Solid-like behavior

Although aH these models provide a description of the rheological behavior of very dry foams, they do not adequately describe the behavior of foams that have more fluid in them. The shear modulus of wet foams must ultimately go to zero as the volume fraction of the bubbles decreases. The foam only attains a solid-like behavior when the bubbles are packed at a sufficiently large volume fraction that they begin to deform. In fact, it is the additional energy of the bubbles caused by their deformation that must lead to the development of a shear modulus. However, exactly how this modulus develops, and its dependence on the volume fraction of gas, is not fuHy understood. 

Galgali and his colleagues [46] have also shown that the typical rheological response in nanocomposites arises from frictional interactions between the silicate layers and not from the immobilization of confined polymer chains between the silicate layers. They have also shown a dramatic decrease in the creep compliance for the PP-based nanocomposite with 9 wt% MMT. They showed a dramatic three orders of magnitude drop in the zero shear viscosity beyond the apparent yield stress, suggesting that the solid-like behavior in the quiescent state is a result of the percolated structure of the layered silicate. 

Various diverse systems qualify as gels if one assumes that in these systems the common features are the solid-like behavior and the presence of a continuous structure of macroscopic nature (6,7). For the purpose of the discussion in this paper, we describe a gel as a colloidal system comprised of a dispersed component and a dispersion medium both of which the junction points are formed by covalent bonds, secondary valence bonds, or long range attractive forces that cause association between segments of polymer chains or formation of crystalline regions which have essentially infinite life time (8). 

A pseudo solid-like behavior of the T2 relaxation is also observed in i) high Mn fractionated linear polydimethylsiloxanes (PDMS), ii) crosslinked PDMS networks, with a single FID and the line shape follows the Weibull function (p = 1.5)88> and iii) in uncrosslinked c/.s-polyisoprenes with Mn > 30000, when the presence of entanglements produces a transient network structure. Irradiation crosslinking of polyisoprenes having smaller Mn leads to a similar effect91 . The non-Lorentzian free-induction decay can be a consequence of a) anisotropic molecular motion or b) residual dipolar interactions in the viscoelastic state. 

In the definition of rheology there are two processes, deformation and flow. Deformation suggests the presence of solid-like behavior and flow suggests the presence of fluid-like behavior. Many foods have both solid and fluid properties. The objective of this section is to provide methods for the evaluation of the rheological properties of foods. In Chapter HI, flow properties of foods are the focus. In Chapter H2, deformation properties are the focus. 

Real world materials are not simple liquids or solids but are complex systems that can exhibit both liquid-like and solid-like behavior. This mixed response is known as viscoelasticity. Often the apparent dominance of elasticity or viscosity in a sample will be affected by the temperature or the time period of testing. Flow tests can derive viscosity values for complex fluids, but they shed light upon an elastic response only if a measure is made of normal stresses generated during shear. Creep tests can derive the contribution of elasticity in a sample response, and such tests are used in conjunction with dynamic testing to quantity viscoelastic behavior. 

The solutions of some polymers have very unusual behavior These fall in the category of non-Newtonian fluids, substances whose viscosity varies with the force applied to them. Some fluids become thinner when stirred or shaken, while others become thicker Still others show solid-like behavior because they have elastic properties under some magnitudes of stress are viscoelastic). 

Noncrystalline or amorphous (i.e without form) ceramics are supercooled liquids. Liquids flow under their own mass, but they can become very viscous at low temperatures. Very viscous liquids (for example, honey in the winter time) have solid-like behavior although they maintain a disordered structure characteristic of a liquid, i.e they do not undergo a transformation to a crystalline structure Thus, noncrystalline ceramics, i.e glasses, may behave, in many respects, like solids but structurally they are liquids. 

A combination of two different supramolecular forces, namely metal-metal bonds and the ureidopyrimidones were investigated by Schubert et al. [136,137] (Fig. 35). A poly(g-caprolactame) was prepared—with a ter-pyridine moiety at one end and an ureidopyrimidone unit at the other end—via tin-octanoate catalyzed polymerization. Together with iron(ll) ions, double supramolecular polymers formed from chloroform solution. Again, solid-like behavior was observed, similar to results for the purely hydrogen-bonded polymers. 

Molecular conformation of bonded ligands and their degree of freedom is dependent on bonding density. The higher the bonding density, the lower the number of possible conformations and thus the less mobility the bonded chains have. Immobilization of ligands on the surface already restrict their mobility, so if we compare the state of free Cl 8 molecules (n-octadecyl) with immobilized octadecyl, we can expect more rigid (or solid-like) behavior of immobilized chain. Indeed, the study of the viscosity of bonded layers [64]... 

Note that at the temperature 150 C, the transition from liquid-like to solid-like behavior occurs at frequency 1 sec, as indicated by the crossover of G and G roughly at this frequency. For this melt, a corresponding crossover in the steady-state shear-viscosity curve from a liquid-like plateau in to a solid-like shear thinning region occurs at a shear rate roughly in the vicinity of 1 sec (see Fig. 1-9). Thus, the crossover shear rate yc in steady shearing is about equal numerically to the crossover frequency coc... 

Figure 5-7 shows the frequency dependences of the storage and loss moduli at various times during the reaction, from 6 minutes before G to 6 minutes after it. Note that at tc (labeled Gel Point in Fig. 5-7), G and G" follow power laws over the entire frequency range For times less than this (labeled —2 and —6 in Fig. 5-7), the curves slope downward at low frequencies, which is indicative of fluid-like behavior, while at times after the gel point (labeled -t-2 and - -6), G flattens at low frequency—a characteristic of solidlike behavior. Thus, the intermediate state with a power-law frequency dependence over the whole frequency range is the transitional state between liquid-like and solid-like behavior, and therefore it defines the gel point. This rheologically determined gel point coincides with the conventional value, namely the maximum degree of cure at which...

Behavior that is intermediate between that of a solid and that of a liquid is perhaps not surprising for a block copolymer with hexagonally ordered cylinders, since such a material has solid-like order in the two directions perpendicular to the cylinders and liquid-like order parallel to the cylinders. Similar behavior is observed in lamellar block copolymers, which has solid-like order in the direction normal to the lamellae and has liquid-like order in the other two directions. For lamellar block copolymers, solid-like behavior at low frequencies typically arises from the disrupting effect of defects, such as those present in smectic liquid crystals (see Section 10.4.8). 

The same t3q)e of thermal history caused solid-like behavior in the supercooled molecular liquid ortho-terphenyl [35], a fragile molecular glass-former, as well as in glycerol, a stronger, hydrogen-bonded one. 

Pharmaceutical materials are rarely described by simple mechanical equivalents such as the Kelvin (solid-like behavior) or the Maxwell (liquid-like behavior) model. 

Fig. 23 (a) Frequency-dependent linear viscoelastic moduli (G closed symbols, G" open symbols) of a colloidal star with nominal values f = 12Sarms and = SOkgmol at a concentration 5 wt% in -tetradecane and different temperatures (circles 40°C, squares. 5O C. triangles 55°C). A liquid-lo-solid transition is marked between 50 and 55°C. Lines with slopes 1 and 2 indicate terminal behavior of G" and G, respectively. Inset The temperature dependence of the hydrodynamic radius /fh of the same star, indicating swelling, (b) Respective moduli for the same system at 4() C in two different solvents, n-decane (circles, solid-like behavior) and n-tetracane (triangles, Uquid-Uke behavior) [26]... 

Other general trends that are described correctly by the model [42] include an increasing r (relative) with particle aggregation (flocculation) and the onset of solid-like behavior (the existence of a yield stress ) in some dispersions at low shear rates. 

GERF (discovered by Wen et.al.) has a yield stress up to 300 kPa in response to an electric field, which provides an alternative choice of digitally controllable microvalve that can respond within 10 pm [13, 43]. Its solid-like behavior sustains shear in the direction perpendicular to the applied electric field, the shear stress can be enhanced when the applied electric field increases, and its rheological variation is reversible upon removal of the electric field (Fig. 4). These marvelous features qualify GERF as an electric-fluid-mechanical interface for digital fluid control in microfluidics [55, 56]. 

At rest, the system with time regains its strength, i.e. restores solid-like behavior (Fig. IX-27). The strength (critical shear stress, x ) of a completely restored structure does not depend on a number of structure disintegration cycles. The time required for a complete thixotropic restoration of a primarily disintegrated structure is referred to as the period of thixotropy, tT. 

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