Influence of Processing in Propeties
`322
`
`
`
`8 Solidification of Polymers 323
`
`—$4
`
`to a lower specific
`volume.
`the volume should jump
`of crystallization, ideally,
`a slow
`However even here, small amorphous regions
`remain which
`permit
`at absolute zero
`flow or material creep. This free volume reduces to
`nothing
`can no
`occur.
`at which heat transport
`temperature
`longer
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`material into a
`or rubberlike substance. Once the material has cooled
`leathery
`becomes stiff and
`the
`transition temperature, 7.,
`below the glass
`polymer
`the
`volume and enthalpy
`brittle. At the glass transition temperature,
`specific
`This can be seen for
`a
`curves
`in slope.
`significant change
`experience
`curve shown in
`8.1. With semi-
`in the enthalpy-temperature
`Fig.
`polystyrene
`near the melting
`at a
`crystallization temperature
`crystalline thermoplastics,
`arranging themselves in small crystalline and
`temperature, the molecules start
`a
`very complicated morphology. During the
`amorphous regions, creating
`structure formation, a
`quantum of energy, often called
`process of crystalline
`orheat
`is released and must be conducted out of the
`heat
`offusion,
`ofcrystallization
`can continue. The heat of fusion is reflected
`material before the cooling process
`curve as shown for polyamide 6.6,
`of the enthalpy-temperature
`in the shape
`in
`8.1. At the onset of crystalline growth,
`and polypropylene
`Fig.
`polyethylene
`are
`notbrittle, since the amorphous regions
`the material becomes rubbery yet
`transition temperature. As seenearlier, the
`transition
`still above the glass
`glass
`far below room
`some
`is
`for
`polymers
`semi-crystalline
`temperature
`For common
`than
`them
`amorphous polymers.
`temperature, making
`tougher
`can be between 30 and
`of
`semi-crystalline polymers, the degree
`crystallization
`and the rest remain
`70%. This means that 30-70%of the molecules form
`crystals
`in an
`is
`for those
`state. The degree
`of
`highest
`crystallization
`amorphous
`faster and more
`can
`materials with short molecules since
`crystallize
`they
`
`
`(J/g)
`
`840
`
`630
`
`easily.
`
`420
`
`2107
`
`0
`
`0
`
`_— i
`160
`
`!
`240
`
`80
`
`p=1 bar
`——
`320
`
` Enthalpy
`
`
`Figure 8.1.
`
`Enthalpy
`
` Temperature, T (°C)
`as a function of temperature for various thermoplastics.
`
`of a
`8.2 [1] shows the volumetric temperature dependence
`polymer.
`Figure
`in which molecules can move
`In the melt state, the chains have
`“empty spaces”
`as
`molecules canstill move as
`freely. Hence, undercooled
`space
`long
`polymer
`at which this free movement ends for a molecule or
`is available. The point
`or solidification
`transition
`segment of chains is called the
`temperature
`glass
`Fig. 8.2, the free volume is frozen-in as well. In the case
`outin
`As
`point.
`pointed
`
` T=0K
`
`T-.
`Tm
`Ty
`Thermal expansion modelfor thermoplastic polymers.
`
`8.2
`
`Tigure
`
`when
`
`even at the
`
`volume of a
`with pressure
`The
`glass
`polymer changes
`specific
`transition temperature. This is demonstrated for an
`amorphous thermoplastic
`8.3 and for a
`8.4.
`in
`in
`Fig.
`semi-crystalline thermoplastic
`Fig.
`It should be noted here that the size of the frozen-in free volume depends
`rates result in a
`on the rate at which a material is cooled; high cooling
`large
`this is very important. When the frozen-in free volume
`free volume. In
`practice
`rates lead to
`the part is less brittle. On the other hand, high cooling
`is
`large,
`or
`parts that are
`which may allow the diffusion of gases
`highly permeable,
`related to the
`rate is also directly
`container walls. The cooling
`liquids through
`rates can often
`of the final part. The effect of
`dimensional stability
`high cooling
`to a
`temperature that enables the molecules to
`be
`the part
`mitigated by heating
`move
`additional chain
`this will allow further
`folding.
`crystallization by
`freely;
`great effect on the structure and properties of the
`This process has a
`and
`crystals
`a
`referred to as
`is
`In
`this
`qualitative
`only signifies
`annealing.
`general,
`and warpage during
`polymerparts. It also affects
`improvement of
`shrinkage
`service life of a
`loaded.
`polymer component, especially when
`thermally
`All these aspects have a
`on
`For
`great impact
`processing.
`example,
`the material can be
`extruding amorphous thermoplastic profiles,
`sufficiently
`to carry its own
`cooled inside the dic so that the extrudate has enoughrigidity
`as it is
`with low
`pulled away from the die.
`Semi-crystalline polymers
`weight
`have a
`melting temperature that is too
`above the
`molecular weights
`viscosity
`low to be able to withstand their own
`as the extrudate exits the die.
`weight
`melting temperature, T,, however cannot be used due
`Temperatures below the
`are encountered in the
`to solidification inside the die. Similar
`problems
`
`
`
`MacNeil Exhibit 2117
`Yita v. MacNeil IP, IPR2020-01139
`Page 172
`
`MacNeil Exhibit 2117
`Yita v. MacNeil IP, IPR2020-01139
`Page 172
`
`

`

`Influence of Processing in Propeties
`324
`thermoforming process in which the material must be heated to a
`point so that
`it can be formed into its final shape, yet has to be able to withstand its own
`weight.
`
`> a1 >a2)sq
`(ag
`
`
`1
`
`
`
`SP OG|
`
`i—*ag2) 1
`|
`|_| Freezing line
`
`|
`
`
`
`Tao?
`
`Ts
`
`Tgo. Tg
`Temperature, T
`for amorphous thermoplastics.
`p-v-T diagram
`
`
`
`>
`
`ag1 >
`
`ag2)
`
`(agg
`
`Melt
`
`\Po
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Figure 8.3
`
`V
`volume,
`Specific
`
`Schematic of a
`
`V
`volume,
`Specific
`
`Figure 8.4
`
`Schematic of a
`
`
`
`
`
`
`
`
`
`
`
`
`
`8 Solidification of Polymers
`
`325
`
`the part; and since there is more
`be removed to
`longer
`shrinkage,
`solidify
`larger pressures must be employed. All this implies longer
`times and
`packing
`times and more
`rates
`during injection molding
`shrinkage. High cooling
`cycle
`will
`reduce the
`of
`of
`semi-crystalline polymers
`degree
`crystallization.
`molecules may lead to some
`state of the
`However, the
`amorphous
`polymer
`after the process, which will result in further shrinkage
`and
`crystallization
`common to follow the whole
`warpage of the final part. It is
`quite
`injection
`in
`molding process in the
`Figs. 8.3 and 8.4, and thus
`p-v-T diagrams presented
`how much the molded component has shrunk.
`predict
`
`8.1.2
`
`Structure
`
`Morphological
`is the order or
`structure. The
`arrangement of the
`possible
`Morphology
`polymer
`can
`“order” between a molecule or molecule segment and its
`vary
`neighbors
`structure to an
`from a
`very ordered
`amorphous
`highly crystalline polymeric
`a structure in greatest disorder or
`The
`possible range of
`structure
`random).
`(i.e.,
`a
`ontheleft side of
`8.5. For
`order and disorderis
`Fig.
`example,
`clearly depicted
`or
`is
`formed only by the
`purely amorphous polymer
`non-crystalline
`is formed
`chain structure, whereas the
`semi-crystalline polymer
`amorphous
`a combination of all the structures
`in
`8.5.
`Fig.
`represented
`of a
`structure as shownin the middle of
`The
`Fig. 8.5,
`image
`semi-crystalline
`with an electron microscope.
`can be
`A
`macroscopic structure, shown
`captured
`with an
`can
`in the
`the
`be
`right hand side of
`optical
`figure,
`captured
`capture the coarser macro-
`can
`An
`microscope.
`optical microscope
`structure such as the
`in
`spherulites
`semi-crystalline polymers.
`morphological
`
`by
`
`ia
`—
`ca. 0.01-0.02 tm
`Charafteristic
`
`\
`
`Ny
`4
`
`Texture
`= >
`W (W)
`ieaind
`rags
` coe
`oe
`Ue
`ie
`/Semi-crystalline Inhomogeneous semi-
`/ structure
`crystalline structure
`|
`Ss
`characteristic size
`Bevan
`1-2 im
`stp
`Schematic diagram of possible molecular structure which occur in
`thermoplastic polymers.
`
`Amorphous
`
`/
`
`Figure 8.5
`
`is defined as
`An
`amorphous polymer
`purely
`having
`quite clear if a
`Howeverit is not
`“purely amorphous” polymer
`Electron microscopic observations have shown
`amorphous polymers
`
`random structure.
`as such exists.
`that are
`
`a
`
`MacNeil Exhibit 2117
`Yita v. MacNeil IP, IPR2020-01139
`Page 173
`
`'
`
` be
`
`T20°
`
`Tmo Tm1
`Temperature, T
`for semi-crystalline thermoplastics.
`p-v-T diagram
`
`Ts
`
`are also at a
`Semi-crystalline polymers
`molding process. Because of the heat needed for
`
`in the injection
`disadvantage
`more heat must
`crystallization,
`
`MacNeil Exhibit 2117
`Yita v. MacNeil IP, IPR2020-01139
`Page 173
`
`

`

`
`|
`
`
`
`8 Solidification of Polymers
`
`327
`
`
`
` 326
`Influence of Processing in Propeties
`composedof relatively stiff chains, show a certain degree of macromolecular
`
`
`or fibrilitic structures.
`structure and order, for example, globular regions
`
`
`
`arestill found to be
`Nevertheless, these types of
`optically
`amorphous polymers
`
`
`with soft and flexible macromolecules, such as
`Even
`isotropic.
`polymers
`
`
`which wasfirst considered to be random, sometimes show band-
`polyisoprene
`
`
`These bundle-like structures are
`weak and
`like and
`relatively
`globular regions.
`
`
`stresses. The shear thinning viscosity
`short-lived when the material
`experiences
`
`is attributed to the
`sometimes
`of
`such
`
`effect of
`breaking
`polymers
`
`macromolecular structures.
`
`8.1.3
`Crystallization
`
`spheru-
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Figure 8.7
`
`Developmentof the spherulitic
`taken at 30 s intervals.
`
`structure in
`
`polypropylene. Images
`
`were
`
`The crystallization fraction can be described by the Avrami equation [5],
`written as follows:
`
`
`Yita v. MacNeil IP, IPR2020-01139
`Page 174
`
`the
`on, before the existence of macromolecules had been
`recognized,
`Early
`Such structures
`structures had been
`presence of
`suspected.
`highly crystalline
`or when
`were discovered when
`cellulose and natural
`stretching
`undercooling
`it was found that a
`order also existed in
`rubber. Later,
`synthetic
`crystalline
`macromolecular materials such as
`and
`polyvinyls.
`polyamides, polyethylenes,
`a 100% degree
`of
`Because of the
`of macromolecular materials,
`polymolecularity
`are referred to as
`cannot be achieved. Hence, these polymers
`crystallization
`structures are
`It is common to assumethat the
`semi-crystalline
`semi-crystalline.
`random or
`or
`connected by
`small
`of alignment
`formed
`crystallites
`regions
`by
`molecules.
`amorphous polymer
`With the use of electron microscopes
`and
`sophisticated optical microscopes
`can be
`structures are now well recognized. They
`the various
`existing crystalline
`listed as follows:
`*
`
`These can form in solutions and
`of
`in the
`study
`help
`Single crystals.
`and sometimes whiskers are
`formation. Here, plate-like crystals
`crystal
`generated.
`
`Spherulites.
`spherulites
`of a
`spherulitic
`in a
`polypropylene
`
`As a
`melt solidifies, several folded chain lamellae
`polymer
`form which are
`up to 0.1 mm in diameter. A
`typical example
`structure is shownin
`8.6 [2]. The
`Fig.
`spherulitic growth
`melt is shownin
`8.7 [3].
`Fig.
`If a
`
`is deformed while
`semi-crystalline polymer
`Deformed crystals.
`oriented lamellae form instead of
`undergoing crystallization,
`lites.
`spherulitic crystals, which are formed by
`Shish-kebab. In addition to
`and ribbonlike structures, there are also shish-kebab, crystals
`plate-
`which are formed by
`and whiskers. Shish-kebab structures
`circular
`plates
`a shear deformation during
`are
`when the melt
`undergoes
`generated
`of a shish-kebab
`is shown in Fig.
`solidification. A
`crystal
`typical example
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`8.8 [4].
` MacNeil Exhibit 2117
`
`MacNeil Exhibit 2117
`Yita v. MacNeil IP, IPR2020-01139
`Page 174
`
`

`

`
`
`
`328
`
`Influence of Processing in Propeties
`
`8 Solidification of Polymers
`
`329
`
`|
`
`x{t)=
`
`x,(1
`
`"|
`
`(8.2)
`
`Degree of
`
`Table 8.1 Maximum
`Crystalline Growth Rate and Maximum
`Crystallinity for Various
`Thermoplastics
`
`(min)
`80
`>1000
`Polyethylene
`Polyamide 66
`1000
`70
`Polyamide 6
`200
`35
`Isotactic polypropylene
`20
`63
`7
`50
`Polyethylene terephthalate
`Isotactic polystyrene
`0.30
`32
`0.01
`25
`Polycarbonate
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`(8.1)
`x(t)=1-e*"
`
`rate
`and temperature dependentcrystallization
`where Z isa molecular weight
`and n the Avrami exponent. However, since a
`cannot reach 100%
`polymer
`
`the maximum
`should be
`the above equation
`multiplied by
`crystallization
`
`of
`x,.
`possible degree
`crystallization,
`-
`
`
`
`
`
`
`
`
`
`
`
`
`
`i) ~—
`
`Folded-chain
`lamella
`
`8.1.4 Heat Transfer
`
`Solidification
`
`During
`are
`can be
`Since
`generally thin, the energy equation!
`polymer parts
`simplified
`to a one-dimensional
`problem. Thus, using the coordinate description
`shown in
`can be reduced to
`8.9 the energy equation
`Fig.
`
`Soliditied layer
`
`
`
`
`
`
`
`
`
`
`diagram of polymer melt inside an
`Figure 8.9
`Schematic
`injection mold.
`
`The energy equation is discussed in Chapter 3 and can be found in its complete form in Appendix A.
`
`
`_
`~
`
`Cooling
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`MacNeil Exhibit 2117
`Yita v. MacNeil IP, IPR2020-01139
`Page 175
`
` Figure 8.8 Model of the shish-kebab morphology.
`
`
`
`
` 1
`
`onthe typeof
`The Avrami exponent, n, ranges between 1 and 4
`depending
`the Avrami exponent for spherulitic
`For example,
`nucleation and growth.
`fromsporadic nuclei is around 4, disclike growth 3, and rodlike growth
`growth
`is activated from instantaneous nuclei, the Avrami exponentis
`2. If the
`growth
`lowered by 1.0 for all cases. The crystalline growth
`rate of various
`polymers
`from one to another. This is demonstrated in Table 8.1
`differ
`significantly
`rate for various thermoplastics. The
`which shows the maximum
`growth
`with a differential
`mass fraction can be measured experimentally
`crystalline
`scanning calorimeter
`(DSC).
`and structure
`A more
`in-depth coverage of crystallization
`Eder and Janeschitz-Krieg][7].
`is
`during processing
`given by
`
`development
`
`
`
`lines
`
`
`MacNeil Exhibit 2117
`Yita v. MacNeil IP, IPR2020-01139
`Page 175
`
`

`

`Influence of Processing in Propetiesce
`330
`
`=
`I ,FT
`as
`C,—
`k—>
`PCy
`Another assumption— and to reduce warpage, usually
`condition:
`symmetry boundary
`
`a
`
`(8.3)
`8.3
`
`is a
`
`requirement—
`
`420
`
`400
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`at z=0
`
`Ho
`az
`If the sheet is cooled via forced convection or the part is inside a
`perfectly
`can be assumed to be the second
`cooled mold, the final temperature of the part
`condition:
`boundary
`
`(8.4)
`
`(8.5)
`
`T=T,
`for a
`its
`A
`properties presented
`polystyrene plate,
`typical temperature history
`8.10. Once the material's temperature drops
`in Table 8.2 [8], is shown in Fig.
`it can be considered solidified. This
`below the
`transition temperature, T,,
`glass
`of the
`in Fig. 8.11. Of importance here is the position
`is shown schematically
`the plate's
`Once the solidification front equals
`solidification front, X(t).
`8.10 it can be
`From
`dimension L, the solidification process is complete.
`Fig.
`shown that the rate of solidification decreases as the solidified front moves
`amorphous thermoplastics, the well-
`further away from the cooled surface. For
`or
`known Neumann solution can be used to estimate the
`of the
`glassy
`growth
`The Neumann solution is written as
`solidified layer.
`
`X(t) «Jar
`
`(8.6)
`
`Figure 8.10
`
`Table 8.2
`
`Material Properties for Polystyrene
`=
`K
`0.117 W/mK
`1185J/keK
`1040
`
`Cp
`p
`
`=
`
`=
`
`=
`
`kg/m?
`80°C
`
`Tg
`=
`E
`=
`Vv
`0.33
`EEE
`
`3.2E9 Pa
`
`Figure 8.11
`
`
`
`polymerplate.
`
`MacNeil Exhibit 2117
`Yita v. MacNeil IP, IPR2020-01139
`Page 176
`
`-
`
`-
`
`-
`
`on
`= 380
`©
`o
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`a
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`
`8 Solidification of Polymers
`
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`Z (mm)
`0.0
`Temperature history of polystyrene
`
`5.0
`cooled inside a 5 mm thick mold.
`
`320
`
`- ry
` Schematic diagram of the cooling process of a
`
`MacNeil Exhibit 2117
`Yita v. MacNeil IP, IPR2020-01139
`Page 176
`
`

`

`
`
`
`8 Solidification of Polymers
`
`333
`
`500
`
`480
`
`460
`
`440
`
`420
`
`400
`
`380
`
`ge0
`
`340
`
`4K
`
`—-A— t=12.5s
`
`—@ (= 25.08
`_-O— t= 50.0s
`EF t=213s
`
`(K)
`
`Temperature
`
`Z (mm)
`Temperature history of polypropylene cooled inside a 5 mm thick mold.
`
`:
`ae
`
`8.12
`
`Figure
`
`1800J/kgK
`
`4
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Influence of Processing in Propeties
`332
`
`out here
`It must be
`where a is the thermal diffusivity
`of the polymer.
`pointed
`is infinite
`that for the Neumann solution, the growthrate of the solidified layer
`as time goes to zero.
`materials is a bit more
`The solidification process in a
`semi-crystalline
`due to the heat of fusion or heat of crystallization,
`nucleation rate,
`complicated
`a
`etc. When measuring the specific heat as the material crystallizes,
`which
`peak
`represents the heat of fusion is detected (see Fig. 4.12). Figure 8.12 shows the
`calculated temperature distribution in a
`semi-crystalline polypropylene plate
`used for the calculations are shown in
`during cooling. The material properties
`is below the
`the material
`that
`Table 8.3 [8]. Here,
`melting temperature,
`has demonstrated
`evidence [9]
`is
`solid2?. Experimental
`considered
`T,,
`is
`in
`rate of the
`that the
`semi-crystalline polymers
`crystallized layer
`growth
`the nucleation occurs
`due to thefact that at the
`finite. This is
`beginning
`mainly
`Eq. 8.6 as well as the
`in
`ata finite rate. Hence, the Neumann solution
`presented
`widely used Stefan condition [10], do not hold for
`semi-crystalline polymers.
`measuredthickness
`demonstrated in Fig. 8.13 [10] which presents
`This is
`clearly
`as a function of time for
`of crystallized layers
`polypropylene plates quenched
`on this important topic the
`at three different temperatures. For further reading
`to consult the literature [11, 12].
`reader is
`encouraged
`
`Table 8.3
`
`Material Properties for Polypropylene
`=
`0.117 W/mK
`K
`
`solid
`
`melt
`
`Cp,
`
`Cp,
`
`0
`
`=
`
`=
`
`=
`
`=
`
`2300J/kgK
`930
`
`kg/m?
`-18°C
`
`Tg
`186°C
`Tm
`=
`209 kJ/kg
`a»
`
`=
`
`
`
`
`
`
`
`2
`
`is maximal
`[tis well-knownthat the growth of the crystalline layer in semi-crystalline polymers
`somewhat belowthe melting ternperature, ata temperature Te. The growth speed of nuclei is zero at
`the melting temperature and at the glass transition temperature.
`
`300 0.0
`
`
`
`
`
`
`100 9G
`=
`
`°
`
`z
`
`cm
`ey
`
`3
`
`2P
`
`ae
`
`;
`
`.
`
`/
`!
`4
`
`0
`
`Oo
`
`i
`5
`
`|
`
`10
`
`120 °C
`
`15
`
`(ta/D2)
`as a function of
`Figure 8.13 Dimensionless thickness of the crystallized layers
`dimensionless time for various temperatures of the quenching surface.
`
`t’
`
`MacNeil Exhibit 2117
`Yita v. MacNeil IP, IPR2020-01139
`Page 177
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`MacNeil Exhibit 2117
`Yita v. MacNeil IP, IPR2020-01139
`Page 177
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`
`Influence of Processing in Propeties
`334
`
`
`
`8 Solidification of Polymers 335
`
`8.2
`
`Solidification of Thermosets
`
`thermosets, such as
`unsaturated
`The solidification process of
`phenolics,
`an exothermic
`is dominated by
`polyesters, epoxy resins, and polyurethanes
`reaction is an irreversible
`reaction. A curing
`chemical reaction called curing
`process that results in a structure of molecules that are more or less cross-
`linked. Some thermosets cure under heat and others cure at room
`temperature.
`are those for which the reaction
`Thermosets that cure at room
`temperature
`is usually
`where the mixing
`two components,
`starts
`immediately after mixing
`part of the process. However, even with these thermosets,
`the reaction is
`the chemical reaction, or the exotheri.
`accelerated by the heat released during
`of
`to activate
`it
`is also
`In addition,
`cross-linking by absorption
`possible
`moisture or radiation, such as
`ultra-violet, electron beam, and laser energy
`sources
`[13].
`
`thermosets are often grouped into three distinct categories,
`In
`processing,
`a
`a /ieat activated cwre, those that are dominated by
`namely those that undergo
`activated cure, and those which are activated by
`the absorption of
`mixing
`or radiation. Examples of heat activated thermosets are
`phenolics;
`humidity
`activated cure are epoxy resins and polyurethane.
`of
`examples
`mixing
`
`Reaction
`
`Examples
`
`of addition
`
`polymerization
`
`are
`
`is water.
`making phenolics
`and epoxies.
`polyurethanes
`reaction of a thermoset by free
`of a
`radical reaction
`An
`example
`cross-linking
`is the co-polymerization of unsaturated polyester with styrene molecules,
`8.14. The molecules contain several carbon-carbon double bonds
`shownin
`Fig.
`which act as
`An
`sites
`of the
`during curing.
`example
`cross-linking
`network after the chemical reaction is shownin
`8.15.
`Fig.
`GOO-CH2-GHp-O0C
`
`resulting
`
`006
`cei a
`COO....
`ae
`COO-CHy-CH,-O0G
`ee
`Polyester
`
`+n+[CHp=CH]
`\
`
`
`O
`Styrene
`
`Polyester
`
` Figure 8.14
`
`Symbolic and schematic representations of uncured unsaturated
`polyester.
`
`Ou
`CH
`CH
`—CH
`eeeeee
`f \-CH
`GH,
`oH,
`|
`du
`€\-cH
`
`Ots
`OOHeeCOC
`CHp
`Orch
`Hot
`CH
`GH
`
`:
`
`8.2.1 Curing
`short groups that are
`In a cured thermoset, the molecules are
`formed by
`rigid,
`reacted or solidified
`connected by randomly distributed links. The
`fully
`does not react to heat as observed with thermoplastic
`thermosetting polymer
`A thermoset may soften somewhat upon heating and but
`then
`polymers.
`a thermoset
`high temperatures. Due to the high cross-link density,
`at
`degrades
`component behaves as an elastic material over a
`large range of temperatures.
`1 to 3%, The most
`strains of usually
`it
`is brittle with
`However,
`breaking
`one of the most
`rigid thermosets, whichconsists
`common
`is
`phenolic,
`example
`it stiff
`aromatic rings that
`of carbon atoms with large
`impede motion, making
`is given in Figs. 3.22 and
`structure after cross-linking
`and brittle. Its general
`3.23.
`‘Thermosets can be broken down into three categories:
`addition
`cure via condensation polymerization,
`those that undergo
`those that cure via
`radiacal
`free
`polymerization.
`is defined as the
`growth process that results
`Condensation polymerization
`from combining two or more monomers with reactive
`end-groups, and leads
`alcohol, water, an acid, etc. A common thermoset that
`by-products such as an
`to
`or
`solidifies via
`condensation polymerization
`is phenol
`polymerizes
`of the reaction when
`3. The by-product
`formaldehyde, discussed in Chapter
`
`thermosets which
`polymerization and
`
`
`
`
`«GH-GH-COO-CHy-CHp-OOC-CH-CH
`On
`O-te
`CHo
`Symbolic and schematic representations of cured unsaturated
`
`LOD
`
`CHp Figure 8.15
`
`polyester.
`
`MacNeil Exhibit 2117
`Yita v. MacNeil IP, IPR2020-01139
`Page 178
`
`MacNeil Exhibit 2117
`Yita v. MacNeil IP, IPR2020-01139
`Page 178
`
`

`

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`
`
`Influence of Processing in Propeties
`336
`
`8.2.2 Cure Kinetics
`
`thermosets can be
`into two
`As discussed earlier, in
`general
`grouped
`processing
`heat activated cure and mixing activated cure thermosets. However, no
`categories:
`its curing reaction can be
`a thermoset belongs to,
`matter which category
`A and B
`the reaction between two chemical groups denoted by
`described by
`chain. The reaction can be followed by
`which link two segments of a
`polymer
`or
`the concentration of unreacted As or Bs, C,
`If the initial
`C,.
`tracing
`degree of cure can be
`concentration of As and Bs is defined as
`the
`and
`C,
`C,,,
`described
`by
`
`8.7)
`
`Ao
`zero when there has been no
`of cure or conversion, C’, equals
`The
`degree
`one when all As have reacted and the reaction is
`reaction and
`complete.
`equals
`to monitor reacted and unreacted As and Bs
`However, it is
`during
`impossible
`reaction of a thermoset polymer.
`that the
`is known
`It
`the
`though
`curing
`can be used to monitor the conversion,
`exothermic heat released
`during curing
`in a
`are
`of an unreacted thermoset
`Cc’. When small samples
`placed
`polymer
`differential scanning calorimeter (DSC), each at a different temperature, every
`will release the same amount of heat, Q,. This occurs because every
`sample
`a reaction releases a small amountof energy in
`that occurs
`during
`cross-linking
`8.16 [14] showsthe heat rate released
`the form of heat. For
`during
`example, Fig.
`isothermal cure of a
`ester at various temperatures.
`vinyl
`of cure can be defined by
`relation
`the following
`»
`=
`Q
`0,
`
`The
`
`degree
`
`@
`
`(8.8)
`8.8
`
`
`
`where Q is the heat released up to an
`
`arbitrary
`
`time t, and is defined by
`
`O=
`
`[Oat
`
`89)
`
`fitted to
`models that accurately describe
`DSC data is
`empirical
`commonly
`the
`reaction. Hence, the rate of cure can be described by
`the exotherm, @,
`curing
`as
`andthetotal heat released
`the
`curing reaction, Q,,
`during
`
`ac 2
`dt
`Q,
`
`(8.10)
`
`
`
`8 Solidification of Polymers 337
`
`
`
`8.10, it is now
`With the use of Eq.
`easy to take the DSC data and find the
`reaction.
`models that describe the curing
`
`flowJ/{sg)
`Heat
`
`Figure 8.16 DSC scans of the isothermal curing reaction of
`temperatures.
`
`vinyl
`
`ester at various
`
` Time (minutes)
`
`
`
`
`viscous
`
`During cure, thermoset resins exhibit three distinct phases;
`liquid,
`in the
`and solid. Each of these three stages is marked
`dramatic
`by
`changes
`gel,
`thermomechanical properties of the resin. The transformation of a reactive
`to a
`two distinct
`solid
`involves
`thermosetting liquid
`glassy
`generally
`and vitrification. Molecular
`transitions: molecular
`macroscopic
`gelation
`is defined as the time or
`at which covalent bonds connect
`temperature
`gelation
`across the resin to form a three-dimensional network which
`rise to
`gives
`long
`range elastic behavior in the macroscopic fluid. This point is also referred to as
`=
`As a
`the
`resin cures, the
`gel point, where C’
`thermosetting
`cross-linking
`C,.
`to a rise in the
`to hinder molecular movement, leading
`transition
`begins
`glass
`nears the processing temperature, the rate of
`temperature. Eventually, when
`T,
`dominated
`diffusion. At this point
`curing reduces
`significantly, eventually
`by
`the resin has reached its vitrification point. Figure 8.17, which presents degree
`of cure as a function of time, illustrates how an
`epoxyresin reaches a maximum
`of cure at various
`at
`processing temperatures. The resin
`degree
`processed
`cure
`200 °C reaches 100% cure since the
`transition temperature of
`glass
`fully
`epoxy is 190 °C, less than the processing temperature.
`On the other hand, the
`sample processed at 180 °C reaches 97% cure and the one
`at 160 °C
`processed
`only reaches 87% cure.
`
`MacNeil Exhibit 2117
`Yita v. MacNeil IP, IPR2020-01139
`Page 179
`
`MacNeil Exhibit 2117
`Yita v. MacNeil IP, IPR2020-01139
`Page 179
`
`

`

`Influence of Processing in Propeties
`338
`
`
`
`8 Solidification of Polymers
`
`339
`
`
`
`Ct=C1
`
`C*=Co
`
`C*=1
`
`Gel
`
`glass
`
`7
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`c[%]
`ofcure,
`Degree
`
`100
`90
`
`80
`
`70
`60
`
`50
`
`40
`
`30
`
`20
`40
`
`8.17
`
`Figure
`
`© 200 [°C] 0
`
`20
`
`40
`
`60
`Time, t [min]
`Degree of cure as a function time for an epoxy resin measured using
`isothermal DSC.
`
`80
`
`100
`
`120
`
`9160 [°C]
`A180 [°C]
`
`reaction is accelerated as
`8.16 and 8.17 also illustrate how the
`curing
`Figures
`processing temperature is increased. The curing reaction of
`cured
`the
`thermally
`thus the blend can be stored in a
`resins is not
`thermoset
`immediate,
`for a short
`of time without having any significant curing
`period
`
`with the
`
`refrigerator
`reaction.
`resins can be
`The behavior of curing thermosetting
`represented
`cure
`diagram developed
`generalized time-temperature-transformation (ITT)
`Enns and Gillham [16]; it can be used to relate the material properties of
`by
`as shown in
`thermosets as a function of time and the processing temperature
`Fig. 8.18.
`
`
`
`eel En aa:
`
`ff
`WL.
`nk
`YY
`YH
`EER SS
`Sac
`—
`CO
`7
`
`
`a FIT EEE EEEEEETEES
`
`5,~Vitrification tine
`
`Tprocess
`
`Temperature
`
`+woaa
`
`4aoa
`
`tg
`Figure 8.18 Time-temperature-transformation (TTT) diagram
`
`log (time)
`
`for a thermoset
`
`
`Solid glass tgel
`
`of cure.
`constant
`The diagram presents various lines that represent
`degrees
`The curve labeled
`gel point and C” =1 the fully cured
`C=C, represents the
`resin. Both curves have their
`transition temperatures, T,,
`corresponding glass
`cured resin andatits
`transition temperature of the
`for the
`and
`fully
`glass
`T,
`transition temperature of the uncured resin,
`The
`gel point, respectively.
`glass
`are also
`and an
`curve labeled “vitrification line,”
`The
`depicted.
`S-shaped
`To,
`transition temperature
`vitrification line represents the
`wherethe
`boundary
`glass
`becomes the processing temperature. Hence, to the left of the vitrification curve
`a
`very slow diffusion process. The TTT-
`the curing process is controlled by
`diagram showsan
`arbitrary process temperature. The material
`being processed
`at
`and the vitrification line at
`reaches the
`r=1r,. At this
`gel point
`t=t,,,
`point
`the material has reached a
`of cure of C, and glass
`transition temperature
`degree
`processing temperature. The material continues to
`of the resin is
`to the
`equal
`cure
`very slowly (diffusion controlled) until it reaches a
`of cure
`just
`degree
`below C,, There are also various regions labeled in the diagram. The one
`labeled “viscous liquid” is the one wherethe resin is found from the
`beginning
`of
`has been reached. The flow and deformation
`processing until the gel point
`occurs
`must occur within this region. The
`or
`during processing
`shaping
`that
`since at
`Tegion labeled “char” must be avoided during processing,
`high
`
`MacNeil Exhibit 2117
`Yita v. MacNeil IP, IPR2020-01139
`Page 180
`
`
`
`
`MacNeil Exhibit 2117
`Yita v. MacNeil IP, IPR2020-01139
`Page 180
`
`

`

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`
`Influence of Processing in Propeties
`340
`
`polymer
`
`will eventually undergo
`
`thermal
`
`processing temperatures the
`degradation.
`resins
`kinetics of thermosetting
`The model that best represents the curing
`is a diffusion modified Kamal-Sourour reaction
`as reflected in a
`TTT-diagram
`the model can be
`cure
`[17, 18, 19]. To model
`model
`kinetics,
`as
`
`applied
`
`autocatalytic
`
`dc
`
`»)
`
`a leeecyi-cy
`where m and n are reaction orders, and k, and k,
`
`are constants defined by
`
`oe
`k
`ky
`Ke
`4
`are Arrhenius overall rate constants defined
`yA
`ki =ae
`
`by
`
`Here, k
`
`and
`
`(11)
`
`(8.12)
`
`(8.13)
`
`ki Jae?
`(8.14)
`where a, and a, are
`fitting parameters, E, and £,, activation energies and R
`8.12 is the diffusion rate constant
`the ideal gas constant. The constant
`k, in
`Eq.
`defined as
`
`Abn
`Hips’
`“"e”?
`
`kp =Gye
`(8.15)
`where a, and b are
`adjustable parameters, E, is the activation energy of the
`diffusion process, and f is the equilibrium fractional free volume given by
`-
`=
`+ 0.025
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`f
`
`7, )
`
`(8.16)
`
`0.00048(7
`cure.
`transition temperature during
`is
`the instantaneous
`where
`glass
`T,
`at one extreme
`Equation (8.12) showsthat the overall rate constant is
`governed
`which is the case
`to
`the Arrhenius rate constant when k, >>k*,
`prior
`by
`the diffusion rate constant when
`the other extreme
`vitrification, and at
`by
`a
`<<
`ki, which is the case well after vitrification. For a
`system exhibiting
`k,
`one-to-one
`between the
`transition temperature and
`relationship
`glass
`unique
`conversion, DiBenedetto’s equation [20] is one of the easiest
`for
`approaches
`a
`stoichiometric ratios to express this relationship using only
`single parameter
`as
`
`8 Solidification of Polymers
`341
`
`=
`
`fs
`T.=T +
`
`Tyo
`Aust
`AC”
`(Ty)
`1-1- AC
`sy
`
`is the
`transition temperature of the uncured resin, T,,
`is the
`where T,,
`glass
`reacted network, and A is a structure
`transition temperature of the
`fully
`glass
`to
`dependent parameter theoretically equated
`A=
`AC
`pl
`Te
`are the differences in the heat capacity between
`The values of
`and
`AC,,
`AC,,
`state for the uncured resin and the fully cured network,
`and
`the glassy
`rubbery
`However the parameter A can also be usedas
`fitting parameter.
`respectively.
`Mixing activated cure materials such as
`start
`will instantly
`polyurethanes
`exothermic heat after the mixture of its two
`components has occurred.
`releasing
`fits this behavior andis
`model
`Castro-Macosko curing
`The proposed
`accurately
`written as
`[15]
`=
`
`6.17)
`8.1
`
`(8.18)
`
`(8.19)
`
`ke*(1-CY
`
`ac
`
`Cure
`
`8.2.3 Heat Transfer During
`is that the thermal and
`in thick section components
`A well-known problem
`become more
`and difficult to
`since the
`analyze
`curing gradients
`complicated
`on both the
`curing behavior of the part is
`temperature and
`highly dependent
`mold temperature and part geometry [21, 22]. A thicker part will result in
`cure distribution during processing.
`higher temperatures and a more
`complex
`concern
`becomes a
`the manufacture of thick
`This
`major
`during
`phenomenon
`high temperatures may lead to thermal degradation.
`A
`components since
`relatively easy way to check temperatures that arise
`and
`during molding
`a one-dimensional form of
`or
`times is desired. For
`curing
`demolding
`example,
`the energy equation that includes the exothermic energy generated during
`can be solved:
`curing
`
`+ pQ
`
`k
`rfapc, a
`mc
`
`(8.20)
`
`is confined between two mold halves at
`the material
`equal
`Assuming
`temperatures, the use of a
`condition at the center of the
`partis valid:
`
`symmetric boundary
`
`MacNeil Exhibit 2117
`Yita v. MacNeil IP, IPR2020-01139
`Page 181
`
`MacNeil Exhibit 2117
`Yita v. MacNeil IP, IPR2020-01139
`Page 181
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`

`

`Influence of Processing in Propeties
`342
`
`
`
`8 Solidification of Polymers 343
`
`
`
`f
`
`Mold
`temperature
`100s
`
`~
`
`200
`
`160}
`
`120
`
`aoo
`
`S
`oO
`7=
`£
`a
`
`5
`
`40 0
`
`4
`2
`3
`1
`Distance from midplane (mm)
`Temperature profile history of a 10 mm thick SMCplate.
`
`5
`
`Figure 8.19
`
`140 5
`120s
`
`100
`
`80}
`
`= 60.
`
`
`
`|
`|
`1]
`
`}
`
`
`
`
`.
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`|
`
`d
`
`of
`“=0 at z=0
`Oo
`
`m
`T=T,
`
`(8.21)
`
`(8.22)
`
`at the mold wall.
`With the useof the finite difference technique and a six constant model that
`of
`8.20-8.22 for the
`Barone and Caulk [23] solved
`represents dC”/dt,
`curing
`Eqs.
`The SMC was
`composed of an unsaturated
`sheet
`molding compound (SMC).
`fiber
`resin with 40.7% calcium carbonate and 30% glass
`by weight.
`polyester
`of cure
`and
`8.19 and 8.20 show
`temperature
`deg