Polymer concentrations, quantitative

At equilibrium, in order to achieve equality of chemical potentials, not only tire colloid but also tire polymer concentrations in tire different phases are different. We focus here on a theory tliat allows for tliis polymer partitioning [99]. Predictions for two polymer/colloid size ratios are shown in figure C2.6.10. A liquid phase is predicted to occur only when tire range of attractions is not too small compared to tire particle size, 5/a > 0.3. Under tliese conditions a phase behaviour is obtained tliat is similar to tliat of simple liquids, such as argon. Because of tire polymer partitioning, however, tliere is a tliree-phase triangle (ratlier tlian a triple point). For smaller polymer (narrower attractions), tire gas-liquid transition becomes metastable witli respect to tire fluid-crystal transition. These predictions were confinned experimentally [100]. The phase boundaries were predicted semi-quantitatively. 

Concentration effects, i.e., the dependences of Vr on injected polymer concentration (Ci), represent a further complicating factor in the quantitative... 

Partially hydrolyzed polyacrylamides, carboxymethylcellulose, polysaccharides, and acrylamido methylpropane sulfonate have been screened to investigate the performance of aluminum citrate as a chelate-type crosslinker. An overview of the performance of 18 different polymers has been presented in the literature [1646]. The performance of the colloidal dispersion gels depends strongly on the type and the quality of the polymer used. The gels were mixed with the polymers at two polymer concentrations, at three polymer-to-aluminum ratios, and in different concentrations of potassium chloride. The gels were quantitatively tested 1,7, 14, and 28 days after preparation. 

Polyvinylchloride was the host polymer in a study of the diffusion of dimethyl-phthalate, dibutylphthalate, and dioctylphthalate, performed by Maklakov, Smechko, and Maklakov 60) between room temperature and 110 °C. Azancheev and Maklakov 61) extended this work to include polystyrene as host, and to dependences of diffusion on concentration. They concluded that the macromolecules did constrain and trap the phthalate molecules at high polymer concentration, but without inhibiting the mobility of these diluents at lower polymer concentrations, e.g., in the gel. They used a version of the free volume theory to give a semi-quantitative explanation of the temperature and molecular size dependence of phthalate diffusion. 

The driving force of the polymerization reaction is the monomer concentration at the surface of the polymer. In this case Langmuir s isotherm (equation 5.4-7) could be used to describe the monomer concentration quantitatively or, more simply, Henry s sorption rule (Eqn 5.4-8) holds true... 

It has been remarked in the preceding sections that the equilibrium concentration of monomer in solution of its living polymer is affected by the nature of the solvent and by the polymer concentration, because these factors influence the activities of the components. A quantitative treatment of these effects, based on Scott s modification of the standard lattice theory of polymer solutions (33), has been outlined recently by Bywater (34). 

The effect of polymer concentration on [M]e has also been shown in the study of Tobolsky et al. (35). Unfortunately, their experimental technique was not sufficiently refined, and the wide scatter of experimental points prevented quantitative deductions from their data. Comment is necessary with respect to one statement made in their paper. The authors assumed that the "true value of [M]e could be derived by linear extrapolation from the experimental [M]e s, obtained at high polymer concentrations, up to the point of intersection with the line [M]e= [M]0. However, this extrapolation is not valid because, as has been shown by Vrancken et al. (13), the results depend on the concentration of living ends. The proper determination of the true [M]e requires studies at low concentrations of living ends, as was done by Worsfold and Bywater (12) and by McCormick (11). 

Homopolymerization can also be reduced by working in the presence of large polymer concentrations, e.g. with polymers swollen in the monomer. In this case, even when the monomer B is sensitive to radiolysis the quantitity of homopolymer Bn remains unimportant. For example, Sebban-Danon(202) studied the effect of y-radiation on solutions of polyisobutylene in styrene. The much higher G-value of the polymer compared to that of styrene enhances the graft copolymerization with respect to the homopolymerization. 

Under constant experimental conditions, the number of Raman scattered photons is proportional to analyte concentration. Quantitative methods can be developed with simple peak height measurements.5 Just as with IR calibrations, multiple components in complex mixtures can be quantified if a distinct wavelength for each component can be identified. When isolated bands are not readily apparent, advanced multivariate statistical tools (chemometrics) like partial least squares (PLS) can help. These work by identifying all of the wavelengths correlated to, or systematically changing with, the levels of a component. Raman spectra can also be correlated to other properties, such as stress in semiconductors, polymer crystallinity, and particle size because these parameters are reflected in the local molecular environment. 

Combination of UV-vis DRS and Raman spectroscopy data has allowed for the quantitative determination of the monomer and polymer concentrations of the surface metal oxide species (Tian et al., 2006). The... 

Because of these uncertainties, equations 1, 2, 3, 4, and 5 may not be relied upon as a means of quantitative evaluation of A until more data for other polymer-solvent systems become available. The equation-of-state thermodynamics is, however, useful in its ability to give us insight into the physical factors and their relative magnitudes which contribute to the polymer-polymer interaction parameter. The results in this work clearly show that the dependence of A on concentration and temperature is moderate. This gives a justification as a good approximation to the use of a constant polymer-polymer interaction parameter in the polymer interface theories where the polymer concentration encompasses the whole range Wi = 0 to 1 across the phase boundary. 

Baumgartner S, Lahajnar G, Sepe A, et al. (Quantitative evaluation of polymer concentration profile during swelling of hydrophilic matrix tablets using H NMR and MRI methods. Eur J Pharm Biopharm 2005 59(2) 299-306. 

To express counterion distributions more quantitatively, counterion concentration c+ profiles for a 64 base-pair DNA at various polymer concentrations are plotted in Figure 4 as functions of the radial coordinate r measured from the axis of the DNA cylinder at its center and in Figure 5 as functions of the z coordinate along the surface of the cylinder. The very high counterion concentration ( 3 M) on the surface of the polyion rapidly decreases in both radial and longitudinal directions, and dilution of the polymer concentration has the slightest effect on these profiles. 

These findings confirm the model of polydisperse systems of homogeneous spheres by exact fits of the static light scattering curves, the expected M a3 dependence for PEC homologues prepared at different polymer concentrations, and the asymptotic q 4 behavior of compact spheres. The quantitative information obtained shows that the concentration of the component solutions does not affect the internal structure of the PECs remarkably but controls their level of aggregation to a great extent. 

Production of acrylamide (Fig. 13) by hydration of acrylonitrile under the action of the intracelluar nitrile hydratase in Rhodococcus rhodochrous (Nitto Chemical Industry Co., Ltd., fed-batch process). The annual production amounts to >30000 tons (see also Table 6). Acrylamide is one of the most important commodity chemicals and is required in large quantities as the pre-polymer of polyacrylamide that is widely used in polymer and floccu-lent applications. The advantages of this hydratase approach in comparison with the classical chemical nitrile hydration are higher product end concentration, quantitative yields, no formation of acrylic acid, no need for copper catalyst, and only five chemical/technical operations instead of seven [73,112,113,171]. An analogous process for nicotinamide is being commercialized by Lonza (see also section 6). 

Rogers et al. [8,23,32,41,51 showed that the pertechnetate anion partitions quantitatively to the PEG-rich phase in a variety of PEG-ABSs. The partitioning behavior of this ion is affected by the numerous variables which affect system composition in an ABS identity of the cation or anion in the phase-forming salt, salt concentration, type and molecular weight of the polymer, polymer concentration, temperature, pH, and the presence of other matrix ions in the ABS. 

The significance of the non-Newtonian characteristics of the resist solution is illustrated in Figure 3. It is apparent that the assumption of Newtonian behavior leads to a weaker dependence of film thickness on spin speed than is observed experimentally, and one which is independent of polymer concentration in the initial resist. The non-Newtonian model not only gives quantitative predictions of the film thickness, but also generates the correct dependence on spinner speed. The dependence on spinner speed is stronger for the higher concentration solutions. This is attributable to the more prominant non-Newtonian behavior of the resist at higher concentrations. 

The steric layer theory of Vincent, Luckham and Waite (1980) also provides reasonable semi-quantitative predictions of the onset of flocculation. According to this theory, the onset of flocculation marks the entrance into the semi-dilute polymer concentration regime (i.e. V2 = C2 ). Flocculation arises because there is a net decrease in free energy when two particles come together and displace into the bulk solution some of the free polymer molecules that are interpenetrating the stabilizing moieties. Restabilization is said to be associated with the onset of the so-called concentrated polymer regime (i.e. 

Post-polymerization functionalization has also been applied to the synthesis of terpyridine-modified polymers [ 126]. In a recent approach, Schubert and colleagues employed this method to prepare poly(pentafluorostyrene) with terpyridines in the side chains [127]. First, poly(pentafluorostyrene) with a narrow polydispersity index of just 1.08 was synthesized by nitroxide-mediated polymerization. In a second step, this polymer was converted with amine-functionalized terpyridine under microwave heating, selectively substituting the para-fluorines. Addition of iron(II) sulfate to a solution of the terpyridine-functionalized polymer in a mixture of chloroform and methanol leads to gelation at a polymer concentration of 33 g In another work, Schubert and coworkers prepared metal-cross-Iinked polymer networks from linear and tri-arm PEG precursors, both functionalized with terpyridine at their OH-termini [128]. Quantitative functionalization of these precursors was achieved by conversion of the hydroxy-functionalized PEG derivatives with 4-chloro-2,2 6, 2"-terpyridine under basic conditions. However, quantitative cross-linking with iron(II) chloride was not observed in methanol solutions, neither at room temperature nor at elevated temperature, but only a small quantity of cross-linked material precipitated from the solution. This observation was attributed to a strong tendency of the tri-arm PEG to form intramolecular complexes, acting as a chain stopper rather than as a cross-linker. 

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