Polymer volume fraction analysis

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.

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. 

The main aim was to determine the distribution of PEO molecules between the gel and the supernatant fluid at r = 0.1, c = 0.1 M, T = 5°C for M = 18,000 (bridging) and polymer volume fractions in the range between v = 0 and v = 0.12. The corresponding neutron diffraction traces are shown in Figure 12.6a. In comparing these structural analyses with an independent analysis of the concentration of the PEO in the supernatant fluid, we established the following protocol in preparing the samples. 

Analysis of the scattering data yielded information about the structure of the polymer layer at the interface and, in particular, allowed determination of the polymer volume fraction profile as a function of distance from the oil-water interface. The profiles obtained were consistent with the hydrophobic poly (propylene oxide) blocks bound to the surface of the droplet while the hydrophilic poly(ethylene oxide) blocks were largely present as tails. The authors also determined the effect of salt on the conformation of the adsorbed polymer layer. 

The contribution to the interaction parameter from free volume dissimilarity persists down to room temperature and below. It accounts for the dominant positive values of Xs noted above (see Table 3.1). It further explains the observed increase in % with increasing volume fraction of polymer found with some systems the extent of condensation of the solvent is related to the amount of polymer present. The greater is the amount of polymer present, the more will the solvent molecules condense onto the polymer segments, thus increasing the numerical magnitude of Xs- If X does not increase with the polymer volume fraction, as not infrequently happens (e.g. polystyrene in toluene), then specific interactions must provide compensatory effects. Such specific interactions appear at present to be beyond the grasp of any fundamental theoretical analysis. 

However, the morphology of an emulsion or blend depends not only on the discussed above dispersive processes, but also on coalescence observed at low dispersed-phase polymer volume fraction, o 0-005 [121]. Analysis of the steady-state shear coagulation of PVC lattices leads to the critical time [122] ... 

Fig. 13. (A) Transmission nexafs images of a saline-swollen microtomed thin section of an SAP bead that wais surface cross-linked with ethylene glycol diglycidyl ether. The images were recorded at 280, 288.8, and 320 eV, as indicated (B) Quantitative map of the polymer volume fraction derived via SVD from the three images (C) Profiles of the polymer volume fraction and the total sample thickness (water and polymer) across the edge of the SAP bead, derived from the SVD analysis in the indicated region. (Data acquired with the ALS BL7.0 STXM.) Courtesy of G. Mitchell (102).

Studies have shown that it is also important to consider a continuous segment concentration profile from the solid surface to the edge of the brush layer, rather than a simple step concentration profile of height h as implied in the above scaling analysis. For example, the theoretical self-consistent field (SCF) analysis of Milner et al. [75] predicts that, given a SCF-calculated equilibrium brush height h, the polymer volume fraction (p(z) in the brush layer follows a parabolic distribution with respect to the distance z from the surface ... 

In Chapter 3 of this book, L. Brannon-Peppas offered a thorough analysis of the preparation and structure of hydrogels. In that chapter. It was noted that the number average molecular weight between crosslinks. Me, and the volume equilibrium swelling ratio, Q, or its reciprocal parameter equilibrium polymer volume fraction, x>2,s. are important parameters for the characterization of the network. It is then necessary to review theories and equations used for calculation of such parameters. 

Recently efficient techniques were developed to simulate and analyze polymer mixtures with Nb/Na = k, k > I being an integer. Going beyond meanfield theory, an essential point of asymmetric systems is the coupling between fluctuations of the volume fraction (j) and the energy density u. This coupling may obscure the analysis of critical behavior in terms of the power laws, Eq. (7). However, it turns out that one can construct suitable linear combinations of ( ) and u that play the role of the order parameter i and energy density in the symmetrical mixture, ... 

The SEM micrographs reveal that the pore size and the volume fraction increases with increasing amount of solvent. This qualitative result is also confirmed by image analysis performed on an average of around 150-250 pores, clearly showing the expected increase of pore size with increasing amount of cyclohexane (Fig. 24). This phenomenon has been observed in any polymer-solvent system studied here. 

A modified Cahn-Hilliard (CH) model [114] is used for the theoretical analysis of the impact of thermal diffusion on phase separation by taking into account an inhomogeneous temperature distribution, which couples to a concentration variation via the Soret effect. The Flory-Huggins model is used for the free energy of binary polymer-mixtures. The composition is naturally measured in terms of volume fraction 0 of a component A, which can be related to the weight fraction c by... 

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