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On the spheroidization of rod-shaped particles of finite length

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Abstract

The governing equation for the capillarity-induced shape changes of a surface of revolution by surface diffusion,

$$\frac{{\partial n}}{{\partial t}} = \frac{B}{y}\frac{\partial }{{\partial s}}\left( {y\frac{{\partial K}}{{\partial s}}} \right)$$

where∂n/∂t is the normal velocity of the surface,y is measured normal to the axis of revolution,s is arc length,K is the total surface curvature andB is a kinetic parameter which is constant for a given temperature and material, is presented. A numerical solution to this equation is used to analyse finite cylinders with hemispherical ends. A critical length-to-diameter ratio (L/D) of 7.2 is predicted, below which only one spheroidal particle results and above which two or more are formed, and is shown to have experimental support in several systems.

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References

  1. 1.

    Lord Rayleigh,Proc. London Math. Soc. 10 (1878) 4.

  2. 2.

    F. A. Nichols andW. W. Mullins,Trans. Met. Soc. AIME 233 (1965) 1840.

  3. 3.

    F. A. Nichols andW. W. Mullins,J. Appl. Phys. 36 (1965) 1826.

  4. 4.

    W. W. Mullins,J. Appl. Phys. 28 (1957) 333.

  5. 5.

    F. A. Nichols,Acta Met. 16 (1968) 103.

  6. 6.

    D. M. Moon andR. C. Koo,Met. Trans. 2 (1971) 2115.

  7. 7.

    G. G. Lemmlein,Proc. USSR Acad. Sci. 85 (1952) 1.

  8. 8.

    M. McLean,Phil. Mag. 27 (1973) 1253.

  9. 9.

    M. McLean andM. S. Loveday,J. Mater. Sci. 9 (1974) 1104.

  10. 10.

    C. Herring,J. Appl. Phys. 21 (1950) 301.

  11. 11.

    A. J. Stapley andC. J. Beevers,J. Mater. Sci. 8 (1973) 1287.

  12. 12.

    Idem, ibid 8 (1973) 1296.

  13. 13.

    C. F. Yen andR. L. Coble,J. Amer. Ceram. Soc. 55 (1972) 507.

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Nichols, F.A. On the spheroidization of rod-shaped particles of finite length. J Mater Sci 11, 1077–1082 (1976). https://doi.org/10.1007/BF00553115

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Keywords

  • Polymer
  • Kinetic Parameter
  • Surface Curvature
  • Shape Change
  • Surface Diffusion