Crystalline polymers density

Thickness of polymer membrane across which diffusion is occurring Weight fraction of molecules that he within the size range i Density of a totally amorphous polymer Density of a completely crystalline polymer Density of polymer specimen for which f>ercent crystahinity is to be determined... 

A) Density of crystalline polymer < density of amorphous polymer... 

Second, in the early 1950s, Hogan and Bank at Phillips Petroleum Company, discovered (3,4) that ethylene could be catalyticaHy polymerized into a sohd plastic under more moderate conditions at a pressure of 3—4 MPa (435—580 psi) and temperature of 70—100°C, with a catalyst containing chromium oxide supported on siUca (Phillips catalysts). PE resins prepared with these catalysts are linear, highly crystalline polymers of a much higher density of 0.960—0.970 g/cnr (as opposed to 0.920—0.930 g/cnf for LDPE). These resins, or HDPE, are currentiy produced on a large scale, (see Olefin polymers, HIGH DENSITY POLYETHYLENE). 

The short side chain branching frequency is inversely proportional to polymer crystallinity. Short branches occur at frequencies of 2—50 per 1000 carbons in chain length their corresponding crystallinity varies from 35 to 75%. Directiy proportional to the polymer density, crystallinity can be calculated by the following formula,... 

Crystallinity and Density. Crystallinity and density of HDPE resins are derivative parameters both depend primarily on the extent of short-chain branching in polymer chains and, to a lesser degree, on molecular weight. The density range for HDPE resins is between 0.960 and 0.941 g/cm. In spite of the fact that UHMWPE is a completely nonbranched ethylene homopolymer, due to its very high molecular weight, it crystallines poorly and has a density of 0.93 g/cm. ... 

Content of Ot-Olefin. An increase in the a-olefin content of a copolymer results in a decrease of both crystallinity and density, accompanied by a significant reduction of the polymer mechanical modulus (stiffness). Eor example, the modulus values of ethylene—1-butene copolymers with a nonuniform compositional distribution decrease as shown in Table 2 (6). A similar dependence exists for ethylene—1-octene copolymers with uniform branching distribution (7), even though all such materials are, in general, much more elastic (see Table 2). An increase in the a-olefin content in the copolymers also results in a decrease of their tensile strength but a small increase in the elongation at break (8). These two dependencies, however, are not as pronounced as that for the resin modulus. 

Crystal Structure. The crystal stmcture of PVDC is fairly well estabhshed. Several unit cells have been proposed (63). The unit cell contains four monomer units with two monomer units per repeat distance. The calculated density, 1.96 g/cm, is higher than the experimental values, which are 1.80—1.94 g/cm at 25°C, depending on the sample. This is usually the case with crystalline polymers because samples of 100% crystallinity usually cannot be obtained. A dkect calculation of the polymer density from volume changes during polymerization yields a value of 1.97 g/cm (64). If this value is correct, the unit cell densities may be low. 

Crystallization kinetics have been studied by differential thermal analysis (92,94,95). The heat of fusion of the crystalline phase is approximately 96 kj/kg (23 kcal/mol), and the activation energy for crystallization is 104 kj/mol (25 kcal/mol). The extent of crystallinity may be calculated from the density of amorphous polymer (d = 1.23), and the crystalline density (d = 1.35). Using this method, polymer prepared at —40° C melts at 73°C and is 38% crystalline. Polymer made at +40° C melts at 45°C and is about 12% crystalline. 

Fig. 22.6. A schematic drawing of a largely crystalline polymer like high-density polyethylene. At the top the polymer has melted and the chain-folded segments hove unwound.

In the case of crystalline polymers better results are obtained using an amorphous density which can be extrapolated from data above the melting point, or from other sources. In the case of polyethylene the apparent amorphous density is in the range 0.84-0.86 at 25°C. This gives a calculated value of about 8.1 for the solubility parameter which is still slightly higher than observed values obtained by swelling experiments. 

In principle the heat required to bring the material up to its processing temperature may be calculated in the case of amorphous polymers by multiplying the mass of the material (IP) by the specific heat s) and the difference between the required melt temperature and ambient temperature (AT). In the case of crystalline polymers it is also necessary to add the product of mass times latent heat of melting of crystalline structures (L). Thus if the density of the material is D then the enthalpy or heat required ( ) to raise volume V to its processing temperature will be given by ... 

Since polyethylene is a crystalline hydrocarbon polymer incapable of specific interaction and with a melting point of about 100°C, there are no solvents at room temperature. Low-density polymers will dissolve in benzene at about 60°C but the more crystalline high-density polymers only dissolve at temperatures some 20-30°C higher. Materials of similar solubility parameter and low molecular weight will, however, cause swelling, the more so in low-density polymers Table 10.5). 

In the crystalline region isotactic polystyrene molecules take a helical form with three monomer residues per turn and an identity period of 6.65 A. One hundred percent crystalline polymer has a density of 1.12 compared with 1.05 for amorphous polymer and is also translucent. The melting point of the polymer is as high as 230°C. Below the glass transition temperature of 97°C the polymer is rather brittle. 

It has proved difficult to decide which of these two theories of polymer crystallisation is correct, since both are consistent with the observed effects of crystallinity in polymers. These effects include increased density, increased stiffness, and higher softening point. However, the balance of opinion among those working with crystalline polymers favours the latter theory, based on lamellae formed by the folding of single molecules. 

Copolymerization e.g., of 1-butene or 1-hexene with ethylene, gives short-chain branching-, e.g., the branches contain three or five carbon atoms. The random location of the side-chains lowers the crystallinity and density. Long-chain branching refers to branches that are similar in length to the polymer backbone and this type occurs in polyethylene manufactured using the... 

Volume and mass-based expressions for the degree of crystallinity are easily derived from the experimentally measured density (p) of a semi-crystalline polymer. The method is based on an ideal crystalline and liquid-like two-phase model and assumes additivity of the volume corresponding to each phase... 

Vc crystalline Va, amorphous). The densities of the pure crystalline (pc) and pure amorphous (pa) polymer must be known at the temperature and pressure used to measure p. The value of pc can be obtained from the unit cell dimensions when the crystal structure is known. The value of pa can be obtained directly for polymers that can be quenched without crystallization, polyfethylene terephtha-late) is one example. However, for most semi-crystalline polymers the value of pa is extrapolated from the variation of the specific volume of the melt with temperature [16,63]. 

Here m is the mode order (m — 1,3,5. .., usually 1 for polyethylenes), c the velocity of light, p the density of the vibrating sequence (density of pure crystal) and E the Young s modulus in the chain direction. The LAM band has been observed in many polymers and has been widely used in structural studies of polyethylenes [94—99,266], as well as other semi-crystalline polymers, such as poly (ethylene oxide) [267], poly(methylene oxide) [268,269] and isotactic poly(propylene) [270,271], The distribution of crystalline thickness can be obtained from the width of the LAM mode, corrected by temperature and frequency factors [272,273] as ... 

Annealing can reduce the creep of crystalline polymers in the same manner as for glassy polymers (89,94,102). For example, the properties of a quenched specimen of low-density polyethylene will still be changing a month after it is made. The creep decreases with time, while the density and modulus increase with time of aging at room temperature. However, for crystalline polymers such as polyethylene and polypropylene, both the annealing temperature and the test temperatures are generally between... 

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