Free volume PALS

The sizes and concentration of the free-volume cells in a polyimide film can be measured by PALS. The positrons injected into polymeric material combine with electrons to form positroniums. The lifetime (nanoseconds) of the trapped positronium in the film is related to the free-volume radius (few angstroms) and the free-volume fraction in the polyimide can be calculated.136 This technique allows a calculation of the dielectric constant in good agreement with the experimental value.137 An interesting correlation was found between the lifetime of the positronium and the diffusion coefficient of gas in polyimide.138,139 High permeabilities are associated with high intensities and long lifetime for positron annihilation. 

Positron annihilation lifetime spectroscopy (PALS) provides a method for studying changes in free volume and defect concentration in polymers and other materials [1,2]. A positron can either annihilate as a free positron with an electron in the material or capture an electron from the material and form a bound state, called a positronium atom. Pnra-positroniums (p-Ps), in which the spins of the positron and the electron are anti-parallel, have a mean lifetime of 0.125 ns. Ortho-positroniums (o-Ps), in which the spins of the two particles are parallel, have a mean lifteime of 142 ns in vacuum. In polymers find other condensed matter, the lifetime of o-Ps is shortened to 1-5 ns because of pick-off of the positron by electrons of antiparallel spin in the surrounding medium. 

Independent of whether or not a well-defined crossover temperature can be observed in NS data above Tg, it has been well known for a considerable time that on heating a glass from low temperatures a strong decrease of the Debye-Waller factor, respectively Mossbauer-Lamb factor, is observed close to Tg [360,361], and more recent studies have confirmed this observation [147,148,233]. Thus, in addition to contributions from harmonic dynamics, an anomalously strong delocalization of the molecules sets in around Tg due to some very fast precursor of the a-process and increases the mean square displacement. Regarding the free volume as probed by positron annihilation lifetime spectroscopy (PALS), for example, qualitatively similar results were reported [362-364]. 

The affect of polymer stereoregularity in the chains on the PAL data has also been studied. Hamielec et al [56] found what appears to be an increased lifetime (hole size) with increased randomness of the chain configuration in a series of polyvinlychloride (PVC) polymers, despite the large degree of scatter in the sample (probably due to the fact that a series of commercially available products were used.). They however found little correlation with tacticity in polypropylene. More recently a PAL study on a series of very well characterized polystyrene and poly(p-methlystyrene) samples of differing tacticity [57] was performed. In addition to finding that the polystyrene samples have smaller free volume holes than the poly(p-methylstyrene) samples, they found that the syndiotactic samples had broader hole distributions than the attactic samples. 

The diffusion of gases through a polymer matrix is determined by the mobility of gas molecules through the matrix. The diffusion coefficient is therefore, at least partially determined by the free volume size of the polymer. It has been shown, for example, that there is a correlation between the free volume measured by PAL and the diffusivity of carbon dioxide in a seriers of polycarbonates [58], In a study of poly (trimethylsilyl propyne) (PTMSP), which has an extremely high gas permeability and diffusion coefficients, it was found that the lifetime data could be resolved into four components [59]. The longest lifetime component (T4) had a lifetime of... 

Hsieh et al [62] found that for a range of thermotropic liquid crystalline polymers, the greater the free volume measured by PAL the greater the chain mobility at Tg and the higher the value of tan S (damping strength) measured by dynamic mechanical analysis. 

The effects of plasticizers has also been studied by PAL [64, 65]. The addition of a plasticizer to polymers generally has the effect of lowering the Tg, however in some cases an anti-plasticization can occur. Borek et al [65] have shown that the fraction of free volume in PVC polymers could be fit with a fourth order polynomial as a function of plasticizer concentration. The decrease in th Tg with increasing amount of plasticizer is attributed to this increase in the free volume of the polymers. 

PAL has been used to study both miscible and immiscible polymer blends [41, 61, 67-70], PAL results have shown both positive and negative deviations from additivity of free volume with blend composition. In the case of multi phase systems, PAL data analysis is complicated by the fact that Ps may diffuse between the different blend phases. 

For DBES data three main factors contribute to the S parameter in polymers (1) free-volume content, (2) free-volume size, and (3) chemical composition. First, larger free-volume content contributes to a larger S value. DBES measures radiation near 511 keV where a major contribution comes from p-Ps. This p-Ps contribution is only 1/3 the o-Ps intensity as that in I3 of PAL data. Second, when p-Ps is localized in a defect with a dimension fix, the momentum Ap has a dispersion according to the Heisenburg uncertainty principle AxAp > h/4n. The S parameter from DBES spectra is a direct measure of the quantity of momentum dispersion. In a larger size hole where Ps is localized, there will be a larger S parameter due to smaller momentum uncertainty. Therefore, in a system with defects or voids, such as polymers, the S parameter is a qualitative measure of the defect size and defect concentration. The value of the S parameter also depends on the momentum of the valence electrons, which annihilate with the positrons. The absolute value of the S parameter therefore, may differ from polymer to polymer. Third, the S parameter depends on the electron momentum of the elements. As the atomic number of the elements increases, the electron momentum increases, and thus the S parameter decreases. Fortunately, in chemicals of... 

The larger free volume and distribution also indicates a larger fraction of free volume near the surface than in the bulk. According to the WFL theory [43], a larger free volume leads to a lower Tg. Indeed a significant Tg depression (as much as 70 °C) has been reported in the surface of polystyrene by using PAL method [10]. Other studies of polymer surfaces have shown that the size of the free volume holes near the surface of polyethylene [47] and polypropylene [48] are larger than the bulk. 

Figure 11.18 Correlations between the loss of free-volume fraction (ffv) from PAL vs mean roughness measured by AFM [30].

Pore dimensions can be determined also by positron annihilation lifetime spectroscopy (PALS). Positron in a solid can create a bound structure with an electron, called positronium (Ps). Its triplet state (ortho-Ps) has an intrinsic lifetime in vacuum 142 ns, but when trapped in a free volume, like a pore, it lives shorter. The o-Ps lifetime is... 

As aging tends to lead to changes in the packing density of the system, PALS was used to study the blends as it will provide qualitative estimate of the free volume in the system. The stress relaxation results were confirmed qualitatively using PALS. It was found that PS/PPE and PS/PVME blends were less dense than PS, while PMMA/PEG was denser than PMMA, thereby making chain relaxation easier in the former and more difficult in the latter. 

Positron annihilation lifetime spectroscopy (PALS) allows the quantitative investigation of the polymer free volume [1, 2]. Additionally, the PALS beam technique makes a direct depth resolution possible, by implanting the probe - the positron - within a definite sample depth interval depending on the positron kinetic energy [3]. It is one of the very few nondestructive techniques for investi-... 

PALS is a well-established technique for studying the free volume of polymers... 

The results of the PALS investigations of the aging behavior of thin epoxy films are presented here. The decisive parameters of the PALS analysis for polymers are the formation probability lo.ps of ortho-positronium and its average lifetime To-ps- While lo-Ps predominantly represents the effectivity of the electron acceptor groups in the polymer, Tq.ps is directly correlated with the sizes of the free-volume voids. 

During the last few years, attention shifted toward the glassy state, where the performance depends on the extent of freezing the free-volume parameter. The physical aging of vitreous multicomponent systems was interpreted successfully by means of the S-S equation of state. These aspects, along with applications of the S-S equation of state to surface tension and to PALS, are discussed in Chapter 8 and Chapters 10-12, respectively. 

In any event, independent of the model of Ps formation, the aforementioned trapping mechanism, based on the Pauli principle (exchange forces), explains well the capability of Ps to probe free-volume sites in polymers. In this connection, PALS measurements in poly(ether ether ketone) (PEEK) [Nakanishi and Jean, 1989], prepared with different degrees of crystallinity, have shown that o-Ps intensity is correlated linearly with the percentage of amorphous phase of the sample. The extrapolated value of the intensity at 100% crystallinity is zero, which strongly supports the idea that Ps is trapped only in the free volume. 

---