Superheated melting kinetics of metastable chain-folded polymer

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Superheated melting kinetics of metastable chain-folded polymer crystals Akihiko Toda, Ken Taguchi, Koji Nozaki, Tatsuya Fukushima, and Hironori Kaji Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.8b00416 • Publication Date (Web): 15 May 2018 Downloaded from http://pubs.acs.org on May 16, 2018

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Crystal Growth & Design

Superheated melting kinetics of metastable chain-folded polymer crystals

Akihiko Toda a*, Ken Taguchi a, Koji Nozaki b, Tatsuya Fukushima c, and Hironori Kaji c a

Graduate School of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima 739-8521, Japan b

Graduate School of Sciences and Technology for Innovation, Yamaguchi University, Yamaguchi 753-8512, JAPAN

c

Institute for Chemical Research, Kyoto University, Uji 611-0011, Japan

* Corresponding author, [email protected], Tel: +81-82-424-6558

1 ACS Paragon Plus Environment

Crystal Growth & Design 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Abstract Unique behavior of superheated melting kinetics of polymer crystals has been examined in terms of the metastable nature of thin polymer crystals with chain folding.

The

superheated melting kinetics was characterized by the heating rate dependence of the melting peak in thermogram.

By examining the behaviors of polyethylene molar mass

fractions, its homolog, hexacontane, and indium, it has been experimentally confirmed that the metastability of crystals with chain folding has an essential role in the superheated melting kinetics; i.e. stable extended-chain crystals of hexacontane melts in the same way as indium without superheating, and metastable chain-folded crystals of higher molar mass polyethylene needs to overcome larger kinetic barrier for melting.


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1. Introduction Melting of polymer crystals examined by thermal analysis shows a unique behavior of superheating [1–5], i.e. shift in the endothermic melting peak of heat flow rate to higher temperature with faster heating rate, β.

Modeling of the melting kinetics explains the

behavior due to a kinetic barrier for melting [2, 4].

Based on a common understanding of

melting, superheating with a kinetic barrier is quite unique because ordinary melting is supposed to proceed at the equilibrium melting point without superheating.

This is

because ordinary crystals can start melting from its corner without creation of any new surfaces, namely with no need of nucleation process. Polymer crystals are very thin in nm scale with chain folding, and hence, due to the Gibbs-Thomson effect of small systems, melting proceeds below the equilibrium melting point of chain-extended infinite-size crystals.

At the front of the melting below the

equilibrium melting point, crystals can re-crystallize and/or re-organize to more stable and thicker crystals.

Therefore, at the melting front, there will be a competition between

melting and the reverse processes of re-crystallization and re-organization, and this competition can be the cause of the kinetic barrier of melting.

If it is really the case,

superheating of melting should be related with the metastability of chain-folded polymer crystals.

The purpose of the present paper is to examine this argument of the influence of

chain folding on the melting kinetics. We have chosen several polyethylene molar mass fractions and its homolog, hexacontane.

Figure 1, the results of small angle X-ray scattering, indicates they are

chain-extended (ECC) or folded (FCC), depending on the molar mass, i.e. chain length, ℓc, and the crystallization conditions. We have examined the heating rate dependence of the melting peak of those materials by conventional and fast-scan calorimetry in comparison with the behavior of melting of a standard material, indium; the typical raw data of conventional thermogram are shown in Fig. 2 which clearly indicates distinguishable behaviors of the heating rate dependence of polyethylene fractions and hexacontane.



0.2 0.10

0.15

0.20

0.0 0.30 1.00.00

0.25

s Icorr /norm.

0.2 0.05

0.10

0.15

0.20

s /nm

0.8

-1

0.15

0.20

0.4

0.4

(e) 52k

0.2 0.05

0.10

0.15

0.20

0.25

0.30

(d) 14k

0.2 0.05

0.10

0.15

0.20

s /nm

0.8

0.25

-1

0.30

(f) 183k

L  43.2nm ℓc  1630.9nm FCC

L  37.0nm 0.6 ℓc  463.4 nm 0.4 FCC

0.6

0.25

s /nm-1

L  30.0nm ℓc  121.2nm FCC

0.0 0.30 1.00.00

0.25

0.10

0.6



0.4

0.05

0.8

L  27.8nm ℓc  57.9nm FCC

0.6

0.0 0.00

0.2

s /nm-1 (c) 7k

0.8

0.0 1.00.00

0.4





s Icorr /norm.

0.05

L  10.4 nm ℓc  9.8nm ECC

0.6



0.4

L  6.9nm ℓ c  7.5nm ECC

(b) 1k

0.8

s Icorr /norm.

0.6

0.0 1.00.00



1.0

(a) C60

0.8

s Icorr /norm.



s Icorr /norm.

1.0

s Icorr /norm.

0.2

0.30

0.0 0.00

0.05

0.10

0.15

0.20

0.25

0.30

s /nm-1

s /nm-1

Figure 1. SAXS patterns of the samples indicated. The intensity profiles are backgroundsubtracted and normalized by the peak heights. L represents the long spacing and ℓchain the mean chain length. Samples are C60H122 (C60) and PE fractions with mean molar mass indicated as 1, 7, 14, 52 and 183×103 /g mol−1. C60

0.3 K min 0.9

In 1k

130 o

Ts / C

140

95

150 -1

endo.

0.3 K min 0.9 2 4 8 12 20

7k

135

T s /o C

105

110

Ts /oC0.3 K min-1

183k

0.9 2 4

30 45 70 100 140 180

(c) 130

(b) 100

HF (norm.)

120

endo.

(a)

125

4 8 12 20 30 45 70 100 140 180

140

endo.

endo.

52k 183k

110

C60 2

HF (norm.)

HF (norm.)

14k

100

-1

7k

HF (norm.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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130

8 12 20 30 45 70 100 140 180

(d) 135

140

T s /o C

145

Figure 2. Melting behaviors of the samples indicated in (a), and the heating rate dependence of the thermogram in (b)–(d) taken by conventional DSC. The double peaks of 1k in (a) is due to the isothermal crystallization at 106◦C and subsequent crystallization on cooling.


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2. Summary of the analysis of the heating rate dependence of melting peak Polymer crystal melting exhibits superheated melting peak with faster heating rate, β. On the other hand, it is known that standard material such as indium also shows the shift due to instrumental thermal lag [6–10].

The distinction between the superheating of

melting kinetics and the instrumental thermal lag has been made on the basis of the following characteristic behaviors. Firstly, with instrumental thermal lag, peak shape is dependent on heating rate and influenced by sample mass, while for melting of polymer crystals, melting peak just shifts to higher temperature with keeping the shape and without the influence of sample mass for relatively slow heating rate and small mass [10]. Secondly, modeling of the melting kinetics and of instrumental thermal lag predicts different behaviors in the β dependence of the peak temperature, as shown below.

2.1. Melting kinetics Experimental heating rate dependence of the melting peak temperature Tpeak can be fit by the following eq. (1) [4, 5, 11]: Tpeak  TMelt  A  z

(1)

where the coefficient, A, and the power, z, are constants, and TMelt represents the melting point of chain-folded polymer crystals under equilibrium with surrounding melt at zero heating rate, so called zero-entropy-production melting point [1].

It is noted that, due to

distribution of melting points in chain-folded polymer crystals, the peak temperature Tpeak represents the melting point of the majority of crystals and the corresponding TMelt is the melting point of those crystals at zero heating rate. The β dependence with the fractional power z ≤ 0.5 has been experimentally confirmed with a number of polymers [2–5, 10–18], and can be predicted as superheated melting kinetics, which is modeled by the following 1-st-order kinetic equation in terms of crystallinity, φ, with the rate coefficient depending on the degree of superheating, ∆T [4, 5]: d   a ( T ) y  d ( t )

(2)

where the ∆T dependence of the melting rate coefficient is characterized by the coefficient, a, and the power, y.

For the heating at constant rate, β, ∆T is expressed as β∆t and the



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following relation is derived from the integration of eq. (2) for the melting peak satisfying d2φ/d(∆t)2 = 0,

y A  ( )1 /(y 1) a z

(3)

1 y 1

(4)

which predicts z less than 1/2 with y larger than 1. In eq. (2), the power, y = 1, i.e. proportional dependence of melting rate on ∆T, corresponds to possible maximum rate without kinetic barrier and limited by the molecular mobility in the crystalline state, and y > 1, i.e. stronger than linear dependence on ∆T, indicates a kinetic barrier for melting, such as of a nucleation.

2.2. instrumental thermal lag

The shift in peak temperature due to instrumental thermal lag without superheating of kinetics has been well described by the Mraw’s model consisting of lumped elements of a differential scanning calorimeter, DSC [6–10].

The experimental results of a standard

material of melting, indium, confirmed the power, z, of eq. (1) showing a crossover change of 1/2 ≤ z ≤ 1 depending on sample mass, which was predicted analytically and verified by numerical results on the basis of the Mraw’s model [10]; as the limiting cases, larger sample mass corresponds to the power, z = 1/2, and smaller mass to z = 1. For the melting without superheating, the sample temperature is kept constant at the equilibrium melting point and the melting peak temperature corresponds to the completion time of melting. The crossover is caused by the strength of the influence of the release of latent heat on melting, as follows. For larger sample mass, the completion time is delayed due to larger latent heat and the melting peak shows an apparent superheating of the β dependence with the power z = 1/2. On the other hand, for smaller sample mass with negligible influence of the latent heat, thermal lag is linearly dependent on β, since thermal conductance is a linear process. The peak temperature of polymer crystal melting also has the influence of released latent heat, though the effect is much weaker than that of indium because of broad distribution of melting points in contrast to the melting of indium, which melts at a single equilibrium melting point. Due to the influence, superheating of polymer crystal melting 6 ACS Paragon Plus Environment

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of larger mass sample has an additional shift included in the experimentally determined power z, which is now an apparent power and can be larger than 1/2.

3. Experimental

Long-chain alkane, hexacontane (>97.0%), C60H122, was purchased from Fluka. Linear polyethylene samples with various molar mass are the followings: 1k (Mp = 1,100 g mol−1 and Mw/Mn = 1.20, Polymer Laboratories), 7k (Mv = 6,500 g mol−1 and Mw/Mn = 1.14, Idemitsu Petrochemical Co.,Ltd.), 14k (Mw = 13,600 g mol−1 and Mw/Mn = 1.19, NIST SRM1482a), 52k (Mw=52,000 g mol−1 and Mw/Mn = 2.90, NIST SRM1475), and 183k (Mw = 183,000 g mol−1 and Mw/Mn = 1.61, Fluka).

Thin foil of Indium (50 µm and

99.999%) was purchased from Nilaco, Japan. A conventional type of DSC, CDSC, measurements were done with a Q100 of TA Instruments in the heating rate range of 0.3–180 K min−1; nitrogen gas was purged at a flow rate of 50 mL min−1 and the reference pan was removed in all experiments.

For the

purpose to minimize thermal contact resistance, silicone grease (Archer, 276-1372) was applied between the bottom surface of sample pan and the stage. In the measurements by conventional DSC, crystallization conditions are the followings.

Indium, In, and

hexacontane, C60, were crystallized on cooling by 50 and 30 K min−1, respectively. PE fractions of 1k, 7k, 14k, 52k and 183k were isothermally crystallized from the melt at Tc = 106, 122, 124.5, 127 and 127◦C for ∆t = 30, 60, 90, 90 and 90 min, respectively. The crystallization time of polyethylenes are set to be long enough to stabilize the crystals and to avoid possible shift in melting peak temperature due to reorganization on heating. For fast scan in the heating rate range of 5–10,000 K s−1, FlashDSC1 of Mettler-Toledo was used with chip sensor of UFS1; nitrogen gas was purged at a flow rate of 30 mL min−1. Sample mass of fast-scan DSC, FSC, was evaluated from the released latent heat compared with that of known sample mass crystallized by conventional DSC under the same condition.

In the measurements by fast-scan DSC, samples were

crystallized isothermally under the following conditions: In at 147◦C for 0.1s, C60 at 99.8◦C for 2s, 1k at 105◦C for 5s, and 52k at 122.6◦C for 100s. The crystallization time was set to be long enough for the completion of crystallization in the primary stage filled by crystalline aggregates such as spherulites, while the applied heating rate >5 K s−1 (=300 K min−1) was fast enough to avoid reorganization on heating. For melting, we may have 7 ACS Paragon Plus Environment


once cooled the sample well below Tc to guarantee steady state heating especially at faster heating rates. However, the melting peak of crystals formed on cooling could superpose on the melting peak of crystals formed isothermally for samples with melting point distribution due to their purity. Therefore, we raised temperature directly from Tc, and subtract the heat flow rate of a run with much shorter isothermal holding time ∆t with practically negligible melting peak as the baseline for the melting peaks in order to determine the peak temperature without the baseline shift due to nonsteady heating. It is noted that the use of this baseline works properly for the peak temperature determination while it may introduce overestimate of the latent heat of melting because this baseline is the endothermic curve of the melt while the true baseline should be with crystal-melt crossover change. The small angle X-ray scattering, SAXS, patterns in Fig. 1 were taken by a system of NANO-Viewer (Rigaku) with Cu-Kα radiation (40 kV and 30 mA) and a two-dimensional detector (PILATUS 100K/RL) with the camera length of 935 or 1,235 mm, equipped with a hot stage. PE fraction, 1k, was only partially crystallized at Tc =106◦C, so that the SAXS pattern was taken isothermally at the same temperature.

4. Results and Discussion 0.0

14k

1k -0.5

0.9 K min-1 m /mg 0.14 C60 0.12 1k 0.10 14k

-1.0

C60 0

2

4

6 o

TsTc / C

8

endo.

HF /mW

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 17

10

Figure 3. Melting peaks plotted against Ts − Tc obtained by CDSC.

Figure 3 shows the raw data of the endothermic melting peaks of hexatriacontane (C60) and PE fractions of 1k and 14k plotted against (Ts − Tc) with Ts and Tc representing sample temperature and crystallization temperature, respectively.

In Fig. 3, negligible

superheating of C60 is apparent, while higher degree of superheating of the melting peak of higher molar mass PE is also clearly discernable.


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Figures 4 and 5 show the heating rate dependence of the melting peak temperature of indium (In), hexacontane (C60), and polyethylene fractions (1k, 14k, 183k) taken by a conventional type of DSC, CDSC.

Firstly, as shown in Fig. 4, the melting of hexacontane

behaves just the same as that of indium.

Depending on sample mass, β dependence

shows a crossover change in the power z of the heating rate dependence from 0.5 up to 1 with decreasing mass; the behavior is just the one predicted by the Mraw’s model as the instrumental thermal lag without superheating of melting, as summarized above.

(b) z

(a) m /mg 160

159

o

o

Tpeak / C

10.13 01.03

Tpeak / C

22.79 03.81 00.04

160

158 157 50

(c) m /mg

103 o

102

100

2.48 0.61 0.14

158

0.0 104

150

-1

/K s

103 o

3.02 0.86 0.31 0.06

Tpeak / C

0

159

101

0.59 0.57 0.73 0.90 1.00

157

In

104

Tpeak / C

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


102

0.2

(d) z

0.65 0.67 1.00 1.00

0.4

0.6

0.8

1.0

0.8

1.0

-1 z

( /200 K s ) 0.66 0.77 1.00

101 100

100

C60 0

50

100

0.0

150

0.2

0.4

0.6 -1

 /K min-1

z

( /200 K min )

Figure 4: Melting peak temperatures, Tpeak, plotted against applied heating rate, β, of indium in (a) and hexacontane in (c) with different sample mass, m, indicated. The plots against βz with the adjustable parameter z for the best fit linear straight lines are in (b) and (d), respectively.

Hence, the melting of extended-chain crystals of hexacontane is completed at the equilibrium melting point without superheating. Secondary, as shown in Fig. 5a–5d, with low molar mass PE fractions of 1k and 14k, the power was close to 1/2 for all sample mass examined. Then, with higher molar mass fraction of 183k in Fig. 5e–5f, the power decreased down to 0.3. Larger superheating with larger sample mass in Fig. 5 will be due to the influence of thermal lag.



(a) m /mg 111

o

o

Tpeak / C

(b) z

1.22 0.34

Tpeak / C

2.55 1.00 0.12

111

110

109

110

109

1k 100

 /K s

2.40 1.13 0.10

135

150

0.0

-1

0.2

0.4

0.6

0.8

1.0

0.8

1.0

0.8

1.0

-1 z (d) z ( /200 K s )

136

1.72 0.51 0.04

135

o

o

Tpeak / C

136

50

(c) m /mg

Tpeak / C

0

134 133

134 133

14k 132 0

50

(e) m /mg

140

1.98 0.33 0.03

132 0.0

150

 /K min 0.96

-1

140

0.09

0.2

0.4

0.6

0.4

0.6

-1 0.5 (f) z ( /200 K min )

139 o

138

100

Tpeak / C

o

Tpeak / C

139

137 136 135

138 137 136 135

134

183k

133 0

50

100

150

134 133 0.0

0.2

 /K min-1

-1

z

( /200 K min )

Figure 5: Melting peak temperatures of polyethylene fractions indicated. 6

(a)

o

4

52k 01k

3 2

14k C60

o

183k 007k In

Log[Tpeak / C]

z~0.3

5

Tshift / C

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0

z~0.4 z~0.5

-1

z~1

1 0

(b)

-2 0

50

100

 /K min

0

150 -1

1

2 -1

Log[ /K min ]

Figure 6: Shift in melting peak temperature, ∆Tshift, plotted against β of the samples indicated in (a) and the double logarithmic plot in (b).

Those behaviors are summarized in the plot shown in Fig. 6 of the data in Figs. 4 and 5 with sample mass small enough to guarantee negligible influence of thermal lag by the released latent heat on melting.

With increasing molar mass, i.e. increasing the

number of chain folding per molecule, melting shows larger superheating in Fig. 6a. The behavior can be well recognized by the double logarithmic plots of Fig. 6b with the slope 10 ACS Paragon Plus Environment

Page 11 of 17

representing the power z. First, hexacontane melts nearly in the same way as indium having the power close to unity. This suggests the shift due to instrumental thermal lag of the melting without superheating. Second, low molar mass fractions of 1k, 7k, and 14k have the power close to 1/2. This means linear dependence on superheating of melting rate coefficient, corresponding to possible maximum rate with kinetic barrier small enough. With increasing molar mass of 52k and 183k, the power decreases down to 0.3 with larger degree of superheating, indicating a stronger than linear dependence of melting rate coefficient on superheating, ∆T, with appreciably larger kinetic barrier. In this manner, molar mass dependence suggests the role of chain folding in the kinetic barrier for melting. 20

(a) Onset T /K

10

(b) Peak

15 10

52k 1k C60 In

5 5

0

0

2000

4000

6000 -1

8000

10000

0

0

2000

4000

(c) Onset

1

8000

10000

(d) Peak

1

z~0.2

6000

K s-1

K s

Log[T /K]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


z~0.3 0.3

0

0.9

0

0.5 1

2

3 -1

4

-1

Log[K s ]

1

2

3

Log[K s-1]

4

Figure 7: Shift in (a) Tonset and (b) Tpeak plotted against β of the samples indicated. The double logarithmic plots are in (c) and (d), respectively. The sample masses are 1.4, 0.2, 0.6, 0.6 ng, and the slopes of the straight fitting lines in (d) are 0.9, 0.77, 0.62 and 0.34 of In, C60, 1k and 52k, respectively.

Figure 7 shows the corresponding results of fast-scan DSC of smallest mass samples examined. In addition to the melting peak temperature, the onset temperature was also examined by FSC because of well defined baseline for the determination of the onset temperature. Both of the linear and double logarithmic plots clearly show the behaviors similar to what were obtained by CDSC in Fig. 6. Here again, with increasing molar mass, melting shows larger superheating of Tonset and Tpeak with smaller power z, indicating larger kinetic barrier. In terms of the onset temperature of C60 in Figs. 7a and 7c, a 11 ACS Paragon Plus Environment


departure from the linear dependence could be seen, which can only be explained as a superheated kinetics.

In comparison with the measurements by CDSC with strong

influence of large heat capacity of sample pan on thermal lag, it is probable that FSC without sample pan can capture a weak sign of the superheated melting kinetics in the onset temperature. On the other hand, the behaviors of Tpeak of all samples in Figs. 7b and 7d showed a linearly dependent behavior on  at faster heating rates. It is reasonable that the linear term, if exists, becomes dominant at faster heating rates in comparison with the kinetic term with fractional power dependence less than one half.

The linear term

suggests the influence of an instrumental thermal lag with a time constant regardless of sample type for Tpeak. The term can also be due to non-steady heating at faster rates because we raised temperature directly from Tc. With increasing molar mass and corresponding increase in the number of chain folding in the crystals, the metastability of crystals also increases, as suggested in Fig. 8 by the increase in peak temperature with longer annealing time under isothermal condition of crystallization; the time dependence is logarithmic similar to the time evolution of thickening of chain-folded crystals [20]. It is noted that the 1k fraction forms basically chain-extended crystals as seen in Fig. 1b, but, with the distribution of molar mass, Mw/Mn =1.20, part of molecules should be chain-folded and the crystals are metastable and undergo the annealing in contrast with hexacontane, C60, the melting point of which was fixed at the equilibrium melting point.

Tshift /K

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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C60 001k 007k 183k

0.5K

1.0

1.5

2.0

log[tc /min] Figure 8: Semi-logarithmic plots of the shift in melting peak temperature against annealing time under isothermal crystallization conditions of the samples indicated.


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It is finally noted that the power z of polymer crystal melting kinetics discussed with Figs. 5-7 is known to be dependent on the stability of crystals formed: i.e. smaller power z of more stable crystals formed at higher Tc [15].

We have set the typical

conditions for the PE fractions examined and believe that the CDSC results of Figs. 5 and 6 and the FSC results of Fig. 7 represent their typical behaviors.

5. Conclusions

For PE fractions, hexacontane, and indium, we have examined the superheated melting kinetics characterized by the power z of the heating rate dependence of melting peak temperature examined by conventional and fast-scan DSC.

Melting of hexacontane

behaved in a way similar to that of indium with the crossover change in the power, 0.5 ≤ z ≤ 1, depending on sample mass, which is ascribed to the instrumental thermal lag with the influence of released latent heat and basically without superheating of melting kinetics. On the other hand, PE fractions showed a systematic change in the power with molar mass, i.e. number of chain folding in the crystals; the power was smaller than 0.5 down to 0.3 with higher molar mass. Based on the modeling of melting kinetics, the power, z, smaller than 1/2 suggests a stronger than linear dependence on ∆T of melting rate, indicating a kinetic barrier for melting. PE crystals undergo the rise in melting point with longer annealing time under isothermal conditions, and the increasing rate becomes faster with higher molar mass, indicating metastable nature of chain-folded polymer crystals. Those experimental results confirm the determining influence of the metastability of chain-folded polymer crystals on the superheated melting with a kinetic barrier. As a candidate of the kinetic barrier for melting, the possibility of nucleation of molten hole in the crystal was ruled out by a microscopic observation of the isothermal melting process of PE single crystals from the outer edge [5].

The present results

confirmed the role of metastability with chain folding [21] and the origin of the kinetic barrier will be related to the competition at the melting front between melting and the reverse processes of recrystallization and reorganization. This process can be modeled by an entropic barrier of metastable pinned state at the melting front [5, 21–24]. The pinned state can be metastable due to entropic contribution and must be removed for the advance of the front, and hence the metastable pinned state can be a barrier for both of crystallization and melting, and represents the competition between those processes. 13 ACS Paragon Plus Environment


Acknowledgment

AT acknowledges the discussion with Dr. Jens Balko of University of Halle. Part of this work was supported by the Collaborative Research Program of Institute for Chemical Research, Kyoto University [2014-86] and by the Grants-in-Aid for Scientific Research -KAKENHI- from the Ministry of Education, Culture, Sports, Science and Technology of Japan [JP16H04206].


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For Table of Contents Use Only

Superheated melting kinetics of metastable chain-folded polymer crystals

Akihiko Toda*, Ken Taguchi, Koji Nozaki, Tatsuya Fukushima, and Hironori Kaji

6

polyethylene fractions

5

-3

molar mass 10 /g mol 183 52 14 1

4

o

Tshift / C

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-1

3 2 1

C60H122 0

0

50

100

 /K min

150 -1

Synopsis: Unique behavior of polymer crystal melting with superheated kinetics is

characterized by the heating rate β dependence determined by the metastable nature with chain folding.


Superheated melting kinetics of metastable chain-folded polymer

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