Elasticity of colloidal clusters with application to carbon-black aggregates in filled rubbers

2013 ◽  
pp. 261-266 ◽  
Author(s):  
R Dargazany ◽  
A Rege ◽  
M Itskov
Keyword(s):  
Carbon Black ◽  
Colloidal Clusters ◽  
Filled Rubbers

A Carbon Black Structure-Concentration Equivalence Principle. Application to Stress-Strain Relationships of Filled Rubbers

1971 ◽  
Vol 44 (1) ◽  
pp. 199-213 ◽  
Author(s):  
Gerard Kraus
Keyword(s):  
Carbon Black ◽  
Primary Structure ◽  
Equivalence Principle ◽  
Chemical Activity ◽  
Cross Linking ◽  
Surface Chemical ◽  
Deformation Structure ◽  
Carbon Blacks ◽  
Filled Rubbers ◽  
Dependent Factor

Abstract It is shown that various modulus values of carbon black reinforced rubber are functions of the product of the actual black loading and a structure dependent factor. The structure factor appears to be a linear function of the so-called 24M4 value of the dibutylphthalate absorption and is independent of elongation, temperature, and degree of cross-linking over the ranges covered by the data reported. An interpretation of the results is offered based on the idea of polymer occluded in the interstices of primary structure aggregates and thereby shielded from deformation. Structure-concentration equivalence can only be demonstrated with carbon blacks differing in (primary) structure alone. Deviations are observed whenever the carbon blacks compared vary significantly in specific surface area and surface chemical activity.

MODIFIED GUTH–GOLD EQUATION FOR CARBON BLACK–FILLED RUBBERS

2013 ◽  
Vol 86 (2) ◽  
pp. 218-232 ◽  
Author(s):  
Y. Fukahori ◽  
A. A. Hon ◽  
V. Jha ◽  
J. J. C. Busfield
Keyword(s):  
Carbon Black ◽  
Volume Fraction ◽  
Solid Particles ◽  
Carbon Particles ◽  
Filler Volume Fraction ◽  
Rigid Filler ◽  
Bound Rubber ◽  
Small Volume Fraction ◽  
Filled Rubbers ◽  
Good Agreement

ABSTRACT The modulus increase in rubbers filled with solid particles is investigated in detail here using an approach known widely as the Guth–Gold equation. The Guth–Gold equation for the modulus increase at small strains was reexamined using six different species of carbon black (Printex, super abrasion furnace, intermediate SAF, high abrasion furnace, fine thermal, and medium thermal carbon blacks) together with model experiments using steel rods and carbon nanotubes. The Guth–Gold equation is only applicable to such systems where the mutual interaction between particles is very weak and thus they behave independently of each other. In real carbon black–filled rubbers, however, carbon particles or aggregates are connected to each other to form network structures, which can even conduct electricity when the filler volume fraction exceeds the percolation threshold. In the real systems, the modulus increase due to the rigid filler deviates from the Guth–Gold equation even at a small volume fraction of the filler of 0.05–0.1, the deviation being significantly greater at higher volume fractions. The authors propose a modified Guth–Gold equation for carbon black–filled rubbers by adding a third power of the volume fraction of the blacks to the equation, which shows a good agreement with the experimental modulus increase (G/G0) for six species of carbon black–filled rubbers, where G and G0 are the modulus of the filled and unfilled rubbers, respectively; ϕeff is the effective volume fraction; and S is the Brunauer, Emmett, Teller surface area of the blacks. The modified Guth–Gold equation indicates that the specific surface volume ()3 closely relates to the bound rubber surrounding the carbon particles, and therefore this governs the reinforcing structures and the level of the reinforcement in carbon black–filled rubbers.

scholarly journals The Payne Effect in Double Network Elastomers

2005 ◽  
Vol 78 (1) ◽  
pp. 76-83 ◽  
Author(s):  
J. Wang ◽  
G. R. Hamed ◽  
K. Umetsu ◽  
C. M. Roland
Keyword(s):  
Carbon Black ◽  
Natural Rubber ◽  
Storage Modulus ◽  
Double Network ◽  
Payne Effect ◽  
Mechanical Hysteresis ◽  
Mechanical Measurements ◽  
Filled Rubbers ◽  
Styrene Butadiene ◽  
Double Networks

Abstract Double network elastomers were prepared by curing under strain previously-crosslinked natural rubber or styrene-butadiene copolymer. The rubbers were reinforced with carbon black, so that the conventional (singly-cured) materials exhibited a substantial Payne effect, reflecting agglomeration of the filler particles. This effect was much reduced in the double networks - the storage modulus varied more weakly with strain amplitude, and the mechanical hysteresis was substantially smaller. Comparable results were obtained for dynamic mechanical measurements employing different test geometries; that is, the effect is independent of the direction of the strain relative to the orientation of the double network. These results indicate that deformation during the imposition of a second network disrupts the carbon black agglomerates, and this deflocculated structure is stabilized by the second crosslinking. Thus, double network processing is a general means to lower the hysteresis of filled rubbers.

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