1. Project No Drip Final update Presentation Jacqueline Greene Michele Dufalla Tania Chan May 3, 2007

2. Main updates Density data of LDPE and HDPE plastics Final shear instron tests using plastic bags Remolding of plastic Modeling of heat conduction during joining process Future plans

3. Density Data Measured the mass of the following plastics: black LDPE, clear LDPE, LDPE campus convenience bag, LDPE Coop bag, LDPE McMaster sheet, HDPE McMaster sheets LDPE average density (n=5) = 0.95 ± 0.27 g/cm^3 HDPE average density(n=4) =0.96 ± 0.04 g/cm^3 Data online: LDPE density= 0.923 (g/cm3) HDPE density=0.954 g/cm3 Khonakdar, H.A. et al. Effect of electron-irradiation on cross-link density and crystalline structure of low- and high-density polyethylene. Radiation Physics and Chemistry. Vol 75(1) Jan. 2006: 78-86.

4. Shear Tests DateSampleMax Load (kN)Stress at Peak (MPa) 4/2/07Black LDPE (110-112°C)0.2260.117 4/2/07Black LDPE (120-123°C)1.3570.701 4/2/07Black LDPE (130-138°C)0.0560.029 4/2/07Black LDPE (155-170°C)0.3540.274 4/2/07Clear LDPE (155-165°C)0.9540.739 4/2/07Clear LDPE (130-134°C)0.2500.129 4/2/07Clear LDPE (115-122°C)0.3180.164 4/2/07Clear LDPE (141-150°C)0.2380.123 4/2/07Clear LDPE (165-180°C)0.9380.727

5. Shear Tests DateSampleMax Load (N)Stress at Peak (MPa) 4/24/07Bag LDPE – 1 (thermocouple)5140.398 4/24/07Bag LDPE – 2 (thermocouple)7100.550 4/24/07Bag LDPE – 5 (thermocouple)9580.742 4/24/07African Bag15131.173 4/26/07Preprocessed Black LDPE – 1 layer 13411.039 4/26/07Preprocessed Black LDPE – 2 layers 5590.433 4/26/07Preprocessed Black LDPE – 2 layers + thermocouple 7570.587 5/1/07Bag LDPE850.066 5/1/07Bag LDPE4100.318

6. Modeling Heat Conduction in HDPE Governing equation:  = density, k = thermal conductivity, c = specific heat, s = heat generation Semi Infinite Solid Polyethylene x = 0 x Constant Heat Flux (q) Boundary Conditions: At t = 0: T = T 0 = 25 o C At x = 0: q At x = ∞: T| x = ∞ = T 0 = 25 o C S = 0, no heat generation

7. Modeling Heat Conduction in HDPE Modified Governing Equation: Thermal Diffusivity: (Materials Parameter) Governing equation can be solved mathematically by Fourier series, Green’s function Simplest computational model is Finite Differences

8. Modeling Heat Conduction: Finite Differences Discretizing space and time: Temperature Derivative Estimate: Second Derivative Approximations: is temperature at position and time

9. Finite Differences: 1-D Conduction Modeling Modified Governing Equation : Finite Differences Approximations:

10. Polymer-polymer interdiffusion at an interface proceeds in two stages 1.At time shorter than reptation time, the diffusion process is explained by the reptation model 2.At time great than reptation time, the diffusion process can be explained by continuum theories, Fick’s Law Reptation: Polymer Diffusion in Melts

11. Short Time Scale: Reptation Model Polymer chain confined within a “tube” defined by neighboring chains Movement of chain limited to along the chain axis Entanglement prevents the polymer chains from crossing the interface, chain ends near the interface dominate movement Diffusion can be scaled with the distance a chain takes to move out of the constraining “tube” cbp.tnw.utwente.nl/PolymeerDictaat/node62.html http://wwwcp.tphys.uni-heidelberg.de/Polymer/day3/p3-1.htm

12. Time Regimes in Reptation Model Below  e : Chain feels the effects of its own connectivity but no the entanglement (w  t 1/4 ) Between  e and  r : Motion perpendicular to the tube is constrained Between  r and  R : Motion parallel to the tube occurs, but dominated by the constraining of the tube Above  R : Chain moves out of tube, Fick’s Law dominates Interfacial width increases at t 1/4 log t 1/4 1/8 1/4 1/2 Log w(t) w  t 1/ 4 w  t 1/ 8 w  t 1/ 4 w  t 1/ 2 At t<

13. At t>, polymer interface diffusion is a Fickian process Long Time Scale: Fickian Diffusion Fick’s First Law: Fick’s Second Law: Diffusion scales: w  t 1/2

14. Final Plans DSC or DMA testing on plastic bag Build final working prototype, using a real jerry can Complete modeling work and illustrations