Density and free volume

As the pressure exerted by the tip is localized and limited in time, a shift in Tg due to the applied load is not expected. The sanple is typically scanned over several pm with a scan rate of 0.5 Hz. Assuming values of 3 to 5 nm and 30 to 80 nm for the contact radius and area, the volume affected would be equal to a cylinder that is 5 times the length of the contact radius with a volume, approximately, 450 to 2000 nm (25). In our case, the radius of gyration Rg, is about 5 nm and the volume occupied by one molecule is F = A 3%Rg - 500 nm (27). This leaves only 1 to 4 molecules in the compression zone. Such a limited volume could not have such a dramatic effect over the properties of the polymer. In fact, the contact radius is so small compared to the scan length, the time of permanence over a specific area is only a few milliseconds per cycle. For the rest of the scan cycle, the molecules are unconstrained and can relax. If creep or thermal drift is taken into consideration, it is quite likely that the tip never passes over the same molecule twice. Hence, the pressure exerted by the tip cannot be considered hydrostatic. In addition, the lateral force is measured after the temperature has stabilized (20, 22, 28-30). Therefore, imder these isothermal conditions, the polymer can be considered incon ressible, i.e. it undergoes mechanical deformations but its density and free volume remain constant. 

Many papers have been published regarding the gas permeation properties of polyimides(7-7). Polyimides are very useful polymers for the analysis of relations between gas permeation properties and polymer structure, because many different structures, based on diadds and diamines, can be prepared from existing compounds. We have previously reported relations between free volume or cohesive energy density and gas diffusivity(8,9). In this study, we prepared five kinds of polyimides and explored correlations between gas diffusivity and parameters such as stor e modulus, cohesive energy density, and free volume. These results were con iared with data from previous studies. We dso discuss the merits of the use of each of these parameters to correlate gas permeability properties of different polymers. 

D2/Di would be expected not only to be <1, but also to decrease as the penetrant becomes more strongly sorbed 61). On the other hand, the absolute values of D1 D2 should obviously be affected in a similar manner by factors such as the size or shape of the penetrant molecule and the cohesive energy density or free volume of the polymer matrix. 

In order to fit our structure model to the experimental data, we have to vary the model parameters packing density and cylinder length and examine the effects on the RDDF of our model via the structure factors S and F. One can easily see that an increase of packing density causes the intermolecular distance correlation range to increase because mobility and free volume are reduced. In other words one can calculate a realistic value of packing density (Le. cylinders per volume) from the experimental RDDF (Fig. 18). 

Retention curves for the FEBEX bentonite at constant and free volume conditions for various dry densities and temperatures have been reported by Villar (2002) and Villar Lloret (2002). Figure 1... 

By comparing the sorption and transport behavior of small molecules in an as-cast, disordered, isotropic sample with those of an annealed, ordered, frozen liquid crystalline sample, the effect of axial ordering on sorption and transport properties may be determined unambiguously. Moreover, the influence of axial ordering on other properties (e.g. density, fractional free volume, glass transition temperature, and free volume accessible to orthoPositronium) may be determined. 

It has been observed [24] that for PEG (200g/mol) modified Pebax membrane for CO2 separation the CO2 permeability increased by a factor of about 2 (from 73 to 151 Barrer) and the separation factor CO2/H2 also increased by PEG addition (50 wt.%). This enhancement was attributed to the appearance of additional ethylene oxide (EO) units and free volume increase. Higher content of EO units results in an increase in the solubility of CO2. Later, the total free volume increase and hence the increase of the permeability was demonstrated by measurements of density and by positron annihilation lifetime spectroscopy (PALS) analysis [75]. 

The kinetics of migration of additives from the package into the (food) contents depends on the characteristics of the plastics such as density or free volume, crystallinity, glass transition temperature (Tg), as well as the polarity, molecular mass, and boiling point of the migrant species. Migration rates also depend on the temperature, relative humidity, pH value, and the composition of the food contents (Sajilata et al., 2007). Given the number of variables that can affect the results, reported data must be compared cautiously. 

Positron Annihilation Lifetime Spectroscopy (PALS) provides a measure of free volume holes or voids, free volume, and free volume distribution, at an atomic scale. The technique exploits the fact that the positively charged positron (e" ), the antiparticle to the electron, preferentially samples regions of low positive charge density. When injected in a polymer matrix, thermalized positrons can combine with an electron to form a bound state, known as positronium (Ps). This species can only exist in a void and it rapidly annihilates on contact with the electron cloud of a molecule. For polymer studies using PALS, it is ortho-positronium (oPs, a triplet state) which is of interest. The oPs spin exchanges with electrons of opposite spin on the walls of the cavity and it is annihilated. Thus, the oPs lifetime, 13, gives a measure of the mean free volume cavity radius, whereas the relative intensity of... 

Another possible approach to indirectly characterize the membrane morphology is based on the investigation of the free volume within the matrix. Density measurements [119,120] and positron annihilation lifetime spectroscopy evaluation [47] are common methods. Typically, the comparison between the theoretical density or free volume (calculated by simple additivity rules) and the experimental one can reveal the presence of a good interfacial morphology or the presence of interface voids or clustering formation. Fig. 7.13 shows the influence of filler content on the morphology of poly(trimethylsilyl propyne) (PTMSP)/Ti02 NCMs in terms of the volumetric fraction of interface voids as calculated from a comparison of the expected and measured membrane density [119],... 

The polymer-penetrant interaction also depends on the nonbonded parameters within the polymer matrix. The deficiencies of isotropic united-atom models have already been mentioned. They have been explained [49] by less efficient packing of united-atom chains. Even if the united-atom model provide the correct density or free volume, it nerates a differmt distribution of voliune not occupied than either the anisotropic united-atom model or an all-atom description. The latter pack more efficiendy and leave smaller interstitial caviti For a detailed discussion, see Ref. [49]. 

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