The structural and mechanical properties of gels formed from biopolymers are discussed both in terms of the techniques used to characterise these systems, and in terms of the systems themselves The techniques included are spectroscopic, chiroptical and scattering methods, optical and electron microscopy, thermodynamic and kinetic methods and rheological characterisation The systems considered are presented in order of increasing complexity of secondary, tertiary and quaternary structure, starting with gels which arise from essentially ‘disordered’ biopolymers via formation of ‘quasicrystalline’ junction zones (eg gelatin, carrageenans, agarose, alginates etc), and extending to networks derived from globular and rod-like species (fibrin, globular proteins, caseins, myosin) by a variety of crosslinking mechanisms Throughout the text, efforts are made to pursue the link (both from experiment and from theory) between the structural methods and mechanical measurements As far as we are aware this is the first major Review of this area since that of J D Ferry in 1948 — The interest shown by polymer physicists in more complex biochemical systems, and the multi-disciplinary approaches now being applied in this area, make the format adopted here, in our opinion, the most logical and appropriate

Structural and mechanical properties of biopolymer gels

For the critical exponents near the sol-gel phase transition, classical theories like those of Flory and Stockmayer predict one set of exponents, whereas scaling theories based on lattice percolation predict different exponents. The two groups of theories differ in their treatment of intramolecular loops, space dimensionality and excluded volume effects. In this article, the differences and similarities between the results of the competing theories are reviewed. For example, a gel fraction like (p-pc)β vanishes for conversion factors p very close to the gel point pc, the weight average molecular weight diverges as (pc-p)−γ for p very slightly below pc, and the radius of macromolecules at the gel point p=pc varies as the ϱ-th power of the number of monomers in that macromolecule. Classical theories predict β=γ=1 and ϱ=1/4 whereas the percolation theory gives β ≃ 0.45, γ ≃ 1.74 and ϱ ≃ 0.40. We also generalize the percolation concept to include interaction effects and concentration fluctuations; in this case the sol-gel phase transition may be connected with a phase separation.

Gelation and critical phenomena

Dynamic mechanical measurements allow direct determination of the instant at which a network polymer gels. In such an experiment, the evolution of G′(t,ω0) and G″ (t,ω0) is measured in small amplitude oscillatory shear as a function of cross-linking time t. The frequency ω0 is kept constant throughout. At the beginning of the experiment, G″ is orders of magnitude larger than G′, and at completion of reaction, this order is reversed. It recently has been suggested by Tung and Dynes that the gel point (GP) might occur at the time at which G′ and G″ cross each other. However, there is much dispute whether GP occurs exactly at the crossover or just somewhere in its vicinity. This study resolves the dispute by modeling the rheological behavior at GP: There is only one class of network polymers for which GP coincides with the crossover. This class of polymers exhibits, when reaching GP, power law relaxation G(t) ∼ t−n with a specific exponent value n = 1/2. Examples are stoichiometrically balanced network polymers and networks with excess cross-linker, however, only at temperatures much above the glass transition. Otherwise, the power law behavior would be masked by vitrification. Power law relaxation seems to be property of polymers at GP in general. However, some polymers have a different exponent value, n ≠ 1/2, in which case the crossover occurs before GP (for n 1/2); i.e. the crossover cannot be used for detecting GP. While there are no networks known to us with n 1/2. A new method is suggested for measuring GP of these imbalanced networks.

Can the gel point of a cross-linking polymer be detected by the G′ – G″ crossover?

Dilute and semi-dilute solution properties of several classes of branched macromolecules are outlined and discussed. The dilute solution properties are needed for a control of the chemical synthesis. The molecular parameters also determine the overlap concentration which is an essential quantity for description of the semi-dilute state. This state is represented by a multi-particle, highly entangled ensemble that exhibits certain similarities to the corresponding bulk systems. Because of the rich versatility in branching the present contribution made a selection and deals specifically with the two extremes of regularly branched polymers, on the one hand, and the randomly branched macromolecules on the other. Some properties of hyperbranched chains are included, whereas the many examples of slight deviations from regularity are mentioned only in passing. The treatment of the two extremes demonstrates the complexity to be expected in the general case of less organized but non-randomly branched systems. However, it also discloses certain common features.

Solution Properties of Branched Macromolecules

Polymeric materials near the liquid-solid transition (LST) exhibit a very distinct relaxation pattern. The reference point for analyzing these patterns is the instant of LST at which relaxation becomes self-similar over wide ranges of the relaxation time. The universality of this transition and its consequences have been explored extensively during the past decade. This study will present an overview of rheological implications inherent in liquid-solid transitions of polymers. The LST can be most reliably detected in a dynamic mechanical experiment in which the frequency independence of the loss tangent marks the LST. A wide variety of rheological observations of materials in the vicinity of an LST are discussed with respect to their universality. It is shown that polymer chemistry, molecular weight, stoichiometry, temperature, inhomogeneities, etc. greatly influence the material behavior near the LST. However, the characteristic self-similar relaxation is shown by all investigated materials, independent of the nature of the LST (e.g., both, physically and chemically crosslinking polymers). Several theories predict chemical and rheological properties in the vicinity of an LST. They are briefly discussed and compared with experimental results. A variety of applications for polymers near LST are presented that either already exist or can be envisioned. The self-similar relaxation behavior which results in a power law relaxation spectrum and modulus is not restricted to materials near LST. Different classes of polymers are described that also show power law relaxation behavior. What makes the self-similar relaxation specific for materials at LST is its occurrence at long times with the longest relaxation time diverging to infinity.

/pdf/rheology-of-polymers-near-liquid-solid-transitions-51fps6zhlz.pdf

Rheology of Polymers Near Liquid-Solid Transitions

The frequency dependence of viscoelastic properties of a branched polymer sample near its gelation threshold has been studied in oscillatory measurements. The results are in agreement with De Gennes' analogy relating the critical behaviour of the elastic moduli G' and G'' to the electrical conductivity of percolation clusters. In particular the increase of both G' and G'' with frequency (0.1 to 10 Hz) can be described by power laws with a common exponent u = t/s + t, and the loss angle δ assumes near the gelation point the universal value δc = πu/2 (t and s denote, respectively, the exponents of elastic modulus and viscosity at zero frequency). The value of u determined in these experiments (u = 0.70 ± 0.02) is in very good agreement with percolation theory.

https://iopscience.iop.org/article/10.1209/0295-5075/3/3/008/pdf

Frequency Dependence of Viscoelastic Properties of Branched Polymers near Gelation Threshold

Etude de l'evolution des proprietes mecaniques en fonction du temps au cours de la gelification

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

Dynamical studies of polymeric cluster solutions obtained near the gelation threshold: Glasslike behavior.

Mechanical properties near gelation threshold, comparison with classical and 3d percolation theories

Small angle neutron scattering experiments were performed on Polyurethane branched polymers synthetized near the gelation threshold. The exponent τ of the size distribution function is measured, on a system cross-linked by polycondensation. We find τ = 2.2 ± 0.04. This leads to a fractal dimension for the polymers in the reaction bath Dp = 2.5 ± 0.09, in agreement with percolation model. In the dilute state, the fractal dimension is D = 1.98 ± 0.03, in agreement with recent predictions. Thus the largest branched polymers are swollen by dilution, and behave as lattice animals.

https://hal.archives-ouvertes.fr/jpa-00210318/document

M. Delsanti

Papers

Frequency Dependence of Viscoelastic Properties of Branched Polymers near Gelation Threshold

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

Dynamical studies of polymeric cluster solutions obtained near the gelation threshold: Glasslike behavior.

Mechanical properties near gelation threshold, comparison with classical and 3d percolation theories

Gelation and percolation: swelling effect