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the pores. The smaller-sized polymer molecules penetrate all the beads in the column since their molecular size (actually their hydrodynamic volume) is smaller than the pore size of the beads with the smallest-sized pores. A larger-sized polymer molecule does not penetrate all the beads since its molecular size is larger than the pore size of some of the beads. The larger the polymer molecular weight, the fewer beads that are penetrated and the greater is the extent of transport through the interstitial volume. The time for passage of polymer molecules through the column decreases with increasing molecular weight. The use of an appropriate detector (refractive index, viscosity, light scattering) measures the amount of polymer passing through the column as a function of time. This information and a calibration of the column with standard polymer samples of known molecular weight allow one to obtain the molecular weight distribution in the form of a plot such as that in Fig. 1-4. Not only does SEC yield the molecular weight distribution, but M n and M w (and also M v if a is known) are also calculated automatically. SEC is now the method of choice for measurement of M n and M w since the SEC instrument is far easier to use compared to methods such as osmometry and light scattering.
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1-5 PHYSICAL STATE 1-5a Crystalline and Amorphous Behavior
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Solid polymers differ from ordinary, low-molecular-weight compounds in the nature of their physical state or morphology. Most polymers show simultaneously the characteristics of both crystalline and amorphous solids [Keller et al., 1995; Mark et al., 1993; Porter and Wang, 1995; Sperling, 2001; Woodward, 1989; Wunderlich, 1973]. X-Ray and electron diffraction patterns often show the sharp features typical of three-dimensionally ordered crystalline solids as well as the diffuse, unordered features characteristic of amorphous solids. (Amorphous solids have sometimes been referred to as highly viscous liquids.) The terms crystalline and amorphous are used to indicate the ordered and unordered polymer regions, respectively. Different polymers show different degrees of crystalline behavior. The known polymers constitute a spectrum of materials from those that are completely amorphous to others that possess low to moderate to high crystallinity. The term semicrystalline is used to refer to polymers that are partially crystalline. Completely crystalline polymers are rarely encountered. The exact nature of polymer crystallinity has been the subject of considerable controversy. The fringed-micelle theory, developed in the 1930s, considers polymers to consist of small-sized, ordered crystalline regions termed crystallites imbedded in an unordered, amorphous polymer matrix. Polymer molecules are considered to pass through several different crystalline regions with crystallites being formed when extended-chain segments from different polymer chains are precisely aligned together and undergo crystallization. Each polymer chain can contribute ordered segments to several crystallites. The segments of the chain in between the crystallites make up the unordered amorphous matrix. This concept of polymer crystallinity is shown in Fig. 1-5. The folded-chain lamella theory arose in the last 1950s when polymer single crystals in the form of thin platelets termed lamella, measuring about 10,000 A 100 A, were grown from polymer solutions. Contrary to previous expectations, X-ray diffraction patterns showed the polymer chain axes to be parallel to the smaller dimension of the platelet. Since polymer molecules are much longer than 100 A, the polymer molecules are presumed to fold back and forth on themselves in an accordionlike manner in the process of crystallization. Chain
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Fig. 1-5 Fringed-micelle model of polymer crystallinity.
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folding was unexpected, since the most thermodynamically stable crystal is the one involving completely extended chains. The latter is kinetically dif cult to achieve and chain folding is apparently the system s compromise for achieving a highly stable crystal structure under normal crystallization conditions. Two models of chain folding can be visualized. Chain folding is regular and sharp with a uniform fold period in the adjacent-reentry model (Fig. 1-6). In the nonadjacent-reentry or switchboard model (Fig. 1-7) molecules wander through the nonregular surface of a lamella before reentering the lamella or a neighboring lamella. In the chain-folded lamella picture of polymer crystallinity less than 100% crystallinity is attributed to defects in the chain-folding process. The defects may be imperfect folds, irregularities in packing, chain entanglements, loose chain ends, dislocations, occluded impurities, or numerous other imperfections. The adjacent reentry and switchboard models differ in the details of
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