Free volume distribution

The details of the spectrophotometric analysis and the interpretation of the results have been published recently [27]. The quantitative results of the cumulative free volume distribution, i.e. the relative trans-cis isomerization of the films compared to the solution are listed in Table 4.2 as a function of the probe size. 

The size of the free volume elements is in the range of about 250-560in Hyflon AD60X and ca. 280-640 in Hyflon AD80X. This means that, if we assume a spherical 

---

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. 

To fully understand the anomalous dynamics of an attractive colloidal fluid from a free-volume perspective, one must consider two effects of attractions on free volumes.75 First, attractions increase the average local space available to the particles and render the free-volume distribution more inhomogeneous than when no attractions exist. These changes act to increase the mobility of the fluid. Second, strong attractions also lead to long-lived... 

Model for the Free-Volume Distributions of Equilibrium Fluids. 

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. 

We believe that, as the very definition of free-volume characterizes the state of ordering in the system (especially for the cases when we consider the free-volume distribution), it may be preferable to apply the thermodynamic description of the processes at glass temperature. 

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. 

Permeability of Small Molecules and Free-Volume Distribution... 

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. 

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. 

Shanarovich, V.P., Azamatova, Z.K., Novikov, Y.A., Yampolskii, Y.P. (1998) Free-volume distribution of high permeability membrane materials . Macromolecules, 31, 3963. 

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. 

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. 

These examples and investigations on azobenzene moieties in polymers show that the photochromic behavior is mainly Gontrolled by the free volume distribution around the chromophore. Tb obtain LBK films in which azobenzene moieties can undergo photoisomerization, therefore, the free volume around the azobenzene chromophore must be controlled precisely to allow for the molecular rearrangement inherent in the reversible tran to cis photo-isomerization. This is possible by (1) mixing with other amphiphiles, (2) adjusting the architecture of the amphiphile, or (3) attaching the chromophore to a polymer either by coulomb interaction or covalently. 

Rigby, D., Roe, R.J. Molecular dynamics simulation of polymer liquid and glass. 4. Free volume distribution. Macromolecules 23(26), 5312-5319 (1990)... 

The main difference between solid-state reactions and those in solution is that of freedom of molecular motion (1-3) due to restriction of mobility of reactants in solids. Another important feature is the heterogeneous progress of reactions (3,4) frequently observed in solid states due to the microscopically heterogeneous states of aggregation or free volume distribution of the reaction media. In the case of poly(methyl methacrylate) (PMMA), which is an organic glass and is usually regarded as an inert matrix for photophysical and photochemical processes, a marked deviation from... 

On the basis of the low compressibilities and the average high packing densities, the protein interior is often considered as a solidlike material with little free volume. However when one considers the free volume distribution, proteins look more like liquids and glasses [30]. The free volume is often called cavities, voids or pockets. Their role in the volume changes of protein reactions or interactions was suggested by Silva and Weber [31]. A recent review paper emphasizes the similarities between the role of hydration and cavities in protein-protein interactions and protein unfolding [32]. 

Photophysical and photochemical processes in polymer solids are extremely important in that they relate directly to the functions of photoresists and other molecular functional devices. These processes are influenced significantly by the molecular structure of the polymer matrix and its motion. As already discussed in Section 2.1.3, the reactivity of functional groups in polymer solids changes markedly at the glass transition temperature (Tg) of the matrix. Their reactivity is also affected by the / transition temperature, Tp, which corresponds to the relaxation of local motion modes of the main chain and by Ty, the temperature corresponding to the onset of side chain rotation. These transition temperatures can be detected also by other experimental techniques, such as dynamic viscoelasticity measurements, dielectric dispersion, and NMR spectroscopy. The values obtained depend on the frequency of the measurement. Since photochemical and photophysical parameters are measures of the motion of a polymer chain, they provide means to estimate experimentally the values of Tp and Tr. In homogeneous solids, reactions are related to the free volume distribution. This important theoretical parameter can be discussed on the basis of photophysical processes. 

Free volume distribution in a polymer matrix, Fluctuation of the local free volume and... 

---