Diffusion below glass transition

There is no fundamental qualitative difference in mechanisms of low molecular weight (MW) penetrant diffusion in polymers above and below glass transition temperature, Tg, of the polymers [5,6]. The difference lies only in the fact that the movement of structural units of the macromolecule that are responsible for the transfer of penetrant molecules takes place at different supermolecular levels of the polymer matrix. At T > Tg the process of diffusion takes place in a medium with equilibrium or near-equUibrium packing of chains, and the fractional free volume, P(, in the polymer is equal to the fractional free volume in the polymer determined by thermal mobUity of strucmral units of macromolecules V((T), i e., V(= vut). At r< Tg the process of diffusion comes about under nonequihbrium packing conditions, although there exists a quasi-equilibrium structural organization of the matrix, where Vf> It is assumed that in this case Vf= where is the fractional free volume... 

In addition to long term influences due to creep and diffusion, at temperatures slightly below glass transition, an aging phenomenon occurs in a polymer which is evidenced by an increase in stiffness with elapsed time. This phenomenon, known as physical aging, can cause a polymer to become... 

P NMR was used to study motion of tri-(2-ethylhexyl) phosphate, TOP, in polycarbonate at different temperatures and concentrations. Brownian rotational motion was observed in TOP but at two different time scales. If TOP was surrounded by other molecules of plasticizer it was capable of rotational diffusion with apparent activation energy of 56 kJ mol". Isolated TOP molecules (surrounded by polymer) showed a temperature dependent movement. These molecules do not diffuse below glass the transition tempera-... 

The absorption of a medium may lower glass transition temperature considerably, depending on the type and amount of medium, which will also change diffusion behavior noticeably. For instance, in amorphous plastics, the diffusion coefficient is very small below glass transition temperature. Medium absorption will increase the diffusion coefficient by entire orders if it lowers the glass transition temperature. 

The processes during transport of low-molecular substances through the polymer matrix thus are temperature dependent. As temperature increases, diffusion rate increases. The increase is significantly lower below glass transition than above it, Figure 5.252 [86]. 

In other work, the impact of thermal processing on linewidth variation was examined and interpreted in terms of how the resist s varying viscoelastic properties influence acid diffusion (105). The authors observed two distinct behaviors, above and below the resist film s glass transition. For example, a plot of the rate of deprotection as a function of post-exposure processing temperature show a change in slope very close to the T of the resist. Process latitude was improved and linewidth variation was naininiized when the temperature of post-exposure processing was below the film s T. 

It is appropriate to differentiate between polymerizations occuring at temperatures above and below the glass transition point(Tg) of the polymer being produced. For polymerizations below Tg the diffusion coefficients of even small monomer molecules can fall appreciably and as a consequence even relatively slow reactions involving monomer molecules can become diffusion controlled complicating the mechanism of polymerization even further. For polymerizations above Tg one can reasonably assume that reactions involving small molecules are not diffusion controlled, except perhaps for extremely fast reactions such as those involving termination of small radicals. 

The transition between crystalline and amorphous polymers is characterized by the so-called glass transition temperature, Tg. This important quantity is defined as the temperature above which the polymer chains have acquired sufficient thermal energy for rotational or torsional oscillations to occur about the majority of bonds in the chain. Below 7"g, the polymer chain has a more or less fixed conformation. On heating through the temperature Tg, there is an abrupt change of the coefficient of thermal expansion (or), compressibility, specific heat, diffusion coefficient, solubility of gases, refractive index, and many other properties including the chemical reactivity. 

Criteria 1-3 are the cardinal characteristics of Fickian diffusion and disregard the functional form of D(ci). Violation of any of these is indicative of non-Fickian mechanisms. Criterion 4 can serve as a check if the D(ci) dependence is known. As mentioned, it is crucial that the sorption curve fully adhere to Fickian characteristics for a valid determination of D from the experimental data. At temperatures well above the glass transition temperature, 7 , Fickian behavior is normally observed. However, caution should be exercised when the experimental temperature is either below or slightly above 7 , where anomalous diffusion behavior often occurs. 

When a penetrant diffuses into a polymer, the perturbation will cause the polymer molecules to rearrange to a new conformational state. The rate at which this conformational adaptation occurs depends on the mobility of the polymer chains. At temperatures well above the glass transition, this occurs quite rapidly and the diffusive process resembles that in the liquid state. At temperatures near or below the glass transition, the conformational change does not take place instantaneously. Instead, there is a finite rate of polymer relaxation induced by the... 

The so-called glass transition temperature, Tg, must be considered below this temperature the liquid configuration is frozen in a structure corresponding to equilibrium at Tg. Around Tg a rather abrupt change is observed of several properties as a function of temperature (viscosity, diffusion, molar volume). Above 7 , for instance, viscosity shows a strong temperature dependence below Tg only a rather weak temperature dependence is observed, approximately similar to that of crystal. Notice that 7 is not a thermodynamically defined temperature its value is determined by kinetic considerations it also depends on the quenching rate. 

The chemical stability of an amorphous formulation is usually also a function of its storage temperatme relative to Tg. The enhanced molecular mobility achieved near the glass transition translates into an increase in translational diffusion-dependent degradation pathways, such as aggregation in proteins. It should be noted that the reaction kinetics near the Tg do not obey Arrhenius kinetics, and that extrapolation of the accelerated stability data generated near the Tg to stability at the storage temperature should be viewed with extreme caution. Amorphous materials must be stored well below the glass transition (at least 10°C, and typically 40 to 50°C below Tg) to maintain their physical and chemical stability. 

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