Objective:
The objective of this lab is to become familiar with x-ray (and neutron) reflectometery.  A hydrophilic polymer grafted to a silicon wafer will be used to demonstrate x-ray reflectometry. 

Instruments to be used:
X-ray reflectometer

Materials:
Thin film of PNIPAM (hydrophilic polymer) grafted onto a silicon wafer (produced by Sandip Argekar in Prof. Schaefer's Group).

Procedure:
The procedure is detailed in the "Reflectivity SOP How to Run Reflectometer.pdf" file in the background section.

Analysis:
Analysis will be done using the Igor Pro programs written by Jan Ilavsky "Irena".  Install as instructed on the linked web page. 
In the SAS menu, fourth block at the bottom is "Reflectivity".  This will open a control panel for data fitting (this is really a calculation with minimization not a fit).
Ilavsky's code has extensive help manuals.  Please find this manual and the section on reflectivity.

Questions:

1) Determine the critical edge and the surface composition that this critical edge corresponds with.
2) Determine the film thickness from the Kiessig fringes.
3) Verify that a log-log plot of reflectivity versus q follows a power-law decay of -4 slope (this may be compromised by background signal and other factors).
*4a)  Use the Ilavsky code to determine the diffusion profile of the film, diffusion coefficient, integrated concentration, and the film thickness.

c(x) = c(surface) {1 - erf[x/(2sqrt(Dt))]}      

where erf() is the error fumction, t is the time from the start of diffusion, D is the diffusion coefficient, x is the distance into the film, and c(surface) is the fixed surface concentration related to the vapor composition (humidity) times the solubility of water in the film. 

4b) If the method of 4a) is not viable the diffusion coefficient can be determined using the method of Vogt et al. and Singh et al.

5) Compare the value of the diffusion coefficient you have obtained with that of water in PNIPAM or of water in other hydrophilic polymers. Is your value reasonable?

*May not work with x-ray reflectivity due to low contrast between water and polymer and narrow q range.  Better for neutron reflectivity using D2O.