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Keywords:

  • annealing;
  • cold crystallization;
  • copolymer;
  • crystal perfection;
  • decoupling;
  • precisely branched polyethylene;
  • reversible melting;
  • temperature-modulated differential scanning calorimetry (TMDSC)

Abstract

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTAL
  5. RESULTS AND DISCUSSION
  6. FINAL DISCUSSION AND CONCLUSIONS
  7. Acknowledgements
  8. REFERENCES AND NOTES

The heat capacity of a linear polyethylene with dimethyl branches, at every 21st backbone atom was analyzed by differential scanning calorimetry (DSC) and quasi-isothermal temperature-modulated DSC. This novel copolyethylene (PE2M) is relatively difficult to crystallize from the melt. On subsequent heating, a first, sharp melting peak is followed by a sharp cold-crystallization and crystal perfection and a smaller endotherm, before reaching the main melting at 315–320 K, close to the melting temperatures of eicosane and tetracontane. The low-temperature melting is sensitive to the cooling rate and disappears below 1.0 K min−1. The cold crystallization can be avoided by heating with rates faster than 80 K min−1. The PE2M exhibits some reversing and reversible melting, which is typical for chain-folded polymers. The glass transition of semicrystalline PE2M is broadened and reaches its upper limit at about 260 K (midpoint at about 0.355 K). Above this temperature, the crystals seem to have a heat capacity similar to that of the liquid. A hypothesis is that the melting transition can be explained by changes in crystal perfection without major alteration of the crystal structure and the lamellar morphology. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3461–3474, 2006


INTRODUCTION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTAL
  5. RESULTS AND DISCUSSION
  6. FINAL DISCUSSION AND CONCLUSIONS
  7. Acknowledgements
  8. REFERENCES AND NOTES

Thermal properties of linear polyethylenes with precisely spaced, identical branches of single methyl-groups (PE1M), dimethyl-groups (PE2M), and single ethyl-groups (PE1E) at every 21st backbone atom were recently analyzed by us.1 These novel copolymers were synthesized via acyclic diene metathesis, ADMET2 and compared to thermal analyses of polymers with similarly precise CH2-sequence lengths: poly(octadecyl acrylate) (PODA),1 which has the CH2-sequences in the side chain, and poly(4,4′-phthaloimidobenzoyldoeicosyleneoxycarbonyl) (PEIM-22),3 which has the CH2-sequences in the main chain. Furthermore, the comparison was extended to a randomly branched, linear-low-density polyethylene of similar 1-octene content (LLDPE),4, 5 as well as a high-density polyethylene (HDPE)1 and the paraffin n-C20H42 (eicosane) and n-C40H82 (tetracontane).6 This research into macromolecules with precise lengths of crystallizable units leads to insights into the nature of crystallization, melting, and decoupling of chain-sequences within macromolecules.

The conclusions from the earlier research were as follows:1 First, it was documented that the melting temperature of the crystallizing sequences is close to Tmath image of eicosane (309.8 K) and tetracontane (333 K), 80–100 K below the melting temperature of HDPE. This decrease is independent of crystallinity and type of crystal, and applies even to the broad peak of LLDPE of the same average length of crystallizable sequences. The entropy effects of mixing and demixing of the defects play a much smaller role than the sequence length. The sharpness of melting, however, increases with precision of the decoupled chain segments. Second, in the precisely controlled copolymers PE1M and PEIM-22 have a crystalline, lamellar morphology of a thickness of 3–4 layers of repeating units.7, 8 The orthorhombic crystal structure of HDPE was not observed in these copolymers.1 Instead, all samples have different, paraffin-like lateral packing, such as the frequently discussed hexagonal, monoclinic or triclinic polyethylene and paraffin structures.9, 10 Third, the crystals are thermodynamically decoupled from the amorphous segments, but transmit strains due to restrictions of volume and conformation, as documented by the broadening of the glass transition to higher temperature. The coupling to the amorphous phase preserves the macromolecular nature of the copolymers and affects the supercooling and rate of crystallization, and also slows reorganization on annealing. The supercooling in the precise copolymers with less hindered points of coupling is smaller than for PE2M (2.0 K for PODA and PE1M, relative to HDPE and LLDPE with 10 and 30 K). This small supercooling approaches the reversibility of crystallization in eicosane and tetracontane. Increasing the hindering, as in PE1E, the supercooling increases to 8 K and PE2M has a dramatically higher supercooling of about 0.30 K, deduced from the peaks in Figure 1.

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Figure 1. Thermal analysis of PE2M on cooling from the melt at 5 K min−1 and on heating by standard DSC at 10 K min−1. Successive curves are shifted vertically for clarity.

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The PE2M is of special interest. When crystallized on cooling from the melt, it reached a crystallinity of 20–30%, lower than the analogous PE1M and PODA. Since the true heats of fusion, ΔHf, are not known this crystallinity, and also those of the other copolymers, is estimated based on of orthorhombic polyethylene. The influence of the copolymer units on ΔHf was neglected, but its temperature-dependence was taken into account. The crystallinities of HDPE, PE1M, PE1E, PODA, and LLDPE at similar cooling rates were 75.5%, 45.5%, 29.6%, 36.1%, and 30%, respectively. At room temperature, the crystal structure of PE2M seemed to show evidence of several paraffinic polymorphs, and on heating after crystallization, a quite unique thermal behavior was revealed with major crystal perfection after initial melting, followed by two additional endotherms, as documented by differential scanning calorimetry (DSC) (center-trace of Fig. 1).1 The bottom curve in Figure 1 shows that on slow, stepwise cooling, as used in quasi-isothermal temperature-modulated DSC (TMDSC), the endotherms change in relative intensity, the sharp cold crystallization exotherm disappears, and the initial crystallinity increases somewhat. This behavior is studied in more detail in this paper to gain a better understanding of the properties of precisely-branched copolymers.

EXPERIMENTAL

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTAL
  5. RESULTS AND DISCUSSION
  6. FINAL DISCUSSION AND CONCLUSIONS
  7. Acknowledgements
  8. REFERENCES AND NOTES

Materials

The polyethylene copolymer with precisely controlled chemical microstructure, PE2M, has a molar mass of 76,000 Da and a polydispersity 1.8. It was synthesized via ADMET.2 The thermal history of the analyzed samples was produced by cooling from the melt, either by continuous cooling at the given rates, by cooling by quasi-isothermal TMDSC with 20 min isotherms at frequent intervals, or by interrupted cooling with or without subsequently continued cooling. Within the melting- and crystallization-peak areas several longer quasi-isothermal TMDSC runs were performed at selected temperatures to detect the level of remaining reversible melting.

Instrumentation

Measurements of heat-flow rates and apparent heat capacities were carried out with a Thermal Analyst 2920™ DSC from TA Instruments, an isoperibol, heat-flux, twin calorimeter, capable of standard and temperature-modulated modes of operation.11 The temperature measurement and modulation control uses the sample-temperature sensor. During the experiments, a refrigerated cooling system with an ultimate cooling capacity to about 210 K was employed, and dry N2 gas with a flow rate of 25 mL min−1 was purged through the DSC cell. The temperature was calibrated in the standard DSC mode, using the onset temperature of the melting-transition peak for indium at 429.75 K, the heat-flow rate was precalibrated at a scanning rate of 10 K min−1 with the specific heat of fusion of indium of 28.62 J g−1.12 After the calibration by standard DSC, the melting temperature of In was measured with quasi-isothermal TMDSC (0.5 K temperature amplitude, modulation period of 100 s) to identify any differences between two modes of measurement. For correction, 0.86 K were added to the average temperatures of the quasi-isothermal TMDSC.

In all experiments, standard aluminum pans of 20 μL volume with covers were used for the sample and as empty reference. Three runs were carried out for the measurements of heat capacity only (1) sapphire versus empty reference pan, (2) empty pan versus empty reference pan, and (3) sample versus empty reference pan.11 A somewhat lighter reference pan was employed for all TMDSC measurements since the reversing heat capacity is identically affected by positive and negative asymmetries due to the 180° shift in phase angle.13 The standard DSC was performed with a heating rate of 10 K min−1 with a 10 min isotherm at the beginning and end. The crystallinity, wc, shown in the figures was calculated from the basic equation

  • equation image(1)

which expresses the differential enthalpy as the sum of the heat capacity effect (∂H/∂T)p,n dT and the latent heat effect (∂H/∂n)p,T dn, where the subscripts p, n, and T indicate the constant p, n, and T during the measurement. The latent heat, ΔH, is the excess above the thermodynamic heat capacity integrated over temperature, so that the crystallinity is taken as wc = ΔHHf, where ΔHf is the heat of fusion at the temperature of the experiment.

The quasi-isothermal TMDSC was performed using sinusoidal modulation about successive base temperatures, To, in steps of 2–30 K, depending on the changes anticipated in the sample response. The modulation period p was 100 s, the amplitude Amath image = 0.5 K (unless otherwise stated). To get information about the reversible cp, waiting times of up to 10 h were employed (see Fig. 9), otherwise, the last 10 of 20 min quasi-isothermal runs were used for the measurement of the apparent, reversing specific heat capacity, cp

  • equation image(2)

where m is the sample mass; cp, the specific heat capacity in J K−1 g−1; and A stands for the respective modulation amplitudes. Note, that Amath imageω is the amplitude of the heating rate for a sinusoidal modulation with frequency ω (= 2π/p, where p is the period in s). The second term in eq 2 contains the calibration factor τ which accounts for the effect of different frequencies. The value of τ is usually evaluated empirically, although for periods of more than 60 s, J is the ratio of the reference heat capacity to the Newton's law constant (J = Cr/K).11

Finally, a note about nomenclature. The cp by TMDSC is usually designated as “reversing” since it may include enthalpy changes due to slow evolution or absorption of latent heat in eq 1. Only if one has established that all irreversible transitions have ceased and that cp is symmetric about To can cp be called reversible, although it may still be an “apparent” cp with contributions from a reversible transition (see Figs. 8 and 9).

RESULTS AND DISCUSSION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTAL
  5. RESULTS AND DISCUSSION
  6. FINAL DISCUSSION AND CONCLUSIONS
  7. Acknowledgements
  8. REFERENCES AND NOTES

Preliminary Results from Standard DSC

Figure 1, above, summarizes the prior standard DSC results for PE2M.1 A single, low-temperature exotherm at 284.4 K characterizes the DSC on cooling. It is interesting that in the subsequent heating, PE2M also starts melting at very low temperature with a melting peak at 290.3 K, followed by an exotherm of cold-crystallization and crystal perfection (annealing) at 293.4 K. Assuming the crystallization and first melting peak refer to the same crystals, their supercooling is only 5.9 K. After crystal perfection, a second and third melting peak appear at 308.4 and 316.5 K, respectively. After long-time annealing, affected by quasi-isothermal TMDSC on cooling, endotherms at lower temperature are visible only as small shoulders and the main peak is moved-up to 317.3 K. The change of crystallinity with temperature was estimated using the two phase model.14

  • equation image(3)

where Cmath image(exp) is the experimental, apparent molar heat capacity in the melting range, Cp(crystal) is the vibrational heat capacity of PE2M, Cp(liquid) is the heat capacity of the melt, wc is the temperature-dependent crystallinity, and the temperature-dependence of ΔHf is calculated from δΔHf(T)/δT = Cp(melt) − Cp(crystal).

Figure 2 displays the crystallinities for the three runs of Figure 1 with approximate baselines. In the heating run after cooling by quasi-isothermal TMDSC, the crystallinity decreases slowly until about 300 K, then it decreases markedly in the region of the melting peak, and at about 320 K, all crystals are molten. During the heating run after cooling at 5.0 K min−1, the crystallinity decreases quickly from about 270 to 293 K, then it increases to 300 K, and finally decreases until all crystals are molten at about 320 K. The first and second decrease in crystallinity represent major melting processes of crystals with largely different perfection, while the increase in crystallinity confirms cold crystallization with crystal perfection. It can be seen from the cooling run, that at 5 K min−1 PE2M starts to crystallize at about 286 K. The discrepancy below 270 K between the two curves in Figure 2 referring to crystals grown at 5 K min−1 is a measure of uncertainty, caused mainly by changes in the baseline between cooling and heating.

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Figure 2. Temperature dependence of the crystallinity for the samples of Figure 1.

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Effect of Annealing on the Melting Behavior Measured by Standard DSC

Judged from the crystallization and melting peaks of Figure 1, the initially growing crystals have a supercooling of only 5.9 K, while relative to the highest melting peak they are 32.9 K supercooled. The dimethyl defects in the PE2M crystals, thus, cause an enormous increase in supercooling when compared to PE1M measured under similar conditions (the crystallization of PE1M shows a supercooling of only 8.9 K from its high-temperature melting peak at 337.1 K).1 To further investigate the endotherms in Figure 1, three cooling experiments from the melt at 10 K min−1 are shown in Figure 3. The first without interruption, the second interrupted for 300 min at 300 K, some 10 K above the low-temperature endotherm in Figure 1, and the third interrupted for 300 min at 313 K, between the last two endotherms in Figure 1. After completion of the cooling at 10 K min−1 to 213 K, the three DSC traces of Figure 3 were performed at 10 K min−1.

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Figure 3. Thermal analysis of PE2M by standard DSC at 10 K min−1 after annealing for 300 min at 300 and 313 K, interrupting the cooling at 10 K min−1. Successive curves are shifted vertically for clarity. The upper curve, as a reference, refers to the continuous cooling as shown in Figure 4.

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The uppermost DSC-trace is similar to the PE2M cooled at 5 K min−1 of Figure 1. After annealing at 313 K, only a small exotherm can be seen in the bottom-trace and the crystallinity is increased to 30.8%, similar to that of PE1E (29.6%).1 The majority species is the high-melting one at 319.8 K. On annealing at 300 K, analyzed with the center-trace, the crystal with intermediate stability is the majority species (Tm = 308.7 K). These experiments demonstrate that the differences in initial crystal growth and perfection follows Ostwald's law of successive states.15 On keeping the sample at 313 K for 300 min, there is little of the lower melting phases seen on subsequent heating. The high-temperature phase is stable over the whole temperature range and the other states are metastable. Cold crystallization and annealing govern the crystal perfection between the two limiting melting peaks.

The Figures 4–6 supply additional details about the cold crystallization and reorganization or annealing. Figure 4 displays the DSC analyses on heating at 10 K min−1 after cooling at rates varying by a factor of 1000. On cooling faster than 5.0 K min−1, the sample temperatures did not maintain the programmed heating rates and did not even reach 213 K after their final isotherm of 5 min. The actual temperatures reached can be read from Figure 4. The fact that increasing the cooling rate towards 100 K min−1 still has an effect on the crystallization can be judged from the decreasing crystallinity.

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Figure 4. Comparison of standard DSC heating-traces after cooling from the melt at 0.1 to 100 K min−1. The dotted vertical lines indicate the three melting peaks on cooling at 5 K min−1. Note that the corresponding curve of Figure 1 was run earlier1 on a somewhat larger sample, causing the 0.1–0.2 K larger peak temperatures. Successive curves are shifted vertically for clarity.

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Figure 5. Thermal analysis of PE2M by standard DSC at 10 K min−1 after quasi-isothermal TMDSC on cooling to the indicated temperatures. Successive curves are shifted vertically for clarity. The dotted top curve is copied from Figure 4 for comparison.

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Figure 6. Comparison of different heating traces by standard DSC after cooling from the melt at 20 K min−1. Successive curves are shifted vertically for clarity.

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On cooling from at 0.1 to 0.5 K min−1, the DSC traces in Figure 4 show that enough time is given for most crystals to assume the high-melting temperature. At faster cooling rates, the low-temperature melting species dominates, and a cold crystallization and annealing exotherm is prominent after the first melting peak, as also seen in Figure 1. On slow cooling, the exotherm is very shallow and can account only for a small fraction of the two higher-melting crystals. The melting peak at the intermediate temperature is seen after cooling at 0.1 K as a shoulder at 305 K, a temperature similar to the long-time annealing at 313 K in Figure 3. This shoulder decreases on cooling at 0.2 K min−1, overlaps on cooling at 0.5 K min−1 with the shallow exotherm moved to higher temperature, to reappear on faster cooling when the exotherm has moved to 295 K and ultimately 290.7 K. These difference in the exotherms may result from some remaining crystallizable and recrystallizable material which undergoes cold crystallization or crystal perfection on heating. The cold crystallization and recrystallization after cooling at 0.1 and 0.2 K min−1 seems to account for most of the crystals melting at the intermediate temperature. Finally, at the slowest cooling rate, a very small, fourth endotherm appears at 276 K, which is of interest in connection with the TMDSC results. Figure 4, thus, illustrates the complex dynamics of crystal perfection during and after crystallization.

With Figure 5 the crystallization during slow cooling in the quasi-isothermal TMDSC is investigated with standard DSC melting curves immediately after completing the TMDSC at the indicated temperatures To. The TMDSC results of all the cooling steps of 20 min each are described with Figure 7, below. First, one can see that waiting at 303 K for 20 min, almost 20 K above the crystallization peak on cooling at 5 K min−1, produces already 0.5% of crystallinity, melting at the temperatures of the last two endotherms. Most likely this indicates that the intermediate crystals grow first under these conditions and anneal at the crystallization temperature to the higher melting crystals. Second, the crystallinities increase with decreasing temperature, as expected. Finally the similarities in the bottom curves of Figures 4 and 5 should be noted. As with the samples cooled at slow rates in Figure 4, there is practically no exotherm and low-temperature melting concentrates in very small endotherms. At 276–277 K, a new, very low-temperature, endotherm is noted (see also Fig. 4), and at 285–289.5 K, a small amount of low-temperature crystals may melt close to the first endotherm seen in Figures 1, 3, and 4.

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Figure 7. Comparison of standard DSC and quasi-isothermal TMDSC. (a) standard DSC on heating after cooling at 5 K min−1 (see Fig. 1) and quasi-isothermal TMDSC on heating after stepwise cooling with TMDSC. (b) standard DSC on cooling (dotted), followed by heating as in Figure 7(a), compared to quasi-isothermal TMDSC on cooling from the melt. (c) Standard DSC and quasi-isothermal TMDSC on heating after stepwise cooling with quasi-isothermal TMDSC from the melt to 217 K. (d) Apparent, reversing Cp on stepwise cooling (filled circles), and reheating (circles).

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One must conclude from these results that on slow cooling crystals grow below 303 K with a melting temperature of 306–308 K which anneal close to the crystallization temperature to melt at about 317 K. Their supercooling is 3–5 K for the as-grown crystals and increases to about 14 K relative to the melting-peak temperature after annealing. The higher crystallinity in Figure 5 (as well as Fig. 4) seems to be caused by residual crystallization at low temperature. One may identify this as secondary crystal growth, influenced by the earlier grown, higher-melting species.

The research of Figure 6, finally, was undertaken to get information about the initial crystals growing on cooling at 1 K min−1 or faster. The starting materials for these experiments were crystallized from the melt by cooling from 443 to 213 K at 20 K min−1. Their melting behavior was checked with a DSC at heating rates varying by a factor 1000. Note, that ratios of heat-flow rate to heating rate are plotted, to be proportional to an apparent cp since the sample mass and placement in the calorimeter were not changed between the runs within the set. After an isotherm of 5 min after cooling, the analyses by heating were begun. On heating at 100 K min−1, which is at the limit of interpretation of the DSC traces set by the instrument lag, the two high-temperature melting peaks have disappeared except for a barely noticeable shoulder at 317 K. Together with Figure 4, this is proof that on cooling at 20 K min−1 or faster, only metastable crystals with a Tm of 290–291 K are produced, and heating at rates above 60 K min−1 eliminates all cold crystallization and annealing.

The overall crystallinity of the different transitions was assessed to be 23.6 ± 2.1% with help of a proper baseline over the heat-flow-rate baselines (see also Fig. 4). The baseline changes from being concave relative to the zero-line, to parallel in the range of highest precision of the DSC from 20 to 1.0 K min−1, to convex at the slowest rates. The crystallinity due to the highest melting peak increases from close to zero at the fastest heating rate to only little more than the overall crystallinity at the lowest heating rate. This suggests that the cold-crystallization exotherm yields little, if any, additional crystallization. The overall process is to be considered a melting and recrystallization and annealing to higher-melting crystals in at least two steps with, overall, only small changes in the heats of fusion.

Reversing Melting of PE2M

Figure 7 presents an overview of the reversing melting. Figure 7(a–c) compares standard DSC and quasi-isothermal TMDSC. In each of the samples there are two small reversing melting peaks. The major one is located in the melting region of the high-temperature crystals (see Figs. 1–7). The minor one is seen at the smallest endotherm in Figures 4 and 5 at 276–277 K. On cooling there are also two reversing crystallization peaks, as can be seen better in Figure 7(d). They agree with the heating experiments, except that the high-temperature peak duplicates only the beginning of melting due to the supercooling before crystallization can begin at 303.1 K.

In Figure 7(c), both the DSC and TMDSC samples were given the same thermal history. The standard DSC and the quasi-isothermal TMDSC traces indicate identical heat capacities from very low temperature to the first reversing endotherm. A comparison with the heat capacity of the liquid and solid from the ATHAS Data Bank16–19 indicates that the glass transition of the semicrystalline PE2M reaches from 220 to about 260 K with a midpoint of 255 K and is followed by an initially fully reversible latent heat for the rather small reversing endotherm at 275 K. All other latent-heat effects which are seen in the standard DSC traces are largely irreversible, except for the shallow reversing high-temperature melting peak at 317.1 K.

Figure 7(d) is an expanded plot of the apparent, reversing Cps in Figure 7(c,b). It permits a comparison of the reversing endotherms on heating and cooling and documents the minimum between the two peaks at the level of the liquid Cp. The peak-heights of the apparent Cp for standard DSC above Cp(liquid) in Figure 7(a) are 1000 J K−1 mol−1 at 290.3 K and 1110 J K−1 mol−1 at 316.5 K, while from TMDSC on heating one finds in Figure 7(d) 23 J K−1 mol−1 at 275.0 K, and 125 J K−1 mol−1 at 317.1 K. In the TMDSC on cooling, the peak-heights in Figure 7(d) above the liquid Cp are 38 J K−1 mol−1 at 277.0 K, and 61 J K−1 mol−1 at 299.1 K. The existence of the reversing endotherm at about 276 ± 1 K on cooling as well as on heating eliminates the possibility that this is a hysteresis peak at the end of the glass transition since hysteresis peaks do not show in the reversing signal in TMDSC and should not appear on cooling.11 A sample history achieved by faster cooling is known to yield a larger high-temperature reversing melting peak20 and can be seen for PE2M in Figure 10(a). The peak height above Cp(liquid) almost triples on cooling at 5 K min−1 (to 325 J K−1 mol−1 at 315.1 K in contrast to the slowly cooled samples of Figs. 7(d) and 9(c).

The dotted lines in Figure 7(c,d) represent the Cp of the amorphous PE2M, while the dashed lines are the vibrational heat capacity of crystalline PE2M. Both were calculated from

  • equation image(4)

where Cp(PE) and Cp(PIBUT) are the respective heat capacities of polyethylene and polyisobutylene from the ATHAS Data Bank.16–19

The reversing and reversible heat capacities, thus, established that only the beginning of low-temperature melting after slow cooling with a peak at 276–277 K is reversible, proven by identical total and reversing Cp in Figure 7(c,d). The main melting peak at 317.1 K has a small fraction of reversing melting, as is common for folded-chain crystals of polymers.20 All other exotherms and endotherms are irreversible. A broadened glass transition is indicated, but no rigid-amorphous fraction is present, an observation also made for HDPE and the other discussed copolymers.1, 20

Details of the Reversing Melting

More details about reversibility in the vicinity of the melting and crystallization peaks are shown in Figure 8(a,b,d,e) graphed as the apparent, reversing heat capacity, the total heat-flow rate 〈Φ〉, and the modulated temperature. Ts. Figure 8(c,f) illustrate the Lissajous figures for the two endothermic peaks. The Lissajous figures are plots of the heat-flow rate versus temperature.

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Figure 8. Detailed analysis in the regions of the reversing peaks of PE2M. Shown are the apparent reversing Cp (upper curves), total heat-flow rate 〈Φ〉 (middle curves), and sample temperature Ts(t) (bottom curves) during cooling (a,b) and subsequent heating (d,e). The corresponding peak temperatures are marked and can be seen in Figure 7(d). Also depicted are two examples of Lissajous figures at the peak temperatures (c,f). In Figure 8(f) the dotted Lissajous figure from a melt measured at slightly higher temperature and rotated by 3°, is superimposed.

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On crystallization when cooling from the melt, as shown in Figure 8(a), both, the total heat-flow rate 〈Φ〉 and the reversing Cp become constant only within the 20 min experiments above 304 K and below 292 K, signaling attainment of instrumental steady state. At the initial crystallization at 303.1 K, both the 〈Φ〉 and the reversing Cp increase slowly with time due to increasing crystal growth. At 299.1 K the crystallization rate is sufficiently fast to reach its maximum in 〈Φ〉, while the reversing Cp increases continuously (indicated by the arrows). Below 297 K through the lowest-temperature endotherm of Figure 8(b) the values of 〈Φ〉 changes too little to show for the chosen scale of the ordinate. The reversing Cp decreases continually, until reaching the minimum at 287.0 K seen in Figure 7(d). Within each quasi-isothermal time period, the reversing heat capacity decreases exponentially, as will be discussed below. The Lissajous figure at the peak temperature of 299.1 K on cooling is shown in Figure 8(c). It starts at a high heat-flow rate for the initial cycles due to the irreversible crystallization and decreases with time, without reaching a constant level of crystallization and melting relative to Lissajous figures from the melting region in the chosen time interval [see also Fig. 9(b)]. Figure 8(b) displays the details on cooling in the vicinity of the small reversing peak at 277.0 K. The peak is clearly visible in the reversing Cp. The exponential decrease with time within each quasi-isothermal time period becomes larger on approaching the peak, and decreases again below the peak temperature. The constant levels reached by the reversing Cp at the high- and low-temperature limits of Figure 8(b) are lower than at 289 K in Figure 8(a), as one expects from the decreasing Cp of liquid PE2M in Figure 7(d). [Note the differences on the scale of the ordinate in Fig. 8(a,b) as well as Fig. 8(d,e) when making quantitative comparisons of the heat capacities].

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Figure 9. Time dependence of the apparent reversing Cp on long-time quasi-isothermal analysis at 299.1 and 277.0 K (a,c), 317.1 and 275.0 K (b,d). See the corresponding temperatures in Figure 7(d).

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Figure 8(d) shows the details about the reversing peak at low temperature on heating from 269 to 283 K [see Fig. 7(d)]. The values of 〈Φ〉 are constant with time after attainment of instrumental steady state and the reversing Cp decrease with time and reach a close-to-constant level after 20 min, qualitatively similar to the cooling runs in this temperature region [see also Fig. 7(d)]. Figure 8(e) shows the details on heating about 299.1 to 323.1 K, the temperature range of the reversing melting peak at high temperature, seen in Figure 7(d). At temperatures ≤309.1 K and ≥321.1 K, the values of 〈Φ〉 start with a slightly more exothermic level before approaching steady state of the instrument. From 311.1–321.1 K, the values of 〈Φ〉 start more endothermic, indicating the major irreversible melting seen in Figure 7(c) in the standard DSC trace. After this irreversible melting is completed, an almost constant total heat-flow rate is reached. The much more expanded scale of the heat capacity illustrates the continuing decrease of the reversing heat capacity toward its reversible limit reached at a much later time, as is shown in more detail in Figure 9(d), below. Only at 323.1 K is Cp(liquid) reached [see Fig. 7(d)].

The Lissajous figure at the peak temperature of 317.1 K is shown in Figure 8(f). It starts at a low heat-flow rate for the initial cycles due to the irreversible melting and decreases more quickly due to the faster melting rate compared to the crystallization [illustrated in Fig. 8(c) and also seen in Fig. 9(d), below]. The experiment approaches an only slowly changing ellipse at the inner part of the figure. This close-to steady state ellipse deviates from an ellipse obtained from the melt at slightly higher temperature (indicated by the superimposed, dotted ellipse). The deviations are close to symmetric melting and crystallization at the high- and low-temperature sides of the ellipse. The beginning of melting and crystallization are separated by about 0.5 K, the estimated lag in sample-temperature relative to the measured temperature.

These experiments in the time and temperature domains support the conclusions of Figure 7 that most of the melting, crystallization, cold crystallization, and annealing are irreversible, in contrast to the behavior of the model-compounds eicosane and tetracontane, which melt fully reversibly. The high-melting peak shows a small amount of time-dependent reversing melting with an even smaller amount of reversible melting, as is common in folded-chain crystals of linear macromolecules. The even smaller reversing endotherm at about 275–277 K, which occurs only on keeping crystals grown at higher temperature for long times at low temperatures, seems to have the behavior of an annealing peak, common also in semicrystalline linear homopolymers.9, 11, 20 The reversible melting within the range of this annealing peak seems to have the level of the thermodynamic heat capacity of the liquid, despite the presence of about 30% crystallinity. By comparison with recent measurements of a large series of poly(oxyethylene)s of different molar masses,21, 22 this high thermodynamic heat capacity may indicate that the heat capacity of the crystals may actually reach that of the liquid because of large-amplitude motion within the crystal. In the case of the poly(oxyethylene)s this could be interpreted as a glass transition of the crystal which occurs somewhat below the melting temperature, as otherwise mainly observed for mesophases of low and high molar mass.23 To resolve this possibility, detailed X-ray data must be obtained, as were for the poly(oxyethylene)s.22

Time Dependence of Reversing Heat Capacities

To identify the changes of the observed reversing melting, which occur before the ultimately remaining reversible melting is reached, the measurement of the time-dependence of the quasi-isothermal TMDSC was extended such that extrapolations to infinite time became possible. In Figure 9 this change of the apparent, reversing heat capacity to the ultimate reversible, apparent heat capacity is illustrated. The reversible apparent heat capacity consists of the thermodynamic heat capacity, known from the expected value from the first two terms of eq 3, and a reversible latent heat, as expressed in eq 1 and the last term in eq 3.

The long-time modulation experiments on cooling at 299.1 and 277.0 K and on subsequent heating at 275 and 317.1 K are marked in Figure 9(a,c), respectively. These four temperatures are at the peak positions for the apparent reversing Cp of Figures 7 and 8. The apparent reversing Cp decreases quickly at the beginning of the experiments, as also seen in Figure 8. After about 50 min, it approaches a constant value. A double-exponential fit to the apparent reversing heat capacities results in the relaxation times τ1 and τ2. The values from Figure 9(b,d) for the high-temperature peak are 23 and 238 min and 12 and 175 min, respectively. The ultimately reached constant levels of apparent reversing heat capacities in Figure 9(a) are 678 and 715 J K−1 mol−1, and in Figure 9(c) they are 662 and 793 J K−1 mol−1 for the two pairs of peak temperatures. These heat capacities are 7.0, 7.4, 5.2, and 14.4% higher than the expected thermodynamic heat capacity from the first two terms in eq 3.

In Figure 9(b), the cooling to 299.1 K is displayed in the time domain. The major irreversible crystallization exotherm initiated by the decrease of temperature lasts for about 30 min as can also be deduced from Figure 8(a) (τ1 = 23 min). The asymmetry of the upper and lower envelope of the modulation indicates that there is an additional exotherm of crystal perfection which relaxes with the much longer time τ2. This slow relaxation in the time scale of hours is thought to describe the perfection of the crystals with a melting peak of 308 K in Figure 3 to such which melt at 317.0 K.

In Figure 9(d), the small first exotherm after heating to 317.1 K shows some evidence of the initial irreversible endotherm of melting in the modulated heat flow-rate [as can be seen better in Fig. 8(e)]. The rate of irreversible fusion in Figure 9(d) is much faster than given by the crystallization exotherm in Figure 9(b). It takes less than 5 min and is mirrored in the small τ1 of 12 min, which contains also contributions from the approach of the DSC to steady state. The subsequent decrease in apparent reversing heat capacity is due, again, to a decreasing exotherm, represented by τ2, and results most likely from the faster perfection of the decoupled segments, which participate in the reversible melting at a higher temperature than in Figure 9(b). The perfected segments will then not contribute to the melting in the subsequent heating half-cycle, just as in initial crystallization of Figure 9(b). If the decreasing apparent heat capacity were due to additional melting, not followed by recrystallization, one would expect the endotherms to decrease more than the subsequent exotherms.

Amplitude and Frequency Dependence of the Reversing Heat Capacity

Figure 10 displays a final set of experiments to check the amplitude and frequency dependence of the reversing melting on quasi-isothermal heating after cooling from the melt at 5 K min−1 and on quasi-isothermal cooling. Figure 10(a) shows the frequency-dependence, while Figure 10(b) gives the amplitude dependence. At lower frequency, i.e., at longer modulation period, the apparent reversing heat capacity in the melting range is higher, i.e., slower processes in the reversible melting can be assessed.20 Below and above the melting range, there is no frequency dependence, as one would expect for an equilibrium Cp caused by a fast molecular vibrational response. Even the isolated conformational response in the liquid is in the picosecond range and practically instantaneous.11

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Figure 10. Frequency and amplitude dependence of the apparent, reversing heat capacity of PE2M on quasi-isothermal TMDSC. (a,b) Changes on heating run after cooling at 5 K min−1 followed by analysis with increasing base temperatures through the transition region. (c,d) Changes on analyzing with decreasing base temperature starting from the melt.

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From the change in reversing Cp with modulation amplitude one expects to image nonlinear transition peaks and see a higher Cp for a smaller Amath image since the deconvolution stretches over a smaller temperature range. One must, however, also consider the effect of the time for one modulation period, which may cause an opposite effect than the pure amplitude dependence. Smaller modulation amplitudes lead at the same period, p, to lower average rates of temperature change, and thus, according to Figure 10(a) to a lower Cp. At the given period of 100 s, Figure 10(b) shows that the observed differences are small, but an amplitude of 0.5 K produces the largest value of the apparent reversing heat capacity, while the amplitude of 0.2 K gave the lowest value, i.e., the results mirror the superposition of the two effects. Furthermore one notes that the observed amplitude-dependence of the reversing Cp for PE2M in the melting range is different from that of poly(oxyethylene) similarly analyzed.21 This difference may indicate differences between the melting and crystallization kinetics of the two polymers. More detailed measurements at larger variation of amplitude and frequency, as is possible with presently evolving new instrumentation, can thus produce more information on melting and crystallization kinetics in the vicinity of the locally reversing melting.

Figure 10(c,d) represent similar results for the quasi-isothermal cooling runs. The initial crystallization leads to a smaller peak height for the higher frequency or shorter period, p since it leaves less time for the overall crystallization and also produces a smaller amount of reversing crystallization. Again, a larger amplitude can yield a larger value of apparent reversing heat capacity since at the same To a lower temperature with faster rate of crystallization can be reached. The time at the lower temperature, however, is also shortened, so that the overall effect in Figure 10(d) is relatively small. In summary, neither frequency nor the amplitude variation show significant effects on the apparent reversing heat capacity over the range of variation applied.

FINAL DISCUSSION AND CONCLUSIONS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTAL
  5. RESULTS AND DISCUSSION
  6. FINAL DISCUSSION AND CONCLUSIONS
  7. Acknowledgements
  8. REFERENCES AND NOTES

Precisely structured PE2M shows a transition behavior different from the conventional, randomly branched polyethylenes copolymers.1, 11 The random copolymers of similar branch-concentration such as LLDPE have a much broader melting range which reaches up to 100 K, compared to the 20 K for each of the three melting peaks of PE2M visible in Figure 3 after the appropriate thermal history. The sharpness of the melting peaks of PE2M and the other precisely structured copolymers is similar to that found for HDPE.1 The observed highest melting-peak temperatures for precisely structured and random copolymers of similar paraffinic sequence-length, in contrast, are similar (PODA = 320 K, PE1M = 337 K, PE2M = 320 K, and LLDPE = 339 K), bracketed by eicosane [Tm(C20H42) = 310 K] and tetracontane [Tm(C40H82) = 333 K].

The more hindered PE2M crystallizes more slowly than PE1M and PE1E, as described earlier,1 and needs more supercooling from the highest melting temperature, which, in turn, leads to an initially lesser crystal perfection, as can be followed with Figures 1–6. Only after slow cooling or cold crystallization and annealing on slow heating do the PE2M samples reach the properties of the less hindered, precisely structured copolymers of the same CH2-sequence lengths (Figs. 3–5). The initial melting endotherm (Tm 290 K) of the quickly crystallized PE2M is followed by a sharp exotherm at 293–296 K and 2nd and 3rd endotherms at 0.305 and 0.317 K, with initial crystallinities between 20 and 30% (when using the heat of fusion of polyethylene for the crystallinity calculation). The thermal history (Figs. 3–5) and heating rates (Fig. 6) have a marked effect on the samples, but show that without recrystallization and annealing, the sample has only the single, low-temperature melting peak. The three distinct melting temperatures, thus, mark increasing levels of crystal perfection. An initial X-ray crystal structure determination at room temperature was interpreted as arising from a simultaneous presence of two or three polymorphs with different paraffinic substructures.1 Preliminary, temperature-resolved data at higher temperature, however, did not show the repeated change to a single polymorph, so that most likely all recrystallization and annealing does not lead to different polymorphs. Further work is planned to address this problem.24 All three melting peaks are sufficiently close to the known melting temperature of eicosane and tetracontane to exclude an increases in the overall lamellar thickness as a reason for the perfection of the crystals which would have to occur in steps of (CH2[BOND])20. Assuming the crystals with highest stability have a similar folded-chain, lamellar crystal morphology of three sequences of (CH2[BOND])20 as in PE1M and PEIM-22,1, 7, 8 perfection of the intralamellar internal defect layers and the crystal-amorphous interface must be the cause for the multiple melting temperatures.

As PE1M, PE1E, and PODA, PE2M exhibits some reversing melting which decreases with crystal perfection (annealing time) to ultimately leave some reversible melting and crystallization. The special signature of this transition is displayed in Figures 7–10. Similar reversible melting is also seen for most other semicrystalline polymer crystals with a folded-chain macroconformation, and is thought to occur on the exposed growth faces of the actively melting crystals.20 Reversing and reversible melting has not been observed for extended-chain crystals of polyethylene,25 poly(oxyethylene),26 and poly(oxytetramethylene)27 and crystals of sharply folded oligomers of poly(oxyethylene).21 For the precisely structured copolymers the reversible melting is also low, in contrast to the random copolymers. It is even less than for the homopolymer HDPE.

On one hand, thus, the melting temperature follows that of a paraffin of a length close to one or two of the 236 crystallizable sequences within the chains of the PE2M. On the other hand, the known reversible melting of paraffins, and their complete crystallization which is typical for chemically pure, oligomeric chains of less than 75 chain atoms is not observed.11 Furthermore, typical properties of semicrystalline polymers and copolymers are observed: A fraction of reversing and reversible melting exists along with the irreversible melting; the glass transition is broadened; and the crystallization is arrested after only a limited crystallinity is reached. All these properties have recently been linked to partial decoupling of chain segments of the polymer molecules.28

This double behavior which points on the one hand to melting as in small segments, and on the other hand to polymers of chain-folded macroconformation9 points to the need to discuss the different types of decoupling of the segments of the precisely structured copolymers. One type is expected to be analogous to the decoupling at the interfaces between lamellar crystals and the amorphous phase, as seen in many semicrystalline, folded-chain polymers.20 It causes a transfer of stress across the phase boundaries between crystalline and amorphous phases and is linked to the broadening of the glass transition to higher temperature and also to the arrest of crystallization before reaching equilibrium.11 In many polymers this transfer of stress is sufficiently severe to cause an additional, rigid-amorphous nanophase with a glass transition fully separated from the bulk-amorphous phase.20 In the present case the observed glass transition in Figure 7(c) is located at about 255 K, in contrast to HDPE, which has a glass transition of 237 K.16 A separate rigid-amorphous phase seems not to be present, as also observed in HDPE and the other discussed copolymers.

The second type of decoupling seems unique for the lamellar crystals of precisely structured copolymers. It is connected to the structure and energetics of the intralamellar defect planes and causes the lowering of the melting temperature to the level of almost fully decoupled oligomeric segments. This lowering of the melting temperature is more than accounted for by the entropy of randomizing of the branch points alone. At the same time, its connectedness along the molecular chain maintains the macromolecular nature of the overall molecule. Further quantitative X-ray diffraction is needed to fully explore the changes causing the three melting points of PE2M and the structural differences from the similarly precisely synthesized PE1M, PE1E, PODA, and PEIM-22.24

Acknowledgements

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTAL
  5. RESULTS AND DISCUSSION
  6. FINAL DISCUSSION AND CONCLUSIONS
  7. Acknowledgements
  8. REFERENCES AND NOTES

This work was supported by the Division of Materials Research, National Science Foundation, Polymers Program, Grant no. DMR-0312233. Some support and use of equipment and laboratory space was provided by the Division of Materials Sciences and Engineering, Office of Basic Energy Sciences, U.S. Department of Energy at Oak Ridge National Laboratory, managed and operated by UT-Battelle, LLC, for the U.S. Department of Energy, under contract number DOE-AC05-00OR22725.

REFERENCES AND NOTES

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTAL
  5. RESULTS AND DISCUSSION
  6. FINAL DISCUSSION AND CONCLUSIONS
  7. Acknowledgements
  8. REFERENCES AND NOTES