Ph. D. Candidate:Guangming Li Supervisor:Prof. Chul B. Park

Ph. D. Candidate: Guangming LiSupervisor: Prof. Chul B. Park

Study of the Solubility of Gas in a Polymer Melt & Cell Nucleation in Die

Microcellular Plastics Manufacturing Laboratory, University of Toronto

OutlineIntroductionObjectives BackgroundApproachExperimentsContributions

Introduction

Plastic Foams

Plastic foams• Decreased density • Cellular structure

Advantages over non-foamed plastic• Insulating properties• Impact resistant characteristics• Buoyancy• Outstanding strength-to-weight ratios

Plastic Foam Processing

Formation of single-phase polymer/gas solution

Cell nucleationCell growth Stabilization

Two system

+

gas

polymer

Two-phase polymer/gas

mixture

Two-phase polymer/gas

mixture

Single-phase

polymer/gas solution

Gas injection Mixing & diffusion Diffusion

Plastic Foam Processing

Formation of single-phase polymer/gas solutionCell nucleation

Cell growth Stabilization

Distance

Psolubility

Die Pressure

Objectives

To systematically investigate the gas solubility for different polymer/gas mixture systems

To verify the solubility pressure inside the die during the continuous plastic foaming process

Background

Pressure Decay + SL-EOS Y. Sato, etc., Fluid Phase Equilibria 162 (1999) 261; for N2 and CO2 in PP, HDPE and PS

Electrobalance + Partial Volume by Henrian Sorption TheoryB. Wong, etc., Journal of Polymer Science (Part B) 36 (1998) 2025;

for PS + CO2 and PVC + CO2

Previous Study of Solubility

Application of Gas Solubility in an Extrusion Die

PR

ES

SU

RE

VOLUME

Isotherm Critical Point

Saturated Vapor

(Binodal)

Liquid Spinodal

Vapor Spinodal

Saturated Liquid

)(3

44 32

oldnewlgo nPPRRW

The minimum work to create a bubble (radius R)

lgo PPRRW 32

3

44

kTW

eJJ

0

The bubble nucleation rate

Approach

Theoretical Prediction of Gas Solubility

The fundamental concept of this approach is that the chemical potential of a vapor is equal to the chemical potential of its condensate in the polymer melt, when the equilibrium condition is reached.

PG11

A(G)

A(P) +B(P)

G1

P1

Equal at equilibrium

A: Gas B: Polymer G: Gas phaseP : Polymer/Gas Solution phase

Segment of Segment of Component AComponent A

Segment of Segment of Component BComponent B

Empty cell (hole)Empty cell (hole)

Equation-of-State for the Multi-component System (Gas/Polymer Mixture)

Lattice-Fluid Model (Sanchez and Lacombe EOS) Hole Model (Simha and Somcynsky EOS)

*

~

P

PP Reduced Pressure;

ρ*

ρρ ~ Reduced Density;

*

~

T

TT Reduced Temperature

* : Characteristic Density of bulk material (g / cm3); T* : Characteristic Temperature (K)

P* : Characteristic Pressure (Pa); r : Number of mer per molecule

SL ModelPGgasgas

10

1

1111

1

1

1011

~ln1~1ln1~

1~~

~

~~

rT

P

TRTrG

~ln1~1ln1~

1~~

~

~~

~2~1ln 0

11

1

1

01

22

11

1221012

2

111

rT

P

TRTr

TP

PPPr

r

rRTP

*

~

P

PP Reduced Pressure;

V*

VV ~

Reduced Specific Volume;

*

~

T

TT Reduced Temperature; y ： Occupied site fraction

S : Number of mer per molecule ; T* : Characteristic Temperature (K);

P* : Characteristic Pressure (Pa); * V : Characteristic Specific Volume (cm3/g)

PGgasgas

01 G

121 x

GxG m

mP

SS Model

(High pressure gas)

Buoyancy Compensation

+ )

Volume of Swelling

Solubility

F(P,T)- F(0,T)+ ρgas× ( + Volume of holder

Initial Volume of pure polymer at P,T

Apparent Solubility

F is Balance Reading

(Vacuum)

F(0,T)microbalance

Polymer Sample

microbalanceF(P,T)

Experimental Measurement of the Solubility by MSB

Volume of Swelling

Swollen volume contributed buoyancy effect is an outstanding factor on solubility measurement in high pressure conditions.

Theoretical method (Equation-of-State) to predict the swollen volume.

Theoretical Estimation of Volume of Swelling

~11~1ln

~~~ 2

rTP

T

QyQTVp ~

)2045.1011.1(2)1(

~/

~~22

1

22 033.3409.2~61

3/1)1ln(1

3QQ

T

y

y

y

s

s

c

s

SL EOS:

SS EOS:

Actual Measurement of Volume of Swelling-Pendent Droplet Method

Pendent drop in high temperature and pressure cell is currently utilized to do the PVT density measurement by examining the final volume after swelling.

Polymer droplet

High T and P cell

Scale

Rod

gas

Experiments

Comparison of SL EOS and SS EOS

Polystyrene (PS, Tg=381.4K, Mw=3.30×105, Mn= 1.07×105), A&M Styrene Corporation, (Kawasaki, Japan).

Carbon dioxide (Coleman grade, 99.99% purity), BOC Canada.

Materials:

Equipment: MSB

a

b

c

d e

f

a: Microbalance b: Measuring cell c: Temperature control device d: Gas dosing system e: Control panel f: Data acquisition system

Schematic of MSB Instrument

MSB

Proposed Procedure to Determine the Solubility

Obtain set of Apparent Solubility (AS) experimentally.

Set an initial value of EOSs interaction parameter(s).

Calculate the difference of the corrected solubility and theoretical solubility: (CSi- Si)2

Obtain the corresponding set of the Theoretical Solubility (S) and the density of polymer/gas mixture based on SS or SL EOS.

Obtain the Corrected Solubility (CS) using the SS-based or SL-based swollen volume.

Decide the optimum interaction parameter(s) by minimizing (CSi- Si)2

0 500 1000 1500 2000 2500 3000 35000

2

4

6

8

10

12

14

Vo

lum

e S

wel

ling

Rat

io (

%)

Pressure (psi)

110 oC SL-based Volume Swelling Prediction

110 oC SS-based Volume Swelling Prediction

Volume Swelling effect prediction (a) SS-based and SL-based prediction at

110oC; (b) SS-based and SL-based prediction at

150 oC;(c) SS-based and SL-based prediction at

200 oC;

0 500 1000 1500 2000 2500 3000 35000

2

4

6

8

10

12

14

Vo

lum

e S

wel

ling

Rat

io (

%)

Pressure (psi)



0 500 1000 1500 2000 2500 3000 35000

2

4

6

8

10

12

14

Vo

lum

e S

wel

ling

Rat

io (

%)

Pressure (psi)



(b)(a)

(c)

0 500 1000 1500 2000 2500 3000 35000.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11S

olu

bilit

y (g

/g)

Pressure (psi)

110 oC SL-based corrected solubility

110 oC SS-based corrected solubility

110 oC Apparent solubility

Solubility of CO2 in Polystyrene at 1100C

0 500 1000 1500 2000 2500 3000 35000.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11S

olu

bilit

y (g

/g)

Pressure (psi)





1000 1500 2000 2500 3000 3500-0.26

-0.24

-0.22

-0.20

-0.18

-0.16

-0.14

-0.12

-0.10

-0.08

-0.06

-0.04

K12

=-0.2015 at 200 oC

K12

=-0.1240 at 150 oC

K12

=-0.0767 at 110 oC

K12

Pressure (psi)

110oC

150oC

200oC

Temperature Effect on Interaction Parameters of EOS

K12 of SL-EOS δe and δv of SS-EOS

δe =1.0638δv = 0.9568

Sub-conclusion

SL EOS and SS EOS predicted different swollen volumes.

Below 1500 psi, corrected solubilities from SL and SS EOS are very close to each other.

Above 1500 psi, there are significant difference between the SL EOS and SS EOS in terms of the solubility measurement.

The interaction parameters for SL EOS and SS EOS show different temperature dependence.

Investigation of the Solubility of CO2 in Branched –PP and Linear-PP

Rheological Behavior Difference Between the Branched-PP and Linear PP

This behavior of LCB-PP is beneficial to all the processes involving extensional flow, such as thermoforming, foaming and blow molding

Branched-PP

Linear-PP Linear-PP

Branched-PP

0 5 10 15 20 25 301.20

1.25

1.30

1.35

1.40

1.45

1.50

Spec

ific

Volu

me(

cm3 /g

)

Pressure (MPa)

Linear PP at 220oC

Linear PP at 200oC

Linear PP at 180oC

Branched PP at 220oC



0 5 10 15 20 25 301.20

1.25

1.30

1.35

1.40

1.45

1.50

Spec

ific

Volu

me(

cm3 /g

)

Pressure (MPa)

Linear PP at 220oC

Linear PP at 200oC

Linear PP at 180oC




0 5 10 15 20 25 301.20

1.25

1.30

1.35

1.40

1.45

1.50

Spec

ific

Volu

me(

cm3 /g

)

Pressure (MPa)

Linear PP at 220oC

Linear PP at 200oC

Linear PP at 180oC




0 5 10 15 20 25 301.20

1.25

1.30

1.35

1.40

1.45

1.50

Spec

ific

Volu

me(

cm3 /g

)

Pressure (MPa)

Linear PP at 220oC

Linear PP at 200oC

Linear PP at 180oC




5% CO2 content

SL-EOS

SS-EOS

10% CO2 content

0 5 10 15 20 25 300.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

Solu

bilit

y (g

/g)

Pressure (MPa)

180oC Apparent Solubility for linear PP

180oC Corrected Solubility for linear PP

180oC Theoretical Solubility for linear PP K

12=-0.2343

180oC Apparent Solubility for branched PP

180oC Corrected Solubility for branched PP

180oC Theoretical Solubility for branched PP K

12=-0.1663

0 5 10 15 20 25 300.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

Solu

bilit

y (g

/g)

Pressure (MPa)




12=-0.2718




12=-0.1968

0 5 10 15 20 25 300.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

Solu

bilit

y (g

/g)

Pressure (MPa)




12=-0.3091




12=-0.2333

Solubility for linear PP/CO2 mixture and branched PP/CO2by SL EOS

0 5 10 15 20 25 300.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

Solu

bilit

y (g

/g)

Pressure (MPa)



180oC Theoretical Solubility for linear PP



180oC Theoretical Solubility for branched PP

0 5 10 15 20 25 300.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

Solu

bilit

y (g

/g)

Pressure (MPa)







0 5 10 15 20 25 300.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

Solu

bilit

y (g

/g)

Pressure (MPa)







Solubility for linear PP/CO2 mixture and branched PP/CO2by SS EOS

Investigation of the Solubility of CO2 in Polycarbonateand the Effect of Crystallinity on Solubility

•Tough

•Transparent

•Crystallizable (regular chemical structure)

•Extremely low crystallization rate (chain rigidity)

Material

Uptake curve for the sorption of CO2 in PC

0 500 1000 1500 2000 2500 3000 3500 40000.00

0.01

0.02

0.03

0.04

0.05

0.06

Time (min)

Appa

rent

Wei

ght g

ain

(g-g

as/g

-pol

ymer

)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Pressure (psi)

0 500 1000 1500 20000.00

0.01

0.02

0.03

0.04

0.05

0.06

Appa

rent

Wei

ght g

ain

(g-g

as/g

-pol

ymer

)

Time (min)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Pressure (psi)

0 500 1000 15000.00

0.01

0.02

0.03

0.04

0.05

0.06

Appa

rent

Wei

ght g

ain

(g-g

as/g

-pol

ymer

)

Time (min)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Pressure (psi)

160 oC 200 oC 240 oC

80 100 120 140 160 180 200 220 240 260 280

Original PC Cooling

Original PC Heating

Temperature (oC)

80 100 120 140 160 180 200 220 240 260 280

PC sample (after sorption experiment at 160oC) Heating

PC sample (after sorption experiment at 160oC) Cooling

Temperature (oC)

Investigation of the Crystallization of PC induced by CO2

at 160 oC

Original PC PC treated with CO2 at 160oC for 24 hrs (crystallinity is 21.66%)

Polarizing Light Microscope

DSC

Solubility of CO2 in PC at 200oC and 240oC

0 500 1000 1500 2000 2500 3000 3500 4000 45000.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11

So

lub

ility

(g

-gas

/g-p

oly

mer

)Pressure (psi)

Apparent Solubility Corrected Solubility Theoretical Solubility (K

12=-0.257875)

240oC

0 500 1000 1500 2000 2500 3000 3500 4000 45000.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11

So

lub

ility

(g

-gas

/g-p

oly

mer

)

Pressure (psi)

Apparent Solubility Corrected Solubility Theoretical Solubility (K

12=-0.18306)

200oC

System Design for Study of Solubility Pressure inside the Die

•Upgrade the primary 1.5" extruder with 30:1 L/D ratio .

•Upgrade gear pump (Zenith, PEP-II 10 cc/rev) for controlling the melt flow rate up to 100 g/min.

•Secondary 1.5" extruder with a mixing screw of 24:1 L/D ratio attached after the gear pump.

•Die design

Contributions

Development of experimental approach to study the solubility of gas in a polymer at elevated temperature and pressure;

Development of a theoretical approach to predict the swollen volume for the polymer/gas mixture;

Investigation of the solubility of various gases in different polymer melts;

Solubility Study

Nucleation investigation

The investigation on the nucleation inside the die theory.

Research Timetable

Please see the attached Report

Thank You!

Ph. D. Candidate:Guangming Li Supervisor:Prof. Chul B. Park

Documents

Transcript of Ph. D. Candidate:Guangming Li Supervisor:Prof. Chul B. Park