Mechanical measurements in the reaction bath during the polycondensation reaction, near the gelation threshold

Microrheological characterisation of Cyanoflan in human blood plasma

Naturally occurring polysaccharidic biopolymers released by marine cyanobacteria are of great interest for numerous biomedical applications, such as wound healing and drug delivery. Such polymers generally exhibit high molecular weight and an entangled structure that impact the rheology of biological fluids. However, biocompatibility tests focus not so much on rheological properties as on immune response. In the present study, the rheological behaviour of native blood plasma as a function of the concentration of a cyanobacterium biopolymer is investigated via multiple particle tracking microrheology, which measures the Brownian motion of probes embedded in a sample, and cryogenic scanning electron microscope microstructural characterisation. We use Cyanoflan as the biopolymer of choice, and profit from our knowledge of its chemical structure and its exciting potential for biotechnological applications. A sol-gel transition is identified using time-concentration superposition and the power-law behaviour of the incipient network's viscoelastic response is observed in a variety of microrheological data. Our results point to rheology-based principles for blood compatibility tests by facilitating the assignment of quantitative values to specific properties, as opposed to more heuristic approaches.

Water-alcohol-TiO2 dispersions as sustainable ink

Nanocrystalline titanium dioxide (TiO₂) is a widespread multifunctional and environmentally friendly material that has numerous applications requiring micro-/nanofabrication or thin film deposition. In most cases, the fabrication of titania films can be achieved using cost-efficient solution chemistry combined with various coating or printing techniques. The practical implementation of these methods requires the preparation of a suitable ink with properly adjusted rheological properties. Conventionally, such adjustments are achieved based on TiO₂ hydrosols containing various organic surfactants and stabilizing agents. However, the use of such additives may affect the properties of the deposited functional layer, which can be crucial for electronic and optical applications. In this work, we address a comprehensive study of simple surfactant-free TiO₂ dispersion systems based on various water-alcohol solvents and demonstrate the possibility of controlling the rheological properties of the titania ink in a wide range that is suitable for several printing applications. As a particular example, we demonstrate the application of a water-i-propanol-TiO₂ dispersion as a functional ink for the offset printing of interference images.

Experimental Observation of Two Features Unexpected from the Classical Theories of Rubber Elasticity

Although the elastic modulus of a Gaussian chain network is thought to be successfully described by classical theories of rubber elasticity, such as the affine and phantom models, verification experiments are largely lacking owing to difficulties in precisely controlling of the network structure. We prepared well-defined model polymer networks experimentally, and measured the elastic modulus G for a broad range of polymer concentrations and connectivity probabilities, p. In our experiment, we observed two features that were distinct from those predicted by classical theories. First, we observed the critical behavior G∼|p-p_{c}|^{1.95} near the sol-gel transition. This scaling law is different from the prediction of classical theories, but can be explained by analogy between the electric conductivity of resistor networks and the elasticity of polymer networks. Here, p_{c} is the sol-gel transition point. Furthermore, we found that the experimental G-p relations in the region above C^{*} did not follow the affine or phantom theories. Instead, all the G/G_{0}-p curves fell onto a single master curve when G was normalized by the elastic modulus at p=1, G_{0}. We show that the effective medium approximation for Gaussian chain networks explains this master curve.

Effect of solvent hydrophobicity on gelation kinetics and phase diagram of gelatin ionogels

We present a systematic investigation of the effect of solvent hydrophobicity (alkyl chain length) on the gelation kinetics and the phase states of the polypeptide gelatin in imidazolium based ionic liquid (IL) solutions. We have observed that IL concentration and hydrophobicity had dramatic influences on the thermal and viscoelastic properties of gelatin ionogels. Gelation concentration cg was observed to increase from 1.75 to 2.75% (w/v) while the gelation temperature Tg was found to decrease from 32 to 26 °C with increase in 1-octyl-3-methyl imidazolium chloride [C8mim][Cl] (most hydrophobic) concentration as compared to the case of the least hydrophobic IL 1-ethyl-3-methyl imidazolium chloride [C2mim][Cl], where the corresponding changes were marginal. Gradual softening of the gel with increase in hydrophobicity and concentration of IL was clearly noticed. The viscosity of the gelling sol diverged as ηr ∼ ε(1)(-k) and storage modulus of gel grew as G0 ∼ ε(1)(t) where ε1 = |1 - c/cg| with the exponents having values k = 1.2-1.8 ± 0.08 and t = 1.2-1.6 ± 0.08, close to but not exactly the same as predicted by the percolation model: k = 0.7-1.3 and t = 1.9. Thus, the gelation kinetics involved in the growth of interconnected networks could be conceived to follow an anomalous percolation model. The temporal growth of self-assembled structures followed a power law dependence given by: ηr ∼ ε(2)(-α) and Rh ∼ ε(2)(-β) where ε(2) = t > tg (α = 1-2.9 ± 0.08 and β = 1-2.7 ± 0.08). The low frequency storage modulus G0, gelation temperature Tg, gelation concentration cg and gelation time tg adequately defined the sol-gel phase diagram. Results clearly revealed that by adjusting the hydrophobic chain length and concentration of IL it was possible to customize both thermal and mechanical properties of these ionogels to match specific application requirements.

Hydration of gelatin molecules in glycerol-water solvent and phase diagram of gelatin organogels

We present a systematic investigation of hydration and gelation of the polypeptide gelatin in water-glycerol mixed solvent (glycerol solutions). Raman spectroscopy results indicated enhancement in water structure in glycerol solutions and the depletion of glycerol density close to hydration sheath of the protein molecule. Gelation concentration (c(g)) was observed to decrease from 1.92 to 1.15% (w/v) while the gelation temperature (T(g)) was observed to increase from 31.4 to 40.7 °C with increase in glycerol concentration. Data on hand established the formation of organogels having interconnected networks, and the universal gelation mechanism could be described through an anomalous percolation model. The viscosity of sol diverged as η ∼ (1 - c(g)/c)(-k) as c(g) was approached from below (c < c(g)), while the elastic storage modulus grew as G' ∼ (c/c(g) - 1)(t) (for c > c(g)). It is important to note that values determined for critical exponents k and t were universal; that is, they did not depend on the microscopic details. The measured values were k = 0.38 ± 0.10 and t = 0.92 ± 0.17 whereas the percolation model predicts k = 0.7-1.3 and t = 1.9. Isothermal frequency sweep studies showed power-law dependence of gel storage modulus (G') and loss modulus (G'') on oscillation frequency ω given as G'(ω) ∼ ω(n') and G''(ω) ∼ ω(n''), and consistent with percolation model prediction it was found that n' ≈ n'' ≈ δ ≈ 0.73 close to gelation concentration. We propose a unique 3D phase diagram for the gelatin organogels. Circular dichroism data revealed that the gelatin molecules retained their biological activity in these solvents. Thus, it is shown that the thermomechanical properties of these organogels could be systematically tuned and customized as per application requirement.

Universal sol state behavior and gelation kinetics in mixed clay dispersions

Sol and gel state behavior, in aqueous salt free dispersions, of clays Laponite (L) and Na montmorillonite (MMT) was studied at various mixing ratios (L:MMT = r = 1:0.5, 1:1, and 1:2). In the sol state, the zeta potential and gelation concentration of L-MMT obeyed the universal relation, X(L-MMT) = (rX(L) + X(MMT))/(1 + r), where X is zeta potential or gelation concentration (c(g)), implying that these properties are linear combinations of the same of their individual components. The low frequency storage modulus (G(0)'), relative viscosity (η(r)), and apparent cluster size (R) could be universally described by the power-law, G(0)' ∼ ((c/c(g)) - 1)(t) (c > c(g)), and η(r), R ∼ (1 - (c/c(g)))(-k,ν) (c < c(g)), with t = 1.5, k = 1.1, and υ = 0.8 close to the gelation concentration, for r = 1:1 cogel, consistent with the percolation model description of gelation. Interestingly, the hyperscaling relation δ = t/(k + t) yielded δ = 0.56 not too different from the predicted value ∼0.7, while the experimental value of δ obtained from G''(ω) ∼ ω(δ) close to c ≈ c(g) yielded δ = 1.5, which was at variance with the hyperscaling result. The experimental data, on hand, mostly supported percolation type gelation mechanism. As the cogels were slowly heated, at a characteristic temperature, T(g), a sharp increase in G' value was noticed, implying a transition to gel hardening (a new phase state). The temperature-dependent behavior followed the power-law description, G' ∼ (T(g) - T)(-γ) (T < T(g)), with γ = 0.40 ± 0.05 invariant of composition of the cogel, whereas for MMT and Laponite, γ = 0.25 and 0.55, respectively. It has been shown that the cogel has significantly enhanced mechanical (G(0) increased by 10 times for r = 1:1 cogel) and thermal properties (T(g) increased by 13 °C for 1:1 cogel) that can be exploited to design customized soft materials.

Mechanical Properties of Aerogels : Brittle or Plastic Solids?

Different sets of silica aerogels (classical aerogels, partially dense aerogels, composite aerogels) have been studied in the objective to understand the mechanical behaviour of these extremely porous solids. The mechanical behaviour of xerogels and aerogels is generally described in terms of brittle and elastic materials, like glasses or ceramics. The main difference compared to silica glass is the order of magnitude of the elastic and rupture modulus which are 104 times lower. However, if this analogy is pertinent when gels are under a tension stress (bending test) they exhibit a more complicated response when the structure is submitted to a compressive stress. The network is linearly elastic under small strains, then exhibits yield followed by densification and plastic hardening. As a consequence of the plastic shrinkage it is possible to compact and stiffen the gel at room temperature. These opposite behaviours (brittle and plastic) are surprisingly related to the same kinds of gel features: pore volume silanol content and the pore size. Both elastic modulus and plastic shrinkage depend strongly on the volume fraction of pores and on the condensation reaction between silanols. On the mechanical point of view (rupture modulus and toughness), it is shown that pores size plays likely an important role. Pores can be considered as flaws in the terms of fracture mechanics and the flaw size, calculated from rupture strength and toughness is related to the pore size distribution.

Critical exponents and self-similarity for sol-gel transition in aqueous alginate systems induced by in situ release of calcium cations

The sol-gel transition in aqueous alginate systems induced by in situ released calcium cations was monitored with rheology methods. Four alginate samples with different molecular weights and M/G ratios were used over the concentration C(Alg) of 2 approximately 6 wt % with different mole ratios f of Ca2+ to the alginate repeat unit. The scaling for the zero shear viscosity eta(0) before the gel point and the equilibrium modulus Ge after the gel point was described as eta(0) approximately epsilon(-k) and Ge approximately epsilon(z), respectively, where the relative distance to the gel point f(gel) was epsilon = (/f-f(gel)/)/f(gel). The relaxation critical exponent n was determined with Winter's criterion, and the critical exponents k and z estimated respectively from independent measurements of eta(0) and Ge gave n from z/(k + z). Before the gel point, the storage and loss moduli G' and G'' obtained at various epsilon can be superposed fairly well to form the master curve. The critical exponents n, k, and z were also evaluated from the shift factors and the structure self-similarity was found in the critical gel. The critical exponents evaluated with different methods agreed well with each other, suggesting two categories of the gelation as growth and cross-link. For the alginate with lower molecular weight, the critical exponents were almost independent of alginate concentration and close to the percolation prediction. For the alginate with higher molecular weight, the critical exponents, however, changed with alginate sample and concentration. The relative alginate concentration C(Alg)/C(Alg)* was found to serve as a criterion to divide these two transitions.

Difference in Concentration Dependence of Relaxation Critical Exponent n for Alginate Solutions at Sol−Gel Transition Induced by Calcium Cations

The sol-gel transition in aqueous alginate solutions induced by chelation with calcium cations from in situ release has been investigated with viscoelastic methods. Two alginate samples having different molecular weights (MW) were used over the concentration C(Alg) of 2 approximately 6 wt % with different mole ratio f of Ca2+ to the alginate repeat unit. The gel point f(gel) and relaxation critical exponent n were determined according to Winter's criterion, the later agrees well with that obtained from the relaxation modulus. The results indicate that the power law is valid for the dynamic relaxation at the gel point and the critical gel possesses the self-similarity in structure. With increasing C(Alg), f(gel) for the alginate with lower MW decreases dramatically and n is almost constant of about 0.71. In contrast, f(gel) for the higher MW alginate with is almost a constant and n decreases from 0.72 then levels off at 0.37 with increasing C(Alg), indicating that the concentration dependence of n varies with MW of alginate in the starting solution. The fractal dimension d(f) estimated from n suggests a denser structure in the critical gel of higher MW alginate. Either n or d(f) has been found to follow one curve for the two samples if plotted against the number of cross-link junctions per polymer chain, which is proportional to the alginate MW.

Rheology of asphalts modified with glycidylmethacrylate functionalized polymers

Asphalt is known to be a colloidal suspension in which asphaltenes are covered by a stabilizing phase of polar resins and form complex micelles that are dispersed in the oily maltenic phase. In order to enhance its mechanical properties (e.g., in road paving), asphalts are often loaded with polymeric materials, thereby obtaining blends that can have different physical or chemical structures, depending on the composition of the added polymer. Asphalts modified by the addition of reactive ethylene terpolymers were prepared and their dielectric and rheological properties were measured both before and after a cure at high temperature. Even if it is not possible to determine the exact nature of the chemical interactions between asphalt and polymer, master curves obtained from dynamic data clearly show that during the cure the material tends to the behavior of a cross-linked network.

Dynamic viscoelastic properties of silica alkoxide during the sol-gel transition

The viscoelastic properties of silica alkoxide gel during the sol-gel transition (SGT) are analysed using an extended shear relaxation modulus expression with a functional form based on a product of power law and Debye-Maxwell relaxation kernels. The dynamic properties are probed by small-amplitude oscillatory shear measurements in three viscoelastic domains (pre-SGT, SGT, post-SGT). Using analytical expressions for the storage G'(omega) and loss G''(omega) moduli in these three domains, it is shown that the divergence of the mean characteristic relaxation time in the pre-SGT domain can be successfully described by a percolation with bond fluctuation dynamics. It is also shown that the equilibrium shear modulus in the post-SGT domain can be successfully described by a percolation model based on an analogy with an electrical network. The amplitude and the critical exponent of the power law relaxation at the gelation time first introduced by Winter and Chambon are estimated in the pre- and post-SGT domains.

Transport properties of incipient gels

We investigate the behavior of the shear viscosity eta(p) and the mass-dependent diffusion coefficient D(m,p) in the context of a simple model that, as the cross link density p is increased, undergoes a continuous transition from a fluid to a gel. The shear viscosity diverges at the gel point according to eta(p) approximately (p(c)-p)(-s) with s approximately 0.65. The diffusion constant shows a remarkable dependence on the mass of the clusters: D(m,p) approximately m(-0.69), not only at p(c) but well into the liquid phase. We also find that the Stokes-Einstein relation Deta proportional, variant k(B)T breaks down already quite far from the gel point.

Model for gelation with explicit solvent effects: structure and dynamics

We study a two-component model for gelation consisting of f-functional monomers (the gel) and inert particles (the solvent). After equilibration as a simple liquid, the gel particles are gradually cross linked to each other until the desired number of cross links have been attained. At a critical cross-link density, the largest gel cluster percolates and an amorphous solid forms. This percolation process is different from ordinary lattice or continuum percolation of a single species in the sense that the critical exponents are new. As the cross-link density p approaches its critical value p(c), the shear viscosity diverges: eta(p) approximately (p(c)-p)(-s) with s a nonuniversal concentration-dependent exponent.

Viscoelasticity near the gel point: a molecular dynamics study

We report on extensive molecular dynamics simulations on systems of soft spheres of functionality f, i.e., particles that are capable of bonding irreversibly with a maximum of f other particles. These bonds are randomly distributed throughout the system and imposed with probability p. At a critical concentration of bonds, p(c) approximately 0.2488 for f=6, a gel is formed and the shear viscosity eta diverges according to eta approximately (p(c)-p)(-s). We find s approximately 0.7 in agreement with some experiments and with a recent theoretical prediction based on Rouse dynamics of phantom chains. The diffusion constant decreases as the gel point is approached but does not display a well-defined power law.

Stress relaxation of near-critical gels

The time-dependent stress relaxation for a Rouse model of a cross-linked polymer melt is completely determined by the spectrum of eigenvalues of the connectivity matrix. The latter has been computed analytically for a mean-field distribution of cross-links. It shows a Lifshitz tail for small eigenvalues and all concentrations below the percolation threshold, giving rise to a stretched exponential decay of the stress relaxation function in the sol phase. At the critical point the density of states is finite for small eigenvalues, resulting in a logarithmic divergence of the viscosity and an algebraic decay of the stress relaxation function. Numerical diagonalization of the connectivity matrix supports the analytical findings and has furthermore been applied to cluster statistics corresponding to random bond percolation in two and three dimensions.

Critical dynamics of gelation

Shear relaxation and dynamic density fluctuations are studied within a Rouse model, generalized to include the effects of permanent random crosslinks. We derive an exact correspondence between the static shear viscosity and the resistance of a random resistor network. This relation allows us to compute the static shear viscosity exactly for uncorrelated crosslinks. For more general percolation models, which are amenable to a scaling description, it yields the scaling relation k=straight phi-beta for the critical exponent of the shear viscosity. Here beta is the thermal exponent for the gel fraction, and straight phi is the crossover exponent of the resistor network. The results on the shear viscosity are also used in deriving upper and lower bounds on the incoherent scattering function in the long-time limit, thereby corroborating previous results.

Semimicroscopic theory of elasticity near the vulcanization transition

Randomly cross-linked macromolecules undergo a liquid to amorphous-solid phase transition at a critical cross-link concentration. This transition has two main signatures: the random localization of a fraction of the monomers and the emergence of a nonzero static shear modulus. In this paper, a semimicroscopic statistical mechanical theory of the elastic properties of the amorphous solid state is developed. This theory takes into account both quenched disorder and thermal fluctuations, and allows for the direct computation of the free energy change of the sample due to a given macroscopic shear strain. This leads to an unambiguous determination of the static shear modulus. At the level of mean field theory, it is found (i) that the shear modulus grows continuously from zero at the transition, and does so with the classical exponent, i.e., with the third power of the excess cross-link density and, quite surprisingly, (ii) that near the transition the external stresses do not spoil the spherical symmetry of the localization clouds of the particles.

Entropic elasticity of two-dimensional self-avoiding percolation systems

The sol-gel transition is studied on a purely entropic two-dimensional model system consisting of hard spheres (disks) in which a fraction p of neighbors are tethered by inextensible bonds. We use a new method to measure directly the elastic properties of the system. We find that over a broad range of hard sphere diameters a the rigidity threshold is insensitive to a and indistinguishable from the percolation threshold p(c). Close to p(c), the shear modulus behaves as (p-p(c))(f), where the exponent f approximately 1. 3 is independent of a and is similar to the conductivity exponent in random resistor networks.

Viscoelasticity of randomly branched polymers in the vulcanization class

We report viscosity, recoverable compliance, and molar mass distribution for a series of randomly branched polyester samples with long linear chain sections between branch points. Molecular structure characterization determines tau=2.47+/-0.05 for the exponent controlling the molar mass distribution, so this system belongs to the vulcanization (mean-field) universality class. Consequently, branched polymers of similar size strongly overlap and form interchain entanglements. The viscosity diverges at the gel point with an exponent s=6.1+/-0.3, that is significantly larger than the value of 1.33 predicted by the branched polymer Rouse model (bead-spring model without entanglements). The recoverable compliance diverges at the percolation threshold with an exponent t=3.2+/-0.2. This effect is consistent with the idea that each branched polymer of size equal to the correlation length stores k(B)T of elastic energy. Near the gel point, the complex shear modulus is a power law in frequency with an exponent u=0.33+/-0.05. The measured rheological exponents confirm that the dynamic scaling law u=t/(s+t) holds for the vulcanization class. Since s is larger and u is smaller than the Rouse values observed in systems that belong to the critical percolation universality class, we conclude that entanglements profoundly increase the longest relaxation time. Examination of the literature data reveals clear trends for the exponents s and u as functions of the chain length between branch points. These dependencies, qualitatively explained by hierarchical relaxation models, imply that the dynamic scaling observed in systems that belong to the vulcanization class is nonuniversal.

Viscosity and elasticity during collagen assembly in vitro: relevance to matrix-driven translocation

In order to better understand the gelation process associated with collagen assembly, and the mechanism of the in vitro morphogenetic phenomenon of "matrix-driven translocation" [S.A. Newman et al. (1985) Science, 228, 885-889], the viscosity and elastic modulus of assembling collagen matrices in the presence and absence of polystyrene latex beads was investigated. Viscosity measurements at very low shear rates (0.016-0.0549 s(-1)) were performed over a range of temperatures (6.9-11.5 degrees C) in a Couette viscometer. A magnetic levitation sphere rheometer was used to measure the shear elastic modulus of the assembling matrices during the late phase of the gelation process. Gelation was detected by the rapid increase in viscosity that occurred after a lag time tL that varied between O and approximately 500 s. After a rise in viscosity that occurred over an additional approximately 500 s, the collagen matrix was characterized by an elastic modulus of the order of several Pa. The lag time of the assembly process was relatively insensitive to differences in shear rate within the variability of the sample preparation, but was inversely proportional to the time the sample spent on ice before being raised to the test temperature, for test temperatures > 9 degrees C. This suggests that structures important for fibrillogenesis are capable of forming at 0 degrees C. The time dependence of the gelation process is well-described by an exponential law with a rate constant K approximately 0.1 s(-1). Significantly, K was consistently larger in collagen preparations that contained cell-sized polystyrene beads. From these results, along with prior information on effective surface tension differences of bead-containing and bead-lacking collagen matrices, we conclude that changes in matrix organization contributing to matrix-driven translocation are initiated during the lag phase of fibrillogenesis when the viscosity is < or = 0.1 Poise. The phenomenon may make use of small differentials in viscosity and/or elasticity, resulting from the interaction of the beads with the assembling matrix. These properties are well described by standard models of concentrated solutions.