Specific volume crystalline

Swan, P. R. Polyethylene specific volume, crystallinity, and glass transition. J. Polymer Sci. 42, 525-534 (1960). 

As noted above, not all techniques which provide information regarding crystallinity are useful to follow the rate of crystallization. In addition to sufficient sensitivity to monitor small changes, the method must be rapid and suitable for isothermal regulation, quite possibly over a range of different temperatures. Specific volume measurements are especially convenient for this purpose. We shall continue our discussion using specific volume as the experimental method. 

Although the extent of crystallinity is the variable under consideration, time is the experimental variable. Accordingly, what is done is to identify the specific volume of a sample at t = 0 (subscript 0) with V, the volume at t = °° (subscript °o) with and the volume at any intermediate time (subscript t) with the composite volume. On this basis, Eq. (4.39) becomes... 

Figure 13.6 shows the influence of temperature on specific volume (reciprocal specific gravity). The exaet form of the eurve is somewhat dependent on the crystallinity and the rate of temperature change. A small transition is observed at about 19°C and a first order transition (melting) at about 327°C. Above this temperature the material does not exhibit true flow but is rubbery. A melt viseosity of 10 -10 poises has been measured at about 350°C. A slow rate of decomposition may be detected at the melting point and this increases with a further inerease in temperature. Processing temperatures, exeept possibly in the case of extrusion, are, however, rarely above 380°C. 

The occurrence of a restricted range within which most of the melting may be confined when conditions conducive to equilibration are adopted lends support to the concept of a crystalline phase, a subdivided one notwithstanding, having approximately uniform properties throughout. (It follows also that although the crystallites which melt under the conditions described may be small by ordinary standards, they are not so small as to cause their stabilities to be much dimin- —Specific volume-temperature... 

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]. 

The heat of fusion AHf (obtained from the area under the DSC melting curve) and percentage crystallinity calculated from AHf is found to be linearly dependent on butadiene content, and independent of the polymer architecture. This is shown in Figure 3. Also, the density of the block copolymers was found to be linearly dependent on butadiene content (see Figure 4). The linear additivity of density (specific volume) has been observed by other workers for incompatible block copolymers of styrene and butadiene indicating that very little change in density from that of pure components has occurred on forming the block copolymers.(32) While the above statement is somewhat plausible, these workers have utilized the small positive deviation from the linear additivity law to estimate the thickness of the boundary in SB block copolymers.(32)... 

Fig. 1 9 Determination of glass transition and crystalline melting temperatures by changes in specific volume.

Figure 1.67 Specific volume as a function of temperature on cooling from the melt for a polymer that tends to crystallize. Region A is liquid, B liquid with elastic response, C supercooled liquid, D glass, E crystallites in a supercooled liquid matrix, F crystallites in a glassy matrix, and G completely crystalline. Paths ABCD, ABEF, and ABG represent fast, intermediate, and very slow cooling rates, respectively. From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc.

The diameter d of a polymer chain can be estimated from (1) hydrodynamic quantities such as intrinsic viscosity and sedimentation coefficient, (2) the partial specific volume vgp of the polymer, and (3) X-ray crystallographic data of the polymer. Table 2 lists the values of d for liquid-crystalline polymers estimated by different methods. Those determined from hydrodynamic data are close to but slightly larger than those from vsp and crystallographic data, though this may not always be the case. 

The present author (Mott 1949,1956,1961) first proposed that a crystalline array of one-electron atoms at the absolute zero of temperature should show a sharp transition from metallic to non-metallic behaviour as the distance between the atoms was varied. The method used, described in the Introduction, is now only of historical interest. Nearer to present ideas was the prediction (Knox 1963) that when a conduction and valence band in a semiconductor are caused to overlap by a change in composition or specific volume, a discontinuous change in the number of current carriers is to be expected a very small number of free electrons and holes is not possible, because they would form exdtons. 

Figure 1. Schematic presentation of volume and enthalpy as functions of temperature in the liquid, crystalline, and glassy state. Tg, melting temperature, TQf glass temperature, IIs, heat of melting, V8, specific volume difference between crystal and melt.

For the PVN-PEO polyblends, volume changes at melting temperature (Figure 6) as well as x-ray data at room temperature (2) show that the 25% (PEO) blend is completely amorphous, and that the 50 and 75% blends contain significant amounts of amorphous PEO. Calculations based on specific volume data indicate that the crystalline part of both the 50 and 75% blends consists of PEO, whereas the amorphous part contains 46% PEO and 54% PVN. Another important result is that the unusual phenomenon of a well in the modulus temperature curves (Figure 1) was observed only for the blends which exhibit crystallinity. Based on these observations, the behavior of blends could be interpreted by postulating that the amorphous PEO forms a complex phase with PVN in the ratio of 3 to 1 monomer units (i.e., 46 wt. % PEO to 54 wt. % PVN), respectively. 

Crystals suitable for protein x-ray studies may be grown by a variety of techniques, which generally depend on solvent perturbation methods for rendering proteins insoluble in a structurally intact state. The trick is to induce the molecules to associate with each other in a specific fashion to produce a three-dimensionally ordered array. A typical protein crystal useful for diffraction work is about 0.5 mm on a side and contains about 1012 protein molecules (an array 104 molecules long along each crystal edge). Note especially that, because protein crystals are from 20 to 70% solvent by volume, crystalline protein is in an environment that is not substantially different from free solution. 

As there exists a phase equilibrium both phases must have reached in the internal thermodynamic equilibrium with respect to the arrangement and distribution of the molecules the measuring time. Therefore, no time effects or path dependencies of the thermodynamic properties in the liquid crystalline phase should be expected. To check this point for the l.c. polymer, a cut through the measured V(P) curves at 2000 bar has been made (Fig. 6) and the volume values are inserted at different temperatures in Fig. 7, which represents the measured isobaric volume-temperature curve at 2000 bar 38). It can be seen from Fig. 7 that all specific volumes obtained by the cut through the isotherms in Fig. 6 he on the directly measured isobar. No path dependence can be detected in the l.c. phase. From these observations we can conclude that the volume as well as other properties of the polymers depend only on temperature and pressure. The liquid crystalline phase of the polymer is a homogeneous phase, which is in its internal thermodynamic equilibrium within the normal measuring time. 

The density of PTFE undergoes complicated changes during processing and can be monitored by the values of true specific volume. Discontinuity in such data show the transitions at 19 and 30°C (66 and 86°F) and also the very pronounced transition at the crystalline melting point of 327°C (621°F), the latter of which is due to the destruction of crystallinity.22 The melting of the polymer is accompanied by a volume increase of approximately 30%.23 The coefficient of linear expansion of PTFE has been determined at temperatures ranging from -190 to +300°C (+572°F).24... 

Lin et al. [66] have exploited this variation in specific volume of the RAF to control the barrier properties of polyester films. An attempt to correlate the mechanical deformation of PET with the amount of RAF present in these films has been made recently. Moreover, the observations have been that a sample with a larger amount of RAF, on uniaxial compression, shows considerable loss in crystallinity compared to a sample having a lower amount of RAF. These findings have been reported in a recent publication [67]. 

Hoffman, J. D., and J. J. Weeks Specific volume and degree of crystallinity of semicrystalline polychlorotrifluoroethylene, and estimated specific volumes of the pure amorphous and crystalline phases. J. Research Nat. Bur. Standards 60, 465-479 (1958). 

Considering the semicrystalline polymers as a two-phase system with a sharp delineation between the crystalline and the amorphous material, we can use the specific volumes to calculate the weight-fraction degree of crystallinity. 

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