Abstract

A mathematical approach developed to correct depth profiles of wet-chemically modified polymer films obtained by confocal Raman microscopy is presented which takes into account scattered contributions originated from a diffraction-limited laser focal volume. It is demonstrated that the problem can be described using a linear Fredholm integral equation of the first kind which correlates apparent and true Raman intensities with the depth resolution curve of the instrument.

The calculations of the corrected depth profiles show that considerable differences between apparent and corrected depth profiles exist at the surface, especially when profiles with strong concentration gradients are dealt with or an instrument with poor depth resolution is used. Degrees of modification at the surface obtained by calculation of the corrected depth profiles are compared with those measured by FTIR-ATR and show an excellent concordance.

© 2006 Optical Society of America

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  1. K. L. Mittal, and K. W. Lee, Polymer Surfaces and Interfaces: Characterization Modification and Application, VSP: (Utrecht, 1997).
  2. J. Sacristán, C. Mijangos, and H. Reinecke, "Surface modification of PVC films in solvent-non-solvent mixtures," Polymer 41, 5577 (2000).
    [CrossRef]
  3. J. Sacristán, C. Mijangos, S. Spells, J. Yarwood, and H. Reinecke, "Selective surface modification of PVC films as revealed by confocal Raman microspectroscopy," Macromolecules 33, 6134 (2000).
    [CrossRef]
  4. R. Tabaksblat, J. Meier, and B. J. Kip, "Confocal Raman Microspectroscopy: Theory and Application to Thin Polymer Samples"Appl. Spectrosc. 46, 60 (1992).
    [CrossRef]
  5. J. Sacristán, C. Mijangos, H. Reinecke, S. J. Spells, and J. Yarwood, "Surface modification of Polystyrene films. Depth profiling and mapping by Raman microscopy" Macromol. Chem. Phys. 203, 678 (2002).
    [CrossRef]
  6. H. Reinecke, S. Spells, J. Sacristán, C. Mijangos, and J. Yarwood, "Confocal Raman depth profiling of surface modified polymer films. Effect of sample refractive index," Appl. Spectrosc. 55, 1660(2001).
    [CrossRef]
  7. G. D. McAnally, N. J. Everall, J. M. Chalmers, and W. E. Smith, "Analysis of Thin Film Coatings on Poly(ethylene terephthalate) by Confocal Raman Microscopy and Surface-Enhanced Raman Scattering," Appl. Spectrosc. 57, 44 (2003).
    [CrossRef] [PubMed]
  8. W. Schrof, E. Beck, G. Etzrodt, H. Hintze-Brüning, U. Meisenburg, R. Schwalm, and J. Warming, "Depth-resolved characterization of UV cured coatings by confocal Raman and two-photon microscopy," Progress in Organic Coatings 43, 1 (2001).
    [CrossRef]
  9. O. S. Fleming, and S. G. Kazarian," Appl. Spectrosc. 58, 390 (2004).
    [CrossRef] [PubMed]
  10. . G. W. M. Peters, A. N. Zdravkov, and H. E. H. Meijer, "Transient interfacial tension and dilatational rheology of diffuse polymer-polymer interfaces," J. Chem. Phys. 122, 104901 (2005).
    [CrossRef] [PubMed]
  11. W. Schrof, J. Klingler, W. Heckmann, and D. Horn "Confocal fluorescence and Raman microscopy in industrial research." Colloid and Polymer Science 276, 577 (1998).
    [CrossRef]
  12. N. J. Everall, "Modelling and Measuring the effect of refraction on the depth resolution of confocal Raman Spectroscopy" Appl. Spectrosc. 54, 773 (2000).
    [CrossRef]
  13. N. J. Everall, "Confocal Raman microscopy: why the depth resolution and spatial accuracy can be much worse than you think," Appl. Spectrosc. 54, 1515 (2000).
    [CrossRef]
  14. S. Michielsen, "Aberrations in confocal spectroscopy of polymeric materials: erroneous thicknesses and intensities, and loss of resolution," J. Appl. Polym. Sci. 81, 1662 (2001).
    [CrossRef]
  15. F. M. Mirabella, "Internal reflection spectroscopy," Appl Spectrosc. Rev. 21, 45 (1985).
    [CrossRef]
  16. A. Gallardo, S. Spells, R. Navarro, H. Reinecke, "Confocal Raman microspectroscopy: calculation of corrected depth profiles of wet-chemically modified polymer films." Macromol. Rapid Commun. 27, 529 (2006).
    [CrossRef]

2006 (1)

A. Gallardo, S. Spells, R. Navarro, H. Reinecke, "Confocal Raman microspectroscopy: calculation of corrected depth profiles of wet-chemically modified polymer films." Macromol. Rapid Commun. 27, 529 (2006).
[CrossRef]

2004 (1)

2003 (1)

2002 (1)

J. Sacristán, C. Mijangos, H. Reinecke, S. J. Spells, and J. Yarwood, "Surface modification of Polystyrene films. Depth profiling and mapping by Raman microscopy" Macromol. Chem. Phys. 203, 678 (2002).
[CrossRef]

2001 (3)

W. Schrof, E. Beck, G. Etzrodt, H. Hintze-Brüning, U. Meisenburg, R. Schwalm, and J. Warming, "Depth-resolved characterization of UV cured coatings by confocal Raman and two-photon microscopy," Progress in Organic Coatings 43, 1 (2001).
[CrossRef]

H. Reinecke, S. Spells, J. Sacristán, C. Mijangos, and J. Yarwood, "Confocal Raman depth profiling of surface modified polymer films. Effect of sample refractive index," Appl. Spectrosc. 55, 1660(2001).
[CrossRef]

S. Michielsen, "Aberrations in confocal spectroscopy of polymeric materials: erroneous thicknesses and intensities, and loss of resolution," J. Appl. Polym. Sci. 81, 1662 (2001).
[CrossRef]

2000 (4)

N. J. Everall, "Confocal Raman microscopy: why the depth resolution and spatial accuracy can be much worse than you think," Appl. Spectrosc. 54, 1515 (2000).
[CrossRef]

N. J. Everall, "Modelling and Measuring the effect of refraction on the depth resolution of confocal Raman Spectroscopy" Appl. Spectrosc. 54, 773 (2000).
[CrossRef]

J. Sacristán, C. Mijangos, and H. Reinecke, "Surface modification of PVC films in solvent-non-solvent mixtures," Polymer 41, 5577 (2000).
[CrossRef]

J. Sacristán, C. Mijangos, S. Spells, J. Yarwood, and H. Reinecke, "Selective surface modification of PVC films as revealed by confocal Raman microspectroscopy," Macromolecules 33, 6134 (2000).
[CrossRef]

1998 (1)

W. Schrof, J. Klingler, W. Heckmann, and D. Horn "Confocal fluorescence and Raman microscopy in industrial research." Colloid and Polymer Science 276, 577 (1998).
[CrossRef]

1992 (1)

1985 (1)

F. M. Mirabella, "Internal reflection spectroscopy," Appl Spectrosc. Rev. 21, 45 (1985).
[CrossRef]

Beck, E.

W. Schrof, E. Beck, G. Etzrodt, H. Hintze-Brüning, U. Meisenburg, R. Schwalm, and J. Warming, "Depth-resolved characterization of UV cured coatings by confocal Raman and two-photon microscopy," Progress in Organic Coatings 43, 1 (2001).
[CrossRef]

Chalmers, J. M.

Etzrodt, G.

W. Schrof, E. Beck, G. Etzrodt, H. Hintze-Brüning, U. Meisenburg, R. Schwalm, and J. Warming, "Depth-resolved characterization of UV cured coatings by confocal Raman and two-photon microscopy," Progress in Organic Coatings 43, 1 (2001).
[CrossRef]

Everall, N. J.

Fleming, O. S.

Gallardo, A.

A. Gallardo, S. Spells, R. Navarro, H. Reinecke, "Confocal Raman microspectroscopy: calculation of corrected depth profiles of wet-chemically modified polymer films." Macromol. Rapid Commun. 27, 529 (2006).
[CrossRef]

Heckmann, W.

W. Schrof, J. Klingler, W. Heckmann, and D. Horn "Confocal fluorescence and Raman microscopy in industrial research." Colloid and Polymer Science 276, 577 (1998).
[CrossRef]

Hintze-Brüning, H.

W. Schrof, E. Beck, G. Etzrodt, H. Hintze-Brüning, U. Meisenburg, R. Schwalm, and J. Warming, "Depth-resolved characterization of UV cured coatings by confocal Raman and two-photon microscopy," Progress in Organic Coatings 43, 1 (2001).
[CrossRef]

Horn, D.

W. Schrof, J. Klingler, W. Heckmann, and D. Horn "Confocal fluorescence and Raman microscopy in industrial research." Colloid and Polymer Science 276, 577 (1998).
[CrossRef]

Kazarian, S. G.

Kip, B. J.

Klingler, J.

W. Schrof, J. Klingler, W. Heckmann, and D. Horn "Confocal fluorescence and Raman microscopy in industrial research." Colloid and Polymer Science 276, 577 (1998).
[CrossRef]

McAnally, G. D.

Meier, J.

Meisenburg, U.

W. Schrof, E. Beck, G. Etzrodt, H. Hintze-Brüning, U. Meisenburg, R. Schwalm, and J. Warming, "Depth-resolved characterization of UV cured coatings by confocal Raman and two-photon microscopy," Progress in Organic Coatings 43, 1 (2001).
[CrossRef]

Michielsen, S.

S. Michielsen, "Aberrations in confocal spectroscopy of polymeric materials: erroneous thicknesses and intensities, and loss of resolution," J. Appl. Polym. Sci. 81, 1662 (2001).
[CrossRef]

Mijangos, C.

J. Sacristán, C. Mijangos, H. Reinecke, S. J. Spells, and J. Yarwood, "Surface modification of Polystyrene films. Depth profiling and mapping by Raman microscopy" Macromol. Chem. Phys. 203, 678 (2002).
[CrossRef]

H. Reinecke, S. Spells, J. Sacristán, C. Mijangos, and J. Yarwood, "Confocal Raman depth profiling of surface modified polymer films. Effect of sample refractive index," Appl. Spectrosc. 55, 1660(2001).
[CrossRef]

J. Sacristán, C. Mijangos, and H. Reinecke, "Surface modification of PVC films in solvent-non-solvent mixtures," Polymer 41, 5577 (2000).
[CrossRef]

J. Sacristán, C. Mijangos, S. Spells, J. Yarwood, and H. Reinecke, "Selective surface modification of PVC films as revealed by confocal Raman microspectroscopy," Macromolecules 33, 6134 (2000).
[CrossRef]

Mirabella, F. M.

F. M. Mirabella, "Internal reflection spectroscopy," Appl Spectrosc. Rev. 21, 45 (1985).
[CrossRef]

Navarro, R.

A. Gallardo, S. Spells, R. Navarro, H. Reinecke, "Confocal Raman microspectroscopy: calculation of corrected depth profiles of wet-chemically modified polymer films." Macromol. Rapid Commun. 27, 529 (2006).
[CrossRef]

Reinecke, H.

A. Gallardo, S. Spells, R. Navarro, H. Reinecke, "Confocal Raman microspectroscopy: calculation of corrected depth profiles of wet-chemically modified polymer films." Macromol. Rapid Commun. 27, 529 (2006).
[CrossRef]

J. Sacristán, C. Mijangos, H. Reinecke, S. J. Spells, and J. Yarwood, "Surface modification of Polystyrene films. Depth profiling and mapping by Raman microscopy" Macromol. Chem. Phys. 203, 678 (2002).
[CrossRef]

H. Reinecke, S. Spells, J. Sacristán, C. Mijangos, and J. Yarwood, "Confocal Raman depth profiling of surface modified polymer films. Effect of sample refractive index," Appl. Spectrosc. 55, 1660(2001).
[CrossRef]

J. Sacristán, C. Mijangos, and H. Reinecke, "Surface modification of PVC films in solvent-non-solvent mixtures," Polymer 41, 5577 (2000).
[CrossRef]

J. Sacristán, C. Mijangos, S. Spells, J. Yarwood, and H. Reinecke, "Selective surface modification of PVC films as revealed by confocal Raman microspectroscopy," Macromolecules 33, 6134 (2000).
[CrossRef]

Sacristán, J.

J. Sacristán, C. Mijangos, H. Reinecke, S. J. Spells, and J. Yarwood, "Surface modification of Polystyrene films. Depth profiling and mapping by Raman microscopy" Macromol. Chem. Phys. 203, 678 (2002).
[CrossRef]

H. Reinecke, S. Spells, J. Sacristán, C. Mijangos, and J. Yarwood, "Confocal Raman depth profiling of surface modified polymer films. Effect of sample refractive index," Appl. Spectrosc. 55, 1660(2001).
[CrossRef]

J. Sacristán, C. Mijangos, and H. Reinecke, "Surface modification of PVC films in solvent-non-solvent mixtures," Polymer 41, 5577 (2000).
[CrossRef]

J. Sacristán, C. Mijangos, S. Spells, J. Yarwood, and H. Reinecke, "Selective surface modification of PVC films as revealed by confocal Raman microspectroscopy," Macromolecules 33, 6134 (2000).
[CrossRef]

Schrof, W.

W. Schrof, E. Beck, G. Etzrodt, H. Hintze-Brüning, U. Meisenburg, R. Schwalm, and J. Warming, "Depth-resolved characterization of UV cured coatings by confocal Raman and two-photon microscopy," Progress in Organic Coatings 43, 1 (2001).
[CrossRef]

W. Schrof, J. Klingler, W. Heckmann, and D. Horn "Confocal fluorescence and Raman microscopy in industrial research." Colloid and Polymer Science 276, 577 (1998).
[CrossRef]

Schwalm, R.

W. Schrof, E. Beck, G. Etzrodt, H. Hintze-Brüning, U. Meisenburg, R. Schwalm, and J. Warming, "Depth-resolved characterization of UV cured coatings by confocal Raman and two-photon microscopy," Progress in Organic Coatings 43, 1 (2001).
[CrossRef]

Smith, W. E.

Spells, S.

A. Gallardo, S. Spells, R. Navarro, H. Reinecke, "Confocal Raman microspectroscopy: calculation of corrected depth profiles of wet-chemically modified polymer films." Macromol. Rapid Commun. 27, 529 (2006).
[CrossRef]

H. Reinecke, S. Spells, J. Sacristán, C. Mijangos, and J. Yarwood, "Confocal Raman depth profiling of surface modified polymer films. Effect of sample refractive index," Appl. Spectrosc. 55, 1660(2001).
[CrossRef]

J. Sacristán, C. Mijangos, S. Spells, J. Yarwood, and H. Reinecke, "Selective surface modification of PVC films as revealed by confocal Raman microspectroscopy," Macromolecules 33, 6134 (2000).
[CrossRef]

Spells, S. J.

J. Sacristán, C. Mijangos, H. Reinecke, S. J. Spells, and J. Yarwood, "Surface modification of Polystyrene films. Depth profiling and mapping by Raman microscopy" Macromol. Chem. Phys. 203, 678 (2002).
[CrossRef]

Tabaksblat, R.

Warming, J.

W. Schrof, E. Beck, G. Etzrodt, H. Hintze-Brüning, U. Meisenburg, R. Schwalm, and J. Warming, "Depth-resolved characterization of UV cured coatings by confocal Raman and two-photon microscopy," Progress in Organic Coatings 43, 1 (2001).
[CrossRef]

Yarwood, J.

J. Sacristán, C. Mijangos, H. Reinecke, S. J. Spells, and J. Yarwood, "Surface modification of Polystyrene films. Depth profiling and mapping by Raman microscopy" Macromol. Chem. Phys. 203, 678 (2002).
[CrossRef]

H. Reinecke, S. Spells, J. Sacristán, C. Mijangos, and J. Yarwood, "Confocal Raman depth profiling of surface modified polymer films. Effect of sample refractive index," Appl. Spectrosc. 55, 1660(2001).
[CrossRef]

J. Sacristán, C. Mijangos, S. Spells, J. Yarwood, and H. Reinecke, "Selective surface modification of PVC films as revealed by confocal Raman microspectroscopy," Macromolecules 33, 6134 (2000).
[CrossRef]

Appl Spectrosc. Rev. (1)

F. M. Mirabella, "Internal reflection spectroscopy," Appl Spectrosc. Rev. 21, 45 (1985).
[CrossRef]

Appl. Spectrosc. (6)

Colloid and Polymer Science (1)

W. Schrof, J. Klingler, W. Heckmann, and D. Horn "Confocal fluorescence and Raman microscopy in industrial research." Colloid and Polymer Science 276, 577 (1998).
[CrossRef]

J. Appl. Polym. Sci. (1)

S. Michielsen, "Aberrations in confocal spectroscopy of polymeric materials: erroneous thicknesses and intensities, and loss of resolution," J. Appl. Polym. Sci. 81, 1662 (2001).
[CrossRef]

Macromol. Chem. Phys. (1)

J. Sacristán, C. Mijangos, H. Reinecke, S. J. Spells, and J. Yarwood, "Surface modification of Polystyrene films. Depth profiling and mapping by Raman microscopy" Macromol. Chem. Phys. 203, 678 (2002).
[CrossRef]

Macromol. Rapid Commun. (1)

A. Gallardo, S. Spells, R. Navarro, H. Reinecke, "Confocal Raman microspectroscopy: calculation of corrected depth profiles of wet-chemically modified polymer films." Macromol. Rapid Commun. 27, 529 (2006).
[CrossRef]

Macromolecules (1)

J. Sacristán, C. Mijangos, S. Spells, J. Yarwood, and H. Reinecke, "Selective surface modification of PVC films as revealed by confocal Raman microspectroscopy," Macromolecules 33, 6134 (2000).
[CrossRef]

Polymer (1)

J. Sacristán, C. Mijangos, and H. Reinecke, "Surface modification of PVC films in solvent-non-solvent mixtures," Polymer 41, 5577 (2000).
[CrossRef]

Progress in Organic Coatings (1)

W. Schrof, E. Beck, G. Etzrodt, H. Hintze-Brüning, U. Meisenburg, R. Schwalm, and J. Warming, "Depth-resolved characterization of UV cured coatings by confocal Raman and two-photon microscopy," Progress in Organic Coatings 43, 1 (2001).
[CrossRef]

Other (2)

. G. W. M. Peters, A. N. Zdravkov, and H. E. H. Meijer, "Transient interfacial tension and dilatational rheology of diffuse polymer-polymer interfaces," J. Chem. Phys. 122, 104901 (2005).
[CrossRef] [PubMed]

K. L. Mittal, and K. W. Lee, Polymer Surfaces and Interfaces: Characterization Modification and Application, VSP: (Utrecht, 1997).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic presentation of true (a) and experimentally obtained (b) depth profiles of a 40 mm thick transparent polymer film of refractive index n=1.

Fig. 2.
Fig. 2.

Resolution curve determined by measuring the Raman response of the signal at 1425 cm-1 of a PVC film.

Fig. 3.
Fig. 3.

Sectioning of the film in a number of finite intervals i. The measured intensity Im(i) of each interval is given by the sum of the true intensity It(i) of this interval plus the contributions made by the intervals in its vicinity.

Fig. 4.
Fig. 4.

Raw data with corresponding fits assuming a constant true function (solid line) for the reference signal and a Lorentzian fit (dotted line) for the true modifier profile.

Fig. 5.
Fig. 5.

Comparison of depth profiles obtained by simple normalization (solid line) and normalization after correction of the data (dotted line) using a Lorentzian relation.

Tables (1)

Tables Icon

Table 1: Comparison of degrees of modification at the surface obtained by confocal Raman spectroscopy (without and with correction) and FTIR-ATR measurement

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

f ( x ) = 0 b [ I ( y ) H ( x , y ) ] d y
H ( x , y ) = A 2 4 ( x y ) 2 + A 2
f ( x ) = 0 b [ k 0 A 2 4 ( x y ) 2 + A 2 ] dy = 1 2 A 2 arctan [ 2 ( b x ) A 2 ] k 0 A 2 + 1 2 A 2 arctan [ 2 x A 2 ] k 0 A 2
f ( x ) = 0 b [ k 1 k 2 4 y 2 + ( k 2 ) 2 A 2 4 ( x y ) 2 + A 2 ] dy
f ( x ) = 1 2 k 1 k 2 A 2 [ 2 x ln ( 4 b 2 + k 2 2 ) k 2 2 A 2 + k 2 arctan [ 2 ( b x ) A 2 ] k 2 2 + A 2 arctan [ 2 b k 2 2 ] A 2 k 2 2 arctan [ 2 b k 2 2 ] + 4 arctan [ 2 b k 2 2 ] x 2 A 2 2 x ln ( 4 x 2 8 xb + A 2 + 4 b 2 ) k 2 2 A 2 + 4 arctan [ 2 ( b x ) A 2 ] x 2 k 2 2 A 2 arctan [ 2 ( b x ) A 2 ] x 2 k 2 2 ] [ ( 8 k 2 2 x 2 + A 4 2 A 2 k 2 2 + 8 A 2 x 2 + k 2 4 + 16 x 4 ) ( k 2 2 A 2 ) ] +
1 2 k 1 k 2 A 2 ( 2 x ln ( k 2 2 ) A 2 + 2 x ln ( 4 x 2 + A 2 ) A 2 + 4 arctan [ 2 x A 2 ] x 2 k 2 2 rc tan [ 2 x A 2 ] ) [ ( 8 k 2 2 x 2 + A 4 2 A 2 k 2 2 + 8 A 2 x 2 + k 2 4 + 16 x 4 ) ( A 2 ) ]

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