Dilute Blends of Linear Polymers

The change in the stress produced by the small amount of macromolecules of another kind is, clearly, determined by the dynamics of the non-interacting impurity macromolecules among the macromolecules of another length, so that this case is of particular interest from the standpoint of the theory of the 

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Pokrovskii VN, Chuprinka VI (1973) The effect of internal viscosity of macromolecules on the viscoelastic behaviour of polymer solutions. Fluid Dyn 8(1) 13-19 Pokrovskii VN, Kokorin YuK (1984) Theory of viscoelasticity of dilute blends of linear polymers. Vysokomolek Soedin B 26 573-577 (in Russian)... 

The quantity y is a characteristic of a macromolecule with molecular weight M in the surrounding, consisting of linear polymer with molecular weight Mq. We shall distinguish the macromolecules, even the system is a polymer melt, M = Mq- It is especially essential, if one consider a system with a small additive of a similar polymer - a dilute blend. 

The investigation of viscoelasticity of dilute blends confirms that the reptation dynamics does not determine correctly the terminal quantities characterising viscoelasticity of linear polymers. The reason for this, as has already been noted, that the reptation effect is an effect due to terms of order higher than the first in the equation of motion of the macromolecule, and it is actually the first-order terms that dominate the relaxation phenomena. Attempts to describe viscoelasticity without the leading linear terms lead to a distorted picture, so that one begins to understand the lack of success of the reptation model in the description of the viscoelasticity of polymers. Reptation is important and have to be included when one considers the non-linear effects in viscoelasticity. 

This method applies for whatever polymer concentration. In practice, it is preferable to use high concentrations in order to increase the signal-to-noise ratio and therefore minimize counting time. However, it can also be applied to semidilute or even dilute solutions where Zimm plots are useful. It also applies not only to linear polymers but also to any form of chain architecture and to deuterated/protonated mixtures in non-solvent matrices such as polymer blends or polymer networks provided that changing the deuterated fraction does not change the homogeneous nature of the mixture (i.e., no change to the chain conformations and interactions). 

In collaboration with Heriot-Watt University (Edinburgh), the University of Surrey and Imperial College, we have carried out a series of SANS experiments which have begun to investigate a wide range of linear and cyclic PDMS polymers in chemically identical blends using the materials described in this chs ter. The preliminary results obtained are extremely interesting. They will be compared with current theories, computer simulations and the results of previous studies in dilute solution and are to be reported in the near fiiture [78]. 

Block copolymers with incompatible blocks which are able to microphase separate are good candidates for PSA properties. Indeed, blends of ABA triblocks and AB diblocks, where the rubbery midblock of the ABA is the majority phase and the glassy endblocks self organize in hard spherical domains and form physical crosslinks, are widely used as base polymers for PSA. The actual adhesives are always compounded with a low molecular weight tackifier resin able to swell the rubbery phase and dilute the entanglement network. Linear styrene-rubber-styrene copolymers, with rubber being isoprene, butadiene, ethylene/propylene or ethylene/butylene, are the most widely used block copolymers in this category. 

The constraint-release models discussed above have been tested by comparing their predictions to experimental data, as shown in Figures 7.9 and 7.10. For linear polymers for which the molecular weight distribution is unimodal, and not too broad, dynamic dilution is not very important, and theories that account for constraint release without assuming any tube dilation are adequate. Such is the case with the version of the Milner-McLeish theory for linear polymers used to make the predictions shown in Fig. 6.13. The double reptation theory also neglects tube dilation. The dual constraint theory mentioned in Chapter 6 does include dynamic dilution, although its effect is not very important for narrowly dispersed linear polymers. As described above, dynamic dilution becomes important for some bimodal blends, and is certainly extremely important for branched polymers, as discussed in Chapter 9. 

Finally, we remark that the idea of self-consistent dynamic dilution was applied first by Marrucci [20] to the case of monodisperse linear polymers, and was then adapted by BaU and McLeish [11] to monodisperse stars. We also note that theories combining reptation, primitive path fluctuations, and constraint release by dynamic dilution have been applied successfully by Milner and McLeish and coworkers to monodisperse linear polymers [21], monodisperse stars [13], bimodal star/star blends [22], and star/linear blends [23], as well as H-branched polymers [24], and combs [25]. The approach taken for all these cases is similar at early times after a small step strain, the star arms and the tips of linear molecules relax by primitive path fluctuations and dynamic dilution. At some later time, if there are linear chains that reach their reptation time, there is a rapid relaxation of these linear chains. This produces a dilation of the effective tubes that surround any remaining unrelaxed star arms by constraint-release Rouse motion (see Section 7.3). Finally, after dilation has finished, the primitive path fluctuations of remaining portions of star arms begin again, in the dilated tube. We refer to this set of theories for stars, linears, and mixtures thereof as the Milner-McLeish theory . The details of the Milner-McLeish theory are beyond the scope of this work, but the interested reader can learn more from the original articles as well as from McLeish and Milner [26], McLeish [14], Park and Larson [27], and by Watanabe [19]. 

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. 

Pingping et al. examined the viscosity behaviour in PCL/PVC blends (50 50 w/w) in dilute solutions (<0.02 g cm" ) in several solvents - 1,2-dichloroethane (DCE), N,N-dimethyl formamide (DMF) and tetrahydrofuran (THF) [97]. In each case the intrinsic viscosity (the limiting values of r p c at zero concentration) of the PCL used was about 0.2 dl g and values of r]gp/c varied Httle with concentration. Intrinsic viscosities of PVC in DCE, THF and DMF were 1.7,1.0 and 0.76 dl g respectively in THF and DMF values of rj p/c increased with PVC concentration but in DCE decreased with increasing polymer concentration. In the three solvents the blends had intermediate viscosity behaviour variations of 77sp/c with concentration were slight and in DCE the dependence was non-linear. The authors defined ideal solution behaviour for a binary mixture of polymers A and B as one for which the relation... 

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