Relaxation curves polystyrene

The data points and the minimized curves based on Equation 1 for the six styrene/MAA-Na copolymers with ionic mole fractions ranging from. 006 to 0.055 are given in Figures la and lb. A polystyrene relaxation curve is also shown. The values of the parameters used are listed in Table 1, together with the Tg s of the copolymers and the standard error of the fit. 

Figure 8.19 Influence of molecular weight on the plateau length of narrow distribution polystyrene. The curves represent the storage relaxation modulus in the frequency domain reduced to 160°C. Viscosity-average molecular weights from left to right, xlO" 58, 51, 35, 27.5, 21.5, 16.7, 11.3, 5.9, and 4.7. (From Ref. 25.)...

Figure 3. The individual stress relaxation curves and master curve reduced to the a glass transition temperature for Nafion acid, compared with those of polystyrene and two styrene ionomers reduced to their glass transition temperatures (31).

In Fig. 12.3, the relaxation modulus of a nearly monodisperse polystyrene of Mui = 4.22 X 10 (F40) at the step shear strain A = 5 is compared with that in the linear region (A = 0.2), both being measured at the same temperature. In the nonlinear relaxation modulus, as expected from Eq. (12.28), two distinctive relaxation processes are visible in addition to the terminal relaxation, a faster process occurs in the time region corresponding to the plateau in the linear G t). The linear and nonlinear relaxation curves are superposable in the terminal region as one of the two curves is allowed to shift along the modulus axis (as explained below, a small shift toward the... 

Plot of slope of the relaxation curve, n, against stiffness index, Ng, for several polymers. Circles are polyurethanes of nearly the same cross-link density, but varying catalyst to prepolymer ratios as indicated [23]. Other polymers and associated references areO - polyisoprene [13,21], - SBR [21,22], polyisobutylene [15,21], 7- polymethyl methacrylate [15,21] and - polystyrene [15,24]. 

The isothermal curves of mechanical properties in Chap. 3 are actually master curves constructed on the basis of the principles described here. Note that the manipulations are formally similar to the superpositioning of isotherms for crystallization in Fig. 4.8b, except that the objective here is to connect rather than superimpose the segments. Figure 4.17 shows a set of stress relaxation moduli measured on polystyrene of molecular weight 1.83 X 10 . These moduli were measured over a relatively narrow range of readily accessible times and over the range of temperatures shown in Fig. 4.17. We shall leave as an assignment the construction of a master curve from these data (Problem 10). 

Several attempts have been made to superimpose creep and stress-relaxation data obtained at different temperatures on styrcne-butadiene-styrene block polymers. Shen and Kaelble (258) found that Williams-Landel-Ferry (WLF) (27) shift factors held around each of the glass transition temperatures of the polystyrene and the poly butadiene, but at intermediate temperatures a different type of shift factor had to be used to make a master curve. However, on very similar block polymers, Lim et ai. (25 )) found that a WLF shift factor held only below 15°C in the region between the glass transitions, and at higher temperatures an Arrhenius type of shift factor held. The reason for this difference in the shift factors is not known. Master curves have been made from creep and stress-relaxation data on partially miscible graft polymers of poly(ethyl acrylate) and poly(mcthyl methacrylate) (260). WLF shift factors held approximately, but the master curves covered 20 to 25 decades of time rather than the 10 to 15 decades for normal one-phase polymers. 

The temperature dependence of the relaxation modulus at 500 seconds of polycarbonate (7), polystyrene (8), and their blends (75/25, 50/50, and 25/75) was obtained from stress-relaxation experiments (Figure 4, full lines). In the modulus-temperature curves of the blends, two transition regions are generally observed in the vicinity of the glass-rubber transitions of the pure components. The inflection temperatures Ti in these transition domains are reported in Table I they are almost independent on composition. The presence of these two well-separated transitions is a confirmation of the two-phase structure of the blends, deduced from microscopic observations. 

The difference in softening temperatures for amorphous and semi-crystalline polymers becomes also clear from Fig. 13.3, where the Young moduli of amorphous and of semicrystalline polystyrene are illustrated. For amorphous polystyrene the two HDTs appear to be 92 and 97 °C and for the semi-crystalline polystyrene 99 and 114 °C. It has to be mentioned, however, that the curves in Fig. 13.3 are the so-called 10 s moduli, i.e. measured after 10 s of stress relaxation, every point at a specific temperature. The measurements in the softening experiments are not in agreement with the determination of the standard Young modulus. 

Figure 4 Master curve for the linear viscoelastic behaviour of entangd polymers in the terminal region of relaxation V Polystyrene, bulk (M=860000, T=190°C) Polyethylene, bulk (M=340000, T=130°C) A Polybutadiene solution (M=350000, <)) polymer=43%, T=20°C) [ om ref.4].

In this work we used polystyrene-based ionomers.-Since there is no crystallinity in this type of ionomer, only the effect of ionic interactions has been observed. Eisenberg et al. reported that for styrene-methacrylic acid ionomers, the position of the high inflection point in the stress relaxation master curve could be approximately predicted from the classical theory of rubber elasticity, assuming that each ion pah-acts as a crosslink up to ca. 6 mol %. Above 6 mol %, the deviation of data points from the calculated curve is very large. For sulfonated polystyrene ionomers, the inflection point in stress relaxation master curves and the rubbery plateau region in dynamic mechanical data seemed to follow the classical rubber theory at low ion content. Therefore, it is generally concluded that polystyrene-based ionomers with low ion content show a crosslinking effect due to multiplet formation. More... 

Figure 8.13 Master curves showing the storage and loss relaxation moduli of a solution of polystyrene in tri-m-tolyl phosphate at the reference temperature To = 0°C. (From Ref 8.)...

The effect of overall molecular weight or the number of blocks on rheological properties for the samples from the second fractionation can be illustrated as a plot of reduced viscosity vs. a function proportional to the principal molecular relaxation time (Figure 2). This function includes the variables of zero shear viscosity, shear rate, y, and absolute temperature, T, in addition to molecular weight, and allows the data to be expressed as a single master curve (10). All but one of the fractions from the copolymer containing 50% polystyrene fall on this... 

Obtain DSC thermal curves of several semicrystaUine polymers such as polymethylmethacrylate (PMMA), polystyrene, polycarbonate, high-density polyethylene, low-density polyethylene and look for the glass transition in these polymers. The DSC run may need to be repeated twice with rapid cooling between runs. Many as received polymers will show a small peak on top of the glass transition on the first mn due to relaxation effects in the polymer. The second run should not show this peak , but only a step change in the baseline. Compare your values of Tg to literature values. Deviations may indicate the presence of plasticizers or other additives in the polymer. 

The change in property measured up to, and past, equilibrium absorption is likely to show a marked change in the shape of the degradation curve. This is very noticeable in compression stress relaxation results on some rubbers in water at ambient temperature when a rise in modulus can be seen due to swelling at times greater than one year. Serebryakov ct al. [15] demonstrate a similar type of effect for the strength of polystyrene. 

The general behavior of a polymer can be typified by results obtained for an amorphous atactic polystyrene sample. The relaxation modulus was measured at a standard time interval of 10 s and logio shown as a function of temperature in Figure 13.1. Five distinct regions can be identified on this curve as follows ... 

Shown in Fig. 4.6 are the curves of relaxation modulus, G t), of a series of nearly monodisperse polystyrene samples of different molecular weights. The higher the molecular weight, the slower the relaxation rate. In these measurements, the step deformation rise time is 0.04 s, which is much shorter than the relaxation times of interest in these curves. The most noteworthy is the appearance of a modulus plateau when the molecular weight is sufficiently large. As will be discussed in the later chapters, the entanglement molecular weight Mg can be calculated from the plateau modulus Gn- The analyses of these relaxation modulus curves in terms of the extended reptation theory developed in Chapter 9 will be detailed... 

Fig. 9.1 Relaxation modulus 0 X,t) in the linear (A 0 ooo) and nonlinear (A = 5 aaa) regions of a nearly monodisperse polystyrene melt (Mw = 4.22 x 10 ). The G(A = 5, t) curve was measured at a temperature different from the reference temperature (127.5° C) of the shown G(A — 0, f) master curve as shown the G(A = 5,t) curve has been shifted along both the time axis and the modulus axis to superpose on the G(A — 0,t) curve in the terminal region. (See Fig. 12.3 for the results of G(A = 0.2, t) and G(A = 5, t), both measured at the same temperature.)...

Equation (9.19) accurately describes the observed characteristics associated with the transformation of the G t) line shape with changing molecular weight. To illustrate the capability of the theory in describing these characteristics, the relaxation modulus curves calculated from Eq. (9.19) at Mw/Me = 10, 20 and 40, all with the polydispersity of Mm/M = 1.05, are shown in Fig. 9.4 for comparison with the experimental results, as shown in Fig. 4.6. In Chapter 10, in terms of the theory, quantitative analyses of the relaxation modulus curves of a series of nearly monodisperse polystyrene samples will be described in detail. 

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