Comprehensive Study Notes on Polymer Structures, Properties, and Processing

Introduction to Polymers and Hydrocarbon Foundations

• Natural Polymers:     - These are derived directly from plants and animals.     - Examples: wood, cotton, wool, silk, and natural rubber.

• Synthetic Polymers:     - These are man-made materials, developed largely since the era of World War II.     - Categories include plastics, rubbers, and synthetic fibers.

• Hydrocarbon and Polymer Molecules:     - Polymeric materials are primarily comprised of Carbon ($C$) and Hydrogen ($H$).     - Hydrocarbons serve as the fundamental building blocks for polymeric materials.     - Mer Units: Simple units that repeat in a chain. Polymers with double or triple carbon-carbon ($C-C$) bonds are referred to as "unsaturated."     - Polymerization: This process occurs when a double bond breaks to link with other molecules, typically initiated by a catalyst denoted as ($R\cdot$).

• Specific Repeating Unit Examples:     - Polyethylene (PE): A chain of repeating ethane units.     - Polytetrafluoroethylene (PTFE): Often known by the trade name Teflon.     - Poly(vinyl chloride) (PVC): Includes a chlorine atom in the repeat unit.     - Polypropylene (PP): Features a methyl group side chain.     - Polystyrene (PS): Features a benzene ring (aromatic ring) side group.     - Poly(methyl methacrylate) (PMMA): Also known as Plexiglas or acrylic.     - Phenol-formaldehyde (Bakelite): A historic, hard, network polymer.     - Poly(hexamethylene adipamide): Commonly known as Nylon 6,6.     - Poly(ethylene terephthalate) (PET): A common polyester.     - Polycarbonate (PC): Known for high toughness and transparency.

Resin Identification Codes and Recycling Impact

• Resin Codes: Numbers on packaging that classify the type of plastic to assist in sorting for recycling. Local recycling rules vary and should be checked based on the code.

• 1: Polyethylene Terephthalate (PET):     - Common items: Water and soda bottles, specific food packaging (e.g., Jif peanut butter, Caesar dressing).     - Recyclability: High. It is the most common and easily recycled plastic. Accepted by all Dakota County haulers.     - Recycle products: New bottles, clothing, carpet.

• 2: High Density Polyethylene (HDPE):     - Common items: Milk jugs, detergent/cleaning bottles, hair care products.     - Recyclability: High. Simple and cost-effective process. Accepted by all Dakota County haulers.     - Recycle products: New bottles, lumber, furniture.

• 3: Polyvinyl Chloride (PVC):     - Common items: Pipes, blister packs, toys, clamshell containers.     - Recyclability: Generally No. It contains toxins. Exceptions are made for certain clamshell containers.     - Recycle products: Pipes, flooring, siding.

• 4: Low Density Polyethylene (LDPE):     - Common items: Shrink wraps, squeezable bottles, grocery/bread/frozen food bags.     - Recyclability: Item-dependent. Plastic bags often require specific drop-offs at grocery stores.     - Recycle products: New bags, mailers, decking.

• 5: Polypropylene (PP):     - Common items: Yogurt containers, straws, medicine bottles, margarine tubs.     - Recyclability: Item-dependent. Check local haulers.     - Recycle products: Bins, buckets, car parts.

• 6: Polystyrene (PS):     - Common items: Styrofoam, CD cases, meat trays, plastic cutlery.     - Recyclability: Generally No. Styrofoam is extremely hazardous to the environment in landfills.     - Recycle products: Jars, picture frames, crown molding.

• 7: OTHER (Mixed/Miscellaneous):     - Common items: Sports water bottles (Nalgene), baby bottles, lids, electronic parts.     - Recyclability: Usually No, due to the broad nature of the category.     - Recycle products: Electronic housing, plastic lumber.

• Economic Market Data:     - Level of plastic waste in U.S. municipal solid waste has increased from nearly zero in 1960 to over $35,000$ tons in 2015, with the vast majority being landfilled rather than recycled or combusted for energy.     - Combined Addressable Market for waste plastics in North America: $\$120B$.     - Polymers (PE, PET, PS): $\$47B$.     - Monomers and Intermediates (Ethylene, Propylene, Styrene): $\$56B$.     - Refined Hydrocarbons, Petrochemicals, and Fuels (Naphtha, Ethane, Propane): $\$17B$.

Molecular Weight and Chain Length

• Length Distribution: Polymer chains do not all reach the same length; they exist in a distribution of lengths and weights.

• Number Average Molecular Weight ($M_n$):     - $M_n = \sum x_i M_i$     - Where $x_i$ is the fraction of total number of chains and $M_i$ is the mean molecular weight of size range $i$.

• Weight Average Molecular Weight ($M_w$):     - $M_w = \sum w_i M_i$     - Where $w_i$ is the weight fraction.

• Degree of Polymerization (DP):     - Represents the average number of repeat units in a chain.     - $DP = \frac{M_n}{m}$     - Where $m$ is the molecular weight of the repeat unit.

• Properties and Weight:     - Typical molecular weights range from $100$ to $10,000,000\,g/mol$.     - Higher molecular weights generally lead to higher melting/softening temperatures.     - Elastic modulus and mechanical strength are dependent on molecular weight.

Molecular Shape, Structure, and Configuration

• Molecular Shape (Conformation):     - Chain bending and twisting are possible via the rotation of carbon atoms around chain bonds.     - No bond-breaking is necessary to alter the conformation.

• Structural Classifications:     - Linear Polymers: Repeat units joined end-to-end (e.g., Spaghetti, HDPE).     - Branched Polymers: Side-branches on main chains; results in lower packing efficiency (e.g., LDPE).     - Crosslinked Polymers: Adjacent chains joined by covalent bonds (e.g., rubber, vulcanization).     - Network Polymers: Three-dimensional networks of highly crosslinked chains (e.g., epoxies, polyurethanes).

• Molecular Configurations and Stereoisomerism:     - Tacticity: The spatial arrangement of R-groups (side groups) along the chain.     - Isotactic: R-groups are all on the same side of the chain.     - Syndiotactic: R-groups alternate regularly from one side to the other.     - Atactic: R-groups are positioned randomly.

• Geometric Isomerism:     - Occurs when a double bond exists between carbon atoms.     - cis-isoprene: H atom and $CH_3$ group are on the same side of the chain. Found in natural rubber.         - Tensile Strength: $\ge 500\,PSI$.         - Elongation: $300\% - 900\%$.     - trans-isoprene: H atom and $CH_3$ group are on opposite sides. Found in gutta percha.         - Tensile Strength: $\ge 1700\,PSI$.         - Elongation: $170\% - 500\%$.     - These isomers cannot be converted from one to another without breaking bonds.

Classification by Thermal Behavior

• Thermoplastic Polymers:     - Soften when heated and harden when cooled; the process is completely reversible.     - Thermal energy breaks secondary bonds (Van der Waals) between chains, allowing them to slide.     - Usually relatively soft.

• Thermosetting Polymers:     - Permanently hardened during their initial formation via network formation.     - Covalent crosslinks resist vibrational and rotational motion at high temperatures.     - They do not soften with heat; they only degrade at extremely high temperatures.     - Generally harder and stronger than thermoplastics.

Polymer Crystallinity and Morphology

• Definition of Polymer Crystal: Large molecules pack together into ordered arrays. Because molecules are long, they are often partially crystalline (semicrystalline).

• Degree of Crystallinity:     - Ranges from amorphous ($0\%$) to approximately $95\%$.     - Formula: $\text{\% Crystallinity} = 100 \times \frac{\rho_c ( \rho_s - \rho_a )}{\rho_s ( \rho_c - \rho_a )}$     - Where $\rho_s$ is the specimen density, $\rho_c$ is the crystalline density, and $\rho_a$ is the amorphous density.

• Factors Influencing Crystallization:     - Cooling Rate: Slower cooling allows more time for ordering.     - Chain Configuration: Longer, complex chains are harder to crystallize.     - Repeat Unit Complexity: Complex units decrease crystallization.

• Crystallite Morphology:     - Spherulites: Bulk polymers often form these structures, consisting of ribbon-like crystallites emanating from a central nucleation site, interleaved with amorphous regions. They mimic grain structures in metals.

• Thermal Transitions:     - $T_m$ (Melting Temperature) and $T_g$ (Glass Transition Temperature) both increase with chain stiffness.     - Stiffness is increased by bulky side groups, polar groups, chain double bonds, and aromatic groups.     - Regularity of repeat units affects $T_m$ specifically.

Mechanical Behavior and Viscoelasticity

• Stress-Strain Profiles:     - Brittle: Fractures with almost no plastic deformation.     - Plastic: Shows yielding (maximum on the curve) and significant plastic deformation before failure (similar to mild steel).     - Elastomer: Exhibits rubbery behavior with large, non-linear elastic deformations.

• Viscoelasticity Concepts:     - Elasticity (Hooke's Law): Stress is proportional to strain ($\sigma = E\epsilon$). It is instantaneous and reversible.     - Viscosity (Newton’s Law): Stress is proportional to strain rate ($\tau = \eta \frac{dv}{dy}$). It is time-dependent and not fully reversible.     - Viscoelasticity: A combination of solid-like and liquid-like properties. Magnitude of response depends on both time (rate) and strain.

• Viscoelastic Parameters:     - $G^*$ (Complex Modulus): Total resistance to deformation.     - $G'$ (Storage Modulus): Measures elastic energy storage ($\text{Solid-like property}$). $G' = \frac{\sigma_0}{\epsilon} \cos(\delta)$.     - $G''$ (Loss Modulus): Measures energy dissipated as heat ($\text{Liquid-like property}$). $G'' = \frac{\sigma_0}{\epsilon} \sin(\delta)$.     - Tan Delta ($\tan(\delta)$): $\frac{G''}{G'}$. Measures material damping (vibration and sound absorption).

• Viscoelastic Relaxation and Creep:     - Relaxation Modulus ($E_r(t)$): $E_r(t) = \frac{\sigma(t)}{\epsilon_0}$. Stress decreases over time at constant strain.     - Creep Modulus ($E_c(t)$): $E_c(t) = \frac{\sigma_0}{\epsilon(t)}$. Strain increases over time at constant stress.

• Fracture and Crazing:     - Ductile-to-Brittle Transition: Occurs at the Glass Transition Temperature ($T_g$).     - Crazing: A precursor to fracture where local plastic deformation forms microvoids and "fibrillar bridges" (highly oriented molecular chains). When bridges break, a crack forms.

Deformation Mechanisms and Influencing Factors

• Semicrystalline Polymer Deformation Stages:     - Stage 1: Chains in amorphous regions align with the stress direction.     - Stage 2: Aligned chains in crystalline regions begin to stretch.     - Stage 3: Crystalline regions fully align with the stress.     - Stage 4: Crystallites segment and slide past each other.     - Stage 5: Blocks of crystals and intermediate chains become fully aligned along the stress axis.

• Elastomer Deformation:     - Primary driving force is entropy. Chains are naturally disordered; stretching them forces alignment (low entropy), and they naturally want to return to a disordered state (high entropy).     - Vulcanization: Cross-linking process using sulfur atoms to bond adjacent chains, providing a restoring force.

• Factors Increasing Strength ($TS$) and Modulus:     - Increased Molecular Weight (more chain entanglement).     - Increased Degree of Crystallinity (more secondary bonding).     - Predeformation by Drawing (aligns chains, making the polymer anisotropic and stronger).     - Heat-treating (Annealing): Increases crystallinity, which increases modulus but decreases ductility (opposite of the effect in metals).

Defects and Molecular Diffusion

• Point Defects: Include impurities, dissimilar chemical chain ends, vacancies near chain ends, and dangling chains/loops.

• Dislocations: Can occur within crystalline regions.

• Diffusion: Generally refers to small molecules ($O_2$, $H_2O$) moving through the polymer.     - Diffusion is faster in amorphous regions than in crystalline regions.     - Permeability Coefficient ($P_M$): $P_M = D \times S$     - Where $D$ is diffusivity and $S$ is solubility.     - Fick’s First Law (at STP): $J = -P_M \frac{\Delta P}{\Delta x}$.