Polybutadiene dynamic moduli

Fig. 10. Concentration dependence of a modulus in the region of low-frequency plateau (i.e. yield stress , measured by a dynamic modulus). Dispersion medium poly (butadiene) with M = 1.35 x 105 (7), silicone oil (2) polybutadiene with M = 1 x I04 (3). The points are taken from Ref. [6], The straight line through these points is drawn by the author of the present paper. In the original work the points are connected by a curve in another manner...

There are plenty of measurements of dynamic modulus of nearly monodisperse polymers starting with pioneering works of Onogi et al. (1970) and Vinogradov et al. (1972a). The more recent examples of the similar dependencies can be found in papers by Baumgaertel et al. (1990, 1992) for polybutadiene and for polystyrene and in paper by Pakula et al. (1996) for polyisoprene. 

The physical data (dynamic modulus, tensile strength, hardness, elongation at break) were investigated by many groups 202,205 210) (cf., Table 4.5 as an example). These results show that the elastomer physical properties become better by increasing the molar ratio of low-molecular-weight diol to hydroxyl-terminated polybutadiene. 

Physical test properties on some cured rubber stocks prepared from lithium-catalyzed butadiene polymers are listed in Tables V and VI with appropriate controls. The results are only roughly indicative of the potential properties of rubbers made from lithium-catalyzed butadiene polymers because of the limited quantity of polymer available. The tensile data in Table VI indicate that compounded stocks from the lithium polymers are about equal or slightly inferior to the emulsion and sodium polymer controls in regard to these properties however, a hot tensile (lOO C.) on a cured compound from lithium polybutadiene was 325 pounds per square inch compared to 200 to 250 for an emulsion polybutadiene control. The internal friction of cured stocks from the lithium-catalyzed butadiene polymers is similar in magnitude to the emulsion or sodium polymer controls at 50 C. but higher at 100 °C. All lithium polymers, even those with low Mooney viscosities, gave cured compounds with high values of dynamic modulus. 

The dynamic viscoelasticity and the thermal behaviour of films of Thermoelastic 125 cast from solutions in four solvents - toluene (T), carbon tetrachloride (C), ethyl acetate (E), and methyl ethyl ketone (M) — have been studied by Miyamato133 The mechanical loss tangent (tan 8) and the storage modulus E dependences exhibit two transitions at —70 °C and 100 °C which have been attributed to onset of motion of polybutadiene and polystyrene segments, respectively. The heights of the polybutadiene peaks on tan 6 curves decrease in the order C > T > E > M, while for polystyrene the order is reversed C < T < E < M. These phenomena have been related to the magnitude of phase separation of the polystyrene and polybutadiene blocks. 

Dynamic Mechanical Properties. Figure 15 shows the temperature dispersion of isochronal complex, dynamic tensile modulus functions at a fixed frequency of 10 Hz for the SBS-PS specimen in unstretched and stretched (330% elongation) states. The two temperature dispersions around — 100° and 90°C in the unstretched state can be assigned to the primary glass-transitions of the polybutadiene and polystyrene domains. In the stretched state, however, these loss peaks are broadened and shifted to around — 80° and 80°C, respectively. In addition, new dispersion, as emphasized by a rapid decrease in E (c 0), appears at around 40°C. The shift of the primary dispersion of polybutadiene matrix toward higher temperature can be explained in terms of decrease of the free volume because of internal stress arisen within the matrix. On the other... 

Figure 13.13 Reduced storage modulus G and dynamic viscosity rj = G /w as functions of reduced frequency uto) for a cylinder-forming polystyrene-polybutadiene-polystyrene triblock copolymer with block molecular weights of 7000-43,000-7000. The curves are time-temperature-shifted to a reference temperature of 138°C the open symbols were obtained in the low-temperature ordered state the closed symbols were obtained in the high-temperature disordered state. (From Gouinlock and Porter 1977, reprinted with permission from the Society of Plastics Engineers.)...

FIGURE 6.19 (Upper panel) Steady-state shear viscosity versus shear rate (soUd symbols), dynamic viscosity versus frequency (open symbols), and transient viscosity calculated from Eq. (6.65) versus the inverse of the time of shearing (solid line). (Lower panel) Dynamic storage and loss modulus master curve for the same entangled polybutadiene solution (Roland and Robertson, 2006). 

Viscoelastic properties of elastomer-based CPNCs were measured at a constant frequency of 1 Hz as a temperature sweep of the dynamic moduli. Exfoliated CPNCs with polybutadiene (PBD) or polyisoprene (IR) matrix were prepared by in situ anionic polymerization, with Tg increasing by about 10°C upon incorporation of 6.2 wt% organoclay [Liao et al 2005,2006]. However, contrary to expectations, these CPNCs did not show improved dynamic tensile storage modulus, E. ... 

The curing and dynamic properties of precipitated nano-silica on NR without and with the sulfur addition (NR with S), synthetic polyisoprene (IR), polybutadiene (BR) and SBR was investigated. Silica was treated with bis(3-triethoxysilylpropyl)tetrasulfane (TESPT) to form bonds at interfaces. Cure, Mooney viscosity, glass transition temperature, bound rubber, crosslink density and DMA were measured. The properties of silica-filled SBR and BR correlated with highest rolling resistance and SBR-silica correlated with best skid resistance. A Payne effect was observed in the loss modulus under some experimental conditions. In addition to possible filler de-agglomeration and network disruption, the nanoscale of the filler may have further contributed to the non-linear response typified by the Payne effect. ... 

Figures shows the calculated and measured dynamic shear modulus of polystyrene, for values of x and B, chosen so as to ensure agreement with the modulus on the plateau and the length of the plateau. Good agreement is achieved at high and low frequencies. The form of the real part of the modulus confirms the assumption about the finite correlation time r in the memory functions (45), but discrepancies in the region of the plateau (especially seen on the G" ijS) plot) witness that other correlation times in the memory function less than r can exist. In fact, to describe the dependencies for monodis-perse polybutadiene and polystyrene empirically, a few relaxation times were introduced [98, 99]. However, the differences in the region of the plateau can also be attributed to the inevitable polydispersity of the samples.

We first consider the behavior of the dynamic storage modulus and the dynamic loss modulus. Colby, et a/. (15) report an extremely extensive series of measurements of the storage and loss moduli of a 925 kDa (M ) polybutadiene having a narrow molecular weight distribution (M /Mn < 1.1 M /Mw < 1-1). Solutions were made in the Theta solvent dioctylphthalate (DOP) at 12°C above the Theta temperature, and the good solvent phenyloctane (PO). Viscosities were reported at 15 volume fractions extending from extreme dilution 0.001) up to the melt full... 

The case of star/linear blends is a challenging one, because the description of constraint release that works best for pure star polymers is dynamic dilution, while for pure linear polymers, double reptation , or some variant of it, seems to be the better description. However, Milner, McLeish and coworkers [23] have developed a rather successful theory for the case of star/ linear blends. In the Milner-McLeish theory, at early times after a step strain both the star branches and the ends of the linear chains relax by primitive-path fluctuations combined with dynamic dilution, the latter causing the effective tube diameter to slowly increase with time. Then, at a time corresponding to the reptation time of the linear chains, the tube surrounding the unrelaxed star arms increases rather quickly, because of the sudden reptation of the linear chains. The increase in the tube diameter would be very abrupt, if it were not slowed by inclusion of the constraint release-Rouse processes, which leads to a square-root-in-time decay in the modulus (see Section 7.3). With this formulation, the Milner-McLeish theory yields very favorable predictions of polybutadiene data for star/linear blends see Fig. 9.13, where the parameters have the same values as were used for pure linears and pure stars. 

The different forms of the modulus are still widely disputed and different opinions are expressed in the literature. Hsu and Mark " " prepared networks of polybutadiene by endlinking. According to dynamic measurements polybutadiene has a high plateau modulus in viscoelasticity and one can expect a strong contribution to the modulus from entanglements. In this study experiments have been fitted to the stress-strain relations with the Flory constraint-fluctuation model as in ref. 245. The authors concluded that there is no contribution from entanglements to the modulus. The same conclusion was drawn in refs. 245-248. 

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