Isotope Effect on the Melt–Isothermal Crystallization of

Nov 4, 2015 - The randomness of D and H units in the copolymers was ... growth dimension (n) were estimated on the basis of Avrami's plot, ... Citatio...
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Isotope Effect on the Melt−Isothermal Crystallization of Polyoxymethylene D/H Random Copolymers and D/H Blend Samples Sreenivas Kummara,† Kohji Tashiro,*,† Tomohiro Monma,‡ and Ken Horita‡ †

Department of Future Industry-Oriented Basic Science and Materials, Graduate School of Engineering, Toyota Technological Institute, Tempaku, Nagoya 468-8511, Japan ‡ Research Center, Polyplastics Co. Ltd., Miyajima 973, Fuji, Shizuoka 416-8533, Japan ABSTRACT: We have successfully synthesized a series of polyoxymethylene (POM) random copolymers between the deuterated (D) and hydrogeneous (H) monomeric units by a cationic polymerization reaction. The randomness of D and H units in the copolymers was characterized by the quantitative analysis of 13C NMR and Fourier transform infrared spectral data. The equilibrium melting point T°m was estimated on the basis of Gibbs−Thomson equation using the experimental data of DSC melting points plotted against the crystallite thickness evaluated from the smallangle X-ray scattering data. The T°m of pure D-POM (208.5 °C) is higher than that of pure H-POM (homopolymer, 190.0 °C). The T°m changes systematically with the D content in the copolymer. The blend samples between D-POM and H-POM (homopolymer) show the similar D content dependence, but the T°m is as a whole higher than that of the copolymer. Another type of blend samples consisting of D-POM and H-POM containing small amount of ethylene oxide (Duracon) shows the similar but slightly different D content dependence of T°m, compared with homopolymer case, since Duracon’s melting point is about 5 °C lower than the latter. The kinetics of melt−isothermal crystallization behavior of these copolymers have been investigated using the time-dependent DSC data collected at the various isothermal crystallization temperatures, from which the crystallization rate constant (k) and growth dimension (n) were estimated on the basis of Avrami’s plot, where the induction time of nucleation was corrected. In parallel, the tangential line of Avrami’s curve at the crystallinity 0.5 was analyzed, from which the crystallization rate was estimated. These two methods of analysis were found to give almost the same results. By comparing the thus-obtained parameters among all the samples, several important results were obtained: (i) the POM-D shows the lowest crystallization rate compared with the POM-H samples; (ii) the crystallization rate decreased gradually with the increment of the D content in both the cases of D/H random copolymers and D/H blends when compared at the same ΔTc or the degree of supercooling; (iii) the existence of regimes I and II has been detected, the boundary temperature of which was found to change systematically depending on the D content. The crystallization rates were compared also between the two types of D/H blend samples, which showed remarkably different behaviors as a whole. In this way the isotopic effect on the thermal and crystallization behavior of D/H POM copolymers and blends has been revealed for the first time.

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INTRODUCTION

evolution process in the isothermal crystallization at the different ΔTc on the basis of the simultaneously measured WAXD (wide-angle X-ray diffraction) and SAXS (small-angle X-ray scattering) data combined with the time-resolved infrared spectral data.24−29 The infrared spectra of POM are quite sensitive to the morphological difference between the folded chain crystal (FCC) and the extended chain crystal (ECC).42,43 For example, in the isothermal crystallization process at 130 °C from the melt, the lamellar structure of FCC morphology is formed at first and the taut tie chains are developed in a later timing which pass through the neighboring lamellae and play an important role so that POM works effectively as an engineering plastic. The generation of taut tie chains were detected at 130 °C, but only the mother lamellae were observed at 150 °C.24−29

As well-known, the crystallization behavior of a crystalline polymer is affected sensitively by the various factors such as the crystallization temperature or the degree of supercooling, the molecular weight of the chain, the structural defect, the external stress, etc.1 In particular, the degree of supercooling, defined as ΔTc = T°m − Tc, is quite important as a thermodynamic parameter.2 Here T°m is an equilibrium melting temperature and Tc is a crystallization temperature. The sample is melted above the melting point and cooled sharply to the Tc and is kept at this temperature (isothermal crystallization). The random coils in the melt are regularized and aggregated together to form the crystalline region. This formation process is affected sensitively by the degree of supercooling ΔTc. In the case of polyoxymethylene (POM, −(CH2O)n−), which will be treated here as a target polymer, the situation is the same. Among the many papers published so far to study the crystallization behavior of POM,3−41 we investigated the structural © 2015 American Chemical Society

Received: July 1, 2015 Revised: October 22, 2015 Published: November 4, 2015 8070

DOI: 10.1021/acs.macromol.5b01448 Macromolecules 2015, 48, 8070−8081

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mentioned above. In the present paper, we will focus on the point 1 and describe the details of the crystallization characteristics for a series of POM D/H random copolymers to reveal the isotope effect on the equilibrium melting point T°m in comparison with that of the D/H blend samples at first. The isotope effect on the crystallization kinetics is also investigated for these two types of D/H-mixed POM samples. The present study of crystallization behavior of D/H random copolymers might be the first report although the D/H random copolymers were reported for the several kinds of polymer including syndiotactic polystyrene54,55 and isotactic polypropylene.56,57 The detailed discussion of the above-mentioned point 2 or the utilization of D/H random copolymers in the evaluation of critical sequence length m* will be reported in a separate paper, where the structural evolution of POM chains in the isothermal crystallization is described concretely using the information on m*. Before the experimental results are described below, it is important to mention here that we need to study the behavior of D/H blend samples for the two types of POM-H species. As well-known, there are two types of commercially available POM-H samples, that is, the homopolymer synthesized from trioxane monomers (Delrin, for example) and the copolymer including a small amount of ethylene oxide (EO), for example (Duracon). In our previous paper,41 we utilized Duracon as POM-H component of the D/H blends. However, the D/H random copolymers to be used in the present paper do not contain any EO monomeric unit in the synthesis process. Therefore, we need to compare the crystallization behavior of the D/H random copolymers with the D/H blend samples without any EO component. In addition, we need to compare the behavior between the two types of D/H blend samples: the blends of POM-D with POM-H homopolymer (Delrin) and those with POM-H-EO copolymer (Duracon). This comparison may reveal the effect of EO monomeric unit on the crystallization behavior in addition to the effect of D species. These data should be quite important also from the industrial point of view.

In the present paper, the random copolymers of POM between the deuterated (CD2O) and hydrogeneous (CH2O) monomeric units are focused on, and the isotopic effect on the isothermal crystallization behavior is investigated in detail. The comparison is also made between these D/H copolymers and the blends between the pure D-POM and H-POM samples. The reasons why we study the isotopic effect of POM are as follows. 1. The deuterated sample and its mixtures with the normal (hydrogenated) sample are useful for the study of crystallization. As is well-known, these samples are used for the trace of the geometrical change of a single chain in the melt and the following crystallization process.44,45 In these cases we must always check the cocrystallization of D and H species in the same crystallite. This type of discussion was limited for the crystalline polymers: for example, the D/H blend samples of isotactic polypropylene46,47 and the mixtures of deuterated high-density polyethylene (DHDPE)/hydrogeneous linear low-density polyethylene (LLDPE).48−50 They can cocrystallize perfectly even when the samples are cooled slowly from the melt. A pair of DHDPE and HDPE cannot cocrystallize perfectly but separates partially when cooled slowly from the melt.51 The blend sample of deuterated POM (POM-D, −(CD2O)n−) and hydrogeneous or normal POM (POM-H, −(CH2O)n−) is also a good candidate for this type of study, since these two isotope polymers are almost perfectly cocrystallizable together, as reported before.41 As mentioned above, the ΔTc is important for the study of the crystallization behavior from the melt. Therefore, in the discussion of cocrystallization phenomenon of the D and H species, the knowledge of T°m is indispensable. POM-D and POM-H were found to have the different T°m from each other.41 However, the blend samples of POM-D and POM-H cocrystallize as known from the observation of a single melting (and crystallization) peak in the DSC thermogram, which shifts continuously depending on the D/H content.41 As for the D/H random copolymers consisting of D- and H-monomeric units, such a cocrystallization can be realized necessarily. However, the crystallization behavior might be different from that of the D/H blend samples, since the translational symmetry along the chain is lost totally in the D/H random copolymer. The study of the difference in the crystallization behavior between the D/H polymer blend and D/H random copolymer might be useful for the clarification of the isotope effect on the crystallization of POM. 2. Another importance of the utilization of D/H random copolymer is in the evaluation of the so-called critical sequence length m* of the helical chain, which is a minimal number of monomeric units included in a helix to be detected by the infrared spectral measurement.52−57 The m* is different depending on the vibrational mode. The observation of the various different m* bands at the different timing in the crystallization process tells us how the regular helical chain is formed in the process. The quantitative evaluation of m* value can be made based on the isotope dilution method using a series of D/H random copolymers.52,53 This method tells us the m* values for both the D and H helical chains. Since the D/H random copolymers contain the different average lengths of −(D)n− and −(H)m− sequences in the chains, the investigation of the infrared bands of the concrete m* values in the crystallization process of the D/H random copolymer may reveal the details of the conformational regularization process, although this type of research was not reported at all. In this way, the two points about the utilization of D/H random copolymers (as well as the D/H blend samples) are

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EXPERIMENTAL SECTION

Samples. The D/H copolymers were synthesized through the cationic polymerization reaction using a mixture of H-trioxane [(CH2O)3] and D-trioxane [(CD2O)3] at a certain molar content (D: 0, 29, 48, 69, and 100 mol %) in the dried cyclohexane solution at 50 °C. A small amount of boron trifluoride butyl ether (BF3OBu2) and butyl ether (OBu2) was added as a catalyst, and the solution was stirred continuously up to getting a white powder precipitation. The samples were purified by washing with ethanol.58,59 The end parts of the chains were capped by acetate groups to protect the samples from the easy thermal degradation in the melt. The POM-H samples used here were of two types. One was a commercially obtained Delrin 100 and Delrin 500 as well as the above-mentioned synthesized one (H100). All of these samples were end-capped by acetate groups. Another one was Duracon (MI90), which is a copolymer between trioxane and small amount of EO units (2.2 mol %). Table 1 shows the characterization result of all these samples. In summary, the following three couples of samples were utilized in the experiments: (1) a series of D/H random copolymers, (2) a series of blend samples between POM-D and H100, and (3) a series of blend samples between POM-D and Duracon. The blend samples were prepared by dissolving the pure POM-D and POM-H samples into hexafluoroisopropanol (HFIP) solvent at predecided molar ratios. 13 C NMR Spectra. The characterization of the thus-prepared D/H copolymers was performed with a high-resolution 13C NMR measurement in the deuterated hexafluoroisopropanol (d-HFIP) solution by using a Bruker BioSpin Avance III with CryoProbe at 318 K. The Power Gate method was applied for deleting the spin coupling between 13C and H spins. 8071

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measured thermal energy change, and then the time dependence of the relative crystallanity was derived for Avrami’s analysis. X-ray Diffraction. The small-angle X-ray scatterings (SAXS) were measured using a Rigaku nanoviewer X-ray diffractometer with a Pilatus 300 detector. The incident X-ray beam was the Cu Kα line. The wideangle X-ray diffraction (WAXD) measurement was performed using a Rigaku TTR-III X-ray diffractometer with Cu Kα line as an incident X-ray beam. Figure 1 shows the SAXS and WAXD data measured for Delrin 100 sample as an example. The crystallite size along the chain axis (LcSAXS) was estimated from the first-order peak of SAXS profile by calculating the correlation function of the 1-dimensionally stacked lamellar model (see Figure 1).60 For comparison, the crystallite sized was also estimated using Scherrer’s equation

Table 1. Molecular Weights of POM Samples sample H-POM Delrin 100 Delrin 500 H100 Duracon MI90 D-POM D/H random copolymer D29/H71 copolymer D48/H52 copolymer D69/H31 copolymer

Mw

Mn

Mw/Mn

198000 108000 52400 169000 172000

64400 39200 20000 72800 64800

3.1 2.8 2.6 2.3 2.7

60400 65400 75300

26400 27600 29800

2.3 2.4 2.5

Lc WAXD = Kλ /(β cos θ)

(1)

where K is a constant (0.9), λ is the wavelength of an incident X-ray beam (1.54 Å), β is a full width at a half-maximum peak intensity (FWHM), and 2θ is the diffraction angle.61 In this case, as seen in the WAXD profile givne in Figure 1, the 009 reflection corresponding to the lattice spacing along the chain axis is too weak and overlapped with stronger 200 reflection peak to use for the evaluation of the crystallite size. Rather, the isolated 118 reflection located at around 2θ = 60° was used here. The normal vector of the 118 planes is tilted by about 48° from the c-axis, and the crystallite size along the c-axis was estimated by the equation LcWAXD(00l) = LcWAXD(118) cos(48°). In this process, the FWHM was corrected for the peak broadening due to the slit system using a Si powder as a standard sample. More ideal analysis may be made by taking the paracrystalline distortion of peak profile into account, but it was difficult in this experiment because a series of reflections (118, 2216, ...) could not be detected at all.

Molecular Weight. The molecular weights (Mw and Mn) were evaluated using a SEC (size exclusion chromatography) equipment (Toso HLC-8229GPA with Super HM-M columns) with hexafluoroisopropanol (HFIP) as a solvent. The molecular weights were estimated in terms of poly(methyl methacrylate)s (Polymer laboratories) as standard samples. FTIR Spectra. The infrared spectra of the copolymers were measured with a Varian FTS 7000 Fourier transform infrared spectrometer at the resolution power 2 cm−1 at room temperature. DSC Thermograms. The DSC thermograms were measured using a differential scanning calorimeter TA DSC Q1000 under N2 gas flow at a heating (cooling) rate of 5 °C/min. The isothermal crystallization study has been performed at the different predetermined crystallization temperatures (Tc) immediately after the jump from the melting temperature after holding the sample for 5 min there. More concretely, the sample put in a DSC aluminum pan was heated and kept for 5 min on the hot plate. Immediately after that, the sample pan was set manually onto the DSC sample stage and the lid was covered quickly, during which the thermal energy change was measured continuously up to the end of crystallization process. The background due to the slight temperature fluctuation in the starting point was subtracted from the

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RESULTS AND DISCUSSION Randomness of the Copolymer Chains. As mentioned in the Experimental Section, the POM D/H copolymers were synthesized from the mixture of H- and D-trioxanes in the solution by a cationic polymerization reaction.58,59 This reaction

Figure 1. SAXS and WAXD data measured for Delrin 100 sample. The first-order SAXS peak was used for the calculation of the correlation function of the stacked lamellar structure (see (b)). In the WAXD profile, the 118 reflection peak is isolated, which was used for the estimation of the crystallite size. 8072

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Macromolecules is basically a ring-opening reaction, and the H- and D-trioxane units might be arranged randomly along the polymer chain as illustrated in Figure 2. However, as another possibility, as shown

Figure 3. High-resolution 13C NMR spectra of POM D/H random copolymers measured in the deuterated HFIP solution.

(DDD), CD2O−CD2O−CH2O (DDH), and CH2O−CD2O− CH2O (HDH) from the higher to lower frequency side. The analyses of the integrated intensities of these subpeaks gave the fractions of diad (DD, DH, and HH) and triad sequential probabilities of CD2O and CH2O units. The “run number (R)”, which is defined as the number of boundaries between the different types of sequences in the chain segment consisting of 100 monomeric units, was calculated from the diad values as shown in Table 2 (for example, R = 2·(HD diad fraction) = 0.38 Table 2. 13C NMR Analysis of Diad Fractions and Run Numbers62 of the D and H Monomeric Sequences in the D/H Copolymers of POM copolymer D29/H71

D48/H52

D69/H31

0.51 0.19 0.19 0.11 0.38

0.28 0.22 0.22 0.28 0.44

0.10 0.20 0.20 0.50 0.40

0.42 0.01 0.60

0.50 0.01 1.00

0.42 0.01 0.60

diad HH HD DH DD observed run number (= 2HD) predicted run number random copolymer block copolymer alternate copolymer

Figure 2. Illustration of cationic polymerization reaction of H- and Dtrioxane monomeric units to obtain the D/H POM random copolymer.

in Figure 2, the CH2OCH2OCH2O sequence is cut on the way to give the radicals (−CH2O* + *CH2O−), and these radicals attack the other monomer sequence (−CD2O−CD2O−CD2O−). This chain transfer occurs repeatedly to give finally the random copolymer between CH2O and CD2O units. The 13C NMR spectra measured for the deuterated-HFIP solutions are shown in Figure 3. A brief description of the NMR data analysis is as below. As seen in the spectrum of D100/H0 sample, the peaks of 13CD2 unit split into five strong peaks (88.8−89.8 ppm) due to the spin−spin couplings between 13C and D atoms (the number of peaks is 2·n·I + 1, where n or the number of D nuclei connected to 13C atom is 2 and the magnetic spin of D nucleus I = 1). The 13CH2 unit peak detected at about 90 ppm is a singlet because of the decoupling between 13C and H spins by the Power Gate method. The five peaks of 13CD2 unit were found to split furthermore into the several subpeaks as seen in the NMR spectrum of D69/H31 sample, for example. This is because the chemical shifts of 13CD2 peaks are sensitively affected by the change in the environment around 13CD2 unit with an increment of H monomer content. That is to say, these subpeaks correspond to the sequences (triad) of CD2O−CD2O−CD2O

for the copolymer of D 29 mol %).62 The thus experimentally evaluated R values were compared with those predicted for the various possible models: random copolymers of CD2O and CH2O units, block copolymer −(CD2O)n−(CH2O)m−, and alternating copolymer of CD2OCH2O sequence. As seen in Table 2, the R numbers predicted for the random sequences of CD2O and CH2O units were found to fit very well to the observed values. The thus-derived conclusion is that the copolymers used here are not the random copolymers between the D- and H-trioxane monomeric units [(CH2O)3 and (CD2O)3], but they are the random copolymers of the CH2O and CD2O units. Rough estimation gave the averaged sequential lengths of CH2O and CD2O units of only 2−4. The conclusion about the random copolymers was supported by the infrared spectra shown in Figure 4a, where the infrared band at around 620 cm−1, assigned to the COC bending mode,63 was found to shift continuously depending on the D/H content. If these copolymers consist of the multiblock sequences of −(CD2O)n− and −(CH2O)n− or the simple mixture 8073

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difference between CH2O and CD2O units is small, but such a slight mass difference causes a slight change in vibrational frequency and so the change of vibrational coupling, resulting in the change in vibrational coupling between these neighboring units or the continuous shift of the band position. Evalution of T°m of Copolymers and Blends. In the discussion of the crystallization behavior from the melt, the T°m values are important. The T°m may be estimated on the basis of the so-called Gibbs−Thomson equation64 given in eq 2. Tm(L) = T °m [1 − (2/ΔHf )(σ /Lc + σside/(LaL b)] ≈ T °m [1 − (2/ΔHf )(σ /Lc)]

(2)

where σ is the surface energies of the lamella ab planes and σside is the energy of the ac and bc side walls. ΔHf is the heat of fusion per unit volume of the repeating unit. The Li (i = a, b, and c) is the size of the lamella. In general, Lc ≪ La and Lb, and so eq 2 is approximately expressed in the second equation. The T°m is estimated from the intercept of the plot Tm (L) vs 1/Lc. As mentioned in the Experimental Section, the lamellar thickness Lc was obtained from both of SAXS and WAXD data analysis. Figure 5a shows an example of the Gibbs−Thomson

Figure 4. (a) Observed infrared spectra of a series of POM D/H random copolymer samples of FCC morphologies in the 600 cm−1 region. (b) The corresponding infrared spectra measured for the blend samples between POM-D and POM-H (H100). The simulated results of infrared spectral profiles of the POM copolymer models with the various D/H contents are also shown in (c), although the corresponding frequency region is deviated from the experimental data probably due to the potential function parameters used in the calculation (COMPASS). Figure 5. Gibbs−Thomson plots made for the variously crystallized POM-D samples: (a) the comparison of the plot between the SAXS and WAXD data and (b) the comparison between POM-H homopolymers (Delrin 100, Delrin 500 and H100) and POM-H copolymer with EO units (Duracon). It should be noted that the T°m extrapolated to d → ∞ is almost the same among the homopolymers, but it is different from the POM-H copolymer including EO units.

of D and H polymers, the infrared band profiles might be an overlap of the two bands corresponding to these D and H sequences. For demonstrating this situation, the infrared spectra of the blend samples with the various contents of POM-D and POM-H (H100) were measured as shown in Figure 4b, denying a possibility of these copolymer samples to be the D/H blend samples. In this way, the continuous shift of the band position can be interpreted reasonably as a result of the random D and H monomeric units along the copolymer chain. In order to confirm this conclusion further, the computer simulation of the infrared spectra was performed for a series of POM crystal models consisting of POM chains with statistically random D and H monomeric units using a commercial program Cerius2 (Biovia, version 4.10) with COMPASS force field. The simulation results shown in Figure 4c gave the good reproduction of the continuous shift of this band. The COC (and OCO) bending mode is the vibrational mode of POM skeletal chain and can be coupled easily with the mode of adjacent monomeric units. The mass

plot made for the variously crystallized POM-D samples. The SAXS and WAXD data gave the different Lc values, but the T°m extrapolated to Lc → ∞ was essentially the same within the experimental error. However, as seen in eq 1, the crystallilte size estimated by Scherrer’s equation is sensitively affected by the various factors including the coefficient K, correction of half width of the reflection, and so on. Therefore, from here, we will use the crystallite size derived from the SAXS data for the evaluation of Lc for all the samples treated here. Figure 5b shows the Gibbs−Thomson plots for the various POM-H samples listed in Table 1. The estimated T°m is found to 8074

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Macromolecules be almost the same between the POM-H homopolymers or Delrin 100, Delrin 500, and H100 samples which have different molecular weights as seen in Table 1. This is reasonable by knowing that the T°m is the melting point of infinitely large crystallite.64 In other words, the T°ms evaluated for the POM samples with the variously different molecular weights may be compared with each other as long as the molecular weight range is not extremely different. The Duracon sample gave the T°m about 5 °C lower than that of the homopolymers, since EO monomeric units included affect the thermal stability of the crystallite. Figures 6 and 7 show the D content dependences of T°m obtained for a series of D/H random copolymers and blend

Figure 8. Schematic illustration of the thermal analysis in the isothermal crystallization process from the melt. Figure 6. Comparison of the D content dependence of equilibrium melting temperature T°m between a series of D/H copolymers and D/H blend samples (POM-D and POM-H homopolymer (H100)). The solid lines are the theoretically calculated results by taking into account the statistical distribution of D and H species in the crystal lattice, which will be reported elsewhere.

Figure 9. Avrami’s plots with and without the effect of induction time (t0). The various parameters (tstart, t1/2, and tend) are defined for the tangential straight line on the bold-line curve.

POM-H species show the different D content dependence since H100 and Duracon have the different T°m. The Tom is thermodynamically expressed by using the change in enthalpy (ΔHm) and entropy (ΔSm) as follows.

Figure 7. Comparison of the D content dependence of equilibrium melting temperature T°m between the two types of D/H blend samples: the blends of POM-D and POM-H homopolymer (H100) and the blends of POM-D and EO-POM-H copolymer (Duracon). The solid lines are the theoretically calculated results by taking into account the statistical distribution of D and H species in the crystal lattice, which will be reported elsewhere.

T °m = ΔHm/ΔSm = (Hm − Hc)/(Sm − Sc)

(3)

The Hm and Hc are the enthalpy of the melt and crystal, respectively, and Sm and Sc are the corresponding entropies. The ΔHm may be assumed almost equal irrespective of the D/H content, since the intermolecular interactions are essentially the same between the H and D species in the first approximation. On the other hand, the ΔSm may be varied sensitively depending on the D content. In particular, the ΔSm is contributed by many factors including the conformational entropy (ΔSconf), the vibrational entropy (ΔSvib), and the statistically irregular arrangement of the D and H monomeric units or D and H chain stems in the crystalline lamellae (ΔSarray). The ΔSconf is mainly governed by the conformational distribution in the melt, but it is not very much affected by the

samples between POM-D and POM-H, where POM-Hs were H100 in Figure 6 and Duracon in Figure 7. All of these cases show the continuous change of T°m, indicating the coexistence of D and H species in the same crystallite. In the case of D/H random copolymers shown in Figure 6, the T°m of POM-D is the highest, and it decreases gradually with a decrement of D content. On the other hand, the blend samples between POM-D and POM-H homopolymer (H100) show slightly different D content dependence from that of the copolymers. Besides, as seen in Figure 7, the blend samples composed of the different type of 8075

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Table 3. Analysis of DSC Data Obtained in the Isothermal Crystallization of POM-H (Duracon) Based on the Avrami’s Equationa supercooling T°m = 457.5 K ΔTc/K 46.1 43.1 39.1 38.1 36.1 35.1 34.1 33.1 32.1 a

induction time t0/s

obsd half-time at X = 0.5 t1/2 (obsd)/s

calcd halftime at X = 0.5 t1/2 (calcd)/s

obsd end time at X = 1.0 tend (obsd)/s

calcd end time at X = 1.0 tend (calcd)/s

obsd crystallization time span Δt (obsd)/s

calcd crystallization time span Δt (calcd)/s

crystallization rate constant log(k/s−1)

Avrami index n

2.4 16.0 22.7 6.0 13.0 15.0 31.0 47.0 63.6

12.4 ± 0.7 41.7 ± 0.1 69.5 ± 2.2 42.1 ± 0.1 87.5 + 0.3 97.6 + 0.5 264.6 ± 0.3 523.3 ± 0.9 1371.8 ± 3.1

12.3 41.9 68.9 41.8 86.7 98.6 263.7 522.2 1365.2

21.1 ± 0.4 64.8 ± 0.l 104.5 ± 0.1 72.4 ± 0.3 141.9 ± 0.7 162.3 ± 1.7 430.2 ± 1.0 846.5 ± 4.3 21 87.5 ± 21.9

21.0 66.4 103.5 73.9 141.1 158.1 429.7 845.8 2154.2

17.4 ± 1.4 46.1 ± 1.2 70.0 ± 10.0 60.6 ± 2.2 108.8 ± 1.0 129.4 ± 3.4 33 l.2 ± l.6 646.4 + 7.0 1631.4 ± 39.6

17.4 49.0 69.2 64.2 108.4 124.8 331.8 647.0 1615.8

−1.07 −1.37 −1.73 −1.64 −1.94 −1.98 −2.43 −2.76 −3.15

1.08 1.18 1.74 1.70 1.94 2.02 2.05 2.13 2.22

The definition of the various parameters is referred to in Figure 9. The t0 was estimated from the first derivative of the observed X(t) curve.

Figure 10. ΔTc dependence of log(k), −log(Δt), t0, and n values evaluated for POM-H sample (Duracon). The almost same curves are seen for log(k) and −log(Δt), indicating the reasonableness of Avrami’s treatment explained in the text. One deflection point was detected for all the curves, suggesting the existence of regimes (see Figure 14).

equilibrium melting temperature of the crystal consisting of only POM-D chains. The details of the whole theory are skipped here, and only the results are given in Figures 6 and 7, where the solid lines are those calculated using the theoretical equations. The observed data were reproduced quite well by these phenomenological equations. Isotope Effect on Isothermal Crystallization Behavior. The isothermal crystallization behavior was investigated for the D/H copolymers and the D/H blend samples by measuring the time dependences of the DSC thermogram or the exothermic energy change detected in the process of the temperature jump from above Tm to Tc as illustrated in Figure 8. The integration of the exothermic energy ΔQ in the time region from t = 0 to t gave the enthalpy change ΔH(t) accumulated so far, and so the corresponding crystallinity X(t) is given as

small mass difference between CD2O and CH2O units. The ΔSvib is affected by the distribution of vibrational frequencies or the density of vibrational state in the crystal phase. The random arrangement of the D and H species in the crystal lattice affects the ΔSarray, which may be different between the cases of D/H random copolymers and D/H blend samples. The concrete evaluations of these individual entropy terms are quite difficult and beyond the scope of the present paper. We have already derived the phenomenological equations to show the content dependence of on the D content for these two types of D/H mixtures, as will be reported in a separate paper. For example, the T°m of the blend samples between the cocrystallized POM-D and POM-H chains is expressed as follows by using the fraction of the D component X. 1/T °m = X2 /T °m (DD) + (1 − X )2 /T °m (HH) + 2X(1 − X )/T °m (HD)

(4)

t

The probability of side-by-side pairing of the POM-D and POM-D chain stems is X2, for example. T°m(DD) is the

X (t ) ∝ H (t ) = 8076

∫t =0 ΔQ dt

(5) DOI: 10.1021/acs.macromol.5b01448 Macromolecules 2015, 48, 8070−8081

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Macromolecules Table 4. Crystallization Rate Constant k, Index n, and Crystallization Time Δt Obtained for Various POM Samples sample POM-D (T°m 481.5 K)

D/H copolymer D69/H31 (472.8 K)

D48/H52 (469.8 K)

D29/H71 (464.2 K)

POM-H H100 (462.5 K)

Delrin 100 (464.4 K)

ΔTc (K)

log(k/s−1)

n

Δt/2 (s)

58.1 55.5 53.5 51.5 50.5 49.5 48.5 45.5

−0.8 −1.3 −1.5 −1.9 −2.1 −2.5 −2.9 −3.9

2.1 1.9 1.9 1.9 1.6 1.8 1.8 1.7

5.0 13.3 25.9 49.0 88.6 261.0 550.0 5333

47.8 45.8 43.8 41.8 39.8 38.8 36.8 46.8 45.8 41.8 40.8 39.8 37.8 43.2 42.2 40.2 37.2 35.2 32.2 31.2

−1.3 −1.6 −1.8 −2.1 −2.7 −2.9 −3.4 −1.2 −1.3 −1.9 −1.9 −2.2 −2.9 −0.97 −1.00 −1.39 −1.71 −2.01 −2.94 −3.26

2.8 2.0 2.0 1.6 1.9 1.9 2.1 2.1 2.1 1.9 1.8 2.0 1.7 1.6 2.0 1.8 1.7 1.9 2.7 2.2

13.3 22.3 39.1 87.8 262.0 572.4 1480 10.0 12.3 49.9 59.9 108.0 548.2 6.9 6.1 16.4 35.0 72.8 462.5 1015

41.5 40.5 39.5 38.5 37.5 35.5 33.5 32.5 31.5 41.4 38.4 36.4

−1.2 −1.2 −1.5 −1.8 −1.8 −2.0 −2.5 −3.00 −3.5 −2.5 −1.9 −2.3

1.5 1.7 1.7 1.6 1.5 1.5 1.7 1.9 1.8 2.0 2.1 2.1

12.3 11.4 19.7 53.4 59.9 78.7 204.3 702.5 2098 20.1 50.2 111.2

sample

POM-H DuraconM90 (457.3 K)

POM-D + POM-H (Duracon) blends D69/H31

D48/H52 (474.7 K)

D29/H71 (467.9 K)

POM-D + POM-H (H100) blend D48/H52 (476.5 K)

(6)

log[− ln(1 − X (t ))] = n log(k) + n log(t )

(7)

log(k/s−1)

n

Δt/2 (s)

35.4 34.4 33.4 32.4

−2.6 −2.7 −3.1 −3.5

2.0 2.2 2.1 1.7

224.9 340.1 762.7 1196

46.3 43.3 39.3 38.3 36.3 35.3 34.3 33.3 32.3

−1.1 −1.4 −1.8 −1.6 −1.9 −2.0 −2.4 −2.8 −3.1

1.1 1.1 1.8 1.7 1.9 2.0 2.0 2.1 2.2

8.7 23.0 34.9 30.3 54.4 64.6 165.6 232.2 815.7

47.0 45.0 44.0 43.0 42.0 51.7 50.7 49.7 46.7 45.7 44.7 42.7 40.7 45.9 43.9 42.9 40.9 38.9 36.9 34.9 32.9

−3.6 −6.0 −11.3 −12.7 −11.6 −1.2 −1.6 −1.7 −2.2 −2.3 −2.7 −3.1 −3.8 −1.4 −1.5 −1.7 −2.0 −2.1 −2.4 −3.2 −3.7

1.8 1.9 3.4 3.5 3.0 1.6 1.7 2.0 1.9 1.9 2.0 2.2 2.4 2.8 2.3 2.0 2.2 2.4 2.6 3.0 2.9

77.3 655.6 675.7 1394 3256 9.7 25.5 34.4 94.5 117.5 310.7 718.9 2879 13.4 17.1 27.7 59.3 81.1 122.2 774.7 2580

52.5 49.5 48.5 46.5 44.5

−1.1 −1.7 −1.9 −2.6 −4.3

1.5 1.5 1.5 1.2 1.6

8.1 32.4 59.7 316.9 12400

the observed X(t) curve. The k and n values were estimated using eq 7. Since the thus-estimated t0 is still ambiguous, we have checked the reasonableness of the estimated k and n values by comparing tstart, t1/2, and tend, which were introduced in the literature and can be evaluated from the tangential line passing through the point X = 0.5, as shown in Figure 9.66,67 The values of t1/2 and tend can be evaluated relatively easily from the X(t) curve even when the t0 cannot be known definitely from the experimentally obtained X(t) curve.

The thus-obtained X(t) curve is treated on the basis of the Avrami’s equation (6) to estimate the crystallization rate constant k and the crystallization dimension n.65 X(t ) = 1 − exp[−(kt )n ]

ΔTc (K)

However, as seen in Figure 8, the isothermal crystallization of polymer materials involves the induction time (t0) for the creation of nuclei. Avrami’s equation must be applied after correcting the t0. The various methods were reported for the estimation of t0.66−69 We estimated the t0 by calculating the first derivative dX(t)/dt, since it should be zero and stands up for the first time when the nucleation is started at t = t0 (see Figure 9). Then, the time axis of X(t) vs t curve was corrected by shifting

t1/2 = t0 + (ln 2)1/ n /k

(8)

tend = t0 + [n ln 2 + 1]/[kn(ln 2)(n − 1)/ n ]

(9)

The detailed derivations of these equations are given in the Appendix. Table 3 shows an example to show the good 8077

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Macromolecules correspondence among k, n, t0, t1/2, and tend obtained for Duracon samples crystallized at the various temperatures. In this table, the time gap Δt (= tend − tstart = 2(tend − t1/2)) is also listed, which is related with k and n as below and an important measure of the crystallization rate. Δt = 2(tend − t1/2) = 2/[kn(ln 2)(n − 1)/ n ]

(10)

As seen in Table 3, the agreement of t1/2 and Δt with those derived from k and n is quite good, indicating the reasonableness of the data treatments in the present paper. The plots of log(k), −log(Δt), n, and t0 estimated for Duracon sample are shown in Figure 10. The curves of log(k) and −log(Δt) plotted against ΔTc are almost the same, indicating the reasonableness of the data treatment. They show a deflection point at around 36 K. This suggests the existence of regimes in the crystallization process as will be discussed in a later section. The Avrami index n changes from 2 to 1 with an increase of ΔTc. (However, it might be difficult to confirm such an apparently systematic change of n values for all the samples used here, as will be seen in a later section. Rather it might be safer to say that the n is in the range of 1.5 ± 0.5.) The induction time t0 changes also systematically, which decreases almost exponentially with an increment of ΔTc, but showing a deflection point: the creation of nuclei starts faster as the crystallization temperature is lower or for the larger ΔTc. Using the above-mentioned method, the k, n, and Δt were evaluated for a series of D/H random copolymers, the blend samples of H100−POM-D pair, and the blend samples of Duracon− POM-D pair. The results are listed in Table 4 and plotted against the degree of supercoooling ΔTc in Figures 11, 12, and 13,

Figure 12. ΔTc dependences of log(k) evaluated for a series of D/H blend samples between POM-D and POM-H homopolymers (H100). In this figure the result of Delrin 100 is also plotted to show the effect of molecular weight difference between H100 and Delrin 100 samples (refer to Table 1).

Figure 13. ΔTc dependences of log(k) evaluated for a series of D/H blend samples between POM-D and POM-H copolymer including EO units (Duracon).

depending on the degree of supercooling ΔTc. In regime I or in the lower ΔTc region, the nuclei are created at a relatively low probability and the surface is covered by a newly grown sheet. In regime II, the nucleation frequency is increased, and the growth of preexistent nuclei and the deposition of new nuclei occur in parallel, giving the relatively rough crystal surface. In regime III, the nucleation occurs frequently, and the surface becomes quite rough. The total growth rate ki (i = I, II, and III) is expressed in the following equations:1,2

Figure 11. ΔTc dependences of log(k) evaluated for a series of D/H random copolymers of POM.

respectively. The inversed Δt, as already introduced in eq 10, is related closely to the crystallization rate: the narrower Δt corresponds to the higher crystallization rate. When the crystallization rate is compared among the various samples at the same ΔTc, the rate is in the order of POM-H > D/H copolymer > POM-D. In the case of D/H random copolymers, the crystallization rate is higher for the copolymer with higher content of H component. As seen for all the POM samples treated here, the rate constant k (and inversed Δt) shows the deflection point at a particular point Tc*. The two regions separated by this Tc* may correspond to the regimes I and II defined in the Hoffman−Lauritzen theory.1,2 According to their theory, the nucleation and growth of the folded chain crystal is classified into the several regimes

regime I ln(kI) = ln(b0L) − ΔE /(RTc) − [K 2T °m /R ][1/(TcΔTc)] (11-1)

regime II ln(kII) ≈ ln(21/2b0) − ΔE /(RTc) − [K 2T °m /(2R )] × [1/(TcDTc)]

(11-2)

regime III ln(kIII) = ln(ab0L) − ΔE /(RTc) − [K 2T °m /R ] × [1/(TcΔTc)] 8078

(11-3) DOI: 10.1021/acs.macromol.5b01448 Macromolecules 2015, 48, 8070−8081

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Macromolecules where the ΔE is the energy for the transport of molecules in the melt. The coefficient of the third term is related to the energy required for the formation of nuclei of critical size. The plot of ln(k) + ΔE/RTc vs 1/(TcΔTc) was made, as an example, for a series of D/H random copolymers as shown in Figure 14.

Figure 14. Plot of log(k) + ΔE/RTc vs 1/(TcΔTc) for a series of D/H random copolymers. The individual curve is divided into two regimes I and II at a deflection point. The ratio of the slopes between regimes I and II is about 2.1 commonly. Figure 15. (a) Avrami’s plots with and without the effect of induction time t0. These curves were calculated using k = 0.02 s−1, n = 3, and t0 = 70 s (refer to the Appendix). (b) Plot of double logarithm of X(t) against log(t). The X1(t) curve without t0 effect can be fitted well using eq 7. The curve of X2(t) including the induction time t0 cannot be fitted at all to Avrami’s equation. The slope and intercept shown there are nonsense when compared with the original n and k values used in the calculation of X2(t) curve.

In this calculation, ΔE = 6.8 kJ/mol was utilized, which is said to almost common to the various polymers.2,11,12,43,39,42,70 The slope (K2T°m/R) was about 2.4 (POM-H) to 5.2 (POM-D), from which the K2 value was estimated: about 8.8 kJ/mol for POM-H (H100) and 17.8 kJ/mol for POM-D species. These values may be reasonable when compared with those of the other polymers.63 It is important to notice that the boundary temperature (Tc*) between regimes I and II is shifted continuously depending on the D/H molar ratio for both of copolymers and blends. The crystallization behavior in these regimes is affected sensitively by the balance of nucleation and growth of polymer chains on the lamellar surface. The difference in mass between the D and H species and the resultant difference in thermal mobility and chemical potential might determine the aggregation process of these samples. Although the concrete reasons are unknown at the present stage, this type of discussion may be quite important for revealing the essential mechanism of crystallization phenomenon of polymer substance. Another point to notice is that the ratio of the slopes between regime I and regime II was about 2.1 for all the D/H copolymer samples, which is close to the value 2 roughly predicted by eq 11. In other words, these D/H copolymers are found to exhibit regimes I and II almost commonly but in the different crystallization temperatures. The blend samples show also the existence of regimes I and II. It must be noted here that the rate constant k (and Δt) is dependent also on the molecular weight of the sample. In fact, Delrin 100 and H100, which have the different molecular weight as seen in Table 1, show the different k (and Δt) values at the same ΔTc. But, the boundary between the regimes I and II is almost common to these samples. (It is additionally noted that Inoue et al.10,12 reported the regimes II and III of POM-H in the Tc region of 154 °C.)

The equilibrium melting temperature T°m is sensitively dependent on the D/H content. The D content dependence of T°m was found to be different between the blend samples and the copolymers. The phenomenological treatment of thermodynamic equations can interpret these differences reasonably as will be reported elsewhere. The crystallization rate k was found to change sensitively depending on the degree of supercooling ΔTc as well as the D content of the copolymer species and blend samples. In this way we can see very remarkable isotopic effect on the melting and crystallization behavior. The existence of regimes I and II was also revealed. Different from the k value or the crystallization rate itself, the slope ln(kI)/ln(kII) between these two regimes is almost common to the copolymers and blends. It must be emphasized that the boundary temperature between regimes I and II is shifted sensitively and systematically depending on the D/H content in these samples. We need to study the difference in thermal mobility and chemical potential between the POM-D and POM-H species from the microscopic point of view. The blend samples of POM-H and POM-D are cocrystallized in the common crystal lattice, and the T°m changes depending on the D/H content. This suggests that the morphology of the sample should be quite different depending on the different isotopic species. In fact, the morphology of the spherulite grown from the melt is sensitively dependent on the D content as well as the crystallization temperature. The details of the spherulite growth will be described in other paper. As mentioned in the Introduction, the information on the thermal and crystallization behavior of the POM copolymers and blends between the D and H species is indispensable for the

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CONCLUSION A series of POM-D/H random copolymers were synthesized for the first time by the cationic polymerization reaction. 8079

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Macromolecules Therefore, the time span Δt from tstart to tend is given as

application of these substances to the detailed study of crystallization phenomenon of this polymer from the various hierarchical levels.

Δt = tend − tstart = 2(t1/2 − tend) = 2/[kn(ln 2)(n − 1)/ n ]

■

(A-5)

APPENDIX. PROBLEMS IN THE DSC DATA ANALYSIS BASED ON THE AVRAMI EQUATION As pointed out in the text, the Avrami equation should not include the induction time t0 necessary for the generation of nucleus in the isothermal crystallization process. As seen in eq 6, when the double logarithm of X(t) is plotted against log(t) without any correction of t0, the crystallization rate constant k and Avrami index n are seriously different from the correct values. One demonstration is given in Figure 15a. The X(t) curve was calculated using the Avrami equation X1(t) = 1− exp[−(kt)n] with k = 0.02 s−1 and n = 3. At the same time, another curve was calculated using an equation X2(t) = 1−exp[−(k(t − t0))n] with the same k and n values and t0 = 70 s. As seen in this figure, the X2(t) curve is obtained by shifting X1(t) curve by 70 s along the time axis. Avrami’s equation (6) was applied to these two curves without any correction of t0 because this value cannot be known usually only from the experimentally obtained X2(t) curve. The result is shown in Figure 15b. The correct plot X1(t) gives the straight line, the slope of which corresponds to the value n and the intercept corresponds to n log(k). However, the X2(t) curve cannot give even the straight line, making it impossible to extract the correct k and n values at all. (Some trial was made as shown in Figure 15b with tremendously curious values.) After subtracting the shift t0 from X2(t) data, then, for the first time, we can get the correct answer. How to estimate the t0 value from the experimental data? There were proposed the various methods for this problem,66−69 but some ambiguity remains always for each method. Our method is to calculate the first derivative of X2(t) curve, which should stand up from the horizontal zero baseline at t = t0 as indicated in Figure 9. Of course, the thus-estimated t0 might have still some ambiguity more or less. Therefore, we need to check the reasonableness of the Avrami treatment carried out after the correction of t0 by comparing the various parameters which can be evaluated experimentally: t1/2, tend, and Δt (see Figure 9). In particular, the Δt (= 2(tend − t1/2)) is obtained from the difference between tend and t1/2 and is not affected by the existence of t0. The relations between these parameters and k and n values are easily derived in the following way. The t1/2 or the time at X2(t) = 0.5 is given by t1/2 = t0 + (ln2)1/ n /k

The slope of this straight line is equal to 1/Δt, which may be a measure of the crystallization rate and related to the k and n as given in eq A-5. In other words, the k and n values obtained by Avrami’s analysis after the correction of t0 should reproduce the values of tend and tstart estimated from the experimental curve X2(t). The actual check was made in Table 3.

■

*E-mail [email protected] (K.T.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was supported financially by MEXT “Strategic Project to Support the Formation of Research Bases at Private Universities (2010−2014)”. The authors thank Dr. Toshiaki Kitano and Mr. Takashi Nishu, Nagoya university, for their kind supply of D-trioxane. They also thank Dr. Masatoshi Iguchi for his discussion about the synthesis of POM samples.

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b = (1 − n(ln 2))/2

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(A-1)

Therefore, the straight line, which passes a point (t1/2, X = 0.5) and is tangential to the curve X2(t), can be expressed as X3(t ) = a(t − t0) + b ,

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a = kn(ln 2)(n − 1)/ n /2, (A-2)

For X3(t) = 1.0 tend = t0 + (1 − b)/a = t0 + [n ln 2 + 1]/[kn(ln 2)(n − 1)/ n ] (A-3)

For X3(t) = 0.0 tstart = t0 − b/a = t0 + [n ln 2 − 1]/[kn(ln 2)(n − 1)/ n ] (A-4) 8080

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