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Nordic Polymer Days 2013 Truly Nordic

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- SvenskaKemistsamfundetsPolymerdagar 1963 organized by Prof. BengtRånby
- 15 Presentations from Sweden
- 2 Presentations from USA
- 1 Presentation from Denmark by a graduate student named Charles M. Hansen
- The “Nordic” requirement, presentations from at least two Nordic countries, was fulfilled.

Mismatch Hansen solubility parameters to get

1. Lower equilibrium absorption, and therefore:

A. Lower concentration gradients

B. Lower diffusion coefficients

C. Lower surface mass transfer coefficients

and

Better Barriers

UNDERSTANDING ABSORPTION IN POLYMERS:KEY TO IMPROVING BARRIER PROPERTIES NORDIC POLYMER DAYS 2013 HELSINKICharles M. Hansen, Actively Retired

- 1963: Drying of solvent from polymer
- 2013: Sorption of solvent by polymer
- Exactly the same equations and data can be used to satisfactorily model desorption (film formation) and absorption, as well as permeation.
- There are no ”Anomalies” in absorption!
- Stress related effects are not (that) signficant

- Laws of Diffusion
- Find correct diffusion coefficients
- Concentration dependent coefficients
- Surface condition can be significant
- Combine these to:
1. Model film formation by solvent evaporation

2. Model ”anomalies” of absorption

Law 1: F = - D0(c/x)

For mass transport in the x Direction, and

Law 2:c/t = /x (D0c/x)

This is also called the Diffusion Equation.

(Accumulation equals flux in minus flux out)

Dimensionless time:

T = D0t/L2 (cm2/s)(s/cm2)

Dimensionless distance:

X = x/L

Dimensionless concentration:

C = (c – c0)/(c - c0)

L is the thickness of a free film

Half-time (t½) equation for measuring D0

Corrections required for concentration

dependence (M) and surface resistance (B)

See also Nordtest POLY 188

D0 = 0.049 L2/t½

Desorption Absorption

Dmax/D0 (Fd)1/2 (Fd)1/4 (Fa)1/2

11.001.00 1.00

21.561.55 1.30

52.702.61 1.70

1014.003.84 2.01

10213.4010.20 3.30

10343.3023.10 4.85

104138.747.40 6.14

105443.089.0 7.63

1061,370.0160.5 8.97

1074,300.0290.0 10.60

10813,670.0 506.0 12.10

- Flux through surface to(from) external phase equals flux through surface from(to) the bulk.
- External Flux to/from surface, Fs, equals mass transfer coefficient, h, (cm/s) times concentration difference, g/cm3 giving g/cm2s
- Flux to/from bulk equals diffusion coefficient (cm2/s) times concentration gradient (g/cm3cm)
- h can be found from h = Fs /(Ceq – Cs) @ t = 0

B1/BFB

01.0

100.11.45

20.53.14

114.95

0.526.8

0.11037.5

The system chlorobenzene in poly(vinyl acetate) has been studied extensively with all relevant data reported in my thesis and subsequent journal articles. These data give a coherent understanding of diffusion in polymers including: Absorption data from one equilibrium to another Desorption data from different equilibrium values to vacuum, and film drying (years), but

only

if one accounts for concentration dependence and significant surface effects when present.

RELATIVE SOLVENT RETENTION (HANSEN, 1967) MOLECULAR SIZE AND SHAPE

Data: Hasimi et al. Eur.Polym.J. 2008;44:4098-4107 ABSORPTION OF WATER VAPOR INTO PVAlc FROM BONE DRY TO 0.748 VOLUME FRACTION

- External phase diffusion from source to film
- Diffusion in stagnant boundary layer at film
- Heat removal on condensation
- Adsorption (How well do HSP match?)
- Orientation (Does n-hexane enter sideways?)
- Absorption site (hole size and shape)
- Transport into bulk (Diffusion coefficient, molecular size and shape)

Solvent Apparent h, cm/s Equilibrium uptake, vol. fraction

Tetrahydrofuran 1.89(10)-40.676

Hexane7.78(10)-60.351

Diethyl ether1.21(10)-60.268

Propylamine1.49(10)-70.181

Ethylene dichloride1.18(10)-70.176

Ethyl acetate1.46(10)-80.076

n-Butyl acetate8.30(10)-100.202

Phenyl acetate 0 0

Acetophenone 0 0

1,4-Dioxane 0 0

- Tetrahydrofuran apparent h is too low since diffusion controls.
- n-Butyl acetate apparent h is strongly lowered by size and shape.

Chapter 16 of Second Edition of Hansen Solubility Parameters: A User’s Handbook, CRC Press, 2007.

Hansen CM. The significance of the surface condition in solutions to the diffusion equation: explaining "anomalous" sigmoidal, Case II, and Super Case II absorption behavior. EurPolym J 2010;46;651-662.

Abbott S, Hansen CM, Yamamoto H. Hansen Solubility Parameters in Practice, www.hansen-solubility.com. (includes software for absorption, desorption and permeation)

Downloads on www.hansen-solubility.com. Including this presentation with comments

Straight line absorption

with linear time cited as

excellent example of

Case II behavior.

This result is duplicated:

Diffusion equation with

significant surface effect

and exponential D(c)

Iodine tracer lags methanol

in PMMA at 30°C showing

apparent step-like gradient.

Methanol does not have this

“advancing sharp front”.

Iodine tracer is far too slow

as shown in the following.

Methanol gradients become

horizontal, not vertical.

Hansen is extraneous; challenges included

Petropoulos JH Sanopoulou M Papadokostaki KG.

Physically insightful modeling of non-Fickian kinetic energy regimes encountered in fundamental studies of isothermal sorption of swelling agents in polymeric media.

Eur Polym J 2011;47:2053-2062.

Hansen cannot explain these data!Next two slides do explain these data for liquid dichloromethane absorption into stretched, confined Cellulose Acetate

CALCULATED ABSORPTION CURVE AND GRADIENTS MATCH EXPERIMENTAL DATA FOR ABSORPTION PERPENDICULAR TO STRETCH DIRECTION: METHYLENE CHLORIDE IN CELLULOSE ACETATE.

CALCULATED ABSORPTION CURVE IS PERFECT, FRONT NOT A SHARP STEP, BUT CLOSE TO EXPERIMENTAL. METHYLENE CHLORIDE IN STRETCH DIRECTION. ARE INITIAL CONDITIONS MAINTAINED? CHANNELS?

- Adsorption (How well do HSP match?)
- Polymer rotation to match HSP of external phase: reason for success with a constant h?
- Orientation (Does n-hexane enter sideways?)
- Absorption site (hole size and shape)
- Number of absorption sites (Equilibrium uptake and similarity of HSP)
- Transport into bulk (Diffusion coefficient, molecular size and shape)

Exclusively bulk phenomena such as stress relaxation or swelling stress need not be invoked to explain the cases examined including Thomas and Windle Case II, Super Case II, and Sigmoidal examples, or the studies of Petropoulos and coworkers.

The diffusion equation can fully describe all of these studies and those of Hansen when the a significant surface condition is included and exponential diffusion coefficients are used.

- Laws of Diffusion are Valid
- Exponential Diffusion Coefficients
- Surface Condition involved with ”Anomalies”
- Combine These - No Anomalies
- Exclusively Bulk Explanations not possible
- Estimate Behavior at Different Conditions
- Improved understanding and modeling of absorption, desorption, and permeation
- Improve Barriers with (HSPp ≠ ≠ HSPs)

Thank you for your attention!

For further contact please visit:

www.hansen-solubility.com

F = p/(L/Papp) = p/(L/P + R1 + R2 + R3 …)

L/Papp = L/P + R1 + R2 + R3 ….

1/Papp = 1/P + (R1 + R2 + R3 ….)/L

Use Plot of 1/P Versus 1/L

- Film: Thickness (L), length (l), width (w)
D0 = Dapp /(1 + L/l + L/w)2

- Circular Film: Thickness (b), Radius (R)
D0 = Dapp/(1 + b/R)2

- For L = 1mm and w = 10mm: Dapp/D0 = 1.21
- Tensile bars (L = 2-4mm, w=10mm): Do not use!

- E = ED + EP + EH
- D - Dispersion (Hydrocarbon)
- P - Polar (Dipolar)
- H - Hydrogen Bonds (Electron Interchange)
- V - Molar Volume
- E/V = ED/V + EP/V + EH/V
2 = 2D + 2P + 2H

HANSEN SOLUBILITY PARAMETERS (HSP)

= Square Root of Cohesion Energy Density

- Ra2 = 4(D1 - D2)2 + (P1 - P2)2 + (H1 - H2)2
- The experimentally verified ”4” is also found in Prigogine’s CST theory
- RED = Ra/Ro (Distance to sphere center divided by its radius)
- (RED)2 = (Ra/Ro)2 corresponds to 12 / c in Huggins/Flory Theory

- Free energy G must be negative for solution
- G = (1/N)øln(ø) + (1 - ø)ln(1 - ø) + Χø(1 - ø)
- ø is the solvent volume fraction
- N is the number of monomers in chain
- Χ = Vm/RT[(D1 - D2)2+ 0.25(P1 - P2)2 + 0.25(H1 - H2)2]
- Χ is the chi parameter, Vm is the molar volume