Frequency dependence of viscoelastic properties of some physical gels near the gel point

The sol-gel and gel-sol transitions of three biopolymer gelling systems (gelatin, iota-carrageenan and xanthan-carob) have been studied by dynamic measurements. At the gel point a power law dependence of the storage (G') and loss (G”) moduli on frequency is observed, with an exponent varying from 0.5 to 0.65. The variation of log(tg^δ = G”/G') versus the gelation (or melting) parameter (time or temperature) at different frequencies leads to a precise determination of the gel point.     

流变学法研究部分水解聚丙烯酰胺/Cr(III)交联反应I.浓度的影响

采用流变学法系统地考察了部分水解聚丙烯酰胺（HPAM）/Cr(III)交联体系的 反应动力学。HPAM溶液的粘性模量G”大于弹性模量G’,且其数值随时间不发生变 化,体系为粘性溶液。而HPAM/Cr(III)体系的G’和G”的数值都随时间变化,G” 在反应开始阶段大于G’,当反应进行一段时间后,G’超过G”占据主要地位,体 系成为弹性体系。交联过程可分为三个阶段：第一上升阶段,平缓上升阶段和第二 上升阶段。利用G’～ t曲线可以推测反应机理。实验发现成胶速率随反应物HPAM 和Cr(III)的浓度的增加而增加,而成胶时间缩短。在羧基浓度过量的情况下,交 联反应对Cr(III)浓度的反应级数是1。凝胶的有效弹性交联密度随聚合物浓度的增 加而增,且随凝胶反应的进行而增加。凝胶的交联点间的平均分子量随Cr(III)浓 度的增加和交联反应的进行而下降。     

Comparison in fractal dimension between those obtained from structure factor and viscoelasticity of gel networks of 1,3:2,4-bis-O-(p-methylbenzylidene)-D-sorbitol in polystyrene melt at gel point

We investigated time evolution of shear moduli in the physical gelation process of 1,3:2,4-bis-O-(p-methylbenzylidene)-D-sorbitol in polystyrene melt. At the gel point, storage and loss shear moduli, G' and G", were described by the power law of frequency omega, G' approximately G" approximately omegan, with the critical exponent n being nearly equal to 2/3, in agreement with the value predicted by the percolation theory. We also investigated the structure factor over two decades in length scale at gel point by using ultra-small-angle X-ray scattering, and small-angle X-ray scattering. We found the power-law behavior in low-q region, indicating that the gel network forms the self-similar structure with mass-fractal dimension. Comparison between the exponent of mass-fractal dimension from structure factor and that from viscoelasticity indicates that hydrodynamic interactions are completely screened out and the excluded volume effects are dominant in the gel. The gel strength was found to increase with the decrease in the lower limit length scale of fractality.     

Effect of deacetylation rate on gelation kinetics of konjac glucomannan

Effect of deacetylation rate on the gelation behaviors on addition of sodium carbonate for native and acetylated konjac glucomannan (KGM) samples with a degree of acetylation (DA) range of 1.38-10.1 wt.% synthesized using acetic anhydride in the presence of pyridine as catalyst was studied by dynamic viscoelastic measurements. At a fixed alkaline concentration (C(Na)), both the critical gelation times (t(cr)) and the plateau values of storage moduli (G'(sat)) of the KGM gels increased with increasing DA. While at a fixed ratio of alkaline concentrations to values of DA (C(Na)/DA), the similar t(cr) and (G'(sat)) values independent of DA were observed. On the whole, increasing KGM concentration or temperature shortened the gelation time and enhanced the elastic modulus for KGM gel. The effect of deacetylation rate related to the C(Na)/DA on the gelation kinetics of the KGM samples were discussed.     

Frequency dependence of the shear moduli of spectrin studied using a multiple lumped resonator viscoelastometer

The frequency dependence (119-7860 Hz) of the storage and loss shear moduli, G' and G', of human erythrocyte spectrin dimer crude solutions at 22.5 degrees C has been measured using a Birnboim-Schrag multiple lumped resonator viscoelastometer. The measurements were carried out on solutions of ionic strength 1 mM containing 1.1-3.7 mg ml-1 spectrin. This corresponds to the terminal zone for G' and G'. Analysis of the data using the standard theory of hybrid relaxation spectra yields a relaxation time of 22.5 +/- 1 microseconds. The pure spectrin dimer relaxation time is estimated to be 16 +/- 3 microseconds. This result suggests that at an ionic strength of 1 mM, the spectrin dimers are extended and that the main relaxation process is simple end-over-end rotation.     

Interfacial rheology of an ultrathin nanocrystalline film formed at the liquid/liquid interface

We report the interfacial properties of monolayers of Ag nanoparticles 10-50 nm in diameter formed at the toluene-water interface under steady as well as oscillatory shear. Strain amplitude sweep measurements carried out on the film reveal a shear thickening peak in the loss moduli (G") at large amplitudes followed by a power law decay of the storage (G') and loss moduli with exponents in the ratio 2:1. In the frequency sweep measurements at low frequencies, the storage modulus remains nearly independent of the angular frequency, whereas G" reveals a power law dependence with a negative slope, a behavior reminiscent of soft glassy systems. Under steady shear, a finite yield stress is observed in the limit of shear rate .gamma going to zero. However, for .gamma > 1 s-1, the shear stress increases gradually. In addition, a significant deviation from the Cox-Merz rule confirms that the monolayer of Ag nanoparticles at the toluene-water interface forms a soft two-dimensional colloidal glass.     

Using in situ rheology to characterize the microstructure in photopolymerized polyacrylamide gels for DNA electrophoresis

Photopolymerized cross-linked polyacrylamide hydrogels are attractive sieving matrix formulations for DNA electrophoresis owing to their rapid polymerization times and the potential to locally tailor the gel pore structure through spatial variation of illumination intensity. This capability is especially important in microfluidic systems, where photopolymerization allows gel matrices to be precisely positioned within complex microchannel networks. Separation performance is also directly related to the nanoscale gel pore structure, which is in turn strongly influenced by polymerization kinetics. Unfortunately, detailed studies of the interplay among polymerization kinetics, mechanical properties, and structural morphology are lacking in photopolymerized hydrogel systems. In this paper, we address this issue by performing a series of in situ dynamic small-amplitude oscillatory shear measurements during photopolymerization of cross-linked polyacrylamide electrophoresis gels to investigate the relationship between rheology and parameters associated with the gelation environment including UV intensity, monomer and cross-linker composition, and reaction temperature. In general, we find that the storage modulus G' increases with increasing initial monomer concentration, cross-linker concentration, and polymerization temperature. The steady-state value of G', however, exhibits a more complex dependence on UV intensity that varies with gel concentration. A simple model based on rubber elasticity theory is used to obtain estimates of the average gel pore size that are in surprisingly good agreement with corresponding data obtained from analysis of DNA electrophoretic mobility in gels cast under identical polymerization conditions.     

Nonlinear viscoelasticity of sorbitan tristearate monolayers at liquid/gas interface

The interfacial rheology of sorbitan tristearate monolayers formed at the liquid/air interface reveal a distinct nonlinear viscoelastic behavior under oscillatory shear usually observed in many 3D metastable complex fluids with large structural relaxation times. At large strain amplitudes (gamma), the storage modulus (G') decreases monotonically whereas the loss modulus (G') exhibits a peak above a critical strain amplitude before it decreases at higher strain amplitudes. The power law decay exponents of G' and G' are in the ratio 2:1. The peak in G' is absent at high temperatures and low concentration of sorbitan tristearate. Strain-rate frequency sweep measurements on the monolayers do indicate a strain-rate dependence on the structural relaxation time. The present study on sorbitan tristearate monolayers clearly indicates that the nonlinear viscoelastic behavior in 2D Langmuir monolayers is more general and exhibits many of the features observed in 3D complex fluids.     

Gelation of PEO-PLGA-PEO triblock copolymers induced by macroscopic phase separation

The gelation behavior of aqueous solutions of poly(ethylene oxide-b-(DL-lactic acid-co-glycolic acid)-b-ethylene oxide) (PEO-PLGA-PEO) triblock copolymer containing short hydrophilic PEO end blocks is investigated using dynamic light scattering, rheology, small-angle neutron scattering (SANS), and differential scanning calorimetry (DSC). For polymer concentrations between 5 and 35 wt %, four distinct regions of the turbidity change depending on temperature were observed. Interestingly, in the turbid solution region, gel phase is formed for polymer concentrations above 14 wt % and an extremely slow relaxation was detected. In fact, a power law, which takes into account the dynamics of percolation clusters, dominates the correlation function. In rheological measurements, the local maximum in G' is observed at around the temperature of maximum turbidity. We further found that G" > G' and G' is highly dependent on frequency at the gel state implying viscoelastic characteristics, which is quite different from general concepts of gels, typically formed by the micellar packing. SANS profiles showing multiple peaks in the sol state rather than in the gel state as well as a DSC exotherm at the temperature of gels can also serve as the evidence of different gel states. Based upon the experimental data obtained in the present study, a new gelation mechanism induced by the macroscopic phase separation of triblock copolymers containing short hydrophilic PEO end blocks such as PEO-PLGA-PEO is proposed. The effect of the type ofhydrophobic middle blocks on the gelation is also discussed.     

Studies on mechanical and swelling behavior of polymer networks on the basis of the scaling concept. 3. The osmotic compressibility of gels

The osmotic compressibility of chemically crosslinked poly(vinyl acetate) (PVAc) gels in equilibrium with pure diluent has been determined by the method of decreasing equilibrium swelling in different swelling agents. The concentration dependence of the osmotic compressibility has been found to follow a scaling law with an exponent which was greater than that predicted by the mean-field theory. A comparison has been made between the elastic moduli determined by unidirectional deformation measurements and the compressional moduli obtained from the osmotic compressibility data.     

Contribution to the Determination of Kinetic Parameters of the Sol-Gel Transformation by Rheological Measurements

The system tetraethoxysilane(TEOS)–water–ethanol has been studied by rheological measurements. Different molar ratios of TEOS : water (1 : 4, 1 : 10, and 1 : 20) are studied at different temperatures (30, 40, and 50°C). The dynamic viscosity (rotating mode) at a constant shear rate (100 s⁻¹) and the elastic and viscous moduli (oscillating mode) at a constant frequency (1 Hz) are determined. The viscosity–time curves are evaluated by application of a nucleation and particle growth model. Good agreement between experiments and theory is observed. The model allows the determination of the complex rate constant of silica precipitation. The temperature-dependent measurements gave the possibility to determine the apparent energy of activation by common methods. The results are in agreement with data from the literature. The gel time defined as intersection point of elastic and plastic moduli and its dependence on temperature are evaluated by the Smoluchowski model. The energy of activation for the coagulation was determined and found to be in the correct order of magnitude.     

Evolution of rheological properties and local structure during gelation of siloxane-polymethylmethacrylate hybrid materials

Hybrid siloxane-polymethylmethacrylate (PMMA) nanocomposites with covalent bonds between the inorganic (siloxane) and organic (polymer) phases were prepared by the sol gel process through hydrolysis and polycondensation of 3-(trimethoxysilyl)propylmethacrylate (TMSM) and polymerization of methylmethacrylate (MMA) using benzoyl peroxide (BPO) as initiator. The effect of MMA, BPO and water contents on the viscoelastic behaviour of these materials was analysed during gelation by dynamic rheological measurements. The changes in storage (G′) and loss moduli (G′′), complex viscosity (η^*) and phase angle (δ) were measured as a function of the reaction time showing the viscous character of the sol in the initial step of gelation and its progressive transformation to an elastic gel. This study was complemented by ²⁹Si and ¹³C solid-state nuclear magnetic resonance (NMR/MAS) measurements of dried gel. The analysis of the experimental results shows that linear chains are formed in the initial step of the gelation followed by a growth of branched structures and formation of a three-dimensional network. Near the gel point this hybrid material demonstrates the typical scaling behaviour expected from percolation theory.     

Thermal gelation of cellulose in a NaOH/thiourea aqueous solution

Utilizing a novel solvent of cellulose, 6 wt % NaOH/5 wt % thiourea aqueous solution, for the first time, we prepared the thermally induced cellulose gel. We investigated the thermal gelation of cellulose solutions with rheometry and the structure of the gel with 13C NMR, wide-angle X-ray diffraction, environmental scanning electron microscopy, and atomic force microscopy. The cellulose solutions revealed an increase in both the storage modulus (G') and the loss modulus (G") with an increase in the temperature during gelation. The temperature at the turning point, where G' overrides G" because of the onset of gelation, decreased from 38.6 to 20.1 degrees C with an increase of cellulose concentration from 4 to 6 wt %. Given enough time, G' of all solutions can exceed G" at a certain temperature slightly lower than the gelation temperature, indicating that the occurrence of the gelation is also a function of time. Each of the assigned peaks of NMR of the cellulose gel is similar to that of the cellulose solution, suggesting that the gelation resulted from a physical cross-linking. The gels were composed of relatively stable network units with an average diameter of about 47 nm. At either a higher temperature (at 60 degrees C for 30 s) or a longer gelation time (at 30 degrees C for 157 s), the gel in the 5 wt % cellulose solution could form. A schematic gelation process was proposed to illustrate the sol-gel transition: the random self-association of the cellulose chains having the exposed hydroxyl in the aqueous solution promotes the physical cross-linking networks.     

Characterization of the Sol-Gel Process Using Raman Spectroscopy Organically Modified Silica Gels Prepared Via the Formic Acid-Alkoxide Route

For precursor mixtures containing tetraethoxysilane (TEOS) and phenyltriethoxysilane (PhTREOS), time of gelation can be reduced by up to two orders of magnitude depending on reaction conditions employed when reacting the silicon alkoxide mixture with formic acid instead of water. Results indicate that time of gelation depends on the amount of PhTREOS in the precursor mixture. Within the range of concentrations investigated, an exponential law describes best the dependence of reduced time of gelation on the molar fraction of PhTREOS. Therefore, we conclude that the phenyl ring acts as a steric hindrance to network formation. Raman spectroscopy is used to characterize the reaction between the alkoxide mixture and formic acid. During the acidolysis reaction, ethanol is formed as an intermediate. A preliminary reaction scheme is proposed to account for the time dependence of species involved. Furthermore, Raman spectroscopy is successfully employed to monitor the effects of post-gelation thermal treatment of the gel samples. The effects observed are interpreted with a model of a phenyl ring trapped in a siloxane cage.     

Effects of the Water Quantity on the Solventless TEOS Hydrolysis Under Ultrasound Stimulation

The acid hydrolysis under ultrasound stimulation of solventless tetraethoxysilane(TEOS)-water mixtures was studied at 40°C, by means of a heat flux calorimetric method, as a function of the initial water/TEOS molar ratio (r) ranging from 2 to 10. The method is based on the time record of the exothermic heat peak of hydrolysis, arising after an induction time under ultrasound stimulation, which is a measure of the reaction rate. The hydrolysed quantity was found to be approximately independent of the water/TEOS molar ratio, even for r < 4. Polycondensation reaction takes place mainly for low water/TEOS molar ratio in order to supply water to allow almost complete hydrolysis. The overall process of dissolution and hydrolysis has reasonably been described by a previous modelling. The dissolution process of water in TEOS, under ultrasound stimulation and acid conditions, was found to be rather dependent of the alcohol produced in the hydrolysis reaction instead of the initial water quantity present in the mixture.     

Surface reactivity of pulsed-plasma polymerized pentafluorophenyl methacrylate (PFM) toward amines and proteins in solution

Pulsed-plasma polymerization has been used to deposit ultrathin layers of pentafluorophenyl methacrylate by using low duty cycles and low power input. The monomer structure can be retained such that the chemical reactivity of the active ester group could be studied using the reaction with a simple amine. The film properties in aqueous phosphate buffer have been investigated using Fourier transform infrared spectroscopy, X-ray photoelectron spectroscopy, and real time surface plasmon resonance spectroscopy. The films react readily with diaminohexane and immunoglobulin (IgG), yet the reactivity shows a dependence on the extent of hydrolysis of the ester group.     

Gelatin hydrogels cross-linked with bis(vinylsulfonyl)methane (BVSM): 1. The chemical networks

This paper deals with chemical gelation of gelatin in the presence of a cross-linker, bis(vinylsulfonyl)methane (BVSM), which is able to create covalent C-N bonds with amine groups. The investigation is performed at 40 degrees C, where no triple helices are present. Gelatin is in random coil conformation. The influence of various parameters (gelatin concentration, cross-linker concentration, and pH (number of reacting sites along the gelatin chain)) was examined. Gel formation was followed by rheological and thermodynamic measurements (microcalorimetry) versus time (kinetic measurements). Furthermore, the storage moduli were compared to the number of links formed in the course of gelation. The experiments show that, within the experimental range investigated, a fully homogeneous network is not reached; the chemical gels, even upon completion of the reactions, are still in the critical domain, near the threshold. A power law behavior was put in evidence for the shear modulus versus the distance to the gel point, expressed as the concentration of links per gelatin chain. The exponent (f = 3.4 +/- 0.3) is close to that expected for the vulcanization of long chains. The storage moduli can be superposed on a single curve where the abscissa is the product of the number of C-N links per unit volume and the gelatin concentration at an exponent equal to -0.76 +/- 0.03. This exponent suggests the role of entanglements for interchain cross-linking.     

Solvent-induced lysozyme gels: rheology, fractal analysis, and sol-gel kinetics

In this work, the gelation kinetics and fractal character of lysozyme gel matrices developed in tetramethylurea (TMU)-water media were investigated. Gelation times were determined from the temporal crossover point between the storage, G', and loss, G', moduli, as a function of the binary solvent composition and of protein concentration. The inverse dependence of the upper limit of the linear viscoelastic region (gamma0) on protein concentration indicate that the lysozyme gels belong to the "strong link" kind, a gel category where interparticle links are stronger than intraparticle ones. Lysozyme gel fractal dimensions (Df) were determined from the analysis of rheological data according to a scaling theory by Shih et al. [Phys. Rev. A 42 (1990) 4772-4779] and were found to be compatible with a diffusion-limited cluster-aggregation kinetics (DLCA) for lysozyme gels formed at the TMU mass fraction in the binary organic-aqueous solvent, wTMU=0.9, and with a reaction-limited cluster aggregation kinetics (RLCA) for wTMU in the 0.6< or =wTMU< or =0.8 range.     

Viscoelastic behaviour during gelation of various molar-mass polyvinylchloride solutions and polymerization temperatures

The gel formation of various 10% molar-mass polyvinyl-chloride (PVC) sample solutions and polymerization temperatures in di-(2-ethylhexyl)phthalate (DOP) was studied by measuring dynamic moduli as functions of gelation (or ageing) time and frequency. The propensity to form gels increases with increasing molar mass and decreasing polymerization temperature. Extraction of a commercial PVC with acetone separates it into a relatively highly crystalline and a nearly non-crystalline polyvinyl chloride.