Gel deformation

Recently, Mitra et al. have prepared chemically crosslinked nanosized gels from different rubber lattices [148,149]. When added in small quantity (2-16 phr), these low moduli deformable gels have been found to influence the mechanical properties of virgin elastomers like NR and SBR considerably. For example, sulfur prevulcanized nanosized SBR latex gels were prepared and characterized using various methods [148]. The morphology of gel-filled NR and SBR systems has been studied... 

Cartesian coordinates in the relaxed state Cartesian coordinates of deformed gel elongation ratio of isotropic gel... 

To have Fel for inhomogeneous cases, we distinguish the Cartesian coordinates of the deformed gel, X = (X, X2, X3), representing the real spatial position, and those in the isotropic, relaxed state, jc0 = (x , x , x ), representing the original position before deformation. We define the deformation tensor,... 

Nonlinear Theory. It is straightforward to generalize the above linear dynamics to cases with general network deformations [12]. This is necessary for description of dynamics in deformed gels and phase separation. First, the relative velocity should be written as... 

In order to find the influence of compression on collapse of the polymer networks, the experiments on the swelling of the deformed gels of AA-SMA in water-methanol and water-dioxane mixtures were performed [29]. It was shown that uniaxial compression of the gel really affects the swelling curves and that, in a good agreement with the theory, the region of stability of the collapsed state increases and the sharpness of collapse decreases under compression. 

L.L. Navickis and E.B. Bagley, Yield Stresses in Concentrated Dispersions of Closely Packed, Deformable Gel Particles, J. Rheol., 27 519-536 (1983). 

Navickis, L. L., and Bagley, E. B. (1983). Yield stresses in concentrated dispersions of closely packed, deformable gel particles. J. Rheol. 27(6), 519-536. 

The concentration dependence of the Brookfield viscosity (Figures 9 and 10) indicates a rapid drop in viscosity upon dilution below a critical concentration. Bagley (7) attributed such rheological behavior to a structure of swollen, deformable gel particles closely packed in intimate contact. Davidson (8) later attributed the thickening efficiency of a cross-linked poly(acrylic acid) to the dispersed rather than the continuous phase. In general, pseudoplastic and viscoplastic rheology is characteristic of dispersions with low... 

Ganago et alP formulated a theory for predicting the order parameter (P2) in gels that are expanded or compressed without change in volume. If a gel is compressed along the x and y axes (or expanded along the z axis), the director n is parallel to the z axis. The deformed gel dimensions are related to the initial dimensions l, ly, /j by... 

Figure 4.44. Profile of time-changes of the electric potential at the interfaee of two gels, one deformed and the second one in free state, respectively. Upper eurve electrie potential lower curve deformation. Gel dimensions 15x10x10 mm [143]. Swelling degree, 167.

The dynamics of the polymer network is assumed to be purely relaxational, so that the forces acting on the deformed gel are balanced by the frictional drag due to the motion of the solvent [33]. Thus, we can write [2] ... 

We represent a 3D reactive, deformable gel by a set of general linear hexahedral elements [37, 38] (see Figure 8.1a). Initially, the sample is undeformed and consists of (I — 1) X (Ly — 1) X (Lz — 1) identical cubic elements here Lj is the number of nodes in the t-direction, i = x,y,z. The linear size of the elements in the undistorted state is given by A. (In the simulations presented below, we set A = 1.) For a homogeneous BZ gel in the undeformed state, the polymer and cross-links are uniformly distributed over the gel sample that is, each undeformed element is characterized by the same volume fraction and cross-link density Co- Upon deformation, the elements move together with the polymer network so that the amount of polymer and number of cross-Hnks within each hexahedral element remain equal to their initial values. 

Fundamental set was tested, which is expected to deform gels into convex shape and concave shape. Then, conditions were changed compared to the first cases. The varied conditions were numbers of anionic or cationic electrodes in the center, distance between the electrodes and the gel, relative position of gels and electrodes. The conditions are summarized in table 5.1. The case of (a-), (b-), (c-) and (d-) are illustrated in Figure 5.22. Common condition was the size of the gel, 16[mm] in length, 4[mm] in width and l[mm] in thickness. 

The results of this study of Marinova et al. [7] are reproduced in Table 6.1. Here the change in time for foam collapse due to antifoam deactivation is compared with microscope observations of the state of the antifoam dispersion. It is obvious from Table 6.1 that the size and proportion of non-deformable gel-like agglomerates increases as the antifoam deactivates. Similarly, the proportion of (antifoam) oil drops decreases. The range of diameters of these oil drops appears to decline... 

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