Adhesion and detachment mechanisms of sugarsurfaces from the solid (glassy) to liquid(viscous) statesBoxin Zhao*, Hongbo Zeng*, Yu Tian*†, and Jacob Israelachvili*‡

*Department of Chemical Engineering, Materials Research Laboratory, University of California, Santa Barbara, CA 93106; †State Key Laboratory ofTribology, Department of Precision Instruments, Tsinghua University, Beijing 100084, People’s Republic of China

Contributed by Jacob Israelachvili, October 27, 2006 (sent for review August 25, 2006)

The viscosity of some sugars varies continuously by �10 orders ofmagnitude over a temperature range of 50°C. Sugars are thereforeideal model materials for studying the failure mechanism of ma-terials as they change from the solid to the liquid state. We haveused a surface forces apparatus coupled to interference and opticalmicroscopy imaging to study the way two sugar surfaces adhereand detach from adhesive contact. The sugar-coated layers on micadisplayed significant loading–unloading hysteresis, and the adhe-sive strength and failure mechanism during a ‘‘loading–unloadingcycle’’ depended on the loading rate, contact time, and unloadingrate. The failure of two glassy sugar surfaces was manifested bythe nucleation of many sharp microcracks at the external boundarythat rapidly propagate along the original contact interface. At theother extreme, when the material is a liquid, ‘‘failure’’ occursthrough the nucleation and inward growth of large roundedripples, characteristic of a Saffman–Taylor fingering instability. Inthe transition from glassy to viscous failure, sharp crack tips andsmooth rounded fingers coexist during the crack propagation. Inaddition, whereas the detachment geometry of two glassy surfaceswas characterized by a peeling-like mechanism along a plane, thefingers associated with the ‘‘snapping’’ of a liquid neck extended inall directions. These findings provide insights into the adhesion andfailure mechanisms of materials at the micro/nanoscales and are alsorelevant to the action of interparticle forces between sugar particles,such as those used in inhalation drug delivery.

adhesive failure � fingering instability � crack propagation �contact dynamics

Everyday experiences tell that solids fracture and liquids flow.However, for many materials there is no clear boundary be-

tween the solid and liquid states (1). Also, a material can behave likeeither a solid or a liquid depending on the time scale of theobservation. A typical material that does this is pitch, which, if hitrapidly with a hammer, shatters like a brittle solid, but can flow likea liquid over periods of years (2). Here, we report on a study of theadhesion and detachment mechanisms of a common sugar, glucose,as it transits from the solid (glassy) to the liquid (viscous) state.

The classic Hertz and Johnson–Kendall–Roberts (JKR) theories(3, 4) describe the adhesion and contact mechanics of solids. Thesetheories have been found to hold well for molecularly smooth andnonhysteretic surfaces both at macroscopic and microscopic lengthscales. However, the adhesion mechanics of viscoelastic materialsand sticky fluids are not so well understood (5–9). The adhesion orfracture energy of viscoelastic, such as some polymer, materials canbe four orders of magnitude greater than the thermodynamic value,which has been attributed to such energy-dissipating processes asmolecular interdiffusion or entanglements across the contact junc-tion and macroscopic viscous/plastic deformations (10–12). Inaddition, detaching viscoelastic materials exhibit various interfacialinstabilities and cavitation, which are also not yet understood(13–16). It has been suggested (17) that conventional theories ofNewtonian liquids could serve as a starting point for understandingthe instabilities associated with detaching viscoelastic materials.

The viscosity of some sugars varies continuously over manyorders of magnitude over a narrow temperature range. Fig. 1 showsthe viscosity of glucose as a function of temperature (18). Unlikepolymers that exhibit similar properties (8), glucose is a smallmolecule, and is therefore an ideal model material for studying thetransition between solid- and liquid-like materials and processes,which has long been a challenge in materials science and engineer-ing. In addition to using sugar as a model material, the adhesionbetween sugar particles is important in its own right in the confec-tion industry (19) and in new biotechnologies such as the proteinencapsulation by sugars and the inhalation of sugar-coated drug-carrying aerosols (20).

Results and DiscussionAdhesion and Detachment of Glassy Surfaces (T < Tg). When twosmooth glucose-coated surfaces of radius R � 2 cm are gentlybrought into contact under zero external load (L � 0), theyimmediately deform because of the attractive intersurface forcesthat pull the two curved surfaces into a flattened circular contactarea of radius r0. On further pressing the surfaces together (L � 0)the contact area A � �r2 increases above �r0

2. Fig. 2A shows a typical(measured) contact diameter 2r as a function of the compressive

Author contributions: B.Z. and J.I. designed research; B.Z. and H.Z. performed research; B.Z.,H.Z., and Y.T. analyzed data; and B.Z. and H.Z. wrote the paper.

The authors declare no conflict of interest.

Abbreviation: JKR, Johnson–Kendall–Roberts.

‡To whom correspondence should be addressed. E-mail: jacob@engineering.ucsb.edu.

© 2006 by The National Academy of Sciences of the USA

Fig. 1. Viscosity of glucose as a function of temperature (18). The glasstransition temperature Tg was measured by differential scanning calorimetryat 10°C/min; the melting point is Tm � 146°C. Also shown is the chemicalstructure of glucose, which has an irregular shape with five exposed hydro-gen-bonding hydroxyl groups.

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load L for two glucose surfaces in the glassy state at 23°C. Once theload had reached a certain value, Lmax, the surfaces were allowedto ‘‘age’’ for a certain contact time, tc, after which the load wasreduced until the surfaces abruptly jumped apart at a negative(tensile) load L � �Lad, commonly referred to as the adhesion or‘‘pull-off’’ force. It is clear from Fig. 2A that the loading andunloading processes are not reversible: there is a strong adhesionhysteresis.

According to the JKR theory (21), an elastic sphere of radius Rwhen pressed by a load L against a flat surface of the same materialof bulk elastic modulus K and surface energy � will have a flatcontact area of radius r given by

r3 �RK �L � 6�R� � �12�R�L � (6�R�)2� . [1]

Furthermore, the loading and unloading paths should be revers-ible, and separation or pull-off should occur when

L � �Lad � �3�R�. [2]

The JKR theory has been found to work well for ‘‘ideal’’ (clean,smooth, elastic) surfaces with known adhesion energies, e.g.,mica coated with surfactant monolayers (22) or smooth layers ofelastomeric polymers (10–12), showing no hysteresis, namely,the loading–unloading paths described by Eq. 1 are reversible,

and predicting the correct (thermodynamic) values for � tobetter than 10%.

The path predicted by the JKR theory for the sugar surfaces isshown by the solid curve in Fig. 2A. The measured loading data fitthe theoretical prediction extremely well, indicating the (initially)elastic nature of the materials and a surface energy of � � 46 � 5mJ/m2, which is close to the thermodynamic value of � � 42 mJ/m2

for glucose at this temperature (23).Fig. 2A further shows that the contact diameter did not change

during the aging. This is reasonable considering the rigidity ofglucose at this temperature. During unloading, instead of retracingthe JKR path down to Lad � 3�R� � 8 mN, the contact radiushardly changed until the surfaces detached abruptly at a muchhigher adhesion force. This ‘‘effective’’ adhesion force, Lad(eff) inFig. 2A, may be used in Eq. 2 to give the effective adhesive strength,�ad (which is to be distinguished from �, the surface energy at truethermodynamic equilibrium). For the system shown in Fig. 2A, theadhesive strength was �ad � 234 mJ/m2, which is �5 times higherthan the thermodynamic value.

Fig. 2B shows the adhesive strength �ad as a function of thecontact time tc at the same maximum load for two unloading ratesdefined in terms of the forces or loads, dL/dt or L (to be distin-guished from separation rate in terms of the distance, defined bydD/dt or D). Within the time scales of our measurements, theadhesive strength increased roughly linearly both with the contacttime tc, and unloading rate dL/dt. Qualitatively, the observed agingand rate-dependent effects are similar to those previously observedfor nonequilibrium (hysteretic) adhesion processes of, for example,surfactant and polymer surfaces (7, 8, 10, 12, 22). However, the

Fig. 2. Adhesion and detachment of glassy surfaces. (A) Typical plot offlattened contact diameter 2r as a function of load L for two initially curvedglucose surfaces (R � 2.0 cm) at 23°C during a loading-hold-unloading cycle. Thecontact time at Lmax was tc � 22 min, and the unloading rate was dL/dt � L � 0.2mN/s.Thesolidcurve is theJKRfit (Eq.1),usingthe initial contactdiameteratzeroload (2r0 � 80 �m at L � 0), which gives K (because K � 12� R2�/r0

3 at L � 0). (B)Measured adhesive strength, �ad � Lad/3�R, as a function of contact time at Lmax

� 40 mN at two different unloading rates of L � 0.2 and 1 mN/s.

Fig. 3. Surface deformations during adhesion and detachment of glassysurfaces. (A) The top-view image right before pull-off after aging for 20 minat 23°C (point P in Fig. 2A). (B) Same as A showing the FECO fringe pattern justbefore pull-off. (C) Top-view image right after pull-off. (D) FECO fringepattern of second contact 2 min after separation. (E) SEM image of theexternal edge of the contact area after detachment following overnight agingin contact (from a different sample).

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unloading curves for these systems were still JKR-like, i.e., curved,rather than the straight, almost horizontal path until the failurepoint.

Some details of the surface deformations in the fracture zone areshown in Fig. 3. Fig. 3 A and B show optical microscope top viewsand FECO images of the surfaces just before their first detachmentfrom contact (point P in Fig. 2A), and Fig. 3 C and D shows thesurfaces after separation and bringing them back into contact again,respectively. It is apparent that the fracture occurred along theoriginal interface, indicating that not enough time was given for thecontacting surfaces to coalesce (sinter or cold weld) into a contin-uous solid. However, at some stage during the contact and detach-ment, the originally smooth surfaces have become rough at thenano scale. Thus, Fig. 3D shows discontinuities in the previouslystraight FECO fringes (compare Fig. 3B) coming from within theflattened contact region, indicative of a local roughness of height�20 nm. Apparently, in the roughened regions, the surfaces have(at least partially) coalesced into bulk material. More quantitativeinvestigation is needed to clarify the coarsening of such fracturezones. Fig. 3E shows a scanning electron microscope (SEM) imageof a detached surface after aging the contacting surfaces overnightbefore detachment. Fig. 3E Left is the contacted region showingsome micro cracks; Fig. 3E Right is the noncontacted surface.

Interestingly, many radial micro waves/ripples can be seen justoutside the contact boundary. Similar features were also observedat higher temperature, as described below.

Adhesion and Detachment of Viscoelastic Surfaces (T � Tg). A secondset of experiments was conducted at 40°C, which is just above theTg of glucose. To put this temperature into perspective, the bulkviscosity of glucose at 40°C is higher than that of pitch (Fig. 1),which behaves like a brittle solid that nevertheless flows like a liquidover periods of years (2). As with the viscosity, the bulk rigidity ofglucose has also been found to decrease rapidly above Tg (24). Fig.4A shows the JKR plot for loading and unloading this material. Nowthe loading branch is less JKR-like, but the unloading branch ismore JKR-like. In other words, the loading behavior is less elastic-like, whereas the unloading is less brittle-like; and the cycle is overallless hysteretic. The JKR prediction is shown by the solid line, againusing the initial contact radius at L � 0 as the reference point.Notably, on first contact, the surfaces do behave like elastic (glassy)solids; this is due to the rapidity of the jump into contact and initialflattening, which occurs in �1 ms. Clearly, the initial contactprocess occurs at a Deborah number, De � 1 (see below).

On loading to Lmax, the contact area increased more steeply thanthe JKR prediction. This finding indicates that there is now some

Fig. 4. Adhesion and detachment of viscoelastic sur-faces. (A) Typical JKR plot for glucose at 40°C. The load-ing and unloading rates were both L � 0.2 mN/s, and thecontact time at Lmax was tc � 22 min. The solid line is theJKR prediction (Eq. 1), constructed as in Fig. 2A. (B and C)Top microscope views and FECO fringe images at point Pin A. (D and E) Top microscope views and FECO fringeimages at point Q in A.

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plastic flow of the glucose under the action of the compressive loadin addition to the purely elastic deformation predicted by the JKRtheory. On unloading, the contact diameter decreased, first linearly,then (after a certain tensile load had been exceeded) much moresharply toward pull-off, but not as abruptly as in the glassy system(Fig. 2). The adhesion strength was now lower than that for theglassy material, but still �3 times higher than the thermodynamicvalue.

Correlating the JKR plots with the changing shapes of the fringes(Fig. 4 C and E), it appears that there are two distinct processes withat least two characteristic time scales in the adhesion-detachmentprocess: (i) elastic flattening and peeling (JKR-like), and (ii)viscosity- and diffusion-controlled flow and molecular reordering.The loading–unloading process is similar to that observed withcertain viscoelastic polymers, which also display a complex hyster-esis on attachment and detachment (10, 25).

The surface images of the detachment at 40°C show morefeatures than for the glassy surfaces. Fig. 4 B–E shows top-viewoptical microscope images and FECO fringe images during thereduction of the contact diameter at points P and Q in Fig. 4A. TheFECO fringes in Fig. 4 C and E were still smooth, indicating thatthe separation occurred along the same plane as the originalinterface, i.e., that the two surfaces had not completely coalesced.Fig. 4B shows two concentric rings, the outer one defining theboundary of the initial contact circle, the inner ring defining the

peeling front. Fig. 4D shows the same location 11 s later, duringthe pull-off process. It can be seen that the outer ring is still at theoriginal position, whereas the inner ring had moved inward. Thedarker region outside the peeling front suggests some fine struc-tures that diffract light differently from the unaffected regions. Thefine details of these structures could not be resolved in this study,and they relaxed after the surfaces detached. These structures maybe similar to the viscous fingering and cavitation bubbles commonlyseen in the peel zones of peeling adhesive tapes and viscoelasticpolymer surfaces (13, 25).

Adhesion and Detachment of Viscous Surfaces (T > Tg). The third setof experiments was conducted at 75°C, �27°C above the Tg ofglucose. Fig. 5A shows the contact diameter as a function of time.In this viscous state, the two surfaces coalesced immediately oncoming into contact, with an outwardly growing meniscus (neck) inwhich waves/ripples developed (even under zero external load).Details of the coalescence process are given in ref. 26; here we focuson the separation process where, on the macroscopic scale, thesurface deformations were very much as expected for a thinningliquid neck that eventually snaps. The adhesion strength was now�80 mJ/m2, about twice the thermodynamic value, and the time tsfor detachment after the start of unloading (ts � 20 s) was muchshorter than for the viscoelastic (ts � 300 s in Fig. 2A) and glassy(ts � 370 s in Fig. 3A) materials.

However, fine features at the boundary of the shrinking fluidneck made this system (or temperature regime) particularly inter-esting. Fig. 5B shows a top view of the surface deformations at anearly stage of separation, revealing micrometer-sized ripples orwaves growing into the fluid, and much finer secondary structuresat the external neck boundary. These ripples are similar to theviscous fingers observed at the peel front during the peeling of‘‘pressure-sensitive adhesive’’ tape from a glass surfaces (27); andsimilar viscous fingers have also been reported in various dynamicstudies of confined viscoelastic polymers (8, 28, 29). In the presentexperimental geometry, when the two coalesced fluid surfaces arepulled apart and the neck thins, fluid flows both axially and radiallyinward toward the center (Fig. 5B). Such flow conditions give riseto Saffman–Taylor fingers (30), seen as the waves/ripples in Fig. 5B and C.

The growth or evolution of these fingers with time is shown in Fig.5 B–E. What is particularly interesting is that the initially roundedripples soon develop into two types of coexisting fingers: roundedand sharp, where the rounded fingers moved in faster than the sharpcrack-like tips, as illustrated in Fig. 5 D and E. Also shown in Fig.

Fig. 5. Detachment/failure of a glucose neck at 75°C (initial film thickness: 56nm). (A) Diameter of the contact neck as a function of time during coalescence(under a low compressive load of 5 mN) and detachment. (B–E) Sequentialtop-view microscope images of the surface deformations during neck thin-ning leading to ultimate detachment. The substrate (mica) surfaces deformedin a Hertzian fashion when under a compressive load, and relaxed to theirundeformed curved geometry on separation.

Fig. 6. Deborah and Weissenberg numbers, De and Wi, as functions of theseparation time ts and velocity of surface separation dD/dt � D at 75°C,calculated based on Eqs. 3–-6.

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5 D and E are vapor bubbles that nucleated (cavitated) within thefluid and grew outward, eventually to meet and join up with theinward-moving fingers.

Rounded Saffman–Taylor fingers and cavitation bubbles arecommon when separating two connected viscous surfaces (30), buttheir appearance with sharp crack-like tips in the same detachmentprocess was unexpected. We suggest that this temperature andunloading rate regime falls between solid like-fracture and liquid-like thinning and snapping. Previous studies on shearing Newtonianliquids have shown that solid-like fracture phenomena occur whenshear rates exceed a critical value that, for both polymer and simplesugar fluids, is a function of temperature or viscosity (31, 32).

At lower temperatures and/or higher unloading rates we observemore crack-like tips, whereas at higher temperatures there are onlyrounded fingers or no fingers at all (see below). Even finerstructures are evident in Fig. 5 that provide further insights: thus,Fig. 5 B–E shows smaller tips (secondary or residual cracks) at theouter boundary, which remained during separation, similar to thesharp microtips seen during the detachment of two glassy surfacesin Fig. 3E.

Regarding the range of temperature (and/or viscosity) andpulling rates where the liquid-to-solid (viscous-to-brittle) transitionoccurred, at the pulling rates used in our experiments the transitionwas observed to occur over the temperature range 50–80°C,corresponding to bulk viscosities � in the range 103 to 107 Pa�s. Thereason for the broad, rather than sharp, transition is that sharp cracktips and smooth rounded fingers coexist within the rupturingjunction over this temperature range.

During a separation the fluid flow within the rupturing neckchanges as a function of time and position. Thus, as a function oftime, because the system starts and ends at rest (there is no flow att � 0 and t � ts), the shear rate � must reach a maximum at somepoint of the process. As a function of position, Chan and Horn (33)have shown that for a sphere of radius R separating from a flatsurface in bulk liquid, at any instant when the surfaces are at aseparation D and are moving normally apart at velocity dD/dt � Dthe maximum shear rate in the fluid is given by

�max � (1�2)(3�2)5�2(R1�2�D3�2)D , [3]

and occurs at the surfaces at a radial distance of r � (2RD/3)1/2 fromthe center (the shear rate is always zero at the center, at r � 0). Notethat, during the detachment process, �max increases from zero(when D � 0) to a maximum value then falls to zero again. Thus,�max itself reaches a maximum value at some point during thedetachment process. No such equations have been derived forfinite-sized liquid necks or bridges between two surfaces, but wemay anticipate that at any instant the shear rate is highest and thefluid is therefore more solid-like close to the outer edge, and moreliquid-like close to the center.

The critical shear rate that describes the transition from onerelaxation process/ mechanism to another is usually given by theDeborah number (De) or Weissenberg number (Wi) (1) defined as

De � ��t f, and Wi � ��, [4]

where � is the characteristic relaxation time of the material at thetemperature of the measurement, tf is the characteristic time of theflow, and � is the shear rate (also sometimes defined as the inverseof the experimental ‘‘observation’’ time, � � 1/tf). The Deborah andWeissenberg numbers are traditionally used in rheology (1): at ahigh Deborah number (De � 1), the flow is fast compared with thefluid’s ability to relax, and the fluid then responds more like a solid,whereas for De � 1 the fluid is more liquid-like. Shull and Creton(17) proposed that the Deborah number can also be used as aquantitative parameter to describe the transition from liquid-like tosolid-like behavior of thin polymer films. In our system, thesituation is much more complicated because both De and �max aredifferent at different times and locations within the neck. For ourgeometry, the Deborah number can be approximated by (8, 34)

De � ��t f � �D�D , [5]

which is not constant during the separation (detachment) process.Likewise, there is no single-valued shear rate � that can be put intothe above expressions for De or Wi. However, one can estimate themaximum values of De and Wi based on the maximum shear rate�max, given by Eq. 3, during the detachment processes. To do this,we first estimate the molecular relaxation time � using (1)

� � ��G � �M�NAkBT , [6]

where G � NAkBT/M is the characteristic modulus, is the densityof the fluid, NA is Avogadro’s number, and M is the molecularweight. For glucose at 75°C, � 1.54 g/cm3, M � 180 g/mol, � �104 Pa�s, so the characteristic relaxation time � is �4 � 10�4 s. Fig.6 shows plots of De and Wi as functions of the separation time tsand the rate of surface separation, D at 75°C. It appears that De andWi peak very sharply at a particular time ts and velocity D duringthe separation (detachment) process. However, the peak in Deoccurs at De � 0.01, which is well below the expected value of 1.0.It is possible that the real value of the molecular relaxation time �is higher than that estimated from Eq. 6, which was calculated interms of the bulk shear viscosity � at zero shear rate.

Adhesion (Coalescence) and Detachment of Liquid Surfaces (T �� Tg).As the temperature increases further, the viscosity of glucosecontinues to decrease until it behaves like a simple low-viscosityNewtonian liquid at the shear rates used in these experiments.Because of limitations of our apparatus, we could not study thehigh-temperature behavior of liquid glucose (at T close to Tm �146°C). However, previous studies on liquids such as n-dodecane(Tm � �9.6°C) and n-hexadecane (Tm � 18°C) have shown that theliquid necks thin and eventually snap at the theoretically expectedadhesion force of Lad � 4�R�, with no ripples or fingers (Table 1,row 5, columns B and C). These phenomena are all describable bysimple macroscopic equations in terms of the surface tension �, i.e.,independent of the viscosity (35, 36).

Table 1. Surface deformations and flows characterizing thetransition from solid to liquid (rows 1 3 5) showing thedeformations associated with adhesion�loading (column A)and separation�detachment�unloading (columns B and C)

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ConclusionsWe have used the simple sugar glucose as a model material to studythe differences between solid- and liquid-like adhesion and failureprocesses, and the transition between them. Our results alsoprovide insights into the adhesion and failure mechanisms ofmaterials at the micro/nano scales. The surface deformations andflows characterizing the transition from the solid state to the liquid(viscous) state are illustrated in Table 1. The two extremes areshown in rows 1 and 5, and the transitional behaviors are shown inrows 2–4.

As mentioned in the introduction, elastic and nonhystereticcontacts (Table 1, row 1) are well described by the classic JKRtheory for two purely elastic materials. The detachment force is Lad� 3�R�. At the other extreme of pure Newtonian liquids, twosurfaces coalesce into a liquid bridge right after contact (Table 1,row 5, column A), and detachment or ‘‘failure’’ occurs by the liquidbridge thinning and snapping (Table 1, row 5, columns B and C),with a detachment force of Lad � 4�R�, which is only 33% largerthan the pull-off force of two elastic solids. Our experimental resultsfall in between the two extreme cases, where the pull-off forces arevery much greater than either the mechanical (JKR) or thermo-dynamic values.

The adhesion of two glassy surfaces was describable by a JKRprocess, but only on loading (Fig. 2A and Table 1, row 2, columnA), whereas separation (unloading) lead to abrupt brittle-likefailure, preceded by the nucleation of many sharp microcracks atthe boundary (Table 1, row 2, columns B and C).

Around the glass transition temperature, the adhesion of thesurfaces on loading was intermediate between that of a JKR elasticdeformation and plastic flow (Fig. 4A and Table 1, row 3, columnA), whereas the deformation on detachment was more JKR-like(compare Table 1 row 3, column B with row 1, column B).

As the material becomes more liquid-like at T � Tg, the surfacescoalesce right after contact (Table 1, row 4, column A), and‘‘viscous failure’’ occurs via the nucleation and inward growth oflarge rounded ripples (Table 1, row 4, column B), characteristic ofa Saffman–Taylor fingering instability. In this regime of the tran-sition, sharp crack tips and smooth rounded fingers coexist duringthe crack propagation. In addition, whereas the detachment geom-etry of the more solid-like surfaces was characterized by a JKR-likepeeling mechanism along a plane (Table 1, column B, rows 1–3), thefingers associated with the snapping of a liquid neck extended in alldirections (Table 1, rows 4 and 5, columns B and C). The transitionfrom solid-like to liquid-like failure occurs through a broad regimewhere cracks and viscous fingers coexist, rather than a sharp,discontinuous transition where one type of failure mechanism isreplaced by the other.

Experimental MethodsThe adhesion (detachment) forces and associated surface defor-mations of glucose-coated mica surfaces were studied using a

surface forces apparatus (SFA) (8, 10–12, 37) coupled to interfer-ence and optical microscopy imaging.

D-glucose from Sigma-Aldrich (St. Louis, MO) was used asreceived. The melting point of glucose is 146°C. Its glass transitiontemperature was measured by differential scanning calorimeteryand found to be 38°C. Uniform glucose films, �40 nm thick (therange of film thicknesses used was 20–60 nm), were fabricated onmolecularly smooth mica surfaces by first dissolving glucose indeionized water to make 1–10 wt% solutions, then depositing adrop of one of the solutions onto two molecularly smooth micasurfaces, then removing the free water from the surface by wickingor spinning. The sugar surfaces were characterized by AFM(Veeco-Digital Instruments, Santa Barbara, CA; dimension 3000),giving an rms roughness of �1 nm. The coated surfaces were keptin a desiccator under reduced pressure overnight. Two such sur-faces were then installed into the SFA, facing each other in a crossedcylinder configuration (cylinder radii R � 2 cm), which is locally thesame as a sphere-on-sphere or a sphere-on-flat geometry. Onceinside the SFA, the glucose films were further dried by purging withdry N2 gas. The SFA box was well sealed with a small container ofP2O5 inside to maintain dryness.

Loading–unloading cycles were carried out by pressing thesurfaces together under a load, keeping them in contact fordifferent times, then separated at various unloading rates, dL/dt orL, until they completely detached. During these loading–unloadingprocesses, the film thickness and contact diameter were measured(recorded) in real time using the FECO optical interferencetechnique, which also allows one to observe the surface shapechanges, laterally on the microscale and normally on the nanoscale.

The experimental procedure involved driving the bottom surfacetoward the top surface until the two surfaces came into contact. Thesurfaces were then pressed together and kept in contact fordifferent times, tc. After this ‘‘contact time,’’ the adhering (and nowpartially fused) surfaces were separated at various rates until theydetached. The experiments were conducted at three temperatures:T � 23, 40, and 75°C. At these three temperatures, bulk glucose (Tg� 38°C) is in the glassy, viscoelastic, and fluid states, respectively(compare Fig. 1).

The FECO fringes and top-view microscope images were con-tinuously recorded at all stages of the approach, coalescence,loading, contact, separation, and detachment of the surfaces. Thecontact diameters 2r were measured both by the FECO fringes andby direct visualization of the surfaces using the top-view micro-scope. Both methods gave the same results within the errors of themeasurements (�5%).

We thank James Langer and Robert McMeeking for helpful discussionsand Greg Carver for technical assistances. This work was supported bythe Materials Research and Science Engineering Center Program of theNational Science Foundation under Award No. DMR05-20415. B.Z. wassupported by a Natural Sciences and Engineering Research Council ofCanada postdoctoral fellowship award, and Y.T. was supported by aTsinghua University Huaxin Distinguished Scientist Scholarship.

1. Larson RG (1999) The Structure and Rheology of Complex Fluids (Oxford Univ Press, NewYork), pp 3–18.

2. Edgeworth R, Dalton BJ, Parnell T (1984) Eur J Phys 5:198–200.3. Johnson KL (1985) Contact Mechanics (Cambridge Univ Press, Cambridge, UK), pp 84–152.4. Israelachvili JN (1992) Intermolecular and Surface Forces (Elsevier, London), pp 312–337.5. Maugis D, Barguins M (1978) J Phys D 11:1989–2023.6. de Gennes PG (1996) Langmuir 12:4497–4500.7. Baljon ARC, Robbins MO (1996) Science 271:482–484.8. Zeng H, Maeda N, Chen N, Tirrell M, Israelachvili JN (2006) Macromolecules 39:2350–2363.9. Shull KR, Chen WL (2000) Interface Sci 8:95–110.

10. Luengo G, Pan J, Heuberger M, Israelachvili JN (1998) Langmuir 14:3873–3881.11. Maeda N, Chen N, Tirrel M, Israelachvili JN (2002) Science 297:379–382.12. Chen N, Maeda N, Tirrel M, Israelachvili JN (2005) Macromolecules 38:3491–3503.13. Zosel A (1998) Int J Adhes Adhes 18:265–271.14. Creton C, Hooker J (2001) Langumir 17:4948–4954.15. Crosby AJ, Shull KR (1999) Adhesive Age 42:28–33.16. Poivet S, Nallet F, Gay C, Fabre P (2003) Euro Phys Lett 62:244–250.17. Shull KR, Creton C (2004) J Poly Sci B 42:4023–4043.18. Weast RC (1986) Handbook of Chemistry and Physics (CRC, Boca Raton, FL), 66th Ed, p F-40.19. Edwards WP (2000) The Science of Sugar Confectionery (R Soc Chem, Cambridge, UK).

20. Fox C (1995) Science 267:1922–1923.21. Johnson KL, Kendall K, Roberts AD (1971) Proc R Soc London Ser A 324:301–313.22. Yoshizawa H, Chen Y, Israelachvili JN (1993) J Phys Chem 97:4128–4140.23. Van Oss CJ (1994) Interfacial Forces in Aqueous Media (Marcel Dekker, New York), p 181.24. Parkes GS, Reagh JD (1937) J Chem Phys 5:364–367.25. Zhang BM, Chaudhury MK (1997) Langmuir 13:1805–1809.26. Zeng H, Zhao B, Tian Y, Tirrell M, Leal LG, Israelachvili JN (2006) Soft Matter,

10.1039/B613198k.27. Frankel F, Whitesides GM (1997) On the Surface of Things (Chronicle Books, San

Francisco).28. Harver JAF, Cebon D (2003) J Mater Sci 38:1021–1032.29. Crosby AJ, Shull KR (1999) Adhesive Ag 42:28–33.30. Saffman PG, Taylor G (1958) Proc R Soc London Ser A 245:312.31. Chen, Y.-L., Larson RG, Patel SS (1994) Rheol Acta 33:243–256.32. Archer LA, Ternet D, Larson RG (1997) Rheol Acta 36:579–584.33. Chan DYC, Horn RG (1985) J Chem Phys 83:5311–5324.34. Zeng H, Tirrell M, Israelachvili JN (2006) J Adhes 82:933–943.35. Willet CD, Adams MJ, Jonson SA, Seville JPK (2000) Langmuir 16:9396–9405.36. Maeda N, Israelachvili JN, Kohonen MM (2003) Proc Natl Acad Sci USA 100:803–808.37. Israelachvili JN (1973) J Colloid Interface Sci 44:259–272.

Zhao et al. PNAS � December 26, 2006 � vol. 103 � no. 52 � 19629

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