Amorphous free volume

In order for a plasticizer to enter a polymer stmcture the polymer should be highly amorphous. Crystalline nylon retains only a small quantity of plasticizer if it retains its crystallinity. Once it has penetrated the polymer the plasticizer fills free volume and provides polymer chain lubrication, increa sing rotation and movement. 

A more polar comonomer, eg, an AN comonomer, increases the water-vapor transmission more than VC when other factors are constant. For the same reason, AN copolymers are more resistant to penetrants of low cohesive energy density. AH VDC copolymers, however, are very impermeable to ahphatic hydrocarbons. Comonomers that lower T and increase the free volume in the amorphous phase increase permeability more than the polar comonomers higher acrylates are an example. Plasticizers increase permeabiUty for similar reasons. 

Polymers are a little more complicated. The drop in modulus (like the increase in creep rate) is caused by the increased ease with which molecules can slip past each other. In metals, which have a crystal structure, this reflects the increasing number of vacancies and the increased rate at which atoms jump into them. In polymers, which are amorphous, it reflects the increase in free volume which gives an increase in the rate of reptation. Then the shift factor is given, not by eqn. (23.11) but by... 

Low-density polyethylene has a gas permeability in the range normally expected with rubbery materials Table 5.11). This is because in the amorphous zones the free volume and segmental movements facilitate the passage of small molecules. Polymers of the Phillips type (density 0.96 g/cm ) have a permeability of about one-fifth that of the low-density materials. 

Lipatov, Y. S. The Iso-Free-Volume State and Glass Transition in Amorphous Polymers New Development of the Theory. Vol. 26, pp. 63 —104. 

The load or stress has another effect on the creep behavior of most plastics. The volume of isotropic or amorphous plastic increases as it is stretched unless it has a Poisson ratio of 0.50. At least part of this increase in volume manifests itself as an increase in free volume and a simultaneous decrease in viscosity. This decrease in turn shifts the retardation times to being shorter. 

The free volume is considered to represent the difference between the actual volume of the liquid (or the amorphous polymer) and the minimum volume which it would occupy if its molecules were packed firmly in contact with each other. Incompressible molecules with rigid dimensions are implied in this definition of a free volume. The unrealistic nature of this implication undermines precise determination, or even an exact definition, of the free volume. The concept has proved useful nevertheless. 

In polymer electrolytes (even prevailingly crystalline), most of ions are transported via the mobile amorphous regions. The ion conduction should therefore be related to viscoelastic properties of the polymeric host and described by models analogous to that for ion transport in liquids. These include either the free volume model or the configurational entropy model . The former is based on the assumption that thermal fluctuations of the polymer skeleton open occasionally free volumes into which the ionic (or other) species can migrate. For classical liquid electrolytes, the free volume per molecule, vf, is defined as ... 

In addition to temperature and concentration, diffusion in polymers can be influenced by the penetrant size, polymer molecular weight, and polymer morphology factors such as crystallinity and cross-linking density. These factors render the prediction of the penetrant diffusion coefficient a rather complex task. However, in simpler systems such as non-cross-linked amorphous polymers, theories have been developed to predict the mutual diffusion coefficient with various degrees of success [12-19], Among these, the most notable are the free volume theories [12,17], In the following subsection, these free volume based theories are introduced to illustrate the principles involved. 

D Turnbull, MH Cohen. Free-volume model of the amorphous phase Glass transition. J Chem Phys 34 120-125, 1961. 

In the glassy amorphous state polymers possess insufficient free volume to permit the cooperative motion of chain segments. Thermal motion is limited to classical modes of vibration involving an atom and its nearest neighbors. In this state, the polymer behaves in a glass-like fashion. When we flex or stretch glassy amorphous polymers beyond a few percent strain they crack or break in a britde fashion. 

As polymers solidify from the molten state, their free volume decreases and their organization increases. Solid polymers fall into one of three classes rubbery amorphous, glassy amorphous, and semicrystalline, which we introduced in Chapter 1. 

The properties of a rubbery amorphous polymer form a continuum ivith those of the polymer in its molten state. Rubbery amorphous polymers exhibit the same range of motions as molten polymers, but they happen much slower, due to reduced thermal motion and the associated decrease in free volume. 

In the molten state polymers are viscoelastic that is they exhibit properties that are a combination of viscous and elastic components. The viscoelastic properties of molten polymers are non-Newtonian, i.e., their measured properties change as a function of the rate at which they are probed. (We discussed the non-Newtonian behavior of molten polymers in Chapter 6.) Thus, if we wait long enough, a lump of molten polyethylene will spread out under its own weight, i.e., it behaves as a viscous liquid under conditions of slow flow. However, if we take the same lump of molten polymer and throw it against a solid surface it will bounce, i.e., it behaves as an elastic solid under conditions of high speed deformation. As a molten polymer cools, the thermal agitation of its molecules decreases, which reduces its free volume. The net result is an increase in its viscosity, while the elastic component of its behavior becomes more prominent. At some temperature it ceases to behave primarily as a viscous liquid and takes on the properties of a rubbery amorphous solid. There is no well defined demarcation between a polymer in its molten and rubbery amorphous states. 

General Aspects and Heat Treatment Effects. After him formation, for most of the hlms aimed at electronic applications (other than amorphous oxides, such as Si02), the hlms are subjected to a heat treatment process for removal of residual organic species (entrapped solvent as well as the organic constituents associated with the precursor species), densihcation (elimination of residual porosity and structural free volume in the him), and crystallization. 

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