Critical complex viscosity

Figure 13 The critical modulus G and critical complex viscosity vs. the applied electric field. Redrawn with permission from T. Hao, Y. Chen, Z. Xu, Y. Xu and Y. Huang, Chin. J. Polym. Sci., 12(1994)97...

The recovery of petroleum from sandstone and the release of kerogen from oil shale and tar sands both depend strongly on the microstmcture and surface properties of these porous media. The interfacial properties of complex liquid agents—mixtures of polymers and surfactants—are critical to viscosity control in tertiary oil recovery and to the comminution of minerals and coal. The corrosion and wear of mechanical parts are influenced by the composition and stmcture of metal surfaces, as well as by the interaction of lubricants with these surfaces. Microstmcture and surface properties are vitally important to both the performance of electrodes in electrochemical processes and the effectiveness of catalysts. Advances in synthetic chemistry are opening the door to the design of zeolites and layered compounds with tightly specified properties to provide the desired catalytic activity and separation selectivity. 

The materials are melt-process able and a critical stress for flow is observed, similar to conventional PP/EPDM-based TPVs. Application of static crosslinking leads to (partial) connectivity of the rubber particles via chemical bridging of grafted PE chains. Dynamic preparation conditions caused the connected structure to break-up, which led to a significant enhancement of the mechanical properties and the melt processability. The addition of 25-80 wt% extender oil resulted in a reduced complex viscosity and yield stress in the melt, without deteriorating the mechanical properties. The relatively good elastic recovery and excellent final properties of these high hardness TPVs can be explained in terms of the submicrometer rubber dispersions. 

Figure 5.8 shows the dependence of complex viscosity (frequency tu = 1 rad/s, strain = 1%) on the concentration of the nanofillers (i.e., MMT-BAPS, SNT, and Zr02) for the current OI-l nanocomposites prepared as already described. The figure shows significant increases ( 3 decades) for the OI/MMT-BAPS and OI/SNT nanocomposites occurring at 2-3 vol% MMT-BAPS and 8-12 vol% SNT nanofiller concentrations, respectively. For the two types of nanocomposites just mentioned, the critical nanofiller concentrations corresponding to the dramatic rise in viscosity were found to be both higher than the percolation threshold values estimated theoretically as already described [i.e.. Pc... 

Chain-growth polymerizations are diffusion controlled in bulk polymerizations. This is expected to occur rapidly, even prior to network development in step-growth mechanisms. Traditionally, rate constants are expressed in terms of viscosity. In dilute solutions, viscosity is proportional to molecular weight to a power that lies between 0.6 and 0.8 (22). Melt viscosity is more complex (23) Below a critical value for the number of atoms per chain, viscosity correlates to the 1.75 power. Above this critical value, the power is nearly 3 4 for a number of thermoplastics at low shear rates. In thermosets, as the extent of conversion reaches gellation, the viscosity asymptotically increases. However, if network formation is restricted to tightly crosslinked, localized regions, viscosity may not be appreciably affected. In the current study, an exponential function of degree of polymerization was selected as a first estimate of the rate dependency on viscosity. 

This definition cannot be applied directly to mixtures, as phase equilibria of mixtures can be very complex. Nevertheless, the term supercritical is widely accepted because of its practicable use in certain applications [6]. Some properties of SCFs can be simply tuned by changing the pressure and temperature. In particular, density and viscosity change drastically under conditions close to the critical point. It is well known that the density-dependent properties of an SCF (e.g., solubihty, diffusivity, viscosity, and heat capacity) can be manipulated by relatively small changes in temperature and pressure (Sect. 2.1). 

Figure 3. Critical concentration behavior of actin self-assembly. For the top diagram depicting the macroscopic critical concentration curve, one determines the total amount of polymerized actin by methods that measure the sum of addition and release processes occurring at both ends. Examples of such methods are sedimentation, light scattering, fluorescence assays with pyrene-labeled actin, and viscosity measurements. Forthe bottom curves, the polymerization behavior is typically determined by fluorescence assays conducted under conditions where one of the ends is blocked by the presence of molecules such as gelsolin (a barbed-end capping protein) or spectrin-band 4.1 -actin (a complex prepared from erythrocyte membranes, such that only barbed-end growth occurs). Note further that the barbed end (or (+)-end) has a lower critical concentration than the pointed end (or (-)-end). This differential stabilization requires the occurrence of ATP hydrolysis to supply the free energy that drives subunit addition to the (+)-end at the expense of the subunit loss from the (-)-end.

The important conclusion drawn from the above studies on PS(OH)/PMMA in solution and bulk is that complexes formed in dilute solutions can be preserved during the process of film casting. In particular, when we use an inert solvent whose Ejp is close to zero, the critical hydroxyl contents in proton-donating polymers for complexation estimated by viscosity or LLS are comparable to that for the miscibility-to-complex transition in bulk, which can be easily detected by DSC or TEM. Therefore, by combining the results from both solution and bulk, it should be possible to construct a map for a given blend system visualizing how the immiscibihty, miscibihty and complexation of the blend depend on the content of interacting sites. 

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