Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in...
Transcript of Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in...
![Page 1: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/1.jpg)
2.882
Chapter 8 of ComplexityReduction of Complexity in Materials through
Functional Periodicity
![Page 2: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/2.jpg)
Functional Periodicity related to materials found in Nature
• Periodic Table of chemical elements• Crystalline solids
• Atomic structure (electrons in valence bands)• Biological systems
![Page 3: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/3.jpg)
Engineered Materials
• Functional Periodicity to to prevent unstable crack growth
•Wire rope
•Fabric•Composites
![Page 4: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/4.jpg)
Crack Growth
• Unstable crack growth
k1 = σ 22∞ c
Figure removed for copyright reasons.See Figure 8.1 in [Complexity]: Suh, N. P. Complexity: Theory and Applications. New York, NY: Oxford University Press, 2005. ISBN: 0195178769.
![Page 5: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/5.jpg)
Crack Growth• Fatigue crack growth under cyclic loading
dcdN
= A∆k1σ Y
⎛
⎝ ⎜
⎞
⎠ ⎟ n
Figure removed for copyright reasons.See Figure 8.2 in [Complexity].
![Page 6: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/6.jpg)
Composites•
Figure removed for copyright reasons.See Figure 8.3 in [Complexity].
![Page 7: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/7.jpg)
Functional Periodicity for Control of Material Properties
•
Edge and Screw Dislocations
Figure removed for copyright reasons.See Figure 8.4 in [Complexity].
![Page 8: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/8.jpg)
Functional Periodicity for Control of Material Properties
•
Stress-Strain Relationship showing work-hardening
Figure removed for copyright reasons.See Figure 8.5 in [Complexity].
![Page 9: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/9.jpg)
Functional Periodicity for Control of Material Properties
•
Annealing to eliminate dislocations
Figure removed for copyright reasons.See Figure 8.6 in [Complexity].
![Page 10: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/10.jpg)
Functional Periodicity for Control of Material Properties•
Wire Drawing
Figure removed for copyright reasons.See Figure 8.7 in [Complexity].
![Page 11: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/11.jpg)
Microcellular Plastics(Distortion of injection molded parts)
![Page 12: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/12.jpg)
Request of Our Research SponsorEastman Kodak (Gordon Brown)
• Provide a means of reducing the consumption of plastics
– Maintaining the same toughness of plastics and the same geometric shape
![Page 13: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/13.jpg)
The “customer needs” may be stated in terms of the following FRs and Cs:
Functional Requirements:FR1 = Reduce consumption of plasticsFR2 = Maintain the toughness of parts
Constraint:The shape of products must remain the same.
![Page 14: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/14.jpg)
Design of Microcellular Plastics
The highest level FRs
FR1 = Reduce the amount of plastic used FR2 = Increase the toughness of the plastic
productFR3 = Make three-dimensional geometrical
shape
![Page 15: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/15.jpg)
Design of Microcellular Plastics
Conceptual Solution
A large number of microscale bubbles
![Page 16: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/16.jpg)
Design of Microcellular PlasticsThe highest level FRs
FR1 = Reduce the amount of plastic used FR2 = Increase the toughness of the plastic
productFR3 = Make three-dimensional geometrical
shape
The corresponding highest level design parameters (DPs) are:
DP1 = Number of cells DP2 = Cell sizeDP3 = Die or mold design
![Page 17: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/17.jpg)
Design of Microcellular Plastics
The design equation for the product:
FR1FR2FR3
⎧
⎨ ⎪
⎩ ⎪
⎫
⎬ ⎪
⎭ ⎪ =
XX00 X000X
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥
DP1DP2DP3
⎧
⎨ ⎪
⎩ ⎪
⎫
⎬ ⎪
⎭ ⎪
![Page 18: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/18.jpg)
What is a Microcellular Plastic?
Microcellular Plastics (MCP) is defined as the plastic that has a large number of small bubbles, typically less than 30
microns.
![Page 19: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/19.jpg)
What is a Microcellular Plastic?
Cell Size (µm) Cell Density (Cells/ cm3)0.1 1015
1 1012
10 109
![Page 20: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/20.jpg)
Morphology of MuCell
Photo removed for copyright reasons.
![Page 21: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/21.jpg)
Polystyrene Products
Photo removed for copyright reasons.
![Page 22: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/22.jpg)
PP Products
Photo removed for copyright reasons.
![Page 23: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/23.jpg)
Photo removed for copyright reasons.
PVC profiles
![Page 24: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/24.jpg)
Injection Molded Printer Chassis
Photo removed for copyright reasons.
![Page 25: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/25.jpg)
Injection Molding of Microcellular Plastics vs Solid Plastics
TRW -- Air bag Canister (Material: 33% glass filled Nylon)
Solid MuCell % red.Part weight 365 gms 252 gms 31%Cycle time 45 sec 35 sec 22%Tonnage 150 tons 15 tons 90%
» (Courtesy of Mar Lee Companies)
![Page 26: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/26.jpg)
Advantages of Microcellular Plastics
• Reduction of material consumption (from 5 to 95 %)
• Faster cycle time• Higher productivity• Greater toughness in some plastics• Dimensional accuracy• Dimensional stability• No warping
![Page 27: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/27.jpg)
Advantages of Microcellular Plastics
• Appearance (no visible cells)• Thin sections• No sink marks• Low temperature process• Low pressure process• Large number of cavities or smaller machines• Most polymers
![Page 28: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/28.jpg)
Advantages of Microcellular Plastics
• Use of non-hydrocarbon solvents -- CO2 and N2
• No additives for nucleation• No reactive components such as viscosity
modifiers• No special equipment other than gas supply
system -- similar conventional machines
![Page 29: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/29.jpg)
Question: What is the physical basis for MuCell technology?
Simultaneous nucleation of an extremely large number of cells!!
![Page 30: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/30.jpg)
How do we achieve the simultaneous nucleation of an
extremely large number of cells?
![Page 31: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/31.jpg)
Design of the Process Technique for Microcellular Plastics
(The first student to work on the batch process --Jane Martini, SM Thesis, MIT)
The processing technique consists of dissolving a large amount of gas to form
polymer/gas solutionand then inducing suddenthermodynamic instability
by either lowering the pressure or raising the temperature to change the solubility of the gas.
![Page 32: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/32.jpg)
Sudden Change in Solubility
• The solubility is a function of two thermodynamic properties, temperature and pressure:
S = S(p, T)
•The change in the solubility can be expressed as:
∆ S =∂S∂p
∆p +∂S∂T
∆T
![Page 33: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/33.jpg)
Microcellular Plastics by Batch Process
(From Cha, Ph.D.Thesis, MIT)
Cell sizes of the microcellular foamed polymers (Ambient temperature foaming). Note: Saturation pressure and temperature of COs were not the same for all polymers.
![Page 34: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/34.jpg)
Microcellular Plastics by Batch Process
(From Cha, Ph.D.Thesis, MIT)
1 2 3 4 5 6 7 8Polymers
Cell density of the microcellular foamed polymers (Ambient temperature foaming). Note: Saturation pressure and temperature of COs were not the same for all polymers.
![Page 35: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/35.jpg)
What is the basic physics behind continuous processes?
![Page 36: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/36.jpg)
Microcellular Plastics - Design of a Continuous Process
To create a continuous process, we must be able to design a process and associated equipment to perform following four functions:
(1) Rapid dissolution of gas into molten, flowing polymer to form a solution,
(2) Nucleation of a large number of cells, (3) Control of the cell size, and (4) Control of the geometry of the final product.
![Page 37: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/37.jpg)
Microcellular Plastics - Design of a Continuous Process
Extruder(1) Rapid dissolution of gas into molten, flowing
polymer to form a solution,
Die/Mold(2) Nucleation of a large number of cells, (3) Control of the cell size, and (4) Control of the geometry of the final product.
![Page 38: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/38.jpg)
Physics of the Continuous Process1. Polymer/Gas Solution in Extruders
Important Parameters for Formation of Polymer/Gas Solution:
1. Temperature
2. Pressure
3. Degree of mixing of gas and polymer
![Page 39: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/39.jpg)
Introduction to Physics of the Continuous Process
i. Gas diffusion and formation of polymer/gas solution
t ∝
2
α
![Page 40: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/40.jpg)
Brief Introduction to Physics of the Continuous Process
Polymer D of CO2 (cm2/s) D of N2 (cm2/s)At 188 C At 200 C At 188 C At 200 C
PS -- 1.3x10-5 -- 1.5x10-5
PP 4.2x10-5 -- 3.5x10-5 --PE -- 2.6x10-6 -- 8.8x10-7
HDPE 5.7x10-5 2.4x10-5 6.0x10-5 2.5x10-5
LDPE -- 1.1x10-4 -- 1.5x10-4
PTFE -- 7.0x10-6 -- 8.3x10-6
PVC -- 3.8x10-5 -- 4.3x10-5
Table 7.1 Estimated diffusion coefficients of gases in polymers at elevated temperatures (From Durril, P. L., Griskey, R. G., AIChE Journal, Vol. 12, p 1147 (1960 and Vol. 15, p 106 (1969)
![Page 41: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/41.jpg)
Table 7.2 Estimated diffusion time at various striation thickness and diffusion coefficients. (From Park 1996)
Brief Introduction to Physics of the Continuous Process
![Page 42: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/42.jpg)
Brief Introduction to Physics of the Continuous Process
Figure removed for copyright reasons.
Deformation of a spherical bubble in a shear field to form an ellipsoid. The distance between the ellipsoids (measured perpendicular to the major axis of the ellipsoids) is the striation thickness. The dissolution rate of gas increases as the striation thickness becomes smaller and as the interfacial area of gas/polymer increases.
![Page 43: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/43.jpg)
Physics of the Continuous ProcessGas solubility
Polymer CO2 weight gain (%) N2 Weight gain (%)
PE 14 3
PP 11 4
PS 11 2
PMMA 13 1
Table 7.3 Estimated gas solubility in polymers at 200°C and 27.6 MPa (4,000 psi) (Park, 1993).
![Page 44: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/44.jpg)
How high should the pressure be in the extruder or the plasticating section of the injection molding
machine?
![Page 45: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/45.jpg)
How high should the pressure be in the extruder or the plasticating section of the injection molding
machine?
Pressure should be high enough to prevent the formation of two phase
throughout the system until ready for cell nucleation.
![Page 46: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/46.jpg)
Physics of the Continuous Process
2. Nucleation of Cells
![Page 47: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/47.jpg)
Physics of the Continuous Process Classical Nucleation Theory
Free energy change due to the formation of bubbles∆G = ∆Gv + ∆Gs
Critical cluster is formed whenddr
(∆G) = 0
![Page 48: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/48.jpg)
Physics of the Continuous Process Classical Nucleation Theory
(From Sanyal, Ph.D.Thesis, MIT)
Nucleation rate
dNdt
= J = N0 f exp − 163kT
πσ 3 RT
Pg A* zU(1− 2ξ) +kT ln(ξ
1− ξ)
⎛
⎝ ⎜
⎞
⎠ ⎟ + RT ln
Pg
P
⎧
⎨ ⎪ ⎪
⎩ ⎪ ⎪
⎫
⎬ ⎪ ⎪
⎭ ⎪ ⎪
⎡
⎣
⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥
![Page 49: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/49.jpg)
Nucleation Theory
Nucleation rate:
dNdt
= N 0λ exp −[∆G − ∆G *(gas concentration)]kT
⎛ ⎝
⎞ ⎠
∆G = Activation energy barrier = f ( impurities, mol.orientation, etc.)
∆G* = Energy change due to supersaturation of gas
![Page 50: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/50.jpg)
Possible Nucleation Sites and ∆G(Approximately Lowest to Highest)
• Solid/polymer interface (heterogeneous nucl.)• Non-polar polymer/polar polymer interface• High strain region• Free volume• Crystalline/amorphous interface in a polymer• Interface between crystallites• Morphological defects in a polymer• Polar groups of polymers
![Page 51: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/51.jpg)
Possible Nucleation Sites and ∆G(Approximately Lowest to Highest)
Potential sites
• Solid/polymer interface• Non-polar polymer/polar
polymer interface• High strain region• Free volume• Crystalline/amorphous
interface in a polymer• Interface between crystallites• Morphological defects in a
polymer• Polar groups of polymers
Rough estimation of potential number of nucleation sites (??)
• 105 to 106 /cc• ---
• ---• 109 /cc• 1012/cc
• 1018 /cc• ---
• 1022 /cc
![Page 52: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/52.jpg)
Probability Distribution of Activation Energy
Prob.D ensity
A ctiv ationEne rgy Leve l
∆Gpd f of ∆G
![Page 53: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/53.jpg)
Effect of Gas on the Probability Density of Activation Energy
Prob.Density
EnergyLevel
∆G- ∆G*
∆G
Effect of gason pdf of ∆G
pdf of∆G
pdf of(∆G-∆G*)
![Page 54: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/54.jpg)
N0 as a function of % gas dissolvedN0
% gasdissolved
(N0)min
(N0)max
![Page 55: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/55.jpg)
How do we achievethe simultaneous nucleation
of an extremely large number of cells?
Answer #1:
By creating a large driving force that can easily overcome all activation energy
barriers for nucleation
![Page 56: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/56.jpg)
How do we achievethe simultaneous nucleation
of an extremely large number of cells?
Answer #2:
By making sure that the nucleation rate is faster than the diffusion rate.
![Page 57: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/57.jpg)
Nucleation Theory
Condition for Simultaneous Nucleation:(From Baldwin, Ph.D.Thesis, MIT)
Characteristic nucleation timeCharacteristic diffusion time
<< 1
αdNdt
dc
<< 1
![Page 58: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/58.jpg)
Nucleation Theory
Condition for Simultaneous Nucleation:(From Baldwin, Ph.D.Thesis, MIT)
Characteristic gas diffusion distanceCharacteristic spacing between stable nuclei
<< 1
2ρc1/ 3 (α tD )1 / 2 << 1
![Page 59: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/59.jpg)
How do we achievethe simultaneous nucleation
of an extremely large number of cells?
Answers:
1. By creating a large driving force
2. By making sure that the nucleationrate is faster than the diffusion rate.
![Page 60: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/60.jpg)
How can we make the nucleation time as short as possible and the
driving force as large as possible?
![Page 61: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/61.jpg)
How can we make the nucleation time as short as possible and make
the driving force as large as possible?
1. Make (-dp/dt) large
![Page 62: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/62.jpg)
Why do we need to make (-dp/dt) large?
∆p
∆ppressu re
Time∆t
![Page 63: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/63.jpg)
How large should dp/dt be?
![Page 64: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/64.jpg)
How large should dp/dt be?
AnswerIt depends on the following:
(1) the temperature of the plastic(2) materials(3) die or mold design
![Page 65: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/65.jpg)
How large should dp/dt be?Polymer D of CO2 (cm2/s) D of N2 (cm2/s)
@ 188 @ 200 C @ 188 C @ 200 C PS -- 1.3x10-5 -- 1.5x10-5
PE -- 2.6x10-6 -- 8.8x10-7
HDPE 5.7x10-5 2.4x10-5 6.0x10-5 2.5x10-5
LDPE -- 1.1x10-4 -- 1.5x10-4
PTFE -- 7.0x10-6 -- 8.3x10-6
PVC -- 3.8x10-5 -- 4.3x10-5
PP 4.2x10-5 -- 3.5x10-5 --
Table 7.1 Estimated diffusion coefficients of gases in polymers at elevated temperatures (From Durril, P. L., Griskey, R. G., AIChE
Journal, Vol. 12, p 1147 (1960 and Vol. 15, p 106 (1969)
![Page 66: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/66.jpg)
How large should (-dp/dt) be?
Typical value:
|dp/dt| > 1 G Pascal / second
![Page 67: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/67.jpg)
How can we make the nucleation cite (N0) as large as possible?
1. Increase the level of supersaturation!!2. Don’t put nucleating agent!!3. Introduce internal strains by stretching,
etc.
![Page 68: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/68.jpg)
Cell Density vs % Gas Dissolved
C o n ce n trati on ofD i ss o l v e d G as
C ellDe n si ty
![Page 69: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/69.jpg)
CELL NUCLEATION DENSITYPolystyrene as a function of N2 Sat Pressure
(from Kumar, Ph.D. Thesis, MIT)
0 500 1000 1500 2000 250010 6
10 7
10 8
10 9
1010
SATURATION PRESSURE, psi
CE
LL D
EN
SIT
Y, c
m-3
![Page 70: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/70.jpg)
CELL NUCLEATION DENSITY Polycarbonate as a function of N2 Sat. Pressure
(From V. Kumar, 2000)
0
5
10
15
20
25
30
35
0 1 2 3 4 5 6 7
SATURATION PRESSURE, MPa
CEL
L D
ENSI
TY(*
109 ),
Cm
-3
![Page 71: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/71.jpg)
Physics of the Continuous Process 3. Cell Growth
![Page 72: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/72.jpg)
Cell Growth in a Batch or Continuous Process (From Baldwin, Ph.D. Thesis, MIT)
Physics of the Process
Governing Relationships
ρ 32
dRcell
dt⎛ ⎝ ⎜
⎞ ⎠ ⎟
2
+ Rcelld 2Rcell
dt2
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
= -4 µRcell
dRcell
dt+ Pg − P∞ − 2σ
Rcell
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
∂∂t
Pg Rcell3
RT
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟ = 3ρp Dr2 ∂c
∂r|Rcell
∂c∂t
+Rcell
2 dRcell
dtr2
∂c∂r
=1r2
∂∂r
r 2D∂c∂r
⎛ ⎝ ⎜
⎞ ⎠ ⎟
![Page 73: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/73.jpg)
Cell Growth in a Batch or Continuous Process
Physics of the Process
Initial conditionc(r, 0) = ci
Boundary conditionsc(Rcell , t) = Ks P
∂c∂t
⎛ ⎝ ⎜
⎞ ⎠ ⎟
t, r→ ∞
= 0
![Page 74: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/74.jpg)
Cell Growth in a Batch or Continuous Process
Physics of the Process
Cell Size Control in Free Expansion
Forces due to the pressure in the bubbleViscous forces resisting the expansion
= 1
f ( p, Tgas , r )g( Texterior layer ,∂T
∂r exterior layer, η )
= 1
![Page 75: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/75.jpg)
Physics of the ProcessCell Growth in a Batch or Continuous Process
Cell Size Control by Imposition of Geometric Constraint
Free expansion of bubblesGeometric constraints
= 1
∆vin
∑g(Geomtry )
= 1
![Page 76: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/76.jpg)
Physics of the Process
For Uniform Cell Growth in an Intermittent Processes
Characteristic flow rate in the moldRate of expansion of cells
> 1
f (Vinjection )g(η, Tpolymer , ctotal gas , α gas in polymer )
> 1
![Page 77: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/77.jpg)
Design of a Continuous Process
• FRs --> DPs
• DPs --> PVs
![Page 78: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/78.jpg)
Design of a Continuous Process for Sheet Extrusion
The highest level FRs
FR1 = Control cell size FR2 = Control the number of cellsFR3 = Control the geometry of the
extrudate
![Page 79: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/79.jpg)
Design of a Tube Die
L (Len gt h o f the Die Lip )
H
Pi
P0
Di e
Cen terLine
![Page 80: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/80.jpg)
Design of Microcellular Plastics Process
The corresponding design parameters (DPs) are:DP1 = Pi*DP2 = dp/dtDP3 = Die shape & Accessories
* Assuming that Pi* is the saturation pressure for the dissolved gas.
![Page 81: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/81.jpg)
Design of Microcellular Plastics
The design equation may be written as
Cell sizeCell densityGeometry
⎧ ⎨ ⎪
⎩ ⎪
⎫ ⎬ ⎪
⎭ ⎪ =
X x 0X X 0x 0 X
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
Pi
dp dtDie & Acc.
⎧ ⎨ ⎪
⎩ ⎪
⎫ ⎬ ⎪
⎭ ⎪
![Page 82: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/82.jpg)
Design of Microcellular Plastics Process
FR3 and DP3 must be decomposed to develop detailed means of controlling the geometry.
![Page 83: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/83.jpg)
Design of Microcellular Plastics
The corresponding Process Variables (PVs) are:
PV1 = Extruder rpm, ΩPV2 = Die length, LPV3 = Means of controlling the geometry of
the extrudate
![Page 84: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/84.jpg)
Design of Microcellular Plastics
The corresponding design equation for the process :
Pi
dp dtDie & Acc.
⎧ ⎨ ⎪
⎩ ⎪
⎫ ⎬ ⎪
⎭ ⎪ =
X x 0XX 00 0 X
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
ΩLMeans ...
⎧ ⎨ ⎪
⎩ ⎪
⎫ ⎬ ⎪
⎭ ⎪
![Page 85: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/85.jpg)
Typical Nucleation Rate in a Parallel DieSchematic Diagram Adapted from Sanyal, PhD. Thesis, MIT
X/L
Nu cl.Ra te
10.5
![Page 86: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/86.jpg)
Typical Cell Growth in a Parallel DieSchematic Diagram Adapted from Sanyal, PhD. Thesis, MIT
X/L
Ce llRa diu s
10.5
![Page 87: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/87.jpg)
Design of a continuous Process
Graph removed for copyright reasons.
Representative pressure profile along the polymer flow field in the extruder and die (From Baldwin, Park and Suh, 1997)
![Page 88: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/88.jpg)
Design of a continuous Process
Diagram removed for copyright reasons.
Figure 7.16 Schematic of the Microcellular extrusion system used for the shaping and cell growth control experiments (From Baldwin, Park and Suh, 1997)
![Page 89: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/89.jpg)
Unanticipated Processing Advantages of Microcellular Plastics
• Decrease in viscosity
• Lowering of the melting point and glass transition temperature
• Elimination of shrinkage
![Page 90: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/90.jpg)
Effect of CO2 on Physical Properties: Viscosity
η
% GasD i ss o lv e d
![Page 91: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/91.jpg)
Rigid PVC @ 340F
Rigid PVC @ 340F
0
200
400
600
800
1000
0 1000 2000 3000 4000 5000Shear Rate(1/s)
Visc
osity
(Ns/
m2 )
No gas0.5% CO2
![Page 92: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/92.jpg)
Santoprene @ 340F
Santoprene @ 340F
0
50
100
150
200
0 5000 10000 15000 20000 25000Shear Rate(1/s)
Visc
osity
(Ns/
m2 )
No gas1.5% CO2
![Page 93: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/93.jpg)
ABS @ 370F
ABS @ 370F
0
100
200
300
400
500
600
0 10000 20000 30000 40000Shear Rate(1/s)
Visc
osity
(Ns/
m2 )
No gas3% CO28% CO212% CO2
![Page 94: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/94.jpg)
Glass Transition TemperatureDMA result (PETG) [From Cha & Yoon, 2001]
Graph removed for copyright reasons.
Behavior of PETG material as a function of temperature.Elastic modulus sharply decreases around the glass transition temperature
![Page 95: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/95.jpg)
Models for estimating Tg [From Cha & Yoon, 2001]
Chow’s Model (1980)
Cha-Yoon Model (1998)
ln )1ln()1( ln θθθθβ +−−=⎟⎟⎠
⎞⎜⎜⎝
⎛
go
g
TT
[ ] )()(exp 4/13/1 αωρ −−−= pgog MTT
ρ : specific density of polymer
α : material constant
ω : % solubility for carbon dioxide in polymer (weight gain)
![Page 96: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/96.jpg)
Glass Transition Temperature[From Cha & Yoon, 2001]
• Comparison of the Two Models
Two graphs removed for copyright reasons.
Experimental results of Tg of PETG
Comparison of Cha-Yoon model vs.Chow’s model
![Page 97: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/97.jpg)
Microcellular Foaming/Forming• Thermoforming : the process of manufacturing products from a
thermoplastic sheet heated to its softening point and formed by pressure difference into a molded shape
Figure removed for copyright reasons.
![Page 98: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/98.jpg)
Experimental- Cha-Yoon model indicates when the weight fraction of
CO2 dissolved in PETG is 7.7% the Tgis lowered to room temperature
Photographs of two cupsmade through microcellularfoaming/forming experimentat room temperature
Photo removed for copyright reasons.
![Page 99: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/99.jpg)
Effect of Dissolved Gas on Processing of Microcellular Plastics
• Higher throughput rate by as much as 50%
• Faster cycle time by as much as x2
• Precision parts
![Page 100: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/100.jpg)
Cycle Time Reduction
Solid
MuCell
Start of Injection
Hold Cooling
Hold Cooling
20% - 50% overall cycle savings
25% less cooling time
Hold & Pack is eliminated
![Page 101: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/101.jpg)
MuCell™ Molding TechnologyOffice Equipment
Dimensional Stability Required:•Glass filled engineering resins such as
PPO, PC or PC/ABS
• Out of spec product made to spec. using MuCell Molding Technology
• 50% reduction in warpage - .060 to .027
• 25% reduction in cycle time, 8% weight reduction
Photo removed for copyright reasons.
Printer Chassis
![Page 102: Chapter 8 of Complexity Reduction of Complexity in … 8 of Complexity Reduction of Complexity in Materials through Functional Periodicity Functional Periodicity related to materials](https://reader033.fdocuments.us/reader033/viewer/2022051803/5affe09d7f8b9a84338bc617/html5/thumbnails/102.jpg)
MuCell™ Molding TechnologyImpact Performance
Printer Chassis:•35% Glass/Mineral filled
PPO/HIPS
•8% weight reduction
Photo removed for copyright reasons.
Drop Weight Impact Notched Izod Impact
Solid 6.7 ft-lb 7.3 kJ/m2
8% Wt. Red. 9.0 ft-lb 9.7 kJ/m2