Free volume and transport properties

Nagel, C., Giinter-Schade, K., Fritsch, D., Strunsky, T., and Faupel, F., Free volume and transport properties in highly selective polymer membranes. Macromolecules, 35, IPflX-lffn... 

Free Volume and Transport Properties of Barrier and Membrane Polymers... 

Figures 6b and 6c present the effect of free volume on methane difrusivity and permeability, respectively. Over the range of free volume explored (0.1 FFV. 16), diffusivity decreases by roughly two orders of magnitude as free volume decreases. The change in permeability with increasing free volume essentially mirrors that of diffusivity, indicating that the most important effect of free volume on transport properties in this family of materials is the impact of free volume on diffusion coefficients.

Volume Theory for Transport Properties and New Trends About the Relationship between Free Volume and Equations of State. 

N.A. Plate and Y.P. Yampol skii, Relationship between Structure and Transport Properties for High Free Volume Polymeric Materials, in Polymeric Gas Separation Membranes, D.R. Paul and Y.P. Yampol skii (eds), CRC Press, Boca Raton, FL, pp. 155-208 (1994). 

Many of the thermodynamic and transport properties of liquid water can be qualitatively understood if attention is focused on the statistical properties of the hydrogen bond network [9]. As an example, let us observe the temperature dependence of density and entropy. As temperature decreases, the number of intact bonds increases and the coordination number is closer to the ideal value 4. Because of the large free volume available the temperature decrease is associated with an increase of the local molecular volume. This effect superimposes of course to the classical anharmonic effects which dominate at high temperature, when the number of intact bonds is smaller. The consequence of both effects is a maximum on the temperature dependence of the liquid density. This maximum is actually at 4°C for normal water and 11 °C for heavy water. Such a large isotopic effect can also be understood because the larger mass of the deuterium makes the hydrogen bonds more stable. 

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. 

Molecular dynamics (MD) simulation studies were carried out to get deeper insight into the free volume structure and its spatial arrangement in the polymers, and into the correlation between the free volume and the transport properties of the materials. It is of crucial importance that MD simulations provide not only local characteristics of the free volume such as FVE size and FVE size distribution, but also information on its topology, enabling a complete visualization in 3D [1,27,32]. 

It is known that glassy polymer membranes can have a considerable size-sieving character, reflected mainly in the diffusive term of the transport equation. Many studies have therefore attempted to correlate the diffusion coefficient and the membrane permeability with the size of the penetrant molecules, for instance expressed in terms of the kinetic diameter, Lennard-Jones diameter or critical volume [40]. Since the transport takes place through the available free volume in the material, a correlation between the free volume fraction and transport properties should also exist. Through the years, authors have proposed different equations to correlate transport and FFV, starting with the historical model of Cohen and Turnbull for self diffusion [41], later adapted by Fujita for polymer systans [42]. Park and Paul adopted a somewhat simpler form of this equation to correlate the permeability coefficient with fractional free volume [43] ... 

N. Plate, Y. P. Yampol skii, Relationship between stmcture and transport properties for high free volume polymeric materials, Boca Raton CRC Press (1994). 

J. Qiu, J.-M. Zheng, K.-V. Peinemann, Gas transport properties of poly(trimethylsilylpropyne) and ethylcellulose filled with different molecular weight trimethylsilylsaccharides impact on fractional free volume and chain mobihty. Macromolecules, 40, 3213-3222 (2007). 

SCFs often have lower density (or, equivalently, higher specific volume) than liquids. Hence, they can be more effective than liquids at increasing the polymer free volume and enhancing transport properties. 

The factors, which influence the permeability or mass transport, are the following chemical composition of the polymer matrix and its free volume. In fact, crystallinity, molecular orientation, and physical aging in turn influence the free volume of a polymer matrix. In addition, porosity and voids, like free volume, offer sites into which molecules can absorb and are far less of a barrier to transport than solid polymer. Temperature also affects permeability and diffusion properties of small molecules in polymers. With increased temperature, the mobility of molecular chains (in polymer) increases and thermal expansion leads to reduced density therefore, the free volume in the system will increase. External tensile stress applied is expected to increase free volume and open up internal voids or crazes, providing additional sites into which molecules can absorb. Of course, there may be unquantified internal residual stresses, arising from processing, present in the polymers. It is well established that the properties of materials... 

Diffusion describes the random motion that transports matter from one part of a system at high concentration to another at low concentration. Mathematically, this process relates the mass-transfer rate of a substance through unit area to the concentration gradient normal to the section by a proportionality constant, D (cmVsec), also referred to as the diffusion coefficient (Crank, 1975). Factors that affect protein diffusion in polymers include properties that alter polymer chain segmental mobility (degree of crystallinity, chain stiffness, degree of cross-linking), deformations that alter the free volume, and factors that can immobilize or denature the protein (Rabek,1980). 

The effect of copolymer composition on free volume and gas permeability of PECT copolymers as well as PET and PCT homopolymers was studied by Hill et al. (97). The free volume was studied by positron annihilation lifetime spectroscopy (PALS) in order to determine the relative size and concentration of free volume cavities in the copolymers. The logarithm of the permeability to oxygen and carbon dioxide increased linearly with the %mol content of 1,4-CHDM units in the copolymer, which was in agreement with the free volume cavity size and relative concentration observed by PALS measurements. Light et al. (98) studied the effect of sub-T relaxations on the gas transport properties of PET, PCT and PECT polyesters. They observed that modification of PET with 1,4-CHDM increased the magnitude of the p-relaxation, as well as the diffusion and solubility coefficients for oxygen and CO. ... 

Positron annihilation lifetime spectroscopy (PALS) is a more recent tool used to probe free volume and free volume distribution in polymers (38, 59). PALS uses orthoPositronium (oPs) as a probe of free volume in the polymer matrix. oPs resides in regions of reduced electron density, such as free volume elements between and along chains and at chain ends (38). The lifetime of oPs in a polymer matrix reflects the mean size of free volume elements accessible to oPs. The intensity of oPs annihilations in a polymer sample reflects the concentration of accessible free volume elements. The oPs lifetime in a polymer sample is finite (on the order of several nanoseconds), so PALS probes the availability of free volume elements on nanosecond timescales (40). The minimum free volume cavity diameter required by oPs for localization is 3.SA (41), which is equal to the kinetic diameter of methane (42). Thus, PALS probes the dynamic availability of free volume elements similar in size to those important for gas separations applications. Several recent studies demonstrate the strong correlation of PALS parameters and transport properties in polymers (34, 38, 43-45). The chapter by Yampol skii and Shantarovich in this book describes the use of PALS to characterize free volume distribution in membrane polymers. 

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