Linear’ polymer

Mathematical models for the calculation of the molecular weight distribution of linear [36] and nonlinear [37-40] polymers are available, but a detailed discussion of this issue is out of the scope of the present chapter. Instead, some simplified equations for the calculation of the molecular weights of linear polymers in the limiting cases of Smith and Ewart [28] will be presented. 

As discussed above, the MWD depends on the number of radicals per particle. Smith and Ewart [28] distinguished three limiting cases In Case 1 0.5 in Case 2 n = 0.5 and in Case 3 it 0.5. In Cases 1 and 2, the probability of having particles with more than one radical is almost negligible, and hence the system may be considered to be formed by particles with no radicals and particles with one radical (zero-one system). In Case 3, the average number of radicals is large and the kinetics is close to bulk polymerization. 

In spite of the limited number of systems investigated and the small deviations observed, it may be concluded that the Zimm theory with ft-M , or non-free draining behavior, is a good approximation for dynamic mechanical properties of flexible polymers in 0-solvents at infinite dilution for low and intermediate frequencies. This conclusion is in accord with that obtained from the molecular weight dependence 

Non-0-SoIutions. A number of data have been published for the intrinsic complex modulus of flexible polymers in good solvents. Tanaka, Sakanishi and coworkers studied the system of PIB in cyclohexane (2,92,98), polymethyl methacrylate (PMMA) in chloroform (2,9/), PMS in benzene and in toluene (94,99) and a few copolymers of styrene-butadiene in toluene and in cyclohexane (100). Schrag, Ferry et al. reported the results on PS in a-chloronaphthalene and in a chlorinated diphenyl (3), polybutadiene (PBD) in a-chloronaphthalene and in Decalin (101) and PMS in Decalin and in a-chloronaphthalene (102). In all these cases, the frequency dependence of the intrinsic complex modulus is qualitatively described as more Rouse-like as compared with the results for -solutions. Apart from the physical appropriateness, any of the three versions of the Zimm theory can be applied to the experimental results the original Zimm integrodifferential equation 

Tanaka, Sakanishi and coworkers employed the Tschoegl version throughout their analysis and evaluated the values of ft for some of the systems. Except for two 0-solutions for which ft- co as shown above, the reported values of ft are relatively small compared with the results of Ferry et al. shown later. The values for PMS in toluene [ft = 1 (94,99)] and for PMMA in chloroform [ft = 0 (2,9/)] are especially small. For a very small value of ft, e has little effect so that the Rouse theory [27) is applicable to these results. Unfortunately, results for these two systems are less reliable that for PMMA is based on measurement at only one frequency, and that for PMS is an overall result for several samples, that is, the theory was compared with a group of experimental points for various molecular weights but the fit of the theory with ft = 1 is not necessarily the best for each particular sample. Measurements at only three frequencies may not be enough for determination of ft. Quite apart 

Another interesting result obtained for solutions of PIB in cyclohexane by Tanaka et al. (2,92) is shown in Fig. 3.4. The reduced storage modulus at infinite dilution is close to the prediction of the Rouse theory while the loss modulus is not. This result indicates the existence of an additional contribution to the intrinsic viscosity at high frequency which might be a frequency-independent high frequency limit [in contrast with the results for PMS (94,99) and for PIB in toluene (2,92)]. We will return to this subject in the following chapter. 

The application of the Tschoegl theory (39) to the measurements by Johnson, Schrag and Ferry gave larger ft values. An example (3) is shown in Fig. 3.5, where the intrinsic complex modulus is plotted 

In a linear polymer molecule, the monomers form a single long backbone chain. A linear polymer can be schematically represented as shown in Fig. 3.1. As the figure illustrates, the polymer may not be totally linear, but branches, if any exist, are quite rare. Examples of linear polymers are HDPE, LLDPE, PET, nylons, PVC, and 

One determinant of the polymer architecture is the functionality of the monomers from which it is formed. Functionality refers to the number of bonds that a monomer can form with other monomeric molecules during the polymerization process. If the monomer is bifunctional (has a functionality of two), it will generally form a linear polymer. A molecule with a functionality of one cannot form a polymer at all. It can react with one other molecule to form a dimer, but since each of the two molecules has used up its ability to react, it cannot grow further into a polymer. Trifunctional (or higher) monomeric units can produce either branched or cross-linked polymers, depending on the functionality of the monomer and the stoichiometry and conversion of the reaction. 

Examples of bifunctional monomers are H2C=CH2, HOOC-C6H4-COOH, and H2C=CHC1. 

One can attempt to predict somewhat more quantitatively what should be observed for r by using Eqs. (19) and (20) of the craze growth model. We require the value of = (U/4a) (Mj,/ gVM) from Eq. (19) everything in this expression is known approximately except which we take to be thermally activated with an activation enthalpy corresponding to that for flow or diffusion of PS at temperatures well above 

From the correspondence between the calculated and experimental curves we can extract other information. For example the temperature (ca. 72 °C) at which x = 1/2 is shown on Fig. 14b. Above this temperature no more chains break at this temperature and higher, the craze growth is disentanglement dominated. We can use the fact that = 1/2 and Eq. (19) to extract a value for the corresponding to disentanglement of chains at the void interface under these conditions this value is 1.5 x 10 N-s/m, a value that is only reached for polystyrene melts (from zero shear viscosity or diffusion measurements) at a temperature of about 120 °C, or 20° above T.  

2 J Craze-shear Deformation Transitions — High Entanglement Density Polymers 

In some cases, monodisperse samples of the polymer of interest are not available. In such a case, use can be made of the universal calibration procedure. This involves the measurement of intrinsic viscosity. As is shown by Eq. 2.87, the product of intrinsic viscosity and molecular weight is proportional to molecular size, i.e., hydrodynamic volume, which is the actual basis of the separation in a chromatography column. 

In universal calibration, samples of a monodisperse polymer, often polystyrene, that is different from the polymer to be analyzed, are dissolved in the solvent of interest, and the intrinsic viscosities of the resulting solutions are measured. Then identical samples are injected into the column to be used, and the refractive index of the effluent is measured as a function of retention volume, V, which depends on V,. Then a calibration plot of [tj] M versus is prepared, and this plot is assumed to be valid also for the polymer to be analyzed. The retention time can also be used as the independent variable, since it is linear in at constant flow rate. It is convenient to fit an equation, for example a third-order polynomial, to the universal calibration curve. Carrying this concept a step further, if an on-line IV detector is used along with the DRI detector, the data from an analysis can be interpreted directly in terms of a molecular size distribution, and from this the MWD can be determined. 

An on-line viscosity detector actually detects the pressure drop AP resulting from flow at a constant volumetric flow rate, Q through a capillary. The viscosity of the solution is then calculated using PoiseuiUe s equation  

it should be pointed out that the thiol-epoxy click reaction is a feasibility implemented in many important biosynthetic and biomedical applications because the base-catalyzed reactions can be easily carried out in water and in solvent-free conditions with high yield. 

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Kremer K and Grest G S 1990 Dynamics of entangled linear polymer melts a molecular-dynamics simulation J Chem. Phys. 92 5057... 

Most properties of linear polymers are controlled by two different factors. The chemical constitution of tire monomers detennines tire interaction strengtli between tire chains, tire interactions of tire polymer witli host molecules or witli interfaces. The monomer stmcture also detennines tire possible local confonnations of tire polymer chain. This relationship between the molecular stmcture and any interaction witli surrounding molecules is similar to tliat found for low-molecular-weight compounds. The second important parameter tliat controls polymer properties is tire molecular weight. Contrary to tire situation for low-molecular-weight compounds, it plays a fimdamental role in polymer behaviour. It detennines tire slow-mode dynamics and tire viscosity of polymers in solutions and in tire melt. These properties are of utmost importance in polymer rheology and condition tlieir processability. The mechanical properties, solubility and miscibility of different polymers also depend on tlieir molecular weights. 

The structure of the linear polymer formed under a particular set of experimental conditions can be formulated in a number of cases after a detailed examination of its properties. 

By controlhng the relative amounts of, for example, glycerol and phthahc anhydride and the experimental conditions of the reaction, various pol5 mers of different properties are obtained. Under mild conditions (ca. 150°) only the primary alcohol groups are esterified and the secondary alcohol group remains free. The structural unit of the resulting linear polymer is ... 

Polymers that soften or melt and then solidify and regain their original properties on cooling are called thermoplastic. A thermoplastic polymer is usually a single strand of linear polymer with few if any cross-links. 

Homopolymer. Acetal homopolymers are prepared from formaldehyde and consist of high-molecular-weight linear polymers of formaldehyde. 

With copolymers, it is not sufficient merely to describe the empirical formula to characterize the molecule. Another question that can be asked concerns the distribution of the different kinds of repeat units in the molecule. Starting from monomers A and B, the following distribution patterns are obtained in linear polymers ... 

In the foregoing discussions of theoretical models and experimental results, we have focused on linear polymers. We have seen the effect of chain substituents on viscosity. All other things being equal, bulky substituents tend to decrease f and thereby lower 17. The effect is primarily due to the opening up of the liquid because of the steric interference with efficient packing arising from the substituents. With side chains of truly polymeric character, the picture is quite different. 

The low-temperature (remember that this is a relative term Tj = 317°C for polyacrylonitrile) behavior of linear polymers may conveniently be divided into three regimes ... 

Table 5.6 Schematic Illustration Showing the Formation of a Linear Polymer by the Reaction of One of the f- 1 Reactive Groups at the End of a Portion of Polymer...

Cellulose and amylose are comprised of the same glucose subunits as the cyclodexttins. In the case of cellulose, the glucose units are attached through 1,4-P-linkages resulting ia a linear polymer. In the case of amylose, the 1,4-a-linkages, as are found ia the cyclodexttins, are thought to confer heUcity to the polymeric chain. 

For example, a polypeptide is synthesized as a linear polymer derived from the 20 natural amino acids by translation of a nucleotide sequence present in a messenger RNA (mRNA). The mature protein exists as a weU-defined three-dimensional stmcture. The information necessary to specify the final (tertiary) stmcture of the protein is present in the molecule itself, in the form of the specific sequence of amino acids that form the protein (57). This information is used in the form of myriad noncovalent interactions (such as those in Table 1) that first form relatively simple local stmctural motifs (helix... 

The linear polymer of PX, poly(p-xylylene) (PPX) (2), is formed as a VDP coating in the parylene process. The energetics of the polymerization set it apart from all other known polymerizations and enable it to proceed as a vapor deposition polymerization. 

Nickel halide complexes with amines give mixtures of linear polymer and cychc trimers (30). Nickel chelates give up to 40% of linear polymer (31). When heated with ammonia over cadmium calcium phosphate catalysts, propargyl alcohol gives a mixture of pyridines (32). 

Upon treatment with suitable cobalt complexes, methylbutynol cyclizes to a 1,2,4-substituted benzene. Nickel complexes give the 1,3,5-isomer (196), sometimes accompanied by linear polymer (25) or a mixture of tetrasubstituted cyclooctatetraenes (26). 

Depending on their stmctural type, PEPE oils are stable up to 300—400°C ia air. Pure oxygen ia a test bomb at 13 MPa (1886 psi) at temperatures up to 400°C was tolerated with no ignition (43). Densities at 20°C vary from 1.82 to 1.89 g/mL, and viscosities from 10 to 1600 mm /s. The pour poiat for low temperature operation usually ranges from —30 to —70° C, and the viscosity iadex varies from about 50 for low viscosity grades up to 150 for more viscous oils and considerably higher for fully linear polymers (43). 

PuUulan [9057-02-7] first described in detail in 1959, is a water-soluble extracellular a-D-glucan elaborated by the fungus yiureobasidiumpullulans (formerly Eullulariapullulans) (285). It is a linear polymer of maltotriose units linked from the reducing end of one trisaccharidic unit to the nonreducing end of the next trisaccharidic unit by a(l — 6) linkages (286) ... 

In 1967, the Polymer Nomenclature Committee of the American Chemical Society pubHshed proposals for naming linear polymers on the basis of their chemical stmcture (97), which were then introduced into Chemical Abstracts (CA) Indexes and pubHshed in their final form in 1968 (98). 

Polyethylene (PE) is a genetic name for a large family of semicrystalline polymers used mostiy as commodity plastics. PE resins are linear polymers with ethylene molecules as the main building block they are produced either in radical polymerization reactions at high pressures or in catalytic polymerization reactions. Most PE molecules contain branches in thek chains. In very general terms, PE stmcture can be represented by the following formula ... 

Linear polymer with molecular weight of over 3 x 10 . ... 

Polymers from either of these homologous series can be made to predominate by usiag a small excess of the diamine or diacid, respectively. In addition to these linear polymers, cycHc oligomers are also formed, though ia this case n... 

As with all thermoplastic elastomers, the copolyesterethers can be processed as thermoplastics. They are linear polymers and contain no chemical cross-links, thus the vulcanisation step needed for thermosetting elastomers is eliminated and scrap elastomer can be re-used in the same process as virgin material (176—180). 

Oxidative coupling polymerizations represent a general reaction for the preparation of high molecular weight linear polymers from many 2,6-di- and... 

This reaction also plays a role in the degradation of polysulftdes. A back-biting mechanism as shown in equation 6 results in formation of the cycHc disulfide (5). Steam distillation of polysulftdes results in continuous gradual collection of (5). There is an equiUbrium between the linear polysulftde polymer and the cycHc disulfide. Although the linear polymer is favored and only small amounts of the cycHc compound are normally present, conditions such as steam distillation, which remove (5), drive the equiUbrium process toward depolymerization. 

The concept of functionaUty and its relationship to polymer formation was first advanced by Carothers (15). Flory (16) gready expanded the theoretical consideration and mathematical treatment of polycondensation systems. Thus if a dibasic acid and a diol react to form a polyester, assumiag there is no possibihty of other side reactions to compHcate the issue, only linear polymer molecules are formed. When the reactants are present ia stoichiometric amouats, the average degree of polymerization, follows the equatioa ... 

The reaction of diphenic anhydride with excess MDA proceeds through an imide ring opening to produce a linear polymer, or it can react with PMDA to form a cross-linked polymer (5). 

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