Glass-rubber transition theories

In fact many important polymers do not crystallize at all but form glasses at low temperatures. At higher temperatures they form viscous liquids. The transition that separates the glassy state from the viscous state is known as the glass-rubber transition. According to theories to be developed later, this transition attains the properties of a second-order transition at very slow rates of heating or cooling. 

For the polymer considered in the previous section the birefringence measurements and the stretching or shrinkage took place at different times the birefringence was measured in the frozen-in state of orientation. It is, however, possible to measure the birefringence of a real rubber when it is still under stress at a temperature above its glass-transition temperature. This provides a simultaneous test of the predictions of the rubber deformation theory for both orientation and stress. 

A new polymer follows the Kelvin model. The quantity rj obeys the WLF eqution, and E obeys rubber elasticity theory. The glass transition temperature of the polymer is 5°C, where it has a viscosity of 1 x 10 poises. The concentration of active chain segments is 1 x 10 mol/cm. The temperature of the experiment is 30°C. 

The conventional, and very convenient, index to describe the random motion associated with thermal processes is the correlation time, r. This index measures the time scale over which noticeable motion occurs. In the limit of fast motion, i.e., short correlation times, such as occur in normal motionally averaged liquids, the well known theory of Bloembergen, Purcell and Pound (BPP) allows calculation of the correlation time when a minimum is observed in a plot of relaxation time (inverse) temperature. However, the motions relevant to the region of a glass-to-rubber transition are definitely not of the fast or motionally averaged variety, so that BPP-type theories are not applicable. Recently, Lee and Tang developed an analytical theory for the slow orientational dynamic behavior of anisotropic ESR hyperfine and fine-structure centers. The theory holds for slow correlation times and is therefore applicable to the onset of polymer chain motions. Lee s theory was generalized to enable calculation of slow motion orientational correlation times from resolved NMR quadrupole spectra, as reported by Lee and Shet and it has now been expressed in terms of resolved NMR chemical shift anisotropy. It is this latter formulation of Lee s theory that shall be used to analyze our experimental results in what follows. The results of the theory are summarized below for the case of axially symmetric chemical shift anisotropy. 

The glass to rubber transition region is determined by the onset of conformational change involving internal rotation of the polymer main chain. The temperature midpoint of the change is called the glass transition temperature, T. There are several glass transition theories, but the one most closely related to the molecular motion approach is the kinetic theory. 

Inspection of Figure 5 shows a very broad glass-to-rubber transition range which extends from below -100°C to above 0°C for the polyurethane adhesive. The relaxation modulus E(t) - 400 Kg/cm which occurs at the rubbery inflection temperature - 40°C - 313 K describes an effective molecular weight M as defined by kinetic theory of rubber elasticity ... 

Polymer networks are conveniently characterized in the elastomeric state, which is exhibited at temperatures above the glass-to-rubber transition temperature T. In this state, the large ensemble of configurations accessible to flexible chain molecules by Brownian motion is very amenable to statistical mechanical analysis. Polymers with relatively high values of such as polystyrene or elastin are generally studied in the swollen state to lower their values of to below the temperature of investigation. It is also advantageous to study network behavior in the swollen state since this facilitates the approach to elastic equilibrium, which is required for application of rubber elasticity theories based on statistical thermodynamics. ... 

Other theories proposed dissipation of energy through crack interaction localised heating causing the material to be raised to above the glass transition temperature in the layers of resin between the rubber droplets and a proposal that extension causes dilation so that the free volume is increased and the glass transition temperature drops to below the temperature of the polyblend. 

The effective molecular mass Mc of the network strands was determined experimentally from the moduli of the polymers at temperatures above the glass transition (Sect. 3) [11]. lVlc was derived from the theory of rubber elasticity. Mc and the calculated molecular mass MR (Eq. 2.1) of the polymers A to D are compared in Table 3.1. 

Small deformations of the polymers will not cause undue stretching of the randomly coiled chains between crosslinks. Therefore, the established theory of rubber elasticity [8, 23, 24, 25] is applicable if the strands are freely fluctuating. At temperatures well above their glass transition, the molecular strands are usually quite mobile. Under these premises the Young s modulus of the rubberlike polymer in thermal equilibrium is given by ... 

Another major discrepancy between theory and experiment is exemplified in Figure 3-21. In this figure, the predicted relaxation according to the Rouse theory is compared with an experimental result for polystyrene in the primary transition region. It is clear that polystyrene undergoes its glass-to-rubber... 

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