afm–ir: combining atomic force microscopy and infrared ... · pdf fileforce microscopy...

focal point reviewALEXANDRE DAZZI

LABORATORIE DE CHIMIE PHYSIQUE, UNIVERSITE PARIS-SUD, 91405

ORSAY, FRANCE

CRAIG B. PRATER AND QICHI HU

ANASYS INSTRUMENTS, 121 GRAY AVENUE, SUITE 100, SANTA

BARBARA, CA 93101 USA

D. BRUCE CHASE AND JOHN F. RABOLT

DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING, THE

UNIVERSITY OF DELAWARE, NEWARK, DE 19716 USA

CURTIS MARCOTT

LIGHT LIGHT SOLUTIONS, LLC, P.O. BOX 81486, ATHENS, GA

30608 USA

AFM–IR: Combining AtomicForce Microscopy and Infrared

Spectroscopy for NanoscaleChemical Characterization

Polymer and life science applications of a

technique that combines atomic force micros-

copy (AFM) and infrared (IR) spectroscopy to

obtain nanoscale IR spectra and images are

reviewed. The AFM–IR spectra generated from

this technique contain the same information

with respect to molecular structure as conven-

tional IR spectroscopy measurements, allowing

significant leverage of existing expertise in IR

spectroscopy. The AFM–IR technique can be

used to acquire IR absorption spectra and

absorption images with spatial resolution on

the 50 to 100 nm scale, versus the scale of many

micrometers or more for conventional IR

spectroscopy. In the life sciences, experiments

have demonstrated the capacity to perform

chemical spectroscopy at the sub-cellular level.

Specifically, the AFM–IR technique provides a

label-free method for mapping IR-absorbing

species in biological materials. On the polymer

side, AFM–IR was used to map the IR

absorption properties of polymer blends, mul-

tilayer films, thin films for active devices such

as organic photovoltaics, microdomains in a

semicrystalline polyhydroxyalkanoate copoly-

mer, as well as model pharmaceutical blend

systems. The ability to obtain spatially resolved

IR spectra as well as high-resolution chemical

images collected at specific IR wavenumbers

was demonstrated. Complementary measure-

ments mapping variations in sample stiffness

were also obtained by tracking changes in the

cantilever contact resonance frequency. Finally,

it was shown that by taking advantage of the

ability to arbitrarily control the polarization

direction of the IR excitation laser, it is possible

to obtain important information regarding

molecular orientation in electrospun nano-

fibers.

Index Headings: Infrared microspectroscopy;

Atomic force microscopy; AFM; IR; Near field;

E. coli; Polymer; Poly(hydroxybutyrate); PHB;

Organic photovoltaics; P3HT; PCMB; Poly(-

hydroxyalkanoate); PHA; Phase separation;

Miscibility; Pharmaceutical formulation;

Nanofibers; Molecular orientation; Poly(vinyli-

dene fluoride); PVDF.

APPLIED SPECTROSCOPY OA 1365

INTRODUCTION

Infrared (IR) spectroscopy in the 2.5to 20 lm (500–4000 cm-1) range(mid-IR) is a direct probe of the

molecular vibrations in a sample. IRabsorption spectra of organic com-pounds are often used to specificallyidentify chemical species. By combiningmicroscopy and spectroscopy, chemicalanalysis can be done on a micrometerscale. Over the last several years,technology upgrades in optics (e.g.,aberration correction and improvementof confocal microscopy) and in detec-tion (e.g., better sensitivity of IR detec-tors and focal plane arrays) haveimproved the performance of microspec-troscopy.1–5 As such, IR microspectros-copy has become an attractive tool forpolymer and life sciences.

One of the main limitations ofconventional IR microspectroscopy,however, is spatial resolution. Theoptical diffraction limit along with otherpractical limitations has limited spatialresolution to the range of 3–30 lm,depending on the wavelength of lightand instrumentation used. There is acompelling need to improve the lateralresolution beyond the diffraction limit inorder to apply the power of IR spectros-copy at finer length scales for a widerange of materials. Several near-fieldapproaches have been developed duringthe past 20 years to overcome thislimitation. In many of these approaches,the sharp tip of a scanning probemicroscope is used to sample and/orenhance the radiation interacting withina nanoscale region of a sample. Re-search advances in near-field optics havebeen numerous and exciting in thevisible range, and in recent years wereextended into the IR.6–17 Although thereis some very good work in IR, there arestill significant challenges. The mainissues are associated with the lack ofbroadly tunable IR sources and chal-lenges associated with obtaining inter-pretable spectra. The spectrum that ismeasured in the near-field regime de-pends not only on sample absorption,but also on complex tip-sample scatter-ing phenomena.18 The observed spectralbands can be shifted with respect toexpected absorption bands, and the shiftdepends on the sample, tip geometries,and tip position.

Therefore it is highly desirable tohave a technique that can provideinterpretable IR absorption spectra thatare comparable to conventional IRspectroscopy techniques such as Fouriertransform IR (FT–IR) spectroscopy.After several years of work in near-fieldIR optics with these different tech-niques, we developed, with our cowork-ers , another method based onphotothermal-induced absorption. Thetechnique, called atomic force micros-copy (AFM)–IR,19 irradiates a region ofa sample with light from a tunable IRlaser and measures the resulting photo-thermal expansion of the sample withthe tip of an atomic force microscope.The first experimental setup was estab-lished in the Centre Laser Infrarouged’Orsay (CLIO) in the Laboratoire deChimie Physique by using a free-elec-tron laser as the tunable IR source. TheAFM–IR instrument at CLIO has beenused for the last five years, resulting inpublications in different domains suchas nanophotonics,20–22 cellular biolo-gy,23 and microbiology.24–26 TheAFM–IR instrument remains availablefor external scientific collaborations as auser facility at CLIO. In 2010, theAmerican company Anasys Instruments,Inc., commercialized a version of AFM–IR27,28 by using a bench-top tunable IRlaser, based on an optical parametricoscillator.

BASIC PRINCIPLES OFAFM–IR

In AFM–IR, the sample is placed onan IR transparent prism (e.g., ZnSe) and

irradiated with a total internal reflectionstyle illumination scheme, as shown inFig. 1. If the IR laser is tuned to awavelength corresponding to absorptionby the sample, the absorbed lightinduces a photothermal response in thesample. That is, the absorbed light isconverted into heat, which results inrapid thermal expansion of the absorb-ing region of the sample.19 The rapidthermal expansion pulse is then detectedwith the tip of an atomic force micro-scope. The thermal expansion signaldetected by the AFM tip is directlyproportional to the absorption coefficientof the sample (a complete derivation ofthis is given in the Appendix.) In brief,thermal expansion of the sample occursonly when molecular vibrations excitedby absorbed IR photons from the tunablelaser source return to their groundvibrational state though the transfer ofenergy in the form of heat to the lattice.Thus, the detection scheme is analogousto photoacoustic spectroscopy, exceptthat the AFM tip and cantilever are usedto detect and amplify the thermalexpansion signal instead of a micro-phone in a gas cell. Because the signaldetected in AFM–IR is in proportion tothe sample absorption, absorption spec-tra obtained by the AFM–IR techniquecorrelate very well to conventional IRabsorption spectra collected in transmis-sion. Using an AFM tip to detect thethermal expansion pulse is the key tomeasuring IR absorption below theconventional diffraction limit. TheAFM tip can sense and map variationsin thermal expansion from IR absorption

FIG. 1. Scheme of the AFM–IR setup. The AFM cantilever ring-down amplitude plotted as afunction of laser excitation wavelength produces the IR spectrum.

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to better than 100 nm spatial resolution.Further, the AFM detection sensitivity issufficient to enable chemical identifica-tion of samples at a scale of tens ofnanometers.

AFM–IR Setup Description. Aschematic of the AFM–IR system isshown in Fig. 1. The tunable IR laserlight enters the IR transparent 458 ZnSeprism (internal reflectance element) atnormal incidence. The laser light isentirely internally reflected at the inter-face between the prism and the samplefor most organic materials, with arefractive index around 1.5. A standingwave, or evanescent field, is produced,which extends through the sample filmto a distance on the order of thewavelength of light. Importantly, thetotal internal reflection conditions of theexperimental setup reduce any back-ground interaction of the tunable laserlight directly with the AFM cantilever.

The tip of the AFM is in contact withthe sample under study. With each laserpulse, the sample’s thermal expansioninduces a brief force impulse on the tip,inducing ringing at the AFM cantile-ver’s resonant frequencies. The oscilla-tion signal of the cantilever is recordedby reflecting a visible laser off the topsurface of the cantilever and measuringits position with the four-quadrantdetector of the AFM. The signal can besimultaneously analyzed via fast Fouriertransform (FFT) to determine the ampli-tudes and frequencies of the cantilevervibrational modes.29,30 The raw cantile-ver ring-down signal usually containsmultiple resonant frequency compo-nents. Measuring the amplitudes of thecantilever oscillation as a function of thesource wavelength creates local absorp-tion spectra. Typically, the height of themost intense cantilever ring-down peakin the FFT spectrum of the raw cantile-ver ring-down signal is measured foreach wavelength as the laser source isstepped one wavelength at a timethrough the spectral region of interest.The IR spectrum is then obtained byplotting the laser wavenumber on the xaxis versus the cantilever ring-downamplitude on the y axis.

Experimental Demonstration.Escherichia coli is a good test samplebecause of the average size of thisbacterium (2 to 6 lm long, 1 lm wide,

500 nm high), and the absorption bandsare known and assigned, for example,amide I at 1650 cm-1, amide II at 1550cm-1, and DNA (phosphate backbone)at 1080 cm-1. To prepare the surface ofthe prism, a large amount of bacteriawere centrifuged and washed withdistilled water to eliminate their nutritiveenvironment. A suspension of bacteriawas then deposited on the prism surfaceand heated at 30 8C to slowly evaporatethe water. The final concentration ofbacteria on the surface was typically 10to 20 bacteria over 100 3 100 lm. Byusing this method, we obtained intactbacteria that kept their original shape.The absorption bands in the mid-IRwere still present even when the bacteriawere dried. After an AFM scan on theprism surface, we could select a singlebacterium and make different analysesas a function of tip position and laserwavelength.

Figure 2 shows some AMF-IR mea-surements on an E. coli cell. First, theAFM tip was positioned on the bacteri-um with a static force of around 10 nN.The laser wavelength was centered onthe amide I band at 1650 cm-1,

corresponding to a strong absorption inprotein. After each laser pulse, weobserved decaying oscillations withinitial amplitude of ~30 nm, whichdecreased with a time constant of closeto 200 ls. The amplitude of oscillations(~30 nm) was always smaller than thestatic deflection (~300 nm at 10 nN ofapplied force), ensuring that the tipstayed in contact with the bacterium.

One potential concern was the possi-bility that the cantilever could responddirectly to IR light striking the cantile-ver, rather than by absorption of IR lightby the sample. Such an effect wasobserved by Hill et al. when using anaxial illumination system.31 To test thispossibility, the cantilever deflection wasrecorded outside the bacterium, keepingthe laser wavenumber at the same valueof 1650 cm-1. In this case (Fig. 3), wedid not observe the background absorp-tion seen by Hill; the measured cantile-ver deflection signal off of the bacteriumshowed only noise. This proves thatcantilever oscillations are only excitedby the bacterium expansion and not byabsorption and heating of the cantilever.This illustrates an advantage of the total

FIG. 2. (a) AFM topography picture of the bacterium; the position of the tip is indicated inblue. (b) FT–IR spectrum; the bacterium absorption spectrum is drawn in green, and thewavenumber of the CLIO laser is indicated by the red arrow. (c) Oscillations recorded by thefour-quadrant detector (in red) as function of time superposed on the CLIO pulse laser(blue).


internal reflection approach in prevent-ing unwanted stray radiation from strik-ing the cantilever.

To test whether the expansion of thebacterium is really related to a specificabsorption of bacterium, we tuned thelaser wavenumber outside the amide Iband to 1800 cm-1 (Fig. 4) and put thetip again on the bacterium. The signalshowed a small oscillation, not morethan 3 nm, which is in good agreementwith the relatively small absorption ofthe bacterium at that wavenumber.

All these experiments have shownthat the detected cantilever oscillation isexcited by the photothermal expansionof the bacterium. As demonstrated in theAppendix, the amplitude of the cantile-ver oscillation is directly proportional tothe IR absorption. One approach toquantifying the cantilever oscillations isto perform a Fourier analysis of thecantilever oscillation signal. An FFT ofthe cantilever deflection on and off anabsorption band of the bacterium isdepicted in Fig. 5. FFT also makes iteasy to notice that the thermal expansionpulse excites different cantilever oscil-lation modes. The strongest mode is thefundamental at a resonance frequency ofaround 62 kHz. Looking at the maxi-mum of the first mode, we can quantify

the amount of absorption in the two

different cases.

Figure 6 shows a comparison of an

AFM–IR spectrum collected one wave-

number at a time by tuning the laser

through the spectral region of interest

with a conventional FT–IR spectrum ofE. coli. While there is significantsimilarity in the spectra, note that theAFM–IR measurement is performed ona localized region of one bacterium,while the conventional FT–IR representsthe average spectrum within a beam areaconsisting of millions of bacteria.

As mentioned previously, chemicalimaging is also possible with the AFM–IR technique. The laser wavenumber isfixed at a value corresponding to aspecific IR absorption band originatingfrom a specific molecular vibration of achemical functional group (e.g., 1660-cm-1 amide I, etc.), and the tip isscanned over the sample. The resultingmap can show the spatial variation inabsorption and hence spatial variation inthe concentration of a specific chemicalspecies. Figure 7 shows different chem-ical maps of E. coli for two differentbands, amide I (at 1660 cm-1) andamide III (at 1240 cm-1), both charac-teristic of protein. The band at 1240cm-1 could also contain some contribu-tions from phosphate group absorbances(related to the DNA backbone). In thiscase, as both IR absorbance images aremainly because of protein, which isdistributed homogeneously throughoutthe E. coli cell, the observed signals

FIG. 4. (a) AFM topography picture of the bacterium, the position of the tip is indicated inblue. (b) FT–IR spectrum, the bacterium absorption bands is drawn in green, and thewavenumber of the IR laser is indicated by the red arrow. (c) Oscillations recorded by thefour-quadrant detector (in red) as a function of time superposed on the IR pulse laser (blue).

FIG. 3. (a) AFM topography picture of the bacterium; the position of the tip is indicated inblue. (b) FT–IR absorption spectrum of the bacterium (in green); the wavenumber of the IRlaser is indicated by the red arrow. (c) AFM cantilever deflection (in red) as a function of timesuperposed on the IR pulse laser (blue).

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were roughly proportional to the AFMtopography signal (i.e., related to thesample thickness). The 1660 cm-1

absorption was globally more intensethan the 1240 cm-1 absorbance (ratio of7:5), which is in good agreement withbulk IR spectroscopy. When the AFMtip was close to the border of thebacterium without touching it, therewas no signal. This result illustrates thesensitivity and spatial resolution of thetechnique. With AFM–IR, it is appar-ently possible to detect an object with asize approaching a few tens of nanome-ters. The resolution limitation in the case

of an isolated object on the surface is infact the resolution of the tip itself andthe sensitivity of the thermal expansiondetection. In the case of non-isolatedobjects, thermal diffusion can limitspatial resolution.

APPLICATIONS IN POLYMERSCIENCE

AFM–IR is now being used inextensive applications in polymer sci-ence. A driving factor is the number anddiversity of polymeric materials thatincorporate micro- and nanoscale struc-ture to achieve desired properties. Suchmaterials include polymer blends, poly-mer composites and nanocomposites,and thin films used in both activedevices and as passive barriers. Thissection outlines applications in many ofthese areas.

Correlation with Conventional FT–IR. One of the first major features of theAFM–IR technique for polymer appli-cations is the strong correlation withmeasurements by conventional FT–IRspectroscopy. As shown in the Appen-dix, the signal measured by AFM–IR isdirectly proportional to the IR absorp-tion coefficient for a material. As such,the absorption spectra are directly relat-ed to conventional IR spectroscopymeasurements. Figure 8 shows a com-parison of AFM–IR and FT–IR mea-surements on polystyrene, a commonreference sample for IR spectroscopy.32

Note the strong agreement between thetwo techniques for both the absorption

peak positions and band shapes. Thiscorrelation allows spectroscopists todirectly apply analytical techniques andexpertise developed over the last 50years or more, including the use ofextensive material databases for theanalysis and identification of unknowncomponents. Databases are available, forexample, with the IR spectra of manythousands of polymer compounds.

Improved Spatial Resolution. An-other benefit of the AFM–IR techniqueis to provide spatially resolved measure-ments of IR absorption spectra on ascale many times smaller than theconventional diffraction limit. This isachieved by virtue of the fact that theAFM tip measures the IR absorption inthe extreme near field. Although the IR

FIG. 5. Fast Fourier transform (FFT) of thecantilever ring-downs of Fig. 2c (red) andFig. 4c (blue). Note the much larger canti-lever oscillation amplitude on the redcurve, corresponding to the bacteriumabsorption at 1650 cm-1 vs. the amplitudeat 1800 cm-1 (blue curve). To obtain an IRspectrum by the AFM–IR technique, oneneeds only to record the amplitude of acantilever oscillation mode as a function ofthe wavenumber of the laser.

FIG. 6. FT–IR spectrum (in green) of anEscherichia coli culture and AFM–IR spec-trum (in red) of a single E. coli bacterium.

FIG. 7. (a) AFM topography picture of a single bacterium Escherichia coli. (b)Corresponding chemical mapping of the amide I band (1660 cm-1). (c) Correspondingchemical mapping of the amide III band (1240 cm-1).

FIG. 8. Comparison of IR absorptionspectra of polystyrene in the CH-stretchingregion by AFM–IR (red) versus FT–IR(blue). Taken with permission from C.Marcott, M. Lo, K. Kjoller, C. Prater, I. Noda.Applied Spectroscopy. 2011. 65(10): 1145–1150. Copyright 2011 The Society forApplied Spectroscopy.


laser spot might be limited in size bydiffraction, absorbing regions that aresmaller than the wavelength will stillresult in thermal expansions that aresmaller that the laser spot size, asillustrated in Fig. 9. The AFM tip canmeasure this thermal expansion andhence IR absorption with very highspatial resolution.

Figure 10 shows the ability of theAFM–IR to clearly discriminate differ-ent materials on the basis of their IRabsorption spectra on a length scale atleast 30 times finer than conventional IRspectroscopy. The measurement in Fig.10 shows a series of AFM–IR spectrataken at the center and edges of apolystyrene bead and just across theboundary in neighboring epoxy. Thespectra change abruptly on a scale ofaround 100 nm.

Complementary Mechanical Stiff-ness Measurements. AFM–IR instru-mentation can also be used to obtaincomplementary measurements of samplestiffness by recording the cantilevercontact resonance frequency, as illus-trated in Fig. 11. When an AFM tip is incontact with a sample surface, it acts likea coupled spring system (Fig. 11A),where the sample stiffness and dampingcan be considered similar to a spring–dashpot system. When the AFM–IRlaser excites a thermal pulse in thesample, producing oscillations of thecantilever, the resonant frequency ishigher on stiff samples and lower onsoft samples (Fig. 11B). The contactresonance frequency has an S-shapeddependence on the sample elastic mod-

ulus; a model curve is shown (Fig. 11C)for a cantilever style often used inAFM–IR measurements. Measuring thiscontact resonance frequency as a func-tion of position enables spatially re-solved maps of sample stiffness to begenerated. Figure 11D shows AFM–IRtopography and contact resonance im-ages at the interface between twopolymer layers (nylon and an ethyleneacrylic acid copolymer) in a multilayerfilm. Although the topography showsvery little contrast, the contact resonanceimage clearly distinguishes the twopolymer materials on the basis ofdiffering elastic modulus.

Figure 12 shows complementary mea-surements of topography, IR absorptionspectra, an IR absorption map, and astiffness map of another multilayer film.Multilayer films are exceedingly impor-tant commercially, being used in appli-cations ranging from food packaging to

adhesives to advanced display technol-ogies for computers and mobile devices.

Organic Photovoltaics. The subjectof organic photovoltaics is an area ofintense international research, with agoal of high efficiency and low-costgeneration of electric power. The AFM–IR technique was applied to bulkheterojunctions made of poly(3-hexylth-iophene) (P3HT) and [6,6]-phenyl-C61-butyric acid methyl ester (PCBM); anexample measurement is shown in Fig.13. These measurements show spatiallyvarying concentrations of P3HT andPCBM on the basis of characteristicpeaks and peak positions associated withthe constituent materials. Phase separa-tion of PCBM and P3HT is commonlyobserved in such polyvinyl blends. Inthis example, a defect can be seen on thesurface in Fig. 13, which shows an AFMimage of a heat-treated P3HT–PCBMsample. The methylene bending modes

FIG. 9. AFM–IR can achieve spatial reso-lutions below the diffraction limit, as itmeasures local variations in thermal ex-pansion because of IR absorption, even ifthe expanding regions are many timessmaller than the incident laser spot.

FIG. 10. Demonstration of spatial resolution of the AFM–IR technique on a modelpolymeric sample. A 3 lm polystyrene (PS) bead was embedded in epoxy and measuredwith the AFM–IR technique. A spectrum near the middle of the PS bead shows thecharacteristic aliphatic and aromatic CH stretching bands in the 2800 to 3200 cm-1

region. Similar spectra are obtained at the left and right edges of the bead. However, just~100 nm across the boundary into the epoxy, very different spectra are obtained,characteristic of the absorption spectra of the embedding epoxy. Conventional IRspectroscopy at this wavelength (~3 lm) would have a practical spatial resolution limit ofabout one to three times the wavelength (depending on technique used), or around 3–9 lm.Thus, a conventional IR microspectroscopy measurement would provide at best spatialresolution equal to the bead size. The approximate spatial resolution of the AFM–IRtechnique (~100 nm) is shown by the size of the small red square.

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at 1444 and 1432 cm-1 correspond toP3HT and PCBM, respectively. The1444 cm-1 band also contains a contri-bution from an overlapping-ring, semi-c i r c l e s t r e t c h i n g m o d e . T h ecorresponding spectrum for the yellowhash mark appears to have both compo-nents. At the outer ring (red mark,spectrum 1), the peak at 1732 cm-1

(PCBM) is small, and the component at1444 cm-1 (P3HT) dominates. At bothgreen and purple hash marks (spectra 3and 4), the band near 1432 cm-1 ismainly contributed by PCBM. Finally,the sharpness of the band at 1432 cm-1

and a stronger 1732 cm-1 signal suggestthe lobe at the center is mostly PCBM.By combining the AFM and IR into asingle instrument, the topological infor-mation is readily correlated with thelocal chemical analysis. The above datasuggest there is local phase separation.

Figure 14 shows a proprietary multi-component polymer blend. Blends withmicro- and nanoscale-sized polymerdomains are increasingly common. Of-ten different combinations of polymersare used to achieve desired strength,toughness, and other performance crite-

ria for a specific application. AFM–IRcan reveal the spatial distribution ofthese polymer components and chemi-cally identify polymer constituents.

APPLICATIONS INMICROBIOLOGY

Location of Poly(hydroxybutyrate)Produced by Rhodobacter capsula-tus.26 Poly(hydroxybutyrate) (PHB) be-longs to the class of polyesters and hasbeen used for several years for theproduction of plastics having similarmechanical and thermoplastic propertiesto those of polyethylene and polypro-pylene, but with the advantage ofbiocompatiblity, making it a renewableresource. Rhodobacter capsulatus is apurple, non-sulfur, photosynthetic bac-terium that produces PHB for energystorage.33–35 Bacterial PHB is stored invesicles of variable size, which aredegraded by the bacterium when itsnutritive resources become limiting. Thepresence of PHB can be probed in themid-IR region by detecting one specificabsorption band at 1740 cm-1 becauseof the ester C=O stretching vibration,which is easily distinguishable fromother bacterial bands (e.g., amides Iand II at 1660 and 1550 cm-1respec-tively).36 Many studies have been con-ducted on the characterization of PHBby using different vibrational spectro-scopic techniques (e.g., Raman, FT–IR).However, these methods often requireprior extraction of PHB37 and do notallow an in situ study because of the lack

FIG. 11. Illustration of mechanical property mapping with the AFM–IR technique. Acantilever in contact with a sample surface acts like a coupled spring system (A) whereinthe sample elasticity changes the frequency at which the cantilever resonates (B, C).Mapping this contact resonance frequency as a function of position (D) allowsdiscrimination of materials based on differing stiffness. The images shown in (D) aretopography (top) and contact resonance frequency (bottom) of an interface region in apolymer multilayer consisting of nylon and an ethylene acrylic acid copolymer.

FIG. 12. Multifunctional measurements performed with the AFM–IR on a polymermultilayer film of polypropylene, polyethylene, and embedding epoxy. The measurementsshow topography (A), representative IR absorption spectra (B), stiffness map (C), and an IRabsorption image at 1456 cm-1 (D).


of resolution in imaging. The AFM–IRtechnique allows the study of PHBdirectly in the cell without extractionor complex sample preparation.

R. capsulatus wild type was grownunder classical conditions. The cellsuspension was spun down by centrifu-gation at 1000 rpm for 15 min. Thesupernatant was removed, and the pelletwas diluted in distilled water. A drop ofthe solution was deposited on the ZnSeprism for AFM–IR studies or on ZnSeglass for FT–IR and dried at roomtemperature for 20 min.

The top panels in Fig. 15 display theAFM topography of R. capsulatus. Thevariations in height are given a red–yellow color code, where the maximumis represented by the yellow. The bottompanels represent the amplitude distribu-tion of the cantilever fundamental mode,with the laser wavenumber tuned at1740 cm-1, which corresponds to thechemical cartography of ester C=Ostretching vibration (specific band ofPHB), on a rainbow scale. The scaleindicates increasing absorption when the

signal shifts from purple to red. On allmaps, round red areas are apparent.These domains correspond to PHBgranules inside the bacterium (Figs.15d through 15f). On each map, it ispossible to estimate the size of granulesby taking the width at half height.26 Fora dozen measurements, we observedround shape sizes in the range of 100to 400 nm, which is consistent with thetransmission electron microscopy(TEM) studies of the same culture madejointly.26

Figure 15d reveals a 210 nm diameterround granule and, and an oval-shapedone only 50 nm across (top of theimage). This oval shape could corre-spond to an alignment of small vesiclesinitially produced by the bacteriummembrane.38 Figure 15e shows onebacterium with, and another without, aPHB vesicle. This suggests that underthese growing conditions, all R. capsu-latus cells do not necessarily producePHB. The PHB-to–bacteria volume ratiois low by looking at our chemicalmapping. This is in good agreement

with the FT–IR spectrum of the bacteriaculture (Fig. 16a, green curve), wherethe ester carbonyl band appears as ashoulder on the amide I band. Figure 15f(zoom of Fig. 15e) shows more clearlythat the absorbing area is in factcomposed of two adjacent vesicles ofdifferent sizes.

One must be careful when interpret-ing AFM–IR chemical images alone,because the contrast can come not onlyfrom IR absorption, but also fromthermomechanical artifacts because ofthe sample mechanical properties. Toprove that the mapping contrast reallyresults from chemical differences, werecorded the spectroscopic response ofthe one vesicle and compared it with theFT–IR spectrum of the bacteria culturein Fig. 16.

The spectrum on a single bacterium(in red in Fig. 16a) was measured by

FIG. 13. AFM–IR measurements of bulk heterojunction P3HT–PCBM film. AFM–IRabsorption spectra were obtained at several points surrounding a defect observed in theAFM topography image (left). The spectra reveal variations in the amplitude of the carbonylpeak (~1730 cm-1) associated with higher concentration of PCBM. Stronger concentrationsof P3HT cause a reduction in the carbonyl peak and a shift in the methylene bendingabsorption from ~1432 to ~1444 cm-1.

FIG. 14. AFM–IR measurements of apolymer blend, including topography im-age (top), IR absorption at 1450 cm-1

(center), and stiffness map (bottom). Whilethe topography image reveals intricatemorphology, it gives only limited cluesabout the chemical and mechanical prop-erties of the sample. The IR absorptionmap (center) and stiffness map (bottom)clearly resolve three different constituentsin this polymer blend. Note for examplethe three shades of green, yellow, andorange in the absorption image (center)image and the three different shades ofpink, light blue, and dark blue in thestiffness map (bottom).

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positioning the tip of the AFM directlyon the maximum of the signal by usingthe chemical mapping of PHB (asindicated by point A in Fig. 16b). Weobserve an intense PHB ester carbonylstretching band (centered at 1740cm-1), whereas the amide I band at1660 cm-1 appears weaker. As the tipis positioned directly over the vesicle,there is no amide I IR absorbancesignal. However, there are many pro-teins surrounding the PHB vesicle,which can generate a small responsein the amide I spectral region. Con-cerning the C=O stretching band of theester, we obtained a clear signaldemonstrating that PHB is almostcertainly responsible for the hot spotsobserved on the 1740 cm-1 mapsshown in Figs. 15 and 16. The secondspectrum (B) shown in Fig. 16a wasrecorded by positioning the tip at pointB in Fig. 16b at the border of thevesicle indicated in the 1740 cm-1

absorption image. The spectrum showsa better signal for the amide I that issimilar to the FT–IR spectrum of thebacteria culture (Fig. 16a in green). Theintensity of the PHB C=O ester bandin that case has decreased compared

with position A, which is consistentwith the PHB chemical mapping. Whenthe tip is moved to position C (Fig.16b), out of the vesicle, the AFM–IRspectrum does not show the C=O band(in violet, Fig. 16a). The behavior ofthe spectra is in good agreement withthe contrast of the chemical mapping.This confirms that the AFM–IR tech-

nique gives us realistic mapping and IRspectra at spatial resolutions ,100 nm.

Characterization of Microdomainsin Poly(hydroxyalkanoate) Copoly-mer Films. As described above, poly-hydroxyalkanoates (PHAs) are a class ofpolyesters that can be accumulated asenergy-storing granules in the cells ofcertain microorganisms such as R.capsulatus. A reason one of the mostcommon PHA polymers, PHB, has notproven a feasible polyolefin replacementis because the material is stiff and brittlebecause of its high degree of crystallin-ity, and it can become thermally unsta-ble during processing. This shortcominghas led to efforts to copolymerize PHBwith other co-monomers to improve itsmechanical properties.39–41 Poly(3-hy-droxybutyrate-co-3-hydroxyhexanoate)[P(HB-co-HHx)], with a melting tem-perature of 110 to 160 8C and 35 to 45%crystallinity, is a typical available grade,and its morphology was explored usingAFM–IR.32

Thin films of P(HB-co-HHx) werestudied in the bulk by IR transmissionspectroscopy in an attempt to understandhow a thermally induced phase transi-tion affects the molecular structure ofthe material.42 Significant spectralchanges were observed in both thecarbonyl ester stretching region(1770-1670 cm-1) and the C-O-Cbackbone stretching region (1400–1200cm-1). The spectral changes observed asthe temperature was increased from 30

FIG. 15. (a) AFM topography of a single Rhodobacter capsulatus. (b) AFM topography oftwo separated R. capsulatus bacteria. (c) AFM zoom on the lowest bacterium localized on(b). (d) Chemical mapping of PHB (at 1740 cm-1) of the corresponding topography (a). (e)Chemical mapping of PHB of (b). (f) Chemical mapping of PHB of (c).

FIG. 16. (a) Comparison between local AFM–IR spectra (A in red, B in orange, C in violet)and a corresponding FT–IR spectrum (in green) of the bacteria culture. (b) Bacteriumchemical mapping of the ester C=O stretching band showing the specific locations of theAFM–IR spectral measurements (A–C).


to 140 8C clearly reflected changes in thepolymer conformational structure.42

Akin to polyethylene and polypropyl-ene, P(HB-co-HHx) materials are semi-crystalline, which means films formedfrom them usually contain both crystal-line and disordered (amorphous) do-mains at room temperature. The sizeand morphology of the resulting micro-domains depend critically on the pro-cessing conditions used to form them, aswell as the sample history. ConventionalFT–IR microspectroscopy typically doesnot have the ability to spatially resolveand spectrally identify individual micro-domains.

Figure 17 shows an AFM topographyimage of a 450 lm-thick P(HB-co-HHx) sample film, whereon an AFM tipheated to 350 8C was brought to within3 lm of a spot slightly above and left ofthe center of the image for 90 s. Theheated tip produced a ‘‘hole’’ in thesample film, as indicated by the darkarea in the image. A series of 42individual AFM–IR spectra were col-lected after the sample cooled back toroom temperature, along the lineshown.32 The spectrum recorded atposition 24, just to the right of the holeproduced by the heated tip, represented

the most well-ordered (crystalline) en-

vironment of the carbonyl functional

group. Figure 18 shows a stack plot of

the expanded regions of the AFM–IR

spectra between 1770 and 1670 cm-1

(left) and between 1400 and 1200 cm-1

(right) of spectra 24 to 36.32 Thespectra in the carbonyl stretching re-gion (left) indicate the presence of threebands, two overlapped bands at 1720cm-1, and a third broader band at 1740cm-1. It is clear that the carbonylintensity is gradually shifting from thetwo overlapped bands at 1720 cm-1 tothe broader feature at 1740 cm-1 as oneprogresses from spectrum 24 to 36.This spectral progression provides in-sights into how this polymeric systemrecrystallizes after the heated AFM tipproduced a nucleation site in the samplefilm. The most crystalline structure, asindicated by the carbonyl band, appearsat the edge of the heated area, and thesample apparently becomes progres-sively more disordered as a functionof distance from this point in a directionaway from the nucleation site. Thecorresponding changes in the C–O–Cbackbone stretching region near 1276cm-1 are much more dramatic andmore difficult to unambiguously inter-pret at the molecular level. It isintriguing that the behavior of the ofthe C=O region AFM–IR band-shapechange relative to the C–O–C backbone

FIG. 18. AFM–IR spectra of P(HB-co-HHx) from positions from 24 to 36 on Fig. 17. Bandsassociated with more ordered (crystalline) structure decrease in intensity, while bandsassociated with less ordered (amorphous) structure increase in intensity as one movesfrom position 24 to 36. Taken with permission from C. Marcott, M. Lo, K. Kjoller, C. Prater, I.Noda. Applied Spectroscopy. 2011. 65(10): 1145–1150. Copyright 2011 The Society forApplied Spectroscopy.

FIG. 17. AFM height image of P(HB-co-HHx) showing a line scan of 42 positions, 200 nm apart,where individual AFM–IR spectra were collected. Position 24 is just left of the dark area (hole) onthe AFM image where the sample was locally heated and allowed to cool before measurement.Taken with permission from C. Marcott, M. Lo, K. Kjoller, C. Prater, I. Noda. AppliedSpectroscopy. 2011. 65(10): 1145–1150. Copyright 2011 The Society for Applied Spectroscopy.

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region band-shape change is exactlyopposite of the bulk IR measurementsrecorded as a function of temperature.42

This suggests that collecting a bulk IRspectrum at higher temperature mightnot necessarily be representative of thesituation in a non-crystalline region of aparticular microdomain at room tem-perature. Thus, the ability to record IRspectra at sub-micrometer spatial reso-lutions could revolutionize the way wethink about the molecular conforma-tions in microdomains of semicrystal-line polymers.

MISCIBILITY INPHARMACEUTICAL BLENDFORMULATIONS

Determining the extent of miscibilityof amorphous components is of greatimportance for certain pharmaceuticalsystems, in particular for polymer-poly-mer and polymer-small moleculeblends. For amorphous solid dispersions,where an amorphous drug is intimately

mixed with a polymeric carrier, forma-tion of miscible systems is desired as itincreases the physical stability of thesystem. Two model systems for poly-mer–polymer43 and drug-polymer44

miscibility were examined and are re-viewed below.

Dextran-Poly(vinylpyrrolidone)Blends. Blends of dextran (DEX) andpoly(vinylpyrrolidone) (PVP) have beenused extensively as model systems forthe study of polymer-polymer miscibil-ity. The miscibility characteristics of aset of 50:50 (wt/wt) polymer blendscomposed of PVP and DEX of varyingmolecular weights were investigated.43

Although differential scanning calorim-etry (DSC) is usually considered thestandard technique for evaluating misci-bility behavior in pharmaceutical blends,a number of issues have been identifiedwith the technique over the years.Typically, a single glass transition (Tg)is expected for a miscible blend, butsometimes identification of all glass

transitions in a thermogram can bedifficult in cases where the pure com-ponents of a mixture have very similarTg values. In addition, a minimal domainsize (e.g., 10 to 50 nm for polymericblends) is typically required for phase-separated domains to produce distin-guishable Tg events.45,46 The width and/or heat capacity changes associated witha glass transition event might also be toobroad or weak to allow for its identifi-cation.

One particular 50:50 PVP–DEXblend system is presented here toillustrate the power of AFM–IR toprovide spatially resolved insights intothe morphology of the blend.43 Specif-ically, PVP90 (MW = 1–1.5 MDa) andDEX40 (MW = 40 kDa) were preparedby mixing equal amounts of 10% (wt/vol) aqueous solutions of the purecomponents. This particular blend sys-tem was determined to be immiscible byDSC. A thin film was formed on thesurface of a ZnSe prism by spin coating100 lL of the polymer blend solutionfor 20 s at 3100 rpm, which wassubsequently evaluated by nanoscalemid-IR spectroscopy by using a nano-IRTM AFM–IR instrument (Anasys In-struments). All data were obtained incontact mode with a three-lever cantile-ver (CSC37-ALBS, Mikromasch, Tallin,Estonia). The IR laser produced 10 nspulses at a repetition rate of 1 kHz. Thepower levels incident on the ZnSe prismwere ~0.5 mW, and the focused laserspot size was about 50 lm at the samplesurface. Local spectra were collectedover a 1200 to 1800 cm-1 spectral rangeby using a data point spacing of 4 cm-1

and the spectral resolution as determinedby the laser line width was ~8 cm-1. Atotal of 128 scans were co-added foreach data point in a given spectrum. IRimages of the DEX40-PVP90 systemwere collected at both 1280 and 1350cm-1, with a contact frequency of 137kHz and a width of 20 kHz. The images25 3 15 lm2 presented correspond to anarray of 512 3 64 measurements. Thus,the spacing between points was about 50nm on the x axis and about 225 nm onthe y axis. Once again, a total of 16cantilever ring downs were co-added ateach spatial location. The raw data of thespectral images were further processedwith Gwyddion (version 2.19, http://

FIG. 19. Localized nanoscale mid-IR spectra of a DEX40-PVP90 blend. (A–C) Topograph-ical images (the positions of the spectral measurements are marked; the distances betweenmeasurement locations are about 2.5 lm). (D) Average local nanoscale mid-IR spectra(1200-1800 cm-1, normalized and offset). From bottom to top: pure PVP90 (n = 10, greendotted line), pure DEX40 (n = 10, red dotted line), PVP-rich phase in the DEX40-PVP90 blend(n = 6, green solid line), and DEX-rich phase in the DEX40-PVP90 blend (n = 4, (red solidline). Black dashed spectra in (D) are those of the average 6 standard deviation. Adaptedwith permission from B. Van Eerdenbrugh, M. Lo, K. Kjoller, C. Marcott, L.S. Taylor.Molecular Pharmaceutics. 2012. 9: 1459–1469. doi:10.1021/mp300059z. Copyright 2012 TheAmerican Chemical Society.


gwyddion.net/). Ratio images were con-structed by dividing the intensities of themap obtained at 1280 cm-1 by thosecollected at 1350 cm-1.

Standard AFM imaging confirms theformation of a phase-separated blend(Figs. 19A through 19C), in agreementwith the DSC results.43 Discrete do-mains with diameters of 5 to 10 lm aredistributed within a thinner continuousphase (Figs. 19A and 19B). The contin-uous phase also contains smaller, dis-crete domains with diameters rangingfrom about a few hundred nanometers toa few micrometers (Figs. 19B and 19C).Nanoscale mid-IR spectral measure-ments performed at select locations areshown in Fig. 19B. These spectra (Fig.19D) show that thicker, DEX-richdiscrete domains are distributed in aPVP-rich continuous phase. Figures20A through 20F show IR images ofthe same DEX40-PVP90 sample col-lected with the fixed laser wavenumbersof 1280 and 1350 cm-1.43 Thesewavenumbers were selected becausepure DEX absorbs more strongly at

1350 cm-1 than it does at 1280 cm-1,while the opposite is true for PVP. Theimage generated by evaluating peakintensity variations at 1280 cm-1 (Fig.20B) shows higher intensities for thecontinuous phase, while in the 1350cm-1 image (Fig. 20C), the discretedomains have higher intensities.43 Theseresults are consistent with the formationof DEX-rich domains within a PVP-richcontinuous phase. As local topographyand mechanical properties can alsoinfluence the spectroscopic intensitiesmeasured in single-wavelength images,it is good practice to confirm theinterpretation by generating ratio imag-es.43,44 When the ratio image of1280:1350 cm-1 (shown in Fig. 20D)is compared with the topographicalimage in Fig. 20A, it is once again clearthat the large discrete domains corre-spond to a DEX-rich phase, while thecontinuous phase is rich in PVP. Figures20E and 20F show the topographicaland ratio images of the upper left-handcorner of Figs. 20A through 20D, withadditional magnification.43 It is clearthat the sub–micrometer-sized discretedomains present in the continuous phasehave lower band ratios (blue regions)compared with those of the continuousphase, indicating that these smallerdiscrete domains are also DEX rich

FIG. 21. Localized nanoscale mid-IR spectra of a 50 : 50 (wt/wt) felodipine–PAA systemobtained at discrete domains (1–4) and in the continuous phase (5–8). (a) Topographicalimage (1.5 3 2.5 lm2, color scale is 100 nm, the positions of the spectral measurements aremarked), (b) nanoscale mid-IR spectra (1200–1800 cm-1, spectra from bottom to topcorresponds to locations 1–8, normalized and offset), and (c) average spectra of bothphases (1 to 4 bottom, 5 to 8 top, n = 4, normalized and offset). Adapted with permissionfrom B. Van Eerdenbrugh, M. Lo, K. Kjoller, C. Marcott, L.S. Taylor. Journal ofPharmaceutical Sciences. 2012. 101(6): 2066–2073. doi:10.1002/jps.23099. Copyright 2012Journal of Pharmaceutical Sciences.

FIG. 20. Nanoscale mid-IR mapping of the DEX40-PVP90 system. (A) Topographicalimage. (B) Mapping image at 1280 cm-1. (C) Mapping image at 1350 cm-1. (D) Ratio image(1280:1350 cm-1). (E) Magnification of the topographical image. (F) Magnification of the ratioimage of 1280:1350 cm-1. Adapted with permission from B. Van Eerdenbrugh, M. Lo, K.Kjoller, C. Marcott, L.S. Taylor. Molecular Pharmaceutics. 2012. 9: 1459–1469. doi:10.1021/mp300059z. Copyright 2012 The American Chemical Society.

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and provide further demonstration of thesub-micrometer chemical imaging capa-bilities of the technique.43

Felodipine–Poly(acrylic acid)Blends. The state of dispersion of anactive pharmaceutical ingredient (API)in a polymeric carrier can have a majorimpact on its release kinetics, stronglyinfluencing the effectiveness of the drug.Dispersions of APIs with polymers canbe on a molecular, nanometer, ormicrometer scale, or some combinationthereof. Manufacturing conditions andformulation variables are important fac-tors influencing the polymer and drugdomain sizes and phase behavior. Inaddition, the state of drug dispersion canchange over time, either during storageor on drug release.44

A model drug–polymer blend systemcomposed of felodipine and poly(acrylicacid) (PAA) was examined with AFM–IR.44 When prepared as an amorphoussolid by solvent evaporation, felodipinehas relatively low crystallization tenden-cy;47,48 therefore, it serves as a goodmodel compound to evaluate drug–polymer miscibility, because it can beassumed that the drug will remainamorphous. PAA is an amorphouspolymer that does not crystallize. Thisparticular drug–polymer combinationappears to be miscible at low and highpolymer concentrations, but phase sep-aration is observed at intermediatecompositions.44 An AFM height imageand local nanoscale mid-IR spectraobtained on a 50:50 (wt/wt) felodi-pine–PAA blend system are shown inFig. 21.44 The average thickness of the

film was approximately 570 nm. Loca-tions where spectra were taken aremarked on the images and correspondto discrete domains (1–4, marked in red)and the continuous phase (5–8, markedin green). As can be seen from theindividual spectra (Fig. 21b) and theiraverages (Fig. 21c), clear spectral dif-ferences can be observed, depending onthe region of the system probed, partic-ularly when comparing the intensity ofthe peak at around 1700 cm-1 with thatfound at 1500 cm-1.44 For the contin-uous phase, the peak at around 1700cm-1 is the dominant peak in the 1200to 1800 cm-1 spectral region comparedwith the peak at 1500 cm-1. For thediscrete domains, peak intensities at1500 cm-1 tend to be somewhat higherthan those obtained at 1700 cm-1.

The IR bands at 1500 and 1700 cm-1

were selected for imaging purposesbecause of their ability to discriminatebetween the felodipine and PAA com-ponents of the bend. Figure 22 showsimages collected with the tunable lasersource tuned to these two wavenum-bers.44 Good correspondence is ob-served between the image obtained at1500 cm-1 (Fig. 22b) and the topo-graphical image (Fig. 22a). Rather thandrawing conclusions based on measure-ments made at a single wavenumber, itis prudent to examine the relativedifferences in response by using imagescollected at multiple wavenumbers. Fig-ure 22c shows an image generated bytaking the ratio of the responses at 1500and 1700 cm-1.44 The blue regions havea propensity to correspond to the PAA-

rich continuous phase, while green andred regions correspond to the felodipinerich discrete domains.

MOLECULAR ORIENTATIONIN ELECTROSPUN FIBERS

Electrospinning has established itselfas an efficient technique to producesmall-diameter (10 nm to 10 lm)polymer fibers. The fibers are fabricatedfrom polymer solutions or melts byusing an applied electric field. Manypolymers were successfully electrospun,and their applications include compos-ites, filtration systems, medical prosthe-sis, tissue templates, electromagneticshielding, and liquid crystal devices.49

Poly(vinylidene fluoride). There isconsiderable interest in electrospun fi-bers of poly(vinylidene fluoride)(PVDF) because of its piezoelectricand pyro-electric properties. Electrospunfibers of PVDF in the b phase wererecently characterized by a variety oftechniques, including by scanning elec-tron microscopy, polarized FT–IR spec-troscopy, TEM, and selected areaelectron diffraction.50 The nanofibers inthis case were collected on aluminumfoil across a 10 lm gap in order to getthem to align so polarized FT–IRmeasurements could be performed, asthe width of an individual fiber was wellbelow the diffraction limit of the IR lightused to make the measurement. Thesemeasurements are important becausethey provide key information about themolecular orientation of the polymerchains within the fibers, which affectstheir properties. Without the capabilityto perform sub–diffraction-limited po-larized IR spectroscopy on an individualnanofiber, it was necessary to collectpolarized FT–IR transmission on amultiple fibers that were forced to beroughly aligned across the 10 lm gap.Although a useful compromise, thefibers were not all 100 percent alignedin exactly the same direction. This madeit difficult to determine with certainty ifany orientation relaxation that mighthave occurred in an electrospun fibermat was because of fiber rearrangementor relaxation in the individual nano-fibers.

Even though the laser source of theAFM–IR instrument is polarized insome direction, up to now, we have

FIG. 22. Nanoscale mid-IR mapping of a 50 : 50 (wt/wt) felodipine–PAA system (1.5 3 1.5lm2). (a) Topographical image (color scale is 250 nm), (b) spectroscopic image obtained at1500 cm-1 (color scale is 0.20–0.75 V), (c) image ratio of 1 500:1 700 cm-1 (color scale is 0.9to 1.9). Adapted with permission from B. Van Eerdenbrugh, M. Lo, K. Kjoller, C. Marcott, L.S.Taylor. Journal of Pharmaceutical Sciences. 2012. 101(6): 2066–2073. doi:10.1002/jps.23099.Copyright 2012 Journal of Pharmaceutical Sciences.


not taken advantage of this to add

potentially valuable molecular orienta-

tion information to what was discussed

so far in this review. For this PVDF-

oriented nanofiber characterization

study, a device enabling arbitrary angle,

broad-band control of the polarization

was added to the AFM–IR instrument

(nano-IR, Anasys Instruments).

Figure 23 shows two IR absorbance

images on two roughly perpendicular

electrospun PVDF fibers approximately

1 lm in diameter. The images wererecorded with two different polarizationswith the pulsed-laser illumination fixedat 1404 cm-1, the wavenumber of one ofthe stronger PVDF absorption bands.The results clearly indicate that theelectric dipole-transition moment of thisIR band, due to CH2 wagging and C–Canti-symmetric stretching vibrationalmotions, was aligned along the fiberaxis.

Figure 24 shows two polarized AFM–IR spectra (bottom) collected from thesame single location on one of the fibersshown in Fig. 23. For comparison, twoaveraged-polarized FT–IR spectra ofmultiple aligned fibers are shown at thetop of Fig. 24. The excellent agreementbetween these two measurements dem-onstrates that we should now be able touse AFM–IR spectroscopy to examinethe molecular structure and orientationat multiple locations on individual nano-fibers.

CONCLUSION

We have demonstrated the broadutility of the AFM–IR technique in thematerial and life sciences. We showedthat there is excellent agreement be-tween AFM–IR and conventional IRspectroscopy measurements, allowingsignificant leverage of existing expertisein IR spectroscopy. In addition, weshowed how the AFM–IR techniquecan be used to acquire IR absorptionspectra and absorption images withspatial resolution on the 50 to 100 nm

scale versus the scale of many micro-meters or more for conventional IRspectroscopy. This review also summa-rizes several applications of AFM–IR inthe life and polymer sciences. In the lifesciences, experiments demonstrated theability to perform chemical spectroscopyat the sub-cellular level. Specifically, theAFM–IR technique provides a label-freemethod for mapping IR-absorbing spe-cies in biological materials. On thepolymer side, AFM–IR was used tomap the IR absorption properties ofpolymer blends, multilayer films, thinfilms for active devices such as organicphotovoltaics, microdomains in a semi-crystalline polyhydroxanoate copoly-mer, as well as model pharmaceuticalblend systems. The ability to obtainspatially resolved chemical spectra aswell as high-resolution chemical imagescollected at specific IR wavenumberswas demonstrated. Complementarymeasurements mapping variations insample stiffness were also obtained bytracking changes in the cantilever con-tact resonance frequency. Finally, it wasshown that by taking advantage of theability to arbitrarily control the polari-zation direction of the IR excitationlaser, it is possible to obtain importantinformation regarding molecular orien-tation in electrospun nanofibers.

ACKNOWLEDGMENTS

We gratefully acknowledge the many collabo-rators who have provided samples and/or mea-surements described in this review. We specificallyrecognize Kevin Kjoller, Michael Lo, Debra Cook,Greg Meyers, Celine Mayet, Ariane Deniset, PierreSebban, Rui Prazeres, Jean-Michel Ortega, Ber-nard van Eerdenbrugh, Lynne Taylor, and IsaoNoda.

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FIG. 23. IR absorbance images of two PVDF fibers collected with the pulsed laser sourcetuned to 1404 cm-1 by using light polarized in the two orthogonal directions indicated.Lighter color indicates stronger absorbance at that wavenumber.

FIG. 24. Two polarized AFM–IR spectra(bottom) collected from the same singlelocation on one of the fibers shown in Fig.23. For comparison, two averaged polar-ized FT–IR spectra of multiple alignedfibers are shown at the top.

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31. G.A. Hill, J.H. Rice, S.R. Meech, D.Q.M.Craig, P. Kuo, K. Vodopyanov, M. Reading.‘‘Submicrometer Infrared Surface ImagingUsing a Scanning-Probe Microscope and anOptical Parametric Oscillator Laser’’. Opt.Lett. 2009. 34: 431-433.

32. C. Marcott, M. Lo, K. Kjoller, C. Prater, I.Noda. ‘‘Spatial Differentiation of Sub-Micro-meter Domains in a Poly(hydroxyalkanoate)Copolymer Using Instrumentation that Com-bines Atomic Force Microscopy (AFM) and

Infrared (IR) Spectroscopy’’. Appl. Spectrosc.2011. 65(10): 1145-1150.

33. R. Kranz, K. Gabbert, T. Locke, M. Madigan.‘‘Polyhydroxyalkanoate Production in Rhodo-bacter Capsulatus: Genes, Mutants, Expres-sion, and Physiology’’. Appl. and Environ.Microbiol. 1997. 63(8): 3003-3009.

34. H.H. Wong, S.Y. Lee. ‘‘Poly-(3-hydroxybuty-rate) Production from Whey by High-DensityCultivation of Recombinant Escherichia coli’’.Appl. Microbiol. Biotechnol. 1998. 50: 30-33.

35. Q. Zhao, G. Cheng. ‘‘Preparation of Biodegrad-able Poly(3-hydroxybutyrate) and Poly(ethyl-ene glycol) Multiblock Copolymers’’. J. Mat.Sci. 2004. 39: 3829-3831.

36. D. Naumann. ‘‘FT-IR and FT-NIR RamanSpectroscopy in Biomedical Research’’. TheEleventh International Conference on FourierTransform Spectroscopy, AIP ConferenceProceedings. 1998. 430: 96-109.

37. S.K. Hahn, H.W. Ryu, Y.K. Chang. ‘‘Com-parison and Optimization of Poly(3-hydroxy-butyrate) Recovery from AlcaligenesEutrophus and Recombinant Escherichia Co-li’’. Korean Journal Chem. Eng. 1998. 15(1):51-55.

38. D. Jendrossek, O. Selchow, M. Hoppert.‘‘Poly(3-hydroxybutyrate) Granules at theEarly Stages of Formation are Localized Closeto the Cytoplasmic Membrane in Caryopha-non Latum’’. Appl. and Environ. Microbiol.2007. 73(2): 586-593.

39. M.M. Satkowski, D.H. Melik, J.-P. Autran,P.R. Green, I. Noda, L.A. Schechtman.‘‘Physical and Processing Properties of Poly-hydroxyalkanoate Copolymers’’. In: Y. Doi,A. Steinbuchel (ed.) Biopolymers, vol. 3B,Weinhiem: Wiley-VCH, 2001. Pp. 231-264.

40. I. Noda, P.R. Green, M.M. Satkowski, L.A.Schechtman. ‘‘Preparation and Properties of aNovel Class of Polyhydroxyalkanoate Copoly-mers’’. Biomacromolecules. 2005. 6(2):580-586.

41. I. Noda, M.M. Satkowski, A.E. Dowrey, C.Marcott. ‘‘Polymer Alloys of Nodax Copoly-mers and Poly(Lactic Acid)’’. Macromol.Biosci.. 2004. 4(3): 269-275.

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43. B. Van Eerdenbrugh, M. Lo, K. Kjoller, C.Marcott, L.S. Taylor. ‘‘Nanoscale Mid-Infra-red Evaluation of the Miscibility Behavior ofBlends of Dextran or Maltodextrin withPoly(vinylpyrrolidone)’’. Molec. Pharm.2012. 9: 1459-1469. doi:10.1021/mp300059z.

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ray Powder Diffraction’’. J. Pharm. Sci. 2008.97: 4840-4856.

47. B. Van Eerdenbrugh, J.A. Baird, L.S. Taylor.‘‘Crystallization Tendency of Active Pharma-ceutical Ingredients Following Rapid SolventEvaporation–Classification and Comparisonwith Crystallization Tendency from Under-cooled Melts’’. J. Pharm. Sci. 2010. 99: 3826-3838.

48. J.A. Baird, B. Van Eerdenbrugh, L.S. Taylor.‘‘A Classification System to Assess theCrystallization Tendency of Organic Mole-cules from Undercooled Melts’’. J. Pharm. Sci.2010. 99: 3787-3806.

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APPENDIX: MATHEMATICALMODEL OF AFM–IR

In this section, we outline the basictheory of the signal detected in AFM–IR. The section below includes adiscussion of the following steps:

� Absorption of IR light by the sample� Generation of heat in the sample and

resulting temperature rise� Thermal expansion pulse of the sample� Excitation of cantilever resonances

from the thermal expansion pulse� Extraction of cantilever amplitudes at

specific resonant modes

The bottom-line of this analysis is that

the amplitude of cantilever oscillation atany IR wavelength is directly propor-tional to the sample absorption coeffi-cient at that wavelength. It is thisunderlying link that allows the AFM–IR technique to provide IR absorptionspectra very well correlated to conven-tional IR spectroscopy.

Absorption of IR Light by theSample. Spectroscopy studies interac-tions of a material with an incident waveas a function of wavelength (or equiv-alently, energy or frequency). In themid-IR range (500 to 4000 cm-1), theenergy of the electromagnetic wavesusually corresponds to molecular vibra-tions. From an optical point of view,materials are characterized by theircomplex optical index:

~nðkÞ ¼ nðkÞ þ ijðkÞ ðA1Þ

where k is the wavelength, n(k) is thereal refractive index, and j(k) theimaginary component of the index isthe extinction coefficient. The wave-length dependence of n(k) represents theoptical dispersion of a material, whilej(k) corresponds to the absorption. Wefocus on the wavelength dependence ofthe absorption, which serves as thefoundation of IR absorption spectra.

When IR radiation impinges on asample, the electric field of the electro-magnetic wave can be absorbed by amolecule in its path if the radiationfrequency matches that of a naturalvibrational frequency and induces adipole moment change in the moleculeas a result of the interaction. Whenmolecular vibrations are excited becauseof absorption of a portion of the incidentradiation into a higher vibrational state,heat is produced in the sample matrixwhen the excited molecules return totheir ground vibrational state. The de-gree of absorption comes from theimaginary part of the dipolar suscepti-bility of the molecular vibration. Theprinciple of spectroscopy is to measurethe intensity of the radiation transmittedthrough the sample as a function of thewavelength. In the IR spectral range, itis more common to use ‘‘wavenumber’’,(a measure of the radiation frequency)instead the wavelength. If we consider ahomogeneous layer of a medium withthickness z and complex optical indexn(k), illuminated by an electromagnetic

plane wave, the transmitted intensity canbe given by the Beer–Lambert Law as(neglecting the index mismatch reflec-tions at the interfaces):

It ¼ Iince-4prjz ðA2Þ

where Iinc is the incident intensity, r thewavenumber, and j the extinctioncoefficient. The transmittance coeffi-cient, T, is defined by the ratio of thetransmitted and the incident intensity:

T ¼ It

Iinc

¼ e-4prjz ðA3Þ

It is convenient to convert this to anabsorbance coefficient, A, which directlygives the variation of the absorptionbands as a function of wavenumber:

A ¼ log1

T¼ 4pz

lnð10ÞrjðrÞ ðA4Þ

This simple expression shows that theabsorbance is in fact the representationof the extinction coefficient multipliedby the wavenumber. This also meansthat to make usable spectra with a near-field technique, the microscope willhave to measure only the imaginary partof the refractive index.

Generation of Heat from IR Ab-sorption and Resulting TemperatureRise. The absorption of the light by amaterial leads to an increase in itstemperature. The evolution of this heatcan be easily described by Fourier’s Law:

qC]T

]t-kDT ¼ QðtÞ

VðA5Þ

where q is the density, C the heatcapacity, k the heat conductivity, V thevolume, Q(t) is the absorbed heat, and Dthe Laplace operator. The full mathe-matical treatment of IR light interactingwith an arbitrary shape is complex. Inanother publication,51 this subject istreated in more detail. In this review,we provide a simplified approximationthat gives the same basic results. If weassume that the intensity of the laser isuniform over the absorbing region of thesample near the atomic force microscopetip and the sample thickness (z) is muchsmaller than the wavelength, then thepower absorbed Pabs can be derivedfrom Eq. A2 as:

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focal point review

Pabs ¼ZS

ðIinc-ItÞdS ¼ 4pIincrjðrÞV

ðA6Þ

where V is the volume of the absorbingobject.

For the sake of simplicity, we con-sider only the case where the pulseduration (tp) is shorter than the thermalrelaxation time of the object. In thiscase, the heat influx from the IRabsorption dominates the heat, leavingthe absorber. Moreover, we assume thatthe heat is absorbed homogeneouslyinside the object (no temperature gradi-ent). Thus, the increase in temperatureduring the illumination can be derivedfrom Eq. A5 and becomes:

TðtÞ ¼ Pabs

VqCt ¼ 4pIinc

qCrjðrÞt ðA7Þ

where C is the sample heat capacity, q isthe density, and V is the volume. FromEq. A7, we can define Tmax, themaximum temperature increase of thesample, as:

Tmax ¼PabstpVqC

ðA8Þ

When the laser pulse ends, the source ofheat disappears and the sample cools.Analytical solutions of the Fourier Eq.A5 are generally possible only forsimple geometries, such as a sphere orthin layer. The complete solution for anisolated sphere was treated by Dazzi etal.51 Even if the temperature behaviorcannot be expressed analytically in allcases, it is possible to use finite-element

software to find ‘‘empirically’’ the phys-ical law. Comparing solutions for threedifferent cases—isolated sphere, depos-ited cube on a surface, and depositedhemisphere on a surface (Fig. A1)—wecan conclude that the temperature decayat the end of the pulse follows the samelaw:

TðtÞ ¼ Tmaxexptp-t

srelax

� �ðA9Þ

where srelax is the key factor necessary todescribe the heat diffusion of thesample. The relaxation time (srelax)depends strongly on the environmentof the sample and on its size:

srelax ¼qC

keff

ap ðA10Þ

where a is the size of the sample (radiusor characteristic length): keff = 3kext andp = 2 for the case of an isolated sphere,with kext being the heat conductivity ofthe surrounding media; keff = a1kext þb1ksurf and p = 1.98 for the case ofdeposited cube on a surface, with ksurf

being the heat conductivity of thesurface and kext the heat conductivityof the surrounding media; and keff =a2kext þ b2ksurf and p = 1.989 for thecase of deposited hemisphere on asurface, with ksurf the heat conductivityof the surface and kext the heat conduc-tivity of the surrounding media.

To summarize this section, we canconclude that the behavior of tempera-ture (Fig. A2) when the laser pulse isshorter than the sample time of relaxa-tion because of photothermal absorption

can be expressed as:

TðtÞ ¼ Tmax

t

tpfor 0 � t � tp

TðtÞ ¼ Tmaxexpt-tpsrelax

0@

1A for t � tp

ðA11Þ

With this theoretical approach, it is easyto understand why the estimation of theincrease of temperature (or Tmax) is alsoa way to measure the absorbance of asample. All physical phenomena arelinear, allowing us to keep the propor-tionality. The maximum increase intemperature is proportional to the powerabsorbed by the sample, which isproportional to the absorbance.

Sample Thermal Expansion. Whenthe temperature increases in the body ofa material, this leads to the increase inthe internal stress, resulting in thermalexpansion. The temperature field insidethe sample is equivalent to a force field,resulting in deformations that depend onthe thermomechanical properties of thesample. An expression that links dis-placement as a function of the temper-ature is:52

ð1-2mÞr2uþrðr3 uÞ¼ 2ð1þ mÞaTrT ðA12Þ

where m is the Poisson coefficient, u isthe displacement vector, T is tempera-ture, and aT the thermal expansioncoefficient. As for the Fourier Law Eq.A5, the analytical solutions for such anequation are only possible for simplecases with high order of symmetry. Withthe same idea as the previous section,we studied three different cases (sphere,cube, and hemisphere) by finite elementanalysis and found that the law of

FIG. A1. Schemes of the three different cases of heating: isolated sphere, deposited cubeon an infinite surface, and deposited hemi-sphere on an infinite surface.

FIG. A2. Evolution of the sample temper-ature (red) illuminated by a pulsed laser(blue).


expansion can be written as:

uðtÞa¼ BaTTðtÞ ðA13Þ

where B is a constant depending on thegeometry case (sphere, cube, and hemi-sphere). The interesting point of Eq.A13 is that it shows the displacementfield (u) directly follows the time-dependent temperature (in the case of anon-viscoelastic material).

Excitation of Cantilever Resonanc-es from the Thermal Expansion. TheAFM–IR technique measures the ther-mal expansion resulting from IR absorp-tion by using the tip of an atomic forcemicroscope probe. The rapid thermalexpansion creates a force impulse on thetip that results in oscillation of thecantilever at its contact resonance fre-quencies. To estimate the reaction of thecantilever when the expansion occursunder the tip, we need to go back to theEuler–Bernoulli beam equation:

EI]4z

]x4þ qS

]2z

]t2þ c

]z

]t¼ Wðx; tÞ ðA14Þ

where E is the cantilever Youngmodulus, I the area moment of inertia,q the density, S the cross section, c thedamping, and W the external mechan-ical source of motion. The cross sectionis S = we and the area moment ofinertia I = we3 in the case of arectangular beam, where w and e arethe width and thickness, respectively.The x coordinate describes the longitu-dinal direction, and z represents thedeflection of the cantilever (Fig. A3).The tip contact on the sample ismodeled by two spring constants, kx

(lateral) and kz (normal). The cantileverlength is L with the clamped extremityat x = 0 and the tip positioned at x = L- dx (Fig. A4).

The general harmonic solution of theEq. (A14) is:

zðx; tÞ ¼ gðxÞhðtÞ ðA15Þwhere

gðxÞ ¼ A½cosðbxÞ þ coshðbxÞ�þ B½cosðbxÞ-coshðbxÞ�þ C½sinðbxÞ þ sinhðbxÞ�þ D½sinðbxÞ-sinhðbxÞ�

and h(t) = exp (ixt), with b being thewave vector and x the complex angularfrequency.

The boundaries conditions of thecantilever imposed by the clamped endand the tip contact can be cast in theform:

x ¼ 0 x ¼ L

gðxÞ ¼ 0 EI]2gðxÞ

]x2¼ M

]gðxÞ]x¼ 0 EI

]3gðxÞ]x3

þ Fz ¼ 0

ðA16Þ

where M is the bending moment and Fz

the reaction force at the lever end. Theexpression for Fz is found if we considerthe deflection g(L) at the end of thelever. The reaction force of the surface isopposite to the displacement at the endof the lever, leading to Fz = kzg(L),where kz is the vertical spring constantassociated with the linear approximationfor a small vibrational amplitude. Thebending moment M ¼ -kxH2 ]g

]x

� �x¼L

canalso be found in relationship to themoment induced by the lateral displace-ment of the tip by knowing the lateralspring constant kx and the tip height H(Fig. A4). Substituting the expressionfor Fz and M into Eq. A16 and using themodal expression of g(x), we obtain theeigenvalue equation of the vibrationalmodes:51

-1þ cosxcoshx-Vx3

ðcosxsinhx þ sinxcoshxÞ-Uxðsinxcoshx-cosxsinhXÞ-UVx4ð1þ cosxcoshxÞ ¼ 0 ðA17Þ

where U ¼ kcL2

3kxH2 ; V ¼ kc

3kz; X ¼ bL.

FIG. A3. Atomic force microscope canti-lever scheme. The lever is embedded at x =0, and the length is L. The tip is positionedat x = L - dx. The contact stiffness isrepresented by two springs, one for thevertical displacement and one for thelateral.

FIG. A4. Scheme of the atomic force microscope tip in contact with the surface. The tiltangle between the cantilever and the surface is a.

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focal point review

This eigenvalue equation is the mostgeneral equation for vibration of thecantilever. If the tip is free (kx = 0 andkz = 0), we find the common equationof modes for a free cantilever 1þ cos xcosh x = 0.53 In the AFM–IR tech-nique, the cantilever tip is kept incontact with the sample by the initialload force. The usual values of thecantilever spring constant kc employedin contact mode are very small (from0.03 to 0.2 N/m) compared with thespring constant kz of the tip-samplecontact (around 105 N/m), so that theparameter V tends to 0. Moreover, wechecked that if we supposed no inden-tation (V = 0), the calculated values offrequencies by the finite element meth-od were in good agreement with thosemeasured experimentally.30 We denotethis specific configuration ‘‘contactresonance’’. This approach is similarto that used by Yuya et al.54 for contactresonance of visco-elasticity, but in ourcase, the tip could move laterally andwas not allowed to produce indentationinto the sample.

As a result, the general eigenvalueequation for the AFM–IR configurationis given by:

-1þ cosxcoshx

-Uxðsinxcoshx-cosxsinhxÞ ¼ 0 ðA18Þ

The spatial distribution of mode n in thecase of contact resonance is describedby:

gnðxÞ ¼ ½cosðbnxÞ-coshðbnxÞ�

-cosðbnLÞ-coshðbnLÞsinðbnLÞ-sinhðbnLÞ

� �½sinðbnxÞ-sinhðbnxÞ� ðA19Þ

where bn is the wavevector of the modessolution of the Eigen Eq. A18. One cannotice that the value of the modedepends on the value of the lateralstiffness. This property is interestingfrom a mechanical point of view,because the frequency of the mode willgive us the stiffness of the sample.51

This sort of analysis is equivalent to thephase imaging of the atomic forcemicroscope tapping mode.55 Combiningchemical and mechanical analysis seemsa potentially powerful approach forenhancing the ability of the technique

to characterize small morphologicalstructures.

In our particular case, the cantileveris excited by a source of motion that isthe thermal expansion. The correspond-ing equation of motion can be writtenas:

EI]4z

]x4þ qS

]2z

]t2þ c

]z

]t¼ Wðx; tÞ ðA20Þ

where W(x,t) is the mechanical source ofmotion, and where the general solutioncan be expanded as a sum over eigen-modes: zðx; tÞ ¼

Pn PngnðxÞhðtÞ, where

Pn is the amplitude coefficient of themode n.

The source term W(x,t) describes thevariation of the force induced on the tipby the expansion of the object. Weassume that the tip is rigid and transmitsthis change of force to the cantilever.The tip contact can be characterized bythe spring constant kz, which dependson the impedance of the Young’smodulus of the tip and the sample,and the radius of the tip, neglecting thesample curvature compared with thetip.56 The force received by the tip isgiven by:

FðtÞ ¼ kzuðtÞ ¼ kzaBaTTðtÞ ðA21Þ

The beam modes have a vanishingamplitude at x = L (Eq. A19). In thismodel, under the expansion of theobject, the tip is not able to induce adirect displacement but creates abending of the lever at x = L.Moreover, the angle between the leverand the surface is usually not null (Fig.A4). In order to account for thisbehavior in the source term, we splitthe force into two (normal and lateral)components that are applied at a pointx = L - dx, with dx ,, L. Thenormal component is Fnorm(t) = F(t)cos (a), and the lateral one isFlatðtÞ ¼ FðtÞsinðaÞ H

dx. Therefore, thesource term is given by:

Wðx; tÞ ¼ dðx-Lþ dxÞFðtÞ¼ Kdðx-Lþ dxÞTðtÞ ðA22Þ

where K ¼ ½cosðaÞ þ Hdx sinðaÞ�BakzaT.

Substituting the expression for thesource term (Eq. A22) into equation ofmotion (Eq. A20) by using Fourier

transformation and modal orthogonalityproperties, we finally find:54

zðx; tÞ ¼X

n

J

xn

]gnðxÞ]x

��x¼L

gnðxÞ

sinðxntÞe-C2t

h i�TðtÞ ðA23Þ

where xn ¼ffiffiffiffiEIqS

qb2

n, C ¼ cqS, J ¼ -½cos

ðaÞdx þ sinðaÞH�kzaBqSL at and * denotes

the convolution product.The signal obtained by the four-

quadrant detector, Q(t), is not thecomplete deformation of the cantileverbut only its extremity deflection. It canbe expressed as the integrated cantileverslope along the diameter D of the laserdiode spot on the cantilever:57

QðtÞ ¼X

n

DJ

xn

]gnðxÞ]x

��x¼L

� �2

sinðxntÞe-C2t

h i�TðtÞ ðA24Þ

Most of the time, the duration tp of thelaser pulse is short (1 to 20 ns)considering the time response of thecantilever (15 to 40 ls). Applyingclassical cantilever parameters used tomake contact and polymer stiffnessimagery to model the sample, thetheoretical oscillation of the lever isshown in Fig. A5. We clearly see severaloscillations of different periodicity thatdecrease until 600 ls. This suggests thatthis analytical approach is sufficient to

FIG. A5. Temporal response Q(t) of thecantilever excited by a temperature in-crease generated by pulse laser of 1 ns.


describe the physical phenomenon in-volved in the technique.

The analysis of the AFM–IR signalis easier to perform in the Fourierdomain, revealing the different excita-tion modes and their amplitudes (Fig.A6). Usually, the analyzed signal is theFourier transform amplitude, i.e., themodulus of the Fourier transform ofQ(t):

~QðxÞ ¼ FourierTransf½QðtÞ�¼X

n

~QnðxÞ

¼X

n

DjJj ]gnðxÞ]x

� �2��x¼L

j~TsphðxÞjffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðx2

n-x2Þ2 þ C2x2

q ðA25Þ

The Fourier analysis shows that theresponse of the cantilever is the productof its mode response multiplied by theenergy induced by the photothermaleffect. In fact, following the expressionin Eq. A25, the behavior of each of themodes is the same as a function oftemperature. It is typically most conve-nient to measure the amplitude changein the absorption signal of the funda-

mental mode, because it possesses mostof the energy. The expression of themaximum amplitude of the mode n (atits resonance) is:

~Snðxn;rÞ ¼ HmHAFMHoptHthrjðrÞðA26Þ

where

Hm ¼ kzaTaB;

HAFM¼1

CxnðcosðaÞdx

þ sinðaÞHÞ D

qSL

]gnðxÞ]x

��x¼L

!2

;

Hopt ¼ 4pIinc;

Hth ¼1

qCtp

tp2þ srelax

�

Even if Eq. A26 seems complex, mostof the parameters are constant and donot change during an experiment. Thefinal expression of the amplitude of themode demonstrates the direct propor-tionality between the absorption of theobject (j) and the signal recorded by theatomic force microscope tip, Sn. As

mentioned above, the manner in which

an IR spectrum of the sample is obtained

is to record the variation of the detector

signal S0 (fundamental mode) as a

function of the wavenumber r. Consid-

ering the size of the tip apex in contact

with the sample (a few nanometers), we

clearly see why there is such interest in a

method to make ultra-local spectroscopy

measurements.

FIG. A6. Fourier transformation repre-sentation of the temporal signal Q(t). Bythis approach, the cantilever modes andtheir amplitudes are directly obtained.

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