Effects of hydrogen-bonding density on polyamide crystallization kinetics

Journal Pre-proof Effects of hydrogen-bonding density on polyamide crystallization kinetics Xiaoheng Li, Yucheng He, Xia Dong, Xiaoning Ren, Hongxu Gao, Wenbing Hu PII:

S0032-3861(20)30010-0

DOI:

https://doi.org/10.1016/j.polymer.2020.122165

Reference:

JPOL 122165

To appear in:

Polymer

Received Date: 9 October 2019 Revised Date:

5 January 2020

Accepted Date: 8 January 2020

Please cite this article as: Li X, He Y, Dong X, Ren X, Gao H, Hu W, Effects of hydrogen-bonding density on polyamide crystallization kinetics, Polymer (2020), doi: https://doi.org/10.1016/ j.polymer.2020.122165. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.

Effects of Hydrogen-Bonding Density on Polyamide Crystallization Kinetics Xiaoheng Li1, Yucheng He1, Xia Dong2, Xiaoning Ren,3 Hongxu Gao,3 Wenbing Hu1* 1

School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China *E-mail: [email protected] 2

CAS Key Laboratory of Engineering Plastics, CAS Research/Education Center for

Excellence in Molecular Sciences, CAS Institute of Chemistry, Beijing 100190, China 3

Science and Technology on Combustion and Explosion Laboratory, Xi’an Modern Chemistry Research Institute, Xi’an 710065, China

Abstract: We employed Flash DSC1 apparatus for fast-scan chip-calorimeter measurement in a broad temperature range to compare the isothermal crystallization rates among six polyamide (PA) samples, i.e. PA 46, PA 66, PA 610, PA 612, PA 1012 and PA 12. The double parabolic curves of crystallization half-time versus crystallization temperature revealed that PA 46 crystallizes relatively fast due to its high hydrogen-bonding density favoring thermodynamic driving forces for crystallization in the high temperature region, while PA 1012 and PA 12 crystallize relatively fast due to their low hydrogen-bonding densities favoring short-range diffusion for crystallization in the low temperature region. Furthermore, the cross-over temperatures between two parabolic curvatures of six samples follow their sequences in hydrogen-bonding density, and the Avrami indexes reveal a potential switching in the modes between heterogeneous and homogeneous crystal nucleation.

Keywords: polyamides; crystallization kinetics; Flash DSC

1

1. Introduction Polyamide (PA), as its bulk materials commonly known as nylon, is a linear polymer holding repetitive structures that form C=O⋅⋅⋅H-N hydrogen-bonding interactions between polymer chains [1]. The hydrogen-bonding offers enhanced mechanical properties, good chemical resistance and high thermal stability for nylon products in broad daily applications [2]. For PA crystallization, hydrogen-bonding dominates the modes of chain packing in the crystalline phases [3], and hence the equilibrium melting points. In practice, the crystals are composed of hydrogen-bonding sheets with chain stems holding adjacent chain-folding, which are the fundamental for the beta-sheet as one of the most basic secondary structures in proteins [4]. There are two hydrogen-bonding schemes of stem packing in the crystalline sheets of PA: terraced or staggered [5-7]. Brill transition can be observed below the melting point of PA [8,9]. The harvest of crystallinity in PA industrial processing is mainly dominated by crystallization kinetics. It is well-known that the hydrogen-bonding has been commonly existing in the melt, but not so much as in the crystalline state. Therefore, hydrogen-bonding densities of PA as determined by the lengths of methylene sequences in diamine alkane and diacid alkane strongly influence the crystallization kinetics. However so far, our knowledge about this influence is still limited. It is well-known that the overall crystallization kinetics in bulk polymers is dominated by primary crystal nucleation. According to the classical nucleation theory, the free energy barrier for crystal nucleation dominates the nucleation rate in the high temperature region, while the activation barrier for short-range diffusion dominates the nucleation rate in the low temperature region [10], as shown in Eqn. (1) for the nucleation rate I, =

exp − ∆

⁄

exp − ∆ ⁄

where the activation barrier for diffusion ∆

⁄

= /

(1) −

with the Vogel

temperature TV about 50 °C below the glass transition temperature Tg, and A is a diffusion constant; ∆

=8

⁄∆

⁄

−

is the free energy barrier

for primary crystal nucleation supposed in a cylindrical bundle, k is the Boltzmann’s 2

constant, Tc is the crystallization temperature, σ and σe are separately the surface free energy densities on the lateral and folding-end surfaces of lamellar polymer crystals, Tm0 is the equilibrium melting point and ∆Hc is the heat of fusion. Therefore, the curvature of crystallization rate (or crystallization half-time) versus crystallization temperature appears as parabolic, with a maximum (or minimum in case of half-time) locating near the middle between Tg and Tm0. Recently, fast-scanning chip-calorimeter technique has significantly expanded our DSC measurement of polymer crystallization behaviors into the low temperature region [11,12]. The isothermal crystallization kinetics of many polymers in the broad temperature range have thus been characterized [13]. In particular, double parabolic curvature was observed [14], which has usually been assigned to heterogeneous nucleation and homogeneous nucleation dominating in the high and low temperature regions, respectively [15]. The crystallization kinetics of PA 6 was compared to that of Polyketone holding similar melting points and heats of fusion but without hydrogen-bonding [16]. The results revealed that the hydrogen-bonding in the melt of PA 6 brings a low mobility to suppress crystallization in the low temperature region, while the hydrogen-bonding in the crystal sheets of PA 6 leads to a low surface free energy to accelerate crystallization in the high temperature region [16]. In this study, we focus our attention on the hydrogen-bonding density and compare the isothermal crystallization kinetics of PA 46, PA 66, PA 610, PA 612, PA 1012 and PA 12 via Flash DSC measurement. The chemical structures of six aliphatic PA samples with a series of hydrogen-bonding densities are demonstrated in Fig. 1. Our results reveal some important effects of hydrogen-bonding density on crystallization kinetics among six PA samples.

3

Figure 1. Demonstration of chemical structures of six polyamide samples with a series of hydrogen-bonding densities.

2. Samples and instruments PA 46 granules used in this work were kindly supplied by DSM Company. The viscosity was 100 Pa.s under the temperature 300 °C and the shear rate 100 s-1. The sample was dried in a vacuum oven at 80 °C for 12 h before use. The equilibrium melting point of PA 46 was 307.1 °C, obtained with conventional DSC measurement [17]. PA 66 (molecular weight 262.35 kg mol-1, density 1.14 g mL-1 at 25 ℃) and PA 12 (density 1.01 g mL-1 at 25 ℃) were obtained from SIGMA-ALDRICH. The equilibrium melting points of PA 66 and PA 12 were separately 303.7 °C [18] and 187 °C [19]. PA 610, PA 612 and PA 1012 were kindly supplied by Shandong Guangyin New Materials Company. Their relative viscosities were 2.3, 2.46 and 2.5, respectively. The 4

equilibrium melting points of PA 610, PA 612 and PA 1012 were separately 238 [20], 247 [21], 206 °C [22]. Flash DSC1 (Mettler-Toledo Company, Switzerland) installed with UFS1 chip-sensor and Huber TC-100 intracooler was employed in this work. The granule samples were cut with the help of scalpel into small pieces and cut further into typically the magnitude of 100 ng mass under the equipped optical microscope. Then by utilizing a string of hair the specimen was transferred into the center area of the chip sensor which had already been conditioned and corrected. Under the protection of 50 mL min-1 nitrogen purge, the positioned specimen was heated to a temperature above the melting temperature to make a perfect thermal contact between the specimen and sensor. After the above preparation of samples, the experiment had four steps: (1) Erasing the thermal history; (2) Cooling experiment; (3) Heating experiment; (4) Isothermal experiment. The experiment of erasing thermal history in the first step was aimed to get the critical temperature to avoid any memory effect of crystallization. The purposes of the critical cooling and heating experiment in the second and third steps was to obtain the critical cooling and heating rates to suppress melt and cold crystallization as much as possible. The first three steps helped us to make sure the experimental conditions for isothermal crystallization experiment in the last step. After these four steps, we could get the temperature dependence of the crystallization half-times to compare isothermal crystallization kinetics among six PA samples.

3. Results and discussion 3.1 Erasing thermal history In order to avoid any memory effect of crystallization in this study, it is necessary for us to erase completely the thermal history of the nascent samples at the very beginning. On the one hand, the sample should be heated to a high enough temperature and stay long enough time to erase its thermal history. On the other hand, the temperature should be lower than the decomposition temperature to make sure the 5

sample is intact. We used PA 610 as an example for demonstration. Firstly, PA 610 sample was heated to 300 °C under the heating rate of 3000 K s-1 and stayed for 0.2 s to melt completely. Secondly, the sample was cooled to -50 °C in a cooling rate of -300 K s-1, which was slow enough for PA 610 to crystallize in the cooling process. Afterwards the sample was heated to various erasing temperatures between 180 and 210 °C under the same fast heating rate of 3000 K s-1 and stayed for 0.2 s. If the melting was incomplete, the subsequent cooling could harvest high crystallinity due to the memory effect, for instance 190 °C. The melting peaks show excellent repeatability when the erasing temperatures are higher than the critical temperature 200 °C. Figure 2a illustrates the detailed temperature program for erasing the thermal history. Figure 2b shows the results of for example PA 610. The similar protocols were used to all other PA samples. The critical temperatures for erasing the thermal history of PA 46, PA 66, PA 610, PA 612, PA 1012 and PA 12 are 270, 240, 200, 200, 170 and 170 °C, respectively. Thus, the nylon sample could be completely amorphous when the melt temperature becomes higher than the critical

PA 610

0.2 s

o

Apparent heat capacity /J K -1

b. a. 300 C

Temperature

T (180-210 oC) 0.2 s

o

-50 C

-1

Heating rate 3000 K s

Endo up

temperature after staying for 0.2 s. PA 610

2×10-8 JK-1 o

180 C 190 200 210

-1

Heating at 3000 K s

Cooling rate -300 K s-1

0

40

80

120

160

200

240

280

o

Time

Temperature / C

Figure 2. a) Illustration of the temperature program for searching the critical erasing temperature of the thermal history in the nascent PA 610 samples; b) Apparent heat capacity of PA 610 samples under the heating rate of 3000 K s-1 after cooled at -300 K s-1 from a stay of 0.2 s at various erasing temperatures as labeled.

6

3.2 Cooling experiment This study focused on the isothermal crystallization kinetics of six PA samples. It is crucial for us to prevent the sample from prior crystallization as much as possible during the fast cooling process before reaching the crystallization temperature. Therefore, we needed to obtain the critical cooling rate for suppressing the melt crystallization on cooling. To that end, at the heating rate of 4000 K s-1, the sample was melted by staying 0.2 s at 300 °C to erase the thermal history. Afterwards the sample was cooled to -50 °C at a series of cooling rates between -40 and -4000 K s-1 followed with heating to 300 °C. Finally, we observed the cooling and heating curves to judge the critical cooling rate. The detailed temperature program is illustrated in Fig. 3.

0.2 s

Temperature

300 oC

o

-50 C

Cooling at

Heating at

-80...-4000 K s-1 3000 or 4000 K s-1

Time

Figure 3. Illustration of the temperature program for searching the critical cooling rate to suppress crystallization of six PA samples on cooling.

The cooling curves at various cooling rates between -80 and -4000 K s-1 for six PA samples are shown in Fig. 4. One can see that, with the increase of the cooling rates, the melt crystallization peaks become vanishing on cooling when the cooling rate exceeds a critical rate, for PA 46 nearly -4000 K s-1, for PA 66 nearly – K s-1, for PA 610 nearly -300 K s-1, for PA 612 nearly -500 K s-1, for PA 1012 nearly -2000 K s-1, and for PA 12 nearly – K s-1. 7

It is interesting to see that the critical cooling rates are not following the sequences of hydrogen-bonding densities of six nylon samples. On the one end, PA 46 crystallizes faster as imaginable; on the other end, PA 1012 and PA 12 crystallize relatively faster as well. The critical cooling rates to suppress melting crystallization reflect the crystallization capability of the nylon samples during the cooling process over the whole temperature range. More detailed kinetic information from the isothermal crystallization kinetics within the broad temperature range will bring the insights, as shown below in section 3.4. The isothermal crystallization temperatures must be higher than the glass transition temperature Tg, and the latter is related to the cooling and heating rates [23]. Therefore, it is crucial to determine Tg at the fast cooling rate -4000 K s-1. According to the standard method of ASTM D3418, Tg is the midpoint of the onset and the end of turning tangent. In our observations, Tg of PA 46, PA 66, PA 610, PA 612, PA 1012

PA 46 -1

Cooling at -80 K s -100 -300 -500 -1000 -2000 -3000 -4000

Cooling 0

40

80

120

160

200

Endo up

b. 8×10-8 JK-1

Apparent heat capacity /J K-1

Apparent heat capacity /J K

-1

a.

Endo up

and PA 12 were 48.3, 38.1, 37.4, 37.5, 28.5 and 23.8 °C, respectively.

5x10-8 J K-1

-100 -300 -500 -1000 -2000 -3000 -4000

Cooling

240

0

40

80

o

-1

Cooling at -80 K s -100 -300 -500 -1000 -2000 -3000 -4000

Endo up

-1

Apparent heat capacity / J K

Endo up

Apparent heat capacity /J K-1

d. PA 610

5x10-8 J K-1

120

5x10-8 J K-1

40

80

120

160

200

240

PA 612

Cooling at -80 K s-1 -100 -300 -500 -1000 -2000 -3000 -4000

Cooling

Cooling 0

160

Temperature /oC

Temperature / C

c.

PA 66

Cooling at -80 K s-1

200

0

240

40

80

120

160

Temperature /oC

Temperature /oC

8

200

240

PA 1012 -1

Cooling at -80 K s -100 -300 -500

-1000 -2000 -3000 -4000

Cooling 0

40

80

120

160

200

Endo up

5x10-8 J K-1

Apparent heat capacity /J K -1

-1

Apparent heat capacity /J K

Endo up

f.

e.

8x10-8 J K-1

PA 12 Cooling at -80 K s-1 -100 -300 -500 -1000 -2000 -3000 -4000

Cooling 0

240

40

Temperature /oC

80

120

160

200

240

Temperature /oC

Figure 4. Apparent heat capacity as a function of temperature on cooling scans at various cooling rates as labeled between -80 and -4000 K s-1 as illustrated in Fig. 3 for six nylon samples of (a) PA 46, (b) PA 66, (c) PA 610, (d) PA 612, (e) PA 1012 and (f) PA 12.

After cooled with various cooling rates, the subsequent heating curves at the high enough heating rate of either 3000 or 4000 K s-1 of six PA samples are shown in Fig. 5. One can see clearly that, with the increase of the cooling rates, the corresponding melting peaks in the subsequent heating processes disappear when the cooling rates

Heating after cooling -1

at -80 K s -100 -300 -500 -1000 -2000 -3000 -4000

-1

Heating at 3000 K s

0

50

100

150

200

250

300

Endo up

b.

PA 46

3×10-8 JK-1

Apparent heat capacity /J K -1

Apparent heat capacity /J K

-1

a.

Endo up

exceed the critical cooling rate for various PA samples.

Heating after cooling at -80 K s-1 -100 -300 -500 -1000 -2000 -3000 -4000

Heating at 4000 K s-1 0

o

PA 66

4x10-8 J K-1

50

100

150

200

Temperature /oC

Temperature / C

9

250

300

d.

Heating after cooling at -80 K s-1 -100 -300 -500 -1000 -2000 -3000 -4000

0

Heating at 4000 K s-1

50

100

150

200

250

Endo up

PA 610

3×10-8 JK-1

Apparent heat capacity /J K-1

Endo up

Apparent heat capacity /J K-1

c.

300

Heating after cooing at -80 K s-1 -100 -300 -500 -1000 -2000 -3000 -4000

0

Heating at 4000 K s-1

50

Heating after cooling -1

at -80 K s -100 -300 -500 -1000 -2000 -3000 -4000

-1

Heating at 3000 K s

0

50

100

150

200

250

300

Endo up

f.

PA 1012

3×10-8 JK-1

100

150

200

250

300

Temperature /oC

Apparent heat capacity /J K -1

-1

Apparent heat capacity /J K

Endo up

Temperature /oC

e.

PA 612

3×10-8 JK-1

Heating after cooling at -80 K s-1 -100 -300 -500 -1000 -2000 -3000 -4000 -1

Heating at 4000 K s 0

o

PA 12

3x10-8 J K-1

50

100

150

200

250

300

Temperature /oC

Temperature / C

Figure 5. Apparent heat capacity as a function of temperature on heating scans at the heating rate of 3000 or 4000 K s-1 after cooling scans at various cooling rates between -80 and -4000 K s-1 as labeled as illustrated in Fig. 2 for six PA samples of (a) PA 46, (b) PA 66, (c) PA 610, (d) PA 612, (e) PA 1012 and (f) PA 12.

3.3 Heating experiment After fast cooling with the rate beyond the critical cooling rate to suppress the crystallization on cooling, we still need to heat the sample fast enough to suppress the cold crystallization on heating. Therefore, we have to learn the critical heating rate in this heating process. The sample at -50 °C was first heated to 300 °C in the heating rate of 3000 K s-1 and stayed for 0.2 s to erase the thermal history. Afterwards, the sample was cooled to -50 °C in -3000 K s-1 followed with heating to 300 °C in various heating rates between 80 and 5000 K s-1. The detailed temperature program is shown in Fig. 6. The last heating curves with various heating rates are summarized in Fig. 7. 10

0.2 s

Temperature

300 oC

-50 oC

Cooling at Heating at -3000 or -4000 K s-1 80, 100...5000 K s-1

Time

Figure 6. Illustration of the temperature program for searching the critical heating rate

-1

Heating at 80 K s 300 500 1000 3000 5000 7000 10000 13000

-1

Heating after cooling at -4000 K s

0

50

100

150

200

250

Endo up

-1

Apparent heat capacity /J K -1

-7

b.

PA46

1 ×10 10 -7 JK -1

Apparent heat capacity /J K

-1

a.

Endo up

to suppress cold crystallization of six PA samples on heating.

2x10-7 J K-1

PA 66

Heating at 80 K s-1 300 500 1000 3000 5000 7000 10000 13000

Heating after cooling at -4000 K s-1

300

0

50

100

300 500 1000 2000 3000 5000

0

-1

Heating after cooling at -3000 K s

50

100

150

200

250

Endo up

d.

PA 610

Apparent heat capacity /J K-1

Endo up

Apparent heat capacity /J K-1

c. 3x10-8 J K-1 Heating at 80 K s-1 100

150

200

250

300

Temperature /oC

o

Temperature / C

Heating at 80 K s-1 100 300 500 1000 2000 3000 5000 Heating after cooling at -3000 K s-1

0

300

Temperature /oC

PA 612

8×10-8 JK-1

50

100

150

200

Temperature /oC

11

250

300

PA 1012 -1

Heating at 80 K s 300 500 1000 3000 5000 7000 11000 13000 15000

Heating after cooling at -3000 K s

0

50

100

150

200

250

-1

Endo up

Apparent heat capacity /J K -1

Endo up

f. 3×10-8 JK-1

Apparent heat capacity /J K

-1

e.

PA 12 Heating at 80 K s-1 300 500 1000 3000 5000 7000 10000 13000

Heating after cooling at -4000 K s-1

0

300

o

8x10-8 J K-1

50

100

150

200

250

300

Temperature / oC

Temperature / C

Figure 7. Apparent heat capacity as a function of temperature on heating scans at various heating rates as labeled after cooled at -3000 or -4000 K s-1 from a stay of 0.2 s at 300 °C as illustrated in Fig. 6 for six PA samples of (a) PA 46, (b) PA66, (c) PA 610, (d) PA 612, (e) PA 1012 and (f) PA 12.

From Fig. 7, one can see that, the cooling rate -3000 K s-1 in general, and -4000 K s-1 specific for PA 46, are high enough to suppress melt crystallization on cooling. With the increase of heating rates, the cold crystallization peaks and the corresponding melting peaks on the heating curves are suppressed for PA 610 and PA 612, and one can obtain the critical heating rate around 2000 K s-1. In these cases for PA 610 and PA 612, both crystal nucleation and crystal growth are suppressed under fast cooling. But for PA 46, PA 1012 and PA 12, even the heating rate 13000 K s-1 cannot suppress the cold crystallization. The heating curves beyond this maximum heating rate exhibit too severe distortion that could not be analyzed. In these cases different from PA 610 and PA 612, the fast cooling can suppress melt crystallization but cannot suppress melt crystal nucleation that raises cold crystallization at subsequent fast heating. In the following isothermal experiments, we would adopt 4000 K s-1 for the heating process, and assumed that for PA 46, PA 1012 and PA 12 the unavoidable primary crystal nucleation on the same cooling processes after the treatment of isothermal crystallization will contribute almost the same melting enthalpy in the last heating curves, which influence not so significant to the judgment of crystallization half-time during the isothermal crystallization process.

12

3.4 Isothermal experiment After the above three experiment parts, we obtained the critical temperatures for erasing thermal histories, the critical cooling rates for suppressing crystallization on cooling, and the critical heating rates for suppressing cold crystallization on heating for various nylon samples in hand. We then chose the high enough cooling and heating rates to carry out the next isothermal crystallization experiment. The samples were heated to 300 °C and stayed for 0.2 s to erase the thermal histories, and then they were cooled at the cooling rate of -4000 K s-1 to various crystallization temperature Tc, which was higher than Tg but lower than Tm. The sample stayed at Tc for various time periods to crystallize. After the specific period of isothermal crystallization, the sample was cooled down to -50 °C under the cooling rate of -4000 K s-1, and then heated back at the heating rate of 4000 K s-1. The last cooling process was to guarantee the completeness of melting peak in the subsequent heating process. If we heat the sample right after the high isothermal temperatures, the melting peak may not be complete for our analysis due to the baseline shifting. Figure 8 illustrates the temperature program of this part.

0.2 s

Temperature

300 oC

Tm Tc, t Tg -50 oC

Cooling rate -4000 K s-1 Heating rate 4000 K s-1

Time

Figure 8. Illustration of the temperature program for isothermal crystallization at various temperatures between Tg and Tm.

We use PA 610 as an example to explain our kinetic analysis of isothermal crystallization. Figure 9a shows the melting curves of PA 610 after isothermal 13

crystallization at 110 °C for various time periods from 0.1 to 30 s. Almost all the melting curves exhibit double melting peaks. The low-temperature peaks can be found to shift to higher temperatures upon the increase of isothermal crystallization periods, indicating more perfect and thickened crystals. In contrast, the high-temperature peaks appear insensitive to the crystallization periods, implying the melt-recrystallization mechanism for double melting peaks. For PA 610, the cooling rate -4000 K s-1 and the heating rate 4000 K s-1 are fast enough to eliminate the crystallization in both cooling and heating processes. Thus, the melting enthalpy ∆Hm in heating obtained by integrating the melting peak represents to the isothermal crystallization enthalpy ∆Hc. As shown in Fig. 9b, the crystallization enthalpy ∆Hc increasing with crystallization time periods exhibits the typical spinodal-shape. The onset and end crystallinity during isothermal crystallization are defined to obtain the crystallization half-time at 1/2∆Hc, as demonstrated in Fig. 9b. The data mainly in the early stage were fitted according to the well-known Avrami equation to obtain the Avrami index, which also gave almost the same crystallization half-time as demonstrated in Fig. 9b. In our supporting information, we provided all the data treatment of six PA samples at

b.

0.004

PA 610

PA 610

2×10-8 JK-1 o

Crystallization temperature 110 C Crystallization time from 0.1 s to 30 s

Melting enthalpy /mJ

Apparent heat capacity /J K

-1

a.

Endo up

various isothermal temperatures, like PA 610 at 110 °C in Fig. 9

0.003

△HC

0.002

t1/2 = 1.346 s 1/2△HC

0.001

Crystallization o temperature 110 C

-1

Heating at 4000 K s 0

50

100

150

200

0.000 0.01

250

o

0.1

1

10

100

Isothermal crystallization time /s

Temperature / C

Figure 9. (a) Apparent heat capacity curves of PA 610 at the heating rate of 4000 K s-1 after isothermal crystallization at 110 °C for various crystallization time periods from 0.1 to 30 s. (b) Time evolution of crystallization enthalpy of PA 610 on isothermal crystallization at 110 °C, and the crystallization half-time is read by the vertical dashed line. The red smooth curve is the fitting curve on the basis of Avrami equation 14

which derives Avrami index.

The characteristic crystallization

half-time representing the isothermal

crystallization rate in the temperature range between Tg and Tm. Beside PA 610, the above measurement has also been applied on PA 46, PA 66, PA 612, PA 1012 and PA 12. Figure 10 summarizes the crystallization half-time results of six PA samples for comparison. One can see that, six PA samples generally exhibit double parabolic curves with various minimum crystallization temperatures. The high temperature branches show roughly faster crystallization with higher melting points. The transition temperatures between two parabolic curves follow the same sequences as the high temperature branches. The low temperature branches show roughly faster crystallization with lower glass transition temperatures. Since the series of hydrogen-bonding density from high to low are PA 46, PA 66, PA 610, PA 612, PA 1012 and PA 12, and they decide the same sequences of melting points from high to low, as well as the same sequences of glass transition temperatures from low to high, the above sequences reveal the significant effects of hydrogen-bonding density in polymer crystallization kinetics. Furthermore, the maximum crystallization rates vary over two magnitudes in Fig. 10. There are experimental researches focusing on the molecular weight effects on polymer crystallization rates [26, 27]. Those extremely low and high molecular weights commonly shift the maximum crystallization rates within one magnitude [26, 27]. In our present study, the molecular weights of six PA samples are mainly in the industrially medium range. Thus, their small differences may take certain effects but could not make two-magnitude changes in crystallization rates.

15

Crystallization half-time /s

100

PA 1012 PA 12

10

PA 612 PA 66 PA 610 PA 46

1

0.1

0.01

1E-3 0

50

100

150

200

250

300

o

Crystallization temperature / C

Figure 10. Temperature dependence of crystallization half-times of PA 46, PA 66, PA 610, PA 612, PA 1012 and PA 12 (as labeled) during isothermal crystallization processes at various temperatures.

According to the classical nucleation theory, the primary nucleation rate I is dominated by the relatively high free energy barrier for crystal nucleation in the high temperature region, and by the relatively high activation barrier for short-distant diffusion in the low temperature region. The free energy barrier is determined by the supercooling away from the equilibrium melting points, and the activation barrier is determined by the temperature deviation away from the glass transition temperatures. Since we have both the melting points and glass transition temperatures for six PA samples in hand, we rescaled the crystallization temperatures of Fig. 10 according to the relative values within the ranges between the glass transition temperatures and the melting points of six PA samples. The rescaled results are summarized in Fig. 11. One can see that the curves are more converging with each other at both ends, confirming the application of the classical nucleation theory in the present cases. One can see that PA 46 crystallizes relatively faster mainly in the high temperature region, benefited from its high hydrogen-bonding density in thermodynamic driving forces for crystallization. PA 1012 and PA 12 crystallize relatively faster mainly in the low temperature region, benefited from its low hydrogen-bonding density in the short-range diffusion for crystallization. 16

After rescaling, it is a bit surprising to see that PA 46 exhibits fast crystallization in the temperature range expanding to the low-temperature region. One possible reason is that PA 46 still contains small amount of water playing the role of plasticizer in short-range diffusion for crystallization in the low temperature region.

2

Crystallization half-time /s

10

1

10

PA 612 0

10

-1

10

PA 610 PA 66 PA 1012 PA12

-2

10

PA 46 -3

10

0.0

0.2

0.4

0.6

0.8

0 (Tc-Tg)/(Tm -Tg)

Figure 11. Crystallization half-time as a function of crystallization temperature Tc in the relative scale between the glass transition temperature Tg and the equilibrium melting points Tm0 for six nylon samples as labeled. The data points are adopted from Fig. 10.

The double parabolic curvature for crystallization half-time versus crystallization temperature has been broadly observed in Flash DSC measurements of polymer materials [11-15]. The high temperature parabolic curve has been assigned to heterogeneous nucleation, while the low temperature parabolic curve has been attributed to homogeneous nucleation. The transition temperature between two parabolic curves is still open for study. In Fig. 10, one can see that the transition temperatures are roughly following the sequences of hydrogen-bonding density in six nylon samples. If there is a transition from heterogeneous nucleation to homogeneous nucleation, the Avrami analysis, as the helpful tool for a time-scaling kinetic analysis, will show the change in Avrami indexes as the consequence of nucleation mode change. 17

The Avrami equation was given as in Eqn. (2) [24], 1-Χ ( t −t0 ) = exp[ − K (t − t0 ) n ]

(2)

where X is the relative crystallinity as a function of time, t the crystallization time and t0 is the onset time for crystallization, K is the overall crystallization rate constant and n is the Avrami index. Before treating with Avrami anlysis, the incubation time for primary crystal nucleation should be subtracted from the real time [25]. The incubation time was read at the onset time, and the saturation time was read at the end time, same as before in reading the crystallization half-time in Fig. 9b. From the Avrami fitting as an example shown in Fig. 9b, we obtained Avrami indexes as a function of crystallization temperature for six nylon samples. The results are summarized in Fig. 12a. In principle, the Avrami index for three-dimensional heterogeneous crystal nucleation is typically around 3, and for three-dimensional homogeneous crystal nucleation is around 4. In Fig. 12a, all the curves exhibit a similar trend. With the decrease of temperatures, the Avrami indexes of PA 46 decay from 3 to around 1.5, then at 160 °C suddenly switch to around 4, and decay again to 1. Note that 160 °C is the transition temperature between its two parabolic curves in Fig. 10. The others are behaving in the similar ways and the switching to 4 starts at the transition temperatures following the sequences in hydrogen-bonding density. From the maximum Avrami indexes, as shown in Fig. 12b, one can see again the sequences of hydrogen-bonding density for six nylon samples. b.

5 PA 66 PA 46 PA 610 PA 612 PA 1012

Avrami index

150 140

o

4

T Peak of Avrami indexes / C

a.

PA 12 3

2

1

PA 46

130 120 110 PA 66 100 PA 610 90 PA 12

80

PA 1012 PA 612 70 60

0 0

50

100

150

200

250

60

300

80

100

120

140

160

180

Amide units per 1000 backbone atoms

o

Isothermal temperature / C

Figure 12. (a) Avrami indexes as fitted from the melting enthalpy versus isothermal crystallization time for six PA samples as labeled. (b) The peak temperatures of 18

Avrami indexes in (a) following the sequence of hydrogen-bonding density in six PA samples as labeled.

4. Conclusion We employed Flash DSC measurement to characterize the isothermal crystallization kinetics of PA 46, PA 66, PA 610, PA 612, PA 1012 and PA 12 in a broad temperature range. The double parabolic curves of crystallization half-time versus crystallization temperature reveal that PA 46 crystallizes fast because of its high hydrogen-bonding density favored by strong thermodynamic driving force for crystallization in the high temperature region, while PA 1012 and PA 12 crystallize also fast because of their low hydrogen-bonding densities favored by fast short-range diffusion for crystallization in the low temperature region. PA 46 extends its fast crystallization into the low temperature region probably due to its high capability of water up-taking, while a small amount of moistures plays the role like plasticizer favored by short-range diffusion for crystallization in the low temperature region. Furthermore, the transition temperatures

between

two

parabolic

curvatures

follow the sequences

of

hydrogen-bonding densities in six PA samples, and their Avrami indexes approve the idea of mode switching between homogeneous and heterogeneous crystal nucleation separately favored in the high- and low-temperature regions. Our observations reveal the effects of hydrogen-bonding density on the crystallization kinetics of polyamides. The knowledge could be fundamental for us to understand better the chain-folding mechanism not only in polyamides but also in proteins.

Acknowledgements We thanks Shandong Guangyin New Materials Company offering PA 610, PA 612 and PA 1012, and DSM China Campus offering PA 46 for this study. The financial support of National Natural Science Foundation of China (Grant Nos. 21474050 and 21973042), Key Lab of National Defense Science and Technology of China (Grant No. 61426030107), Program for Changjiang Scholars and Innovative Research Teams 19

(IRT1252) and the CAS Interdisciplinary Innovation Team are appreciated.

References [1] L.R. Schroeder, S.L. Cooper, Hydrogen Bonding in Polyamides, Journal of Applied Physics 47 (10) (1976) 4310-4317. [2] B.R. Wang, Polyamides, Acta Polymerica Sinica 1 (4) (1957) 179-195. [3] C.W. Bunn, E.V. Garner, The Crystal Structures of Two Polyamides (‘Nylons’), Proceedings of the Royal Society of London Series a-Mathematical and Physical Sciences 189 (1016) (1947) 39-68. [4] W.B. Hu, The Physics of Polymer Chain-folding, Phys. Rep. 747 (2018) 1-50. [5] N.A. Jones, E.D.T. Atkins, Polyamides with a Choice of Structure and Crystal Surface Chemistry. Studies of Chain-Folded Lamellae of Nylons 8 10 and 10 12 and Comparison with the Other 2N 2(N + 1) Nylons 4 6 and 6 8, Macromolecules 30 (1997) 3569-3578. [6] N.A. Jones, E.D.T. Atkins, M.J. Hill, Comparison of Structures and Behavior on Heating of Solution-Grown, Chain-Folded Lamellar Crystals of 31 Even-Even Nylons, Macromolecules 33 (7) (2000) 2642-2650. [7] N.A. Jones, E.D.T. Atkins, M.J. Hill, Investigation of Solution-crown, Chain-folded Lamellar Crystals of the Even-even Nylons: 6 6, 8 6, 8 8, 10 6, 10 8, 10 10, 12 6, 12 8, 12 10, and 12 12, J. Polym. Sci. Part B: Pol. Phys. 38 (9) (2000) 1209-1221. [8] H.J. Biangardi, Brill Transition of Polyamide 612, J. Macromol. Sci., Phys. (B) 29 (1990) 29 139-153. [9] R. Androsch, M. Stolp, H.J. Radusch, Crystallization of Amorphous Polyamides from the Glassy State, Acta Polymerica Sinica 47 (2-3) (1996) 99-104. [10] W.B. Hu, Polymer Physics: A Moleculai Approach, Springer, Vienna (2013) pp. 187. [11] A. Toda, R. Androsch, C. Schick, Insights into Polymer Crystallization and Melting from Fast Scanning Chip Calorimetry Schick, Polymer 91 (2016) 239-263. [12] Z.L. Li, D.S. Zhou, W.B. Hu, Recent Progress on Flash DSC Study of Polymer Crystallization and Melting, Acta Polymerica Sinica 09 (2016) 1179-1197.

20

[13] Y.C. He, K.F. Xie, Y.H. Wang, D.S. Zhou, W.B. Hu, Characterization of Polymer Crystallization Kinetics via Fast-scanning Chip-calorimetry, Acta Phys Chim Sin (2019) doi: 10.3866. [14] F. De Santis, S. Adamovsky, G. Timomanlio, C. Schick, Isothermal Nanocalorimetry of Isotactic Polypropylene, Macromolecules 40 (25) (2007) 9026-9031. [15] R. Androsch, M.L.D. Lorenzo, C. Schick, Optical Microscopy to Study Crystal Nucleation in Polymers Using a Fast Scanning Chip Calorimeter for Precise Control of the Nucleation Pathway, Macromol. Chem. Phys. 219 (3) (2018) 1700479. [16] Y.C. He, R.Q. Luo, Z.L. Li, W.B. Hu, Comparing Crystallization Kinetics between Polyamide 6 and Polyketone via Chip Calorimeter Measurement, Macromolecular Chemistry and Physics 219 (3) (2018) 1700385. [17] Q.X. Zhang, Z.H. Zhang, H.F. Zhang, Z.S. Mo, Isothermal and Nonisothermal Crystallization Kinetics of Nylon-46, J. Polym. Sci. Part B: Pol. Phys. 40 (16) (2002) 1784-1793. [18] S.S. Lee, P.J. Phillips, Melt Crystallized Polyamide 6.6 and its Copolymers, Part I. Melting Point - Lamellar Thickness Relations in the Homopolymer, European Polymer Journal 43 (2007) 1933-1951. [19] S. Gogolewski, K. Gzerniawska, M. Gasiorek, Effect of Annealing on Thermal Properties and Crystalline Structure of Polyamides. Nylon 12 (Polylaurolactam), Colloid & Polymer Sci 258 (1980) 1130-1136. [20] J.E. Mark, Physical Properties of Polymers Handbook Second Edition, Springer, New York (2007) pp. 180. [21] A.

Xenopoulos,

B.

Wunderlich,

Thermodynamic

Properties

of

Liquid

and

Semicrystalline Linear Aliphatic Polyamides, J. Polym.Sci., Polym. Phys. Ed. 28 (1990) 2271-2290. [22] Y.J. Li, X.Y. Zhu, G.H. Tian, E.L. Zhou, Multiple Melting Endotherms in Melt-crystallized Nylon 10,12, Polymer International 50 (2001) 677-682. [23] J.E.K. Schawe, Measurement of the Thermal Glass Transition of Polystyrene in a Cooling Rate Range of More Than Six Decades, Thermochimica ACTA 603 (2015) 128-134. 21

[24] M. Avrami, Granulation, Phase Change, and Microstructure Kinetics of Phase Change. III, J. Chem. Phys. 9 (1941) 177-184. [25] A.T. Lorenzo, A.J. Müller, DSC Isothermal Polymer Crystallization Kinetics Measurements and the Use of the Avrami Equation to Fit the Data: Guidelines to Avoid Common Problems. Polymer Testing 26 (2007) 222-231. [26] L. Mandelkern, J.G. Fatou, K. Ohno, The Molecular Weight Dependence of the Crystallization Rate for Linear Polyethylene Fractions. J. Polym. Sci. Polym. Lett. Ed. 6 (1968) 615-619. [27] N. Okui, S. Umemoto, Maximum Crystal Growth Rate and its Corresponding State in Polymeric Materials. Lect. Notes Phys. 606 (2003) 343–365.

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Highlights 1. Crystallization kinetics of six polyamide samples were compared via Flash DSC measurement. 2. High and low hydrogen-bonding densities favor fast crystallization with different mechanisms. 3. Avrami indexes approve the cross-over between homogeneous and heterogeneous nucleation.

Declaration of interest statement There is no declare of conflict interests!