Effects of Filler Morphology and Loading on Tire Innerliner Permeability A Computational Study

Transcription

1 Effects of Filler orphology and Loading on Tire Innerliner Permeability A Computational Study By: Dr. Tyler Gruber, Dr. Charles Herd, Dr. Paul Smith, and Steve Crossley Columbian Chemicals Company Outline Introduction Permeability odel Effects of Loading on Permeability Effects of Particle Size on Permeability Effects of Particle Size Distributional Width on Permeability Summary and Conclusions 2 1

2 Introduction This Study Focuses on Understanding the Effects of Carbon Black orphology and Loading on the Permeability Characteristics of Innerliner Compounds A Computational Algorithm was Developed Utilizing a Biased Random Walk odel to imic Diffusion of Gaseous olecules Through a Volume (in this case assumed to be an innerliner compound) odel simple as it assumes carbon black aggregates are spheres rather than their accurate, complex, morphology This odel Allows Wide Variation and Evaluation of the Effects of: Loading Particle Size, and Particle Size Distributional Width In-Rubber Properties were not Considered nor Optimized; Rather the Goal of this Study was to Understand the Fundamental Effects of orphology and Loading on Permeability, Allowing Compounders to Optimize their Formulations within Their Performance Requirements 3 Permeability in Rubber Compounds STEP (1): olecule,, Solubilizes at Surface 1 STEP 2: olecule,, Diffuses through Rubber Compound 1 2 STEP 3 : olecule,, Evaporates from Surface 2 {C 1 } {C 2 } Where: {C 1 }>{C 2 } or {P 1 }>{P 2 } Q = D S Q = Permeability D = Diffusivity S = Solubility G.J. van Amerongen, RC&T, 37, 1065,

3 Permeability in Rubber Compounds any Factors can Affect Permeability in a Rubber Compound and Include: Polymer Type Service Temperature Filler Type and Loading Sulfur Groups and Crosslinks Compound Formulation and Age of Compound Chemical and olecular Configuration of Diffusing olecule 5 odeling Criteria for Gaseous olecule Biased Random Walk Diffusion Through Innerliner Compound Cubic repeatable cell has size = 20 * (mean particle size) Cell space is randomly filled with 1000s of log-normally distributed carbon black particles (3D coalescence/interpenetration not allowed) Random vector added to constant bias vector for each step of gas molecule When molecule encounters carbon black particle, it collides, and undergoes specular reflection ( i = r) When gas molecule encounters the cell boundary, it reappears at the opposite wall olecule travels 50 microns parallel to bias vector 20 repetitions for each experiment yields 1 mm total travel for 1 nm bias vector (1,000,000 steps, mean, for 6 unfilled rubber) X 20 per experiment 3

4 Random Walk Schematic (2D): When olecule Encounters a Carbon Black Particle, it Collides, and Undergoes Specular Reflection ( i = r) 7 The Total Number of Steps Required to Travel Through the Volume is Assumed to be Inversely Proportional to the Indicated Permeability of the Compounds Top View (along Z-axis) Side View (along Y-axis) 8 Arrows indicate bias vector direction 4

5 Computational Experimental Design and Results Independent Variables of Filler Loading and orphology Evaluated for their Effects on Permeability (Computational) Case 1: Filler Loading Phr: Case 2: ean Particle Size: (30, 50, 70, 100, 150, 300, 500 nm) with log-normal distribution HI = 1.5 Case 3: Particle Size Distributional Width (defined by Heterogeneity Index, W/. Varied from 1.5, 2.0, 2.5, to 3.0). PS = 100 nm Weight ean = Σnd 4 /Σnd 3 ean = Σnd/n t 10 5

6 Case 1: Effects of Filler Loading on Permeability (Computational Prediction): Higher Filler Loading Reduces Permeability 11 Loading: Two-Dimensional Slices of Cubic Volumes Showing Increased Number of Particles with Increasing Loading 20 phr 40 phr 60 phr 80 phr 100 phr 120 phr 12 6

7 Case 2: Particle Size Distributions (log-normal) for ean Particle Sizes with Constant Distributional Width, HI = Effects of Particle Size and Filler Loading on Permeability: Smaller PS Decreases Permeability 14 7

8 ean Particle Size (PS): Two-Dimensional Slices of Cubic Volumes Showing Decreasing PS (log-normal) in a Given Volume (Constant Loading) 500 nm PS 300 nm PS 150 nm PS 70 nm PS 50 nm PS 30 nm PS nm Smaller Particle Size Imparts a Significantly Higher Number of Particles per Unit Volume at any Given Loading 16 8

9 Case 3: Constant ean Particle Size with Wider PSD (larger HI) eans Lower Surface Area 17 Effects of Distributional Width on Permeability: Broader PSD Gives Neutral to Slightly Negative Effect on Permeability 18 9

10 Particle Size Distributional Width (HI): Two-Dimensional Slices of Cubic Volumes Showing Increased Distributional Width (Lower Surface Area) for a Constant ean Particle Size in a Constant Volume HI = 1.5 HI = 2.0 Constant ean Particle Size with Wider PSD (larger HI) eans Lower Surface Area HI = 2.5 HI = Summary and Conclusions For Increased Carbon Black Loading in a Rubber Compound or Innerliner: The number of aggregates per unit volume increases. ore collisions become statistically possible, increasing the path length or tortuosity of the diffusing gaseous molecule. Permeability is Predicted to Decrease. For Increased Carbon Black ean Particle Size at a Given Loading and Distributional Width: The number of aggregates per unit volume decreases with increasing mean particle size. Fewer collisions become statistically possible with increasing mean particle size or decreasing surface area, decreasing the path length or tortuosity of the diffusing gaseous molecule. Permeability is Predicted to Increase with Increasing ean Particle Size (at Constant Loading). For Constant ean Particle Size with Increasing Distributional Width (HI) at a Given Loading: The number of aggregates per unit volume decreases slightly with increasing distributional width. Fewer collisions become statistically possible with increasing distributional width. Permeability is Predicted to Remain essentially constant with Increasing Particle Size Distributional Width (or HI) within the range studied in this work

11 Recommendation and Further Work / Next Steps Recommendation for Optimum Permeability Use a Carbon Black with a small of Particle size/low structure and at as High of a Loading as Practical (to maintain rubber properties) Recommendation for Lowest Cost Use as High of a Loading as Possible, and will Require a Large Particle Size/Low Structure Carbon Black Future Work Aggregation: Effects of structure can be considered as only spherical particles were modeled odel Variables: Effect of Step and Bias vector lengths, Rubber Shells and Polymer obility (hole formation) can be considered 21 11