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     

Rheology and gelation kinetics of PVC plastisols

Oscillatory rheological experiments at different temperatures and over a wide range of frequencies have been used to investigate the gelation process and, more particularly, the sol–gel transition of various poly(vinyl chloride) (PVC) plastisols. The sol–gel transition process was found to be universal with respect to the temperature and solid volume fraction according to the similarity of the fractal structure in PVC plastisols. The variation of the gel time (t _gel) with temperature for any composition of PVC plastisols was predicted from the Dickinson’s model (E. Dickinson, J Chem Soc Faraday Trans, 93:111–114, 1997). Dynamic viscoelastic properties of PVC plastisols have also been studied as a function of temperature that allowed us to follow the gelation process of various plastisols. Thus, the influence of the type and concentration of PVC resins in gelation process was investigated. The variation of the complex shear modulus at a constant frequency was depicted by a master curve regarding the dependence of the moduli on PVC concentrations.     

Conditions near the electrode in a plasma with an alkali admixture

An analysis is made of the effects of certain processes in the interior of the gas and at the electrode surface on the potential drop near the electrode in a discharge in a dense, slightly ionized gas. Thermionic emission from the electrode, the Schottky effect, diffusion, and volume and surface ionization and recombination are taken into account. The analysis is carried out for a simple discharge-gap geometry: two infinite, plane-parallel electrodes. Relations are found for the potential drop near the electrode in a two-temperature plasma as a function of the discharge parameters and emission characteristics of the material. The calculated results are compared with experiment.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 3–12, July–August, 1971.The authors thank G. A. Lyubimov for interest in the study and for discussion of the results, and B. V. Parfenov for graciously furnishing the necessary experimental data from [13].     

Dynamic rheological analysis of the gelation behaviour of waxy crude oils

In this work we have characterised the viscoelastic behaviour of paraffin crystals in three different complex crude oils, close to the gelation threshold and after curing the gels under quiescent isothermal conditions, by means of oscillatory shear measurements. An increase in gelation temperature is observed with increasing oils molecular weight. The interactions between wax crystals and the formation of the space-filling network of interlocking wax crystals are thus facilitated by the presence of paraffins with higher molecular weight. The apparent gelation time, obtained from isothermal curing experiments, decreases as the curing temperature was decreased, and it is highly temperature-dependent.The presence and the importance of the ageing of the wax were established under isothermal conditions. It must result from a coarsening of the crystallites presents in the oil and it is, more important, close to the gel point where its full development is very slow taking several days to occur. After ageing the gels, the connective domains or junction zones linking the crystal arrays fail when relatively small strains are applied to the system and the mechanical spectra of the gels reveal an imperfect elastic network, typical rheological characteristics of a particle gel. Despite the compositional differences among the samples, the similarity of their mechanical behaviour is quite remarkable indicating that in all cases the gel-like organisation of the waxy material results from the formation of identical structures in the different oils, which is related not only to the wax content but also to the presence of other material that may reduce the crystallinity of the structure.The low fractal dimensionality obtained indicates elongated substructures. These results, together with the very high elastic modulus obtained at low volume fractions of crystallised material, are indicative of network structures with high degree of porosity: a lattice of wax crystals with large spaces among them filled by the oil and non-precipitated material.This paper was presented at the first Annual European Rheology Conference (AERC) held in Guimarães, Portugal, September 11-13, 2003.     

Heat of evaporation and critical parameters of the alkali metals

An expression containing one universal constant is proposed for the dependence of the heat of evaporation of the alkali metals on the specific volume of the liquid phase. The critical parameters of the alkali metals are are refined.     

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.     

New insight into the kinetic behavior of the structural formation process in agar gelation

Experimental investigations based on our custom-built torsion resonator were carried out on the kinetics and relaxation of the structural formation process in three agar–water solutions with agar concentrations of 0.75, 1.0, and 2.0 % w/w under natural cooling. An interesting temperature-dependent oscillatory decaying behavior of the structure development rate (SDR) in the agar gelation process is observed. This oscillatory SDR-decaying behavior is indicative of a sum of multiple SDR-determining relaxation processes and could be quantitatively described by a multiple-order Gaussian-like equation, i.e., $dG^{\prime }/dt\equiv \sum \nolimits _{n=0}^{m}{dG^{\prime }/dt}^{(n)}=\sum \nolimits _{n=0}^{m}K_{n}{\rm exp}[-2(T-T_{n})^{2}/W_{n}^{2}]$ . The ${\rm T}_{n}$ dependences of ${\rm W}_{n}$ in the gelation zone were also found to follow the Arrhenius law with activation energies of 39–74 kJ/mol for three investigated samples, indicating the important role of formation or fission of the hydrogen bonding interaction playing in the agar structural network formation. These findings provide insights into the mechanical properties and distinctive structure development rates of agar sols that dynamically and naturally evolve to form gels.     

Gelatinization and gelation of corn starch followed by dynamic mechanical spectroscopy analysis

The structural evolution of a maize flour was followed by means of oscillatory shear measurements during heating at a rate of 10 °C/min in presence of water. These measurements were performed in a special plate and plate vessel designed to prevent moisture loss. The phenomena of gelatinization and gelation were clearly identified and their connection with the moisture content also demonstrated. Moreover, the complex mechanisms involved in gelatinization and gelation in native starch were separated. Softening of the amylose zones, exchange of water and amylose within the starch granules followed by amylopectin melting leads to the gelation of starch.     

Field-induced gelation, yield stress, and fragility of an electro-rheological suspension

 Electro-rheological suspensions (ERS) are known to undergo liquid-to-solid transition under the application of an electric field. Long-range interaction between neighboring particles results in sample-spanning particulate structures which behave as soft solids. Here, we studied the rheological expression of this field-induced transition which has many similarities with chemical gelation. This similarity shows in mechanical spectroscopy on a suspension of monodisperse silica in PDMS as model ERS. Upon application of the electric field, dynamic moduli G′, G′′ grow by orders of magnitude and evolve in a pattern which is otherwise typical for gelation of network polymers (random chemical or physical gelation). At the gel point, the slow dynamics is governed by power-law relaxation behavior (frequency-independent tan δ). A low field strength is sufficient to reach the gel point and, correspondingly, the percolating particle structure at the gel point is still very fragile. It can be broken by the imposition of low stress. For inducing a finite yield stress, the field strength needs to be increased further until the long-range electrostatic interaction generates string-like particle alignments which become clearly visible under the optical microscope. The onset of fragile connectivity was defined experimentally by the tan δ method. The ERS was probed dynamically at low frequencies where the transition is most pronounced, and also in steady shear where the rate of structure formation equals the rate of internal breaking. Received: 1 May 2001 Accepted: 11 August 2001     

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     

Rheology of crosslinking poly vinyl alcohol systems during film formation and gelation

Gelation of crosslinking polymers, with ionic groups, is of interest in membrane processing of these materials. The gelation of polyvinyl alcohol in the presence of an ionic crosslinker, sulfosuccinic acid, was monitored through rheological measurements. The evolution of rheological material functions during film formation, which involves solvent evaporation and crosslinking, was observed at different polymer and crosslinker concentrations. Relative effect of water evaporation leading to physical gelation and the chemical crosslinking was examined. To understand the effect of crosslinker type, the rheology of nonionic crosslinker, glutaraldehyde was also examined. The gel points as well as network parameters for these covalent networking systems were different and depended on crosslinker type and polymer/crosslinker concentrations. However, qualitative evolution of rheological behavior during film formation was largely similar, demonstrating the dominating effect of solvent evaporation. Crosslinking in the absence of solvent evaporation was examined at different temperatures. It can be concluded that similar mechanism was involved, independent of temperature, in the temperature range of interest. The effect of crosslinker concentration on evolution of rheological properties near gelation was insignificant for ionic crosslinker though marginally significant for nonionic crosslinker.     

Rheology of carbon black suspensions. V. Heat-induced gelation and its reversibility

Linear viscoelastic properties of carbon black (CB) suspensions in a mixture of a rosin-modified phenol resin-type varnish (Varnish-1)/an alkyd resin-type varnish (Varnish-2), which exhibited a sol?Cgel transition on an increase in CB concentration, were investigated from 30°C to 80°C. The viscoelastic properties were reversible from 30°C to 60°C. In contrast, at temperatures above 60°C, the storage (G??) and loss (G??) moduli were irreversible and increased significantly with increasing temperature. This increase in the moduli is due to a change of the dispersion state to agglomerated state by heating. The agglomerated state was held, when the suspensions were lowered at 30°C. However, the G?? and G?? recovered to the original values upon shearing. This heat-induced gelation should be a universal feature for suspensions of weakly attractive particles. The temperature and shearing histories of the suspensions were discussed in relation to adsorption of polymeric component in the varnish on the CB particles.     

Pattern discrimination and firing behavior of cold receptor model aided with noise

A method for characterizing and identifying firing patterns of neural spike trains is presented. Three characteristic variables defined at sequential moments, including two formal derivatives and the integration of the counting process, are introduced to reflect the temporal patterns of a spike train. This paper also examines how noise interacts with encoding mechanisms of neuronal stimulus in a cold receptor. From ISI series and bifurcation diagrams it is shown that there are considerable differences in interval distributions and impulse patterns caused by purely deterministic simulations and noisy simulations. The ISI-distance can be used as an effective and powerful way to measure the noise effects on spike trains quantitatively. It is found that spike trains observed in cold receptors can be more strongly affected by noise for low temperatures than for high temperatures in some aspects; meanwhile, spike train has greater variability with the noise intensity increasing.     

Heat transfer in nucleate pool boiling of aqueous SDS and triton X-100 solutions

Variation in degree of surface wettability is presented through the application of Cooper’s correlative approach (h ∝ M ^−0.5 q _w ^″0.67) for computing enhancement (ϕ) in nucleate pool boiling of aqueous solutions of SDS and Triton X-100 and its presentation with Marangoni parameter (χ) that represents the dynamic convection effects due to surface tension gradients. Dynamic spreading coefficient defined as σ _dyn N _a , which relates spreading and wetting characteristics with the active nucleation site density on the heated surface and bubble evolution process, represents cavity filling and activation process and eliminates the concentration dependence of nucleate pool boiling heat transfer in boiling of aqueous surfactant solutions. Using the dynamic spreading coefficient (σ _dyn N _a  = 0.09q _w ^″0.71), correlation predictions within ±15% for both SDS and Triton X-100 solutions for low heat flux boiling condition (q _w^″ ≤ 100 kW/m²) characterised primarily by isolated bubble regime are presented.     

Rheological studies of the gelation of aqueous solutions of acrylamide-acrylic acid copolymers in the presence of chromium chloride

The gelation kinetics of aqueous solutions of acrylamideacrylic acid copolymers in the presence of chromium ions was studied with different rheometers. The gel time is found to vary with the principle of the apparatus because of a low shear dependence of the elongation of the macromolecules. The variations of the gel time with the experimental conditions of the gel preparation were investigated and we conclude that the gelation is governed by the oligornerization kinetics of the chromium ions which are instantaneously, complexated by the carboxylate groups of the polymer. The variation laws of the gel time and of the elastic modulus with chromium and polymer concentrations, temperature and ionic strength are in qualitative agreement with the structure of the temporary network of the semi-dilute solutions of these copolymers.     

Rheological aspects of the hardening of water-borne alkali silicate zinc-rich paints

Summary The kinetics of the reaction between zinc dust and alkali silicate in water-borne silicate zinc-rich paints was investigated on the basis of rheological measurements. The paints studied were formulated with the same zinc dust/silicate vehicle ratio. Different zinc dusts were employed. The vehicle was a litiumsodium silicate solution. Formulation included a rheological agent to prevent rapid settling of suspended zinc dust.Rheological tests were carried out at various time intervals after paint mixing. Each sample was subjected, stepwise, to increasing and decreasing shear rate sequences, each shear rate being applied until stress steady values were attained. Shear rates were within the range 2.35 to 1700 s^–1; subsequently, hysteresis cycles were traced. Equilibrium data were fitted with the Bingham equation.Yield values and ultimate viscosities obtained at the various test time intervals were compared. Both parameters were found to increase with increasing time after mixing. Their increase in time brings out the fact that two successive processes take place; accordingly, structural hypotheses were suggested taking into account the modification set up in the system by the zincsilicate reaction.

---

Zusammenfassung Die Kinetik der Reaktion zwischen Zinkstaub und Alkalisilikat in wäßrigen Silikat-Zink-Farben wurde mit Hilfe rheologischer Messungen erforscht. Die untersuchten Farben wurden stets mit dem gleichen Verhältnis von Zinkstaub zu Silikat-Träger formuliert. Dabei wurden verschiedene Zinkstäube eingesetzt. Der Träger bestand aus einer Lithium-Natrium-Silikat-Lösung. In der Formulierung war außerdem ein rheologischer Wirkstoff, der das schnelle Absetzen des suspendierten Zinkstaubes verhindern sollte, enthalten.Die rheologischen Messungen wurden zu verschiedenen Zeiten nach dem Farbmischen durchgeführt. Jede Probe wurde einer auf- und absteigenden Stufenfolge von Schergeschwindigkeiten unterworfen, wobei die Scherung solange konstant gehalten wurde, bis sich ein stationärer Wert eingestellt hatte. Die Schergeschwindigkeiten lagen dabei in einem Bereich zwischen 2,35 und 1700 s^–1. Anschließend wurden Hysteresisschleifen aufgenommen.Die Gleichgewichtswerte ließen sich mit der Bingham-Gleichung beschreiben. Fließgrenzen und Endviskositäten, die nach verschiedenen Zeitdauern gemessen worden waren, wurden miteinander verglichen. Beide Parameter nahmen mit der Zeit zu. Daraus ist erkennbar, daß zwei aufeinanderfolgende Prozesse stattfinden. Dementsprechend werden Strukturmodelle vorgeschlagen, welche die Veränderungen in Rechnung stellen, die als Folge der Zink-Silikat-Reaktionen in dem System stattfinden.

---

List of symbols shear rate - ÿ shear acceleration - _r relative viscosity - _R reduced viscosity - ₀ continuous phase viscosity - , _,0, _,t ultimate shear rate, at the beginning of the reaction, at timet - shear stress - _R reduced shear stress - ₀, _0,0, _0,t yield stress, at the beginning of the reaction, at timet - , _max disperse phase volume fraction, maximum volume fraction - a, a , a shift factor, viscosity shift factor, shear stress shift factor - a _1,, a_2, see eq. [4] - k ₁,k₂ reaction rate constants - K _E see eq. [5] - t time - t _C characteristic time Abbreviations MSD mean square deviation (=( _exp — _calc)²/(n — K);n = number of experimental points,K = number of parameters) Paper presented at the Joint Conference of the British, Italian and Netherlands Societies of Rheology, Amsterdam, April 18–20, 1979.With 6 figures and 3 tables