Internal molecular free volume

N.T. Tsui, A.J. Paraskos, L. Torun, TM. Swager, E.L. Thomas, Minimization of internal molecular free volume a mechanism for the simultaneous enhancement of polymer stiffness, strength, and ductility. Macromolecules 39 (9) (2006) 3350-3358. 

The scope of discussions of porous polymers in this book is limited to polymers synthesized by the widely known concave-like monomers, which lead to high international molecular free volumes. The resulting free volume is interpenetrated and is fully open or accessible to make the polymer act as a host. The typical porous polymers discussed in this book are hyper-crosslinked polymers (HCPs), polymers of intrinsic microporosity (PIMs), covalent organic frameworks (COFs), conjugated mieroporous polymers (CMPs), and porous aromatie frameworks (PAFs). 

The Free Volume Theory. The Free Volume Theory is a further extension of the lubricity and gel theories and can be used to explain both external and internal plasticization. Free volume is a measure of the internal space available in a polymer for the movement of the polymer chain, which imparts flexibility to the resin. Plasticizers increase the free volume of the resin and ensure that free volume is maintained as the resin-plasticizer mixture is cooled from the melt, preventing interactions between neighboring polymer chains. For the plasticized resins, free volume can arise from motion of the chain ends, side chains, or the main chain. The fact that free volume increases with molecular motion is useful in explaining internal plasticization achieved by side-chain addition, where each side chain acts as a small molecule and free volume of the system is increased. 

Johannes van der Waals developed his famous equation of state by the introduction of both the attractive and the repulsive forces between the molecules. First he postulated that the gas behaves as if there is an additional internal pressure to augment the external applied pressure, which is based on the mutual attraction of molecules since the density of molecules is proportional to 1/V, the intensity of the binary attractive force would be proportional to 1/V. Then he postulated that when the measured total volume begins to approach the volume occupied by the real gaseous molecules, the free volume is obtained by subtracting the molecular volume from the measured volume. Then he introduced the parameter a, which represents an attractive force responsible for the internal pressure, and the parameter b, which represents the volume taken by the molecules. He arrived at... 

If an amorphoiis polymer is cooled it will usually attempt to crystallize, but because of the high internal viscosity of the medium it is often precluded from packing into its lowest energy conformation. At 0 K, the lack of thermal excitation prevents the occurrence of most photochemical reactions. As the temperature is increased, the specific volume of the polymer will also increase as a result of forming "free volume", that is, space vdiich is not occupied by hard-shell dimensions of the atoms comprising the polymeric structure. The amount of free volume will depend to a certain extent on the previous thermal history. As free volume increases along with thermal excitation, various kinds of molecular motions will be observed in the polymer vdiich can be detected by I ysical measurements. 

Measurements of molecular density and intrinsic viscosity of PAMAM dendrimers indicate an unusual variation with dendrimer generation. Minimum density and maximum intrinsic viscosity were observed at around G4, which suggests that the fully developed dendrimers have a high accessible internal surface area in a solvent-filled intramolecular free volume that may consist of internal cavities and channels. Similar findings were reported by Mourey et al. for PBE monodendrons (based on dihydroxybenzyl alcohol) and tridendrons produced by coupling these dendrons to a trifunctional core, l,l,l-tris(4 -hydro-xyphenyl)ethane prepared by the convergent method. A maximum intrinsic viscosity occurred at G3 for tridendrons and G5 for monodendrons, consistent with the model developed by Lescanec and Muthukumar... 

These models have been quite useful as a means of explaining some of the phenomena associated with the rate of positron annihilation. Other experiments, however, seemed to indicate that the "free volume" model includes far too few properties apart from the factor of density as to satisfactorily explain variations in the positron lifetimes which occur as a result of phase transitions. It would appear that in this case an important part in the positron annihilation process is played by the nature of the intermolecular Interaction and by the internal order of the structures of the molecular substance. 

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... 

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