Isotropic gels

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

In isotropic gels, we may discuss the volume-phase transition on the basis of the total free energy F regarding the volume V (or 4> = 4>o F0/F) as the order... 

Let us examine the critical dynamics near the bulk spinodal point in isotropic gels, where K + in = A(T — Ts) is very small, Ts being the so-called spinodal temperature [4,51,83-85]. Here, the linear theory indicates that the conventional diffusion constant D = (K + / )/ is proportional to T — Ts. Tanaka proposed that the density fluctuations should be collectively convected by the fluid velocity field as in near-critical binary mixtures and are governed by the renormalized diffusion constant (Kawasaki s formula) [84],... 

This chapter deals primarily with examples in the semidilute concentration range, corresponding to overlapped chainlike aggregates of isotropic gels." As mentioned, the heterogeneity of the networks makes possible the existence of more concentrated microdomains, where chains are somewhat ordered in crystalline or lyotropic structures (corresponding to anisotropic gels). 

Let us examine the oitical dynamics near the bulk spinodal point in isotropic gels, where K A T — 2 ) is very small, T, being the so-called spinodal... 

There are various types of molecular orientations possible in the surfactant film. The surfactant molecules may be in the form of crystals, isotropic gels or one or more of several different types of mesophases (33). The techniques which may be used to study the molecular orientations inside these surfactant films have been reviewed by Singer (34). 

At low temperatures the nematic gel coexists with excess solvent, i.e., the i-N biphasic coexistence. Above the triple point TJ, excess solvent coexists with an isotropic gel, i.e., the i-I coexistence. Also, above this temperature, the isotropic and the nematic phases of a gel can coexist, i.e., I-N phases. Beyond the phase gap, a single nematic phase exists. The I-N region terminates at the = 1 axis. This is at T the N-I transition temperature of the undiluted network which, in turn, is close to Tni, the transition temperature of the uncrosslinked polymer melt from which the network derives. The nematic order is not expected for any 4> for T above. This is the limit of stability for even the undiluted case. 

I) isotropic gel (II) and (III) nematic gel. Tt is the i-I-N triple-point temperature. (From Warner Wang, 1992a.)... 

Fig. 12a,b. Phase diagram of clay suspensions vs clay and NaCl concentrations, (circles, F) Flocculated samples (squares, IL) isotropic liquid samples (lozenges, IG) isotropic gel samples (crosses, NG) nematic gel for a bentonite b laponite. (Reprinted from [4b], copyright (2000) from John Wiley and Sons)... 

Figure 7.21 shows micrographs taken in polarized light for dry beads of the initial styrene-0.5% DVB copolymer (Fig. 7.21a) and hypercrosslinked polymer on its base (Fig. 7.21b). Both the polymers are transparent, though the hypercrosslinked one is a highly porous material with a significant free volume and apparent specific surface area as large as 1300 m /g. If now one crosses the polaroids, the dry bead of the isotropic gel-type polymer remains transparent (Fig. 7.21c), while the hypercrosslinked polymer reveals its inner stains and optical anisotropy in the form of a clear Maltese cross (Fig. 7.21d).

The polymer volume fraction 0 plays the role of a nonconserved order parameter. In (small) homogeneous and isotropic gels, its time evolution is assumed to satisfy the following Landau type equation... 

In isotropic gels, aU values of y between 0 and 180° will occur and a statistical mathematical treatment would be necessary to reveal as to which tendency predominates in a given case. Whichever the result will be, it is clear that always a new equilibrium condition is reached. The swelling, due to the tendency of the system as a whole to reach a state of greater dilution, will be set a limit at a certain degree of extension of the molecular entropy springs. 

Anisotropic gels produced in the laboratory owe their orientation to a previous deformation. This may be either effected by mechanical deformation of an isotropic gel or by preventing the gel from isotropic contraction, for instance during drying. In both cases the random orientation of the structural elements of the frame work is changed into a more or less preferred one in one or two directions of space. 

It has already been stressed above, that orientation in man-made colloidal systems is always due to the previous agency of some external force applied to the system, from which a deformation of the system has arisen. If an isotropic gel is extended or compressed in one direction only, the resulting birefringence is uniaxial with the optical axis in the direction of the deformation. The sign of the birefringence depends on the kind of gel, but it is always opposite for extension and com-... 

Isotropic gels, when allowed to swell or contract freely, change their dimensions to the same proportion in all directions. Orientated gels, on the contrary, show aniso-... 

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