Gravimetric Water Vapor Permeability of Flat Materials and Finished Objects

Transcription

1 Gravimetric Water Vapor Permeability of Flat Materials and Finished Objects Beyond Certification Under ISO L. Lundquist, C. Pelletier, Y. Wyser, Lausanne Switzerland

2 Purpose Show dominant contributions to gravimetric WVTR uncertainty, depending on measurement procedure and measured barrier properties Limitations of the current method NOT discuss all contributions in detail 2

3 Outline WV-TR Method description Uncertainty: Causes & Relevant Effects Implications & Next steps 3

4 Samples Vapor Barrier Film Rigid containers HIGH Metallized PET Jar Co-E-P/EVOH/Co-E-P LOW Pure PET Beverage bottle PET/MXD-6/PET 4

5 Method Flow Chart Reference sealing Only with small number of specimens Volume measurement Container sealing Film dish sealing Stabilisation climatic chamber 23 C 85% RH 1 month, t 0 Specimen Blank Picture NA, t n-1 Blank Specimen hrs, t n 5

6 The WVTR mathematical expression does not account for all sources of uncertainty Method Blank (Films & Containers) Reference vol. (Only Containers) Rigid container [mg/pack.day] Flexible film [g/m 2.day] WVTR WVTR = = b b ( mn mn 1) ( mn mn 1) A ( t t ) m = specimen mass [mg,g] t = time [days] m b = blank weight [mg,g] V s = sample volume [cm 3 ] m r = reference weight [mg,g] V r = reference volume [cm 3 ] A = film surface area [m 2 ] n n 1 r r ( mn mn 1) ( mn mn 1)( Vs Vr) ( t t ) n n 1 Buoyancy Driving force Wall H 2 O content Buoyancy 6

7 Outline WV-TR Method description Uncertainty: Causes & Relevant effects Implications & Next steps 7

8 Cause & Effect Diagram m n (sample) linearity m n-1 (sample) Weight increase, Dm Readability m n (ref/blank) m n-1 (ref/blank) Buoyancy & Driving force, Dmr/b linearity Readability Final volume reading Final volum reading Reading Reading Tolerance glassware Vr Tolerance glassware Vs linearity Readability linearity Readability WVTR Clock precision t n Clock precision Temperature Relative humidity Regression Template t n-1 Time H2O Partial pressure Film surface 8

9 Weight change Dm/Dt, Dm b,r /Dt m mn m = t t t ( ) n 1 ( ) n n 1 u linearity = 0.001g u readability = g Sample (average of several specimens) Repeatability m/ t 1 u m t SD u u t (( ) 2 ( ) 2 ) 2 ( / ) = rep + 2* linearity + readability Reference/blank (one specimen) 1 u( m / t) = 2* SD + u + u t (( ) 2 ( ) 2 ( ) 2 ) rb, rep linearity readability 9

10 Driving force is H 2 O Partial pressure not RH Climate T= 23.4 u(t) = 0.3 C RH = 81.5 u(rh) = 0.8 %RH Driving force F (P ext -P int ) P int = 0 P ext = f(t,rh) u(p RH ) = u(rh)*17.56 u(p RH ) Psat WV [mm Hg] Source u(p regr ) u(p T ) u(p RH ) u(p regr ) u(p T ) uj Temperature [ C] uj 2 7.0E S (uj 2 ) u P Rel u P Rel contrib. 5.5E

11 Combined Uncertainty: Films PET (low barrier) Source Value uj ci (ujci)^2 urel m/ t mb/dt A Total (ciuj)^ Total (ciuj) [g/m2.day] Relative (ciuj) 0.07 Relative contribution Met-PET (high barrier) Source Value uj ci (ujci)^2 urel m/ t mb/dt A Total (ciuj)^ Total (ciuj) [g/m2.day] Relative (ciuj) 0.86 Relative contribution

12 Combined Uncertainty: Rigid containers & Blank Bottle (low barrier) Source Value uj ci (ujci)^2 urel m/ t mb/dt Total (ciuj)^ Total (ciuj) [mg/pack.day] Relative (ciuj) 0.01 Relative contribution Jar (high barrier) Source Value uj ci (ujci)^2 urel m/ t mb/dt Total (ciuj)^ Total (ciuj) [mg/pack.day] Relative (ciuj) 0.31 Relative contribution

13 Combined Uncertainty: Rigid containers & Reference Volume Bottle (low barrier) Source Value uj ci (ujci)^2 urel m/ t mr/dt Vs/Vr P H2O Total (ciuj)^ Total (ciuj) [mg/pack.day] Relative (ciuj) 0.02 Jar (high barrier) Source Value uj ci (ujci)^2 urel m/ t mr/dt Vs/Vr P H2O Total (ciuj)^ Total (ciuj) [mg/pack.day] Relative (ciuj) 0.16 Relative contribution Relative contribution

14 Cause & Effect Diagram m n (sample) linearity m n-1 (sample) Weight increase, Dm Readability m n (ref/blank) m n-1 (ref/blank) Buoyancy & Driving force, Dmr/b linearity Readability Final volume reading Final volum reading Reading Reading Tolerance glassware Vr Tolerance glassware Vs linearity Readability linearity Readability WVTR Clock precision t n Clock precision Temperature Relative humidity Regression Template t n-1 Time H2O Partial pressure Film surface 14

15 Refined Cause & Effect Diagram Repeatability m m n (sample) linearity m n-1 (sample) Weight increase, Dm Readability m n (ref/blank) m n-1 (ref/blank) Buoyancy & Driving force, Dmr/b linearity Readability Final volume reading Final volum reading Reading Reading Tolerance glassware Vr Tolerance glassware Vs linearity Readability linearity Readability WVTR Clock precision t n Clock precision Temperature Relative humidity Regression Template t n-1 Time H2O Partial pressure Film surface 15

16 Expanded Uncertainty Containers: Reference gives different result for low barriers Barrier Method Value Expanded uncertainty (k=2) Comparison of means & variances 5% significance Blank LOW NOT DIFFERENT Reference Blank HIGH DIFFERENT! Reference

17 Outline WV-TR Method description Uncertainty: Causes & Relevant Effects Implications & Next steps 17

18 Implications & Next Steps Present method suited for low to medium barrier applications MU for intermediate barriers Reference volume should be used with caution for medium to low barrier materials For reference volume method the climate control dominates uncertainty for low barriers, while remaining significant for high barriers Method improvement Increase time-span between weighing not possible Use balance with higher sensitivity Linear regression over several measurements 18

19 Film surface area, A D = 79.8 ± 0.2 mm c D 2 πd πd = = D 4 2 A [m2] interval distribution uj ci ciuj rectangular E-05 Urel

20 Sample volume/reference volume Uncertainty of one volume measurement Source interval distribution uj ci ciuj (ciuj)^2 urel filling 20 rectangular reading 20 rectangular line marking 28 rectangular Total (ciuj)^ Total (ciuj) 23.0 Expression Vs Vr Sensitivity coefficients (ci) for combined uncertainty Vs Vr 1 = Vs Vr Combined uncertainty beverage bottle, u(v) Source Value uj ci (ujci)^2 urel Vs Vr Tot (ujci)^ Tot (ujci) Rel u(v) Vs Vr Vs = Vr Vr 2 20