Melting in Semicrystalline Polymers PDF

19. Melting in semicrystalline polymers 19.1. Melting of polymer crystals There are several characteristics of the melting behavior of polymers that distinguish them from other materials. They can be summarized as follows. It is not possible to define a single melting temperature for a polymer s...

19. Melting in semicrystalline polymers 19.1. Melting of polymer crystals There are several characteristics of the melting behavior of polymers that distinguish them from other materials. They can be summarized as follows. It is not possible to define a single melting temperature for a polymer sample as the melting generally takes place over a range of temperatures. The melting behavior depends upon the specimen history and in particular upon the temperature of crystallization. The melting behavior also depends upon the rate at which the specimen is heated. The value of Tmo can be estimated by a simple extrapolation procedure. It is found that the observed melting temperature, Tm, for a polymer sample is always greater than the crystallization temperature, Tc and a plot of Tm versus Tc is usually linear. The point at which the extrapolation of the upper line meets the Tm=Tc line then represents the melting temperature of a polymer crystallized infinitely slowly and for which crystallization and melting would take place at the same temperature. This intercept therefore gives Tmo. There is found to be a strong dependence of the observed melting temperature Tm of a polymer crystal upon the crystal thickness l. This can be explained by considering the thermodynamics of melting a rectangular lamellar crystal with lateral dimensions x and y. If it is assumed that the crystal has side surface energy of γs and top and bottom surface energies of γe, then melting causes a decrease in surface free energy of (2xlγs + 2ylγs + 2xyγe). This is compensated by an increase in free energy of ΔGV per unit volume due to molecules being incorporated in the melt 1 rather than in a crystal. The overall change in free energy on melting the lamellar crystal is given by ΔG= xylΔGV - 2(x+y)lγs - 2xyγe For lamellar crystals, the area of the top and bottom surfaces will be very much larger than the sides and so the term 2l(x + y)γs can be neglected. At the melting point of the crystal, ΔG = 0. 2𝛾𝑒 𝑇𝑚𝑜 𝑇𝑚 = 𝑇𝑚𝑜 − 𝑙𝛥𝐻𝑉 where ΔHV is the enthalpy of fusion per unit volume of the crystals. Inspection of this equation shows that for finite size crystals Tm will always be less than 𝑇𝑚𝑜. Also it allows 𝑇𝑚𝑜 and γe to be calculated if T m is determined as a function of l. A plot of Tm against 1/l is predicted to have a 𝑜 2𝛾𝑒 𝑇𝑚 slope of – with 𝑇𝑚𝑜 as the intercept. 𝛥𝐻𝑉 19.2. Annealing When crystalline polymers are heated to temperatures just below the melting temperature there is an increase in lamellar crystal thickness. The driving force is the reduction in free energy gained by lowering the surface area of a lamellar crystal when it becomes thicker and less wide. The lamellar thickening only happens at relatively high temperatures when there is sufficient thermal energy available to allow the necessary molecular motion to take place. This means that the measured melting temperature will depend upon the heating rate because annealing effects will be lower for more rapid rates of heating. 19.3. Factors affecting Tm. 19.3.1. Chemical structure a. Stiffness of the main polymer This is controlled by the ease at which rotation can take place about the chemical bonds along the chain. In general, incorporation of linking groups such as −O− or −CO−O− in the main chain increases flexibility and so lowers Tm (Table 17.4). On the other hand, the presence of a p- 2 phenylene group in the main chain increases the stiffness and causes a large increase in Tm. b. Polar groups Amide linkage −CONH− that allows intermolecular hydrogen bonding to take place within the crystals. The melting points of different polyamides are very sensitive to the degree of intermolecular bonding and the value of the Tm is reduced as the number of −CH2− groups between the amide linkages is increased. Alignment of amide linkages is also important. 3  c. Type and size of side groups For short side groups, the steric effect decreases chain flexibility. This is most easily shown when the effect of having different hydrocarbon side groups in vinyl polymers of the type (-CH2-CHX-)n is considered. The presence of a -CH3 side group regularly placed on each alternate carbon atom along the polyethylene chain leads to a reduction in chain flexibility and means that polypropylene has a higher melting point than polyethylene. 4 However, if the side group is long and flexible, the Tm is lowered as its length is increased. On the other hand, an increase in the bulkiness of the side group restricts rotation about bonds in the main chain and so has the effect of raising Tm. generally, factors that affect the T m of a polymer also change the glass transition temperature Tg and in general these two parameters cannot be varied independently of each other. Also, changing the structure of the polymer may affect the ease of crystallization and although the potential melting point of a crystalline phase may be high, the amount of this phase that may form could be low. d. Molar mass and branching For a particular type of polymer, the value of Tm depends upon the molar mass and degree of chain branching. This is because of the effects of chain ends, which are in low molar mass polymers and the branches in non-linear polymers, both have the effect of introducing defects into the crystals and so lower their Tm. If the molar mass of the polymer is sufficiently high for the polymer to have useful mechanical properties, the effect of varying M upon Tm is not strong. In contrast, the presence of branches in a high-molar-mass sample of polyethylene can reduce Tm by 30 K. Chains ends and branches can be thought of as impurities that depress the melting temperatures of polymer crystals. The behavior can be analyzed in terms of the chemical potentials per mole of the polymer repeat units in the crystalline state µ𝑐𝑢 and in the pure liquid µ𝑜𝑢 (the standard state). For the pure polymer, which is a single-component system µ𝑐𝑢 − µ𝑜𝑢 = −𝛥𝐺𝑢 = −(𝛥𝐻𝑢 − 𝑇𝑆𝑢 ) Where G u is the free energy of fusion per mole of repeat units ΔH u and ΔSu are the enthalpy and entropy of fusion per mole of repeat units. ΔH and ΔS would not be expected to be very temperature dependent between Tm and Tmo, 𝑇𝑚 µ𝑐𝑢 − µ𝑜𝑢 = −𝛥𝐻𝑢 (1 − ) 𝑇𝑚𝑜 µ𝑐𝑢 − µ𝑜𝑢 = 𝑅𝑇𝑙𝑛𝑎 a is the activity of the crystalline phase, which is less than unity due to the presence of the ‘impurity,’ that depresses the melting point to Tm 1 1 𝑅 − 𝑜 =− 𝑙𝑛 𝑎 𝑇𝑚 𝑇𝑚 𝛥𝐻𝑢 5 If the mole fraction of crystallizable polymer is XA, and that of the impurity XB, then to a first approximation Equation becomes, assuming ideal behavior 1 1 𝑅 − 𝑜 =− 𝑙𝑛 𝑋𝐴 𝑇𝑚 𝑇𝑚 𝛥𝐻𝑢 For small values of XB, -ln XA ≈XB, 1 1 𝑅 − 𝑜= 𝑋 𝑇𝑚 𝑇𝑚 𝛥𝐻𝑢 𝐵 Linear polymers have two chain ends and so the mole fraction of chain ends is given approximately by 2/ xn. If these chain ends are considered to be the ‘impurity,’ then 1 1 𝑅 2 − 𝑜= 𝑇𝑚 𝑇𝑚 𝛥𝐻𝑢 𝑥̅ 𝑛 It is easy to modify the Equation to account for branches where the term 2/xn becomes y/xn if there are y ends per chain. e. Copolymer Random or statistical copolymers: the structure is very irregular and so crystallization normally is suppressed, and the copolymers usually are amorphous. In block and graft copolymers, crystallization of one or more of the blocks may take place. 6