Plastics chain relaxation

Brostow W. The Chain Relaxation Capability. Ch. 5. In performance of Plastics. Ed. W. Brostow, Hanser, Munich-Cincinnati, 2000. 

Examination of the Long-Richman solution to Eq. (1) indicates that the quantity defined previously, i. e., the time for the inflection point on the sigmoid second stage portion, is very nearly equal to 1/2/8, provided D/L2 is not too small compared with /8. If, as has been discussed in section 3.3, it is plausible to interpret / as being related to the rate of relaxation motions of polymer molecules, then the second stage portion should shift to the short time region as the initial concentration of the experiment becomes higher, since as the solid contains more diluent it is more plasticized and thus the chain relaxation becomes more rapid [Fujita and Kishimoto (1958)]. This expectation is borne out by the data shown in Fig. 9. 

Another bent-strip method for evaluating the ESCR is presented in ISO 4599. In this test, strips of a plastic are positioned in a fixed flexural strain state and exposed to a stress cracking agent for a predetermined period. The test is uniaxial and simple to perform, and the deformation is constant. Because of the molecular chain relaxations, the stress state is well defined only at the beginning of the test. After exposure to the medium, the strips are removed from the straining rig, examined visually for changes in appearance, and then tested for some indicative property such as tensile strength. 

From the above argument, we expect that the complexity is reduced when the difference of the relaxation times of the PI and PtBS chains decreases. This expectation is confirmed for the PI20/PtBS16 blends with Wp, = 70 and 80 wt%, as shown in the panels (b) and (c) of Figure 3.21. The increase of xvp enhances plasticization of PtBS16 due to POO to reduce the difference of the relaxation times of these components, thereby allowing the ensemble of POO chains to obey the superposition as a whole. In particular, in the blend with Wpi = 80 wt%, the POO chains relaxed slower than the PtBS chains (as noted from the coincidence of the dielectric and viscoelastic terminal relaxation times of the blend cf. Chen et al., 2008 Takada et al., 2008) and the dielectric data exhibit excellent superposition. 

The use of CO2 to prepare such materials involves the plasticization of the polymer matrix followed by the impregnation of the chromophore. The apphcation of an electric field results in the ahgnment of the dye molecules, and this is followed by depressurization of the system, which results in the rapid escape of CO2 and the consequential freezing" of the dye alignment in the matrix. A specific benefit of this method is that the rapid release of CO2 enables the matrix to be frozen , and hence the dye molecules do not have time to reorientate [76]. A general problem with the polymeric guest-host system is the instability of the system due to polymer chain relaxation, which can result in the loss of the necessary alignment. Supercritical fluid treatment of such materials allows one to process them at lower temperatures because of plasticization and thus possibly to achieve better orientation of the dyes in the polymer matrix. 

Sufficient free volume is essential for these processes. An increase in Vf results in an increase in the number of conformational changes in the chains enhancing the chain relaxation capability (CRC) (Brostow and Macip 1989 Doolittle 1951 Akinay et al. 2001). Brostow and Macip (1989) defined CRC as the amount of external energy dissipated by a relaxation process in a unit of time and unit mass of the polymer. The excess energy that cannot be dissipated by relaxational processes can go into destructive processes (irreversible changes in response to an applied force and/or temperature such as bond fracture and plastic deformation). The theory of the chain relaxation capability is discussed in detail in several references (Akinay et al. 2002 Brostow and Kubat 1996 Brostow 2000 Brostow et al. 2000 Brostow et al. 1999a, b). 

Brostow, W. (2000), Chain Relaxation Capability in Performance of Plastics, Hanser/ Gardner, Munich/Cincinnati, Chapter 5. 

Although many different processes can control the observed swelling kinetics, in most cases the rate at which the network expands in response to the penetration of the solvent is rate-controlling. This response can be dominated by either diffu-sional or relaxational processes. The random Brownian motion of solvent molecules and polymer chains down their chemical potential gradients causes diffusion of the solvent into the polymer and simultaneous migration of the polymer chains into the solvent. This is a mutual diffusion process, involving motion of both the polymer chains and solvent. Thus the observed mutual diffusion coefficient for this process is a property of both the polymer and the solvent. The relaxational processes are related to the response of the polymer to the stresses imposed upon it by the invading solvent molecules. This relaxation rate can be related to the viscoelastic properties of the dry polymer and the plasticization efficiency of the solvent [128,129],... 

In a further development of the continuous chain model it has been shown that the viscoelastic and plastic behaviour, as manifested by the yielding phenomenon, creep and stress relaxation, can be satisfactorily described by the Eyring reduced time (ERT) model [10]. Creep in polymer fibres is brought about by the time-dependent shear deformation, resulting in a mutual displacement of adjacent chains [7-10]. As will be shown in Sect. 4, this process can be described by activated shear transitions with a distribution of activation energies. The ERT model will be used to derive the relationship that describes the strength of a polymer fibre as a function of the time and the temperature. 

The transition from ideal elastic to plastic behaviour is described by the change in relaxation time as shown by the stress relaxation in Fig. 66. The immediate or plastic decrease of the stress after an initial stress cr0 is described by a relaxation time equal to zero, whereas a pure elastic response corresponds with an infinite relaxation time. The relaxation time becomes suddenly very short as the shear stress increases to a value equal to ry. Thus, in an experiment at a constant stress rate, all transitions occur almost immediately at the shear yield stress. This critical behaviour closely resembles the ideal plastic behaviour. This can be expected for a polymer well below the glass transition temperature where the mobility of the chains is low. At a high temperature the transition is a... 

In the high concentration regime, our SCP is different from a typical SCP observed in Case II diffusion. Specifically, our SCP lacks the sharp solvent front(fig.8). The abrupt increase in solvent concentration normally observed is due to the long relaxation time of the polymer chain in response to solvent plasticization. Then, the absence of this feature points to a very rapid relaxation of PMMA chains by MEK. This is probably due to a good match in the solubility parameters of PMMA and MEK ( =9.3 for both). 

In a subsequent communication, Elliott and coworkers found that uniaxially oriented membranes swollen with ethanol/water mixtures could relax back to an almost isotropic state. In contrast, morphological relaxation was not observed for membranes swollen in water alone. While this relaxation behavior was attributed to the plasticization effect of ethanol on the fluorocarbon matrix of Nafion, no evidence of interaction between ethanol and the fluorocarbon backbone is presented. In light of the previous thermal relaxation studies of Moore and co-workers, an alternative explanation for this solvent induced relaxation may be that ethanol is more effective than water in weakening the electrostatic interactions and mobilizing the side chain elements. Clearly, a more detailed analysis of this phenomenon involving a dynamic mechanical and/ or spectroscopic analysis is needed to gain a detailed molecular level understanding of this relaxation process. 

A second difference from the continuum model is that large stresses near the reaction center should undergo thermally activated relaxation. According to the molecular mechanism of stress relaxation proposed above, such irreversible, or plastic, deformations occur in UP when the two decyl radicals back away from the reaction center by rotational translation along their long axes. In the process of making more room for the two new C02 molecules, each radical chain is driven into the adjacent interface between two layers of peroxide molecules. Introduction of a defect or a hole at the end of the peroxide chain should facilitate this motion and allow efficient relaxation of the stress. 

A good elastomer should not undergo plastic flow in either the stretched or relaxed state, and when stretched should have a memory of its relaxed state. These conditions are best achieved with natural rubber (ds-poIy-2-methyl-1,3-butadiene, ds-polyisoprene Section 13-4) by curing (vulcanizing) with sulfur. Natural rubber is tacky and undergoes plastic flow rather readily, but when it is heated with 1-8% by weight of elemental sulfur in the presence of an accelerator, sulfur cross-links are introduced between the chains. These cross-links reduce plastic flow and provide a reference framework for the stretched polymer to return to when it is allowed to relax. Too much sulfur completely destroys the elastic properties and produces hard rubber of the kind used in cases for storage batteries. 

Carbon-13 rotating-frame relaxation rate measurements are used to elucidate the mechanism of gas transport in glassy polymers. The nmr relaxation measurements show that antiplasticization-plasticization of a glassy polymer by a low molecular weight additive effects the cooperative main-chain motions of the polymer. The correlation of the diffusion coefficients of gases with the main-chain motions in the polymer-additive blends shows that the diffusion of gases in polymers is controlled by the cooperative motions, thus providing experimental verification of the molecular theory of diffusion. Carbon-13 nmr relaxation... 

The average relaxation rate of the methylene- and methine-carbons in PVC decreases with the addition of TCP up to about 15 weight % (Table I). Based on standard relaxation rate theory (29), reduced relaxation rates are indicative of a shift in the average cooperative motions to lower frequencies. These results prove that antiplasticization is associated with reduced cooperative motions of the polymer chains. As the concentration of TCP in PVC is increased above 15 weight %, the average relaxation rate of the methylene- and methine-carbons in PVC increases (Table I), showing that plasticization leads to increased cooperative motions in the glass. 

In conclusion, the average rotating-frame relaxation rate of the methylene- and methine-carbons correlate with the apparent diffusion coefficients for H2 and CO in PVC when the main-chain molecular motions of the polymer are altered by an additive. (Fig. 2). These results provide experimental evidence that main-chain cooperative motions control the diffusion of gases through polymers. In Section IIB we will show that perturbation of polymeric cooperative motions is not restricted to classical plasticizing additives. 

The influence of temperature and strain rate can be well represented by Eyring s law physical aging leads to an increase of the yield stress and a decrease of ductility the yield stress increases with hydrostatic pressure, and decreases with plasticization effect. Furthermore, it has been demonstrated that constant strain rate. Structure-property relationships display similar trends e.g., chain stiffness through a Tg increase and yielding is favored by the existence of mechanically active relaxations due to local molecular motions (fi relaxation). 

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