Free volume analysis

Almeida PEE, Vaz WLC, Thompson TE. Lateral diffusion in the liquid phases of dimyriostoylphosphatidylcholine/cholesterol lipid 50. bilayers a free volume analysis. Biochemistry 1992 31 6739-6747. 

Using the adjustable parameters and the suggested model, we compared the experimental diffusion dafa bofh below and above Tg with the predictions of fhe model. Our resulfs are shown in Figure 46.3. Values estimafed wifh free volume analysis are in good agreemenf wifh fhe experimental data. In the... 

Chang KS, Tung CC, Wang KS, Tung KL (2009) Free Volume Analysis and Gas Transport Mechanisms of Aromatic Polyimide Membranes A Molecular Simulation Study). Phys. Chem. B. 113 9821-9830. 

The view that the free volume at the glass transition temperature should be a constant was first introduced by Fox and Flory. The magnitude is reasonable, but no precise significance can be attached to it because the concept of V/ as originally introduced remains operationally undefined. Nevertheless, fractional free volumes thus calculated from the dependence of relaxation times on temperature are consistent with those calculated independently from a free-volume analysis of dependence of relaxation times on pressure (Section D) and dilution with solvent (Chapter 17), and this consistency reinforces the utility of /in equation 32. It should be noted that fg as calculated from equation 39 depends on the time scale of the experiment in which Tg was determined, and the values in the table refer to the usual scale—unspecified, but probably of the order of an hour. If the time scale were varied sufficiently to lower Tg by 8° (the extreme shown in Fig. 11-8),/ would be reduced from 0.025 to 0.022. Other concepts of free volume may lead to somewhat larger numerical values but these are irrelevant to the treatment here. 

After construction of the amorphous cell using the method of Theodorou-Suter ° and geometric free volume analysis of the cell several (four to six) penetrant molecules to improve sampling are inserted at the free volume positions. The cell is further relaxed by 100 ps of a NPT-MD (constant particle number, temperature and pressure) simulation at 1 bar and room temperature before starting a longer (nanoseconds) NVT dynamics. The recorded trajectories of each penetrant gas molecule are analyzed and the diffusion coefficient is determined by means of relation (eqn (1.5)). In Figures 1.2 and 1.3 the packed cell model of polydimethylsiloxane (PDMS) and the trajectory of N2 molecules in the PDMS matrix are reported. The MD simulations show two types of motions of the N2 molecules jumps between cavities and local motion inside cavities. 

These results make sense physically what we must remember is that they follow from an analysis of the vanishing free volume. 

The thermodynamic analysis of conformational and structural transformations in the melt at high pressures34 showed that the free volume and free energy minimum required for hydrostatic compression is attained as a result of the transition of the molecules in the melt into a more extended conformation (gauche —> trans transitions) since the extended molecules ensure a more compact packing of the chains at compression. Chain uncoiling leads to a decrease in their flexibility parameter f with increasing pressure p ... 

Network properties and microscopic structures of various epoxy resins cross-linked by phenolic novolacs were investigated by Suzuki et al.97 Positron annihilation spectroscopy (PAS) was utilized to characterize intermolecular spacing of networks and the results were compared to bulk polymer properties. The lifetimes (t3) and intensities (/3) of the active species (positronium ions) correspond to volume and number of holes which constitute the free volume in the network. Networks cured with flexible epoxies had more holes throughout the temperature range, and the space increased with temperature increases. Glass transition temperatures and thermal expansion coefficients (a) were calculated from plots of t3 versus temperature. The Tgs and thermal expansion coefficients obtained from PAS were lower titan those obtained from thermomechanical analysis. These differences were attributed to micro-Brownian motions determined by PAS versus macroscopic polymer properties determined by thermomechanical analysis. 

Experimental data on nitrogen obtained from spin-lattice relaxation time (Ti) in [71] also show that tj is monotonically reduced with condensation. Furthermore, when a gas turns into a liquid or when a liquid changes to the solid state, no breaks occur (Fig. 1.17). The change in density within the temperature interval under analysis is also shown in Fig. 1.17 for comparison. It cannot be ruled out that condensation of the medium results in increase in rotational relaxation rate primarily due to decrease in free volume. In the rigid sphere model used in [72] for nitrogen, this phenomenon is taken into account by introducing the factor g(ri) into the angular momentum relaxation rate... 

Analysis of mixture models, established techniques, 61 Analysis of styrene suspension polymerization continuous models, 210-211 efficiency, 211,212f,213 free volume theory, 215,217 initiator conversion vs. 

The catalytic test of propane ODH reaction was performed in the 350-600°C range in a quartz fixed bed flow reactor with on line GC analysis. The free volume of the reactor after the catalyst bed was filled with quartz particles to minimize the homogeneous reactions. All the testing set was placed in a thermostat with heated lines to the gas chromatographs at about 100°C to prevent water condensation. The feed gas composition was C3H8/02/N2 = 20/10/70 vol.% at total gas flow 50 cm3 min-1. Catalyst fractions of 0.2-0.315 mm particle size and of 80 mg weight were loaded into the reactor. Before the reaction, the catalyst samples in the reactor were kept under airflow at 600°C for lh. 

Besides temperature and addition of non-solvent, pressure can also be expected to affect the solvency of the dispersion medium for the solvated steric stabilizer. A previous analysis (3) of the effect of an applied pressure indicated that the UCFT should increase as the applied pressure increases, while the LCFT should be relatively insensitive to applied pressure. The purpose of this communication is to examine the UCFT of a nonaqueous dispersion as a function of applied pressure. For dispersions of polymer particles stabilized by polyisobutylene (PIB) and dispersed in 2-methylbutane, it was observed that the UCFT moves to higher temperatures with increasing applied pressure. These results can qualitatively be rationalized by considering the effect of pressure on the free volume dissimilarity contribution to the free energy of close approach of the interacting particles. 

The above example gives us an idea of the difficulties in stating a rigorous kinetic model for the free-radical polymerization of formulations containing polyfunctional monomers. An example of efforts to introduce a mechanistic analysis for this kind of reaction, is the case of (meth)acrylate polymerizations, where Bowman and Peppas (1991) coupled free-volume derived expressions for diffusion-controlled kp and kt values to expressions describing the time-dependent evolution of the free volume. Further work expanded this initial analysis to take into account different possible elemental steps of the kinetic scheme (Anseth and Bowman, 1992/93 Kurdikar and Peppas, 1994 Scott and Peppas, 1999). The analysis of these mechanistic models is beyond our scope. Instead, one example of models that capture the main concepts of a rigorous description, but include phenomenological equations to account for the variation of specific rate constants with conversion, will be discussed. 

Recent work by Zhang and LeBoeuf (in review) examined the effects of the presence of three solvents—water, acetone, and benzene—on the molecular mobility and structural relaxation of a humic acid through DSC analysis combined with molecular dynamics. Again, antiplasticization behavior was observed in two of the three systems (i.e., HA-water and HA-acetone) where solvents present in relatively low concentrations exhibited potential to form hydrogen bonds with the humic acid. Antiplasticization and plasticization behaviors were further interpreted from the perspective of hydrogen bonding analysis and free volume theory. 

In this system the a relaxation can be analyzed by the symmetric equation of Fuoss-Kikwood and a new model which is similar to Havriliak- Negami equation used in the analysis of dielectric spectroscopy. According to the Tg values calculated for these systems, the free volume can be appropriately described by the free volume theory. The analysis of these families of poly(methacrylate)s allow to understand in a good way the effect of the structure and nature of the side chain on the viscoleastic behavior of polymers [33],... 

On the other hand, as in the analysis of the previous systems the temperature dependence of the a relaxation follow the Vogel-Fulcher-Tamman-Hesse (VFTH) [88-90], The 7% values obtained are 337 5 and 274 5 for PBCHM and PBCHMM respectively. By this way and using equation (2.31) the m parameter obtained are 1579 and 1804 and the relative free volumes at Tg are 3.2 and 2.6% for PCBuM and PCHBMM, respectively, in good agreement with the free volume theory. 

---