Free Volume Dependence

A modified version of (5.8) can be employed when fitting it against experimental 

A suitable selection of O should match two-stage diffusion data. If the second stage is barely noticeable until time t = may well be that replacing Mr(0 by — fv)//(f — fv) in (5.10) would provide a yet better agreement. 

It was observed (Bond 2005) that the two-stage model, with just one retardation time considered in (5.9), approximates the two-phase model for large values of t.  

A comparison between yet another form of weight gain data that may resemble curve S in Fig. 4.2 was shown (De WUde and FroUcovic 1994) to concur with a surface evaporation boundary condition (Crank 1980) 

In the above, is the actual boundary concentration within the material, while mo corresponds to the concentration required to maintain equilibrium within the 

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Fluorescence probes to study micro- and macromolecular motions, interactions and reactions continue to attract much interest. The moisture content in silk has been found to shift its intrinsic fluorescence spectrum338 while the physical aging of epoxy resins has been monitored using a free volume dependent fluorescent probe... 

The free-volume dependence of the ) f s is derived from Eq. (4.4). The explicit dependencies are [Robertson, 1992]... 

Utracki, L. A., and Sedlacek, T., Free volume dependence of polymer viscosity, Rheol. Acta,... 

If an elastomer is really tightly bound or adsorbed to reinforcing filler surfaces, should not molecular mobility of the polymer chains be restricted accordingly In particular, should not the glass transition temperature, thermal expansion coefficient, and free volume depend upon reinforcement Surprisingly, these properties turn out to be only modest functions of filler level. 

The extent of molecular motion depends on the free volume. In the glassy state, the free volume depends on the thermal history of the polymer. When a sample is cooled from the melt to some temperature below Tg and held at constant temperature, its volume will decrease (see Rgure 8.18). Because of the lower free volume, the rate of stress relaxation, creep, and related properties will decrease (29-33). This phenomenon is sometimes called physical aging (29,32), although the sample ages in the sense not of degradation or oxidation but rather of an approach to the equilibrium state in the glass. 

The curvature in Fig. 17-1 can be explained by assuming that the fractional free volumes are not quite additive, so the total fractional free volume depends on (volume) composition as follows ... 

The availability of bonding sites and free volume depends strongly on departures from stoichiometry of various polymeric components, like those in epoxy. Such departures may occur within the interphase regions surroxmding the fibers bringing about the accumulation of water therein (Gupta et al. 1985 Grave et al. 1998). 

A similar equation can be derived for the enthalpy. It turned out that this modification to give the retardation time a free volume dependence, was successful in describing one-step isothermal recovery but unsuccessful in describing memory effects. Kovacs, Aklonis, Hutchinson and Ramos (1979) attributed the latter to the contributions of at least two independent relaxation mechanisms involving two or more retardation times. These authors proposed a multiparameter approach, the so-called KAHR (Kovacs-Aklonis-Hutchinson-Ramos) model. The recovery process is divided into N subprocesses, which in the case of volumetric recovery may be expressed as ... 

As noted in the introductory section, our purpose is to use the excimer fluorescence technique to study the flexibility of various pol3nner chains in polymer matrices. One question which arises is to know if the probe undergoes a conformational change via a free-volume dependent molecular relaxation process related to the glass transition of the polymer matrix. The free volume of a polymer at a given temperature should qualitatively relate to its Tg value. 

Where b is linked to the penetrant size and it the polymer free volume depending on the difference between temperature and T of the polymer amorphous phase. Since is not expected to signi cantly change after crosslinking, it is thus not surprising that D was found to be extremely close in unirradiated and irradiated PE [66]. 

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