Polymers - Volume

Thus, for a polymer witli N= 10, tire chains are isolated in solution only if tire polymer volume... 

Because of the rotation of the N—N bond, X-500 is considerably more flexible than the polyamides discussed above. A higher polymer volume fraction is required for an anisotropic phase to appear. In solution, the X-500 polymer is not anisotropic at rest but becomes so when sheared. The characteristic viscosity anomaly which occurs at the onset of Hquid crystal formation appears only at higher shear rates for X-500. The critical volume fraction ( ) shifts to lower polymer concentrations under conditions of greater shear (32). The mechanical orientation that is necessary for Hquid crystal formation must occur during the spinning process which enhances the alignment of the macromolecules. 

Polymer Volume resistivity (fl m) Dielectric strength (kV/cm) (J in sample) Dielectric constant Power factor ... 

The purpose of this case study was to develop a simple neural network based model with the ability to predict the solvent activity in different polymer systems. The solvent activities were predicted by an ANN as a function of the binary type and the polymer volume frac-... 

Volume 14 Degradation of Polymers Volume 14A Free-radical Polymerisation... 

If the solvent concentration is very small, as in the case of gas sorption, the polymer volume fraction is near to unity and Eq. (1) becomes ... 

It should he noted that polymer volume fraction is readily converted to conversion. 

Figure 1 Is a flow sheet showing some significant aspects of the Iterative analysis. The first step In the program Is to Input data for about 50 physical, chemical and kinetic properties of the reactants. Each loop of this analysis Is conducted at a specified solution temperature T K. Some of the variables computed In each loop are the monomer conversion, polymer concentration, monomer and polymer volume fractions, effective polymer molecular weight, cumulative number average molecular weight, cumulative weight average molecular weight, solution viscosity, polymerization rate, ratio of polymerization rates between the current and previous steps, the total pressure and the partial pressures of the monomer, the solvent, and the nitrogen.

Theta temperature (Flory temperature or ideal temperature) is the temperature at which, for a given polymer-solvent pair, the polymer exists in its unperturbed dimensions. The theta temperature, , can be determined by colligative property measurements, by determining the second virial coefficient. At theta temperature the second virial coefficient becomes zero. More rapid methods use turbidity and cloud point temperature measurements. In this method, the linearity of the reciprocal cloud point temperature (l/Tcp) against the logarithm of the polymer volume fraction (( )) is observed. Extrapolation to log ( ) = 0 gives the reciprocal theta temperature (Guner and Kara 1998). 

Figure 6 Micrographs of drawn samples of polyethylene films of Mw = 1.5 X 10 and Mn = 2 x 10 crystallized from solutions in decalin, and from the melt (see Reference 1 for details). The initial polymer volume fractions were (a) - 0.005 (b) - 0.02 (c) - 0.1 (d) - 1.

Polymer Particle Balances (PEEK In the case of multiconponent emulsion polymerization, a multivariate distribution of pjarticle propierties in terms of multiple internal coordinates is required in this work, the polymer volume in the piarticle, v (continuous coordinate), and the number of active chains of any type, ni,n2,. .,r n (discrete coordinates), are considered. Therefore... 

Figure 4. Particle polymer volume distrit tions at three times (A S H=33. 33 gr) 1 = 15 min 2=40 min 3=100 min.

Figure 5. Average particle polymer volume (1) and average total particle volume (2) vs. time (A=S=H=33. 33 gr)...

By combining these two expressions, one can relate the diffusion coefficients to the polymer volume fraction ... 

The cross-link density obtained in this manner (p() is referenced to the swollen polymer volume at the time of compression. For comparison to theory or to similar polymers swollen to different extents, the cross-link density can be redefined in terms of moles of chains per unit volume of dry polymer (p,). This conversion is simply... 

E. Ott, H. M. Spurlin, M. W. Grafflin, High Polymers, Volume V, Cellulose, Wiley-Interscience, New York 1955 Part III. 

Fig. 28. NSE spectra in polyethylene melts at 509 K for three different polymer volume fractions in Rouse scaling. Upper diagram 0 = 1, central diagram O = 0.5, lower diagram O = 0.3. The solid lines correspond to a fit with the Ronca model. (Reprinted with permission from [60]. Copyright 1993 American Chemical Society, Washington)...

Particle Size Development. Now that a general total property balance equation has been developed (equation (II-9)), one can use it to obtain ordinary differential equations (ode s) which will describe particle size development. What is needed with equation (II-9) is an expression for dp(t,t)/dt, where p denotes a specific property of the system (e.g. particle size). Such an expression can be written for the rate of change of polymer volume in a particle of a certain class. The analysis, which is general and described in Appendix III, will finally result in a set of ode s for Np(t), Dp(t), Ap(t) and Vp(t). 

The rate of change of polymer volume in a particle of a certain class born at time x, now being at time t, is given by the following expression ... 

Fig. 20 Mean-square end-to-end distance of chains vs. chain length in a 32 (or above)-sized cubic lattice. The data are those of the polymer volume fractions (Hu and Frenkel, unpublished results)...

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