Organic Peroxide

Organic Peroxide-Initiated Crosslinking Study of Cable Compounds Suh Joon Han, Larry H. Gross The Dow Chemical Company Somerset, NJ, USA + 1-732-271-2078 [email protected] + 1-732-271-7940 [email protected]

Abstract One of the most widely used crosslinking methods for wire and cable compounds in electrical applications is radical reaction by organic peroxides to enhance both dimensional stability at elevated temperatures and physical integrity under high electrical stress of the compounds. A moving die rheometer (MDR) has been a useful instrument to investigate the various crosslinking stages and crosslinking kinetics of the peroxide based thermal vulcanization of compounds with organic peroxide. In this study, we obtained the dynamic properties of polyethylene compounds with dicumyl peroxide (one peroxy group) and α,α’-bis(tertbutylperoxy)diisopropylbenzene (two peroxy groups) from 150 oC to 200 oC. It was found that the thermal decomposition of the peroxide follows the first order free-radical decomposition reaction and therefore, half-lives at various temperatures can be estimated from the kinetic data. The compound containing dicumyl peroxide crosslinked faster than the compound with α,α’-bis(tert-butylperoxy)-diisopropylbenzene, but it would also generate scorch faster at the lower temperature range. The activation energy of the compounds with dicumyl peroxide was estimated slightly higher than that of α,α’-bis(tert-butylperoxy)diisopropylbenzene. For another kinetic study approach, the time dependent torque from the MDR is assumed to be equivalent to the modulus of the compounds during the crosslinking process, and described by the concept of a non-equilibrium thermodynamic fluctuation theory of characteristic exponential decay behavior. It was found that the activation energy of relaxation for crosskinking of dicumyl peroxide is slightly lower than that of α,α’-bis(tert-butylperoxy)-diisopropylbenzene in polyethylene. The understanding of these concepts can help to achieve an improved balance of processability and cure performance for potential new compounds in wire and cable applications. Keywords: Organic peroxide; MDR; crosslinking kinetics; polyethylene; exponential decay behavior; rate constant; half life; activation energy.

1. Introduction Polyethylene has been the base resin of choice for insulation materials in medium and high voltage power cable applications for the last three decades. The insulation is typically based on vulcanizable polyethylene formulations to enhance its dimensional stability at elevated temperatures and physical integrity under high electrical stress [1]. Organic peroxides are widely used as cross-linking agents due to their high efficiency and low cost. The modern power cable manufacturing process consists of triple extrusion of peroxide-crosslinkable polymeric cable component layers on a copper or aluminum conductor, followed by a continuous vulcanization process and a cooling step. The peroxide containing polymer compounds are extruded in the range of 110 oC to 140 oC at various line speeds, followed by vulcanization under 100~200 psi of dry hot nitrogen in a tube

with a residence time to obtain the desired crosslinking of the compounds. The temperature is a key factor to induce decomposition of the peroxide, which initiates the crosslinking process in the polymer compounds. Therefore, the crossslinking condition is very sensitive to the heat transfer condition of the continuous vulcanization (CV) tube and cable construction. The quality of the vulcanizable insulation compounds is strongly dependent on the efficiency of an organic peroxide to achieve the desired state of crosslinking at a given peroxide concentration level. It is very important to understand the cure kinetics to define a proper crosslinking performance in the commercial CV tube conditions for optimum cable manufacturing process. In this study, we investigated the cure kinetics of two organic peroxides in polyethylene on the efficiency of crosslinking, utilizing the first order cure kinetics approach [2] and compared with the concept of a non-equilibrium thermodynamic fluctuation theory of chemical relaxation [3].

2. Experimental The polyethylene sample in this study is a commercial grade, which has a melting point of 80 oC in differential scanning calorimetry. The polydispersity is about 2. The two peroxides in this study are dicumyl peroxide (Mw= 270.37, melting point= 39~41 oC, active oxygen content = approximately 5.8 %) and α,α’-bis(tert-butylperoxy)-diisopropylbenzene (Mw= 338.49, melting point= 35~45 oC, active oxygen content= approximately 9.1 %). (A) (B) Figure 1 Structural formula of organic peroxides: (A) dicumyl peroxide (B) α,α’-bis(tert-butylperoxy)diisopropylbenzene The polyethylene base resin crosslinking kinetics were determined by monitoring torque rise in the RPA 2000 (Alpha Technologies) moving die rheometer (MDR) in a temperature range of 150 to 200 oC. The sample size was set to approximately 5.5 g, and the RPA 2000 was set to 0.5o arc and 100 cpm frequency (0.7 sec-1 shear rate). LOES Form Number 310-02101

3. Results and Discussion 3.1 The First Order Cure Kinetics

The peroxide crosslinking mechanisms in polyethylene are described in the literature elsewhere [4] [5] [6]. In principle, the unimolecular thermal decomposition of dicumyl peroxide results in the formation of cumyloxy radicals which may then abstract hydrogen from a carbon atom in the backbone of a polymer chain to give cumyl alcohol or undergo β-scission to acetophenone and methyl radicals. Two carbon radicals in two separate polymer backbones then combine to form a crosslink. On the other hand, α,α’-bis(tert-butylperoxy)-diisopropylbenzene that undergoes thermolytic decomposition results in tert-butyl peroxy radicals which will abstract hydrogen from polyethylene to give tert-butyl alcohol or further decompose to give acetone and methane radicals. The molar ratio of tert-butyl alcohol to acetone gives the relative rates of the mechanistic pathways. In this study, the RPA rheometer was used to collect cure kinetic data in the temperature range of 150 oC to 200 oC. The RPA produces a sinusoidal alternating torsional strain in the test sample which then generates a sinusoidal shear force or torque, which depends on the stiffness of the sample. The modulus of the sample increases as the crosslinking reaction progresses. Crosslinking is directly proportional to the peroxide decomposition. The test is completed when the recorded force or

torque rises to either an equilibrium or maximum value or a predetermined test time has passed. The time required to obtain a cure curve is dependent on the test temperature and the characteristics of the cross-linkable formulation. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 2000 4000 6000 8000 10000 12000 Time, second ln {[Po]/[P]} 150 C 160 C 170 C 180 C 190 C 200 C

Figure 2 Cure rates of dicumyl peroxide in polyethylene 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 2000 4000 6000 8000 10000 12000 Time, second Ln {[Po]/[P]} 150 C 160 C 170 C 180 C 190 C 200 C

Figure 3 Cure rates of α,α’-bis(tert-butylperoxy)diisopropylbenzene in polyethylene We evaluated the differences in the peroxide decomposition kinetics for polyethylene with dicumyl peroxide and α,α’-bis(tertbutylperoxy)diisopropylbenzene in terms of the decomposition rate constant and the half-life. For the first order kinetics, the decomposition rate constant, kd, can be expressed as [2], -d[P]/dt = kd [P] (1) which on integration yields: ln {[P0]/[P]} = kd t (2) where [P0] is the peroxide concentration at the start of decomposition and [P] is the peroxide concentration at time t. The peroxide decomposition rate constants can be estimated as crosslinking rate constant with the RPA data by plotting ln{[P0]/[P]} versus t in Equation (2) in a linear relationship as shown in Figure 2 and Figure 3. The slope from regression analysis is the decomposition rate constant, kd. The half-life, t1/2 is obtained as t1/2 = ln(2)/kd (3) Half-life is the time it takes for one-half of any quantity of peroxide in the formulation to thermally decompose. The time is independent of the quantity of the peroxide in the formulation and is primarily dependent on the temperature and type of peroxide. The reactivity of the two organic peroxides was also compared by the use of the half life at various temperatures as shown in Figure 4. The reactivity of the peroxide depends on the peroxide group configuration and on the type of the constituents (e.g.

dialkylperoxide vs peroxyketal structure). The reactivity of dicumyl peroxide is about 68 percent faster in average than α,α’bis(tert-butylperoxy)-diisopropylbenzene in polyethylene in the testing temperature range. LOES Form Number 310-02101

The effect of temperature on the decomposition rate is another important factor in characterizing the crosslinking behavior of the formulations. Increasing crosslinking temperature increases the 1 10 100 1000 10000 120 140 160 180 200 220 Temperature , oC Half Life, second Di-cumyl peroxide bis (tert-butylperoxy)diisopropylbenzene

Figure 4 Half-life times of dicumyl peroxide and α,α’bis(tert-butylperoxy)-diisopropylbenzene in polyethylene as function of temperature decomposition rate. The crosslinking rate constant can be expressed by an Arrhenius-type relationship. ln kd = ln A – Ea/ RT (4) where A is the collision frequency factor, Ea is the Arrhenius activation energy, R is the gas constant, and T the temperature ( kelvins). A plot of ln kd versus 1/T yields a linear relationship as shown in Figure 5 and allows the determination of Ea and A from the slope and intercept, respectively. Table 1 summarizes the activation energy of dicumyl peroxide and α,α’-bis(tertbutylperoxy)diisopropylbenzene in polyethylene from the liner regression analysis. The activation energy of dicumyl peroxide is approximately 9 percent higher than that of α,α’-bis(tertbutylperoxy)diisopropylbenzene in polyethylene. The half life can also be expressed in terms of activation energy and collision frequency factor by putting equation (4) into equation (3). The half life is exponentially proportional to the activation energy and inversely proportional to the collision frequency factor at the given temperature as expressed in equation (5). t1/2 =ln(2) A-1 exp [Ea/(RT)] (5) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 0.0021 0.00215 0.0022 0.00225 0.0023 0.00235 0.0024 1/T, K-1 ln(Kd) Dicumyl peroxide bis(tert-butylperoxy)diisopropylbenzene Linear (Dicumyl peroxide) Linear (bis(tert-butylperoxy)diisopropylbenzene)

Figure 5 Arrhenius activation energy plot of dicumyl peroxide and α,α’-bis(tert-butylperoxy)diisopropylbenzene in polyethylene Table 1 Activation energy of dicumyl peroxide and α,α’bis(tert-butylperoxy)-diisopropylbenzene in polyethylene from the first order cure kinetics dicumyl peroxide α,α’-bis(tert-butylperoxy)diisopropylbenzene Ea, activation

energy, kJ/mol 160.9 147.1 A, collision frequency factor, 1/second 3.628×1016 5.354×1014

3.2 Cure Kinetic Model from the Concept of Nonequilibrium Thermodynamic Fluctuation Theory The time dependence of the shear modulus, G(t) of the polyethylene compounds in the MDR curve can be expressed by G(t) = G∞ - (G∞ -G0) × ψ(t) (6) where G∞ is the shear modulus at the final equilibrium state after crosslinking and G0 is the initial shear modulus and G(t) is the shear modulus at time t. The crosslinking kinetic behavior is related to the function, ψ(t), which is assumed to be independent of both G∞ and G0. The boundary condition of this function is ψ(0) =1 and ψ(t→∞) =0. It can be rewritten as ψ(t ) = [G∞ - G(t)] / [G∞ -G0] (7) The time dependence of the crosslinking behavior of dicumyl peroxide in polyethylene from the MDR curve is estimated in terms of equation (7). It shows an exponential decay behavior as shown in Figure 6. A similar exponential decay behavior of crosslinking reaction was also observed from the MDR crosslinking behavior of α,α’-bis(tert-butylperoxy)diisopropylbenzene in polyethylene. LOES Form Number 310-02101

Figure 6 Time dependence of crosslinking function for dicumyl peroxide in polyethylene H. S.-Y Hsich proposed a kinetic model for this type of behavior from the concept of nonequilibrium thermodynamic fluctuation theory [3]. The crosslinking reaction can be considered as multiple chemical reactions, which are associated with a thermodynamic function. Then, a variation of the shear modulus during crosslinking can be expressed as the time correlation function of the mean square fluctuations of thermodynamic parameters. It is useful to generalize the crosslinking reaction to be a relaxation process describable by a sum of constant stress relaxation (or retardation) times. Relaxation time, τ, refers generally to the time-dependent characteristic response of a system to a well-defined external stimulus; it can also represent the time required for an exponential variable to decrease to 1/e of its initial value. Using such an exponential model, the distribution function relaxation spectrum can be represented as shown in equation (8), which is a function of time t. ψ(t) = [G∞ -G(t)]/[ G∞ -G0] = exp [- (t /τ)β] (8) and τ = τ0 exp [Ea/RT] (9) where β is the exponential constant describing the width of the relaxation spectrum (β >0), τ0 is a constant, R is the gas constant, T is the absolute temperature, and Ea is the activation energy of the crosslinking reaction. The time dependent decay function in equation (8) is in a sense, very similar to the empirical Kohlrausch-Williams-Watts (KWW) exponential expression, which is also widely used to correlate dielectric relaxation, quasi elastic light scattering, and stress relaxation behavior of polymers [7][8]. In MDR experiments, the MDR curve initially decreases to a minimum value before it starts to increase. This is due to the fact that the modulus of the sample, which is conditioned at room temperature, is higher than at crosslinking temperature before the

reaction takes place. For MDR curve fittings with the model, the induction time, tI (which is the time for the torque to reach a minimum value) must be subtracted from t in equation (8). It can be expressed as [G∞-G(t-tI)]/[G∞-G0] = exp [- {(t –tI)/τ}β] (10) G(t) = G0 + [ G∞ Y®_MÓž_'†¢-G0] [1- exp [-{(t –tI)/τ}β]] (11) By using equation (11), τ can be obtained from the MDR cure curve by calculating the value of G(t) at t = tI + τ. The calculation for G(tI + τ) is G(tI + τ) = G0 + [ G∞ -G0] (1- e-1) (12) It was found that the characteristic response time (i.e. relaxation time) of dicumyl peroxide is about 42 percent shorter on average than that of α,α’-bis(tert-butylperoxy)-diisopropylbenzene in polyethylene in the temperature range. From the relaxation time, time behavior is normalized as exp (t/τ) and a master curve of reduced crosslinking reaction can be constructed as shown in Figure 7. The trend shows that the initial onset of crosslinking function for dicumyl peroxide in polyethylene increases as temperature increases and the slope of curve becomes steeper. It results in a stretched exponential decay behavior where the breadth is dependent on the exponential constant, β. The value of β increases as the temperature increases. A similar trend is observed with α,α’-bis(tertbutylperoxy)diisopropylbenzene in polyethylene. Figure 7 Reduced crosslinking function for dicumyl peroxide in polyethylene The activation energy, Ea is obtained from the relationship between relaxation time τ at the crosslinking temperature, T, from an Arrheniuns relationship in equation (9). As shown in Figure 8, it follows the linear relationship in ln (τ) versus 1/T. Figure 8 Arrheniuns relationship of relaxation time and activation energy of dicumyl peroxide and α,α’-bis(tertbutylperoxy)diisopropylbenzene in the polyethylene compounds ln (τ), second 0 1 2 3 4 5 6 7 8 9 0.0021 0.00215 0.0022 0.00225 0.0023 0.00235 0.0024 1/T, K-1 Dicumyl peroxide bis(tert-butylperoxy)-diisopropylbenzene Linear (Dicumyl peroxide) Linear (bis(tert-butylperoxy)diisopropylbenzene)

[G∞ -G(t)]/[ G∞ -G0] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 10 100 1000 10000 100000 T ime. Second 150 C 160 C 170 C 180 C 190 C 200 C

[G∞ -G(t)]/[ G∞ -G0] EXP(t /τ) 0 0.2 0.4 0.6 0.8 1

1.2 1 10 100 1000 10000 100000 150 C 160 C 170 C 180 C 190 C 200 C

LOES Form Number 310-02101

The activation energy of dicumyl peroxide is slightly lower than that of α,α’-bis(tert-butylperoxy)-diisopropylbenzene in polyethylene from relaxation approach and summarized in Table 2. Table 2 Activation energy of dicumyl peroxide and α,α’bis(tert-butylperoxy)-diisopropylbenzene in polyethylene from the crosslinking relaxation spectrum dicumyl peroxide α,α’-bis(tertbutylperoxy)diisopropylbenzene Ea, activation energy, kJ/mol 139.8 147.4 τ0, second 9.932×10-15 2.254×10-15

4. Conclusions The cure kinetics of dicumyl peroxide and α,α’-bis(tertbutylperoxy)diisopropylbenzene in polyethylene were presented in this paper. The MDR tests at six different temperatures were performed using MDR instrument. The cure kinetics follows the first order decomposition kinetics. The reactivity of dicumyl peroxide in terms of half life is about 68 percent faster in average than α,α’-bis(tert-butylperoxy)-diisopropylbenzene in polyethylene in the testing temperature range. The activation energy of dicumyl peroxide is approximately 9 percent higher than that of α,α’-bis(tert-butylperoxy)-diisopropylbenzene in polyethylene. The cure kinetics of the polymer compounds from the MDR curve is expressed in terms of the time decay of correlation functions, ψ(t). It was found that the activation energy of crosslinking relaxation for dicumyl peroxide is slightly lower than that of α,α’-bis(tert-butylperoxy)-diisopropylbenzene in polyethylene. The implications from this work on the development of crosslinkable compounds for electrical applications include cure optimization and scorch modeling for continuous vulcanization cable manufacturing process.

5. Acknowledgements The authors would like to thank Dr. Scott Wasserman for helpful suggestions and the support to pursue this work.

6. References [1] R. Bartnikas, K. D. Srivastava, “Power and Communication Cables: theory and Applications”, IEEE Press, 122-137 (2000) [2] G. Ordian, “Principle of Polymerization,” 3 rd edition, A Wiley-Interscience Publication, 212-214 (May, 1990). [3] H. S.-Y. Hsich, “Kinetic Model of Cure Reaction and filler Effect”, Journal of Applied Polymer Science, Vol. 27, 32653277 (1982). [4] P. E. Gloor, Y. Tang, A. E. Kostansk, A. E. Hamielec, “Chemical Modification of Polyolefins by Free Radical Mechanisms: A Modeling and Experimental Study of Simultaneous Random Scission, Branching, and Crosslinking”, Polymer, Vol. 35, No. 5, 1012-1030 (1994). [5] T. Bremner, A. Rudin, “Peroxide Modification of Linear Low-Density Polyethylene: A Comparison of Dialkyl Peroxides”, Journal of Applied Polymer Science, Vol. 49, 785-798 (1993).

[6] J. Lal, J. E. McGrath, R. D. Board, “Effect of Polymer Structure on Ease of Hydrogen Abstraction by Cumyloxy Radicals”, Journal of Polymer Science, Part A-1, Vol. 6, 821-828 (1968). [7] I. Bahar, B. Erman, “Intramolecular Contributions to Stretched-Exponential Relaxation Behavior of Polymers”, Macromolecules, Vol. 27, 5200-5205 (1994). [8] Y. K. Kim, S. R. White, “Stress Relaxation Behavior of 3501-6 Epoxy Resin During Cure”, Polymer Engineering and Science, Vol. 36, No. 23, 2852-2862 (1996).

Authors Dr. Suh Joon Han is a Senior R&D Specialist for the Wire and Cable Compounds group of The Dow Chemical Company. He holds a Ph. D. degree in Polymer Science and Engineering from Lehigh University of Bethlehem, Pennsylvania. Since 1998, he has been involved in the research and development projects for semiconductive shields compounds and insulation materials in power cable applications. He is a member of IEEE Dielectrics and Insulation Society, and ACS Division of Polymeric Materials Science and Engineering. He is an author of more than 22 technical papers and presentations, and holds 2 patents. Dr. Laurence H. Gross is a Senior Scientist in the Wire and Cable Research Group of The Dow Chemical Company. After he received his Doctorate in Polymer Science from Princeton University, Larry completed two post-doctoral positions in Switzerland and Israel. He has led numerous research and development projects for insulation materials for low, medium, and high voltage power cable applications. Larry is a member of the IEEE and a voting member of the ICC. He is the author of about 25 papers and presentations and holds 16 patents. LOES Form Number 310-02101 LOES Form Number 310-02101