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Optical Microscopy for Kinetics of Spherulitic Growth

Objective: To measure the growth rate and Avrami parameters for spherulitic growth using optical microscopy and a video attachment.

Materials: Several blends of isotactic and atactic polyhydroxybutyrate (PHB) and copolymers of polyhydroxybutyrate and polyhydroxyvalerate (PHB-co-PHV) will be used.

Procedure: The polymer samples will be sandwiched between glass cover-slips and heated to above the melting point (about 180°C), then quenched to an isothermal crystallization temperature. The radial spherulitic growth rate will be measured at a number of quench temperatures using an optical microscope under crossed polarizers. After isothermal crystallization is complete you should heat the polymer from a lower temperature at a slow rate and determine the melting point.

Required Analysis: (Please number in your report)

  1. Make plots of spherulitic radius (µm) versus time (minutes) for a number of quench temperatures, these curves should be linear at early stages of growth.
  2. Make a plot of linear growth rate, G, versus crystallization temperature (Tc), this should lead to a bell shaped curve if sufficient data is taken, i.e. there is a maximum growth rate temperature that you should determine.
  3. Make a Hoffman-Weeks plot of Tc versus Tm for your spherulites by cooling the samples after isothermal crystallization and slowly heating until the melting point is observed in the microscope. This plot should yield T°.
  4. Make a simplified Hoffman plot for growth kinetics of log (G) versus Tc in an attempt to observe the Regime I to Regime II or Regime II to Regime III transitions (see web notes, for instance, for a description of the Hoffman Regimes of growth, also see L. H. Sperling "Introduction to Physical Polymer Science", Figure 6.33 pp. 243.).
  5. Estimate the volume fraction crystalline in your micrographs either visually or using the Scion Image (NIH Image), image analysis program. This will be estimated from an area fraction crystallinity since the micrographs are 2-d. There are several algorithms for estimation of the volume fraction crystallinity from such area fractions assuming the spherulites are spherical (see L. C. Sawyer and D. T. Grubb "Polymer Microscopy" Chapman and Hall 1987 or Campbell and White "Polymer Characterization").
  6. From the estimated volume fraction crystallinity, fc(t), as a function of time for a fixed temperature make several Avrami plots ln(ln(1-fc)) versus ln(time).
  7. From the Avrami plots determine the Avrami index, n, and the Avrami coefficient, K.
  8. From the micrographs estimate the band spacing for your sample at different isothermal crystallization temperatures. Construct a plot of band spacing versus crystallization temperature.

Questions:

  1. Why do polymers form spherulites rather than grains such as in a sample of aluminum?
  2. What causes a spherulitic band?
  3. Why do you think the band spacing changes with isothermal crystallization temperature?
  4. Why are crossed polarizers used in this lab? Explain the meaning and physical origin of the "Maltese Cross" observed under crossed polarizers. For a fiber with the fiber axis pointing in the analyzer's direction of polarization what will be observed in the optical micrograph.
  5. Do you expect the growth rate to be linear? Why?
  6. Why is the linear growth rate plot versus temperature curve expected to be bell shaped? Give equations. Why is there a maximum in the growth rate?
  7. Explain the meaning of Regime I, Regime II and Regime III from Hoffman theory. Which of these is normally observed?
  8. What is the theoretical basis of the Hoffman-Weeks plot, i.e. why does the melting point not equal the crystallization temperature?
  9. How do you expect the lamellar thickness to vary with isothermal crystallization temperature?
  10. What type of nucleation and what shape of growth do you see in your data form the Avrami analysis? How are the Avrami parameters related to nucleation and growth geometry?
  11. What other techniques could be used to determine the Avrami coefficients. Are these better than the technique you used in this lab?