Non-isothermal crystallization kinetics of silane crosslinked polyethylene

Polymer Testing 24 (2005) 71–80 www.elsevier.com/locate/polytest

Material Behaviour

Non-isothermal crystallization kinetics of silane crosslinked polyethylene Chuanmei Jiao, Zhengzhou Wang*, Xiaoming Liang, Yuan Hu State Key Lab of Fire Science, University of Science and Technology of China, Anhui 230026, China Received 8 June 2004; accepted 20 July 2004

Abstract The non-isothermal crystallization kinetics of silane crosslinked polyethylene (SXPE) and dicumyl peroxide (DCP) modified polyethylene (DMPE) were studied by differential scanning calorimetry at different cooling rates. Three methods, namely, the Avrami, the Ozawa, and the Mo, were applied to describe the crystallization process of virgin LLDPE, DMPE and SXPE under non-isothermal conditions. The values of half-time of crystallization t1/2, and the parameter Zc in the Avrami method which characterize the kinetics of non-isothermal crystallization, show that the crystallization rates of virgin LLDPE and DMPE are faster than that of SXPE at the same cooling rate, and crystallization rates of all samples increase as the cooling rate increases. The Ozawa model is also suitable to describe the process of the non-isothermal crystallization kinetics of all samples. In the Mo method, it has been found that the F(T) values of virgin LLDPE and DMPE are lower than that of SXPE, meaning that the crystallization rate of virgin LLDPE and DMPE is faster than that of SXPE. q 2004 Elsevier Ltd. All rights reserved. Keywords: Polyethylene; Silane crosslinking; Non-isothermal crystallization; Crystallization kinetics

1. Introduction Polyethylene is widely used in many sectors of industry, but one of its major drawbacks is a relatively low upper use temperature [1]. Crosslinking can extend the uses of thermoplastic PE by raising the upper temperature limit of application and improving the mechanical properties of this polymer. There are three main crosslinking methods, i.e. radiation crosslinking [2–5], peroxide crosslinking [6–8] and silane crosslinking [9,10]. Among the crosslinking methods, silane crosslinking is cost-effective and easily operated [11], this crosslinking technology is, therefore, commonly employed to produce wire and cables, plastic pipes, etc. There have been some articles published on

* Corresponding author. Tel.: C86-551-3601642; fax: C86-5513601669. E-mail address: [email protected] (Z. Wang). 0142-9418/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymertesting.2004.07.007

the technology of silane grafting and moisture crosslinking of polyethylene. Sen et al. [11–13] reported grafting reaction kinetics, melting behavior, thermal properties which were studied by differential scanning calorimetry (DSC), dynamic mechanical properties which were studied by DMA and structural parameters which were studied by X-ray diffraction analysis on silane grafting and moisture crosslinked polyethylene and ethylene propylene rubber. Shieh et al. [14,15] also investigated the silane grafting and crosslinking reactions of LDPE, HDPE and LLDPE by means of DSC and found the extent of silane grafting reactions of polyethylenes are in the order LLDPEO LDPEOHDPE. In our previous publication [16], we studied the thermal behavior of silane-crosslinked polyolefins, and the combustion characteristics of flame retarded and silane crosslinked polyethylene (SXPE). Crystallization of polymers is usually studied by the DSC method. The crystallization process can proceed under either isothermal condition or non-isothermal

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Table 1 Formulations containing different initiator levels Sample code

LLDPE

VTMS (phr)

DCP (phr)

DBDL (phr)

A B C D E F

100 100 100 100 100 100

– 3.0 3.0 3.0 3.0 –

– 0.05 0.1 0.2 0.4 0.2

– 0.2 0.2 0.2 0.2 –

conditions. From the practical view, the non-isothermal crystallization is more useful than the isothermal crystallization. There are many papers on studying the crystallization kinetics of polyethylenes or polyethylene composites [17–20], but few publications have been found concerning the crystallization kinetics of crosslinked polyethylenes [21,22], especially SXPEs. The purpose of this article is to investigate the non-isothermal crystallization kinetics of SXPE and DCP modified polyethylene (DMPE) based on their differential scanning calorimeter (DSC) data using different analysis methods.

2. Experimental

Fig. 2. Non-isothermal crystallization exotherms of samples A–F at a cooling rate of 10 8C/min.

and dibutyltin dilaurate was added into the apparatus and mixed for about 3 min. The temperature was raised to 160 8C in a transient period of about another 3 min. The mixture was then mixed at 32 rpm at 160 8C for 15 min. The grafted samples were first compression molded at approximately 130 8C into 1 mm thick sheets under a pressure of

2.1. Materials Linear low density polyethylene (LLDPE) with a melt flow index (MFI) of 2.0 g/10 min was supplied by Zhongyuan Petrochemical Company, China. Vinyl trimethoxysilane (VTMS) and dibutyltin dilaurate (DBDL) are standard laboratory reagents used as received. Dicumyl peroxide (DCP) was recrystallized using anhydrous ethanol.

Table 2 Tonset, Tp, DHc and tp of samples A–F at different cooling rates Sample

R (8C/min)

Tonset (8C)

DHc (J/g)

Tp (8C)

A

5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20

115.8 113.8 113.0 112.2 115.9 115.6 114.7 114.0 115.6 115.3 114.2 114.1 116.0 114.7 113.5 113.2 117.1 115.7 114.7 114.1 116.0 115.0 113.1 112.0

83.2 82.9 82.2 82.8 72.6 72.4 72.8 73.2 76.9 76.8 76.6 76.4 79.7 79.0 78.4 78.5 70.2 70.5 70.4 70.7 81.7 82.0 82.3 82.2

– – – – 104.7 103.7 102.0 100.4 104.3 102.7 100.2 101.5 104.0 101.4 99.2 99.2 104.9 102.7 100.7 99.6 – – – –

2.2. Preparation of samples

B

Vinyl trimethoxysilane (VTMS) grafting of LLDPE was carried out in a Brabender-like apparatus. After LLDPE melted at about 120 8C, the mixture of VTMS, DCP

C

D

E

F

Fig. 1. Effect of DCP concentration on the gel content of SXPE.

tp (s) 113.7 110.8 109.8 108.8 113.4 112.1 110.6 109.1 113.1 111.3 110.8 108.7 112.9 110.0 107.4 107.2 113.8 112.1 110.0 109.3 113.4 111.4 109.4 108.3

25 18 13 10 134 71 51 41 136 76 56 38 144 80 57 42 146 78 56 44 31 22 15 11

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The extracted samples were washed using acetone and then dried to a constant weight. The gel content is expressed in terms of the percentage of the weight remaining   W K W1 Gel ð%Þ Z 1 K !100% G where G is the weight of the sample, W is the total weight of the sample and copper net before being extracted, and W1 is the total weight of the sample and copper net after being extracted.

Fig. 3. Plots of 1/tp versus cooling rate of samples A–F.

9 MPa for 10 min, then immersed in water at 90G2 8C for 10 h. The formulations are shown in Table 1.

2.4. Differential scanning calorimetry (DSC) measurement

About 0.2–0.3 g weighed samples of small pieces in a copper net were put into boiling xylene for 24 h.

The DSC experiment was performed using a Perkin– Elmer Pyris 1 analyzer. The samples were first heated up to 180 8C from room temperature at 40 8C/min, and held there for 5 min to remove the thermal history of the polymer, then cooled to room temperature at 5, 10, 15 and 20 8C/min, respectively.

Fig. 4. Plots of Xc versus T for crystallization of (a) sample A and (b) sample E.

Fig. 5. Plots of Xc versus t for the non-isothermal crystallization of (a) sample A and (b) sample E.

2.3. Determination of gel content

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3. Results and discussion 3.1. Effect of initiator concentration on the gel content of SXPE The effect of initiator concentration on the gel content of silane-crosslinked LLDPE (SXPE) is shown in Fig. 1.

Clearly, the gel content increases rapidly at first, and then increases slightly as the DCP concentration increases. This observation indicates that at higher DCP concentrations it has no obvious effect on the silane-grafting and the grafting degree reaches a limit. For peroxide (DCP) modified polyethylene (DMPE), only several percent gel was found.

Fig. 6. Plots of ln[Kln(1KXc)] versus ln t for the non-isothermal crystallization of (a) sample A; (b)–(e) samples B–E; and (f) sample F.

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3.2. Non-isothermal crystallization behavior of SXPE and DMPE The non-isothermal crystallization of PE, DMPE and SXPE from the melt at different cooling rates ranging from 5 to 20 8C/min was studied using DSC. Fig. 2 shows the nonisothermal crystallization exotherms of samples A–F at a cooling rate of 10 8C/min. It can be seen from Fig. 2 that virgin LLDPE has a single peak at about 110 8C, whereas SXPE has double peaks, one at about 110 8C and another at about 100 8C. The appearance of the new peak at the lower temperature for SXPE is caused by the silane crosslinking. Polyethylene after the crosslinking forms a net structure, which makes the macromolecule chains less flexible, so the crystallization temperature becomes lower and crystallization becomes more difficult. Table 2 lists the onset temperature (Tonset), which is the temperature at the crossing point of the tangents of the baseline and the high temperature side of the exotherm, the peak temperature (Tp) and the crystallization enthalpy (DHc) of nonisothermal crystallization exotherms of LLDPE, DMPE and SXPE at different cooling rates. Apart from the appearance of a new peak at 100 8C, the silane crosslinking seems not to affect the Tp value at about 110 8C. As for the DHc, which is proportional to the degree of crystallinity Table 3 Non-isothermal crystallization kinetic parameters based on the Avrami method Sample

A

B

C

D

E

F

R (8C/min) 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20

-n

Zc (min )

n n1

n2

Zc1

Zc2

1.61 1.63 1.63 1.64 1.16 1.48 1.55 1.61 1.33 1.50 1.63 1.54 1.48 1.56 1.66 1.61 1.60 1.58 1.65 1.70 1.01 1.14 1.20 1.25

0.79 0.87 0.83 0.82

0.92 1.04 1.08 1.08 0.76 0.91 0.98 1.00 0.73 0.91 0.97 1.00 0.68 0.91 0.96 1.00 0.66 0.91 0.98 1.00 0.84 0.97 1.00 1.02

0.88 0.99 1.02 1.03

t1/2 (s)

75

(Xc), its value decreases with the increase in the degree of crosslinking. For DMPE, its crystallization peak is similar to that of the virgin LLDPE. The Tonset, Tp and DHc values of DMPE are very comparable to the ones of virgin LLDPE as shown in Table 2. Table 2 lists the value of the crystallization peak time tp, which is denoted as the time the sample spends during the temperature drop from Toneset to Tp. The tp decreases roughly with increase of the cooling rate, meaning the increase in the rate of crystallization. It can also be seen that the value of tp of the control sample (virgin LLDPE) is smaller than that of SXPE, indicating that the crystallization of SXPE is more difficult than that of virgin LLDPE. For easy comparison, the reciprocal values of the time tp versus cooling rates for all samples are plotted in Fig. 3. It was found that for a certain sample, the rate of non-isothermal crystallization increases with increasing the cooling rate. The rate of crystallization of virgin LLDPE is the highest at all cooling rates, and the rate of DMPE is located between the rates of virgin LLDPE and SXPE. The difference in the rates of SXPE samples is very small. The relative degree of crystallinity Xc is a function of temperature which is plotted in Fig. 4. If the X-axis of Fig. 4 is changed into a time axis, we obtain Fig. 5 from which it can be seen that the higher the cooling rate, the shorter the time spent for completing the crystallization process.

4. Non-isothermal crystallization kinetics of silane crosslinked LLDPE 4.1. Avrami method

92 48 30 23 145 86 59 46 153 86 65 44 173 89 68 47 176 88 60 49 100 57 42 32

It is well known that isothermal crystallization kinetics of polymers is commonly studied by the Avrami method [23] 1 K Xc ðtÞ Z expðKZt tn Þ

(1)

where n is the Avrami crystallization exponent dependent on the mechanism of nucleation, t is the time taken during the crystallization process, Zt is a crystallization rate constant, and Xc (t) is relative crystallinity of polymers at different temperatures. Both Zt and n are constants which are denoted as a given crystalline morphology and type of nucleation at a particular crystallization condition [24]. Using Eq. (1) in double-logarithmic form ln½Kln½1 K Xc ðtÞ Z ln Zt C n ln t

(2)

and plotting ln[Kln[1KXc(t)]] versus ln t for each cooling rate, a straight line is obtained. From the slope and intercept of the lines, one can determine the Avrami exponent n and the crystallization rate Zt. Eq. (1) is suitable for an isothermal crystallization system. Just like isothermal analysis, non-isothermal crystallization can also be analyzed by the Avrami equation, but, considering the non-isothermal characterization of the process

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investigated, Jeziorny [25] presented the final form of the parameter characterizing the kinetics of non-isothermal crystallization as follows: ln Zc ¼ ln Zt =R

(3)

where R is the cooling rate. Fig. 6 shows the plot of ln[Kln[1KXc(t)]] versus ln t at different cooling rates for samples A–F. For sample A, the curves in Fig. 6a can be divided into two linear portions, which means that

the virgin LLDPE has two crystallization processes. However, the curves at different cooling rates in Fig. 6b–e are roughly linear, and are almost parallel to each other. This phenomenon illustrates that there is possibly only one process of crystallization for the SXPE and DMPE samples. The values of the Avrami exponent n, crystallization rate constant Zc and t1/2 for each sample are given in Table 3. For all samples, the n value varies from 0.79 to 1.70. It is clear that virgin LLDPE has two n

Fig. 7. Plots ln[Kln(1KXc)] versus ln(R) for the non-isothermal crystallization of (a) sample A; (b)–(e) samples B–E; and (f) sample F.

C. Jiao et al. / Polymer Testing 24 (2005) 71–80

values, whereas DMPE and SXPE have only one n value. The n value of SXPE is similar to the n1 value of virgin LLDPE, indicating that the mechanism of nucleation of SXPE is about the same as the one of the first stage of crystallization of virgin LLDPE. As for DMPE, its n value is smaller than that of SXPE and n1 of virgin LLDPE, indicating the mechanism of nucleation of DMPE is different from that of virgin LLDPE and SXPE. The data listed in Table 3 show that for all samples Zc increases and t1/2 decreases as the cooling rate increases. The increase in Zc and the decrease in t1/2 mean an increase of rate of crystallization. From Zc and t1/2 values, it can be seen that the rate of crystallization changes in the following order: virgin LLDPEODMPEOSXPE.

The non-isothermal crystallization can also be analyzed using the Ozawa method [26]. The Ozawa equation is as follows m

1 K Xc Z exp½KkðTÞ=R 

Sample

Temperature (8C)

m

K (T) (8C/minK1)

r

A

85 90 95 100 105 85 90 95 100 105 85 90 95 100 105 85 90 95 100 105 85 90 95 100 105 85 90 95 100 105

0.15 0.13 0.13 0.14 0.18 0.12 0.17 0.25 0.37 0.52 0.23 0.22 0.25 0.32 0.40 0.24 0.24 0.31 0.43 0.53 0.23 0.23 0.28 0.37 0.42 0.28 0.25 0.26 0.32 0.49

4.20 3.04 2.27 1.68 1.28 2.96 2.49 2.12 1.80 1.37 3.66 2.68 2.00 1.51 0.95 3.39 2.53 2.04 1.70 1.07 4.09 2.92 2.23 1.67 1.02 5.01 3.50 2.68 2.17 1.98

0.99 0.99 0.98 0.99 0.99 0.95 0.94 0.95 0.96 0.97 0.96 0.95 0.93 0.93 0.94 0.95 0.94 0.95 0.96 0.97 0.95 0.96 0.97 0.98 0.99 1.00 1.00 1.00 0.99 0.99

B

D

(4)

where k(T) is the crystallization rate constant, Xc is the relative crystallinity, R is the cooling rate, and m is the Ozawa exponent depending on the crystal growth and nucleation mechanism. Results of the Ozawa analysis are shown in Fig. 7, which plots ln[Kln(1KXc)] versus ln R for temperatures ranging from 85 to 105 8C for the nonisothermal crystallization. A least-square line is drawn for each temperature. A series of lines for a certain sample are nearly parallel, indicating that the Ozawa approach is appropriate for describing the non-isothermal crystallization kinetics of virgin LLDPE, DMPE and SXPE. The Ozawa rate constant, k(T) is the antilogarithmic value of the y-intercept, and the Ozawa exponent m is the negative value of the slope. Values of m and k(T) as well as the corresponding correlation coefficient r for each sample are listed in Table 4. It was found from Table 4 that for each sample the Ozawa exponent m roughly increases with increasing temperature, and Ozawa rate constant k(T) decreases with increasing temperature, indicating that for each sample the lower the temperature, the faster it crystallizes. Based on the correlation coefficient listed in Table 4 and the fact that all lines gained are parallel, it is fair to conclude that the Ozawa method is a satisfactory description of the non-isothermal crystallization kinetics of all samples [27]. 4.3. The Mo method A method modified by Mo was also employed to describe the non-isothermal crystallization, which combines the Avrami equation with the Ozawa equation. Its final form is given as below [28,29] lnðRÞ Z ln FðTÞ K a ln t

Table 4 Non-isothermal crystallization kinetic parameters based on the Ozawa method

C

4.2. The Ozawa method

(5)

77

E

F

where F(T)Z[K(T)/Zt]1/m represents the value of cooling rate, which must be chosen within unit crystallization time when the measured system amounted to a certain degree of crystallinity; a refers to the ratio of the Avrami exponent n to the Ozawa exponent m (aZn/m). The plots of ln(R) versus ln t for all samples are given in Fig. 8, from which the values of a and F(T) can be obtained by the slopes and the intercepts of these lines, respectively (Table 5). It can be seen from Table 5 that the values of F(T) systematically increase with an increase in the relative degree of crystallinity. At a given degree of crystallinity, the higher the F(T) value, the higher cooling rate is needed within unit crystallization time, indicating the difficulty of polymer crystallization. By comparing the values of F(T) of different samples, we have found that the values of virgin LLDPE and DMPE are lower than that of SXPE, meaning that the crystallization rate of virgin LLDPE and DMPE is faster than that of SXPE. This is in accordance with the result obtained from the Avrami approach. However, the values of a nearly remain constant for LLDPE, DMPE and SXPE.

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Fig. 8. Plots of the ln(R) versus ln t for the non-isothermal crystallization of (a) sample A; (b)–(e) sample B–E; and (f) sample F.

5. Conclusions A systematic study of the non-isothermal crystallization kinetics of virgin LLDPE, DMPE and SXPE has been performed by the DSC technique. The crystallization kinetics of each sample was investigated according to

three different kinetic models, namely, the Avrami, the Ozawa and the Mo. All the three models can describe the experimental data very well. In the Avrami method, the parameters Zc and t1/2 suggest that for all samples the rates of crystallization increases with increasing cooling rate. It has been found that the rate of

C. Jiao et al. / Polymer Testing 24 (2005) 71–80 Table 5 Non-isothermal crystallization kinetic parameters based on the Mo method Sample

Xc!102

a

F (8C/min)

A

10 20 30 40 50 60 70 80 90

1.15 1.15 1.08 1.06 0.95 0.92 0.94 0.96 0.97

1.50 2.39 3.48 4.77 7.03 10.02 13.70 18.00 23.90

B

10 20 30 40 50 60 70 80 90

1.17 1.16 1.09 1.10 1.05 1.07 1.03 1.04 0.986

3.41 6.44 9.66 12.29 14.90 17.90 21.0 25.72 30.50

10 20 30 40 50 60 70 80 90

1.14 1.23 1.07 1.15 1.08 1.12 1.06 1.10 1.07

3.73 6.00 9.65 12.21 15.30 18.29 21.80 27.29 34.10

D

10 20 30 40 50 60 70 80 90

1.17 1.15 1.12 1.10 1.09 1.09 1.07 1.07 1.07

3.98 7.12 10.5 13.19 16.10 19.29 23.00 27.98 35.60

E

10 20 30 40 50 60 70 80 90

1.16 1.07 1.09 1.07 1.05 1.05 1.03 1.05 0.99

3.87 7.36 9.66 13.04 14.9 18.37 21.0 25.62 30.50

F

10 20 30 40 50 60 70 80 90

1.53 1.67 1.42 1.28 1.20 1.16 1.12 1.10 1.09

1.13 1.78 3.75 6.36 9.30 12.66 16.70 21.92 29.4

C

79

crystallization changes in the following order: virgin LLDPEODMPEOSXPE. The changes of the n value illustrate that the crystallization mechanism of virgin LLDPE, DMPE and SXPE is different. The Ozawa method has also been found to be a satisfactory description of the non-isothermal crystallization process of virgin LLDPE, DMPE and SXPE samples. From the Mo method, we have found that the F(T) values of virgin LLDPE and DMPE are lower than that of SXPE, which shows that the crystallization rate of virgin LLDPE and DMPE is faster than that of SXPE.

Acknowledgements The financial support from the China National Key Basic Research Special Funds project (No. 2001CB409600) and from the National Natural Science Foundation of China (No. 50273036) is greatly acknowledged.

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