The Polymerization of Ethylene under High Pressure using the Semiconductor Model

Zeljko Prebeg, Lermanova 12a, 10000 Zagreb, Croatia


Abstract: By examining the process of heat transfer at tubular reactor for LD-PE  synthesis, it can  be  concluded that  free  electrons  exists  during  polymerization.  Additionally,  no  free electrons occur in the absence of polymerization.  A model  that can  explain and  describe  this behavior of ethylene under high pressure is the semiconductor model.

Keywords: high-pressure, polymerization, ethylene, semiconductor, Pauli exclusion principle, molecular interaction.



For examination of  physical and  chemical  states of  ethylene under  syntheses condition,  heat transfer in a reactor for LD-PE synthesis is used. Polymerization of ethylene is highly exothermic reaction.  The  heat of  polymerization  ( 94.5 kJ mol-1 ) is  continually  removed  by  conduction trough reaction medium or by convection through the reactor's wall.  In a  high-pressure  tubular reactor,  about  50%  heat of   polymerization is   carried  out  through the  reactor's  wall.   The resistance to heat transfer is significant.  Common opinion1 is that polymer's deposit isolates  the wall of the reactor.



Figure 1. Reactor for LD-PE synthesis.


The shape of the reactor is  tubular where 50% of fresh  ethylene is injected  at several places down reactor’s length (figure 1).  The reactor is divided into several heating and cooling zones. The first zone is used for the heating of  ethylene to the reaction temperature and while in other zones  where the  reactions  take  place, heat  is being removed. To calculate the  heat transfer coefficient,  the  temperature and flow of  cooling  water along  with the temperature within the reaction medium are continually measured as shown in figure 2 below.

Figure 2. Measuring of temperature, cooling water flow and temperature of reaction's medium in tubular reactor for LD-PE synthesis.


Flow is measured with the orifice, while temperatures are measured by a thermocouple. During the measuring of temperatures in  reactor, high  fluctuations have occurred ( +/- 0.5 - 5.0 0C). These  fluctuations are proper  and are caused by dissipation of the high local energy from the heat  of  polymerization. In absence of   polymerization,  these  fluctuations do  not exist. Heat transferred into the cooling water per unit of time is calculated by following equation:

Q = G*Cp*(tin – tout)

Where: Q (kJ s-1) is heat transferred into the cooling water

G (kg s-1) is the water flow

Cp is specific heat capacity of water at constant pressure (4.19 kJ/kg/K)

t (K) is the temperature of cooling water.


The transitivity of heat through the wall of the reactor is calculated by equation:

K*A = Q/Dtavg

Where: K (kW m-2 K-1) is the heat transfer coefficient

A (m2) is the surface area for the transfer of heat

Dtavg (K) is average logarithm's difference of temperature

K*A (kW K-1) is the transitivity of heat2 through the wall of reactor.


The average log (temperature) is calculated by the equation, Dtavg = (Dt1-D t2) / log(Dt1/Dt2), with the terms for Dt1 and Dt2 being shown in figure 3 below.


Figure 3. Dt1, Dt2 for a) countercurrent, b) concurrent heat exchanger.



Table 1. Flow, input, and output temperature of cooling water and transferred heat in reactor for LD-PE synthesis.


Table 2. Transitivity of heat trough the wall of reactor


Figure 4. Transitivity of heat through the wall of the reactor (according table 2).



Table 2 and moreover figure 4, show the transitivity of heat through the wall of the reactor.  The behavior of second zone is unusual. Heat, liberated by polymerization  reaction, heat reaction of the medium itself. None of  heat is  transferred through the wall of  reactor. Other  zones show a large  resistance for  heat  transfer  through  the  wall, but  this  resistance   decreases  along  the reactor. If the polymer film isolates within the reactor, then according to common  interpretation, the  largest  concentration  of  polymer  would  be on  the  end  of  reactor  causing  the   largest resistance. In  reality it  is  the  opposite. Along the end  of  reactor,  resistance to  heat  transfer through the  wall of  reactor  decreases ( figure 4, table 2 ).  It especially occurred in ALD  zone where concentration of polymer is greatest, while the transitivity of heat is same as in  first  zone. From this observation it can be concluded that the polymer does not  represent  resistance in the heat transfer during polymerization. Similar  results are  presented by Molen3 in the  investigation of two  different  configurations of  heater-reactor system (figure 5).  In a TT  configuration, heat transfer  and  conversion   in the   second   reactor  is  lower than  in the  first  reactor. In  a  VT configuration,  conversion in the  tubular  reactor is not  under significant  influence from polymer that is formed in the vessel  reactor.  In other  words, if  through the  second  reactor  passes the same quantity of polymer formed at the vessel or tubular heater, the heat transfer trough the wall of the reactor is higher in the VT configuration.  This fact shows  that the  deposit of  polymers is not the cause of heat transfer resistance through the wall of the tubular reactor.



Figure 5. Configuration of heater-reactor system. (a) TT (b) VT


Figure 6. Shows the ratio of heat  transferred through the wall of reactor and  autothermics heat. At conversion  of  13 %  at  first  reactor,  second  reactor  ( configuration TT )  works   adiabatic. (Hw/Ha=0). At same conversion of 13%, configuration VT shows heat transfer through the wall of reactor (Hw/Ha=1/2). This fact shows that deposit of polymers are not cause of  autothermic heat transfer.


But, if the heat transfer is examined as transfer of heat by the lowest resistance, then it can next be concluded that during the polymerization, heat is transferred  through  the  reaction  medium (conduction )   better  then   through  the   reactor's  wall   ( convection ).   In  the  absence  of polymerization, the reaction medium shows resistance.  Heat is transferred through the reactor's wall.  It is well known that free electrons cause conduction's heat transfer and since heat can be transferred by conduction, it can therefore be  concluded that  during  the  polymerization,  free electrons exist.  The model which describes this behavior of matter, is known, and it is used for the interpretation of semiconductor properties.  Before deduction of the semiconductor  model, the chemical bond will be discussed. 

The chemical bond is formed between two atoms by valence electrons. Three kinds of chemical bonds are known. Covalent bonds are formed between atoms of similar electronegativity (figure 7a) where each atom gives one electron to form the bond.  An ionic  bond has formed  between atoms of different electronegativity (figure 7b).  In this case, the bonding orbit has  moved in  the direction of the electronegative atom.  The  ionic  bond can be  viewed as a  special case of  the covalent bond.  The third kind of chemical bond is the metallic bond ( figure 7c ).   It  is  formed between a group of atoms where common orbits are connected and  form a  common  band.  It will be showed that the metallic bond is a kind of super-bonding of the  covalent  or  ionic  bond and strongly depends on the state of the matter.


Figure 7. Chemical bond a) covalent, b) ionic, c) metallic

The ethylene molecule has six chemical bonds.  Four of the bonds are formed between carbon and hydrogen  (E=411 kJ/mol).   Two  other  bonds  are formed  between  the  carbon  atoms (Esigma=335 kJ/mol, Epi=607 kJ/mol as shown in figure 8 below).

Figure 8. The energy of bonds of the ethylene molecule.

Valence electrons of molecule of ethylene are electrons on highest energy level. They are forming outer sphere for interaction (figure 9 below).


Figure 9. Interaction


According to the presented knowledge about behavior of  ethylene  under  synthesis  conditions and on the base of the semiconductor theory, the following model of  organization for ethylene is proposed.  The  deduction of  the  semiconductor  model is  based  upon  an  organized  system called a bimolecule.

Figure 10. Bimolecule forming (Pauli exclusion principle).


The bimolecule of ethylene is formed between two molecules by the  excitation  of the pi-bound electrons (figure 10).  Common orbits are formed at the highest  energy  levels,  while  other  pi-bound electrons stay unpaired.  This transformation, results from the  transfer  of  the  pi-bound electrons from the base to excited state using the energy obtained through compression.  Proposal for the existence of bimolecule is not a new.  Even Pease4 in 1931, during investigation of thermally initiated polymerization at low pressure, proposed that the step before the  chemical reaction is the formation of a dimmer of ethylene.  On the  basis of  experimental  measurements of the energy of activation and order of reaction, Buback5 concludes that  through the  thermally initiated polymerization, a biradical  dimmer is formed. This authors did not  examine the dimmer as a  stable  form.  Stoiljkovic6,  had the  opinion that  bimolecule is a  stable particle  and that is base of the organization of ethylene.  This model is similar to his interpretation of the bimolecule, while the semiconductor model examines energetic transformation.


Figure 11. Valence band formation.


In an organized system, the valence band is forming by a partial  crossing of  outer  orbits of bimolecules (figure 11).  Electrons are dislocated, but they are still bonded to the bimolecule.  This bond is then weakly bonded in the isolated bimolecule.  

The analogy to the semiconductor model proposes that  forbidden zone also exists.  The  energy of this forbidden zone is higher than the valence band but lower than that of the conduction band ( as shown in  figure 12 ).  In  addition, a  subvalence zone  exists too. The  subvalence  zone  is formed by unpaired electrons. It is via these definitions that the semiconductor model of ethylene is defined (as illustrated in figure 12). 



Figure 12. The semiconductor model of ethylene organization.


The  semiconductor   model  differs  from  Stoiljkovic’s  model,  which  proposes  existent   of oligomolecules in Sr<1 (gamma-phase) and bimolecules in Sr>1  (beta-phase).   According  to the semiconductor model, the beta-phase is ordered by the probable transfer of electrons from valence band to the conduction band.  

The initiation of polymerization can occur in different ways ( thermally,  chemically,  by  gamma ray, UV).  Understanding the thermal  activation of  polymerization  helps in  understanding  the analogy  between  the  behavior  of  an  ideal  semiconductor  and  that of  ethylene  under  high pressure. For instance, it is well known  that  in  lower  temperatures,  the  ideal  semiconductor behaves as an isolator, (i.e. free electrons do not exist).   Increasing  of  the  temperature,  some electrons from  the  valence  band  get  enough  energy  to  transfer  from  the  valence  band  to conduction band.  In the valence band, a hole is formed while the free electron being dislocated in the conduction band. 


Figure 13. The initiation of polymerization.


After the excitation of the electron in the conduction band ( figure 13a ), an  unpaired  electron from the valence zone can stay in the  valence zone (figure 13b) or it can be  transferred to  the subvalence level (because holes exist in subvalence level).. In the  latter case an  electron - hole cup is formed.  The  electron  is  dislocated  at  conduction  band,  while a  hole is  relocated at subvalence zone.  This pair plays a specific role in the chemical reaction and may be  described as a primary radical - terminator pair.  Primary radical  plays  a  role  in  starting  polymer chain growth, while terminator plays a role at the  end of the  polymer chain  growth. These cups  are connected with beta-phase while cups are not formed in the  gamma-phase. There istherefore a significant difference  between  the radical and  terminator. While the radical is being dislocated (being put in motion), the terminator is being located, (becoming motionless). 

According to the classical explanation, polymer growth is occurring by chain reaction. The  heat of polymerization is high, and once it polymerizes 2-3 molecules of ethylene, the  breaking of the C-C bound is possible.  If efficiently heat transfer does not exist then the formed polymer will be of low molecular weight.  It can be shown7 that for a 50% probability of getting a polymer chain of 1000 monomer  units,  probability  for  each  step  of  polymer  growth  must be  higher  then 1400/1. This shows that an efficient  mechanism  for  stabilization  of a  radical  must  exist.  The growing of a polymer chain occurs by the filling of holes in the  subvalence zone.   After the  first hole of bimolecule (figure 14a) is filled, a common electron cup has unformed.  One electron fills each particular bimolecule,  (figure 14b)  while  the other is  free to  transfer to   hole of  nearest bimolecule (figure 14 b, c).


Figure 14.  Polymer chain growth.

The bimolecule is polymerized in the basic growth reaction. The electrons are transferred from the highest to the lowest energy state, causing the  liberation  of  energy.  Polymerization  is  an exothermic reaction.  Unpaired  electrons  in  valence  band  are  partially  dislocated,  but  still connected to a particular bimolecule. It can therefore  be  reasoned  that  an  external  force  is necessary for this  movement  to  occur.  Growing  a  polymer  chain is a  diffusion - controlled reaction, and the radical is stable, while being partially dislocated at the valence band. 

According to classical model, a reaction of end chain growth is made by the  interaction  of  two radicals. This reaction is connected to the free hole in the subvalence level (i.e. terminator).  The free electron from valence band fills the free  holes in  subvalence zone  and  the  polymer  chain growth is then finished. (figure 15).  If a terminator does not exist then the growth of the polymer chains will continue and the polymer chain will have high molecular weight. 


Figure 15. End of chain growing



The heat transfer by convection in  absence of  polymerization and heat  transfer by  conduction through the reaction medium  during  polymerization  shows  that free  electrons exist during  the polymerization of ethylene under high  pressure.  These facts  indicate that  ethylene  under  high pressure is semiconductor. Existence of a valence and conduction zone makes possible efficient transfer of the heat of polymerization, without the breaking of the polymer chain. The long life of radicals shows that a mechanism for his stabilization exists and one way is the dislocation of free electrons  in the  valence or conduction  band. During the initiation of  polymerization, a  primary radical - terminator  pair   is  formed.  Primary  radical  plays  a  role  in  starting  polymer  chain growth, while terminator plays a role at the end of  the  polymer  chain  growth.  If  a  terminator does not exist then the growth of the polymer chains will continue  and  the  polymer  chain  will have high molecular weight. Future direct measurement of the electrical properties would be the best way to proving this semiconductor model of ethylene polymerization.



  1. Hwu M.C., Foster R.D., Chem.Eng.Prog., 78, 62 (1982)
  2. Dordevic B, Valent V, Serbanovic S, Termodinamika i termotehnika, IRO "Gradevinska knjiga", Beograd, 1987
  3. Molen WD, VIIth Int. AIRAPT Conf.,le Creusot, Franse (1979)
  4. Pease RN, J.Am.Chem.Soc., 53,613 (1931)
  5. Buback M, Macromol.Chem., 181,373 (1980)
  6. Stoiljkovic D, Jovanovic S., Acta Polym., 39,670 (1988)
  7. Hunter E, Chemistry & Industry, 396 (1955)


I wish to acknowledge Prof. Mitsuo Sawamoto for his useful suggestions in the preparation of this manuscript.  Also, many thanks to Victoria at the Journal of Theoretics.


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