AFM/ESEM Lab
    Two common techniques for observation of 2D surface
      structure in polymer samples are atomic force microscopy (AFM) and
      environmental scanning electron microscopy (SEM).  AFM has
      two main advantages over SEM, samples do not need to be coated and
      there is no electron charge buildup on non-conducting
      surfaces.  AFM has the potential for much higher resolution
      compared to SEM but is difficult to use as a screening technique
      to find a region of interest.  For polymers both techniques
      are invasive in that there is some potential for sample
      modification during analysis.  We will use the ESEM
      instrument which is an SEM with an elaborate vacuum system that
      allows about 20 Torr of pressure of an arbitrary gas at the sample
      position while maintaining high vacuum at the electron gun. 
      Different detectors are used in the ESEM.  For polymers ESEM
      is of importance due to the breakdown of polymers in the electron
      beam leading to significant offgassing which can corrupt
      conventional SEM and TEM instruments.  Localized heating can
      lead to melting of polymer crystals and other thermally induced
      modifications of morphology.  
    Several samples will be imaged using the ESEM and AFM. The lab
      highlights some applications of ESEM and AFM to scientific issues
      in polymer science.
    
      - Calculation of dispersion and correlation in phase separated
        domains by calculation of the correlation function and the
        particle size distribution. 
- Observation and quantification of disorganized particulate
        filler in polymers.
- Observation and description of polymer crystal structure 
- Observation and description of fibrillation in
        semi-crystalline polymers. 
- Observation and description of mass fractal structure in two
        common polymer additives, organic pigments and inorganic filler
        aggregates. 
Please read the linked web pages for more detailed information on
      these instruments.
    Experimental:
    The following samples will be prepared prior to lab, a Jimble
      will assist you in obtaining images from these samples.
    Samples: (Other samples may be substituted)
    
      - HIPS Phase Separated Domains 
- PE, PP, PHB Crystals 
- Fiber PP from mechanical testing 
- Organic Pigment, Fractal Structure 
- Titania, Fractal Structure 
Analysis
    
      - Phase separated domains: Measure the diameter, aspect ratio of
        a number of rubber domains in HIPS. Also measure the size of a
        number of inclusions within the rubber domains. Calculate the
        mean and standard deviation for these two structures. Plot a
        particle size distribution curve for both of these structures.  (Link
            to Needle Throwing Method for Pairwise Correlation Function)
- Measure the average fiber diameter and standard deviation for
        fibrils in the PP fibers. 
- Measure the mean primary particle size, mean aspect ratios and
        standard deviations for the organic pigment and the titania
        samples.
- Measure the mean aggregate size and standard deviation. 
- Estimate the mass fractal dimension, df, for both
        of these samples. (M ~ Rdf, M is mass of the
        aggregate and R is the aggregate size.  Here M ~ N where N
        is the number of primary particles and R ~ R/dpp
        where dpp is the size of a primary particle, so df
        = ln(M)/ln(R/dpp)).
- For several images use ImageJ shareware to determine the
        autocorrelation function p(r) using an ImageJ plugin available
        from their web page.  
 p(r) = 1 -S/(4V) + ... for very small r near 0.  You need
        to scale your image in ImageJ to the micron scale bar. 
        Determine the Sauter mean diameter from S/V, dp = V/(6S).
- Describe other features of p(r).  If there are peaks in
        p(r) explain what feature in the micrograph corresponds to the
        peaks.
 
- Use ImageJ to determine the average particle size using thresh
        holding in several micrographs.  
 
Questions
    
      - Comment on the problems you encountered in quantifying sizes
        from micrographs. Especially consider the usefulness of 2d
        depictions to describe 3d structure.
- Are the domains (particles) you observed randomly distributed?
        Give support from your data and analysis using the correlation
        function. 
- Describe the differences between the mass fractal structures
        observed. 
- Do the mass fractal structures reflect reaction or transport
        limited growth? Give a possible aggregate growth mechanism for
        both systems and support it with your data. (web
          link for this question.)