Emerging Issues in the Mechanisms of High Pressure Free Radical Ethylene Polymerization: A Review

The need to improve the performance of the high pressure polymer production process, and timely introduction of new and functionalised products even at reduced production cost which is becoming critical to staying in business has given room for overall studies of the ethylene polymerizat ion process. In this review, emerging issues in the high pressure ethylene polymerization process through free radical approach is unveiled and presented. Different views and approaches of several authors on the tasking issues were compiled, analysed and discussed. Future researchable areas were made clear in this study. Further investigations were also made to model kinetically the high pressure ethylene polymerization react ion in tubular reactors only using mass balances and moment analysis. Although not discussed in this paper, the modeling of heterogeneous polymerization reactions such as precipitation polymerization and emulsion polymerizat ion remains a challenge.


Introduction
The most important industrial reaction of ethylene is its reaction with itself (Poly merizat ion) [1] . Poly merization as defined by Carothers [2] is the intermo lecular co mbinations that are funct ionally capable o f p roceed ing indefin itely. Polyethylene, the product of the indefinite comb ination of ethylen e mono mers at h igh p ressure in th e p resence of in itiato rs was the u nexp ected resu lt o f an exp eriment undertaken in the course of a fundamental research in the early 1930`s without a direct co mmercial target in view. Imperial Chemical Industries (ICI) in England decided to evaluat e th e effect o f u lt ra-h igh p ressures on so me 50 chemical react ions. In 1933, an experiment was carried out, compressing ethylene gas to 1400 bar. A white solid was fo rmed in the heavy steel vessel, wh ich p roved t o be low-density polyethylene (LDPE). Subsequent work showed t h at min u t e t ra c es o f o xy g e n h ad c aus e d t he polymerization [3]. Polyethylene accounted for 30 % of the total annual world po ly mer consumption in 2007 (more than 70 million tonnes in 2007) [4] and are the most widely 70 million tonnes in 2007) [4] and are the most widely utilized synthetic poly mers. Tubular process using a very long small diameter tubular reactor and an autoclave process using a well stirred tank reactor are co mmonly used industrial process for polyethylene synthesis. Hee-Jong Lee et al [5] confirmed that polyethylene products manufactured by these processes differ in their mo lecular architecture and end use properties. Majid [6] reported the scientific, industrial and commercial reasons for the enormous consumption, such as good chemical resistance, zero toxicity, bio-acceptability, good physical and mechanical properties, low cost, ease of fabrication, good raw material availab ility and low environmental impact [7][8][9][10][11]. Fro m the S curve of polyethylene technology [12][13], it can be seen that polymerization processes caused revolutionary improvements in polyethylene technology as shown in Figure 1.
In most textbooks and monographs on free radical ethylene polymerization, only very few if any at all commented on the challenges, emerging issues, unsolved problems and future opportunities of this part of macro molecular chemistry (Ethylene poly merization). Therefore, this mini rev iew deals mainly with the identification of cloudy areas and gaps uncovered with a view of creating future researchable areas in free radical ethylene polymerization.

Kinetics of Ethylene Polymerization
The industrial importance of ethylene polymerization has led to extensive studies of its kinetics [14][15][16][17] . In this section, a set of reaction mechanisms required to model the kinetics of free rad ical poly merization of ethylene is described. A unique and unified set of elementary steps for free radical ethylene polymerizat ion is still being debated and yet to be found in open literature. Buback, [18] studied the thermally initiated poly merization of ethylene. His results from the kinetic experiments on pure ethylene carried out at temperatures 180 -250 ℃ and pressures up to 2500 bars showed that a very slow thermally in itiated react ion resulting in high mo lecular weight polyethylene could be established. The actual mechanism is not known but it can be written as an overall third order react ion. However, many workers in this field [14,[19][20][21][22] and recently by Kiparissides [23][24] proposed the kinetic mechanism described as follows; 1. In itiation : (Activation) with Pero xides, Azo Co mpounds or Oxygen: (1) n is the number of radicals generated which is usually 2 for nonfunctional in itiators.
2. Chain Init iation: 3. Thermal In itiation: 4. Propagation (Growth): 5. Termination by Co mb ination: 6. Termination by Disproportionation: 7. Chain Transfer to Monomer: 8. Chain Transfer to Poly mer (Intermo lecular transfer/LCB): [25] (8) 9. Chain Transfer to So lvent/Modifier/Agent: (9) 10. Backb iting (Intermolecular transfer/SCB): (10) 11. β-Scission: (11) Tsutomu and Masatsugu [26] in their co mprehensive review on the kinetics of polymerizat ions of various types classified poly merization according to: • the type of initiators, • kind of mono mer, • mode of the addit ion of mono mer to the propagating species, • or electronic structures of the propagating species. He further argued that the qualitative nature of elementary reactions of polymerization in the frame of these classifications can be conveniently expressed. Polyethylene has been manufactured by the high pressure process for over 50 years but profound comprehension of the reaction mechanis ms and kinetic analysis of the process has posed a challenge in developing a cohesive understanding of the process as witnessed by the survey of the literature [27-35 ,21 ].

Chemistry and Effectiveness of Initiators
According to Zabisky [36] , Oxygen initiat ion of ethylene polymerization was first reported by Fawcett et al and has been used commercially in both tubular and batch reactors. It is well known that oxygen serves as an inhibitor in free radical poly merization at lo wer temperatures. Oxygen may react with rad icals or mono mers to form poly meric pero xides. These peroxides may then decompose to initiate the polymerization. Several authors including Thies and Schoenemann [37] have tried to model o xygen in itiation by assuming an overall second order reaction of the type neglecting the inhibition reactions but with moderate success. (12) This initiation method is very convenient due to availability of o xygen, its cost and simplicity of its supply into the reaction system without additional components and special installations. However, o xygen init iation is also known to have some significant drawbacks. Kondratiev and Ivanchev [38] reported that oxygen init iation is only possible at temperatures above 170℃ and pressures above 860 bars. However, the application of low temperature pero xides in oxygen in itiated processes affords the advantage of additional poly mer y ield at the low temperature init iation step (increase of conversion by 1 %). Dh ib and Nidawy [39] stated in their report that the chemistry and thermal behaviour of organic pero xides used as initiators in free radical poly merizat ion have been the focus of many researchers who are investigating potential routes to improve the efficiency of poly merization reactions. Under thermal effects, organic peroxides exhibit different rates of decomposition owing to their dissimilar half-life temperatures. Focusing on the chemistry and kinetics of certain organic peroxides, Luft and Seid l [40] carried out a series of sound detailed studies on their kinetic decompositi on, reaction rates, effectiveness and effects on polyethylene product [41-43 ,40 ,44]. The studies incorporated the setting-up of a database of the most common pero xide initiators in the production of polyethylene. Over 20 initiators have been used in experiments to produce LDPE polymers and the consumed amount of each init iator constituted the basic criterion of assessing the initiator effectiveness. Continuing a previous experimental work Luft and Seidl, [40] , Luft and Dorn [44] as reported by Dhib and Nidawy [39] studied the effectiveness of four difunctional in it iato rs : 2,5-dimethylhexane-2-t-butylpero xy-5-perpivalat e, 2,5-d imethylhexane-2,5-b is-perpivalate, 2,2-bis(tert-utylp ero xy ) butane and 2,5-dimethylhexane-2,5-di-t-butyl-pero xi de, that were judged suitable for high-pressure polymerization of ethylene at optimu m temperatures of 273, 235, 268 and 287 ℃ , respectively where difunctional initiators were observed to accelerate the polymerization rate and produce polymers of h igher molecu lar weight at high temperature co mpared to monofunctional in itiators. Besides, the difunctional in itiator can produce special polymers like star and hyperbranched polymers. Puts and Sogah [45] and Hawker et al [46] in their report explained that the use of a dual initiator (also named bifunctional in itiator, asymmetric difunctional in itiator or ''double-headed'' init iator), or mo re generally a heterofunctional in itiator, shows many advantages compared to the classical methods for the synthesis of block copolymers by comb ination of mechanistically incompatib le mono mers ( Fig.2). Heterofunctional init iators contain two o r mo re different initiat ion sites that are capable of init iating concurrent polymerization mechanis ms independently and selectively. This approach provides the opportunity to combine mechanistically incompatib le mono mers into one macro molecule without the need for intermediate transformation and protection steps, which can offer new opportunities in the design and applicat ion of functional organic materials. In contrast to mechanism transformat ion, where a transformation of the propagating chain end takes place, heterofunctional init iators can init iate several polymerization mechanis ms, yielding block copoly mers in a direct way. A requirement fo r such a mechanism is that each initiat ing group is stable in the different poly merization circu mstances of the other type of polymerization.
Though mult ifunctional init iators are believed to provide two advantages over traditional monofunctional initiators, with a higher nu mber of functional sites per molecule, they are able to increase polymer production while simu ltaneously maintaining or increasing polymer mo lecular weight. Examination of the literature indicates the majority of academic and industry published studies have investigated difunctional initiators with most focusing on styrene. Matthew [48] in h is Ph.D thesis reported that Ethylene Polymerization: A Review tetrafunctional initiator, JW EB 50, was systematically investigated for a variety of monomer systems in order to develop a better understanding of the behaviour of mu ltifunctional in itiators in free radical poly merizat ions. But, in all the kinetic decomposition of mu lti/difunctional peroxides is still a controversial issue according to Dhib and Nidawy [39].

Kinetic Parameters and Estimation
For each of the elementary steps stated in equation (1) to (11), three parameters were used to determine the value of their kinetic rate constant at any temperature and pressure according to the modified Arrhenius equation: (13) Where k o = frequency factor (1/ mo l.s) E a = activation energy (ca l/ mol) V a = activation volu me (ca l/at m.mo l) P = pressure (atm) T = temperature ( K) Examination of co mpilations of literature values of rate parameters often reveals a very wide range of reported values for any particular rate parameter in spite of the great number of papers published on the modeling of LDPE reactors. Gupta et al [32] , Ehrlich and Mortimer [14] , Goto et al [21] , Lee and Marano [30], Takahashl and Ehrlich [33] , Thies and Schoenemann, [37]. Kiparissides et al [49] in their review attributed the inconsistency of published set of rate constants to the complexity of the react ion, the large number of kinetic parameters to be determined experimentally and the wide range of experimental conditions over which the kinetic parameters were estimated. With such a wide range of values, it is often possible that conflict ing mechanistic suppositions can be supported with 'evidence' fro m the literature. To overco me the wide divergence in literature values of kinetic parameters for free rad ical poly merizations under ostensibly the same conditions, agreed values are given to some fundamental kinetic parameters for simp le mono mers. If we just consider the rate of polymerizat ion, the ratio k p /k t 0.5 is important. Fig. 3. shows this ratio as reported by several authors. As discussed recently in [50], evidence of significant variat ion of kinetic parameters was further revealed as contained in Table 1.0 where, so me of the rate constants of propagation, termination and transfer to mono mer are tabulated with other values from literature.

Ethylene Conversion/Polymer Molecular Weight
Literature search shows that common ethylene conversion obtained by various researchers falls within the range of 14 -24 % as shown in Table 2.
Dhib and Nidawy, [39] however observed that the thermodynamic conditions of the process hinder ethylene fro m going to full conversion. Other than recycling the product, one way of improving the mono mer conversion is to initiate the poly merization with difunctional organic peroxides. Due to the dual functionality of difunctional peroxide, the ethylene conversion they obtained from their model was about twice as much as that obtained with monofunctional pero xide, for only a half amount of the initial init iator concentration. However, the setback of obtaining only limited low conversion of ethylene in high-pressure polymerization has been persistently an unpleasant and discouraging reality in spite of the classical approach to enhancing the conversion upon recycling the product. Another route of imp roving ethylene conversion in this kind of poly merization process is to investigate the effectiveness of initiators.
Aside the conversion, the production of polymers with desired end-use properties is of significant financial importance to the poly mer industry. One of the most important mo lecular propert ies that control the end-use characteristics of poly mers is the mo lecular weight distribution (MWD) as it directly affects the physical, mechanical and rheological properties of the final product [55] . The molecu lar weight distribution of a polymer can be characterized by the number average molecular weight (Mn), weight average mo lecular weight (Mw), and polydispersity (PD). MWD/PDI is considered as a fundamental property that determines polymer properties and thus its applications. An ideal polymer contains only one type of polymer with the same architecture, microstructure and chain length as shown for the polymer chain composition I in Scheme 1 [56]. Such a polymer chain co mposition has a molecular weight distribution of 1.00, as the molecu lar weight distribution (MWD) is a quotient of the weight average molecular weight Mw and the number average mo lecular weight Mn. In general, the MWD g ives a value of the uniformity of the polymer samp le. The h igher the MWD value, the poorer is the uniformity of the poly mer's chain co mposition. Principally, poly meric chain co mpositions can be divided into the five different types shown in Scheme 1 (Fig.4.)

Harsh Operating Conditions
Large number of the now available poly mers are obtained, on industrial scale, through high pressure process and any improvement of the industrial process has important economic consequences. In both tubular and autoclave reactors , a free radical mechanism using init iators such as peroxides or oxygen takes place at pressures ranging from 1,000 to 3000 at m [49]. Free rad ical poly merizat ion of ethylene is carried out at high pressure and elevated Ethylene Polymerization: A Review temperature [57]. Temperatures exceeding 300 ℃ cause ethylene to decompose and are not recommended in practice. The high-pressure process is usually a bulk poly merization initiated by organic pero xide. The high pressures (>2000 bars) and temperatures (>250℃) make it difficult to obtain accurate kinetic constants using small scale laboratory experiments. Thus, one has to rely on published literature for kinetic data. Unfortunately, there is very little agreement between the various publications.
Over the last few decades, a lengthy list of academicians and industrialists incessantly attempted to establish a unifed tangible understanding of ethylene polymerisation in high-pressure autoclave reactors [21,[58][59][60] and tubular reactors [28,61] mainly because the technical propert ies of polymer products are mainly determined by the conditions of the polymerizat ion reaction. Kiparissides et al. [49] reported that low p ressure ionic ethylene poly merization processes have been developed for the production of h igh density polyethylene and mediu m density polyethylene.The process requires low pressure(8-80 at m) and temperatures less than 150 o C using a t ransition metal catalyst of the Ziegler-Natta or Ph illip type. Though the process has gained a lot of popularity in the polyolefin industry still, there is the need for a strong reconsideration of poly merization processes of the most common monomers such as ethylene with emphasis on new init iating systems under low pressure and "uncatalyzed" polymerizations. Similarly, despite the commercial success of gas phase ethylene polymerization technology, the public literature contains no accounts of fundamental scale-up studies of gas phase processes. There is further need, therefore, for a co mprehensive understanding of detailed polymerization behavior in gas phase polymerization. A challenge for academic researchers studying gas phase polymerization of ethylene is how to scale down commercial p rocesses for experimental laboratory studies.

Ethylene Polymerization Kinetic Model Development for a Tubular Reactor
According to Xie et al. [62] reactor modeling is the determination of a quantitative relationship between reactor performance and reactor operating conditions. It requires comprehensive understanding of polymerizat ion processes, physical phenomena, and chemical reaction mechanisms. The importance and benefits of reactor modeling have been widely recognized by both industrial and academic researchers. The application capability o f a model depends on scope of the modeling effort. Ray [63][64] defined a modeling hierarchy as microscale, mesoscale, and macroscale, according to the characteristics of the polymerization reactor systems. The relationships between modeling scale and poly merization systems are similarly outlined in Figure 5 after Ray [63][64]. The emphasis of each modeling level, in particu lar for ethylene poly merization systems, can be summarized as follows:

1.
Microscale modeling: Poly merization rate development, or poly mer yield; reactant species distribution; mo lecular weight development and its distribution; chemical composition of poly mer chains and its distribution; microstructures of polymer chains, including chain branching, unsaturated groups, and sequence distribution.
2. Mesoscale modeling: Interphase heat and mass transfer; intraphase heat and mass transfer; flu id mechanics and micro -mixing; poly mer part icle morphology development; polymer particle size and distribution.
3. Macroscale modeling: macro-mixing and residence time distribution; overall material and energy balance; heat and mass transfer fro m the reactor; reactor dynamics and control; polymer grade transition and control.  [63][64] There are no definit ive boundaries between these modeling levels. In fact, they often overlap during modeling studies. For instance, knowledge of some microscale modeling is required for mesoscale modeling studies, and macroscale modeling depends upon understanding of microscale and mesoscale phenomena. A co mplete model for ethylene polymerization, including all three levels, has not been developed in the literature. However, significant modeling efforts with emphasis on specific levels have been published. Microscale and mesoscale modeling studies are normally reported as kinetic modeling in the literature. Macroscale modeling is often referred to as dynamic modeling.
Therefore , search for more realistic kinetic schemes, able to describe to a greater extent the processes and having general applicability to different mono mers, homopolymerizat ion and co-poly merization to co mplete conversion should be an area of focus by researchers.To describe the conservation of various mo lecular species present in a reactor, there is the need to know their corresponding net production rates. The expressions for these rate functions can be obtained by comb ining the various elementary reactions describing the generation of and the consumption of in itiator(s), mono mers, solvents, dead and live macro mo lecules.
The application of mass balances to the Equation (1) to (11) leads to the following:  By introducing the zeroth, first and second mo ments, the kinetic mechanisms can be represented with a finite nu mber of model equations and the mathematical models are capable of p redicting the nu mber and weight average mo lecular weights and the polydispersity of the polymer produced; The leading mo ments of the total number chain length distributions (TNCLDs) of live and dead poly mer chains are defined by Arriola [65] as: Following the approach of Zabisky et al. [36] and Metzler et al. [66], the first three mo ments of polymer radicals were used to calculate the number and average molecular weights. The Nu mber-and weight-average molecular weights are defined respectively as:  (25) Live Po ly mer Chains Moments Multiplying Equation (17) by i k rλ k =[ k CI C M C R -k p ∑C P i−1 C M − k p ∑C Pi C M -k trm ∑C Pi C M + k trp ∑C Pj ∑i.C Di -k trp C Pi j.C Dj -k trs C S ∑C Pi -k tc ∑C P i ∑C Pj -k td ∑C P i ∑C Pj -k bb ∑C Pi ] i k (26) Dead Poly mer Chains Moments Multiplying Equation (18) by j k rμ k =[k trm ∑C Pi C M + k trp ∑C Pi ∑j.C Dj -k trp ∑C Pj ∑i.C Di + k trs C S ∑C Pi + 0.5k tc ∑C P j ∑C Pi-j + k td ∑C P i ∑C Pj ] j k (27) The other reaction rates of interest can be expressed in terms of mo ment equations as: Initiator consumption rate: r I = -k I C I (28) Primary Rad ical rate: r R = 2fk I C I -k CI C M C R (29) Monomer Consumption rate: r M = -[ k CI C M C R + k p λ 0 C M + k trm λ 0 C M ] (30) Solvent (CTA) rate: r S = -k trs C S λ 0 (31) LCB reaction rate: r LCB = k trp λ 0 μ 1 (32) SCB reaction rate: r SCB = k bb λ 0 (33) Usually, one needs to know the leading mo ments (i.e., λ 0 , λ 1 , λ 2 and μ 0 , μ 1 , μ 2 of the "live" and "dead" poly mer distributions) to calculate the values of the number-average molecu lar weight (Mn), and number-average mo lecular weights(Mw).
where = Following the approach of Zabisky et al. [36] , as reported by Fred et al. [51] , the concentration of live poly mer concentration is considered to be constant so that There is a higher mo ment, 3 wh ich would require an additional differential equation. Following the approach of several authors [36 ,39] , the closure of Hu lburt and Katz [67] gives the following expression for Zabisky et al [36] as reported by Fred et al. [51] have satisfactorily tested this method by comparing simu lation results with the data from a co mmercial p lant.

Conclusions
In this review, some issues concerning the mechanism of ethylene polymerizat ion, chemistry and effectiveness of initiators, ethylene conversion/polymer mo lecular weight, harsh operating conditions, model parameters estimation techniques, were d iscussed. The areas that need further research attention have been identified. One of the outstanding issues is to develop more efficient parameter estimation techniques to strictly limit the wide discrepancies in published data on ethylene polymerization kinetic parameters and the possibility of synthesizing polyethylene of improved quality under mild conditions. Kinetic modeling plays an important role in the design of polymerization reaction conditions with which to tailor a polymer's mo lecular arch itecture. Th is area was not left out as attempt was also made to develop appropriate kinetic model for ethylene polymerization in a tubular reactor based on experimentally determined elementary steps found in the literature which could be used in estimat ing the first three mo ments of both the live and the dead radicals which are used to estimate nu mber average mo lecular weight, weight average mo lecular weight and polymer po lydispersity.

SYMBOLS USED
C I Concentration of initiat ion, mol/ L C M Concentration of monomer mo l/ L C R Concentration of free rad ical 1/S C S Concentration of solvent mol/ L D i ead poly mer or dead chains f Efficiency of orig inal init iation I Initiat ion k bb Rate constant of backbiting 1/ S k I Rate constant of oxygen/peroxide init iation, 1/S k P Rate constant of propagation, 1/mo l.S k tc Rate constant of termination by combination, 1/ mol.S k th Rate constant of monomer thermal in itiation, 1/S k trm Rate constant of chain transfer to mono mer, 1/ mo l.L k trp Rate constant of chain transfer to polymer,1/ mo l.S k trs Rate constant of chain transfer to solvent,1/S k β Rate constant of β-scission to secondary radical.1/S LCB Long chain branching M Monomer M wo Monomer mo lecular weight P i Live rad ical, radical poly mer, live poly mer or live chains PDI Polydispersity Index R Init iator rad ical S Solvent SCB Short chain branching λ Live poly mer mo ment μ Dead poly mer mo ment λ 0 Zeroth live poly mer mo ment λ 1 First live poly mer mo ment λ 2 Second live poly mer mo ment μ 0 Zeroth dead polymer mo ment μ 1 First dead polymer mo ment μ 2 Second dead polymer mo ment i,j Ultimate monomer unit in the radical chain