die aus in bestimmter Weise auf reihenförmig angeordnete Keime aufgewachsenen Kristallitstrukturen bestehen. Solche linienförmigen Aggregate sind in der Lage, ein Stromlinienbild der Strömung in der Schmelze im erstarrten Polymer wiederzugeben. Für ein LDPE vom Spritzgußtyp konnte die Entwicklung der Einlaufwirbel mit wachsender Schergeschwindigkeit dargestellt werden. Die hochmolekularen Polymertypen erwiesen sich schon bei geringsten Durchsätzen als instabil, die Einlaufwirbel verschwanden dabei vollständig, und die Bilder des erstarrten Polymers legen einen Mechanismus der Instabilitäten nahe, bei dem jeweils unterschiedliche Teilvolumina zeitweise in die Kapillare einströmen, bei Überschreiten einer kritischen Deformation jedoch abreißen und zurückschnellen, während andere Volumenelemente ihren Platz einnehmen. Das Verhalten der Suspensionen unterscheidet sich diesbezüglich nicht von dem der ungefüllten Schmelzen.Ein signifikanter Einfluß der Füllstoffe zeigt sich jedoch beim Einströmen in Kapillaren. Während die ungefüllten Schmelzen nach sehr kurzer Zeit ein laminares Strömungsprofil ausbilden, findet man mit zunehmender Füllung im Bereich stabiler Einströmbedingungen einen sehr hohen Einlaufdruckverlust bei kurzen Kapillaren, nicht jedoch bei Lochdüsen. Dies deutet auf einen Verfestigungsmechanismus bei der Ausbildung des laminaren Strömungsprofils hin, der durch Aggregierungsvorgänge im Bereich der hohen Dehnbeanspruchung in der konvergenten Einlaufströmung bewirkt wird.

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For the visualization of polymer flow in the entry region of a capillary, a method has been developed that uses distinct crystallization phenomena of the partially crystalline polymer itself solidifying from a presheared melt. The solid polymer shows so-called flow lines made up of transcrystalline overgrowth on rows of nuclei capable of showing a picture of the past melt-flow streamlines. The development of circulating flow in the entry region of capillaries could be shown with an injection-molding type LDPE. The higher molecular-weight types appeared to show unstable flow with disappearing circulating flow in the corners even at very low flow rates. The bulk polymer seems to flow into the capillary from certain parts of the reservoir until a critical strain is reached, then snaps back, giving way for the same flow type from another part of the reservoir. The behaviour of the suspensions does not differ in this respect from that of the pure melts.A significant filler influence is, however, shown within the capillary. While unfilled polymer melts reach steady flow conditions only one or two diameters downstream of the capillary entrance, an entry pressure loss increasing with increasing filler content is found in short capillaries (l/d = 5 – 15), but not in no-land dies (l/d 1). This seems to indicate a flow hardening mechanism in the region where the steady laminar flow profile develops and which might result from the very high extensional strain (next to instability) in the converging flow of the capillary entrance.

Zweiter Teil einer vom Fachbereich Chemietechnik der Universität Dortmund genehmigten Dissertation.     

Formation des gels d'agar et seuil d'écoulement

Résumé Les seuils de plasticité de gels d'agar a différentes concentrations ont été déterminés par différentes méthodes et comparé entre eux. Le seuil de contrainte qui apparaît au cours du refroidissement de la solution indique le début de la formation du réseau gélifié. II définit une température d'apparition du seuil de plasticite. La determination de cette temp6rature critique montre que la formation du gel est soumis aux conditions de refroidissement de la solution: le processus de gelification est accéléré par un refroidissement rapide des solutions et débute à une température plus basse. La formation du gel peut être suivie dans des conditions plus proches des réalités industrielles de fabrication de ces milieux.

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The yield stress of agar gels has been measured by different methods and the results compared. The yield stress which occurs during cooling of polymer solutions indicates the beginning of crystalline network formation. This point defines the temperature of plastic flow; its determination shows that the gel formation is subordinated to cooling conditions of the solution: the process of gelification is retarded by very fast cooling, and is induced at a lower temperature than occurs with slow cooling. We follow the formation of gels in conditions similar to those used in manufacturing processes.

     

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.     

Anisotropic conduction of heat caused by molecular orientation in a flowing polymeric liquid

To demonstrate the influence of molecular orientation on the heat conduction in a flowing polymeric liquid, we consider a variant of the Graetz-Nusselt problem. A polymeric liquid is flowing between two flat, parallel plates with a sudden change in the wall temperature. The temperature distribution in the entrance region is calculated numerically taking viscous dissipation into account. It is assumed that the material properties are independent of the temperature. It is shown that the change in the temperature distribution in the fluid caused by molecular orientation is large enough to affect polymer processing significantly.