Adsorption behavior of partially collapsed polyacrylate coils on mica surfaces: A reciprocal space approach

Adsorption Behavior of Partially Collapsed Polyacrylate Coils on MicaSurfaces: A Reciprocal Space Approach

PRASHANT SINHA,1* SEBASTIAN LAGES,2y ANTON KIRIY,1 KLAUS HUBER,2 MANFRED STAMM1

1Department of Nanostructured Materials, Leibniz-Institut fur Polymerforschung Dresden e.V., 01069 Dresden, Germany

2Chemistry Department, Universitat Paderborn, D-33098 Paderborn, Germany

Received 6 June 2009; revised 29 September 2009; accepted 11 October 2009

DOI: 10.1002/polb.21959

Published online in Wiley InterScience (www.interscience.wiley.com).

ABSTRACT: In this article, we investigate tapping mode atomic

force microscopy images of intermediate states along the coil

to globule transition of sodium polyacrylate coils containing

Ca2þ as specifically binding ions. The structural correlations

within single adsorbed molecules are established using power

spectral density (PSD) curves. The PSD curves of several single

molecules are averaged to give the so called 2D form factor so

as to obtain information of higher statistical merit. A proper

interpretation of the 2D form factor and comparison with form

factor analysis of the very same sample solution available

through small angle neutron scattering provides an alternative

quantification of changes in conformation which a single poly-

acrylate molecule undergoes as it moves from 3D solution to

2D surface and is inevitably distorted in shape because of sam-

ple history. VC 2010 Wiley Periodicals, Inc. J Polym Sci Part B:

Polym Phys 48: 1553–1561, 2010

KEYWORDS: atomic force microscopy (AFM); conformational

analysis; polyelectrolytes; power spectral density (PSD); small

angle neutron scattering (SANS)

INTRODUCTION Single molecule studies using atomic forcemicroscopy (AFM) are currently opening a new window ofopportunities into biology and material science. However, akey disadvantage of this technique is the deformationinduced in the adsorbed molecules because of interactionswith the solid substrate, the extent of deformation dependingupon the adsorption conditions.1–3 The adsorption process isbetter understood in terms of sample history. The latter is arather all encompassing term and for the sake of conven-ience, can be divided into two parts—preadsorption historyand postadsorption history.

In the preadsorption phase, conditions are set for the mole-cules to adsorb on the surface. There are two driving forces foradsorption: solvent quality4–6 and substrate-sample interac-tions. The latter become more important when solvent qualityis good, i.e., when solvent does not promote adsorption. Thesubstrate-sample interactions include electrostatic and van derWaals forces acting at the substrate-sample interface. In princi-ple, two extreme cases7 can be described. (1) The moleculefreely equilibrates on the surface before it is trapped in a par-ticular conformation. (2) The molecule is trapped before it getsa chance to laterally equilibrate on the surface. It is this secondscenario which any study directed toward a comparison of so-lution and surface conformations of molecules tries to achieve.

The postadsorption phase refers to the solvent removal/evaporation once the polyelectrolyte has been adsorbed on

the surface. In what is known as dry AFM imaging, this isusually done with a N2 or Ar flux. The flux quickly removesthe solvent but also generates two powerful forces. One ofthem is shear. However, if adsorption forces are relativelyhigh, shear cannot change the conformation of molecules.The magnitude of shear can be counterchecked easily withthe help of a 2D-Fast Fourier Transform (2D-FFT) analysis ofthe scanned surfaces. The lack of a detectable specific orien-tation in the 2D-FFT would indicate either an absence ofshear field or its trace presence which can be ignored. Sol-vent evaporation, apart from shear, also generates a secondforce. It is a kind of a capillary force which tends to shrinkthe molecules. This capillary force can have a strong influ-ence on the surface conformation of the adsorbed molecules,especially when interactions with the surface are weak.

It has always been tempting to compare solution and surfaceconformations of adsorbed molecules in a bid to quantizethe effects of sample history. In course of time, Stamm andcoworkers8,9 have taken up what may be classified as twolimiting cases.

The first limiting case provides a scenario when adsorptionof the molecules on surfaces is rather strong. A case in pointis one of the previous studies by Stamm and coworkers8

regarding the formation of intermediate states along the coilto globule transition of poly(methacryloyloxyethyl dimethyl-benzylammonium chloride) (PMB) in pH 3 aqueous solution

P. Sinha, S. Lages, A. Kiriy, and K. Huber dedicate this article to Prof. Dr. Manfred Stamm on the occasion of his 60th birthday.

*Present address: University of Geneva, Sciences II-CHIAM, 30 Quai Ernest-Ansermet, 1211 Geneva 4, Switzerland.†Present address: University of Fribourg, Adolphe Merkle Institute, Route de l’ancienne Papeterie CP 209, 1723 Marly 1, Switzerland.

Correspondence to: P. Sinha (E-mail: [email protected])

Journal of Polymer Science: Part B: Polymer Physics, Vol. 48, 1553–1561 (2010) VC 2010 Wiley Periodicals, Inc.

PARTIALLY COLLAPSED POLYACRYLATE COILS, SINHA ET AL. 1553

induced by the addition of Na3PO4 salt. The intermediatestates were visualized by adsorption on mica surfaces. PMBis a strong cationic polyelectrolyte with a sufficiently bulkybackbone. Thus, it adsorbs strongly on mica surfaces. Allexperiments could be conducted at pH 3 (near isoelectricpoint of mica) so that charge density of mica surfaces didnot play any role. It could be speculated by the authors thatthe polyelectrolyte undergoes a collapse in the direction per-pendicular to the plane of adsorption but does not getnoticeably altered parallel to the plane of adsorption, evenafter flux drying. Later, Minko and coworkers2 used this verysystem to provide the first qualitative glance into how sam-ple history may affect surface conformations. The latterauthors found that AFM scans produced in a fluid cell andthose produced in air (flux dried samples) were substantiallydifferent. The response of the polyelectrolyte coil toward for-mation of an intermediate state was a bit delayed in fluidcell environment. At 8-mM Na3PO4 concentration, for exam-ple, AFM scans in a fluid cell showed little to no signs of for-mation of pearl necklace structures, with most of the mole-cules being random coils having a globular structure,whereas those produced in air (flux dried samples) showeda highly compact pearl necklace morphology. Similarly, at 24-mM Na3PO4 concentration, AFM scans in a fluid cell showeda pearl necklace morphology, whereas those produced in air(flux dried samples) showed a nonresolvable compact glob-ule like morphology. The authors speculated that van derWaals interactions associated with the substrate-sampleinterface stabilize the polyelectrolyte coil in the fluid cellenvironment.

The second limiting case provides a scenario when adsorp-tion of the molecules on surfaces is weak. To cite an exam-ple, Borkovec and coworkers10 observed necklace like inter-mediates with poly(vinylamine). In the latter experiment, adirect discharge of the respective poly(vinylammonium) saltwas achieved by decreasing the pH. A low molecular weightof poly(vinylamine), a weak cationic polyelectrolyte, was cho-sen for imaging on mica surfaces, in a marked departurefrom preceding works.8 Although the authors do mentionthe role of sample history, they stop short of comparisonswith solution conformations of the same coils. Later, Huberand coworkers9 studied the formation of intermediate statesalong the coil to globule transition of sodium polyacrylate(NaPA) in pH 9 aqueous solution containing Ca2þ as specifi-cally binding ions. The transition itself was induced by anincrease of temperature. The structure of intermediate stateswas studied in solution through light scattering and SANS,and on surfaces through AFM. Qualitatively, the picture couldbe described in this way. At the equilibration temperature of15 �C, NaPA-Ca2þ coils showed a randomly coiled shape insolution. The corresponding shape on surface however indi-cated the first signs of formation of pearls along the molecu-lar contour. At the equilibration temperature of 30 �C, NaPA-Ca2þ coils adopted a necklace like shape in solution with alarge majority of dumbbells while the corresponding shapeon surface was a mixture of compact elliptical globules,11

sausage like structures and dumbbells. This qualitative pic-

ture is illustrated in Figure 1. Since NaPA is an example of aweak anionic polyelectrolyte with a non bulky backbone,adsorption on mica surfaces was weak. It is exactly thisweak adsorption case where sample history effects dominateand molecules are expected to undergo a relatively large dis-tortion upon adsorption. The authors therefore comparedthe radii of gyration (Rg) of adsorbed coils on surface withthose in solution at the equilibration temperature of 30 �C.Capillary forces created during drying procedures reduce thecomponent of radius of gyration parallel to the surfaces.Apart, the component of radius of gyration perpendicular tothe surface may also undergo a collapse, both due to solventevaporation and interactions with the substrate.12–15

While Rg values, as evaluated in ref. 9 for adsorbed coils atthe equilibration temperature of 30 �C, are indicative of theaverage 3D shape of a molecule adsorbed on the surface,they fail to capture the exact structural correlations withinit. Thus, a comparison of Rg (AFM) and Rg (light scattering)alone cannot reveal all the effects of sample history. Subtlechanges may take place at the local level as the polyacrylatecoil adsorbs on the surface, which are not reflected in theglobal dimensions. In this article, we analyze the same sys-tem as in ref. 9 but instead using power spectral density(PSD) curves at the single molecular level to provide a newcharacterization tool, which is sensitive to subtle changes inlateral distribution of molecular roughness. When properly

FIGURE 1 Schematic illustration to show the effects of sample

history on the conformations adopted by adsorbed sodium

polyacrylate coils containing Ca2þ as specifically binding ions,

at two different equilibration temperatures.

JOURNAL OF POLYMER SCIENCE: PART B: POLYMER PHYSICS DOI 10.1002/POLB

1554 INTERSCIENCE.WILEY.COM/JOURNAL/JPOLB

interpreted, it provides information which can hardly beobtained through Rg evaluation or through conventional pro-file measurements. To give statistical relevance to our work,we have evaluated the so called 2D form factor, an averageof PSD curves generated for many isolated single molecules.The information retrieved through the 2D form factor con-veys structural correlations within a single molecule after itadsorbs on the surface, just like SANS does for the samplesolution. A comparison of structural information of a singlemolecule revealed through these two methods gives us aunique quantitative insight into the extent up to which a sin-gle polyacrylate coil changes its conformation as it movesfrom a 3D solution to a 2D surface and is inevitably affectedby sample history.

EXPERIMENTAL

SamplesThe same sample solutions were used as in ref. 9, namely,SASE (0.2346 g/L NaPA solution in D2O containing 1.00 mMCa2þ and 8.00 mM Naþ) and SASH (0.1300 g/L NaPA solu-tion in D2O containing 0.65 mM Ca2þ and 8.70 mM Naþ).The NaPA had a weight averaged molar mass of 783 KDa indilute aqueous solution in the presence of 10.00 mM NaCl asan inert electrolyte. A pH of 9 was maintained for both thesample solutions. The coil to globule transition was inducedin both the sample solutions by increasing the equilibrationtemperature from 15 �C to 30 �C. The sample solutions wereadsorbed on freshly cleaved mica surfaces pretreated with0.01 g/L of an aqueous solution of LaCl3 (treatment time 1min). The pretreated surfaces were also equilibrated at thesame respective temperatures as the sample solutions priorto adsorption.

Atomic Force MicroscopyAFM setup, as described in ref. 9, is reproduced. Experi-ments were performed in dry state with an AFM instrumentMultimode (Digital Instruments, Santa Barbara, CA). TheMultimode was operated with amplitude feedback and in a‘‘light’’ tapping mode configuration. The amplitude setpointwas set to the maximum possible value. Silicon tips with aspring constant of 30 N/m and a resonance frequency of250–300 KHz were used after calibration with gold nanopar-ticles (of diameter 5.22 nm) to evaluate the tip radius. Thetips with radius 14.9 6 1.9 nm were used for most of themeasurements. For quantitative analysis of the AFM images,WSxM 4.0 software package16 and Origin 8.0 (Northampton,MA) were used, as specified.

ANALYSIS OF AFM IMAGES

Identification of Single MoleculesThe PSD analysis in this article has been carried out on con-firmed single molecules only, irrespective of their shape. Thecriterion to qualify as a single molecule was chosen to be acase-by-case volume analysis17,18 of the structures visible onthe AFM scan. Assuming the dry state density of NaPA-Ca2þ

system to be 1 g/cc, we can approximate the volume of asingle molecule with a molecular weight of 783 000 g/molto be 1685 nm3. Any structure with a significantly larger vol-

ume was deemed to be an aggregate.9,10 Likewise, any struc-ture with a significantly lower volume was deemed to be asection of a coil, a large part of which has remained invisibleto the AFM scan given the noise levels at which experimentswere performed.9,10

Generation of 2D Form Factor CurveA randomly rough surface feature scanned through a tappingphysical probe shows the presence of many different spatialfrequencies. This is quantitatively expressed by the PSDcurve, giving the relative strength of each roughness compo-nent of a surface feature as a function of spatial frequency.Mathematically, PSD is evaluated by squaring the magnitudeof the Fourier Transform of a surface feature.

For an AFM scan, the Fourier Transform usually evaluated isthe 2D-FFT. It is defined according to eq 1 below19

2D-FFTðKx;KyÞ ¼ L

N

� �2XN�1

x¼0

XN�1

y¼0

zðx; yÞ

cos 2pKxx

Nþ Kyy

N

� �� þ i sin 2p

Kxx

Nþ Kyy

N

� �� ; ð1Þ

where L is the size of the image, N is the number of pixelsper line, z(x, y) is the topographic height at the spatial piezodisplacements,20 (x,y) and (Kx, Ky) are the spatial frequencycoordinates corresponding to the piezo displacements.Because only real numbers can be displayed, the magnitudeof 2D-FFT calculated according to eq 1 forms the spectralpresentation of the Fourier Transform of an AFM scan. A typ-ical AFM scan of 1 lm size consisting of 512 � 512 datapoints has a pixel size of approximately 1.95 nm. It is note-worthy that this pixel size availability has a profound impacton the 2D-FFT spectra and restricts conformational analysiswithin the limits of resolution. The 2D-FFT is converted intoa PSD by an angular average using the radius in reciprocalspace as the spatial frequency according to eq 2 below19

PSDðKhÞ ¼ 1

L

� �2XNn¼0

2D� FFTðKx;KyÞ�� 2;

where

K2h ¼ K2

x þ K2y ; (2)

PSD then evidently carries the dimensions (length).4 Wehave followed the same convention throughout this article.In the derivation of eq 2, PSD is normalized with the numberof pixels of every Kh. This is done because the number ofpixels contributing to the averaging process increases as Kh

increases. In this way, we also make sure that intensities ofcorrelation maxima occurring at different spatial frequenciescan be compared and conclusions drawn.

As a single molecule is almost never centro-symmetric, therisk in adhering to the angular average protocol describedabove is a smearing of correlation peaks. Central slice exci-sion of the 2D-FFT can prevent this. However, in the context

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of this work, central slice excision of the 2D-FFT was ruledout because such a procedure would miss a large number of‘‘reflections’’ originating from the molecular morphology.Central slice excision of 2D-FFT has been followed by someauthors21 where the direction of anisotropy is known before-hand and correlations are required only along that direction;this is not our case. Hence, to observe the correlation peaksclearly, we follow a background subtraction procedureinstead. This procedure works remarkably well for our case.The background subtraction method used here is similar tothe one recently used in the PSD analysis of lateral packingarrangement of a single structural (capsid) protein inside avirus.22

We began by analyzing rotational isotropy in the spread ofmolecules on the surface and exclude the possibility of thepresence of any shear field during drying procedures. Thus,2D-FFTs of the scanned images were evaluated. Figure 2(a–d) shows exemplary real space AFM scans of SASE and SASHat the equilibration temperatures of 30 �C and 15 �C. Thecorresponding 2D-FFTs of the scanned surfaces are shown inthe insets. In all the cases, no specific orientation could bedetected implying shear fields, even if present, are too weakand can be ignored. More importantly, this would mean anabsence of any dominant intermolecular correlation lengthscale on the surface. Thus, all subsequent results obtainedfor surface features in this article arise only because of two

reasons—loss of one degree of freedom as the moleculemoves from 3D solution to 2D surface and of course, samplehistory. By comparing our results with SANS, it is essentiallythe extent of these two factors which we are measuring.Intermolecular correlations do not play a significant role andcan be neglected. It must be mentioned here that the imageprocessing protocols used at the single molecular level, asdetailed in the following paragraphs, would remainunchanged even if global rotational isotropy is not found onthe surface. The presence of global rotational isotropy is nota mandatory condition for evaluation of PSD curves at thesingle molecular level. In our case, its presence just helps usto neglect intermolecular correlations while interpreting ourresults.

In the second step, PSD analysis was carried out on eachcompletely isolated single molecule. The evaluation of a PSDcurve for a single molecule equilibrated at 30 �C and at 15�C is shown in Figure 3(a–b), respectively. The snapshotsshown are taken from the AFM scans of sample SASE at dif-ferent equilibration temperatures, respectively, but may notrepresent the very same molecule. A rectangular windowhaving a single molecule was zoomed out of the AFM scanand was ‘‘flooded’’ to set all those pixel values to zero, whichrepresent a part of the mica substrate and not the molecule.‘‘Flooding’’ is an inbuilt parameter of the WSxM softwaresuite which allows an AFM statistician to choose a threshold

FIGURE 2 Exemplary real space AFM scans (expanded and flattened for better view) of samples (a) SASE equilibrated at 30 �C, (b)SASH equilibrated at 30 �C, (c) SASE equilibrated at 15 �C, and (d) SASH equilibrated at 15 �C. The corresponding 2D-FFTs of the

scanned surfaces are shown in the insets. In all the cases, no specific orientation could be detected.



height in close agreement with mica surface roughness andtreat only those parts of the surface structure which areabove the threshold. Similar methods have been used earlierfor size analysis of surface structures present on an AFMscan.17,18 Next, to perform 2D-FFT, and dictated by the algo-rithm of 2D-FFT, the zoom-rectangular window needed to betransformed so that the width and the height are an integerpower of 2. This can be achieved in one of the two ways,scale the image up to the nearest integer power of 2 orzero-pad to the nearest integer power of 2. The secondoption was chosen here to maintain consistency with‘‘flooded’’ portion of the window. The PSD function was thenmeasured for this ‘‘flooded’’ and zero padded window. Fur-ther, a background PSD function was evaluated. A simple

way to define a background is to filter the image in such away that all pixel heights above a certain threshold areexcluded. This can be done using ‘‘equalize’’ filter of theWSxM software suite. The threshold can be chosen byextracting the baseline from lateral profile measurements.Once the background image has been generated, the back-ground PSD function can be evaluated exactly in the sameway as done for the original image. Finally, the backgroundPSD function was subtracted from the total PSD function togive us a background-subtracted-PSD function of the mole-cule. A single molecular background-subtracted-PSD curveshowed maxima suggesting structural correlations within themolecule. Note that these maxima represent correlationlengths within the molecule and in no case, can be

FIGURE 3 Image processing protocol for (a) a molecule trapped at equilibration temperature of 30 �C and (b) a molecule trapped

at equilibration temperature of 15 �C. Step 1: A single molecule is zoomed out of an AFM scan and subsequently, ‘‘flooded’’ and

zero padded. Step 2: The image is ‘‘equalized.’’ Step 3: Both the original and the ‘‘equalized’’ image are Fourier transformed and

converted into PSD by an angular average. Step 4: Background is removed by subtracting PSD of ‘‘equalized’’ image from PSD of

original image. All y axes shown have the units Log[PSD(nm4)].

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interpreted to be associated with the size parameters of themolecule like end to end distance (or major axis when endsare not decipherable) and width. This is because the correla-tion maxima for such parameters are present both in thePSD curve of the original image and the PSD curve of thebackground image. During subtraction, these peaks areremoved. Many single molecular background-subtracted-PSDcurves belonging to different molecules of a sample weremathematically averaged to generate the 2D form factorcurve for that sample. Only overlapping frequency rangeswere included in the 2D form factor. Fluctuations at verylow and very high frequencies were sliced off during averag-ing. The sudden fluctuation visible at very low frequencies isattributed to the application of ‘‘equalize’’ filter while gener-ating the background image and has been reported by otherauthors23,24 using similar filtering. Large deviations at veryhigh frequencies occur due to aliasing effects caused by pixelresolution and small height differences between scan lines.24

Any subtraction or averaging, whenever mentioned in thisarticle, was done after interpolation, using bicubic splinemethod, to first generate data sets with common abscissas.

Removal of ArtifactsA spatial frequency bandpass filtering is often applied23,24 toenhance contrast by ‘‘flattening’’ the image. The ‘‘flatten’’ fil-ter of the WSxM software suite is a combination of twoGaussian filters: a high pass filter, to remove long rangetopographic effects like bow, and a low pass filter, to sup-press local noise. However, one should always check the sig-nal on the original image first.25 Thus, PSD analysis for sin-gle molecules was done using zoomed out windows from theoriginal scan on which no ‘‘flattening’’ filter was applied apriori. ‘‘Flattening’’ usually has only aesthetic importance any-way but in this case could have interfered with the antici-pated peaks by cutting off the high and low frequencies evenbefore the analysis had begun. In the rare case when the 2D-FFT of a zoomed out window containing a single moleculeshowed bow and/or noise, the artifacts were selectivelyremoved on a case-by-case basis. Bow occurs due to drift ofthe piezoscanner along the y axis (the slow scan axis) andshows up in the 2D-FFT as a bright line along the same axis.The entire line can be simply removed before the angular av-erage is taken by using an appropriate cut filter. Noise, onthe other hand, occurs due to acoustic vibrations duringimaging and shows up in the 2D-FFT as two bright spotsplaced symmetrically opposite to each other. Noise too canbe removed from the 2D-FFT by using a suitable cut filterbefore angular averaging.

RESULTS AND DISCUSSION

In lieu of an analytical or theoretical curve against which thegenerated 2D form factor curve can be fitted, relating the 2Dform factor curve to the structure of the molecule is a chal-lenging task.

At the Equilibration Temperature of 30 8CFigure 4(a) shows 2D form factor curves for SASE and SASHequilibrated at 30 �C. The curves have been shifted along the

y axis for greater clarity. A set of 100 single molecules weretaken into account for generating each of the 2D form factorcurves. A high-intensity peak at low frequency and a low-in-tensity peak at high frequency typify the 2D form factorcurves of both SASE and SASH at this equilibration tempera-ture. The corresponding real space AFM scans are presentedin Figure 2(a) (SASE-30 �C) and Figure 2(b) (SASH-30 �C).We shall discuss the low frequency peaks first and then thehigher frequency peaks.

We observe that the low frequency peaks in the 2D form fac-tor curves are quite sharp. This can be interpreted to meanthat there is a great degree of uniformity in the lateral struc-tures adopted by different molecules adsorbed on the sur-face. If this would not have been the case, the averaging pro-cess would have broadened the peaks. The situation issummarized in Table 1(a) top row. The low frequency peaks(Log K ¼ �1.20 in SASE and Log K ¼ �1.30 in SASH) corre-spond to correlation lengths of 15.85 nm and 19.95 nm,respectively. We interpret the observed length scales to rep-resent the average separation between pearls formed on thesurface.

SANS results9 for sample solutions equilibrated at 30 �Cindicate a necklace like structure with a large majority ofdumbbells. Pearls of both SASE and SASH have an averageseparation of about 80.0 nm. Monte Carlo simulation stud-ies26 have shown that collapsing annealed polyelectrolytes,like polyacrylates, show formation of pearls which are con-siderably charged as long as the polyelectrolyte is in a close-to-h-point regime and its monomers are only weaklycoupled. This may indeed hold true for our case. As it is thepearls which carry most of the charge, we anticipate thatwhen this necklace like structure moves closer to the pre-treated substrate, the pearls interact more strongly with thesurface than the intervening strings. As such, it may be safeto assume that the strongest intensity peak observed in the2D form factor is related to the existence of pearls in solu-tion. In this case, a nearly constant ratio of 0.2 betweenpearl separation distance on surface and the correspondingseparation distance in solution is observed in both SASE andSASH A five fold decrease of pearl separation distance uponadsorption is remarkable. It points to isotropic adsorption(due probably to electrostatic repulsive forces at the

FIGURE 4 2D form factor curves for (a) SASE and SASH equili-

brated at 30 �C. (b) SASE and SASH equilibrated at 15 �C.Curves are shifted along the y axis for the purpose of clarity.

All y axes shown have the units Log[PSD(nm4)].



substrate-sample interface)12 and the shrinking effect of cap-illary forces. It is worth mentioning here that the correlationlengths obtained for adsorbed molecules on surfaces are atbest 3D to 2D projections of the correlation lengths in solu-tion. A direct quantitative comparison has to be seen withinthis limitation. Once the first points of adsorption are formedby the pearls, the remaining lateral packing arrangement ofthe molecule is strongly dictated by these fixed adsorptionpoints.

The reason for the appearance of a second correlation lengthat a higher frequency in the 2D form factor curves of bothSASE and SASH is not readily understood. The high fre-quency correlation maxima are weak in both the samplesand the maximum is, in fact, almost completely smeared outin SASE. The frequencies Log K ¼ �1.01 for SASE and Log K¼ �1.09 for SASH correspond to length scales of 10.23 nmand 12.30 nm, respectively, as summarized in Table 1(a) bot-tom row. Electrostatic interactions between the molecule andthe surface perhaps destabilize the dumbbell giving rise toformation of substructures which are not present in thesolution.

At the Equilibration Temperature of 15 8CFigure 4(b) shows 2D form factor curves for SASE and SASHequilibrated at 15 �C. The curves have been shifted along they axis for greater clarity. At this equilibration temperature,SASE’s 2D form factor curve shows a single maximum, whilethat of SASH shows two clearly distinguishable maxima. Thecorresponding real space AFM scans are presented in Figure2(c) (SASE-15 �C) and Figure 2(d) (SASH-15 �C).

We can immediately observe two noticeable differencesbetween the 2D form factor curves evaluated at equilibrationtemperature of 30 �C and the corresponding curves at equili-bration temperature of 15 �C. First, the 2D form factorcurves at equilibration temperature of 15 �C have shifted toa lower frequency range. This would mean that an increaseof temperature induces a collapse of the molecules. Notethat the precise range of this shift is rather qualitativebecause of fluctuations at very high and very low frequen-cies, which are always likely to accompany the generated 2Dform factor curves. Second, we observe that the low fre-quency correlation peaks at equilibration temperature of

15 �C are less sharp than the peaks at equilibration tempera-ture of 30 �C. This smearing of peaks at the equilibrationtemperature of 15 �C would suggest a lack of uniformity inthe lateral packing structure of adsorbed molecules. SASEshows only one characteristic correlation peak at Log K ¼�1.32 corresponding to a length scale of 20.89 nm. SASHexhibits two correlation peaks—a higher intensity peak atLog K ¼ �1.33 corresponding to a length scale of 21.38 nmas well as appearance of a low intensity peak at Log K ¼�1.64 corresponding to a length scale of 43.65 nm. Thesefrequencies and the corresponding correlation length scalesare summarized in Table 1(b).

SANS results9 for sample solutions equilibrated at 15 �Cindicate a randomly coiled behavior for SASE and a ratherextended behavior for SASH. SANS results9 confirm that atthe mentioned equilibration temperature, polyacrylate coilsdo not show the existence of pearls in solution, yet the coilsare largely collapsed compared with their unperturbeddimensions. However, the presence of correlation maxima inthe 2D form factor curves indicates that pearl formationbegins on the surface, which is not identifiable in solution.We can therefore argue that interactions associated withsample history have pre-empted the formation of an inter-mediate coil to globule state on the surface.

At 0.01M total salt concentration, the coil has enough coun-terions in its proximity. When such a coil from solution isdeposited on the surface, the loss of one degree of freedomcauses a rapid confinement of the polymer backbone. Thiscreates sections within the molecule having a very high den-sity of counterions. It is these sections which interact verystrongly with pretreated mica surface and are sensed by the2D form factor. The presence of the first length scale ataround 21 nm is exhibited in adsorbed molecules from bothSASE and SASH. Strikingly, SASH also shows a quite distin-guishable second length scale at 43.65 nm. There may betwo possible explanations for the appearance of these lengthscales.

The first possibility is that both SASE and SASH exhibit apearl–pearl separation distance of about 21 nm on the sur-face. The length scale of 43.65 nm unique to SASH can thenbe attributed to the nonuniform distribution of charge along

TABLE 1 Data Table Showing Frequencies at which Correlation Maxima are Observed

(a) 30 �C (b) 15 �C

SASE SASH SASE SASH

Log K ¼ �1.20

(15.85 nm)

Log K ¼ �1.30

(19.95 nm)

Log K ¼ �1.32

(20.89 nm)

Log K ¼ �1.64

(43.65 nm)

Log K ¼ �1.01

(10.23 nm)

Log K ¼ �1.09

(12.30 nm)

Log K ¼ �1.33

(21.38 nm)

SANS-78.5 nm

(pearl–pearl

separation)

SANS-82.0 nm

(pearl–pearl

separation)

SANS-random

coil

SANS-extended coil

The respective correlation lengths are mentioned within brackets. Corresponding SANS results9 for the sample solution are also indicated. (a) Equili-

bration temperature of 30 �C. (b) Equilibration temperature of 30 �C.

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the chain in solution, especially in case of annealed polyelec-trolytes like polyacrylates.26–29 As an excess charge tends toaccumulate toward the chain ends, the farther a section ofthe chain is from the middle, the stronger its interactionwould be with pretreated mica substrate during adsorption.This results in formation of larger pearls as one moves far-ther from the middle of the chain. The 2D form factor is ableto sense this minute detail in case of SASH but not in case ofSASE. This can happen if SASH, in general, adopts a moreextended conformation of molecules on the surface whencompared with SASE because it is only when a molecule isextended that electrostatic potential energy at different loca-tions of the chain would be different. On similar lines, wemay speculate that greater the extension exhibited by anadsorbed molecule, larger the number of low frequencypeaks which appear in the 2D form factor curve. Not onlyshould the number of low frequency peaks increase withincreasing extension of the adsorbed molecule but also theintensity of such peaks. This follows from the predictedincrease of charge accumulation as one moves farther fromthe middle of the chain. In a nearly rigid rod conformation,the lowest frequency peak in the 2D form factor curve wouldbe quite intense and correspond to the end to end distanceof the adsorbed molecule. However, in this article we havenot experimentally verified our predictions regarding theresponse of 2D form factor curve to increasing extension ofadsorbed molecules. Such a study may be conducted using alarge number of samples with known solution conformationsranging from randomly coiled to nearly rigid rod and thenanalyzing the 2D form factor curve for each sample.

There is also a second possible interpretation of the 2D formfactor curve of SASH at the equilibration temperature of15 �C. The first correlation length scale of 21.38 nm mayrepresent the pearl size, whereas the second correlationlength scale of 43.65 nm represents the pearl-pearl separa-tion distance on the surface.

Note that the correlation lengths on surfaces and solutionhave to be seen within the limitations of our selection pro-cess for the molecules. Aggregates, for example, were notincluded in the 2D form factor analysis, which if present insolution could affect the SANS curves.

CONCLUSIONS

The conformation of a single polyacrylate coil in solutionand on surface is not the same because the adsorption forcesare weak. The question is how much does it differ? We haveargued that shifting the problem to reciprocal space is a pos-sible way forward in quantitatively establishing the differen-ces in conformation of a single molecule as it moves from3D solution to 2D surface and is affected inevitably by sam-ple history. We have interpreted our results solely on the ba-sis of loss of a degree of freedom and sample history. Inter-molecular correlations do not enter our picture because ofthe presence of global rotational isotropy on the surface.However, the image processing protocol used at the singlemolecular level would hold even in the absence of a globalrotational isotropy. Of course, in such a case, the interpreta-

tion of results would have become much more complicated.In generating our 2D form factor curves, we have not preas-sumed any directional orientation of adsorbed molecules andall ‘‘reflections’’ arising due to surface morphology have beenincorporated. We observe that a background subtraction pro-cedure may be effectively used to counter smearing of peaksfor non centro-symmetric molecules.

For the system under consideration, when the structure insolution does not contain any pearls, the structure on sur-face already begins to show signs of pearl formation. Thiswas visible in the form of correlation maxima in the 2D formfactor. We further speculate that lower the frequency atwhich a maxima occurs, more extended the adsorbed coil is,in line with charge inhomogeneities present in polyacrylatecoils. When the structure in solution shows pearls, the struc-ture on surface is a mixture of compact elliptical globules,sausage like structures and dumbbells. Probing deeper intostructural correlations within these structures, we concludethat the packing arrangement is strongly governed by pearlseparation distance in solution.

It must be emphasized that the proposed reciprocal spaceapproach for analysis of AFM images would be better vali-dated when applied to a system which undergoes a gradualcoil to globule transition. Provided successive stable interme-diate states in solution can be accessed and characterizedthrough scattering, the subtle changes in correlation lengthsas each of these intermediate states is trapped on the sur-face can be tabulated. This will be the subject of a futurestudy.

Financial support of the Deutsche Forschungsgemeinschaft(grant STA-324/23 of Dresden group and HU807/7 of Pader-born group) as well as helpful discussions with Prof. PeterMuller-Buschbaum are gratefully acknowledged.

REFERENCES AND NOTES

1 Sheiko, S. S.; Moller, M. Chem Rev 2001, 101, 4099–4123.

2 Roiter, Y.; Jaeger, W.; Minko, S. Polymer 2006, 47, 2493–

2498.

3 Gallyamov, M.; Khokhlov, A. R.; Moller, M. Macromol Rapid

Commun 2005, 26, 456–460.

4 Dubas, S. T.; Schlenoff, J. B. Macromolecules 1999, 32,

8153–8160.

5 Poptoshev, E.; Schoeler, B.; Caruso, F. Langmuir 2004, 20,

829–834.

6 Kotov, N. A. Nanostruct Mater 1999, 12, 789–796.

7 Netz, R. R.; Joanny, J. F. Macromolecules 1999, 32,

9013–9025.

8 Kiriy, A.; Gorodyska, G.; Minko, S.; Jaeger, W.; Stepanek, P.;

Stamm, M. J Am Chem Soc 2002, 124, 13454–13462.

9 Lages, S.; Lindner, P.; Sinha, P.; Kiriy, A.; Stamm, M.; Huber,

K. Macromolecules 2009, 42, 4288–4299.

10 Kirwan, L. J.; Papastavrou, G.; Borkovec, M.; Behrens, S. H.

Nano Lett 2004, 4, 149–152.



11 Liao, Q.; Dobrynin, A. V.; Rubinstein, M. Macromolecules

2006, 39, 1920–1938.

12 Reddy, G.; Chang, R.; Yethiraj, A. J Chem Theory Comput

2006, 2, 630–636.

13 Kong, C.; Muthukumar, M. J Chem Phys 1998, 109,

1522–1527.

14 Panwar, A.; Kumar, S. J Chem Phys 2005, 122, 154902–

154913.

15 Beltran, S.; Hooper, H.; Blanch, H.; Prausnitz, J. Macromole-

cules 1991, 24, 3178–3184.

16 Horcas, I.; Fernandez, R.; Gomez-Rodriguez, J. M.; Colchero,

J.; Gomez-Herrero, J.; Baro, A. M. Rev Sci Instrum 2007, 78,

13705–13713.

17 Gorodyska, G.; Kiriy, A.; Minko, S.; Tsitsilianis, C.; Stamm,

M. Nano Lett 2003, 3, 365–368.

18 Kiriy, A.; Gorodyska, G.; Minko, S.; Tsitsilianis, C.; Stamm,

M. Macromolecules 2003, 36, 8704–8711.

19 Fang, S. J.; Haplepete, S.; Chen, W.; Helms, C. R.; Edwards,

H. J Appl Phys 1997, 82, 5891–5898.

20 Digital Instruments Veeco Metrology Group In MultiModeTM

SPM InstructionManual; 1997; Version 4.31ce, Chapter 15, pp 1–3.

21 Carbone, D.; Alija, A.; Plantevin, O.; Gago, R.; Facsko, S.;

Metzger, T. H. Nanotechnology 2008, 19, 35304–35308.

22 Briggs, J. A. G.; Johnson, M. C.; Simon, M. N.; Fuller, S. D.;

Vogt, V. M. J Mol Biol 2006, 355, 157–168.

23 Ruppe, C.; Duparre, A. Thin Solid Films 1996, 288, 8–13.

24 Jiang, T.; Hall, N.; Ho, A.; Morin, S. Thin Solid Films 2005,

471, 76–85.

25 Haubruge, H. G.; Gallez, X. A.; Nysten, B.; Jonas, A. M.

J Appl Crystallogr 2003, 36, 1019–1025.

26 Uyaver, S.; Seidel, C. J Phys Chem B 2004, 108, 18804–

18814.

27 Berghold, G.; van der Schoot, P.; Seidel, C. J Chem Phys

1997, 107, 8083–8088.

28 Castelnovo, M.; Sens, P.; Joanny, J. F. Eur Phys J E 2000, 1,

115–125.

29 Zito, T.; Seidel, C. Eur Phys J E 2002, 8, 339–346.

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Adsorption behavior of partially collapsed polyacrylate coils on mica surfaces: A reciprocal space approach