Lecture 6 - Surface fundamentals

Lecture 6 - Surface fundamentals - MSE 803: NANOMATERIALS...

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MSE 803: N ANOMATERIALS AND N ANOTECHNOLOGY Professor Xudong Wang 213 MSE Building Spring 2010 Class 6: Fundamentals of Solid Surfaces
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Reduction of Surface Energy: Total NP system Mechanisms for reducing overall surface energy Combining of individual nanostructures to form larger structures lower SE Agglomeration of individual nanostructures without altering individual structure Sintering and Ostwald ripening processes: (a) Sintering combines individual particles to form bulk material (b) Oswald ripening merges smaller particles into a larger particles Both Sintering and Ostwald ripening reduce solid-gas surface area Material always transferred from smaller to larger particle To quantify process need to understand chemical potential
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Chemical Potential Introduced by William Gibbs, 1876:---- If add an infinitesimal mass of matter to any homogeneous mass, whose mass, entropy and volume essentially remains unchanged, then the increase in energy of the mass divided by the quantity of mass added is the potential for that mass Thus the chemical potential, μ , of a thermodynamic system is the amount by which the energy of system changes if an additional particle is introduced, with the entropy and volume held constant If a system contains more than one species of a particle, there is a separate chemical potential associated with each species For a thermodynamic system with N constituent species, at constant temperature and pressure, the chemical potential of an atom is the partial derivative of the Gibbs free energy: i j N P T i i N G , ,
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Chemical potential will be dependent on surface curvature Result of transferring δ n atoms from a flat surface to a particle with radius R the volume change in sphere, dV is equal to atomic volume, , times δ n . The work per atom, Δμ , equals change in chemical potential where μ c and μ Combining gives: The Young-Laplace equation Chemical Potential of Particles dn dA c R . 2 n dV
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Chemical Potential: Curved Surfaces Generalizing for any curved surface: System reconfigures to achieve lowest surface energy: Mass transfer from flat to convex surface results in increase in surface chemical potential
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This note was uploaded on 03/23/2010 for the course MATERIAL S 803 taught by Professor Samuel during the Spring '10 term at Wisconsin.

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Lecture 6 - Surface fundamentals - MSE 803: NANOMATERIALS...

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