Polymers volume fraction

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. 

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.

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

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)...

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)...

Fig. 51 Phase diagram for PS-PI diblock copolymer (Mn = 33 kg/mol, 31vol% PS) as function of temperature, T, and polymer volume fraction, cp, for solutions in dioctyl ph-thalate (DOP), di-n-butyl phthalate (DBP), diethyl phthalate (DEP) and M-tetradecane (C14). ( ) ODT (o) OOT ( ) dilute solution critical micelle temperature, cmt. Subscript 1 identifies phase as normal (PS chains reside in minor domains) subscript 2 indicates inverted phases (PS chains located in major domains). Phase boundaries are drawn as guide to eye, except for DOP in which OOT and ODT phase boundaries (solid lines) show previously determined scaling of PS-PI interaction parameter (xodt

Here, u2,r is the polymer volume fraction in the relaxed state, which is defined as the state of the polymer immediately after crosslinking but before swelling. 

Here, a is the elongation ratio of the polymer chains in any direction and (r/j1/2 is the root-mean-square, unperturbed, end-to-end distance of the polymer chains between two neighboring crosslinks (Canal and Peppas, 1989). For isotropically swollen hydrogel, the elongation ratio, a, can be related to the swollen polymer volume fraction, u2,j> using Eq. (11). 

The theta (0) conditions for the homopolymers and the random copolymers were determined in binary mixtures of CCl and CyHw at 25°. The cloud-point titration technique of Elias (5) as moaified by Cornet and van Ballegooijen (6) was employed. The volume fraction of non-solvent at the cloud-point was plotted against the polymer concentration on a semilogarithmic basis and extrapolation to C2 = 1 made by least squares analysis of the straight line plot. Use of concentration rather than polymer volume fraction, as is required theoretically (6, 7 ), produces little error of the extrapolated value since the polymers have densities close to unity. 

If the polymer concentration increases so that the number of high order bead-bead interactions is significant, c>>c =p, (when c is expressed as the polymer volume fraction. Op), the fluctuations in the polymer density becomes small, the system can be treated by mean-field theory, and the ideal model is applicable at all distance ranges, independent of the solvent quaUty and concentration. These systems are denoted as concentrated solutions. A similar description appHes to a theta solvent, but in this case, the chains within the blobs remain pseudoideal so that =N (c/c ) and Rg=N, i.e., the global chain size is always in-... 

For small chains in solution the translational diffusion significantly contributes to the overall decay of Schain(Q>0- Therefore precise knowledge of the centre of mass diffusion is essential. Combing dynamic light scattering (DLS) and NSE revealed effective collective diffusion coefficients. Measurements at different concentrations showed that up to a polymer volume fraction of 10% no concentration dependence could be detected. All data are well below the overlap volume fraction of (p =0.23. Since no -dependence was seen, the data may be directly compared with the Zimm prediction [6] for dilute solutions ... 

N is the total number of monomers, (p the polymer volume fraction and Pi and Pi/2 the form factors of the total copolymer and of the single blocks respectively. 12=Vd=Vh is the excluded volume interaction parameter which relates to the second virial coefficient A2=vN/ 2Mc). 

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