Exploring the High-Temperature AFMand Its Use for Studies of Polymers

ByD. Ivanov,R. Daniels andS. Magonov

Introduction

Atomic force microscopy (AFM)is a well-established surfacecharacterization techniqueinitially introduced for high-resolution surface profiling. Fastdevelopment of AFM instrumen-tation has significantly extendedits capabilities, which now alsoinclude measurements of localmechanical, adhesive, magnetic,electric and thermal properties.The spectrum of materials thatcan be examined by AFM ispractically unlimited. Of specialinterest are studies of soft materi-als, such as polymers and biologi-cal samples, whose mechanicalstiffness is comparable to or lessthan the stiffness of commercialAFM probes. This fact allowsextraction of structural data fromthe analysis of these materials atdifferent tip-force levels. Forexample, low-force imaging isoptimal for the correct determina-tion of surface profiles of suchsamples, whereas imaging atelevated forces can be useful forsurface compositional analysis andfor recognition of individualcomponents in heterogeneouspolymer materials or biologicalsystems [1].

Most AFM studies to date havebeen conducted at ambienttemperature. This presents asubstantial limitation wheninformation about the thermalbehavior of the sample surface isdesirable. For example, perfor-mance of plastics is stronglytemperature dependent due totheir multiple phase transitions,such as melting, crystallization,recrystallization, as well as glassand sub-glass transitions. Experi-ments illustrating in situ AFMmonitoring of polymer crystalliza-

tion show the unique capability ofthis technique for measuring thegrowth of individual crystallinelamellae [2]. This informationcould not have been obtained withany other microscopic technique.The polymers chosen for theabove cited studies undergocrystallization at room tempera-ture (RT); yet the majority ofpolymers undergo phase transi-tions above RT. To study thesepolymers, early experiments wereconducted on samples heatedexternally for different time

Figure 1. (a) MultiMode microscope head with the thermal accessoryinstalled; (b) temperature controller; (c) main components of the thermalaccessory assembled on the piezo-scanner.

(a)

(b)

(c)

Probeholder

Sampleheater Rubber

seal

TheWorldLeader In3D SurfaceMetrology

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periods and then placed on theAFM and examined at RT [3].This approach is laborious since itrequires repeated high-precisionlocation of the same spot on thesample surface. In addition, thisprocedure is not always acceptablebecause of the changes that canoccur in the polymer structure oncooling to RT. Therefore, in situAFM studies at elevated tempera-tures are invaluable for analysis ofpolymers. The work described hereillustrates how this can be accom-plished with the MultiModeTM

AFM [4] equipped with therecently introduced High Tem-perature Heater Accessory. Anumber of important issuesrelevant to AFM studies at elevatedtemperatures are addressed below.Also several examples of AFMimaging of polymer materials attemperatures up to 250°C areprovided.

Historical Background

The importance of AFM measure-ments at elevated temperatures hasbeen recognized for some time,and several heating stages havebeen described in the literature [5-8]. By placing a resistive heater (ora Peltier element) guided by atemperature controller on top ofthe scanner, AFM measurementswere performed at temperatures upto 100°C. These first stages weredesigned for contact mode AFM[5-7], and several examples ofimaging under these conditionshave been reported [7]. However,contact mode AFM is oftenproblematic for polymer samplesbecause of the strong tip-sampleinteraction, especially the lateralforces which can cause damage tothe sample surface. This problembecomes even more serious at high

temperatures. Therefore, the useof TappingModeTM, in which thetip-sample contact occurs inter-mittently without strong lateralforce interaction, is necessary forhigh-temperature AFM studies ofpolymers.

The first heating accessory for theMultiMode AFM was designed forTappingMode operation attemperatures up to 100°C [8]. Indescribing this accessory, theauthors discussed the need forthermal isolation of the piezo-scanner from the heated sample.To reduce the heat transfer fromthe sample, a thermal insulatingblock of balsa wood was applied.This eliminates the risk of thepiezo depoling and minimizesdistortions of the scanner motioncaused by the heating of thescanner. The temperature calibra-tion was performed using athermocouple placed on a piece ofSi wafer. The thermocouplereading was in good agreementwith the surface temperature ofthe Si piece measured with Ramanspectroscopy. Yet the authorspointed out that this geometry isnot identical to that for trueimaging conditions when ametallic probe holder is located inthe immediate vicinity of thesample surface. It was found thatheating the sample to 100°C ledto heating of the probe holder to50°C. They concluded that thethermal balance in the location ofthe probe can be perturbed by thepresence of the holder. Heating ofthe holder was one of the possiblereasons for the drop of theamplitude of the probe, which wasdriven by a piezo-ceramic stackplaced inside the holder. Theauthors also noticed a linearreduction of the resonant fre-

Figure 2. Temperature dependence of theresonant frequency of a Si cantilever.Symbols: circles are the data obtained withthe MultiMode AFM; squares are the datarecalculated from the temperaturedependence of the elastic modulus of Si (100)[14]. Solid line presents a linear fit to both setsof data.

Figure 3. Relationship between the voltageapplied to the probe heater and the probetemperature. The probe was located within5µm of the sample surface heated to the sametemperature.

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quency of the Si etched probewith temperature. This requiredre-tuning of the probe for imagingat different temperatures. Never-theless, the first step towards AFMstudies of polymers at elevatedtemperatures was made andmelting/crystallization experi-ments were performed on anumber of systems [8-9].

Heater DesignConsiderations

In addition to the issues discussedabove, expansion of the tempera-ture range to higher temperaturesis obviously desirable. The designof the high-temperature heateraccessory for the MultiMode AFM(Figure 1) addresses these issuesand provides sample heating up to250°C. This heater uses thecommercial temperature controller“Eurotherm 2216” and a Ptresistive heater. Heating of thesample to the target temperature,defined by the operator, iscontrolled with feedback from athermocouple positioned underthe sample. In addition to thebasic components used in otherhot stages, this design includesseveral new features:

• a plug-in sample heater• a water-cooled scanner• a probe holder with an addi-

tional heater, and• an environmental enclosure.

The plug-in heater is made of aceramic and its top contains the Ptresistive heater, a thermocouple,and a small magnet to hold thesample. The heater is mechanicallyinserted into the top of thescanner. Electric wires, whichconnect the heating element andthermocouple with the controller,are incorporated inside the

cylindrical tube of the piezo-scanner. This plug-in geometry ofthe heater provides mechanicalstability of the heater’s contactwith the scanner and avoidsmechanical interference from anyexternal connections (e.g. wires)to the heater during scanning. Thetop part of the piezo-scannerincludes a small reservoir wherethe cooling water circulates. Thewater is driven from an outsidepool by a peristaltic pump andefficiently reduces the heattransfer to the scanner. With thisdesign, the temperature of thescanner never exceeds 45°C at asample temperature of 250°C,which ensures stable performance.

To enhance the stability of theprobe oscillations, the probeholder used in the high-tempera-ture accessory is made of fusedsilica and contains a heatingelement for the AFM probe.Amplitude of the oscillating probecan substantially change withtemperature because heating ofthe probe holder influencesmechanical coupling between theprobe and the holder. However,for most applications this is not aconcern because the amplitudecan be brought to a desiredmagnitude by varying the ampli-tude of the driving signal appliedto the piezo-stack. The holdertogether with a rubbery siliconeseal forms a gas-tight enclosure forthe sample, which can be used tocreate controlled atmosphereconditions. For example, inert gaspurging can be necessary to avoidoxidative degradation of samplesat high temperatures. The func-tion of the probe heater and theenvironment control is describedin more detail below.

Figure 4. (a) Difference between thetemperature of the sample and the probe atdifferent sample temperatures; (b) relationshipbetween the voltage applied to the probeheater and the probe temperature.

(a)

(b)

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From the first AFM studies atelevated temperatures, it becameclear that Si etched probes withoutany coating are preferred for suchmeasurements. Coated probes canbend and/or twist at elevatedtemperatures. It has also beenfound that water condensationoccurs when operating inTappingMode at high tempera-tures. When the sample tempera-ture approaches 100°C and theprobe is slightly colder, watercondensation in the form of smalldroplets is typically observed onthe probe’s backside. In somecases, the volatile components ofthe heated sample can also causethe droplet formation. Heating ofthe probe was implemented toavoid this problem [10]. Byplacing a heater close to the probemount it became possible tochange the probe temperature byregulating the voltage on theheater. In this case, heating of theprobe and the probe holderassembly to the target temperaturealso induces heating of the samplefrom above, which can signifi-cantly improve the homogeneityof the temperature distributionthroughout the sample. This dualheating is of particular importancefor thicker samples and formaterials with low heat conductiv-ity.

In order to quantify and controlthe probe temperature and theconditions of imaging, accuratemeasurement of the probetemperature is required. Todetermine the temperature of theprobe itself, we use the resonantfrequency of the probe as ameasure of its temperature. Theangular resonant frequency of arectangular lever without aconcentrated load is given by [11].

where t and l denote the thicknessand length of the lever, E theelastic modulus and ρ the massdensity. The variation of ω

0 with

temperature can be accounted forby the thermal expansion of thelever and by the temperaturevariation of the elastic modulus.However, for the single crystallinesilicon material of the Tapping-Mode probes in the temperaturerange of our measurements, thelatter contribution dominates.Thus one obtains

where To denotes some reference

temperature (in our case To =

25°C). To correctly determine thethermal variation of the cantileverresonant frequency, we placed thehead of a MultiMode AFM intoan oven and recorded the resonantfrequency of the Si probe as afunction of temperature [12]. Theresults of these measurements aregiven in Figure 2. On the samegraph, we plot the values of theresonant frequency recalculatedfrom the recent literature data[13] on the temperature depen-dence of the elastic modulus of Si[14]. Notice that the resonantfrequency is changing almostlinearly with temperature between25°C and 250°C. In addition, thefrequency-versus-temperatureresults correlate well with theliterature data obtained with asimilar AFM probe [8]. Theaverage coefficient of 3.1x10 -5 ±5x10 -7␣ °C-1 describes the relativedecrease of the cantilever resonantfrequency with temperature. ForSi etched probes (225µm long and

Figure 5. Time dependencies of the probetemperature after stepwise changes of thevoltage applied to the probe heater. Red linecorresponds to the probe heating after thejump from 9.1 to 17.0V. Purple linecorresponds to the probe cooling after thevoltage was decreased from 14.8 to 9.1V.

ωο = (1),t El 2 ρ

ωο (Τ) E (T)ωο (Το ) Ε (Το )= (2),

5

30-40µm wide, with a stiffness~40␣ N/m) this variation results in~5.2 Hz/°C.

Next, we used the calculatedresonant frequency-versus-tempera-ture relationship to generate thethermal equilibrium conditions atthe sample location under the AFMprobe. To achieve this, the voltageapplied to the probe heater ischosen from the curve (Figure 3)such that the temperature of theprobe matches that of the sample.By contrast, if the probe heater isnot activated, the temperatures ofthe sample and the probe can differsubstantially (Figure 4a). Similarly,by applying the voltage to the probeheater while the sample heater isoff, one can locally change thetemperature of the surface under-neath the probe. The correspondingdependence between the probetemperature and the voltage (V) isshown in Figure 4b. It can be seenthat the temperature difference(∆T) scales as the square of thevoltage, which is logical since theheat flux released by the heater isproportional to V2 and the heatexchange between the probe and itssurroundings is proportional to ∆T.

This separate control of the sampleand probe temperatures opens theway to perform well-defined in situthermal treatments. With polymers,the thermal history (heating andcooling rates) is important indefining the final morphology. Themaximum heating rate provided bythe sample heater is up to 50°C/min, as measured with a thermo-couple underneath the sample. Inorder to evaluate the maximumattainable heating and cooling ratesof the probe, we applied a speciallydesigned electronic set-up fortracking the cantilever resonant

frequency and performing dataacquisition at 1 sample/s. Thecorresponding results given inFigure␣ 5 show that the heating andcooling rates of the probe can beextraordinarily high. The heatingrate of the probe when the tem-perature was brought from 100 to200-250°C reached 960°C/min;the corresponding cooling rateattained values as high as 600°C/min. These heating rates at thesurface are much higher than areobtainable with other methods.Obviously, the heating rate of thebulk sample with this accessory willbe much less than that of the probe,allowing studies of differentiallocalized heating and cooling at thesurface of the sample.

As mentioned above, environmen-tal control is a necessary require-ment for high-temperature AFMmeasurements of polymers.Helium atmosphere is recom-mended because of the highsensitivity of the oscillating probeto the air-to-He exchange. Higherresonant frequency and a largerquality factor characterize the probeoscillation in He (Figures 6 a-b) ascompared to air. It is worth notingthat the silicon rubber seal isrequired for better gas exchange(Figure 6b). Monitoring thecantilever resonant frequency afterthe purging starts allows estimationof the rate and the extent of the gasexchange in the sample environ-ment (Figure 7). The gas exchangeis complete in 20␣ seconds at apurging rate of 40 ml/min. Lowerpurging rates can increase theequilibration time.

In practice, high-temperature AFMimaging of polymer samples sharesmany similarities with imaging at

Figure 6. (a) Amplitude-versus-frequencycurves obtained in air (black line) and in He(purpl line); (b) amplitude-versus-frequencycurves after re-tuning in air (black curve), inthe sample environment partially filled with He(the rubber seal was not installed, greencurve) and in He environment (the rubber sealwas installed, purple curve). The red solidlines correspond to the fits of the data to theapproximate expression (Equation 3 inReference 12). The quality factors calculatedfrom the fits are 494, 632 and 910 for theblack, green and purple curves, respectively.

(a)

(b)

6

H(CH2)12OO(H2C)12H

H(CH2)12O

H(CH2)12O

H(CH2)12O

H(CH2)12O

H(CH2)12O O(H2C)12H

O

O

O

O

CH2O

CH2O

O

O

O

H2Cn

RT. Small sample size ensuresbetter conditions for fast heatingand equilibration of the sampletemperature. Polymer films andsmall polymer blocks (with a topsurface prepared with an ultrami-crotome), which are placed on ametal puck (6mm in diameter)have been routinely examinedwith the heater accessory. Duringsample heating the probe isdisengaged from the sample andthe driving frequency is re-tunedat each temperature. For imagingof polymers close to their meltingpoints it is generally preferable touse larger oscillating amplitudes ofthe probe in order to overcome theadhesive tip-sample interactions.

Practical Examples

To illustrate application of theheater accessory to polymers, wehave chosen several examplesshowing the most importantperformance features: sub-micronimaging in a broad temperaturerange and the ability to monitorstructural changes at the samesurface location. The first exampleis taken from AFM studies of self-organization of polymers withmini-dendritic side groups ongraphite. These macromoleculeswith side alkyl chains exhibitepitaxial order on graphite. Theimages of the samples prepared byspin-casting from very dilutesolutions on graphite revealindividual macromolecules inextended-chain conformation thatallow quantification of theirmolecular weight [15]. It isimportant to follow the process ofpolymer chain ordering ongraphite, which occurs after theirspin-casting [16]. The AFMimage, which was obtained on thesample immediately after it was

spin-cast, shows small aggregatesformed by a few macromolecules,which are hidden amidst patchesof non-ordered material (Figure8a). These patches disappearedafter heating of the sample to50°C, indicating that they aremost likely of low molecularweight (Figure 8b). With increas-ing temperature, the mobility ofthe chains increases and theirattachment to graphite loosens. Asa result, the AFM probe can easilydisplace them from the surface;thus the single macromolecules areno longer seen at temperaturesabove 75°C and only thick islandsare found [16]. At these tempera-tures, the displaced polymermaterial, most likely floats in aliquid overlayer, which is oftenpresent on surfaces at ambientconditions. When the sampletemperature was lowered to RT,the polymer chains reattached tothe substrate again. Two kinds ofdomains – thin and thick – areseen in the images recorded at RT(Figure 9a). Single layer domains,which exhibit well-orderedmacromolecular arrangement,surround the thicker domains(Figure 9b). In the layer lyingdirectly on the graphite, cylindri-cal-shaped macromolecules arealigned along the main axes of thesubstrate and, therefore, the chainsfold at regular angles of 60 and120 degrees. After the sample washeated to 150°C, only thickdomains were observed (Figure9c). One of the three thickdomains seen at RT has disap-peared and the other two havebecome larger. This observationindicates that some transfer ofmaterial has been assisted by theAFM probe at these high tempera-ture.

Figure 7. Time dependencies of the proberesonant frequency in the environmentalsample enclosure during purging of He at 40(1), 10 (2) and 4 ml/min (3) purging rates.

Figure 8. (a-b) Height images of samplesprepared by spin-casting of a dilute solution ofa polymer with mini-dendritic blocks (see thechemical structure below) on graphite.1µm scans.

(a) 1µm T = 30°C (b) 1µm T = 50 °C

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The second example (Figure 10)shows morphologic changesobserved at the same location in athin film of syndiotactic polypro-pylene (sPP) upon crystallizationat two different temperatures,125°C and 130°C. A featurelessarea is seen in the image in Figure10a, representing the surface ofsPP in the melt when the sampletemperature is around 155°C.After the sample temperature islowered to 125°C, polymercrystallization proceeds withformation of spherulite-likemorphology. The polymercrystallization is substantiallyslower at higher temperatures(T=130°C), yet the final crystal-line morphology with spherulite-like structures does not vary muchfor these temperatures. The flat-onlying lamellae, which grew fromcenters of the spherulites, resemblesingle crystal sPP platelets.Additional AFM results, whichreveal morphologic andnanostructural changes duringmelting and crystallization ofsingle sPP crystals, have beenpublished [17].

In in situ AFM studies of polymercrystallization, one should beaware that crystallization can beinduced by the tip-sampleinteraction during repeatedimaging of the same sample area.A simple check on these tip-induced effects consists of laterscanning of a larger area thatincludes the area scanned duringthe experiments. For example, theimage in Figure 10f shows an80µm scan of the sPP sample,which exhibits similar crystallinemorphology over the entire area,

(a) 3µm T = 30 °C (b) 250nm T = 30 °C (c) 3µm T = 150 °C

Figure 9. (a, c) Height images; samples prepared by spin-casting of dilute polymer solution with mini-dendritic blocks ongraphite. Images were taken at different temp-eratures.(b) Height image of the smaller area, shown in box in (a).

Figure 10 (a-f) Height images of syndiotactic polypropylene(sPP) film at different temperatures. (a) Image of the sPP melt.Images in (b) and (c) were obtained during crystallization at125 °C for periods indicated above the images. Images in (d) and(e) were obtained during crystallization at 130°C. Image in (f)shows the final morphology after crystallization at 130°C in thearea surrounding the location (box) shown in (d) and (e).

(a) 40µm T = 155 °C

Zoomout

(b) 40µmT = 124 °C 22 min.

(c) 40µmT = 124 °C 100 min.

(d) 40µmT = 130 °C 122 min.

(e) 40µmT = 130 °C 1,575 min.

(f) 80µmT = 130°C

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regardless of where previousscanning occurred during crystalli-zation. This result indicates thatthe probe has not caused morpho-logical modification of the surface.

Conversely, Figure 11 demon-strates the acceleration of polymercrystallization due to the probe,which was colder than the sample.After melting of a relatively thick(0.5mm) block of isotacticpolypropylene (iPP) at 150°C, thetemperature was decreased to140°C, and morphologic changesaccompanying polymer crystalliza-tion were monitored in the 10µmarea. Due to the high temperature,this process was relatively slow.The first indications of polymercrystallization appeared after onehour, and several flat-on and edge-on oriented lamellae were re-corded after two hours (Figures11a-b). Further progressive growthof lamellar aggregates, which wasmonitored at a neighboring 10µmlocation, is demonstrated inFigures 11c-d. Thermal flow ofthis sample (most likely due to itssubstantial thickness) was morepronounced compared to otherexamples. Yet the flat-on lamellaerelevant to both locations can beseen in the larger-scale image inFigure 11e. In Figure 11b-e thelamellae are marked with differ-ently colored stars. The large-scaleimage (Figure 11e) also revealsthat crystallization was muchfaster in the area where theimaging was performed. This areain the left top corner of the imagein Figure 11e is completelycovered by lamellae. During thisexperiment, the voltage applied tothe probe heater was 10V. Thisvalue is lower that that needed toachieve 140°C (see graph in

(e) 25µm

(a) 3µm b) 3µm

T = 230 °C

(c) 3µm

Figure 12. Phase images showing the growth of crystallinelamellae during the melt-crystallization of poly(ethyleneterephthalate) at 230°C; the images were taken at the samelocation. The arrows indicate the places where the crystalgrowth proceeds via the stack thickening mechanism.

(c) 10µm 169 min. (d) 10µm 274 min.

(a) 19µm 70 min. (b) 10µm 135 min.

Figure 11. (a-d) Phase images obtained during crystallizationof isotactic polypropylene at 140oC for different times. (e)Phase image showing a larger area of the sample includingthe location where the crystallization proceeded mostefficiently (top left corner). Colored stars indicate the sameplace in the respective images.

★

★★

★

★

▲

▲

▲

▲

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Figure 3). We conclude that thetip and, therefore, the surfacelocation under the probe, werecolder than the surroundingmaterial, and this accelerated thepolymer crystallization.

The last example demonstrates theability of AFM to monitorpolymer crystallization at tem-peratures well above 200°C. Threesnapshots of the real-time melt-crystallization of poly(ethyleneterephthalate), or PET, at 230°Care presented in Figure␣ 12. It isimportant to emphasize that wewere able to monitor high-temperature PET crystallizationby performing imaging at thesame location with sub-micronresolution. Notice the appearanceof individual crystalline lamellae(approximately 9nm in width),and their growth, as well as theirpronounced tendency to formstacks. The arrows in Figure 12indicate the same locations on thesample surface where the growthproceeds via stack thickening, i.e.via increasing the number oflamellae per stack. These stackseventually form a space-fillingcrystalline structure.

Despite the fact that PET, atypical aromatic polyester withsemi-rigid chains, has beenintensively studied for many years,direct microscopic observation ofits structure and evolution at thenanometer scale had not yet beenachieved [18]. Visualization ofPET’s sub-micron organization,which is now possible with AFMat elevated temperatures, offersnew insights into the lamellarstructure and crystallizationbehavior of this polymer [19].These insights can also help to

correctly interpret SAXS (smallangle X-ray scattering) data usingthe direct-space informationobtained by AFM. In particular,one can readily see from the AFMimages in Figure 12 that thecrystalline lamellae of PET arethinner than the interlamellaramorphous layers. Finally, the X-ray data can be quantitativelycompared with AFM data byperforming a reciprocal-spacetreatment of AFM images, asdescribed elsewhere [20].

Conclusions

The described HighTemperatureHeater Accessory for theMultiMode AFM meets the strongdemand for AFM measurementsat elevated temperatures. Theaccessory accommodates severalnew features: probe heater, water-cooled scanner and environmentalcontrol for ensuring stableimaging of samples at tempera-tures up to 250°C. The practicalexamples selected for this workdemonstrate the capabilities ofhigh-temperature AFM studieswith this accessory. Several otherapplications, which were accom-plished using different prototypesof the heating stage, were reportedearlier [20,21]. We believe that abroader use of this accessory forAFM applications to polymerswill bring invaluable informationfor academic and industrialresearchers.

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[2] T. J. McMaster, J. K. Hobbs, P.J. Barham, M. J. Miles, "AFMStudy of in situ Real TimePolymer Crystallization andSpherulite Structure," ProbeMicroscopy 1997, 1, 43;“Direct Observation of Growth ofLamellae and Spherulites of aSemicrystalline Polymer by AFM”Lin Li, Chi-Ming Chan, KingLun Yeung, Jian-Xiong Li, Kai-Mo Ng, Yuguo Lei, Macromol-ecules, 2001, in press.

[3] D.A. Ivanov, A.M. Jonas“Isothermal growth and reorgani-zation upon heating of a singlepoly(aryl-ether-ether-ketone)(PEEK) spherulite, as imaged byatomic force microscopy”,Macromolecules, 1998, 31, 4546-4550.

[4] With the MultiMode AFM,the sample is placed on the top ofthe scanner and imaging isperformed by rastering the sampleunderneath an immobile probe. Inother SPM microscopes, e.g.DimensionTM Series, the probe isattached to the scanner and it ismoved over the fixed samplesurface.

[5] I. Musevic, G. Slak, R. Blinc,“Temperature controlledmicrostage for an atomic forcemicroscope” Rev. Sci. Instrum.1996, 67, 2554

[6] T. R. Baekmark, T. Bjornholm,O. G. Mouritsen, “Design andconstruction of a heat stage forinvestigations of samples byatomic force microscopy aboveambient temperatures” Rev. Sci.Instrum. 1997, 68, 140.

[7] H. D. Sikes, D. K. Schwartz“Two-Dimensional Melting of anAnisotropic Crystal Observed atthe Molecular Level” Science1997, 278, 1604-1607.

[8] S. G. Prillman, A. M.Kavanagh, E. C. Scher, S. T.Robertson, K. S. Hwang, V. L.Colvin “An in-situ hot stage fortemperature-dependent tappingmode atomic force microscope”Rev. Sci. Instrum. 1998, 69,3245-3250.

[9] R. Pearce, G.J. Vancso, “Real-time imaging of melting andcrystallization in poly(ethyleneoxide) by atomic force micros-copy” Polymer 1998, 39, 1237-1242.

[10] R. Daniels, S. Magonov“Method and system for increas-ing the accuracy of a probe-basedinstrument measuring a heatedsample”, US Patent ApplicationNo 09/354,448, 15 July 1999.

[11] D. Sarid “Scanning forcemicroscopy with applications toelectric, magnetic, and atomicforces’’, Oxford University Press,1991.

[12] It should be noted howeverthat the value that we are measur-ing in ambient conditions with anAFM cantilever is not strictlyequal to dω

0/dT. Indeed, already

in a very simple model of theforced damped oscillator theresonant frequency (ω

r) and ω

0 are

slightly offset [Fowles, Grant R.“Analytical Mechanics”, SaundersGolden Sunburst Series, 1986]:

Acknowledgements

The authors are thankful to theircolleagues at Digital Instruments/Veeco Metrology Group: RussMead for his contribution inconverting the prototype of theheating accessory to the finalproduct, Karl Koski for his finemechanical work in assemblingsample heaters and other compo-nents of the accessory, and MonteHeaton for reviewing and editingthe manuscript. The authors aregrateful to Zhor Amalou(Université Libre de Bruxelles) forpreparation of a PET sample andalso to Naoki Ono (MitsubishiMaterials Corp. , Silicon ResearchCenter) for kindly providing thenumerical data on the temperaturedependence of the elastic modulusof Si. D.A.I. is thankful to DigitalInstruments/Veeco MetrologyGroup for the support of his stayin Santa Barbara, where thisresearch work was accomplished.

References

[1] For recent reviews, see S. N.Magonov “Atomic force micros-copy in analysis of polymers” in“Encyclopedia of AnalyticalChemistry”, R. A. Myers (Ed.),pp. 7432-7491, Wiley & Sons,Chichester, 2000; V. J. Morris, A.R. Kirby, A. P. Gunning “Atomicforce microscopy for biologists”,World Scientific Publishing,Singapore, 1999.

ωο = ωο2 – 2γ 2

11

where γ denotes the dissipationterm in the differential equationof the cantilever motion. Thus thepresence of damping somewhatslows down the oscillator. Thedissipation term γ can be relatedto the quality factor (Q) of theoscillator as

We have calculated the values ofQ by fitting the amplitude of thecantilever oscillation as a functionof frequency to the standardapproximate expression

It was found that Q does notchange significantly in all thetemperature range of the measure-ments. Thus we believe that thedifference between the relativevariations of dω

0/dT and dω

r/dT

can be neglected in our case.

[13] N. Ono, K. Kitamura, K.Nakajima, Y. Shimanuki “Mea-surement of Young’s modulus ofsilicon single crystal at hightemperature and its dependenceon boron concentration using theflexural vibration method” Jpn. J.Appl. Phys. 2000, 39, 368-371.

[14] The results presented inFigure 2 correspond to thetemperature dependence of theelastic modulus of the B-doped Si(resistivity 10␣ Ohm.cm) in the(100) direction, which is a typicalorientation of the AFM probe.The impact of doping on thetemperature behavior of the elasticmodulus was found to be verysmall [13] and can be safelyignored.

[15] S. A. Prokhorova, S. S.Sheiko, M. Moeller, C.-H. Ahn,V. Percec “Molecular imaging ofmonodendron jacketed linearpolymers by scanning forcemicroscopy” Macromol. RapidCommun. 1998, 19, 359-366.

[16] S. N. Magonov, “Visualiza-tion of polymers at surfaces andinterfaces with atomic forcemicroscopy” in Handbook ofSurfaces and Interfaces (H.S.Nalwa Ed.), Academic Press, 2001submitted.

[17] W. Zhou, S. Z. D. Cheng, S.Putthanarat, R. K. Eby, D. H.Reneker, B. Lotz, S. Magonov, E.T. Hsieh, R. G. Geerts, S. J.Palackal, G. R. Hawley, M. B.Welch “Crystallization, meltingand morphology of syndiotacticpolypropylene fractions. 4. In situlamellar single crystal growth andmelting in different sectors”Macromolecules 2000, 33, 6861.

[18] F. Dinelli, H.E. Assender, K.Kirov, O.V. Kolosov “Surfacemorphology and crystallinity ofbiaxially stretched PET films onthe nanoscale” Polymer 2000, 41,4285-4289; D. A. Ivanov, T. Pop,D. Yoon, A. Jonas “Direct spacedetection of order-disorderinterphases at crystalline-amor-phous boundaries in a semicrystal-line polymer” (submitted toPolymer).

[19] D. A. Ivanov, Z. Amalou,S.N. Magonov “Real-timeevolution of the lamellar organiza-tion of poly(ethylene terephtha-late) during crystallization fromthe melt: high-temperature AFMstudy” Macromolecules 2001,submitted for publication.

[20] C. Basire, D. A. Ivanov“Evolution of the lamellarstructure during crystallization ofa semicrystalline-amorphouspolymer blend: time-resolved hot-stage SPM study” Physical ReviewLetters, 2000, 85, 5587-5590.

[21] Yu. K. Godovsky, S. N.Magonov “AFM Visualization ofMorphology and Nanostructure ofUltrathin Layer of Polyethyleneduring Melting and Crystalliza-tion” Langmuir 2000, 16, 3549-3552; S. A. Ponomarenko, N. I.Boiko, V. P. Shibaev, S. N.Magonov, “AFM Study of Struc-tural Organization of CarbosilaneLiquid Crystalline Dendrimer”Langmuir 2000, 16, 5487-93.

ωο2 – 2γ 2

2γQ =

A(ω) = (3). Α

max ωο

4Q 2 (ωο – ω) 2 + ωο

2

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