Polymers system

For higher molecular weight polymers, whether melts or more concentrated solutions, a pronounced plateau region is seen. Examples of increasing molecular weight and resulting deepening of the G valley and the introduction of other 

This deepening of the G valley with increase in molecular weight is particularly well illustrated in figure 22. 

In qualitative terms the oscillatory curves give a fingerprint of the state of the microstructure in the same way as does an NMR or an infrared spectrum. Just as various mechanisms can be identified and quantified by the position on the frequency axis and the height of the signal so too can oscillatory curves. A number of examples are follow  

Once a plateau modulus Gp has been evaluated, it can be used for a number of purposes, see figure 33. First, for polymeric systems, the value of the molecular weight of the chain segments between temporary entanglements. Me, can be evaluated, since Me = pRT/Gp where R is the imiversal gas constant (8.314 J mol-i K-i), p is the polymer density and T is the absolute temperature, see figure 34. 

In disperse systems, the inter-particle force may be evaluated from the value of Gp, since the plateau modulus is given by a mathematical function that contains the radial distribution function and the force that particles exert on one another as a fimction of their separation, see [32]. If one makes various approximations to the radial distribution function such as a delta function or a cubic lattice, then the force between the particles can be calculated. An example of the use of the plateau modulus for emulsions is given by Sanchez et al [33]. 

All studies on the high-temperature SEC of polymer systems have much in common, in that the same problems crop up again and again and there is a limited number of solutions available. There are few molecular mass standards for commercial polymers, and in order to calibrate and determine molecular mass distribution from the chromatogram, various procedures have been developed. See Chapter 3 for a detailed consideration of the problems associated with calibration. 

In the classic 1967 film The Graduate, the protagonist, Benjamin (Dustin Hoffman), is attempting to plan his postcollege path. His neighbor provides one word of advice, Plastics. This counsel has become part of American culture and is often parodied. But, it is good advice, because not since the transformations from stone to bronze and then to iron have new materials so completely transformed a society. Plastics made from synthetic polymers are ubiquitous, from Tupperware to artificial hearts. About half the world s chemists work in polymer-related industries. 

In most industrial processes, nonlinear behavior is seen not as an advantage but as something to be avoided. However, we will look at several reaction-diffusion systems that have desirable properties precisely because of their nonlinear behavior. Replication of RNA is autocatalytic and can occur as a traveling front. 

Since not all RNA molecules replicate equally well, faster mutants gradually take over. At each mutation, the front propagates faster. Evolution can be directly observed in a test tube. Propagating polymerization fronts of synthetic polymers may be useful for making new materials, and they are interesting because of the rich array of nonlinear phenomena they show, with pulsations, convection, and spinning fronts. Finally, we will consider photopolymerization systems that exhibit spatial pattern formation on the micron scale, which can be used to control the macroscopic properties. 

Nonlinear phenomena in any system require some type of feedback. The most obvious source of feedback in polymerization reactions is thermal autocatalysis, often called thermal runaway in the engineering literature. The heat released by the reaction increases the rate of reaction, which increases the rate of heat release, and so on. This phenomenon can occur in almost any reaction and will be important when we consider thermal frontal polymerization. 

The gel effect represents a different type of feedback than we have encountered so far, because it is not true autocatalysis. No species is produced that increases its own rate of production. In fact, the rate at which a polymer chain grows (recall that each chain has a very short lifetime) actually goes down slightly. The rate at which the chains are terminated decreases even more, so the overall rate of monomer consumption increases. 

Hydrophobically associating polymers are water soluble polymers containing a small amount of hydrophobic functionality. The conformation of the polymer in solution is influenced by a variety of structural parameters. Polymer architecture, such as random or blocky arrangement of the hydrophobic groups will have a significant influence on polymer conformation and interactions in solution. The presence of hydrophobic functionality can result in inter- or intramolecular association or some combination of both. The relative amounts of these types of association will affect the conformation of the molecules in solution and in turn the properties of the solution. While many chemically different systems, such as hydrophobically modified cellulose [19], urethanes [15], and others [11] have been described in the literature, we will focus on only a few critical structures. To illustrate the relationships between structure and the observed solution phenomena, three types of hydrophobically associating polymers will be discussed as shown in Fig. 3.1. These are  

It has been first demonstrated in 1977 by MacDiarmid et that films of polyacetylene can be chemically doped to semiconducting and metallic states. Shortly thereafter the possibility of electrochemical doping, resulting in highly conducting materials, had been shown not only for polyacetylene but also for a number of other polyenes, polyphenylenes and polychalcogenides.  

Electrochemical doping is reversible and thus polymers which can be successfully cycled between two dopant levels can serve as rechargeable electrodes. Only polyacetylene, poly(p-phenylene) and poly(p-phenylene sulfide) are both oxidizable and reducible. Other conducting polymers can only be either p- or n-doped. 

The first rechargeable cells described in 198were based on a doped polyacetylene film serving as a positive electrode coupled with the negative lithium electrode in a nonaqueous electrolyte. Later versions included cells constructed of p- and n-doped polyacetylene films. Since then, several other systems have also been studied for potential battery applications. They include doped 

In most cases, difficulties in achieving doping levels which would ensure sufficiently high specific energy. 

Concerns about stability of electrodes under conditions of prolonged cycling. 

The spinodal curve and the critical points (including multiple critical points) only depend on few moments of the molar-mass distribution of the polydisperse system while the cloud-point curve the shadow curve and the coexistence curves are strongly influenced by the whole curvature of the distribution function. The methods used that include the real molar-mass distribution or an assumed analytical distribution replaced by several hundred discrete components have been reviewed by Kamide. In the 1980s continuous thermodynamics was applied, for example, by Ratzsch and Kehlen to calculate the phase equilibrium of a solution of polyethene in supercritical ethene as a function of pressures at T= 403.15 K. The Flory s model was used with an equation of state to describe the poly-dispersity of polyethene with a a Wesslau distribution. Ratzsch and Wohlfarth applied continuous thermodynamics to the high-pressure phase equilibrium of ethene [ethylene]-I-poly(but-3-enoic acid ethene) [poly(ethylene-co-vinylace-tate)] and to the corresponding quasiternary system including ethenyl ethanoate [vinylacetate]. In addition to Flory s equation of state Ratzsch and Wohlfarth also tested the Schotte model as a suitable means to describe the phase equilibrium neglecting the polydispersity with respect to chemical composition of the 

Beginning in the 1990s calculations of high-pressure phase equilibria of polydisperse polymer systems were performed. For example, Enders and de Loos calculated cloud-point and spinodal curves in the high-pressure range for methylcyclohexane + poly(ethenylbenzene) and compared their results with experimental data. Enders and de Loos ° used a Gibbs-energy model with pressure dependent parameters and models that include an equation of state, such as the lattice fluid model introduced by Hu et for the monodisperse and 

U= ) illustrating the hour-glass behaviour of the cloud-point and the 

The Sako-Wu-Prausnitz equation of state was also applied to high-pressure phase equilibria of polyolefin systems by Tork et alP The calculations were based on the pseudo-component method where the number of pseudo-components used were between 2 and 8. The small number of pseudo-components is a result of the very efficient estimation method used to adjust the pseudo-components to the moments of the distribution function (described in section 9.3.1). In so doing Tork et alP were able to provide a good description of the experimental data and show, perhaps not surprisingly, the agreement between calculated and experimental data improved with increasing number of pseudo-components. 

Browarzik et used the Sako-Wu-Prausnitz equation of state to study 

---

Foreman K W and Freed K F 1998 Lattioe oluster theory of multioomponent polymer systems ohain semiflexibility and speoifio interaotions Adv. Chem. Phys. 103 335... 

Hong K M and Noolandi J 1981 Theory of inhomogeneous multioomponent polymer systems Macromolecules 14 727... 

Semenov A N 1996 Theory of long-range interaotions in polymer systems J. Physique II 6 1759... 

In tire limit of a small defonnation, a polymer system can be considered as a superjDosition of a two-state system witli different relaxation times. Phenomenologically, tire different relaxation processes are designated by Greek... 

The complexity of polymeric systems make tire development of an analytical model to predict tlieir stmctural and dynamical properties difficult. Therefore, numerical computer simulations of polymers are widely used to bridge tire gap between tire tlieoretical concepts and the experimental results. Computer simulations can also help tire prediction of material properties and provide detailed insights into tire behaviour of polymer systems. A simulation is based on two elements a more or less detailed model of tire polymer and a related force field which allows tire calculation of tire energy and tire motion of tire system using molecular mechanisms, molecular dynamics, or Monte Carlo teclmiques 1631. 

Doi, M. and Edwards, S.F., 1978. Dynamics of concentrated polymer systems 1. Brownian motion in equilibrium state, 2. Molecular motion under flow, 3. Constitutive equation and 4. Rheological properties. J. Cheni. Soc., Faraday Trans. 2 74, 1789, 1802, 1818-18.32. 

Quantum meehanieal modeling of polymer systems is reviewed in... 

Comparable but equally specific considerations must be applied to other condensation polymer systems. The following example is an illustration of the application of these ideas to the molecular weight of polyamides. 

The methods we consider have been developed by Stockmayer and Flory and have been applied to quite a variety of polymer systems and phenomena. 

This contrasts with a limiting ratio of 2 for the case of termination by disproportionation. Since and can be measured, this difference is potentially a method for determining the mode of termination in a polymer system. In most instances, however, termination occurs by some proportion of both modes. Although general expressions exist for the various averages and their ratio when both modes of termination are operative, molecular weight data are generally not sufficiently precise to allow the proportions of termination modes to be determined in this way. 

Dyeing accelerants Dyeing classes Dyeing of leather Dyeing paper Dyeing processes Dye initiators Dye-in-polymer systems Dye intermediates... 

Cychc acroleki acetals are, ki general, easily formed, stable compounds and have been considered as components ki a variety of polymer systems. Table 6 Hsts a variety of previously prepared cychc acroleki acetals and thek boiling points (69). 

Polymer systems have been classified according to glass-transition temperature (T), melting poiat (T ), and polymer molecular weight (12) as elastomers, plastics, and fibers. Fillers play an important role as reinforcement for elastomers. They are used extensively ia all subclasses of plastics, ie, geaeral-purpose, specialty, and engineering plastics (qv). Fillets are not, however, a significant factor ia fibers (qv). 

The assessment of the contribution of a product to the fire severity and the resulting hazard to people and property combines appropriate product flammabihty data, descriptions of the building and occupants, and computer software that includes the dynamics and chemistry of fires. This type of assessment offers benefits not available from stand-alone test methods quantitative appraisal of the incremental impact on fire safety of changes in a product appraisal of the use of a given material in a number of products and appraisal of the differing impacts of a product in different buildings and occupancies. One method, HAZARD I (11), has been used to determine that several commonly used fire-retardant—polymer systems reduced the overall fire hazard compared to similar nonfire retarded formulations (12). 

Brominated Diphenyl Oxides. Brominated diphenyl oxides are prepared by the bromination of diphenyl oxide. They are often referred to as diphenyl ethers. Taken together, the class constitutes the largest volume of brominated flame retardants. They range ia properties from high melting sohds to hquids. They are used, as additives, ia virtually every polymer system. 

Antagonism between antimony oxide and phosphoms flame retardants has been reported in several polymer systems, and has been explained on the basis of phosphoms interfering with the formation or volatilization of antimony haUdes, perhaps by forming antimony phosphate (12,13). This phenomenon is also not universal, and depends on the relative amounts of antimony and phosphoms. Some useful commercial poly(vinyl chloride) (PVC) formulations have been described for antimony oxide and triaryl phosphates (42). Combinations of antimony oxide, halogen compounds, and phosphates have also been found useful in commercial flexible urethane foams (43). 

Phase Separation. Microporous polymer systems consisting of essentially spherical, intercoimected voids, with a narrow range of pore and ceU-size distribution have been produced from a variety of thermoplastic resins by the phase-separation technique (127). If a polyolefin or polystyrene is insoluble in a solvent at low temperature but soluble at high temperatures, the solvent can be used to prepare a microporous polymer. When the solutions, containing 10—70% polymer, are cooled to ambient temperatures, the polymer separates as a second phase. The remaining nonsolvent can then be extracted from the solid material with common organic solvents. These microporous polymers may be useful in microfiltrations or as controlled-release carriers for a variety of chemicals. 

Acetylene is condensed with carbonyl compounds to give a wide variety of products, some of which are the substrates for the preparation of families of derivatives. The most commercially significant reaction is the condensation of acetylene with formaldehyde. The reaction does not proceed well with base catalysis which works well with other carbonyl compounds and it was discovered by Reppe (33) that acetylene under pressure (304 kPa (3 atm), or above) reacts smoothly with formaldehyde at 100°C in the presence of a copper acetyUde complex catalyst. The reaction can be controlled to give either propargyl alcohol or butynediol (see Acetylene-DERIVED chemicals). 2-Butyne-l,4-diol, its hydroxyethyl ethers, and propargyl alcohol are used as corrosion inhibitors. 2,3-Dibromo-2-butene-l,4-diol is used as a flame retardant in polyurethane and other polymer systems (see Bromine compounds Elame retardants). 

Dyes for WORM-Disks. Regarding their memory layer, dye-in-polymer systems show advantages over metal layers in their higher stabiHty, lower toxicity, lower heat conductivity, lower melting and sublimation temperature, and simpler manufacturing technique (substrate coating by sublimation or spincoating). 

An important direct use of phosgene is in the preparation of polymers. Polycarbonate is the most significant and commercially valuable material (see Polycarbonates). However, the use of phosgene has been described for other polymer systems, eg, fiber-forming polymeric polyketones and polyureas (90,91). 

---