April 1, 1921 



THE INDIA RUBBER WORLD 



493 



occupies a soinevvhat anomalous position in the energy column. 

 It is, namely, a more active pigment than would be indicated by 

 its developed surface. Briefly, any pigment of a degree of sub- 

 division corresponding to a surface development of over 150,000 

 square inches per cubic inch may be expected to belong to the 

 active class. It must of course be remembered that the activity 

 of a pigment depends entirely upon the percentage present in the 

 mixing. Ma.ximum activity is developed for volume percentages 

 lying between 5 and 25. Inert pigments, of course, develop no 

 activity — no matter how much or how little is added. 



THE STRUCTURE OF COMPOUNDED RUBBER 



In view of the iin|)ortant role played by surface energy in the 

 properties of compounded rubber, and also in view of the recently 

 demonstrated tact of the physical separation of the constituent 

 particles from their rubber matrix under conditions of strain, it is 

 clearly of importance that we should know something about the 

 spacial distribution of the component particles of a mixing. Thus, 

 for example, how much barytes may one add to a compound be- 

 fore the particles actually toucli each other? How far apart are 

 the particles of zinc oxide in a tread compound containing, say, 

 20 volume.-; of this pigment? 



These interparticle distances are of theoretical importance, not 

 only for the proper calculation of the forces acting upon the rub- 

 ber phase occupying the interstices, but also in connection with the 

 influence, if any, of electrostatic charges upon the pigment par- 

 ticles during mixing. 



Let us first assume that sufficient pigment has been added to 

 cause actual contact between the particles.. Now it is not at all 

 a simple matter to calculate what percentage must be added to 

 bring about this condition. The question involves a study of the 

 theory of piling. Thus, for example, if we fill a quart measure 

 with marbles, the number we can get into the measure depends 

 upon the character of the piling which they assume. If, after 

 laying in the first layer we place succeeding layers in such a way 

 that each marble lies vertically over and touching the one be- 

 neath, we obtain what is known as cubical or loose piling. If, 

 however, we shake the marbles down until they lie together as 

 closely as possible, the piling assumes a totally different charac- 

 ter, known as normal, close, or tetrahedral piling. 



This question of cubical or tetrahedral piling is important in 

 all studies of granular bodies. Thus, for example, the rigidity 

 of mortar under the trowel, and the firmness of the wet sand 

 on the sea.'ihore under foot, are both due to the fact that the 

 granules are in a condition of close or normal piling, the dis- 

 turbance of which by an external force requires an increase in the 

 over-all volume, which in turn is resisted by the vacua which 

 tend to be formed. 



If a test tube be loosely filled with sand and subsequently 

 gently tapped, the sand will settle down a considerable distance 

 in the tube. The sand was originally more or less loosely piled. 

 It was certainly not piled in the most loose manner possible, 

 namely, cubically, but occupied some intermediate position. On 

 gently tapping the tube the particles are freed, and, attracted 

 downward by the force of gravity, assume a spacial arrange- 

 ment more nearly normal or tetrahedral. 



The Piling of Compounding Ingredients. — We have now to 

 consider what happens when a pigment is worked into the rubber 

 in a plastic state on our mix mills. Owing to the high viscosity 

 of the gum the force of gravity is not free to act as it did in the 

 case of the sand in the test tube or the marbles in the quart 

 measure. Taking first a case where so much pigment is added 

 that the particles are compelled to touch each other, it is possible 

 to calculate the amount of pigment required on the assumption, 

 first, that the particles are arranged aibically or loosely, and, 

 second, tetrahedrally or closely. 



On the former assumption, irrespective of the size of the par- 

 ticles (which are. however, assumed to be uniformly spherical), 



the amount required would be 52.4 per cent of the total by volume. 

 On the second assumption, the figure comes out at 74.1 per cent. 



It is a well-known fact in mill practice that a compound con- 

 taining 50 per cent by volume of pigment is almost unmanage- 

 able on the mill. We therefore deduce that with the customary 

 amount of milling the pigment particles probably exist in a con- 

 dition more closely approximating the loose or cubical piling than 

 the close or tetrahedral piling. The writer has, however, observed 

 that in working with extremely heavily loaded stocks it is pos- 

 sible, by continued milling, to bring about a more or less sharply 

 defined increase in plasticity with the possibility of working in 

 an additional amount of pigment. With due regard to the break- 

 ing down of the rubber owing to this excessive milling, it still 

 remains highly probable that the additional mastication has caused 

 a more even distribution of the rubber phase throughout the mass, 

 which is equivalent to saying that the particles have been re- 

 arranged to more nearly normal piling. The writer has in fact 

 succeeded m milling in over 60 per cent by volume of pigment 

 in this way (i. e., 60 volumes pigment to 40 volumes rubber). 



Spacial Arrangement When Not in Contact. — Fig. 7 shows 

 interparticle distances for percentages of pigment ranging all the 

 way from to 80 per cent. The ordinate D shows the distance 



between the particles re- 

 ferred to their radius as 

 unity. The upper curve 

 shows conditions when the 

 particles are tetrahedrally 

 disposed. Under working 

 conditions in the factory 

 very few compounds contain 

 more than 35 per cent by 

 volume of pigment. Taking, 

 for example, a typical tire 

 80 tread compound containing 

 20 per cent of pigment by 

 Fjc 7 Interparticle Distance vs.^o'u"ie and assuming tetra- 

 VoLUME Per Cent Pigment h-^^ral arrangements, the 



particles will be distant 

 from each other by a little 

 over their own radius. .\ssuming cubical arrangement they 

 would be closer together, namely, distant by about three-quarters 

 of their radius. This of course presupposes spherical shape. In 

 actual practice, the pigment particles are by no means spherical, 

 but on the average they are more nearly spherical than of any 

 other definite geometrical shape, and the error due to assuming 

 sphericity will not be large. 



The question as to whether in such cases where the particles are 

 not in actual contact one ought to assume a tetrahedral or a 

 cubical space arrangement is (at least to the writer) very diffi- 

 cult to answer by mathematical analysis. It should be quite 

 possible, however, to reach an appro-ximate solution by numerous 

 direct microscopic measurements on thin sections by transmitted 

 light, and we hope to secure results of this kind in the near future. 

 In any case, the values shown on this chart represent the extremes 

 between which the true values must lie, and we are of the 

 opinion, as intimated above, that the action during milling is 

 that the rubber phase will tend to become as evenly distributed as 

 possible, and that therefore the tetrahedral arrangement is the 

 more nearly in accordance with actual conditions. 



The writer fully realizes that the foregoing analysis hardly 

 scratches the surface of the problem of the structure of com- 

 pounded rubber. Of cardinal importance are, for example, the 

 direct measurement of the surface tension between zinc oxide 

 and rubber, carbon blacks made under different conditions and 

 rubber, and so on. When these values are once determined the 

 capacity factor of the surface energy as measured by the average 

 degree of dispersion of any given pigment can in our opinion be 

 most accurately measured by its admixture under standard con- 

 ditions in a rubber compound, and the determination of the 



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