Photoinitiated crosslinking of low density polyethylene I: Reaction and kinetics

P hotoi ni tia ted Cross1 i n ki ng of Low Density Polyethylene I: Reaction and Kinetics

YAN QING, XU WENYING, and BENGT RANBY*

Department of Material Science and Engineering University of Science and Technology of China

Hefei, Anhui 230026, P.R. of China

The kinetics of the reaction in photocrosslinking of the low density polyethylene-benzophenone-triallyl cyanurate (LDPE-BP-TAC) system was studied by theoretically deriving a kinetic equation and comparing it with the results from crosslinking, extraction and swelling experiments. It was found that the rate of crosslinking is proportional to the square of light intensity. The roles of the crosslinker (TAC) were to capture the excited initiators efficiently to form free radicals and to act as a carrier of the active radicals. The ratio of degradation/ crosslinking was extrapolated to be around 0.28, and compared with 0.44 in the y-irradiation process for the same material.

INTRODUCTION

t was first proposed by Oster in the 1950s that I polyethylene can be crosslinked with ultraviolet light in the presence of photo-initiators (1, 2). Recent developments of Ranby and co-workers (3-6) sug- gest the UV method to be applicable to industrial crosslinked polyethylene (XLPE) production. There are only few papers concerning the theoretical analysis of this process (7, 8), and no study of the mechanism of the crosslinker has been reported.

In this work, we will derive the kinetic equation and compare it to experimental data. The effect of light intensity and the role of the crosslinker will also be discussed. Moreover, we will estimate the degree of degradation during UV-irradiation quanti- tatively by a combination of the Charlesby-Pinner formula with the kinetic equation.

EXPERIMENTAL

Materials

Low density polyethylene resin (LDPE 112A-1) was obtained from YanShan Petrochemical Co. (China). d = 0.921, M.Z. = 2 (21190); = 1036000, and flu /an = 36 (results from GPC analysis).

Initiator: benzophenone (BP). Crosslinkers: triallyl cyanurate (TAC) and its iso-

mer triallyl isocyanurate (TAIC).

UV irradiation

High pressure mercury lamps GGZ-500 (500W) and GGZ-1000 (lOOOW) were used as the source of UV light (Fig . 1 a). The irradiation was carried out in

*Visiting professor from: Dept. of Polymer Technology, Royal Institute of Technology, S-100 44 Stockholm Sweden. To whom correspondence should be addressed.

a UV-CURE equipment constructed in this labora- tory (Fig. 1 b).

Sample preparation LDPE granules were mixed with desired amounts

of initiator and crosslinker at about 110°C. The compound was hot-pressed into sheets with certain thicknesses (130"C, 3 min). Then the sheets of sample were irradiated in N, atmosphere at 130°C in the UV-CURE reactor. No gel fraction was formed before UV irradiation.

Characterization Gel content was measured by extraction with xy-

lene in a Soxhlet extractor for at least 24 h. The gels were allowed to swell in p-xylene at 81

1°C for 4 h to reach equilibrium (9). The swelling

200 300 400 500

Wavelength (nm)

Fig. la . Emission spectral distribution of the GGZ UV lamps.

POLYMER ENGINEERING AND SCIENCE, NOVEMBER 1991, Vol. 31, No. 22 1561

thermometer

Fig. 1 b. Sketch of irradiation apparatus.

ratio is calculated as follows:

where Q, is the swelling ratio: W,, W, represent the weight of the gel before and after swelling: pZlec= 0.85, p;'"= 0.87 are the densities of solvent and polymer, respectively (10).

In the thermal elongation experiment, dumb-bell shaped crosslinked samples were strained with a stress of about 0.1 MPa in an oven at 200 k 1°C. After 15 min equilibration, the elongation is measured: X = L/L,.

THEORETICAL SECTION

Crosslinking Density

According to the theory for rubber elasticity (1 l), the crosslinking density (the number of crosslinking units per volume) can be obtained from the results of swelling or thermal elongation experiments.

In swelling experiment, there is the Flory-Rehner Equation :

where is the effective crosslinking density in the gel: up = 9;' is the volume fraction of the polymer in the swollen gel: V, is the molar volume of the solvent, which can be calculated from its density: x = 0.3381 at 81°C is the polymer-solvent interac- tion parameter for polyethylene in p-xylene (9).

For thermal elongation studies, stress is given by the relation:

where v, is the effective crosslinking density in the whole sample (including gel and sol), and v, = vLg)/( 1 + S) , S is the sol content (1 1): T is the stress and h is the elongation: R is the gas constant: T is the abso- lute temperature.

Considering that the terminal chain segments do not contribute to the elastic force, the number aver-

age molecular weight between the adjacent crosslinks (G,) can be obtained from the effective crosslinking density:

1 2 vp +- _ - Gc -M, p, (3)

where p;loc = 0.87, 2oo"c = 0.75 (12) in each case. From the results listed in Table 1 , it is obvious

that the two experiments are identical. Now the most important data for us, gross cross-

linking density v can be obtained from the relation:

pP

(4)

Y a n Qing, X u Wenying, and Bengt R6nby

1562 POLYMER ENGINEERING AND SCIENCE, NOVEMBER 1991, Vol. 31, No. 22

where p, = d = 0.921 at room temperature. The results are also listed in Table 1 . The

crosslinking density increases steadily with irradiation time, but the gel content reaches a maximum during the photo-irradiation. The decrease in gel content at the later stage is due to chain scission.

Kinetic Equation

The reaction model for photocrosslinking may be illustrated as follows: Initiation

(5) deactivation

A+ ' ( A ) " '5' ' ( A ) * -A ki k : k- I

' ( A ) * + P 2 A ' + P

' ( A ) * + T 2 A ' + T ' (7) Propagation

k4 T + P ' + P - T

(9) k5

T + T ' + T - T '

Termination k6

P'+ T ' + P - T

k8 P ' + P ' + P = ( - H ) + P ( + H )

k9 P'+ A' + P - A

where A is photoinitiator which can be excited by UV photons to the singlet excited states S , and then through inter-system crossing (ISC) to the triplet state T , ( E q 5): P is polymer molecules whose radicals P ' can terminate each other by combination ( E q 1 1 ) or disproportionation ( E q 12); T is the multi-functional crosslinker if added, which can be involved in the abstraction of its ally1 hydrogens ( E q 7) and addition to its double bonds ( E q 8).

Since each molecule of the crosslinker has several positions which can take part in the reaction, it is reasonable to assume that if only the polymer macromolecules connect with the crosslinkers, they are regarded as connected to the crosslinking net-

Photoinitiated Crosslinking of LDPE. I

Table 1. Results of Photocrosslinking of LDPE.

Irradiation Time 5 10 20 40 60 120 Isec) 0

62.0 69.8 76.4 77.8 77.6 Gel Content (%) 0 47.4 - MC (swelling) - 15,000 14,000 12,300 10,900 10,400 9,900 -

- - 14,200 12,200 10,600 10,500 9,900 Mc (thermal elongation) Crosslinking Density (1 o - mol/cm3) 0 2.19 4.08 5.26 6.62 6.90 7.19

work. So the rate of crosslinking can be represented as

dv - = k 4 [ P ' ] [TI + k 6 [ P ' ] [ T ' ] + 2 k 7 [ P ' ] " (14) d t

If the steady-state approximation is adopted (where k , = k ; + k y ) :

-- d [ A * l - k , l n [ A ] - k - , [ A * ] d t

- k , [ A * ] [ P ] - k 3 [ A * ] [ T ] = O (15)

-- d [ p ' l - k 2 [ A*] [ P ] - ( k 4 [ P ' ] [ T ] + k 6 [ P ' ] [ T ' ] d t

+ 2 k 7 [ P ' ] " ) - 2k , [ P ' I 2 - k g [ P ' ] [ A ' ] = 0

( 16)

then the kinetic equation of photocrosslinking reaction can be derived from Eqs 14, 15, and 16:

dv dt = K , K p K , K l l n [ A ] (17)

where n is the order of the reaction to the light intensity I, which will be discussed later.

The meaning of the coefficients K,, K,, and K , are as follows:

k 2 b 4 * l [ P l + k 3 E A * l [ T l K 1 = k - , [ A * ] + k , [ A * ] [ P ] + k 3 [ A * ] [ T ]

K , is the ratio of the excited photosensitizers which initiate the reaction to all those that have been excited.

(19)

K , is the ratio of polymer radicals to all the radicals initiated by the excited photosensitizers.

k , [ P ' ] [ T ] + k s [ P ' I [ T I + 2 k 7 [ P ' I k 4 [ P ' ] [ T ] + k 6 [ P ' ] [ T ' ] + 2 k 7 [ P . ] "

K , =

+ 2 k,[ P ' ] + k,[ P ' ] [ A ' ]

k 4 [ T ] + k 6 [ T ' ] + 2 k 7 [ P ' ] k 4 [ T ] + k 6 [ T ' ] + 2 k 7 [ P ' ] + 2 k , [ P ' ] + k g [ A ' ]

- -

( 2 0 )

K , is the ratio of crosslinks to all the products containing the polymer chains.

If the deactivation of the excited initiators can be ignored, then

- 4 A1 = - k , l n [ A ] d t

Integrated:

[ A ] = [ A],exp( - k , l " t ) ( 2 2 ) Therefore, the kinetic equation ( E q 1 7 ) can be

expressed as: dv

= K,K,K,kll"[ A],exp( - k l l n t ) ( 2 3 )

Provided that the coefficients K,, K,, and K , can be treated as constants when integrated, the relationship between the crosslinking density v and the irradiation time t is available (where K is a constant):

v = K [ A],( 1 - e-kl'"t)

v = 7.1 x 1 0 - 5 ( 1 - e-0.075t 1

(24) Fitting with the experimental data in Table 1 , it

becomes

( 2 5 ) The coincidence of our theoretical and experimen-

tal results shown in Fig. 2 indicates that the kinetic

8

0 20 40 60 8 0 100 1 0

lrradiatlon Time (sec)

Fig. 2. Theoretical kinetic curve compared with experimental data referred to in Table 1 .


Yan Qing, X u Wenying, and Bengt R&nby

equation derived in this work can predict the tend- ency of photocrosslinking quite well, even though it is rather approximate.

RESULTS AND DISCUSSION

Effect of Crosslinker

can be derived similarly: In the case without crosslinker, a kinetic equation

dv - = K I " K c " k , l n [ A] d t (17')

where the coefficients have the same meaning but [TI = I T * ] =0:

Comparing these relations with E q 18 through 20, even though K," = 1 >K,, it is apparent that:

K," < K , ; K," K , (26)

This is the reason why the crosslinker can promote the photocrosslinking reaction so significantly as shown in Fig. 3.

1. The crosslinker molecules can capture the excited initiators much more efficiently than the polymer macromolecules themselves and this over- whelms the deactivation reaction, i.e. k , B k , and k - so that K , = 1. In this way, more excited photosensitizers can be used to initiate radical chain reactions which lead to crosslinking. 2. In the presence of the crosslinker, it becomes more important that the polymer chains connect through crosslinker molecules to form the crosslinking network. Otherwise the chains have to connect only by the much less probable combination of two macroradicals. That means that the crosslinker

In concrete terms, Eq 26 implies two facts:

loo d 80 t 0 1 % TAC

0 O%TAC

c

Q C 0 0

c

0 80 160 240 320

irradiation Time (sec)

Fig. 3. Effect of crosslinker on photcrosslinking (Lamp: 1 OOOW, 1 0 cm).

makes the crosslinking easier and relatively re- strains some side reactions, e.g. disproportionation.

From a practical point of view, the following facts are very important.

First of all, after photo-initiation, the active ally1 radicals can be preserved and transmitted by the "dark reactions" of the crosslinker. Therefore, the limitation of the photocrosslinking method to thin samples due to poor penetration of UV light can be overcome to a great extent.

Secondly, because the irradiation time can be re- duced and degradation and disproportionation are limited, the structural perfection of the macromolecules will be less affected, avoiding weakness in the chains.

Two crosslinkers were studied in this work, TAC and TAIC, with almost identical effects on the crosslinking process [Fig. 4). Structure transformation was found in study of the polymerization of these multi-functional monomers ( 13):

UAC) C r A W This transformation can be the reason for the coincidence.

Effects of Sample Thickness

Attenuation of light intensity with penetration into the sample surface was not taken into account when the kinetic equation was derived. But the thickness of the sample does have a great effect on the rate or degree of crosslinking.

Figure 5 shows the crosslinking results for samples of different thickness. It is found that with increase in thickness, the rate of crosslinking at the first stage is lower, but the degree of crosslinking reaches the same level at long exposure (up to at least 5 mm thick).

100, I

80 t

I I . 1 0 60 120 180

irradiation Time (see)

Fig. 4 . Crossl inking resul ts w i t h the two different crosslinkers T A C a n d TAIC [Lamp: 500W, 10 cm).

1564 POLYMER ENGINEERING AND SCIENCE. NOVEMBER 1991, Vol. 31, No. 22

Photoinitiated Crosslinking of LDPE. I

The thicker sample (3.5 mm) was cut into 0.5 mm thick slices layer by layer from the top surface. The gel content of each layer was measured. Figure 6 shows that the homogeneity of photocrosslinking through the depth is satisfactory. This is also an effect of the presence of the crosslinker (4).

Effects of Light Intensity

The relationship between crosslinking rate and light intensity in the photocrosslinking of polyethylene has been of interest for a long time (7). In this work the efforts to determine the reaction order “n” in Eq 17 have been made.

With variation in the light intensity as follows:

I,: lOOOW, 10cm I , : 500W, 10cm

12: lOOOW, 1 4 c r n ,

from the index supplied by the manufacturer,

I, = 1 / 2 6 ;

L I

Irradiation Time (sec)

Fig. 5. Crosslinking results for the samples wi th different thicknesses (Lamp: 1 OOOW, 10 cm).

100

i

50

- s

0 1 2 3 4

Depth from Surface (rnrn)

Fig. 6. Crosslinking homogeneity of the 3.5 mm thick sample (Lamp: 1 OOOW, 1 0 cm; irradiated for 90 seconds).

and by the rule of 10: 1 / r ’, we conclude

l2 = 1/210.

Comparing the crosslinking results, if the time axis of 1,’s is enlarged 4 times as shown in Fig. 7, all the data from the three different light intensities are positioned on an identical kinetic curve (assuming that gel content is proportional to crosslinking density). Alternatively, when the light intensity is re- duced to half of the original, it will take 4 times longer to get the same degree of crosslinking.

Since v 0: 1 - exp( - k , l n t ) ( E q 24), it follows that n = 2.

The conclusion is that the photocrosslinking is a second order reaction to light intensity, i.e., increas- ing the light intensity is a favorable way to raise the rate and efficiency of the photocrosslinking reaction.

Effects of Degradation

there is the relation: In Charlesby’s random crosslinking theory ( 14),

where y = 1 / (S + 6) is the “crosslinking index” and S = 1 - g is the sol content in crosslinked network: p , , q , are numbers of the units degraded or crosslinked, respectively, induced by per unit dose of irradiation: R is the radiation dose: and u1 is the original number average degree of polymerization of the polymer chains.

In our case of photocrosslinking, the dose of photons absorbed by sample, R should be proportional to the conversion of the initiator (Y = 1 - [A]/[ A],.

From Eq 22, CY is available:

a = 1 - exp( - k , I 2 t )

Using Eq 24, we determine that

Raa0:v

irradlation Time for 10 (sec)

,,,, 0 , 1,O , 2,O , 3,O . “0 , 5,O . 60

8o t 0 10: 1 OOOW, l o cm

40 11: 500W, lOcm

Q 12: lOOOW, 14 cm

-- 0 4 0 8 0 1 2 0 1 6 0 Z O O 2 4 0

irradiatlon Tlme for I1 & 12 (sec)

Fig. 7. Effect of light intensity on the rate of gel forma- tion.


Yan Q i n g , X u W e n y i n g , and Bengt R&by

0,4 - 0,2 -

and the Charlesby formula of Eq 27 can be expressed as

y = 0,44080 + 7,4549X R"2 = 0,996

1 Po A0 - +-

Y 40 v

0,o

where v is crosslinking density and A, is a constant.

F i g u r e 8 shows a linear relation between 1 / y and 1 / v , which extrapolated to 11 v = 0 gives p o / q, 0.28.

For comparison, the granules of the same resin were irradiated by cobalt-60 y-rays (60,000 curie) in a closed bottle with air inside. When the results were treated by the Charlesby formula, a straight line was obtained ( F i g . 9) with the intercept p o / q o = 0.44 for 1/R = 0.

It is concluded that the degradation effect in photocrosslinking is less than that in the high energy irradiation method. But even under radiation of UV light with mainly X > 300 nm, the chair-degradation is important and cannot be ignored.

During an extended period of photo-irradiation, the rate of crosslinking will slow down rapidly due to the consumption of initiator, whereas the rate of degradation changes rather slowly. The effect of

, . . , . . I . .

? . d

0,998

1 /v Fig. 8. Photocrosslinking d a t a treated b y the Charlesby Equat ion (R "2 is the correlation coeflcient) .

?- \ d

1IR (Mrad)

degradation will become more and more pro- nounced when the process takes a long time. Thus, minimizing the irradiation time is important not only for efficiency or energy saving, but also for the properties of the crosslinked product.

CONCLUSION

A kinetic equation for the photocrosslinking reaction of polyethylene with an added multi-functional crosslinker has been derived and shown to agree with experimental results. From a comparison of the kinetic equation with the experimental data, it is found that photocrosslinking is a second order reaction to light intensity.

Regarding the mechanism of the process, for the crosslinker to promote the crosslinking reaction significantly both in rate and depth, it is suggested that the crosslinker reacts with the excited initiator and forms active free radicals which lead to crosslinking by radical reactions with other crosslinkers and by combination with polymer chain radicals. This crosslinking mechanism is in agreement with results for model compounds of diene copolymers as previously reported ( 15).

Degradation in the photcrosslinking process is still notable, though it is less than in y-irradiation. It is harmful to prolong the crosslinking time, because degradation will increase significantly during the extended irradiation.

REFERENCES

1. G. Oster, J. Polym. Sci., 22, 185 (1956). 2. G. Oster, G. K. Oster, andH. Moroson, J . Polym. Sci.,

34, 671 (1959). 3. B. Ranby, in Polymer Science i n the Next Decades,

International Symposium Honoring Herman F. Mark on his 90th birthday, May 1985, 0. Vogl and E. H. Immergut, eds., pp. 121-133, J. Wiley, New York ( 1987). B. Ranby, Y. L. Chen, B. J. Qu, and W. F. Shi, pre- sented at IUPAC International Symposium on Poly- m e r s f o r Advanced Technologies, pp. 162-181, Jerusalem, Aug. 16-21, 1987, VCH Publ., New York (1988).

5. Y. L. Chen and B. Ranby, J . Polym. Sci. Polym. C h e m . Ed., 27, 4061 (1989).

6. Y. L. Chen and B. Ranby, J. Polym. Sci. Polym. C h e m . Ed., 27, 4077 (1989).

7. Qian Bao-Gong, Jiang Bing-Zheng, Liao Yu-Zhen, Liang Ying-Qiu, Wang Xia-Yu, and Fan Chui-Chang, Polymer Conference of Academia Sinica, 1961, p. 336, Science Press, Beijing (1963). Yan Qing, Du Dingzhum, Xu Wenying, and Bengt Ranby, Progress Mater. Sci., 3, 181 (1989). Soong Ming-Shi, Hu Gui-Xian and Chen Jiao-Yang, J . Univ. o f S c i . Tech. China, 3, 106 (1973).

10. J. Brandrup and E. H. Immergut, Polymer Hand- book, 2nd Ed., Wiley-Interscience, New York (1975).

11. P. J. Flory, Principles of Polymer Chemistry , Cornell Univ. Press, Ithaca, N.Y. (1953).

12. U. W. Gedde, Polymer, 27, 269 (1986). 13. B. H. Clampitt, D. E. German, and J. R. Galli, J.

Polym. Sci., 27, 515 (1958). 14. A. Charlesby and S. H. Pinner, Proc. R. SOC., A249,

367 119591.

4.

8.

9.

Fig. 9. ?-irradiation crosslinking d a t a treated b y the Charlesby Equat ion (R "2 is the correlation coefficient).

15. J. Hilborn'and B. Ranby, Macromolecules, 22, 1154 ( 1989).

1566 POLYMER ENGINEERING AND SCIENCE, NOVEMBER 1991, Vol. 31, No. 22

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Photoinitiated crosslinking of low density polyethylene I: Reaction and kinetics