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Homework 2 

CM4655 Polymer Rheology Laboratory

    Due: Week 10, Friday 5pm to me or in my mailbox in 203 Chem Sci (paper) or by email midnight (PDF).

For the data in this file (click here to download) please make the following calculations.  Note that all your plots should be log-log; adjust the number of decades shown to focus in on your data.  Do not plot fractional decades (only full decades).

  1. Calculate G* from "viscous modulus" (G") and "elastic modulus" (G').  Plot your caclulated G* versus frequency (in rad/s) on the same axes (log-log) as the "complex modulus" data that is in the data file.  Are they the same?  (They should be).
  2. Calculate eta* from "complex modulus".  Plot your calculated eta* versus frequency (in rad/s) on the same axes (log-log) as the "complex viscosity" data that is in the data file.  Are they the same?  (They should be).
  3. Calculate tan delta from the "phase angle" data.  Calculate tan delta as tan delta=G"/G' (see formulas in Table 5.1 page 156).  Are they the same?  They should be.  (Note in Excel when you take the tangent of an angle, the angle must be in radians).  Plot your calculations on the same graph (log log, versus frequency in rad/s).
  4. Calculate G' and G'' from "stress", "phase angle" and "strain" using equations 5.128 and 5.129 on page 155 of the text.  Do they match the "elastic" and "viscous" moduli given?  They should.  Plot your calculations on the same axes (log-log, versus frequency, rad/s).
  5. Calculate the frequency omega, where omega is frequency in radians per second (instead of Hz, which is cycles per second, 2*Pi radians per cycle).  Plot G', G'', and eta * versus omega on a log log plot.  This is usually how we report this data.