Intrinsic Linkage Reinforcement ϕ0 from Swelling Measurements of Effective Values ϕ

1971 ◽  
Vol 44 (5) ◽  
pp. 1249-1255
Author(s):  
A. F. Blanchard
Keyword(s):  
Volume Fraction ◽  
Basic Theory ◽  
Particulate Reinforcement ◽  
Filler Volume Fraction ◽  
Equilibrium Swelling ◽  
Hard Fraction

Abstract The writer has introduced for rubber with particulate reinforcement the concept of linkage reinforcement ϕ derived from the volume fraction v of rubber or νc of rubber-filled compound at equilibrium swelling in a solvent. Basic elastomer theory was modified to allow for the filler volume fraction C by an effective hard fraction Cm per cm3 of compound, the Flory or Flory-Rehner function F(νr) being replaced by F(νc), and the measure νc of swelling being a compound index replacing the usual νr. On this development of the basic theory, and defining linkage reinforcement ϕ as the ratio of the effective crosslinking of reinforced networks to the 1/Fo(νr) fix points of corresponding gum vulcanizates :

Effect and Detection of Loose Chain Ends in Crosslinked Polyurethane Elastomers

1971 ◽  
Vol 44 (1) ◽  
pp. 152-165 ◽  
Author(s):  
A. E. Oberth
Keyword(s):  
Crosslink Density ◽  
Volume Fraction ◽  
Present Theory ◽  
Swelling Ratio ◽  
Polyurethane Elastomers ◽  
Equilibrium Volume ◽  
Equilibrium Swelling ◽  
Volume Swelling

Abstract The effect of loose chain ends on tensile properties and equilibrium swelling of crosslinked polyurethane rubbers is studied. As in plasticized elastomers, tensile strength and elastic modulus are reduced approximately by a factor (1−νE,P)2, where νE,P is the volume fraction of loose chain ends, plasticizer, or both. This effect is much larger than predicted by present theory. Also the equilibrium volume swelling ratio, V0/V, of rubbers having terminal chains or an equal volume of plasticizer is the same, provided they do not differ in crosslink density. However, the volume fraction of “network rubber” in the equilibrium swollen specimen, ν2, differs owing to the non-extractability of terminal chains. On this basis a method is proposed which allows experimental determination of the volume fraction of loose ends. Elastomers abounding in loose chain ends show markedly less long term stress relaxation. This effect is not clearly understood but is useful to detect the presence of non load-bearing network.

scholarly journals Modelling the Molecular Permeation through Mixed-Matrix Membranes Incorporating Tubular Fillers

Membranes ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 58
Author(s):  
Ali Zamani ◽  
F. Handan Tezel ◽  
Jules Thibault
Keyword(s):  
Aspect Ratio ◽  
Relative Permeability ◽  
Polymer Matrix ◽  
Volume Fraction ◽  
Mixed Matrix Membranes ◽  
Analytical Prediction ◽  
Mixed Matrix ◽  
Permeability Ratio ◽  
Filler Volume Fraction ◽  
Matrix Membranes

Membrane-based processes are considered a promising separation method for many chemical and environmental applications such as pervaporation and gas separation. Numerous polymeric membranes have been used for these processes due to their good transport properties, ease of fabrication, and relatively low fabrication cost per unit membrane area. However, these types of membranes are suffering from the trade-off between permeability and selectivity. Mixed-matrix membranes, comprising a filler phase embedded into a polymer matrix, have emerged in an attempt to partly overcome some of the limitations of conventional polymer and inorganic membranes. Among them, membranes incorporating tubular fillers are new nanomaterials having the potential to transcend Robeson’s upper bound. Aligning nanotubes in the host polymer matrix in the permeation direction could lead to a significant improvement in membrane permeability. However, although much effort has been devoted to experimentally evaluating nanotube mixed-matrix membranes, their modelling is mostly based on early theories for mass transport in composite membranes. In this study, the effective permeability of mixed-matrix membranes with tubular fillers was estimated from the steady-state concentration profile within the membrane, calculated by solving the Fick diffusion equation numerically. Using this approach, the effects of various structural parameters, including the tubular filler volume fraction, orientation, length-to-diameter aspect ratio, and permeability ratio were assessed. Enhanced relative permeability was obtained with vertically aligned nanotubes. The relative permeability increased with the filler-polymer permeability ratio, filler volume fraction, and the length-to-diameter aspect ratio. For water-butanol separation, mixed-matrix membranes using polydimethylsiloxane with nanotubes did not lead to performance enhancement in terms of permeability and selectivity. The results were then compared with analytical prediction models such as the Maxwell, Hamilton-Crosser and Kang-Jones-Nair (KJN) models. Overall, this work presents a useful tool for understanding and designing mixed-matrix membranes with tubular fillers.

scholarly journals Potentialities of a Laser-Induced Breakdown Spectroscopy Technique in the Study of Polymer Composites

2020 ◽  
Vol 74 (6) ◽  
pp. 655-660
Author(s):  
Sebastián Tognana ◽  
Cristian D'Angelo ◽  
Walter Salgueiro ◽  
Susana Montecinos
Keyword(s):  
Polymer Composites ◽  
Potential Application ◽  
Volume Fraction ◽  
Filler Content ◽  
Epoxy Composites ◽  
Laser Induced Breakdown Spectroscopy ◽  
Spectroscopy Technique ◽  
Breakdown Spectroscopy ◽  
Filler Volume Fraction ◽  
Laser Induced Breakdown

A laser-induced breakdown spectroscopy (LIBS) technique was used to evaluate the filler content in particulate epoxy–copper composites. A potential application for a direct and fast measurement of the filler in composites through the LIBS results is suggested using calibrated samples. The methodology used in this work makes possible the incorporation of LIBS as a quantitative technique for the study of particle metal-filled epoxy composites, providing a method to obtain a direct estimation of the filler volume fraction.

Thermodynamic Properties and Polymer Solvent Interaction Parameters for Silicone Rubber Networks

1968 ◽  
Vol 41 (3) ◽  
pp. 608-620 ◽  
Author(s):  
R. D. Seeley
Keyword(s):  
Thermodynamic Properties ◽  
Network Structure ◽  
Silicone Rubber ◽  
Volume Fraction ◽  
Swelling Behavior ◽  
Effective Number ◽  
Solvent Interaction ◽  
Molecular Weights ◽  
Linear Relationships ◽  
Equilibrium Swelling

Abstract The relationships of the volume fraction of rubber (silica reinforced silicone rubber vulcanizates) at equilibrium swelling to a corresponding solvent-rubber interaction parameter have been found to agree quite well with theory throughout the entire range of volume fractions investigated. Composite sigmoidal curves were constructed from the ϕrs versus μ data for the different vulcanizates. Temperature and solvent effects were found to merely shift the plotting points along the curves for the respective vulcanizates. Contrary to other work linear relationships between ϕrs and μ were found in this investigation only in the range of moderate dilations. Such relationships could lead to serious misinterpretations if the investigations involved ϕrs versus μ data near an inflection point. Thus, the value of μ relative to a corresponding ϕrs not only depend upon solvent (s) and temperature, but also upon the level of vulcanization at moderate to high dilations. The entropy, enthalpy, and free energy changes associated with the configurational changes occurring in the network structure of the rubber were calculated. The thermodynamic properties were found to be consistent and uniform throughout the dilation range. Limiting osmotic pressures were determined to obtain effective number average molecular weights of the crosslinked chains. The molecular weight values were found to average slightly less than three times those obtainable from ve/Vr data. Finally, this investigation has shown that reinforced silicone rubber vulcanizates at equilibrium swelling in a variety of solvents exhibit the swelling behavior predicted by theory. However, swelling behavior at moderate to high swelling was found to be unrelated to the rubber in general, but related more specifically to the network structure of the vulcanizate. At low dilations, the characteristics of the silicone rubber species control the swelling behavior.

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 influence of the filler volume fraction on the mechanical behaviour of thermoplastic materials

PAMM ◽  
2004 ◽  
Vol 4 (1) ◽  
pp. 223-224
Author(s):  
Thomas Kletschkowski ◽  
Uwe Schomburg ◽  
Albrecht Betram
Keyword(s):  
Mechanical Behaviour ◽  
Volume Fraction ◽  
Filler Volume Fraction

Improving the Electrical Conductivity of Composites Comprised of Short Conducting Fibers in a Nonconducting Matrix: The Addition of a Nonconducting Particulate Filler

1995 ◽  
Vol 390 ◽  
Author(s):  
Pu-Woei Chen ◽  
D. D. L. Chung
Keyword(s):  
Electrical Conductivity ◽  
Percolation Threshold ◽  
Silica Fume ◽  
Carbon Fibers ◽  
Volume Fraction ◽  
Filler Volume Fraction ◽  
Conducting Filler ◽  
Particulate Filler

ABSTRACTThe addition of a second discontinuous filler (silica fume) that is essentially nonconducting to a composite with a comparably non-conducting matrix (cement) and a conducting discontinuous filler (carbon fibers) was found to increase the electrical conductivity of the composite when the conducting filler volume fraction was less than 3.2%. The maximum conducting filler volume fraction for the second filler to be effective was only 0.5% when the second filler was sand, which was much coarser than silica fume. The improved conductivity due to the presence of the second filler is due to the improved dispersion of the conducting filler. The silica fume addition did not affect the percolation threshold, but the sand addition increased the threshold.

Characterization of Fillers in Vulcanizates According to the Einstein-Guth-Gold Equation

1990 ◽  
Vol 63 (1) ◽  
pp. 32-45 ◽  
Author(s):  
Siegfried Wolff ◽  
Jean-Baptiste Donnet
Keyword(s):  
Surface Activity ◽  
Deformation Temperature ◽  
Volume Fraction ◽  
Crosslinking Density ◽  
High Accuracy ◽  
Effectiveness Factor ◽  
Stress Strain ◽  
Filler Volume Fraction

Abstract 1. Up to now, the application of the Einstein-Guth-Gold equation seemed to be limited to inactive fillers. 2. However, in the form of Equation (6), it describes with high accuracy the moduli of vulcanizates containing active fillers as a function of the filler volume fraction at least up to ϕ=0.22 at uniaxial elongations and for any given value of λ. 3. The effectiveness factor ƒ is independent of crosslinking density, but is dependent on deformation, temperature, and the surface activity of the filler. 4. If ƒ as a function of elongation is known, the respective stress-strain curves of filled networks can be calculated in advance for any given crosslinking density. 5. The interpretation of the effectiveness factor will require further investigations, especially with regard to the influence of the structure and surface activity of the filler.

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