Density of polymer

Mc - Molecular weight of effective chains pp = Density of polymer (g/cm3)... 

Catalysts Temperature of polymerization (°C) Density of polymer Mn Number of methyls per 1000 C atoms Number of vinyls per 1000 C atoms Trans, internal double bonds per 1000 C atoms Number of methyls per chain Number of terminal double bonds per chain... 

At high concentrations the expansion factor approaches unity and this convergence can be used to define cWhen the concentration c is exceeded, the density of polymer segments becomes nearly uniform in solution. In this case we could estimate c as 0.11 gem-3. At concentra-... 

Non-dilute solutions also allow for theoretical descriptions based on scaling theory [16, 21]. When the number of polymer chains in the solution is high enough, the different chains overlap. At the overlapping concentration c , the long-scale density of polymer beads becomes uniform over the solution. Consequently c can be evaluated as... 

The introduction of branching in the Kirkwood formula and the KR calculations can be accomplished in a relatively easy way if Gaussian statistics corresponding to ideal chains are maintained. This description cannot, however, be very accurate in molecules with centers of high functionality because of the presence of cores with a high density of polymer units, which profoundly perturbs the internal distribution of distances. Stockmayer and Fixman [81 ] employed the Kirwood formula and Gaussian statistics to calculate h in the case of uniform stars, obtaining an analytical formula. They also performed a KR evaluation of the viscosity and proposed that g could be evaluated from the approximation... 

Qiu, D.Q. and Prentice, P., Influence of Pressure on Bulk Density of Polymer Solid Granules at Different Temperatures, Adv. Polym. TechnoL, 17, 23 (1998)... 

The densities of polymers can be determined by the pyknometer technique or by the flotation method. In the pyknometer technique the liquid volume displaced by the polymer sample is determined by weighing. Most polymers have a density larger than that of water, which can, therefore, be used as the liquid. Polymers in the form of powders or pressed discs tend to adsorb or occlude air bubbles, which can lead to serious errors. This can be largely prevented by careful degassing of the pyknometer and polymer sample under vacuum before filling with liquid, and/or by addition of a small amount (0.1%) of commercial detergent to lower the surface tension of the water. 

In order to calculate polymer/filler interaction, or more exactly the reversible work of adhesion characterizing it, the surface tension of the polymer must also be known. This quantity is usually determined by contact angle measurements or occasionally the pendant drop method is used. The former method is based on the Young, Dupre and Eowkes equations (Eqs. 21,8, and 10), but the result is influenced by the surface quality of the substrate. Moreover, the surface (structure, orientation, density) of polymers usually differs from the bulk, which might bias the results. Accuracy of the technique maybe increased by using two or more liquids for the measurements. The use of the pendant drop method is limited due to technical problems (long time to reach equilibrium, stability of the polymer, evaluation problems etc.). Occasionally IGC is also used for the characterization of polymers [30]. 

When plasticized polymers are in contact with the mother polymers, plasticizers are likely to migrate to mother polymers and the extent of their migration depends on a number of factors such as polymer-plasticizer system, polarity of polymer and plasticizer, crosslink density of polymer, molecular weight of plasticizer etc. 

As mentioned above, the grafting to technique enables in a one-pot reaction the synthesis of Au NPs stabilized by sulfur-containing polymers, which bear functional groups such as dithioester, trithioester, thiol, thioether and disulfide at the end of a polymer chain or in the middle. This method leads to nanoparticles similar to those obtained by the Brust-Schiffrin method in which alkanethiol-protected Au NPs of small size are obtained. This grafting to technique leads to very stable nanomaterials that also present a high surface graft density of polymer brush on the Au NP surface. 

The viscoelastic properties of solutions of linear and 4-armed star polybutadienes were studied by Osaki and co-workers (117), who compared the storage and loss shear moduli extrapolated to zero concentration with theoretical values. The results for the branched polymer could be accounted for well in terms of the Zimm and Kilb theory (34) a lower value of the hydrodynamic interaction parameter was indicated for the branched polymer than for the linear one, which may be associated with the higher density of polymer segments in the former. 

Comparison between curves NW(P) obtained for different charge densities of polymer networks (curves 1, 2, 3 in Fig. 32) indicates that the value of Nw increases with decreasing charge density of the gel. 

---