Project No DripFinal update Presentation

Jacqueline Greene

Michele Dufalla

Tania Chan

May 3, 2007

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

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.

Shear TestsDate Sample Max Load (kN) Stress at Peak (MPa)

4/2/07 Black LDPE (110-112°C) 0.226 0.117

4/2/07 Black LDPE (120-123°C) 1.357 0.701

4/2/07 Black LDPE (130-138°C) 0.056 0.029

4/2/07 Black LDPE (155-170°C) 0.354 0.274

4/2/07 Clear LDPE (155-165°C) 0.954 0.739

4/2/07 Clear LDPE (130-134°C) 0.250 0.129

4/2/07 Clear LDPE (115-122°C) 0.318 0.164

4/2/07 Clear LDPE (141-150°C) 0.238 0.123

4/2/07 Clear LDPE (165-180°C) 0.938 0.727

Shear TestsDate Sample Max Load (N) Stress at Peak (MPa)

4/24/07 Bag LDPE – 1 (thermocouple) 514 0.398

4/24/07 Bag LDPE – 2 (thermocouple) 710 0.550

4/24/07 Bag LDPE – 5 (thermocouple) 958 0.742

4/24/07 African Bag 1513 1.173

4/26/07 Preprocessed Black LDPE – 1 layer

1341 1.039

4/26/07 Preprocessed Black LDPE – 2 layers

559 0.433

4/26/07 Preprocessed Black LDPE – 2 layers + thermocouple

757 0.587

5/1/07 Bag LDPE 85 0.066

5/1/07 Bag LDPE 410 0.318

Modeling Heat Conduction in HDPE

c Tt

k2Tx 2

sGoverning 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 = T0 = 25oC

At x = 0: q

At x = ∞: T|x = ∞ = T0 = 25oC

S = 0, no heat generation

Modeling Heat Conduction in HDPE

Tt

2Tx 2Modified Governing Equation:

k

cThermal Diffusivity:

(Materials Parameter)

•Governing equation can be solved mathematically by Fourier series, Green’s function

•Simplest computational model is Finite Differences

Modeling Heat Conduction: Finite Differences

Discretizing space and time:

x x i1 x i

t tn1 tn

Tt xi ,tn1/2

Ti,n1 Ti,n

t

Tx xi1/2 ,tn

Ti1 Ti

x

Temperature Derivative Estimate:

2Tx 2

Tx xi1/2,tn

Tx xi 1/2,tn

xTi 1,n 2Ti,n Ti1,n

x 2

Second Derivative Approximations:

Ti,n is temperature at position

x i

tnand time

Finite Differences: 1-D Conduction Modeling

Tt

2Tx 2

Modified Governing Equation:

Finite Differences Approximations:

Ti,n1 Ti,nt

Ti 1,n 2Ti,n Ti1,nx 2

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0 20 40 60 80 100 120 140 160 180 200

Temperature (C)

Po

lye

thyle

ne

Th

ickn

ess (

m) 0 sec

5 sec10 sec15 sec20 sec25 sec30 sec35 sec40 sec45 sec50 sec55 sec60 sec

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

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.htmlhttp://wwwcp.tphys.uni-heidelberg.de/Polymer/day3/p3-1.htm

Time Regimes in Reptation Model

•Below e: Chain feels the effects of its own connectivity but no the entanglement (wt1/4)

•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 t1/4

log t

1/41/8

1/4

1/2

e

r

R

Log

w(t

)

wt1/4 wt1/8 wt1/4 wt1/2

At t<

r

• At t> , polymer interface diffusion is a Fickian process

Long Time Scale: Fickian Diffusion

r

Fick’s First Law:

Fick’s Second Law:

Diffusion scales: wt1/2

Final Plans

• DSC or DMA testing on plastic bag

• Build final working prototype, using a real jerry can

• Complete modeling work and illustrations