Polymer concentration, relationship between

Because of its simplicity, a particularly important method for determining molar masses is the measurement of the intrinsic viscosity [ j] for a polymer solution. This quantity is defined as the limit of ( j — s)/( %) as the concentration c of the solution tends to zero, where rj and re the viscosities of the solution and of the pure solvent, respectively. For a mono-disperse polymer the relationship between [ ] and the molar mass... 

The depolymerizing effect of ultrasound is more pronounced for hi er molecular weights of the polymer. This relationship between degradation rate and chain length has been found by all investigators. The rate of degradation depends mainly on the duration of the treatment, on the concentration of the. solution, tm... 

Viscosity—Concentration Relationship for Dilute Dispersions. The viscosities of dilute dispersions have received considerable theoretical and experimental treatment, partly because of the similarity between polymer solutions and small particle dispersions at low concentration. Nondeformable spherical particles are usually assumed in the cases of molecules and particles. The key viscosity quantity for dispersions is the relative viscosity or viscosity ratio,... 

Decrease hinder viscosity. Lower hinder concentration. Change hinder. Decrease any diluents and polymers which act as thickeners. Raise temperature for processes without simultaneous drying. Lower temperature for processes with simultaneous drying since hinder concentration will decrease due to increased hqiiid loading. This effect generally offsets inverse relationship between viscosity and temperature. 

This equation is not particularly useful in practice, since it is difficult to quantify the relationship between concentration and ac tivity. The Floiy-Huggins theory does not work well with the cross-linked semi-ciystaUine polymers that comprise an important class of pervaporation membranes. Neel (in Noble and Stern, op. cit., pp. 169-176) reviews modifications of the Stefan-Maxwell approach and other equations of state appropriate for the process. 

Fig. 14.2 Relationship between the logarithm of the resistance of D and / Aims of a penta-erythritol alkyd paint, containing 6-1% iron oxide by volume, and the concentration of the potassium chloride solutions in which they were immersed (courtesy Bril. Polym. J., 3, 41...

The combination of Equations (2) and (3) actually predicts a linear relationship between ln(r) and (p. However, according to the Ogston s model, for a homogeneous gel = kkcC, where is the radius of the polymer chain and c is the polymer chain concentration and a linear relationship is expected between ln(r) and c, too. Similarly, the combination of Equations (2) and (4) predicts a linear relationship also between ln(D) and both (p and c. 

Table 5.5 shows the main characteristics of UV spectrophotometry as applied to polymer/additive analysis. Growing interest in automatic sample processing looks upon spectrophotometry as a convenient detection technique due to the relatively low cost of the equipment and easy and cheap maintenance. The main advantage of UV/VIS spectroscopy is its extreme sensitivity, which permits typical absorption detection limits in solution of 10-5 M (conventional transmission) to 10 7 M (photoacoustic). The use of low concentrations of substrates gives relatively ideal solutions [20]. As UV/VIS spectra of analytes in solution show little fine structure, the technique is of relatively low diagnostic value on the other hand, it is one of the most widely used for quantitative analysis. Absorption of UV/VIS light is quantitatively highly accurate. The simple linear relationship between... 

The viscosity of the oxidized polymer (VIII) was determined using DMF as a solvent. Chloroform was not a good solvent because it was too volatile and resulted in poor reproducibility. The reduced viscosities are plotted against polymer concentration (Figure 6). Polymer VIII behaved like a polyelectrolyte, the reduced viscosities increased sharply on dilution in a salt free solution. The addition of 0.01 M KBr did not completely suppress the loss of mobile ions however, at 0.03 M KBr addition a linear relationship between the reduced viscosities and concentration was established. 

Note that in the component mass balance the kinetic rate laws relating reaction rate to species concentrations become important and must be specified. As with the total mass balance, the specific form of each term will vary from one mass transfer problem to the next. A complete description of the behavior of a system with n components includes a total mass balance and n - 1 component mass balances, since the total mass balance is the sum of the individual component mass balances. The solution of this set of equations provides relationships between the dependent variables (usually masses or concentrations) and the independent variables (usually time and/or spatial position) in the particular problem. Further manipulation of the results may also be necessary, since the natural dependent variable in the problem is not always of the greatest interest. For example, in describing drug diffusion in polymer membranes, the concentration of the drug within the membrane is the natural dependent variable, while the cumulative mass transported across the membrane is often of greater interest and can be derived from the concentration. 

A series of experiments were carried out at varying polymer concentrations to examine the effect of varying nitrile concentration (the nitrile concentration range was 86-258 mM). The relationship between polymer (nitrile) concentration and reaction rate for this system is shown in Figure 3. It shows that increasing the NBR concentration, (increase in the concentration of nitrile functionality) inhibits the catalytic activity of the catalyst i.e. the observed rate constants showed an inverse dependence on nitrile concentration. 

A simple way to disentangle the information is obtained when the relationship between sensor responses and concentrations of analytes is linear, such as found in polymer coated TSMR ... 

Within the temperature range from 10 to 40°C, both PAMAM dendrimers in EDA [5] and PPI dendrimers in water [22] showed a linear relationship between In r and /T, in good agreement with the kinetic rate theory of flow [46]. The apparent activation energies of flow (En) were constant and independent of temperature, and it was shown for PAMAM/EDA systems that the dependence of En on solution concentration was linear for all generations examined [5]. This was considerably different from the typical relationships for the solutions of linear and/or randomly branched chain polymers, where a break in the slope of... 

Figures 20.13 and 20.14 describe the effect of dibutyltin dilaurate (DBTDL) on the tensile strength and tensile modulus for the 25/75 LCP/PEN blend fibers at draw ratios of 10 and 20 [13]. As expected, the addition of DBTDL slightly enhances the mechanical properties of the blends up to ca. 500 ppm of DBTDL. The optimum quantity of DBTDL seems to be about 500 ppm at a draw ratio of 20. However, the mechanical properties deteriorate when the concentration of catalyst exceeds this optimum level. From the previous relationships between the rheological properties and the mechanical properties, it can be discerned that the interfacial adhesion and the compatibility between the two phases, PEN and LCP, were enhanced. Hence, DBTDL can be used as a catalyst to achieve reactive compatibility in this blend system. This suggests the possibility of improving the interfacial adhesion between the immiscible polymer blends containing the LCP by reactive extrusion processing with a very short residence time.

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