Polymerization-time superposition

The calculation of residual stresses in the polymerization process during the formation of an amorphous material was formulated earlier.12 The theory was based on a model of a linear viscoelastic material with properties dependent on temperature T and the degree of conversion p. In this model the effect of the degree of conversion was treated by a new "polymerization-time" superposition method, which is analogous to the temperature-time superposition discussed earlier. 

When polymer blends and alloys are considered, a problem arises for the application of the principle of temperature-time superposition to the systems consisting of two and more phases. A variant of this superposition has been proposed for such materials [175]. The main feature of the temperature-time reduction in this case is the dependence of the reduction coefficient on the variables—temperature and time. The expression for the reduction coefficient may be obtained via the Taylor expansion of the relaxation function with respect to variable t and T. Phase-separated IPNs relate to thermorheologically complicated materials, hi principle, in these systems two different mechanisms of relaxation exist, each of them being characterized by its own temperature coefficient. Because of this, the application of traditional temperature-frequency superposition to IPNs is restricted. However, even in those cases when this approach is not entirely vahd, it may be used for approximate calculations. Thus, the apphcation of the temperature-time superposition to heterogeneous polymeric materials shows that the method may be very valuable for prediction of the viscoelastic properties, in spite of the necessity of further developing the theory. 

To obtain as much information as possible on a material, an empirical technique known as time-temperature superposition (TTS) is sometimes performed. This technique is applicable to polymeric (primarily amorphous) materials and is achieved by performing frequency sweeps at temperatures that differ by a few degrees. Each frequency sweep can then be shifted using software routines to form a single curve called a master curve. The usual method involves horizontal shifting, but a vertical shift may be employed as well. This method will not... 

Two typical cases are illustrated in Fig. 2.24 the first scheme (Fig. 2.24 a) is related to high-temperature polymerization, in which newly formed polymer is molten and the processes of polymerization (part Ob of the full curve) and crystallization (part bK of the full curve) are separated in time. The second case (Fig. 2.24 b) illustrates low-temperature polymerization in this situation crystallization starts before the full process of polymerization is completed. This is typical superposition of two kinetic processes, and the shape of the curve in Fig. 2.24 b does not allow the separation of these processes without additional information and assumptions.The net heat effect is the same in... 

Important viscoelastic principles include the time-temperature superposition principle and its resultant WLF equation. These can be applied to understand the relationship between literature values of the glass transition temperature and actual needs. Thus, by using the growing amount of science now available in the field of damping, one can select that polymeric material which will damp most effectively. 

Relaxation curves recorded from polybutadiene solutions have been shown to satisfy such a property, provided measurements are performed at a temperature higher than a temperature threshold which will be called Tg, hereafter Tg is higher than the Tg glass transition temperatiure of the polymeric system (Tg - Tg = 80K). Above tms temperature threshold, the mathematical structure of the relaxation fimction is kept invariant except for the time scale. Because of the property of superposition, normalized relaxation curves can be characterized by chosing a given amplitude A and by measuring the time interval corresponding to this amplitude... 

Implications. These results have an important implication concerning the use of Fourier analysis of DC transients in polymeric materials to extract the frequency-dependence of the dielectric response (12)- In order for the principle of superposition to apply the electric field inside the material being measured must be time- and space-invariant. This critical condition may not be met in polymers which contain mobile ionic impurities or injected electrons. Experimentally, we can fix only the average of the electric field. Moreover, our calculations demonstrate that the bulk field is not constant in either time or space. Thus, the technique of extracting the dielectric response from the Fourier components of the transient response is fundamentally flawed because the contribution due to the formation of ionic and electronic space-charge to the apparent frequency-dependent dielectric response can not generally be separated from the dipole contribution. 

By use of the time-temperature equivalence principle, the viscoelastic response of a given polymeric material over a wide temperature range can be accommodated in a single master curve. By use the superposition principle, this master curve can be used to estimate the time-dependent response to time-dependent stresses in simple tensile or shear specimens or to nonhomogeneous time-dependent stresses arising in stressed objects and structures. 

In immiscible blends, the t-T principle does not hold. Eor immiscible amorphous blends it was postulated that two processes must be taken into account the t-T superposition, and the aging time [Maurer et al, 1985]. On the other hand, in immiscible blends, at the test temperature, the polymeric components are at different distance... 

The adhesive of this study has been designed for an automotive under-hood application. Accordingly, It was Important to understand the behavior of the adhesive over a wide frequency (engine RPM) and temperature range. Time-temperature superposition allows characterization beyond the frequency range of our Instrumentation (4). More significantly. It Is hoped to use time-temperature superposition data to explore the molecular weight Implications of Incomplete polymerization. 

As Indicated above a goal of the next phase of this work Is to study the molecular Implications of Incomplete polymerization. Wu (6) has proposed that this can be done by studying the terminal plateau modulus data for a series of test specimens. Accordingly, we attempted in this phase to show that the mechanical spectroscopy data generated from the adhesive specimens could be subjected to time-temperature superposition to yield complete modulus mapping over an extended frequency scale. Figure 9 Illustrated the Isothermal frequency scans obtained for time-temperature superposition. A master curve was constructed at reference temperature (To 75°C) approximately equal to the glass transition temperature (Tg.)... 

While this paper reports only preliminary findings. It does Illustrate the usefulness of photocalorimetry to define optimum cure conditions for UV curable adhesives. In addition, once the mechanical spectrum of fully cured adhesive has been mapped, mechanical spectroscopy can be used to monitor cure efficiency. In this paper we have not explored the molecular weight Implications of Incomplete polymerization. Preliminary evaluation of loss and storage modulus data would suggest that time-temperature superposition may be necessary to evaluate molecular welght/degree of cure relationships and terminal, plateau, and transition zones (4). 

Monte Carlo simulation results for the non-equilibrium and equilibrium d3oiamics of a glassy polymer melt are presented. When the melt is rapidly quenched into the supercooled state, it freezes on the time scale of the simulation in a non-equilibrium structure that ages physically in a fashion similar to experiments during subsequent relaxation. At moderately low temperatures these non-equilibrium effects can be removed completely. The structural relaxation of the resulting equilibrated supercooled melt is strongly stretched on all (polymeric) length scales and provides evidence for the time-temperature superposition property. 

Because this observation was obtained independently from three structurally different types of micelles, it was concluded that the broad relaxation is an inherent property of block copolymer micelles. Consistent with these findings is the almost linear dependence of R t) on a log-time scale of PS-PEP micelles in squalane presented by Choi et al. [63]. They used TR-SANS to study two pairs of PS-PEP micelles, d-PS-h-PEP-l/h-PS-h-PEP-1 and d-PS-h-PEP-2/h-PS-h-PEP-2 with different PS degrees of polymerization pair 1, Aps 255 and pair 2, Aps 412. Each specimen was measured at three different temperatures. Individual master curves for R(f) were obtained by time-temperature superposition principles. A comparison of R f) of the two PS-PEP samples was done at a reference temperature of 125°C and... 

The molecular theory predicts strong temperature dependenee of the relaxation ehar-acteristics of polymeric systems that is described by the time-temperature superposition (TTS) principle. This principle is based on numerous experimental data and states that with the change in temperature flie relaxation spectrum as a whole shifts in a self-similar manner along t axis. Therefore, dynamie functions corresponding to different temperatures are similar to each otiier in shape but are shifted along the frequency axis by the value a flie latter is named the temperature-shift factor. With war for an argument it becomes possible to plot temperature-invariant curves Re G (War) and lm G, (war). The temperature dependence of a is defined by the formula... 

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