Polymer volume distribution

Any polymer contains some inner free space free volume distributed in a dynamic manner between its molecular chains (see Section 23.2). When it is exposed to a fluid (liquid or gas) the physical possibility exists for fluid absorption by the polymer, if the fluid molecules or atoms are small enough to fit into local regions of this distributed space during kinetic movements. As this happens, subsequent kinetic chain motion must allow for the newly absorbed fluid molecules and, hence, the polymer s overall volume will adjust accordingly this action will coincide with the formation of more free space around these fluid molecules—so the polymer will swell a little. This process will be continued until an equilibrium is reached ( equilibrium swelling ), by which time the extent of swelling can be considerable. The amount of fluid taken up and the rate at which this happens are both important, and are discussed in this and following sections. 

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... 

Advanced computational models are also developed to understand the formation of polymer microstructure and polymer morphology. Nonuniform compositional distribution in olefin copolymers can affect the chain solubility of highly crystalline polymers. When such compositional nonuniformity is present, hydrodynamic volume distribution measured by size exclusion chromatography does not match the exact copolymer molecular weight distribution. Therefore, it is necessary to calculate the hydrodynamic volume distribution from a copolymer kinetic model and to relate it to the copolymer molecular weight distribution. The finite molecular weight moment techniques that were developed for free radical homo- and co-polymerization processes can be used for such calculations [1,14,15]. 

VOLUME DISTRIBUTION OF POLYMERS AND PLASTICS (Production Volume >1,000,000 Lbs/Yr)... 

Santora BP, Gagne MR, Moloy KG, Radu NS. Porogen and cross-linking effects on the surface area, pore volume distribution, and morphology of macroporous polymers obtained by bulk polymerization. Macromolecules 2001 34 658-661. 

Boss, et al., fitted Gq. (17) to their data vs. vdi enabling them to determine fp and D . At solvent concentration approaching vdiI = 0.95, the data revealed an enhancement above the value predicted by Eq. (17) as fitted to the lower-concentration data. The authors argued that under these circumstances macroscopic inhomogeneities in concentration (and hence in the free-volume distribution) should exist and enhance the diffusivity. Above v > 0.99 the polymer coils no longer overlapped substantially, depriving the solvent molecules of a set of obstacles fixed with respect to the laboratory, and solvent diffusion became related principally to intrinsic viscosity. 

From the point of view of the ideas discussed above concerning the variability on the free-volume fraction at Tg, even for the same modes of molecular motion in different polymers, there is great interest in some new concepts about the free-volume distribution, in the system, first proposed in 24. The starting point is the suggestion that all molecular motions, like transfer phenomena, can take place only when the size of the voids or holes in the system exceeds a critical value v. This critical volume appears as a result of redistribution of the free-volume within the system. 

Kiparissides, et al. (8) developed mathematical models of two levels of sophistication for the vinyl acetate system a comprehensive model that solved for the age distribution function of polymer particles and a simplified model which solved a series of differential equations assuming discrete periods of particle nucleation. In practice, the simplified model adequately describes the physical process in that particle generation generally occurs in discrete intervals of time and these generation periods are short in duration when compared with operation time of the system. The simplified model is expanded here for a series of m reactors. The total property balances for number of particles, polymer volume, conversion, and area of particles, are written as ... 

Most important macroscopic transport properties (i.e., permeabilities, solubilities, constants of diffusion) of polymer-based membranes have their foundation in microscopic features (e.g., free-volume distribution, segmental dynamics, distribution of polar groups, etc.) which are not sufficiently accessible to experimental characterization. Here, the simulation of reasonably equilibrated and validated atomistic models provides great opportunities to gain a deeper insight into these microscopic features that in turn will help to develop more knowledge-based approaches in membrane development. 

While in rubbery polymers differences in the segmental mobility can be more important than differences in the free-volume distribution for glassy polymers often certain basic correlations can be found between the permeability of small molecules and free-volume distribution. Other important factors are the molecular mobility of chain segments and the local chemical composition. 

Makrolon has a mean free pore-volume of 0.1 nm3 and the width at half-height of the corresponding distribution is 0.04 nm3 [22], The polymer layer reacts to the exposition of the analyte molecules by swelling and by changes of the refractive index. Due to the pore-volume distribution (see Fig. 1), the interaction kinetic depends on the molecule size [23], The analytes used in this work are methanol with a size smaller, ethanol with a size almost equal to and 1-propanol with a size bigger than the mean free pore-volume. 

Fig. 1 Pore-volume distribution of the ultramicroporous polymer and the accessible volume for analytes in dependence of the molecule volume (a). Scheme of interaction between pores and different sized molecules for smaller analytes more pores are accessible and the interaction between molecules and polymer backbone is weaker (b)...

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. 

A number of techniques have been employed to examine free volume properties of polymers. These include small angle x-ray scattering and neutron diffraction that have been used to determine denisty fluctuations to deduce free volume size distributions [4-7]. Photochromic labelling techniques by site specific probes have been developed to monitor the rate of photoisomerizations of the probes and from this deduce free volume distributions [8-11]. Additional probing methods used to probe voids and defects in materials such as scanning tunneling microscopy (STM) and... 

Kristiak, J., Kristiakova, K., Sausa, O., Bandzuch, P., Bartos, J. (1993) Temperature dependence of free volume distributions in polymers studied by position lifetime spectroscopy . Journal De Physique IV. 265. 

Wang, C.L., Hirata, T., Maurer, F.H.J., Eldrup, M., Pedersen, N. J. (1998) Free- volume distribution and positronium formation in amorphous polymers temperature and positron-irradiation-time dependence . J. Chem. Phys. 108(11), 4654. 

Deng, Q., Zandie H.G., Jean, Y.C. (1992) Free volume distribution of an epoxy polymer probed by positron annihilation by positron annihilation spectroscopy . Macromolecules. 25, 1090. 

Let N cylindrical rods be situated in volume V, their concentration being c = N/V. The polymer volume fraction in the solution is then - jrpcd V4. Let us introduce the orientational distribution function for the rods f(u) cf(u)df2 is the number of rods per unit volume, which have the orientations within the small spatial angle dQ around the unit vector u. It is dear that in the isotropic state f(u) = const = l/4a. In the liquid-crystalline state the function f(u) has two maxima along the anisotropy axis. 

Fig. 8. (a) Spatial distribution of the polymer volume fraction if in the large globule, d,rpolymer volume fraction in the middle of the globule (b) field of orientations of the director of mesophase... 

Figures 7 and 8 show typical particle size distributions for vinyl acetate emulsions produced in a single CSTR. A large number of particles,are quite small with 80 to 90% being less than 500 A in diameter. The large particles, though fewer in number, account for most of the polymer mass as shown by the cumulative volume distributions. Data are also presented on Figures 7 and 8 for the number of particles based on diameter measurements (N ), the average number of free radicals per particle, and the steady state conversion.

Figure 3-22. Cumulative pore volume distribution of different HPLC columns indicating monomodal pore size distribution for polymer monolith and bimodal distributions for both packed particulate silica and silica monolith columns. (Reprinted from reference 90, with permission.)...

Reorientation dynamics of molecular tracers in polymers is not only important for the understanding of slow relaxation phenomena in glassy polymers but plays also a critical role in practical problems such as molecular design of nonlinear optical materials with long-term stability based on dyes/polymers complexes. We show here the reorientation dynamics of molecular tracers in glassy polymers obtained by the armealing-after-irradiation method described below. These experimental results are compared to the local relaxation processes of glassy polymers obtained by the already established measurement techniques such as dielectric relaxation and solid state NMR. Finally, the molecular interpretation of the relaxation of free-volume distribution in polymers will be discussed. 

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