Polystyrene shear modulus

Figure 5.18 The high frequency shear modulus versus volume fraction for a polystyrene latex for three different electrolyte concentrations. The symbols are the experimental data and the solid lines are calculated fits using a cell model. The radius of the latex particles was 38 nm...

Table 8. Young s modulus E, shear modulus G and tensile stress a as calculated for the deformation entropy —R/2 according to Table 7, of sorbed polystyrene coils of given degree of polymerization P which form n contacts with the linear polystyrene gel at the temperatures 283 and 293 K...

Experimental evidence of this hypothesis is given in Fig. 18. Two monodisperse polystyrene samples (N = 50 and P = 5) are blended with different concentrations and the complex shear modulus is measured in a wide range of fi quendes allowing us to scan the relaxation of the two components. The reduced imaginaiy part of the complex viscosity ( n" = G /o)) shows, at intermediate concentrations, two maxima connected to the relaxation time of each component (x=l/tOmax)- The most striking point is the large decrease of the relaxation time of the longest N-chains (increase of (Omax ) ... 

Figure 27 Experimental complex shear modulus of unentangled polystyrene (M 8 500 g.mol-i) compared to the Rouse model [37].

As an example of comparison of theory and experiment the shear modulus dependence on volume concentration of phases for the system polybutadiene-polystyrene [140] is presented (Fig. 51). 

Figure 18.6. Calculated Young s modulus (thin line) and shear modulus (thick line) of polystyrene as functions of the temperature. A logarithmic y-axis has been used for clarity.

The product studied was produced in THF with a diphenylphos-phine-lithium catalyst it had a molecular weight of 8300. After shear modulus plotting over temperature, a glass stage of 81 °C, a modulus of elasticity of 32,000 kg/cm2 (poly styrene 30,000), and a flexural strength of 661 kg/cm2 (polystyrene 1000) were found. The glass temperature was 20 °C lower than that of polystyrene, but the polymer is more resistant to swelling by aromatics. 

In these equations, the subscripts h and s refer to the hard continuous phase and the soft rubbery phase, respectively, E = Young s modulus, G = shear modulus, vh = Poisson s ratio (— 0.35 for polystyrene and most rigid polymers), and cj>8 and h = volume fractions of the components. 

Fig, 1. Shear modulus of natural rubber (NR) mixtures with 50 wt.% of polystyrene (PS) as a function of temperature. 

Shear modulus of the polybutadiene mixture with oxidized polystyrene as a function of temperature ... 

It was found that mixtures of modified polystyrene with elastomers, e.g. cis-1,4-polybutadiene, behave like the SBS triblock copolymers. The changes of the shear modulus as a function of temperature are similar in both cases mentioned above but quite different from the ordinary mixture of polystyrene and polybutadiene (Fig. 9). 

Fig. 7.17 Variations of shear modulus G and tan (5 with temperature for polystyrene. (Reproduced by permission of Oxford University Press.)...

Dynamic elastic shear modulus compared to linear polystyrene TVQ... 

One of the first fundamental studies illustrating the effects of fillers on modulus was described by Nielsen et al. (1955), who showed that the shear modulus of polystyrene in the glassy state was increased by the incorporation of from 20 to 60 vol % of mica, calcium carbonate, or asbestos. The magnitude of the increase depended on the filler, about eightfold for mica, but less for asbestos. In addition, as shown by damping measurements, the apparent glass temperature was increased by the presence of the filler, by up to 15°C. 

Other parameters such as the glass transition temperature, programming temperamre, relaxation time during cold-compression programming, and glassy shear modulus can be found from the test results presented in Chapter 3. The determined model parameters for the polystyrene based thermosetting SMP arc summarized in Table 4.2. 

Figure 2.61 Shear modulus vs. temperature for two BASF Polystyrene resins [6].

The validity of scaling laws has been tested on several swollen network systems (Table 29.9). Munch et al. [99] studied the concentration dependence of the shear modulus for polystyrene model networks synthesized by copolymerization of styrene and divinylbenzene and swollen to equilibrium in benzene (good solvent for polystyrene). It was found that the modulus obeys a scaling law with equilibrium concentration, similar to that obtained for semidilute polymer solutions. The best fit to the equation G = Brpi yields... 

However, both the imiltifold cxjmpriJssion modulus K and the shear modulus /i are proportional to the cross-link numerical density (de Gennes, 1976a) and scaling behaviour of both the mechanical gi and optical g moduli with respect to polymer concentration rniist be the same. Indeed, an experiment with polystyrene-benzene networks (Candau ct al., 1979) has shown the validity of Equation 102. 

Figure 9.5 Shear modulus G and logarithmic decrement for an immiscible polyblend of polystyrene and a styrene-butadiene copolymer (Reproduced with permission from Nielsen, Mechanical Prpperitei o/5o/iiis, Van Nostrand-Reinhold, New York, 1962)...

Figure 9.21 illustrates the rubbery plateau (see Section 8.2) for a dynamic mechanical study of polystyrene as a function of frequency. The plateau shear modulus, near 3 x 10 dynes/cm, corresponds to a number of active network chains of near 1 x 10 mol/cm, nearly independent of the molecular weight of the polymer. 

Figure 13.7 A series of filled polystyrenes, illustrating the increases in glassy shear modulus, and apparent or slight increases in the glass transition temperature. Material , control v, 20% mica A, 40% mica o, 20% calcium carbonate 40% asbestos o, 60% mica >, 20% asbestos , 60% asbestos.

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