Polyethylene Production

In this project the focus lies on the thermoplastic low density polyethylene (LDPE). Polyethylene polymer chains are produced by addition polymerization of ethylene. Ethylene is obtained from cracking ethane/propane, naphtha or gas oil. LDPE is typically manufactured during high pressure operations.

The first steps in the production of polyethylene under high pressure took place in the ’30, when the British chemists Fawcett and Gibson synthesized the first grams of polyethylene in 1933, using high pressure and small amounts of oxygen. However, further productions were cancelled because of

6 extreme hazardous risks: Fawcett and Gibson worked in open laboratories while the systems were highly instable and explosive.⁸ Perrin and Manning took over the program in 1935, constructed equipment that handled the required high pressures.

The polymerization of ethylene takes place at high pressure (1000-3000 bar) and temperature (420-570 K). Conversion rates of 15-30% are obtained with short residence times around 20-50 seconds.¹ Oxygen and/or organic peroxides are used as an initiator to start the radical polymerization (Eq. 1.1-1.2).

Termination of the radical species occurs by combination, coupling of two living polymers to form a single polymer chain (Eq. 1.4), or disproportioning, where a hydrogen atom is removed to form a double bound and to terminate a chain radical on another living polymer (Eq. 1.5). 𝐷_𝑛 is the dead chain with 𝑛 number of monomers. Note that the dead polymer chain with the double bound can be activated; leading to possible branch formation.

Combination

𝐿^∗_𝑛 + 𝐿_𝑚^∗ ⟶ 𝐷_𝑛+𝑚 (1.4)

Disproportioning

𝐿^∗_𝑛 + 𝐿_𝑚^∗ ⟶ 𝐷_𝑛⁼ + 𝐷_𝑚 (1.5)

Because of the elevated pressure and temperature during polymerization, several additional reactions take place. Eq. 1.6 displays the radical chain transfer to species 𝐴, being initiator, monomer, solvent or transfer agents. Intramolecular chain transfer (back-biting) of the polymer chain results in short-chain branching (Eq. 1.7) and intermolecular chain transfer leads to long-chain branching (Eq. 1.8). The secondary radicals formed during inter- and intramolecular chain transfer are also able to divide the polymer chain in two parts by chain scission (Eq. 1.9).

Chain transfer to X

𝐿^∗_𝑛 + 𝐻 − 𝑋 ⟶ 𝐷_𝑛 + 𝑋^∗ (1.6)

Intramolecular chain transfer

𝐿^∗ _𝑚 ⟶ 𝐿^∗_𝑚 (1.7)

Intermolecular chain transfer

7

𝐿^∗_𝑛 + 𝐷_𝑚 ⟶ 𝐷_𝑛 + 𝐿^∗_𝑚 (1.8)

Chain scission

𝐿^∗_𝑚 ⟶ 𝐿^∗_𝑥+ 𝐷_𝑚−𝑥 (1.9)

The polymerization of LDPE is typically conducted in autoclave or tubular reactors. Autoclave reactors are comparable with continuous stirred tank reactors (CSTR) and are operated around 1800 bar and 530 K. The final LDPE weight distribution is broad and the chains are highly branched.

Tubular reactors consist of a very long tube wherein the reaction mixture is transported as a plug flow (PFR). These reactors are operated around 2700 bar and include various heat zones, with peak temperatures of around 570 K. Because less back mixing takes place in the tubular reactors, the resulting weight distribution is often narrower than for the autoclave reactor and less long chain branching takes place.⁹ An example of the different weight distributions is shown in figure 1.1.

In the last stage of the polymer production process the polymers are shaped into granules during an extrusion step. These granules are typically cylindrical or spherical to ensure the product can be transported and handled with ease. Hereafter the granules can be deformed for various applications by making use of processes like film blowing, film/sheet casting and extrusion blow molding. In all processes the granules need to be melted to reach desired flow properties. This is achieved by making use of a second extrusion step. In figure 1.2 a schematic cross section of a single-screw extruder is shown. Granules are added to the feed hopper and a viscoelastic polymer melt is produced by the heater and the rotating screw. The polymer melt is subsequently deformed in a shaping device (film blowing etc.) and cooled down to obtain the final product.

W eigh t F ra ct ion

Molar Mass

Tubular Autoclave

Figure 1.1 - Hypothetical molecular weight distribution of LDPE produced in a tubular (blue) or autoclave (red) reactor type.

8 1.1.2 Polymer Characteristics

The configuration of the monomers in the polymer chain determines the polymer architecture or topology. To describe the architecture of a polymer chains different properties are defined. The property degree of polymerization (DP) is used to account for the number monomers present in the polymer chain. DP multiplied with the molar mass of the monomer results in the total molar mass of the polymer chain. For linear chains, DP also describes the size of the polymer chain, but for branched polymers additional definitions are needed.

Degree of branching is another property that refers to the number of branch points present in the polymer chain. Branching occurs for example in LDPE production by back biting or intermolecular chain transfer. Here a distinction is made between short chain branches and long chain branches.

Short chain branches are associated with oligomers (for example methyl, propyl or hexyl side groups) that are present on the chain backbone. Short chain branches typically decrease the crystallinity of the material, because these chains permit the chains to align next to each other. Long chain branches are much longer than short chain branches and influence the rheological properties of the material. The minimum length of a long chain branch is not defined, but the property entanglement length can be used to define a criterion for long chain branches. In polymer melts, polymer chains are intertwined and form loops or connection points that impact the flow behavior.

Here the mass between two connection points (entanglement molar mass) can be determined from rheological experiments by making use of an analogy with crosslinked rubbers.¹⁰ Polyethylene at 140°C is determined to have an entanglement molar mass of 1000 g/mol and when divided with the

Star Comb Cayley Tree Random Tree

Figure 1.3 – Different polymer structure types. From left to right: star, comb, cayley tree and random tree shape.

Figure 1.2 – Schematic cross section of a single screw extruder. Granules are added to the feed hopper and a viscoelastic polymer melt is produced by the heater and the rotating screw.

9 molar mass of the monomer ethylene (28 g/mol), the entanglement length of PE is equal to ~36 ethylene units.¹⁰ For this case, long chain branches should be around or larger than 36 ethylene units.

The final property needed to define the polymer architecture is the monomer and branch distribution on the polymer chain. Different options exist when incorporating these distributions in polymer chains, resulting in different polymer architectures as shown in figure 1.3. The first structure shown is a star shaped chain, where all branches (or arms) are connected to one single branch point. A comb structure consists of a backbone chain with a number of distributed linear branches attached to it. Cayley trees are typically defined in terms of generations. For the 1^st generation Cayley trees the structure is identical to a star with 3 arms. The 2^nd generation contains the 3-armed star, but now two segments are added to all free chain ends of the star, which results in a branch-on-branch structure as shown in figure 1.3. To obtain the next generation, segments are added to the free chain ends of the previous generation. Random trees consist of randomly distributed branches that are connected to the backbone or to other branches. The length of the segments in the polymer chain can be irregular for all previously described structures.

After polymerization a mixture of polymer chains is obtained, where nonuniformities are typically found in mass, branching and structure. During polymerization, polymers are mixed and exposed to different reactions, resulting in a distribution in mass, branching and structure. Here the term polydispersity is used to indicate the nonuniformity of the polymer mixture. In the next section, different analytical techniques are explained to find the polydispersity of the polymer mixtures.

1.2 Polymer Characterization

In this project, triple detector GPC (3D-GPC) and rheometer measurements are conducted to obtain information about the mass, branching and structure of the polymer samples. 3D-GPC makes use of several analytical methods to find the polymer characteristics, including size exclusion chromatography (SEC), light scattering (LS) and viscosity measurements. In the following section, the principles that are used to find polymer characteristics are explained.

1.2.1 Characterization of Molar Mass 1.2.1.1 Size Exclusion Chromatography

In Size Exclusion Chromatography (SEC) the differences in size of polymer molecules in dilute solutions are used to separate large molecules from small molecules. Here a column is filled with porous particles (the stationary phase) and subsequently filled with a liquid (the mobile phase).

When the polymer solution is added to the column, the small polymers are able to enter the pores and penetrate deep, while the large polymers that are larger than the pore size are not able to enter the pores at all. Therefore large polymers exit the column first and the small polymers last. This mechanism is named steric exclusion, where certain pore volume fractions are accessible for certain polymer sizes. Eq. 1.10 shows the relation between elution volume 𝑉_𝑒, solvent volume outside the pores 𝑉₀, solvent volume inside the pores 𝑉_𝑖 and distribution coefficient 𝐾_𝑑.¹¹

𝑉_𝑒= 𝑉₀+ 𝐾_𝑑𝑉_𝑖 (1.10)

10 The distribution coefficient 𝐾𝑑 is dependent on the size of the polymer chains and the used porous particles. Polymers that are larger than the largest pore size leave the column at elution volume 𝑉0

and polymers that are able permeate into all pores leave the column at elution volume 𝑉𝑖. The relation between elution volume and polymer size is shown in figure 1.4.

Ideally the distribution coefficient 𝐾_𝑑 is directly related with the size and even molar mass of the polymers. This, however, has proven to be difficult because there are multiple separation mechanisms occurring during size exclusion chromatography.¹¹ To obtain the absolute mass a calibration curve is sometimes used where the masses of known polymers are used. The calibration curve provides an easy way to obtain molar masses, but this method has a major pitfall. SEC only separates particles based on their hydrodynamic size and this size is, besides being dependent on the molar mass, dependent on the degree of branching and structure. Branching for example decreases the size of the polymers, resulting in a possible underestimated molar mass when using calibration curve. This is why additional analytical equipment in combination with SEC is needed to accurately determine the absolute mass of polymers.

1.2.1.2 Light Scattering

One of the few methods to for obtaining the absolute mass of polymers is light scattering. In light scattering, the oscillating field of the electric part of light creates dipoles from neutral molecules.

These polarized molecules are now able to affect the trajectory of incident radiation, resulting in a scattered beam. This event can take place multiple times, which impacts the intensity of the radiation beam. The decrease of intensity can be related with the mass, the Zimm formula is typically used:¹²

𝐾𝑐

𝑅_𝜃=_{𝑀𝑃(𝜃)}¹ + 2𝐴_𝑐𝑐 + ⋯ (1.11)

𝐾 is the optical constant, 𝑐 the concentration of the particles, 𝑅𝜃 the excess Rayleigh ratio, 𝑀 the molar mass, 𝑃(𝜃) the particle scattering function and 𝐴2 the second viral coefficient. The excess Rayleigh ratio 𝑅_𝜃 is dependent on the intensity of the scattered light beam (Eq. 1.12). The particle scattering function 𝑃(𝜃) is dependent on the shape of the particle, but 𝑃(𝜃) can also be

Polym er Siz e

Elution Volume 𝑉

_𝑒

𝑉 _𝑖 𝑉 ₀

Figure 1.4 – Hypothetical elution curve: elution volume 𝑽𝒆 versus polymer size. 𝑽𝟎 is the solvent volume outside the pores, 𝑽𝒊 the solvent volume inside the pores.

11 approximated with Eq. 1.13, for 𝑞²𝑅_𝑔² < 0.3.¹³ 𝑅_𝑔 is the radius of gyration and the scattering vector 𝑞 is dependent on the angle and wavelength of the incident light (Eq. 1.13).¹¹

𝑅_𝜃 =^𝑟2

𝑉

𝐼_𝜃−𝐼_{𝜃,𝑠𝑜𝑙𝑣𝑒𝑛𝑡}

𝐼₀ (1.12)

𝑃(𝜃) = 1 +^𝑞2₃^𝑅𝑔2 (1.13)

𝑞 =^4𝜋

𝜆 sin (^𝜃

2) (1.14)

𝐼_𝜃, 𝐼𝜃,𝑠𝑜𝑙𝑣𝑒𝑛𝑡 and 𝐼0 are the intensities of the solution, solvent and the used light, 𝑟 is the distance between the solution and detector and 𝑉 is the solution volume. 𝜆 and 𝜃 are the wavelength in a solvent and angle of the used light beam.

With equation 1.11 the molar mass of polymer particles can be determined by static light scattering.

During static light scattering, the light intensity fluctuations are averaged over time. The averages are determined for various angles and concentrations and subsequently can be used to construct a Zimm-plot where the molar mass is obtained by doing extrapolations for 𝑐 → 0 and 𝑞 → 0. A hypothetical Zimm-plot is shown in figure 1.5. The spacing parameter 𝑘 is chosen arbitrarily to simplify the extrapolation process.

The Zimm-plot however is only useful in ‘batch mode’, where concentrations can be varied. In 3D-GPC experiments the elution volumes from the SEC equipment are analyzed by light scattering online, where the concentration is fixed and typically low. For these measurements high-intensity laser lights are applied to give reliable results. Low angle laser light scattering (LALLS), used to measure scattering at a very low angle (at ~7 degrees), or multiple angle laser light scattering (MALLS), where multiple angles are used (~15-160 degrees), measure the light scattering and facilitate the determination of the absolute molar mass.

12 1.2.2 Characterization of Architecture

The absolute molar mass of polymers is found by combing SEC and LS. However, obtaining detailed information about the branching or structure is more complicated, because there is no direct method available to determine this. In this project intrinsic viscosity and rheological measurements are used to estimate the degree of branching and structure.

1.2.2.1 Dilute Solution Viscosity

When adding polymers to a solution the viscosity of solution increases. Here the hydrodynamic volume that is occupied by the polymer chain increases the viscosity. Specific viscosity 𝜂𝑠𝑝 is used to define the difference between the viscosity with and without the polymer (Eq. 1.15).

𝜂_𝑠𝑝=^{𝜂−𝜂𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛}

𝜂_{𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛} (1.15)

The specific viscosity can be measured by determining the flow rate in glass capillaries or by a differential viscometer.¹⁴ If the concentration of these polymers in solution is low enough, polymers are assumed to be isolated and therefore intermolecular polymer-polymer interactions are typically neglected. From here the limit 𝑐 → 0 can be taken to calculate the intrinsic viscosity [𝜂] of the polymer chain (Eq. 1.16).

[𝜂] = lim_𝑐→0𝜂_𝑠𝑝 (1.16)

For linear polymers, the Mark-Houwink equation is used to relate the intrinsic viscosity with molar mass (Eq. 1.17). 𝑀𝑣 is the viscosity average molar mass and 𝐾 and 𝛼 are constants that depend on

Figure 1.5 – Hypothetical Zimm-plot. The molar mass, radius of gyration and second viral coefficient are determined for various angles and concentrations and their quantity is obtained by doing extrapolations for c→0 and q→0.

13

[𝜂] = 𝐾𝑀_𝑣^𝛼 (1.17)

Both hydrodynamic volume and intrinsic viscosity are dependent on the degree of polymerization, degree of branching, structure and polymer-solvent interaction. The hydrodynamic volume is typically defined in terms of radius of gyration (Eq. 1.18). The mean square radius of gyration is the average square distance between monomer 𝑖 and all other monomers. The average distance is required if the polymer chain fluctuates in size over time (for instance because of Brownian motion).

< 𝑅_𝑔²> = ¹

2𝑁²∑^𝑁_𝑖=1∑^𝑁_𝑗=1< (𝑅_𝑖− 𝑅_𝑗)²> (1.18)

For polymers with the same molar mass, linear polymers have a larger hydrodynamic volume than highly branched and compact polymers, resulting in a larger contribution to the viscosity. Branching ratios 𝑔 and 𝑔′ are used to compare branched chains with its linear equivalent for both hydrodynamic volume and intrinsic viscosity:¹²

𝑔 =^<𝑅_<𝑅^{𝑔2>𝑏𝑟𝑎𝑛𝑐ℎ𝑒𝑑} relationship. Now 𝑔′ can be calculated directly. When evaluating 𝑔 and 𝑔′ for polymers with specific architecture, the “shielding effect” has to be taken in account.

If we consider a polymer in dilute conditions, the chain segments at the edges of the polymer particle alter the flow of the solvent near the chain segments at the center in such a way that these are partially shielded from hydrodynamic interaction with the solvent flow outside the particle. For large polymers, the contribution of the center segments becomes negligibly small to the resistance to the flow of solvent outside the particle.^15,16 Additionally, the amount of branching and the architecture of the polymers affect this contribution.

To include this effect in the evaluation of the two branching ratios, Zimm and Stockmayer defined the structure factor 𝜀:¹²

𝑔^′= 𝑔^𝜀 (1.21)

This structure factor is derived to be 𝜀 = 0.5 for non-free drained star branched polymers and estimated to be 𝜀 = 1.5 for comb shaped polymers, where the branches are small relative to the backbone.¹⁷ For autoclave and tubular LDPE, the values 𝜀 = 1.2 and = 2.0 , respectively, have been found by Kuhn.¹⁸ Scholte et al. report values of 𝜀 = 0.8 − 1.0 for low-density polyethylene.¹⁹ Tackx et al. determined the 𝑔 factor with SEC-MALLS measurements and found 𝜀 to decrease with increasing molar weight. The structure factors varied for one size autoclave and tubular LDPE between 𝜀 = 1.0 − 1.5 and 𝜀 = 1.2 − 1.8. In general a value for 𝜀 is chosen between 0.5 and 2.0.

𝑔 can be calculated by using relationships derived by Zimm and Stockmayer.²⁰ The first relation is valid for polydisperse trifunctional randomly branched polymers.

14 molecule. For monodisperse trifunctional randomly branched polymers the next relation can be used:

In this relation the average 𝑔 per molecule is described in the average branch points per molecule 𝑚. In addition, Zimm and Stockmayer give a relation to find the structure factor when using the relation mentioned above:

𝑔^′= 𝑔^𝜀 = 𝑔^2−𝛼 (1.24)

Here 𝛼 is the exponent in the semi-empirical law [𝜂] = 𝐾𝑀^𝛼 for linear polymers. However, Zimm and Stockmayer note “it is still hazardous to draw inferences about branching from empirical viscosity-molecular weight relationships”.²⁰

1.2.2.2 Rheology

An additional way to find more information about the structure of polymers is by conducting rheological measurements. Rheology is used to describe the flow behavior of materials under stress and it is shown that rheological measurement are able to reveal the structure and the degree of branching of polymers.^21,22 Introducing even low amounts of long chain branches to linear polymers has a significant effect on the rheological properties.

To measure rheological behavior an oscillatory rheometer is typically used. Here a sinusoidal shear deformation is applied to the sample from which the stress response is measured. In figure 1.6, a rheometer is schematically shown, where the bottom plate oscillates with a certain frequency and the top plate measures the stress response. . Because of the rotating bottom plate, the strain is time dependent (Eq. 1.25). In this equation 𝜔 is the frequency of the strain and 𝑡 the time. The stress response can be proportional to the strain or, for most polymers, can lag behind. Here Eq. 1.26 is used, where 𝛿 is the phase lag.

𝜀(𝑡) = 𝜀₀sin(𝜔𝑡) (1.25)

𝜎(𝑡) = 𝜎₀sin(𝜔𝑡 + 𝛿) (1.26)

When a material is ideally elastic, the stress response is proportional to the applied strain (figure 1.6). This behavior is modeled by using a Hookean spring, where the applied stress 𝜎 is equal to the strain 𝜀 times the spring (or elastic) constant 𝐸. Equation 1.27, similar to Hooke’s law, is used to model the elastic behavior. The phase lag 𝛿 can be found by inserting Eq. 1.25 and Eq. 1.26 to 1.27.

For an ideally elastic material the phase lag is equal to zero, because the stress is proportional to the strain.

𝜎(𝑡) = 𝜀(𝑡)𝐸 (1.27)

15 The stress response of an ideally viscous material is proportional to the applied strain rate (figure 1.6). A Newtonian dashpot model can be used to describe the viscous response. Eq. 1.28 is used here, where the applied force 𝜎 is equal to the strain rate 𝑑𝜀 𝑑𝑡⁄ times the viscosity. Here the phase lag is shifted one fourth of a period (𝛿 =^𝜋₂).

𝜎(𝑡) = 𝜂^{𝑑𝜀(𝑡)}_𝑑𝑡 (1.28)

Most polymers are viscoelastic, showing both viscous (dashpot) and elastic (spring) behavior. The phase lag has therefore a value between 0 and ^𝜋₂. An example of a simple model for viscoelastic behavior is the Maxwell model. In a Maxwell model, the spring and dashpot are connected in series.

The overall strain rate equation results in: ^𝑑𝜀_𝑑𝑡 =^𝑑𝜀_𝑑𝑡|

𝑆+^𝑑𝜀_𝑑𝑡|

𝐷=¹_𝐸^𝑑𝜎_𝑑𝑡+^𝜎_𝜂. Dynamic modulus 𝐺 can be derived from this equation, that is the ratio of stress 𝜎 over strain 𝜀. This modulus can be split into two elements, storage modulus 𝐺′ and loss modulus 𝐺′′, that represent the elastic and viscous behavior of the viscoelastic material, respectively.¹⁰ Rheometer measurements typically give the storage and loss moduli.

In these measurements, it is assumed that the applied strain scales linearly with the stress response.

Therefore the dynamic moduli are independent of the applied strain if this assumption holds true.

When the strain amplitude is increased however, deformations, structural changes and phase

When the strain amplitude is increased however, deformations, structural changes and phase

In document Eindhoven University of Technology MASTER Structural modification of LDPE during high-temperature processing Simons, Jérôme (pagina 6-0)