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Cell[CellGroupData[{
Cell[TextData[{
  StyleBox["FREQUENCY MODULATION DYNAMIC FORCE SPECTROSCOPY \n", "Subtitle",
    FontSize->28],
  StyleBox["Determination of Force and Energy vs Separation from Frequency vs \
Separation Data\n", "Subtitle"],
  StyleBox["[JE S", "Subtitle",
    FontSize->16],
  StyleBox["ader",
    FontSize->16],
  StyleBox[" ",
    FontSize->16,
    FontSlant->"Italic"],
  StyleBox["and SP Jarvis",
    FontSize->16,
    FontVariations->{"CompatibilityType"->0}],
  StyleBox[", ",
    FontSize->16],
  StyleBox["Applied Physics Letters",
    FontSize->16,
    FontSlant->"Italic"],
  StyleBox[", 84, 1801-1803 (2004)]",
    FontSize->16]
}], "Title"],

Cell[TextData[{
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " notebook to implement the conversion procedure [Sader",
  StyleBox[" et al",
    FontSlant->"Italic"],
  "., ",
  StyleBox["Applied Physics Letters",
    FontSlant->"Italic"],
  ", ",
  StyleBox["84",
    FontWeight->"Bold"],
  ", 1801 (2004)] for determining force and/or energy vs separation from \
frequency shift vs separation data obtained using frequency modulation atomic \
force microscopy measurements. Procedure is valid for any amplitude of \
oscillation. \n\n",
  StyleBox["INSTRUCTIONS:",
    FontWeight->"Bold"],
  "\n(1) Enter operating conditions for experiment and conversion under the \
\"Operating conditions\" heading.\n(2) Enter required datafile name and \
directory containing file under \"",
  StyleBox["INPUT DATA - Frequency shift vs separation",
    FontFamily->"Times New Roman",
    FontVariations->{"CompatibilityType"->0}],
  "\" heading. The datafile must contain two columns:\nfirst is separation \
(metres), second is frequency shift (Hz). Separation should preferably \
increase with increasing line number in the datafile. Smaller separation \
corresponds to tip being closer to the sample. See Notes (d) and (e) below.\n\
(3) Select all headings, and then execute by pressing Enter.\n(4) Program \
returns Force (nN) and/or Energy (aJ) vs separation (nm).\n(5) All plots are \
given under the \"Plotting results\" heading.\n\n",
  StyleBox["NOTES:",
    FontWeight->"Bold"],
  " (a) Procedure is for constant cantilever oscillation amplitude \
measurements only.\n\t    (b) The smallest separation is normalised to zero \
by the program.\n\t    (c) Frequency shift must go to zero at the largest \
separations - corresponding to no interaction force.\n\t    (d) ",
  StyleBox["If separation is not increasing with line number, a warning \
message is given in \"INPUT DATA ",
    FontWeight->"Bold"],
  StyleBox["- Frequency shift vs separation",
    FontFamily->"Times New Roman",
    FontWeight->"Bold",
    FontVariations->{"CompatibilityType"->0}],
  StyleBox["\" section\n\t        and the datafile is subsequently sorted in \
order of increasing separation.\n",
    FontWeight->"Bold"],
  "\t    (e) ",
  StyleBox["If repeated separation values are encountered in the datafile, \
only one of these repeated separation values is retained. \n\t        A \
warning is given in \"INPUT DATA ",
    FontWeight->"Bold"],
  StyleBox["- Frequency shift vs separation",
    FontFamily->"Times New Roman",
    FontWeight->"Bold",
    FontVariations->{"CompatibilityType"->0}],
  StyleBox["\" section.",
    FontWeight->"Bold"]
}], "Text",
  TextJustification->0],

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Cell[TextData[{
  "Loads ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " package"
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Cell[BoxData[
    \(\(<< NumericalMath`ListIntegrate`;\)\)], "Input"]
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Cell[CellGroupData[{

Cell["Operating conditions", "Section"],

Cell["Nanometre definition:", "Text"],

Cell[BoxData[
    \(\(nm = 10^\(-9\);\)\)], "Input"],

Cell["Cantlever spring constant (N/m):", "Text"],

Cell[BoxData[
    \(\(kspring\  = \ 4;\)\)], "Input"],

Cell["Resonant frequency - far from surface (Hz):", "Text"],

Cell[BoxData[
    \(\(f0\  = \ 20\ 10^3;\)\)], "Input"],

Cell["Amplitude of oscillation (m):", "Text"],

Cell[BoxData[
    \(\(amp\  = \ 0.43\ nm;\)\)], "Input"],

Cell["Smoothing - number of points to average:", "Text"],

Cell[BoxData[
    \(\(\(set\  = \ 20;\)\(\ \)\)\)], "Input"],

Cell["\<\
Frequency offset at large distances. Ensures frequency shift in given data is \
zero at large separations. (Hz):\
\>", "Text"],

Cell[BoxData[
    \(\(freqoffset\  = \ 0;\)\)], "Input"],

Cell["Force conversion - (Yes = 1; No = 0):", "Text"],

Cell[BoxData[
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Cell["Energy conversion - (Yes = 1; No = 0):", "Text"],

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  FontSize->16,
  FontWeight->"Bold"]], "Section",
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Cell["\<\
Reads in frequency shift vs separation data from specified file. Frequency is \
in Hertz. Separation in metres.\
\>", "Text"],

Cell["Directory containing file:", "Text"],

Cell[BoxData[
    \(\(SetDirectory["\<C:\Documents and Settings\SADERJ\>"];\)\)], "Input"],

Cell[BoxData[
    \(\(\(data\  = \ 
        ReadList["\<datafile.txt\>", \ Number, \ 
          RecordLists \[Rule] True\ ];\)\(\ \)\)\)], "Input"],

Cell["\<\
Folloing procedure checks that separation is increasing with line number - if \
this is not the case it sorts the datafile in order of increasing separation.
Also checks that each separation value is unique, and eliminates non-unique \
separation values:\
\>", "Text"],

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    \(\(errororder\  = \ 0;\)\ \), "\n", 
    \(\(\(checkeliminate\  = \ 0;\)\(\n\)
    \)\), "\n", 
    \(\(\(m\  = \ 1;\)\(\n\)
    \)\ \ \ \ \), "\n", 
    \(\(\(For[i\  = \ 1, \ i\  <= \ len\  - \ 1, \ \(i++\), \n\t
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          lineerror[m]\  = \ i; \ m\  += \ 1; \ 
          errororder\  = \ 1]];\)\(\[IndentingNewLine]\)
    \)\), "\[IndentingNewLine]", 
    \(\(\(m\  -= \ 1;\)\(\[IndentingNewLine]\)
    \)\), "\n", 
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        Print["\<WARNING: Input datafile. Separation not increasing with \
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            m]]; \[IndentingNewLine]Print["\<WARNING: Input datafile has been \
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        data\  = \ Sort[data];\[IndentingNewLine]];\)\(\[IndentingNewLine]\)
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          reset[n]\  = \ i\  + \ 1; \ n\  += \ 1; \ 
          checkeliminate\  = \ 1]];\)\(\[IndentingNewLine]\)
    \)\), "\[IndentingNewLine]", 
    \(\(\(n\  -= \ 1;\)\(\n\)
    \)\), "\n", 
    \(\(tabdelete\  = \ Table[{reset[j]}, \ {j, \ 1, \ n}];\)\), "\n", 
    \(\(\(data\  = \ Delete[data, \ tabdelete];\)\(\n\)
    \)\), "\[IndentingNewLine]", 
    \(\(\(If[checkeliminate\  == \ 1, \ 
        Print["\<WARNING: Repeated separation values have been \
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    \)\), "\n", 
    \(\(ClearAll[m, \ n, \ i, \ j, \ len];\)\)}], "Input"],

Cell["\<\
Converts datafile into \[CapitalDelta]f/f vs separation(m) data, and \
normalises separation so that zero separation corresponds to smallest \
separation:\
\>", "Text"],

Cell[BoxData[{
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            Length[data]}];\)\), "\[IndentingNewLine]", 
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Plot of frequency vs separation data is given in \"Plotting results\" \
heading.\
\>", "Text"]
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Cell[CellGroupData[{

Cell["Smoothing algorithm and numerical derivative calculation", "Section"],

Cell["Smoothing procedure (repeats procedure once):", "Text"],

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                  set}]}, \ \ {i, \ set\  + \ 1, \ 
            Length[data1]\  - \ set}];\)\(\[IndentingNewLine]\)
    \)\), "\n", 
    \(\(smooth\  = \ 
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            Length[data2]\  - \ 1}];\)\)}], "Input"],

Cell["Numerical derivative computation:", "Text"],

Cell[BoxData[
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                1]\)], \ \((data2[\([i\  + \ 1, \ 2]\)]\  - \ 
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                      1]\)]\  - \ data2[\([i\  - \ 1, \ 1]\)])\)}, \ {i, \ 
            2, \ Length[data2]\  - \ 1}];\)\)], "Input"],

Cell["\<\
Plot of smoothed data and its derivative given in \"Plotting results\" \
heading.\
\>", "Text"]
}, Closed]],

Cell[CellGroupData[{

Cell["Force evaluation", "Section",
  CellDingbat->"\[FilledSquare]"],

Cell["\<\
Evaluates integral to determine force vs separation data from frequency shift \
vs separation data.\
\>", "Text"],

Cell[BoxData[
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        Table[{smooth[\([t, \ 
                1]\)], \ \((1\  + \ \(Sqrt[amp]\ /\ 8\)\ /\ 
                      Sqrt[Pi\ \((smooth[\([t, \ 1]\)]\  - \ 
                              smooth[\([z, \ 1]\)])\)])\)\ smooth[\([t, \ 
                    2]\)]\  - \ 
              Sqrt[amp]^3\ /\ 
                  Sqrt[2\ \((smooth[\([t, \ 1]\)]\  - \ 
                          smooth[\([z, \ 1]\)])\)]\ deriv[\([t, \ 
                    2]\)]}, \ {t, \ z + 1, \ Length[smooth]}];\)\)], "Input",
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Cell["\<\
These functions account for the integrable singularity at t = z:\
\>", "Text"],

Cell[BoxData[{
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        smooth[\([z, \ 2]\)]\ \((smooth[\([z + 1, \ 1]\)]\  - \ 
              smooth[\([z, \ 1]\)])\);\)\), "\[IndentingNewLine]", 
    \(\(correct1[z_]\  := \ 
        2\ \((\(Sqrt[amp]\ /\ 8\)\ /\ Sqrt[Pi])\)\ smooth[\([z, \ 2]\)]\ Sqrt[
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              smooth[\([z, \ 1]\)]];\)\), "\[IndentingNewLine]", 
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          z_]\  := \ \(-\ 
            2\)\ \((Sqrt[amp]^3\ /\ Sqrt[2])\)\ deriv[\([z, \ 2]\)]\ Sqrt[
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              smooth[\([z, \ 1]\)]];\)\)}], "Input",
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  CellDingbat->"\[FilledSquare]"],

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Evaluates integral to determine force vs separation data from frequency shift \
vs separation data.\
\>", "Text"],

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            smooth[\([t, \ 
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                      smooth[\([z, \ 1]\)])\)\  + \ 
                  Sqrt[amp]\ /\ 
                      4\ Sqrt[\((smooth[\([t, \ 1]\)]\  - \ 
                            smooth[\([z, \ 1]\)])\)\ /\ Pi]\  + \ 
                  Sqrt[amp]^3\ /\ 
                    Sqrt[2\ \((smooth[\([t, \ 1]\)]\  - \ 
                            smooth[\([z, \ 1]\)])\)])\)}, \ {t, \ z + 1, \ 
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These functions account for the integrable singularity at t = z:\
\>", "Text"],

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        2\ /\ 3\ \((\(Sqrt[amp]\ /\ 4\)\ /\ Sqrt[Pi])\)\ smooth[\([z, \ 
              2]\)]\ Sqrt[
              smooth[\([z + 1, \ 1]\)]\  - \ 
                smooth[\([z, \ 1]\)]]^3;\)\), "\[IndentingNewLine]", 
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            smooth[\([z + 1, \ 1]\)]\  - \ 
              smooth[\([z, \ 1]\)]];\)\)}], "Input",
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Cell[BoxData[
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        Energydata\  = \ 
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  CellDingbat->None],

Cell["Plot of force data given in \"Plotting results\" heading.", "Text"]
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Cell["Plotting results", "Section"],

Cell[BoxData[{
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        Table[{data[\([i, \ 1]\)]\ \ /\ nm, \ data[\([i, \ 2]\)]}, \ {i, \ 
            1, \ Length[data]}];\)\), "\[IndentingNewLine]", 
    \(\(smoothplot\  = \ 
        Table[{smooth[\([i, \ 1]\)]\ \ /\ nm, \ 
            smooth[\([i, \ 2]\)]}, \ {i, \ 1, \ 
            Length[smooth]}];\)\), "\[IndentingNewLine]", 
    \(\(derivplot\  = \ 
        Table[{deriv[\([i, \ 1]\)]\ \ /\ nm, \ 
            deriv[\([i, \ 2]\)]\ nm}, \ {i, \ 1, \ 
            Length[deriv]}];\)\), "\[IndentingNewLine]", 
    \(\(If[Forceconvert\  \[Equal] \ 1, \ 
        Forcedataplot\  = \ 
          Table[{Forcedata[\([i, \ 1]\)]\ \ /\ nm, \ 
              Forcedata[\([i, \ 2]\)]\ 10^9}, \ {i, \ 1, \ 
              Length[Forcedata]}]];\)\), "\[IndentingNewLine]", 
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        Energydataplot\  = \ 
          Table[{Energydata[\([i, \ 1]\)]\ /\ nm, \ 
              Energydata[\([i, \ 2]\)]\ 10^18}, \ {i, \ 1, \ 
              Length[Energydata]}]];\)\)}], "Input"],

Cell[BoxData[
    \(\(\( (*\ 
      Plots\ frequency\ vs\ separation\ data\ \
*) \)\(\[IndentingNewLine]\)\(\(Print["\<\>"];\)\[IndentingNewLine]
    Print["\<(Number of data points = \>", \ Length[data], "\<)\>"]; 
    Print[StyleForm["\<Original Frequency Shift Ratio Data:\>", \ 
        FontFamily -> "\<Arial\>", \ FontWeight \[Rule] "\<Bold\>", \ 
        FontSize \[Rule] 14]];\[IndentingNewLine]
    \(porig\  = \ 
        ListPlot[dataplot, \ PlotRange \[Rule] All, \ Frame \[Rule] True, \ 
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          FrameLabel \[Rule] {"\<Separation (nm)\>", \ \
"\<\[CapitalDelta]f/f\>"}];\)\n\[IndentingNewLine] (*\ 
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*) \[IndentingNewLine]
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          FontFamily -> "\<Arial\>", \ FontWeight \[Rule] "\<Bold\>", \ 
          FontSize \[Rule] 14]];\)\[IndentingNewLine]
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          PlotStyle \[Rule] {RGBColor[1, 0, 0]}];\)\n\[IndentingNewLine]
    \(Print["\<\>"];\)\[IndentingNewLine]
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        StyleForm["\<Comparison of Original and Smoothed Frequency Shift \
Data:\>", \ FontFamily -> "\<Arial\>", \ FontWeight \[Rule] "\<Bold\>", \ 
          FontSize \[Rule] 14]];\)\[IndentingNewLine]
    \(pcomp\  = \ 
        Show[psmooth, \ porig, \ 
          PlotRange \[Rule] All];\)\[IndentingNewLine]\[IndentingNewLine]
    \(Print["\<\>"];\)\[IndentingNewLine]
    \(Print[
        StyleForm["\<Numerical Derivative of Frequency Shift Data:\>", \ 
          FontFamily -> "\<Arial\>", \ FontWeight \[Rule] "\<Bold\>", \ 
          FontSize \[Rule] 14]];\)\[IndentingNewLine]
    \(pderiv\  = \ 
        ListPlot[derivplot, \ PlotRange \[Rule] All, \ Frame \[Rule] True, \ 
          Axes \[Rule] False, \ DefaultFont \[Rule] {"\<Arial\>", \ 12}, \ 
          FrameLabel \[Rule] {"\<Separation (nm)\>", \ \*"\"\<\!\(\[PartialD]\
\_z\) \[CapitalDelta]f/f (\!\(nm\^\(-1\)\))\>\""}];\)\[IndentingNewLine]\n
    \(If[Forceconvert\  \[Equal] \ 1, \[IndentingNewLine] (*\ 
          Plots\ recovered\ force\ vs\ separation\ data\ \
*) \[IndentingNewLine]Print["\<\>"]; \[IndentingNewLine]Print[
          StyleForm["\<Recovered Force vs Separation Data:\>", \ 
            FontFamily -> "\<Arial\>", \ FontWeight \[Rule] "\<Bold\>", \ 
            FontSize \[Rule] 14]]; \[IndentingNewLine]pforcedata\  = \ 
          ListPlot[Forcedataplot, \ PlotRange \[Rule] All, \ 
            Frame \[Rule] True, \ Axes \[Rule] False, \ 
            FrameLabel \[Rule] {"\<Separation (nm)\>", \ "\<Force (nN)\>"}, \ 
            DefaultFont \[Rule] {"\<Arial\>", \ 
                12}];\[IndentingNewLine]];\)\n\[IndentingNewLine]
    \(If[Energyconvert\  \[Equal] \ 1, \[IndentingNewLine] (*\ 
          Plots\ recovered\ energy\ vs\ separation\ data\ \
*) \[IndentingNewLine]Print["\<\>"]; \[IndentingNewLine]Print[
          StyleForm["\<Recovered Energy vs Separation Data:\>", \ 
            FontFamily -> "\<Arial\>", \ FontWeight \[Rule] "\<Bold\>", \ 
            FontSize \[Rule] 14]]; \[IndentingNewLine]penergydata\  = \ 
          ListPlot[Energydataplot, \ PlotRange \[Rule] All, \ 
            Frame \[Rule] True, \ Axes \[Rule] False, \ 
            FrameLabel \[Rule] {"\<Separation (nm)\>", \ "\<Energy (aJ)\>"}, \
\ DefaultFont \[Rule] {"\<Arial\>", \ 
                12}];\[IndentingNewLine]];\)\)\)\)], "Input",
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*)



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End of Mathematica Notebook file.
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