Linear Plateau modulus

Investigation of the linear viscoelastic properties of SDIBS with branch MWs exceeding the critical entanglement MW of PIB (about -7000 g/mol ) revealed that both the viscosity and the length of the entanglement plateau scaled with B rather than with the length of the branches, a distinctively different behavior than that of star-branched PIBs. However, the magnitude of the plateau modulus and the temperature dependence of the terminal zone shift factors were found to... 

The Gge contribution of the form given Eq.(2) represents the simplest form of permanent interchain interactions. The value of Gee at Teg=1 and w =1, i.e. the Gge contribution of a perfect network, has been assumed equal to the plateau modulus of the corresponding linear polymer (10,15,23). This assumption has not always been confirmed and, therefore, for the purpose of this work we prefer to consider g of g" as proportionality constants. 

It is not clear why this transition should occur at such a higher level of arm entanglement for polystyrene stars than for other star polymers. This observation is in direct conflict with the standard assumption that through a proper scaling of plateau modulus (Go) and monomeric friction coefficient (0 that rheological behavior should be dependent only on molecular topology and be independent of molecular chemical structure. This standard assumption was demonstrated to hold fairly well for the linear viscoelastic response of well-entangled monodisperse linear polyisoprene, polybutadiene, and polystyrene melts by McLeish and Milner [24]. 

According to a report presented by Fu et al. [180], the influence of POSS-triol on epoxy-amine reaction depends mostly on the magnitude of AT (Tg -Tc) used. Since Tg for epoxy cured with linear aliphatic diamine—2-methyl-1,5-pentadiamine (MPDA)—was higher than the Tg of the same epoxy cured with diamine-terminated polypropylene oxide (PPO), when cured at the same temperature, epoxy-cured MPDA showed a greater improvement in the value of Tg. Moreover, the addition of POSS-triol in tetraglycidyl diamino diphenyl methane (TGDDM) cured with MPDA also increased the rubbery plateau modulus (Fig. 6). 

For oscillatory strains less than approximately 0.03-0.04, the suspensions showed linear viscoelastic response with the plateau modulus. Go, being independent of frequency (Chow and Zukoski, 1995b). Because Go increases exponentially with volume... 

The factor of 5 is introduced into the definition of Q so that Q equals the linear viscoelastic strain, y, when the strain is small. G% — vk T is then the plateau modulus. When the... 

It is expected that the same picture that gives a good account of the linear viscoelastic behavior of polymer melts should also hold for semidilute and concentrated solutions. In the case of semidilute solutions some conclusions can be drawn from sealing arguments (19,3, p. 235). In this way, concentration dependence of the maximum relaxation time tmax the zero shear rate viscosity r Q, and the plateau modulus G% can be obtained, where t is the viscosity of the solvent. The relevant parameters needed to obtain Xmax as a function of concentration are b, c, N, kgT, and Dimensional analysis shows that... 

Doi and Edwards were able to develop an equation for the stress relaxation modulus G(t) of monodisperse entangled linear chain liquids in the terminal region without resorting to the independent alignment approximation From G(t), expressions can be obtained for the plateau modulus, the steady-state viscosity and steady-state recoverable compliance. The following dependences on chain length are obtained ... 

The expression for plateau modulus (Gh = G(o) in Eq. 69) is the same as that for free linear chains ... 

Therefore, it is well established that topological entanglements dominate and control the modulus of polymer networks with long network strands. The Edwards tube model explains the non-zero intercept in plots of network modulus against number density of strands (see Figs 7.11 and 7.12). The modulus of networks with very long strands between crosslinks approaches the plateau modulus of the linear polymer melt. The modulus of the entangled polymer network can be approximated as a simple sum. 

Modulus of end-linked PDMS networks with/= 4 at 30 °C from S. K. Patel etal.. Macromolecules 25, 5241 (1992). The line has an intercept determined by the plateau modulus of a melt of high molar mass PDMS linear polymers-----------... 

Dilution effect on the plateau modulus of linear polymers, Filled diamonds are polystyrene in cyclohexane at 34.5 °C (0-solvent), open squares are polystyrene in benzene at 25 °C (good solvent), filled circles are polybutadiene in dioctylphthalate at 25°C (near ... 

Enormously long linear chains may have a many-chain effect that retards their reptation. The plateau modulus of an entanglement network is given by Eq. (9.18). In equilibrium there are small fluctuations of stress Acr(r)... 

Generally PSAs are well known for their very viscoelastic behavior, which is necessary for them to function properly. It was therefore important to characterize first the effect of the presence of diblocks on the linear viscoelastic behavior. Since a comprehensive study on the effect of the triblock/diblock ratio on the linear viscoelastic properties of block copolymer blends has recently been reported [46], we characterized the linear viscoelastic properties of our PSA only at room temperature and down to frequencies of about 0.01 Hz. Within this frequency range all adhesives have a very similar behavior in terms of elasticity, as can be seen in Fig. 22.10. The differences appear at low frequency, a regime where the free iso-prene end of the diblock chain is able to relax. This relaxation process is analogous to the relaxation of an arm of a star-like polymer [47], and causes G to drop to a lower plateau modulus, the level of which is only controlled by the density of triblock chains actually bridging two styrene domains [46]. 

Another strong indication of the entanglement effect is the observation of a clear plateau in the linear relaxation modulus amj storage modulus spectrum when the polymer has a sufficiently high molecular... 

---