`
`PE-HD
`
`%.( Arrangement of Polymer Molecules
`
`$(
`
`Linear molecule
`ca. 4 to 10 short side chains
`per 1000 C - atoms
`
`PE-LD
`
`Long chain branching
`
`PE-LLD
`
`Linear molecule
`ca. 10 to 35 short side chains
`per 1000 C - atoms
`
`Figure 3.14 Schematic of the molecular structure of polyethylene with different densities
`
` (cid:132) 3.5 Arrangement of Polymer Molecules
`
`As mentioned in Chapter 1, polymeric materials can be divided into two general
`categories: thermoplastics and thermosets. Thermoplastics are materials that have
`the ability to remelt a!er they have solidified, and thermosets are those that solid-
`ify via a chemical reaction that causes polymer molecules to cross-link. These
`cross-linked materials cannot be remelted a!er solidification.
`As thermoplastic polymers solidify, they take on two different types of structure:
`amorphous or semi-crystalline. Amorphous polymers are those where the mole-
`cules solidify in a random arrangement, whereas some of the molecules in semi-
`crystalline polymers align with their neighbors, forming regions with a three-
`dimensional order. In semi-crystalline polymers, the molecules that do not align
`into crystals remain amorphous structures.
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 77
`
`

`

`%)
`
`3 Structure of Polymers
`
`3.5.1 Thermoplastic Polymers
`
`The formation of macromolecules from monomers occurs if there are unsaturated
`carbon atoms (carbon atoms connected with double bonds), or if there are mono-
`mers with reactive end-groups. The double bond, say in an ethylene monomer, is
`split, which frees two valences per monomer and leads to the formation of a macro-
`molecule such as polyethylene. This process is o!en referred to as polymerization.
`Similarly, monomers (R) that possess two reactive end-groups (bifunctional) can
`react with other monomers (R’) that also have two other reactive end-groups that
`can react with each other, also leading to the formation of a polymer chain. A list of
`typical reactive end-groups is given in Table 3.2.
`
`Table 3.2 List of Selected Reactive End-Groups
`
`Hydrogen in aromatic monomers
`Hydroxyl group in alcohols
`Aldehyde group as in formaldehyde
`
`Carboxyl group in organic acids
`
`Isocyanate group in isocyanates
`Epoxy group in polyepoxys
`
`Amido groups in amides and polyamides
`Amino groups in amines
`
`– H
`– OH
`
`– N (cid:308) C (cid:308) O
`
`– CO – NH2
`– NH2
`
`3.5.2 Amorphous Thermoplastics
`
`Amorphous thermoplastics, with their randomly arranged molecular structure,
`are analogous to a bowl of spaghetti. Due to their random structure, the character-
`istic size of the largest ordered region is on the order of a carbon-carbon bond. This
`dimension is much smaller than the wavelength of visible light and so generally
`amorphous thermoplastics are transparent.
`Figure 3.15 [4] shows the shear modulus5, G’, versus temperature for polystyrene,
`one of the most common amorphous thermoplastics. The figure shows two general
`
`5  The dynamic shear modulus, G’, is obtained using the dynamic mechanical properties test described in
`Chapter 9.
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 78
`
`

`

`
`
`%.( Arrangement of Polymer Molecules
`
`%!
`
`Energy elastic region
`
`Ts
`
`Tg
`
`104
`
`MPa
`
`103
`
`102
`
`101
`
`Shear modulus, G
`
`100
`
`Entropy elastic region
`
`Viscoelastic region
`
`10-1
`-160 -120 -80 -40 0
`40 80
`Temperature, T
`Figure 3.15 Shear modulus of polystyrene as a function of temperature
`
`°C 160
`
`200
`
`regions: one where the modulus appears fairly constant6, and one where the modu-
`lus drops significantly with increasing temperature. With decreasing tempera-
`tures, the material enters the glassy region where the slope of the modulus
`approaches zero. At high temperatures the modulus is negligible and the material
`is so! enough to flow. Although there is not a clear transition between “solid” and
`“liquid”, the temperature that divides the two states in an amorphous thermo-
`plastic is referred to as the glass transition temperature, Tg. For the polystyrene in
`Fig. 3.15 the glass transition temperature is approximately 110 °C. At tempera-
`tures below the glass transition temperature the material behaves like a visco-
`elastic solid, the area in the curve denoted as energy elastic region. Once the
`material is above the glass transition temperature, it enters the so-called entropy
`elastic region. At this point the material can be more easily deformed, such as is
`done during the thermoforming process. However, in order for the material to flow,
`its temperature must be above a so!ening temperature, Ts, at which point it behaves
`like a viscoelastic fluid. The so!ening temperature defines the point where the
`viscous forces during deformation (loss) exceed the elastic forces during deforma-
`tion (storage), and for amorphous thermoplastics it typically ranges about 50 K
`
`6 When plotting G’ versus temperature on a linear scale, a steady decrease of the modulus is observed.
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 79
`
`

`

`%*
`
`3 Structure of Polymers
`
`above the glass transition temperature. Storage and loss moduli are discussed in
`more detail in Chapter 10.
`It should be mentioned here that the curve shown in Fig. 3.15 was measured at a
`constant frequency. If the frequency of the test is increased – reducing the time
`scale – the curve is shi! ed to the right, because higher temperatures are required
`to achieve movement of the molecules at the new frequency. Figure 3.16 [5] dem-
`onstrates this concept by displaying the elastic modulus as a function of tempe r-
`ature for polyvinyl chloride at various test frequencies. The relation between time
`scale and temperature, also known as the time-temperature superposition principle,
`is discussed in detail Chapter 9. A similar eff ect as observed with time scale and
`temperature can be seen when the molecular weight of the material is increased.
`The longer molecules have more diffi culty sliding past each other, thus requiring
`higher temperatures to achieve “fl ow.”
`
`MPa
`
`1000
`
`E
`
`100
`
`10
`
`0
`
`5 Hz
`50 Hz
`500 Hz
`5000 Hz
`
`80
`40
`Temperature, T
`
`°C
`
`160
`
` 
`
` Figure 3.16 Modulus of polyvinyl chloride
`as a function of temperature at various test
`frequencies
`
`3.5.3 Semi-Crystalline Thermoplastics
`
`Semi-crystalline thermoplastic polymers show more order than amorphous ther-
`moplastics. The molecules arrange in an ordered crystalline form as shown for
`polypropylene in Fig. 3.17. The crystalline structure shown in the photograph is
`composed of spherulites, which are formed by lamellar crystals. The formation of
`spherulites during solidifi cation of semi-crystalline thermoplastics is covered in
`Chapter 8. The schematic in Fig. 3.18 shows the general structure and hierarchical
`arrangement in semi-crystalline materials, using polyethylene as an example. The
`spherulitic structure is the largest domain with a specifi c order and has a cha-
`racteristic size of 50 to 500 μm. Some of the polypropylene spherulites in the
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 80
`
`

`

`
`
`%.( Arrangement of Polymer Molecules
`
`%+
`
`micrograph presented in Fig. 3.17 are about 150 μm in diameter. The size of spher-
`ulites is much larger than the wavelength of visible light, making semi-crystalline
`materials translucent and not transparent.
`However, the crystalline regions are very small with molecular chains comprised
`of both crystalline and amorphous regions. The degree of crystallinity in a typical
`thermoplastic will vary from grade to grade. For example, in polyethylene the
`degree of crystallinity depends on the branching and the cooling rate. A low den-
`sity polyethylene (LDPE) with its long branches (Fig. 3.14) can only crystallize to
`approximate 40 – 50 %, whereas a high density polyethylene (HDPE) crystallizes to
`up to 80 %. The density and strength of semi-crystalline thermoplastics increase
`with the degree of crystallinity, as demonstrated in Table 3.3 [6], which compares
`low and high density polyethylene. Figure 3.19 shows the different properties and
`molecular structure that may arise in polyethylene plotted as a function of degree
`of crystallinity and molecular weight.
`
`Table 3.3 Influence of Crystallinity on Properties for Low and High Density Polyethylene
`Property
`Low density
`High density
`0.91 – 0.925
`0.941 – 0.965
`Density (g/cm3)
`% crystallinity
`42 – 53
`64 – 80
`Melting temperature (°C)
`110 – 120
`130 – 136
`Tensile modulus (MPa)
`17 – 26
`41 – 124
`Tensile strength (MPa)
`4.1 – 16
`21 – 38
`
` Spherulites
`
` 
`
` Figure 3.17 Micrograph of
`the spherulitic crystal line
`structure in a poly proylene
`poly mer (Courtesy of the
`Institute of Plas tics Technology,
`LKT, Uni versity of Erlangen-
`Nurem berg)
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 81
`
`

`

`%#
`
`3 Structure of Polymers
`
`Optical microscope
`
`W
`
` Spherulite
` 1-500µm
`
`Polymer
`component
`
`Crystal
`lamella
`
`Scanning electron microscope
`
`0.492 nm
`
`0.736 nm
`
`Atom probe microscope
`
`0.252 nm
`
` Lamella
`20 to 60 nm
`
`t
`
`Figure 3.18  Schematic representation of the general molecular structure and arrangement of
`typical semi-crystalline materials
`
`Brittle gray
` wax
`
`Hard
`
`PE-LD
`
`PE-HD
`
`Similar to
`bees wax
`
`Jelly
`
`0 500 2,500
`
`10,000
`
`20,000
`
`40,000 Molecular weight
`
`100
`
`%
`
`50
`
`25
`
`0
`
`Crystallinity
`
`Figure 3.19  Infl uence of degree of crystallinity and molecular weight on diff erent properties
`of polyethylene
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 82
`
`

`

`
`
`%.( Arrangement of Polymer Molecules
`
`%$
`
`Figure 3.20 [4] shows the dynamic shear modulus versus temperature for a high
`density polyethylene, the most common semi-crystalline thermoplastic. Again,
`this curve presents data measured at one test frequency. The fi gure clearly shows
`two distinct transitions: one at about –110 °C, the glass transition temperature, and
`another near 140 °C, the melting temperature. Above the melting temperature, the
`shear modulus is negligible and the material will fl ow. Crystalline arrangement
`begins to develop as the temperature decreases below the melting point. Between
`the melting and glass transition temperatures, the material behaves like a leathery
`solid. As the temperature decreases below the glass transition temperature, the
`amorphous regions within the semi-crystalline structure solidify, forming a glassy,
`stiff , and in some cases brittle polymer.
`To summarize, Table 3.4 presents the basic structure of several amorphous and
`semi-crystalline thermoplastics with their melting and/or glass transition temper-
`atures.
`Furthermore, Fig. 3.21 [7] summarizes the property behavior of amorphous, crys-
`talline, and semi-crystalline materials using schematic diagrams of material pro-
`perties plotted as functions of temperature.
`
`104
`
`MPa
`
`103
`
`102
`
`101
`
`Shear modulus, G
`
`100
`-160 -120 -80 -40 0
`40 80
`Temperature, T
`
`°C 160
`
` 
`
` Figure 3.20 Shear modulus of a high
`density polyethylene as a function of
`temperature
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 83
`
`

`

`%%
`
`3 Structure of Polymers
`
`100% Amorphous
`
`100% Crystalline
`
`Semi-crystalline
`
`T
`
`T
`
`T
`
`T
`
`T
`
`T
`
`T
`
`T
`
`T
`
`T
`
`T
`
`T
`
`V
`
`(cid:95)
`
`cp
`
`(cid:104)
`
`lnG
`
`Volume
`
`Thermal expansion
`
`Specific heat
`
`Heat conductivity
`
`Modulus
`
`Tg
`Tm
`Tg
`T
`T
`T
`Figure 3.21  Schematic of the behavior of some polymer properties as a function of
`temperature for different thermoplastics
`
`Tm
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 84
`
`

`

`
`
`%.( Arrangement of Polymer Molecules
`
`%&
`
`Table 3.4  Structural Units for Selected Polymers with Glass Transition and
`Melting Temperatures
`
`Structural unit
`
`Polymers
`
`CH2 CH2
`
`Linear polyethylene
`
`Tg = -125 °C
`Tm = 135 °C
`
`CH2
`
`CH
`CH3
`
`CH2
`
`CH
`C2H5
`
`CH2
`
`CH
`CH
`CH3
`
`CH3
`
`CH2
`CH
`
`CH2
`
`CH3
`
`CH
`CH3
`
`CH2 CH
`
`Isotactic polypropylene
`
`Tg = -20 °C
`Tm = 170 °C
`
`Isotactic polybutene
`
`Tg = -25 °C
`Tm = 135 °C
`
`Isotactic poly-3-
`methylbutene-1
`
`Tg = 50 °C
`Tm = 310 °C
`
`Isotactic poly-4-
`methylpentene-1
`
`Tg = 29 °C
`Tm = 240 °C
`
`Isotactic polystyrene
`
`Tg = 100 °C
`Tm = 240 °C
`
`CH3
`O
`CH3
`
`Polyphenylether (PPE)
`
`Tg = 210 °C
`Tm = 261 °C
`
`▸
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 85
`
`

`

`%’
`
`3 Structure of Polymers
`
`Table 3.4  Structural Units for Selected Polymers (continued)
`
`Structural unit
`
`Polymers
`
`Polyacetaldehyde
`
`Tg = -30 °C
`Tm = 165 °C
`
`Polyformaldehyde
`(polyacetal,
`polyoxymethylene)
`
`Tg = -85 °C
`Tm ≈ 190 °C
`
`Isotactic
`polypropyleneoxide
`
`Tg = -75 °C
`Tm = 75 °C
`
`Poly-[2.2-bis-(chlormethyl)-
`trimethylene-oxide]
`
`Tg = 5 °C
`Tm = 181 °C
`
`Isotactic polymethylmeth-
`acrylate
`
`Tg = 50 °C
`Tm = 160 °C
`
`Polychlortrifluoroethylene
`
`Tg = 45 °C
`Tm = 220 °C
`
`O
`
`CH
`CH3
`
`O CH2
`
`CH2
`
`O
`
`CH
`CH3
`
`O
`
`CH2
`
`Cl
`CH2
`CH2
`C
`CH2 Cl
`
`CH2
`
`CH3
`C
`CO2 CH3
`
`CF F
`
`l F
`CC
`
`CF2 CF2
`
`Polytetrafluoroethylene
`
`Tg1 = -113 °C
`Tg2 = 127 °C
`Tm = 330 °C
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 86
`
`

`

`
`
`%.( Arrangement of Polymer Molecules
`
`%(
`
`Table 3.4  Structural Units for Selected Polymers (continued)
`
`Structural unit
`
`Polymers
`
`Polyvinylidenechloride
`
`Tg = -19 °C
`Tm = 190 °C
`
`Polyvinylidenefluoride
`
`Tg = -45 °C
`Tm = 171 °C
`
`Polyvinylchloride (PVC) -
`amorphous
`
`Tg = 80 °C
`Tm = –
`
`Polyvinylchloride (PVC) -
`crystalline
`
`Tg = 80 °C
`Tm = 212 °C
`
`Polyvinylfluoride (PVF)
`
`Tg = -20 °C
`Tm = 200 °C
`
`Cl
`C
`Cl
`
`F F
`
`C
`
`CH2
`
`CH2
`
`CH2
`
`CH
`Cl
`
`CH2
`
`CH
`Cl
`
`FC
`
`H
`
`CH2
`
`CO2
`
`CO2 CH2 CH2 O
`
`Polyethyleneterephtalate
`(PET) (linear polyester)
`
`Tg = 69 °C
`Tm = 245 °C
`
`CO [CH2]4
`
`CO NH
`
`[CH2]6
`
`NH
`
`Polyamide 66
`
`Tg = 57 °C
`Tm = 265 °C
`
`▸
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 87
`
`

`

`&)
`
`3 Structure of Polymers
`
`Table 3.4  Structural Units for Selected Polymers (continued)
`
`Structural unit
`
`Polymers
`
`CO [CH2]8
`
`CO NH
`
`[CH2]6
`
`NH
`
`Polyamide 610
`
`Tg = 57 °C
`Tm = 265 °C
`
`CO [CH2]5 NH
`
`Polycaprolactam,
`Polyamide 6
`
`Tg = 75 °C
`Tm = 233 °C
`
`Polycarbonate (PC)
`
`Tg = 149 °C
`Tm = 267 °C
`
`O
`
`CO
`
`O
`
`CH3
`C
`CH3
`
`CH2
`
`CH2
`
`Poly-(p-xylene) (Parylene
`|| R)
`
`Tg = –
`Tm = 400 °C
`
`C
`O
`
`[CH2]2
`
`O
`
`C
`O
`
`n
`
`C O
`O
`PET
`
`PHB
`
`O
`
`m
`
`Polyethyleneterephtalate /
`p-Hydroxybenzoate-
`copolymers LC-PET,
`polymers with flexible
`chains
`
`Tg = 75 °C
`Tm = 280 °C
`
`N
`
`O
`
`Polyimide (PI)
`
`Tg: up to 400 °C
`
`C CO
`
`O
`
`Polyamidimide (PAI)
`
`Tg ≈ 260 °C
`
`R
`
`N
`H
`
`C O
`
`C CO
`
`O
`
`C CO
`
`O
`
`N
`
`N
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 88
`
`

`

`
`
`%.( Arrangement of Polymer Molecules
`
`&!
`
`Table 3.4  Structural Units for Selected Polymers (continued)
`
`Structural unit
`
`Polymers
`
`Polyetherimide (PEI)
`
`Tg ≈ 215 °C
`
`O
`
`CH3
`C
`CH3
`
`O
`
`C CO
`
`O
`
`N
`
`Polybismaleinimide (PBI)
`
`Tg ≈ 250 °C
`
`HH
`
`CC
`
`CO
`
`C
`
`O
`
`N
`
`R
`
`N
`
`CO
`
`C
`
`O
`
`CC
`
`HH
`
`Polyoxybenzoate (POB)
`
`Tg ≈ 290 °C
`
`O
`
`O
`C
`
`CO
`
`O
`
`Polyetherketone (PEEK)
`
`Tg = 145 °C
`Tm = 335 °C
`
`Polyphenylene-sulfide
`(PPS)
`
`Tg ≈ 230 °C
`
`Polyethersulfone (PES)
`
`Tg = 85 °C
`Tm = 280 °C
`
`O
`
`Polysulfone (PSU)
`
`Tg ≈ 180 °C
`
`O
`C
`
`O
`
`S
`
`CH3
`C
`CH3
`
`O
`
`O
`
`O O
`
`S
`
`O
`
`O
`
`O O
`
`S
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 89
`
`

`

`&*
`
`3 Structure of Polymers
`
`3.5.4 Thermosets and Cross-Linked Elastomers
`
`Thermosets, and some elastomers, are polymeric materials that have the ability to
`crosslink. The crosslinking causes the material to become heat resistant a!er it
`has solidified. A more in-depth explanation of the chemical crosslinking reaction
`that occurs during solidification is given in Chapter 8.
`The crosslinking usually is a result of the presence of double bonds that break,
`allowing the molecules to link with their neighbors. One of the oldest thermoset-
`ting polymers is phenol-formaldehyde, or phenolic. Figure 3.22 shows the che-
`mical symbol representation of the reaction, and Fig. 3.23 shows a schematic of
`the reaction. The phenol molecules react with formaldehyde molecules to create a
`three-dimensional crosslinked network that is stiff and strong. The by-product of
`this chemical reaction is water.
`
`HH
`
`OH
`
`O C
`
`HH
`
`OH
`
`HH
`
`H
`+
`+
`H
`H
`H
`H
`H
`Formaldehyde
`Phenol
`Phenol
`OH
`
`HH
`
`HO
`
`H
`
`CH2
`H
`H
`+ H2O
`
`H
`
`HH
`
`CH2
`
`CH2
`OH
`
`H2C
`
`OH
`
`CH2
`OH
`
`CH2
`
`CH2
`
`OH
`
`CH2
`
`CH2
`H
`
`OH
`
`CH2
`
`CH2
`H
`
`CH2
`
`
`
`OHOH
`
`CH2
`
`OH
`
`CH2
`
`CH2
`
`OH
`
`CH2
`
`Figure 3.22  Symbolic representation of the condensation polymerization of phenol-
`formal dehyde resins
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 90
`
`

`

`
`
`%.# Copolymers and Polymer Blends
`
`&+
`
`H2O
`
`H2O
`
`Figure 3.23 Schematic representation of the
`condensation polymerization of phenol-formal-
`dehyde resins
`
` (cid:132) 3.6 Copolymers and Polymer Blends
`
`Copolymers are polymeric materials with two or more monomer types in the same
`chain. A copolymer that is composed of two monomer types is referred to as a
`bipolymer, and one that is formed by three different monomer groups is called a
`terpolymer. Depending on how the different monomers are arranged in the polymer
`chain, one distinguishes between random, alternating, block, or gra& copolymers.
`The four types of copolymers are schematically represented in Fig. 3.24.
`A common example of a copolymer is ethylene-propylene. Although both mono-
`mers would result in semi-crystalline polymers when polymerized individually,
`the melting temperature disappears in the randomly distributed copolymer with
`ratios between 35/65 and 65/35, resulting in an elastomeric material, as shown in
`Fig. 3.25. In fact, EPDM7 rubbers are continuously gaining acceptance in industry
`because of their resistance to weathering. On the other hand, the ethylene-propyl-
`ene block copolymer maintains a melting temperature for all ethylene/propylene
`ratios, as shown in Fig. 3.26.
`Another widely used copolymer is high impact polystyrene (PS-HI), which is
`formed by gra!ing polystyrene to polybutadiene. Again, when styrene and buta-
`
`7  The D in EP(D)M stands for the added unsaturated diene component which results in a crosslinked
`elastomer.
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 91
`
`

`

`&#
`
`3 Structure of Polymers
`
`diene are randomly copolymerized, the resulting material is an elastomer called
`styrene-butadiene-rubber (SBR). Another classic example of copolymerization is
`the terpolymer acrylonitrile-butadiene-styrene (ABS).
`
`Random copolymer
`
`Alternating copolymer
`
`Block copolymer
`
`Graft copolymer
`
`Figure 3.24 Schematic representation of diff erent copolymers
`
`Tm
`
`Tm
`
`Elastomer
`no melting
`temperature
`
`Tg
`
`20
`
`80
`
`60
`40
`Ethylene
`60
`40
`Propylene
`
`%mol
`
`%mol
`
`100
`
`0
`
`Figure 3.25 Melting and glass transition
`temperature for random ethylene-propylene
`copolymers
`
`200
`
`°C
`
`100
`
`50
`
`0
`
`Temperature, T
`
`-50
`
`-100
`
`-150
`
`0
`
`100
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 92
`
`

`

`
`
`%.) Polymer Additives
`
`&$
`
`Polymer blends belong to another family of polymeric materials that are made by
`mixing or blending two or more polymers to enhance the physical properties of
`each individual component. Common polymer blends include PP-PC, PVC-ABS,
`and PE-PTFE.
`
`Tm
`
`melt begin
`
`200
`
`°C
`
`150
`
`125
`
`100
`
`Melting Temperature, Tm
`
`0
`
`0
`
`100
`
`20
`
`80
`
`60
`40
`Ethylene
`60
`40
`Propylene
`
`%mol
`%mol
`
`100
`
`0
`
` 
`
` Figure 3.26 Melting temperature for
`ethylene-propylene block copolymers
`
` (cid:132) 3.7 Polymer Additives
`
`There are many polymer additives that are mixed into a polymer to improve the
`mechanical, optical, electrical, and acoustic – to name a few – performance of a
`component.
`
`3.7.1 Flame Retardants
`
`Since polymers are organic materials, most of them are fl ammable. The fl ammabil-
`ity of polymers has always been a serious technical problem. A parameter that can
`be used to assess the fl ammability of polymers is the limiting oxygen index (LOI),
`also known as the critical oxygen index (COI). This value defi nes the minimum vol-
`ume percent of oxygen concentration, mixed with nitrogen, needed to support
`combustion of the polymer under the test conditions specifi ed by ASTM D 2863.
`Since air contains 21 % oxygen by volume, only those polymers with an LOI greater
`than 0.21 are considered self-extinguishing. In practice, an LOI value higher than
`0.27 is recommended as the limiting self-extinguishing threshold. Table 3.5 pre-
`sents LOI values for selected polymers.
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 93
`
`

`

`&%
`
`3 Structure of Polymers
`
`It is impossible to make a polymer completely inflammable. However, some addi-
`tives containing halogens, such as bromine, chlorine, or phosphorous, reduce the
`possibility of either starting combustion within a polymer component or, once
`ignited, reduce the rate of flame spread. When rating the performance of flame
`retardants, bromine is more effective than chlorine.
`In the radical trap theory of flame retardancy it is believed that bromine or phos-
`phorous containing additives compete in the reaction of a combustion process. To
`illustrate this we examine two examples of typical combustion reactions. These
`are:
`
`CH OH
`+
`4
`
`→
`
`CH H O
`+
`3
`2
`
`and
`
`CH H O
`CH O
`→
`+
`+ +
`3
`2
`4
`2
`where OH and H are active chain carriers. With the presence of HBr the following
`reaction can take place
`
`OH HBr
`+
`
`H O Br
`+2→
`
`Table 3.5 LOI Values for Selected Polymers
`Polymer
`Polyformaldehyde
`Polyethylene oxide
`Polymethyl methacrylate
`Polyacrylonitrile
`Polyethylene
`Polypropylene
`Polyisoprene
`Polybutadiene
`Polystyrene
`Cellulose
`Polyethylene terephthalate
`Polyvinyl alcohol
`Polyamide 66
`Epoxy
`Polycarbonate
`Aramid fibers
`Polyphenylene oxide
`Polysulfone
`Phenolic resins
`
`LOI
`0.15
`0.15
`0.17
`0.18
`0.18
`0.18
`0.185
`0.185
`0.185
`0.19
`0.21
`0.22
`0.23
`0.23
`0.27
`0.285
`0.29
`0.30
`0.35
`
`▸
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 94
`
`

`

`
`
`%.) Polymer Additives
`
`&&
`
`Table 3.5 LOI Values for Selected Polymers (continued)
`Polymer
`Polychloroprene
`Polyvinyl chloride
`Polyvinylidene fluoride
`Polyvinylidene chloride
`Carbon
`Polytetrafluoroethylene
`
`LOI
`0.40
`0.42
`0.44
`0.60
`0.60
`0.95
`
`where the active chain carrier was replaced by the less active Br radical, helping
`with flame extinguishment. Similarly, with the presence of Br the following reac-
`tion can take place
`
`→
`HBr CH
`CH Br
`+
`4 +
`3
`Table 3.6 [8] lists selected polymers and commonly used flame retardants.
`
`Table 3.6 Selected Polymers with Typical Commercial Flame Retardants
`Polymer
`Flame retardants
`Acrylonitrile butadiene styrene
`Octabromodiphenyl oxide
`High impact polystyrene
`Decabromodiphenyl oxide
`Polyamide
`Dechlorane plus
`Polycarbonate
`Tetrabromobisphenol A carbonate oligomer
`Polyethylene
`Chlorinated paraffin
`Polypropylene
`Dechlorane plus
`Polystyrene
`Pentabromocyclododecane
`Polyvinyl chloride
`Phosphate ester
`
`3.7.2 Stabilizers
`
`The combination of heat and oxygen will bring about thermal degradation in a
`polymer. Heat or energy will produce free radicals that will react with oxygen to
`form carbonyl compounds, which give rise to yellow or brown discolorations in the
`final product.
`Thermal degradation can be slowed by adding stabilizers such as antioxidants or
`peroxide decomposers. These additives do not eliminate thermal degradation, but
`they slow down the reaction process. Once the stabilizer has been consumed by
`the reaction with the free radicals, the protection of the polymer against thermal
`degradation ends. The time period over which the stabilizer renders protection
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 95
`
`

`

`&’
`
`3 Structure of Polymers
`
`against thermal degradation is called induction time. A test used to measure ther-
`mal stability of a polymer is the Oxidative Induction Time (OIT) by differential scan-
`ning calorimetry (DSC). The OIT test is defined as the time it takes for a polymer
`sample to thermally degrade in an oxygen environment at a set temperature above
`the polymer’s transition temperature. The transitions must occur in a nitrogen
`environment. The standard test is described by ASTM D 3895. Another test used to
`measure the thermal stability of a polymer and its additives is the thermal gravi-
`metric analysis (TGA) discussed in Chapter 4.
`Polyvinyl chloride is probably the polymer most vulnerable to thermal degrada-
`tion. In polyvinyl chloride, scission of the C-Cl bond occurs at the weakest point of
`the molecule. The chlorine radicals will react with their nearest CH group, forming
`HCl and creating new weak C-Cl bonds. A stabilizer must therefore neutralize HCl
`and stop the auto-catalytic reaction, as well as prevent corrosion of the processing
`equipment.
`
`3.7.3 Antistatic Agents
`
`Since polymers have such low electric conductivity, they can build-up electric
`charges quite easily. The amount of charge build-up is controlled by the rate at
`which the charge is generated compared to the charge decay. The rate of charge
`generation at the surface of the component can be reduced by reducing the in -
`timacy of contact, whereas the rate of charge decay is increased through surface
`conductivity. Hence, a good antistatic agent should be an ionizable additive that
`allows charge migration to the surface, at the same time as creating bridges to the
`atmosphere through moisture in the surroundings. Typical antistatic agents are
`nitrogen compounds, such as long chain amines and amides, polyhydric alcohols,
`among others.
`
`3.7.4 Fillers
`
`Fillers can be divided into two categories: those that reinforce the polymer and
`improve its mechanical performance and those that are used to take up space and
`so reduce the amount of actual resin to produce a part – sometimes referred to as
`extenders. A third, less common, category of filled polymers are those where fillers
`are dispersed into the polymer to improve its electric conductivity.
`Polymers that contain fillers that improve their mechanical performance are o!en
`referred to as composites. Composites can be divided into two further categories:
`composites with high performance reinforcements, and composites with low per-
`formance reinforcements. In high performance composites the reinforcement is
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 96
`
`

`

`
`
`%.) Polymer Additives
`
`&(
`
`placed inside the polymer in such a way that optimal mechanical behavior is
`achieved, such as unidirectional glass fibers in an epoxy resin. High performance
`composites usually have 50–80 % reinforcement by volume and the composites are
`usually laminates, tubular shapes containing braided reinforcements, etc. In low
`performance composites the reinforcement is small enough that it can be dis-
`persed well into the matrix, allowing to process these materials the same way their
`unreinforced counterparts are processed. The most common filler used to reinforce
`polymeric materials is glass fiber. However, wood fiber, which is commonly used as
`an extender, also increases the stiffness and mechanical performance of some
`thermoplastics. To improve the bonding between the polymer matrix and the rein-
`forcing agent, coupling agents, such as silanes and titanates are o!en added. Poly-
`mer composites and their performance are discussed in more detail in Chapters 8
`and 9.
`Extenders, used to reduce the cost of the component, o!en come in the form of
`particulate fillers. The most common particulate fillers are calcium carbonate, sil-
`ica flour, clay, and wood flour or fiber. As mentioned earlier, some fillers also
`slightly reinforce the polymer matrix, such as clay, silica flour, and wood fiber. It
`should be pointed out that polymers with extenders o!en have significantly lower
`toughness than the unfilled resin. This concept is covered in more detail in Chap-
`ter 10.
`
`3.7.5 Blowing Agents
`
`The task of blowing or foaming agents is to produce cellular polymers, also referred
`to as expanded plastics. The cells can be completely enclosed (closed cell) or they
`can be interconnected (open cell). Polymer foams are produced with densities
`ranging from 1.6 kg/m3 to 960 kg/m3. There are many reasons for using polymer
`foams, such as their high strength/weight ratio, excellent insulating and acoustic
`properties, and high energy and vibration absorbing properties.
`Polymer foams can be made by mechanically whipping gases into the polymer, or
`by either chemical or physical means. Some of the most commonly used foaming
`methods are [9]:
` (cid:131) Thermal decomposition of chemical blowing agents, which generates nitrogen
`and/or carbon monoxide and dioxide. An example of such a foaming agent is
`azodicarbonamide, which is the most widely used commercial polyolefin foaming
`agent.
` (cid:131) Heat induced volatilization of low-boiling liquids such as pentane and heptane in
`the production of polystyrene foams, and methylene chloride when producing
`flexible polyvinyl chloride and polyurethane foams.
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 97
`
`

`

`’)
`
`3 Structure of Polymers
`
` (cid:131) Volatilization by the exothermic reaction of gases produced during polymeri-
`zation. This is common in the reaction of isocyanate with water to produce car-
`bon dioxide.
` (cid:131) Expansion of the gas dissolved in a polymer upon reduction of the processing
`pressure.
`The basic steps of the foaming process are nucleation of the cells, expansion or
`growth of the cells, and stabilization of the cells. The nucleation of a cell occurs
`when, at a given temperature and pressure, the solubility of a gas is reduced, lead-
`ing to saturation, expelling the excess gas to form a bubble. Nucleating agents are
`used for initial formation of the bubbles. The bubble reaches an equilibrium shape
`when the pressure inside the bubble balances with the surface tension surround-
`ing the cell.
`
`Examples
`
`1. What is the maximum possible separation between the ends of a high
`density polyethylene molecule with an average molecular weight of
`100,000.
`Our first task is to estimate the number of repeat units, n, in the poly-
`ethylene chain. Each repeat unit has  carbon and  hydrogen atoms. The
`molecular weight of carbon is  and that of hydrogen . Hence,
`MW/repeat unit = () + () = .
`The number of repeat units is computed as
`n = MW/(MW/repeat unit) = ,/ = , units.
`Using the diagram presented in Fig. ., we can now estimate the length
`of the fully extended molecule using
`(
`) =
`
`0 252.
`nm
`3571
`890
`nm
`
`0 89.
`μm
`
`l =
`
`=
`
`0.252 nm
`
`CH2
`
`CH2
`
`CH2
`
`CH2
`
`CH2
`CH2
`Polyethylene repeat unit
`
`CH2
`
`CH2
`
`Figure 3.27  Schematic diagram of a polyethylene molecule
`
`As we know, even high density polyethylene molecules are branched and
`therefore our result is an overprediction.
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 98
`
`

`

`
`
`Problems
`
`Problems
`
`’!
`
` 1. Estimate the degree of polymerization of a polyethylene with an average
`molecular weight of 150,000. The molecular weight of an ethylene
`mono mer is 28.
` 2. What is the maximum possible separation between the ends of a poly-
`styrene molecule with a molecular weight of 160,000?
` 3. To enhance processability of a polymer, why would you want to decrease
`its molecular weight?
` 4. Why would an uncrosslinked polybutadiene flow at room temperature?
` 5. What role does the cooling rate play in the morphological structure of
`semi-crystalline polymers?
` 6. Explain how crosslinking between the molecules affect the molecular
`mobility and elasticity of elastomers.
` 7. Increasing the molecular weight of a polymer increases its strength and
`stiffness, as well as its viscosity. Is too high of a viscosity a limiting factor
`when increasing the strength by increasing the molecular weight? Why?
` 8. Given two polyethylene grades, one for extrusion and one for injection
`molding, which one should have the higher molecular weight? Why?
` 9. A fractional analysis of a commercial polypropylene sample has a distri-
`bution of chain lengths from which the following data is obtained:
`
`
`Table 3.7 Chain Length Distribution of a Commercial Polypropylene
`Degree of Polymerization
`Mole fraction
` 200
`0.08
` 400
`0.12
` 600
`0.15
` 900
`0.34
`1500
`0.16
`2000
`0.15
`
`What is the number-average molecular weight? What is the weight ave-
`rage molecular weight and what is the polydispersity index of the samp-
`le? Derive the equations that can also represent these molecular weights
`using the mole fraction (xi) and weight fraction (wi) of polymers with simi-
`lar molecular weight.
`10. Which broad class of thermoplastic polymers densifies the least during
`cooling and solidification from a melt state into a solid state? Why?
`11. What class of polymers would you probably use to manufacture frying
`pan handles? Even though most polymers could not actually be used for
`this particular application, what single property do all polymers exhibit
`that would be considered advantageous in this particular application.
`
`MacNeil Exhibit 2178
`Yita v. MacNeil IP, IPR2020-01139, Page 99
`
`

`

`’*
`
`3 Structure of Polymers
`
`12. In terms of recycling, which material is easier to handle, thermosets or
`thermoplastics? Why?
`13. Polymers are considered flammable materials. How can flammability of a
`polymer