Lecture11Notes

# Lecture11Notes - Lecture 11 Glass transitions and Liquid...

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Lecture 11 Glass transitions and Liquid Crystalline Behavior 1 Wednesday, November 3, 2010

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Glass Transition Temperature (T g ) 2 Wednesday, November 3, 2010
Order of Phase Transitions We can plot free energy as a function of temperature for a crystalline (or glassy) material, and free energy as a function of temperature for a melted material In the crystalline state, the configurational entropy is small because they are arranged in an ordered conformation and locked into that position At low temperatures, the attractive forces between the chains dominate the free energy; at higher temperatures, the entropic portion increases, and the liquid form becomes more favorable At the melting point, the free energy of the crystal and the melt are equal Free energy is continuous as a function of temperature, but there is a shift from one curve to the other at the melting point 3 Wednesday, November 3, 2010

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Order of Phase Transitions A first order phase transition occurs when the first derivative of free energy wrt T is discontinuous (volume, enthalpy, entropy) Example: the slope of the curves of crystallization and melting are different when they meet at the melting point, leading to an abrupt change T m is first order; T g is not 4 Wednesday, November 3, 2010
Order of Phase Transitions A second order phase transition occurs when the second derivative of free energy wrt T is discontinuous (heat capacity, C P , compressibility, κ , and α , thermal expansion coefficient) Polymer crystallization and melting are true first order transitions, and the glass transition may be related to a second-order transition (pseudo-second order) 5 Wednesday, November 3, 2010

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Motion In the gaseous state, translational motion is easy to picture In the crystalline state, translational motion is restricted, but there are still oscillations about an average or mean position In the liquid state, motions are coupled 6 Wednesday, November 3, 2010
Motion and Polymers Polymers are not well approximated by spheres Chains can interpenetrate (remember theta conditions) and entangle Large scale motion in the melt is prevented by random close packing of the chains 7 Wednesday, November 3, 2010

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Nature of T g Is T g a thermodynamic or kinetic phenomenon? The observed T g depends on thermal history, so there is a kinetic component But is there an underlying thermodynamic transition? 8 Wednesday, November 3, 2010
Free Volume In a crystalline lattice, there is empty volume (volume between atoms); this is NOT what we mean when we discuss free volume Molecules have thermal motion For a material in the glassy state, we can think of this motion in terms of a sphere which oscillates in a cage of its neighbors These oscillations create some free volume over and above the empty space characteristic of random close packing For polymers, the sphere represents a segment, not a whole chain 9 Wednesday, November 3, 2010

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Free Volume Free volume is not unoccupied or empty volume Free volume increases with increasing temperature, as the oscillations (and their amplitude) increase
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