Density of polyethylene

Use the unit cell dimensions cited above to determine the crystal density of polyethylene. Examine Fig. 4.10 to decide the number of repeat units per unit cell. 

The physical characteristics of polyethylene resins vary widely as a function of their density. The density of polyethylene is highest when it has very few branches to impede the crystallization process. A 3 mm thick plaque of high density polyethylene is an opaque white solid that can... 

The amount of grafted styrene is given by the increase in weight of the film. It may also be calculated quite well from the densities of polyethylene (d ), polystyrene (d2), and the graft copolymer (dj) according to the following Eq.3.31 ... 

Example 2.2 Consider an impact between a polyethylene particle (dp = 1 cm) and a copper wall. The incident velocity is 2 m/s, and the incident angle is 30°. The friction coefficient of the interface is 0.2. The densities of polyethylene and copper are 950 and 8,900 kg/m3, respectively. What is the contact time duration for the collision Estimate the rebound velocity of the particle. Repeat the problem for a copper particle colliding with a polyethylene wall. 

Schuyer showed that for polyethylenes the Rao function according to Eq. (14.8) does not vary with the density, irrespective of whether variations in density are caused by changes in temperature or in structure. Since v is nearly independent of the density, Eq. (14.9) predicts that the longitudinal sound velocity will be roughly proportional to the third power of the density of polyethylene. This is confirmed by Fig. 14.6. 

The polymers mostly used in pharmaceutical packaging are polyethylene, polypropylene, PVC, polyamide, polystyrol, nylon, cellulose acetate, polyethylene terephthtalate, and blends thereof. Copolymers and rubbers are also used. The DSC melting curve of polyethylene used for packaging purposes is characteristic. Low- and high-density polyethylene are differentiated by their melting points. " Melting point and density of polyethylene are linearily correlated. " Crystallinity may be determined as described above for amorphous state. 

The density of polyethylene and other thermoplastic polymers is affected by the shape and spacing of the molecular chains low-density materials have highly branched and widely spaced chains, whereas high-density materials have comparatively straight and closely aligned chains. Polymers of the latter type are called linear. The physical properties are markedly affected by increasing density. 

The mechanisms of the photooxidation of polyethylene and polypropylene have been discussed in depth with particular emphasis on the importance of hydroperoxides as the precursor to free radical formation . Both the kinetics and nature of the photooxidation products of the polymers are markedly controlled by these species especially polypropylene. On the other hand the density of polyethylene has been found to play an important role on the photooxidation rate of the polymer . Here the photostability of the polymer decreased with decreasing film density indicating that oxygen diffusion is impaired by the crystallites and therefore improves stability. In fact, other workers have found that the crystalline regions of polyethylene are unaffected by irradiation in air . These workers also found new crystalline regions are formed on irradiation due to the smaller polymer fragments... 

The British standards BS 2782, Methods 620 A-D [6]. are identical to ISO 1183. ASTM D 792 [7] covers the displacement method and has two procedures, one for the displacement of water and one for that of other liquids. It is not clear why it has been split in this way, and it is notable that there is no mention of using a sinker, nor does it include a pycnometer method. The density gradient method is given in ASTM D 1505 [8] and is very similar to the ISO procedure. There is also an ASTM method for density of polyethylene by means of ultrasound, ASTM D 4883 (9). This works on the principle of measuring sound velocity in the plastic, which correlates to density. The apparatus requires calibrating with reference materials but is claimed to give accuracies of 0.08% or better. The use of the method would mostly be in quality control, and it is questionable whether it should have been standardized. Essentially it describes the use of a commercial in.strumcnt with no apparatus details, not even the frequency used. 

Figure 8.8. The temperature dependence of the crystal unit cell density of polyethylene.

A key to the new low-pressure LDPE technology is the family of transition metal catalysts that triggers the polymerization reaction at very low pressure and temperature. Moreover, most of these new low-pressure processes utilize higher a-olefins such as butene-1 or hexene-1 as a comonomer to regulate the density of polyethylene. The a-olefins comonomers add side groups which spread the plates of the polyethylene crystal apart sufficiently to reduce the density of the polyethylene to 0.920 g/cc or even lower. 

In (semi-)crystalline polymers, the measured density of a sample provides a simple way to estimate the degree of crystallinity. For example, the density of polyethylene shows a strong linear correlation with percent crystallinity... 

HOPE, LDPE, and LLDPE are the three main types of commercial polyethylenes with a combined global consumption of >80 Mt/year. HDPE is a strictly linear homopolymer while LDPE is a long-branched homopolymer because of the different methods of polymerization. LLDPE, on the other hand, is a linear ethylene copolymer with small amounts of a-olefin comonomers such as butene, hexene, or octene. Traditionally, polyethylenes are classified according to the densities. The density of polyethylene decreases as the branching and/or comonomer content increases. The crystallinity and the properties associated with crystallinity, such as stiffness, strength, and chemical resistance, progressively decrease from HDPE to LDPE/LLDPE to POE grades. 

In the simulations with the united atom model (CH2 represented by an appropriate atom of mass 14), the crystal expands or shrinks, depending on the starting temperature and then shows a breathing-mode vibration. The density plots in Fig. 3 show such oscillations about the average which is close to the experimental density of polyethylene. At about the same temperature, different initial structures have slightly different density fluctuations in direction and amplitude, but the same frequency ( 3 x 10 Hz). Assuming that one sees the... 

This dimension is varied in limits 1internal freedom degree (mobility) of pointed chain part. The purpose of present paper is the application of a model [4] for deseription of deformability of carbon plastics based on the high density of polyethylene (HDPE). 

Small differences in crystallinity affect the density. For an exact and reproducible density determination the specimen must be eonditioned and the history of the specimen preparation must be known. Density is often measured together with the melt mass-flow rate and both serve as characteristic material parameters. Therefore, preparation and conditioning method based on the ASTM D2839-87 Standard Practice for Use of a Melt Index Strand for Determining Density of Polyethylene has proved suitable The density is determined on extrudates fi om the melt mass-flow rate measurement after boiling in water for one hour. 

ASTMD2839 1987 Standard Practice for Use of a Melt Index Strand for Determining Density of Polyethylene... 

ASTM D4883 1999 Standard Test Method for Density of Polyethylene by Ultrasonnd Techniqne... 

Representative spectra showing the microstructure of select diene polymers, several copolymers, the effect of density of polyethylene, and the effect of crystallinity on the spectrum of poly(ethylene terephthalate) (PET) are shown in Figs. 18-21, respectively. 

Figure 6.2 Dependence of 100-sec tensile creep modulus at 1% strain on density of polyethylene...

Here Ms is the sample mass Pp, p , and are the densities of polyethylene, nanopartides, and air, respectively Vpe, V , V jp and Vs are the volumes of polyethylene, nanopartides, air, and the entire sample, respectively. Assuming that the sample mass (VsPs), the mass of nanopartides (VpPn), and the densities of all materials are known, Eqs. (7.1) and (7.2) can be used to determine the volume of air (Vair) and its percentage fraction Vair/Vj. The calculations were performed for Pair = 1.3kg/m pM o = 5180kg/m pcds = 4820 kg/m Ppe = 960kg/m and it was assumed that pair Ppe- The values of porosity (the percentage air fraction) and densities of all samples are listed in Table 7.1. The error was determined primarily by the scatter of sample thicknesses ( 4%) and masses ( 0.5%) so that the total error of the measurement did not exceed 4.5%. 

X-ray diffraction measurements show that polyethylene crystallizes in a body-centered orthorhombic unit cell with lattice parameters a = 0.7417 nm, /> = 0.4945 nm, and c = 0.2547 nm at 25 °C. The a, b, and c axes are orthogonal. The chain axes run in the c direction and there are two repeating units per unit cell (one running up the center and one-quarter in each of the four comers). Calculate the crystal density of polyethylene. 

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