Polydispersities medium

For continuum percolation, the percolation probability is replaced by a percolation volume fraction, given by Xc = Pcf, where / is the filling factor (Hunt, 2005). For a polydisperse medium, Xc is a monotonically decreasing function of the polydispersity. 

The UF-resin itself is formed in the acid condensation step, where the same high molar ratio as in the alkaline methylolation step is used (F/U = 1.8 to 2.5) the methylolureas, urea and the residual free formaldehyde react to form linear and partly branched molecules with medium and even higher molar masses, forming polydispersed UF-resins composed of oligomers and polymers of different molar m.asses. Molar ratios lower than approx. 1.7-1.8 during this acid condensation step might cause resin precipitation. 

Organism (temperature, C) medium) (mg/g cells) acetone (overall content) (kDa) (kDa) Polydispersity... 

Okubo et al. [87] used AIBN and poly(acrylic acid) (Mw = 2 X 10 ) as the initiator and the stabilizer, respectively, for the dispersion polymerization of styrene conducted within the ethyl alcohol/water medium. The ethyl alcohol-water volumetric ratio (ml ml) was changed between (100 0) and (60 40). The uniform particles were obtained in the range of 100 0 and 70 30 while the polydisperse particles were produced with 35 65 and especially 60 40 ethyl alcohol-water ratios. The average particle size decreased form 3.8 to 1.9 /xm by the increasing water content of the dispersion medium. 

To run the residence time distribution experiments under conditions which would simulate the conditions occurring during chemical reaction, solutions of 15 weight percent and 30 percent polystyrene in benzene as well as pure benzene were used as the fluid medium. The polystyrene used in the RTD experiment was prepared in a batch reactor and had a number average degree of polymerization of 320 and a polydispersity index, DI, of 1.17. 

The theory of regular solutions applied to mixtures of aromatic sulfonate and polydispersed ethoxylated alkylphenols provides an understanding of how the adsorption and micellization properties of such systems in equilibrium in a porous medium, evolve as a function of their composition. Improvement of the adjustment with the experimental results presented would make necessary to take also in account the molar interactions of surfactants adsorbed simultaneously onto the solid surface. 

The tendency of nitrones to react with radicals has been widely used in new synthetic routes to well-defined polymers with low polydispersity. The recent progress in controlled radical polymerization (CRP), mainly nitroxide-mediated polymerization (NMP) (695), is based on the direct transformation of nitrones to nitroxides and alkoxyamines in the polymerization medium (696, 697). In polymer chemistry, NMP has become popular as a method for preparing living polymers (698) under mild, chemoselective conditions with good control over both, the polydispersity and molecular weight. 

Hybrid scorpionate/cyclopentadienyl-Mg (63) and -Zn (64,65) complexes were structurally characterized and reported to catalyze the formation of PLAs with medium molecular weights and narrow polydispersities [85]. Among them, the magnesium complex 63 is much more active than the others, giving a polymerization of L-lactide in toluene at 90 °C with 97% conversion in 2.5 h. However, it takes 30 h for zinc complexes 64 and 65 to reach similar results under the same conditions. Some representative structures of magnesium and zinc complexes are summarized in Table 2 as they display closely related ROP activity of lactide, and often stmcrnrally similar ligand systems are employed to construct these initiators. 

Theories based on the uniformly effective medium have the practical advantage that they can be extended quite easily to polydisperse systems (227). Viscosity master curves can be predicted from the molecular weight distribution, for example. The only new assumption is that the entanglement time at equilibrium for a chain of molecular weight M in a polydisperse system has the form suggested by the Rouse theory (15) ... 

An important example of this phenomenon is to be found in the ageing of colloidal dispersions (often referred to as Ostwald ripening). In any dispersion there exists a dynamic equilibrium whereby the rates of dissolution and deposition of the dispersed phase balance in order that saturation solubility of the dispersed material in the dispersion medium be maintained. In a polydispersed sol the smaller particles will have a greater solubility than the larger particles and so will tend to dissolve, while the larger particles will tend to grow at their expense. In... 

The old work on crystal thickening was confined to medium to high molar mass polyethylenes with molar mass polydispersity, and the results obtained were in some respects different from the more recent findings obtained on strictly monodisperse w-alkanes. 

The formulas derived above, despite their cumbersome look, are very practical. Indeed, they present the nonlinear initial susceptibilities of a superparamagnetic particulate medium as analytical expressions of arbitrary accuracy. Another remarkable feature of the formulas of Section III.B.6 is that with respect to the frequency behavior they give the exact structure of the susceptibilities and demonstrate that those dependencies are quite simple. This makes our formulas a handy tool for analytical studies. Yet they are more convenient for numerical work because with their use the difficult and time-consuming procedure of solving the differential equations is replaced by a plain summation of certain power series. For example, if to employ Eqs. (4.194)-(4.200), a computer code that fits simultaneously experimental data on linear and a reasonable set of nonlinear susceptibilities (say, the 3th and the 5th) taking into account the particle polydispersity of any kind (easy-axes directions, activation volume, anisotropy constants) becomes a very fast procedure. 

The miktoarm stars were characterized by medium polydispersities (Mw/Mn=I=l.33-1.50) probably due to incomplete hydrosilylation. It is characteristic that only small molecular weight P2VP arms were used to facilitate the linking reaction. This is evidence of the limitations of the hydrosilylation reaction for the preparation of miktoarm stars. 

K (D/Am, np/nm), the extinction coefficient, is in the general case a complicated function of the particle diameter D, the wavelength in the medium m, and the refractive indices np and nm of the particles and the medium, respectively. K can be calculated from the general Mie theory (3). For a polydisperse suspension ... 

Polydispersity of the copolymer is still narrow (Mw/Mn = 1.36) whereas it increases to 4.21 in the absence of Tempo, leading to a bimodal molecular weight distribution. Such a process is also applied in aqueous medium [70] for the polymerization of styrenesulfonic acid sodium salt with narrow molecular weight distribution (Mw/Mn as low as 1.18). 

---