Influence of Nanoscale Surface Roughness on Colloidal Force

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Influence of Nanoscale Surface Roughness on Colloidal Force Measurements Yi Zou, Sunil Jayasuriya, Charles W Manke, and Guangzhao Mao Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.5b02672 • Publication Date (Web): 03 Sep 2015 Downloaded from http://pubs.acs.org on September 8, 2015

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Influence of Nanoscale Surface Roughness on Colloidal Force Measurements Yi Zou,1 Sunil Jayasuriya,2 Charles W. Manke, 1 and Guangzhao Mao1,* 1

Department of Chemical Engineering and Materials Science, College of Engineering, Wayne

State University, 5050 Anthony Wayne Drive, Detroit, MI 48202 2

BASF Corporation, 1609 Biddle Avenue, Wyandotte, MI 48192

*

To whom correspondence should be addressed. E-mail: [email protected].

KEYWORDS: Colloidal probe microscopy, direct force measurement, surface roughness, polystyrene latex, colloidal dispersion

1 ACS Paragon Plus Environment

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ABSTRACT Forces between colloidal particles determine the performances of many industrial processes and products. Colloidal force measurements conducted between a colloidal particle AFM probe and particles immobilized on a flat substrate are valuable in selecting appropriate surfactants for colloidal stabilization. One of the features of inorganic fillers and extenders is the prevalence of rough surfaces - even the polymer latex particles, often used as model colloidal systems including the current study, have rough surfaces albeit at a much smaller scale. Surface roughness is frequently cited as the reason for disparity between experimental observations and theoretical treatment but seldom verified by direct evidence. This work reports the effect of nanoscale surface roughness on colloidal force measurements carried out in the presence of surfactants. We applied a heating method to reduce the mean surface roughness of commercial latex particles from 30 nm to 1 nm. We conducted force measurements using the two types of particles at various salt and surfactant concentrations. The surfactants used were pentaethylene glycol monododecyl ether, Pluronic® F108, and a styrene/acrylic copolymer Joncryl® 60. In the absence of the surfactant, nanometer surface roughness affects colloidal forces only in high salt conditions when the Debye length becomes smaller than the surface roughness. The adhesion is stronger between colloids with higher surface roughness and requires a higher surfactant concentration to be eliminated. The effect of surface roughness on colloidal forces was also investigated as a function of the adsorbed surfactant layer structure characterized by AFM indentation and dynamic light scattering. We found that when the layer thickness exceeds the surface roughness the colloidal adhesion is less influenced by surfactant concentration variation. This study demonstrates that surface roughness at the nanoscale can influence colloidal forces significantly and should be taken into account in colloidal dispersion formulations.


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INTRODUCTION Colloidal stability is essential for dispersion formulations in food, pharmaceuticals, adhesives, coatings, inks, and paints.1, 2 Colloidal forces impact dry powder handling, transport, blending, and fluidization. Colloidal dispersions are commonly stabilized by surfactants of polymeric, nonpolymeric, ionic, or nonionic in nature. The adsorbed surfactant layer provides electrostatic and steric barriers against colloidal coagulation and aggregation. Dispersion formulations can be guided by knowledge of interparticle force-versus-distance curves, for example, the use of adhesion minima to predict degrees of particle coagulation and sedimentation rates. The interparticle forces are generally described by the theory of Derjaguin, Laudau, Verwey, and Overbeek (DLVO), which consists of the attractive Van der Waals term and the repulsive electrostatic double-layer term.3 The actual surface forces may deviate from the DLVO prediction due to surface roughness, which changes the local distance between the two surfaces and non-uniform surface charge density.4, 5 Surface roughness can influence particle deposition on surfaces, colloidal stability, and flow through porous media.6, 7, 8 Surface roughness has been frequently cited as the reason for disparity between experimental observations and theoretical treatment but is seldom verified by direct evidence. A few studies went further by subjecting the particles to surface treatment potentially leading to lower surface roughness and demonstrating better agreement of their behavior with theoretical predictions. However, even model particles, such as the frequently used monodisperse styrene lattices, exhibit substantial surface roughness to cause order-of-magnitude discrepancies between measured forces and DLVO predictions.5 AFM using colloidal probes (colloidal probe microscopy or CPM) has become a valuable tool for direct measurements of force-versus-distance curves with a variety of microparticles including polystyrene.9, 10 While most of the studies have shown agreements with the DLVO


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theory, deviations from the theory have been observed particularly when the separation distance is small (< 3 nm),9, 11 salt concentration is high (> 1 M),12, 13 and the surface roughness effect is non-negligible. For example, CPM measurements between an iron oxide particle and a flat silica surface showed that the magnitude of the adhesion is significantly less than the DLVO prediction.14 The discrepancy has been attributed to a large effective separation at contact as a result of the surface roughness. In the same study, it has been found that the pull-off force increases with the loading force. In another CPM study between a silica particle and a planar silica surface, adhesion between surfaces with non-negligible double-layer interactions is lower than the theoretical value;15 however in this case the difference has been attributed to a shortrange repulsive hydration force, ~ 1 nm, and not the surface roughness. The adhesion between smooth silica particles measured by the CPM has been shown to increase with particle radius16 consistent with the Johnson, Kendall, and Roberts (JKR)17 and Derjaguin, Müller, and Toporaov (DMT)18 models. However, the adhesion measured between carbonyl iron powder particles showed no correlation with the particle radius, which has been attributed to the higher surface roughness of the carbonyl iron powder.19 Theoretical modeling of the surface roughness effect has shown that at large separations, surface roughness has a greater impact on the electrostatic repulsion by reducing the secondary potential energy minimum and moving it to larger separation distances; and at smaller separations, surface roughness has a greater impact on the Van der Waals attraction by lowering the height of the primary barrier to coagulation.20 On the other hand, the adhesion force between rough particles may be overestimated due to the reduced area of contact between asperities if using a contact area value calculated from the overall particle radius.1 Others have attributed the reduction in the van der Waals force between rough


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surfaces compared with smooth surfaces to the surface roughness as a diffuse film accounted in the Lifshitz continuum theory.21 In order to better understand surface roughness effect on colloidal forces, it is necessary to isolate the surface roughness contribution from other variables by using model colloids with well defined surface roughness. In this study, polystyrene latex particles with 1 nm surface roughness were prepared from commercial polystyrene particles - a common probe material used in CPM. We conducted CPM measurements using commercial polystyrene particles with a diameter of 15 µm and root-mean-square (RMS) surface roughness of 30 nm (denoted here as PSR) and heattreated polystyrene particles with roughness reduced to 1 nm (denoted here as PSS). The two types of particles are otherwise identical to each other and thus afford us a simple model system to investigate the effect of nanoscale surface roughness on colloidal force measurements. Approaching and retracting force curves between pairs of PSR and PSS were measured in various salt and surfactant solutions. The surfactants used were monomeric nonionic surfactant pentaethylene glycol monododecyl ether (C12E5), polymeric nonionic surfactant poly(ethylene oxide)x–poly(propylene oxide)y–poly(ethylene oxide)x (Pluronic® F108), and polymeric ionic styrene/acrylic surfactant Joncryl® 60. C12E5 is a common surfactant whose phase and adsorption behaviors have been extensively studied.22, 23 F108 is a surfactant used widely in consumer and industrial products as foaming agents, wetting agents, dispersants, and thickeners.24 Joncryl 60 is used for coating, emulsion, pigment dispersion, and in new flexo inks. The results show that surface roughness at the nanoscale can influence colloidal forces significantly and should be taken into account in colloidal dispersion formulations.

EXPERIMENTAL


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Materials. Deionized water with 18 MΩ·cm resistivity (Nanopure system, Barnstead) was used. Grade 2 muscovite mica was purchased from Mica New York and hand-cleaved just before use. Polystyrene latex suspensions (1.0 wt%) containing particles of 15 µm in diameter were purchased from Polyscience. The suspension was dialyzed in order to remove soluble impurities. GC grade C12E5 (98%) was purchased from Sigma-Aldrich and used as received. Pluronic F108 and Joncryl 60 were provided by BASF and used as received. The chemical structures of the three surfactants are shown in Scheme 1.

Scheme 1. Chemical structures of C12E5 (top), Pluronic F108 (middle), and Joncryl 60 (bottom). Reduction of colloidal surface roughness by heating. The surface roughness of polystyrene latex particles was reduced by heating above its glass transition temperature (~ 105°C). The polystyrene particles diluted to 0.01-0.001 wt% were cleaned by serum replacement (centrifugation), dialysis, and ion exchange. The cleansed polystyrene particles were further


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diluted with deionized water to approximately 0.005 wt% in a stainless steel bomb, and the bomb was placed in an oven at 120°C in N2 for different lengths of time. Agglomeration was not observed by optical microscopy due to low particle concentration used. Polystyrene particles with the lowest surface roughness were obtained after 4 h in the oven and were used in this study together with untreated particles. AFM imaging. AFM imaging was conducted using VEECO Dimension 3100 with a G scanner. The particle morphology was determined by AFM height, amplitude, and phase images in the tapping mode in ambient air. Uncoated silicon probes (TESP, VEECO) with a factoryspecified spring constant of 40 N/m, length of 125 µm, width of 40 µm, and nominal probe radius of curvature less than 10 nm were used. The scan rate used is in the range of 0.1-1.0 Hz with a scan size range of 1-30 µm. Integral and proportional gains are approximately 0.1-0.4 and 0.2-0.8, respectively. Images were analyzed using the Nanoscope software from Digital Instruments (Version 5.12). The surface roughness was determined using the root-mean-squared roughness RMS=[Σ(zi2/N)] 1/2 where zi is the height value of each measurement point and N is the number of measurement points. The zi values are height deviations taken from the mean data plane. The mean is calculated by the average of all the z values within the enclosed area. All RMS values reported were obtained on AFM height images of size 500×500 nm2. CPM. Colloidal probes were prepared following the literature.11 Epoxy glue (Epo-Tek377, Epoxy Technology) was heated in water bath at 80°C for 30 min in order to reach an appropriate viscosity. A small amount of the glue was transferred to a glass slide. A tip-less AFM cantilever (PNP-TR-TL-20, Nanoandmore) was moved, using the Dimension 3100 automatic stage as a micro-manipulator, first to contact the glue and then a polystyrene particle so that the particle was glued to the end of the cantilever. Only 10 µL or less glue is needed in this operation. The


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colloidal probe was placed in a desiccator for at least 24 h before use. A typical colloidal probe constructed is shown in Figure 1.

Figure 1. SEM image of a polystyrene colloidal probe. The bar length is 10 µm.

The AFM force-versus-distance curves were obtained in the liquid contact mode using the force calibration command between the colloidal probe and the colloids immobilized on mica or glass. The colloids were glued on the solid substrate using epoxy. When the probe was brought to rest in a close proximity to the colloidal layer on the substrate and was equilibrated for 1 h at 25°C before each measurement. It was reported that Pluronic surfactants reached adsorption plateau after 30 min.25 We found no variation in adsorbed structure for all three surfactants studied after 1 h adsorption time. Liquid in the amount of 100 µl was injected into the liquid cell. The center-to-center alignment of the two colloids was conducted first by a coarse alignment using the integrated optical microscope followed by a fine alignment using the AFM height images. After the coarse alignment several AFM height images were taken at different spots close to the center of the colloid in question, and the spot that gave the best fit between the top portions of the height image and those of an ideal spherical cap shape was chosen for subsequent force measurements. The alignment error of this procedure was estimated to be less than 50 nm 8 ACS Paragon Plus Environment

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for 15 µm particles. In one study using 4.8 and 6.9 µm colloids,26 the force curves showed no changes when the center of one colloid was moved 200 nm off the center of the other colloid. Therefore we conclude that our measurements accurately represent colloidal forces between particles aligned along their central axes. Each force curve reported here has been compiled from 20 or more force measurements. The force calibration curves are typically plotted as the photodiode signal (in volts) versus piezoelectric scanner position (in nanometer). The force calibration curves were converted to the force-versus-distance curves by defining sensitivity, zero force (F = 0), and zero separation (D = 0). The sensitivity in nm/V was obtained from the slope of the constant compliance regime of the retraction curve and was multiplied by the raw voltage value to yield the cantilever deflection, ZC. The force is F = k ⋅ ZC . k is the spring constant of the cantilever. The nominal spring constant provided by the manufacturer is 0.08 N/m. We measured the spring constant of the colloidal probe with the attached polystyrene colloid in deionized water using the Thermal Tune command by Bruker, which is based on the thermal noise method.27, 28 The measured value is 0.088 ± 0.018 N/m (N = 6), and 0.09 N/m was used here. Zero force was determined by identifying a linear region at large separation where the deflection is constant. Zero separation was determined from the constant compliance region at high force where the deflection was linear with the expansion of the piezoelectric crystal. When the separation is zero, it is assumed that the two PS colloids are in hard contact. In the nonlinear regime, the separation distance D = ∆(piezo position)-ZC. Surface roughness contributes uncertainty and error in zero separation determination and there is no simple solution to this problem.29 AFM force measurements were conducted in the surfactant solution on the immobilized colloidal layer in order to determine the adsorbed surfactant layer thickness and apparent elastic


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modulus. The force calibration curves were converted to the force-versus-indentation curves. The contact point, i.e., δ = 0, is defined as the point where the force becomes repulsive. The indentation into the surfactant layer is defined as (Eqn.1):

∆ ( piezo position ) − ZC (ZC > 0) (ZC = 0) 0

δ =

Eqn. 1 .

The adsorbed layer thickness was estimated at the point of the hard-contact (constant compliance). It is noted that AFM force measurements sometimes underestimates the film thickness due to incomplete penetration by the AFM probe into the adsorbed layer down to the bare substrate. This underestimation was estimated to be about 1-2 nm for Pluronics.30 There is also uncertainty in the probe/layer contact point determination. We determined the contact point as follows. In the CPM the contact point was determined as the intersection between the extrapolation of the non-contact regime and constant compliance regime. Dynamic light scattering (DLS). The polystyrene latex diameter in different surfactant solutions was determined by DLS (Zetasizer Nano ZS, Malvern). For the DLS and zeta potential measurements smaller polystyrene particles (100 nm in diameter) were used. The effective hydrodynamic radius (RH) was measured. The backscattering angle Θ was fixed at 180° with a laser wavelength λ = 633 nm. The size measurement range was set between1 nm and 6 µm. RH is a function of the diffusion coefficient (D), temperature (T), and viscosity (η) according to the Stokes-Einstein equation (Eqn. 2): RH =

kT . 6πηD

Eqn. 2

k is Boltzmann constant, T is 25°C, and D was obtained from autocorrelation function via the cumulant fitting. The electrophoretic mobility of the 100 nm latex particles was measured using the laser Doppler velocimetry and phase analysis light scattering technique of the Malvern 10 ACS Paragon Plus Environment

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Zetasizer. The electrophoretic mobility was converted into zeta potential using the Smoluchowski equation using the Malvern software.31

RESULTS AND DISCUSSION Characterization of polystyrene particles with different surface roughness. The colloids glued to the mica were imaged by AFM. Figure 2 shows the AFM images (high and low magnifications) of untreated colloids (a−b) and colloids heated for 4 h (c−d) and 12 h (e−f). The colloids heated for 4 h exhibited the lowest surface roughness with an RMS = 1.0 nm. The untreated colloids have an RMS of 30.0 nm and the colloids heated for 12 h have an RMS of 2.0 nm. Both the treated and untreated colloids exhibited uniform surface roughness values across the whole particle surface. Small particulates were seen on the colloids heated for 12 h. Similar debris have been found by others and attributed to small precursor particles formed during the latex synthesis.32 In the following experiments, two types of colloids were used: smooth colloids after 4 h heating (denoted as PSS) and untreated colloids (denoted as PSR).


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a)

b)

c)

d)

e)

f)

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a

a

Figure 2. AFM height images of the PS spheres: a−b) untreated colloids (scan size and z range for a) are 15µm and 2µm, respectively, and for b) are 750 nm and 20 nm, respectively); c−d) colloids heated for 4 h (scan size and z range for c) are 20 µm and 2 µm, respectively, and for d) are 1 µm and 20 nm, respectively; and e−f) colloids heated for 12 h (scan size and z range for e) are 20 µm and 5µm, respectively, and for f) are 1.5 µm and 30 nm, respectively).

Surface roughness effect on surface force profiles in the absence of the surfactants. First, we compare force curves between a colloidal probe, PSR or PSS, and mica in deionized water with or without 1 mM NaCl. The approaching force (F) divided by the colloidal probe radius R versus separation distance (D), F R vs. D, curves are plotted in Figure 3. The curves were fitted with the DLVO theory (Eqn. 3):3, 33 F R=−

A 128πnkT + Γ1Γ2 exp(− κD) . 2 κ 6D

Eqn. 3


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We assume a non-retarded Van der Waals interaction, the Derjaguin approximation for a sphere (1) with radius R interacting with a surface (2) at small D and a constant surface potential. R was fixed at 7.5 µm. A is the Hamaker constant and was fixed at 6.1×10-21 J for mica-waterpolystyrene and 9.5×10-21 J for polystyrene-water-polystyrene.34, 35 k is the Boltzmann constant. T is temperature (= 298 K). 1/κ is the Debye length. n is the bulk electrolyte concentration.  ze Ψ1  .  zeΨ 2 Γ1 = tanh   Γ2 = tanh  4 kT    4 kT

 . z is ionic valence. e is the charge constant of an electron. Ψ  1 

is the surface potential of the colloid, which was adjusted in our fitting procedure. Ψ2 is the surface potential of the mica, which was fixed at -63 mV based on the literature value36 in order to obtain more accurate fit. The linear superposition approximation was used here that assumes the midplane potential (not the surface potential) is less than 25 mV. We also followed the method of incorporating surface roughness into the DLVO calculations with the surface roughness modelled as a probability distribution.4 In Figure 3, the F/R data for PSS-Mica and PSR-Mica in deionized water were fitted with the smooth DLVO interaction potential given in Eqn. 3. A nonlinear regression fit using the Debye length and PS surface potential as the adjustable parameters yielded best-fit values of (1/κ) = 28 nm and Ψ1 = -4.95 mV. The smooth DLVO force potential with these parameters gives an excellent fit to both the PSS-mica and the PSR-Mica F/R data in deionized water. There is no apparent effect of surface roughness for the PSR-Mica force curve in deionized water. The fitted Debye length also corresponds to a higher ionic strength than the theoretical value expected for the measured deionized water pH of 5.6. The higher than expected ionic strength is likely due to electrolyte contamination in the measurement cell. In contrast to the deionized water data, the F/R curves for PSS and PSR in 1mM NaCl exhibit a clear separation from each other that can be explained by accounting for surface roughness. 13 ACS Paragon Plus Environment

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The F/R data for PSS-Mica in 1mM NaCl is very well fitted by Eqn.3, with a Debye length of 7.7 nm, which is in reasonable agreement with the expected Debye length of 9.6 nm for 1mM ionic strength, and Ψ1 = -4.95 mV. The Ψ1 value is identical for deionized water and 1 mM NaCl. To describe the F/R data for PSR-mica, we followed the literature method4 by multiplying the exponential part of the interaction potential in Eqn. 3 by the factor exp(σm2κ/2) to represent the effect of Gaussian-distributed surface roughness for the case where the separation distance D is greater than σm2κ. Using the values (1/κ) = 7.7 nm and Ψ1 = -4.95 mV, which were determined from the F/R data for PSS-mica in 1 mM NaCl, σm was optimized as the single adjustable parameter in a nonlinear regression fit of the F/R data for PSR-mica in 1 mM NaCl, yielding a best-fit roughness value σm = 7 nm. The fit of this roughened DLVO force curve to the F/R data for PSR-mica in 1 mM NaCl is excellent.

F/R (µN/m)

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80

PSS no salt Series1

70

PSR no salt Series2

60

PSS 1mM NaCl Series4

50

Series5 PSR 1mM NaCl

40

Series6 Fitting curves

30 20 10 0 5

25

45

65

85

Separation (nm)

Figure 3. Approaching force curves between PSS (or PSR) probe and mica in deionized water and 1 mM NaCl. The solid lines are DLVO fits of the experimental data.

The data suggest that an increase in surface roughness from 1 to 30 nm only affects force measurements in higher salt conditions in which 1/κ values becomes comparable to the surface roughness. In other words, the surface roughness is covered up by a thick double-layer in low 14 ACS Paragon Plus Environment

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salt and in high salt when the double-layer becomes thinner the surface roughness emerges. Similar observations were made in AFM force measurements between pairs of silica colloids, which revealed the failure of the DLVO theory to predict the electrostatic potentials at high ionic strength (> 5 mM KNO3).13 The jump-in distance, defined by the jump-in point where the force curve becomes discontinuous, for PSS is 7.6 ± 1.3 nm in deionized water and 6.0 ± 0.6 nm in 1 mM NaCl, while it increased to 12.5 ± 3.1 nm in deionized water and 12.2 ± 1.0 nm in 1 mM NaCl for PSR. The standard deviation for jump-in distance was calculated based on 20 force curves. The data show that the net attraction shifts to a longer range with increasing surface roughness. Next we present approaching force curves measured between a pair of colloids of either the PSS type or the PSR type (Figure 4). The nanometer surface roughness appears to affect force curves in both low salt (deionized water) and high salt (1 mM NaCl) conditions. The jump-in distances, marked by the arrows in Figure 4, are 6.6 ± 1.0 nm in deionized water and 5.9 ± 1.3 nm in 1 mM NaCl for PSS and 12.9 ± 3.4 nm in deionized water and 15.1 ± 2.6 nm in 1 mM NaCl for PSR. Here the surface roughness affects the particle/particle attraction in both low and high salt conditions. The pull-off force corresponding to the maximum adhesive force in the retracting force curve (not shown) is 3.4 ± 0.5 nN for PSS and 37 ± 8 nN for PSR (Table 1). The particle/particle adhesion increases with surface roughness. We observe little effect by salt on the particle/particle adhesion measurements. One of the most commonly used models to describe adhesion between colloidal particles containing nanoscale roughness is the Rumpf37 or the modified Rumpf model shown below (Eqn. 4): 38

Fadhesion =

AR 1 1 ( + ). 2 12 H 0 1 + R /1.48RMS (1 + 1.48RMS / H 0 )2

Eqn. 4


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The first term is the interaction of the adhering particle in contact with a single hemispherical asperity. The second term is the interaction between the adhering particle and the surface with the asperity separated by the height of the asperity. H0 is the contact distance, which is defined as the closest approach between the two surfaces. For polystyrene, it was reported to be 0.28 nm according to single crystal X-ray diffraction.39 Thus, the modified Rumpf model predicts Fadhesion = 2.3 nN for RMS = 1 nm and 0.9 nN for RMS = 30 nm (A is assumed to be 9.5×10-21 J and R is assumed to be 7.5 µm). The Rumpf prediction matches closely the experimental value between PSS but not that between PSR. The disparity may result from the fact that the Rumpf model does not consider multi-point contacts between opposing particles. On the other hand, our results of increased adhesion with increasing surface roughness are consistent with other theory modeling surface roughness as hemispherical asperities of fixed radius20 and experimental observations.40, 41, 42, 43

In addition to surface roughness (or local curvature at the area of contact) the pull-off

force is generally a function of the compressive force during approach and the physical properties of the particles including Young’s modulus, Poisson’s ratio, surface hardness, interfacial energy, and radius of the particle.1 Both JKR and DMT models indicate

Fadhesion ∝ a ∝ E −2/3 ,44 where a is contact area and E is Young’s modulus. In an indentation study,45 the apparent Young’s modulus is 0.3 GPa for an outer rough layer and 4 GPa for the inner core material. Thus, PSR may appear to have a smaller E and undergoes a higher degree of deformation, which may contribute to a stronger adhesion.46


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50

S no salt PS Series1

Jump in

R no salt PS Series3

40 F/R (µN/m)

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S 1mM NaCl PS Series5

30

R 1mM NaCl PS Series7

Fitting Series8 curve

20 10 0 5

25

45

65

85

Separation (nm)

Figure 4. Approaching force curves between a colloidal probe and an immobilized colloid on a flat substrate of either the PSS or PSR type. The solid lines are DLVO fits of the experimental data.

Surfactant

Adsorption layer thickness h (nm)

Elastic modulus (MPa)

Adhesion force (nN) for PSS

Adhesion force (nN) for PSR

No surfactant

0

0

3.4±0.5

37±8

C12E5 0.2%

2.5±0.3

0.20±0.05

0

2.0±0.3

C12E5 1%

3.1±0.1

0.25±0.04

0

1.0±0.4

C12E5 5%

3.0±0.2

0.26±0.04

0

0.5±0.1

F108 0.2%

11±1

0.46±0.01

0

0

F108 1%

12±0.5

0.48±0.01

0

0

F108 5%

16±1

0.47±0.02

0

0

Joncryl 60 0.2%

5.0±0.8

0.66±0.02

0

46±10

Joncryl 60 1%

8.0±0.5

0.69±0.04

0

0.10±0.03

Joncryl 60 5%

10±1

0.88±0.08

0

0

Table 1. List of layer thickness, elastic modulus, and adhesion values extracted from AFM force curves measured between the two types of polystyrene particles with different surface roughness.

The force curves between two polystyrene colloids were fitted using Eqn. 5 assuming a nonretarded Van der Waals force, Derjaguin approximation for two identical spheres of radius R:3 F R=−

A 64πnkT 2 + Γ1 exp(− κD ) . 2 12 D κ

Eqn. 5


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For PSS, the fitted Debye length and surface potential are 32.9 nm and -22.8 mV in deionized water, and 9.0 nm, -15.7 mV in 1 mM NaCl. For PSR, the fitted Debye length and surface potential are 26.0 nm, -22.9 mV in deionized water and 11.6 nm and -13.8 mV in 1 mM NaCl. Here the surface roughness effect predicted by the statistically distributed surface roughness was not present in the F/R data between two PS particles.

Surface roughness effect on surface force profiles in the presence of surfactants. Three surfactants were used in this study: nonionic non-polymeric C12E5, nonionic polymeric Pluronic F108, and anionic and polymeric Joncryl 60. The force curves were measured in three weightbased concentrations relevant to industrial use: 0.2%, 1%, and 5%. The CMC values at 25°C of C12E5 and F108 are 2.8×10-5 g/ml21, 22 and 4.5×10-2 g/ml,24 respectively. Other CMC values of F108 have been reported.47, 48 Here we chose one of those reported numbers. Pluronic surfactants such as F108 display aggregation over a range of concentration. It is common to report the limiting aggregation concentrations as their CMC values. We measured the CMC of Joncryl 60 using the surface tension measurement (Figure 5). The CMC of Joncryl 60 was determined to be 2×10-4 g/ml. The CMC was determined from a plot of surface tension vs. log(surfactant concentration). In the case of most commercial surfactants and particularly commercial polyelectrolytes (such as Joncryl 60), one would always observe a curved region in the plot near the CMC. In these cases, a common strategy, which is used here, is to use the intersection of the two linear segments of the semi-logarithmic plot as the CMC value. The concentrations used, 0.20%, 1%, and 5% are 71, 357, and 1786 times the CMC for C12E5, 0.04, 0.22, and 1.1 times the CMC for Pluronic F108, and 10, 50, and 250 times the CMC for Joncryl 60. In this concentration range, the adsorbed surfactant layer coexists with the micellar phase in solution for C12E5 and Joncryl 60. In the case of F108, its CMC is in the concentration range used.


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Surface tension (mN/m)

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75.00 70.00 65.00

Joncryl 60

60.00 55.00 50.00 45.00 40.00 1.00

10.00

100.00

1000.00

Concentration (mg/L)

Figure 5. Surface tension measurement for Joncryl 60. We consider the approaching force curves between a pair of colloidal particles, either the PSS or PSR type, in the presence of a surfactant solution to contain two repulsive force terms, a longrange electrostatic force term (Felec) and a short-range steric repulsion term (Fsteric).49, 50 The force curves measured here do not generally display an attractive force portion as reported by others because our measurements were conducted in the surfactant solution rather than in deionized water or salt solution. The force curves presented here are dominated by steric and electrostatic repulsions. Figure 6 is a force curve measured between two PSS particles in 5% F108. It seems to display two exponentially dependent regimes that correspond to one dominated by the steric repulsion and the other by electrostatic repulsion. Since F108 polymer segments are uncharged, the electrostatic portion either comes from the charges of the underlying substrate or the presence of micelles in the solution. Therefore, we fit our data using the biexponential equation (Eqn. 6) in which the Felec and Fsteric terms are expressed by Eqn. 7 and Eqn. 8, respectively: F Felec + Fsteric = R R

Eqn. 6

 zeΨ  −1 Felec = k e exp (− κD ) = 64πRnkT tanh 2  κ exp (− κD )  4 kT 

Eqn. 7


Langmuir

Fsteric = k s exp (− D λ )

Eqn. 8

The fitting parameters are listed in Table 2. Eqn. 7 contains assumptions similar to those made in Eqn. 3. In Eqn.8, ks is related to the surfactant layer packing density, and λ is a characteristic decay length corresponding to a brush layer thickness.51 In the case of C12E5, ks is smaller for PSR indicating more disordered layer due to surface roughness. The force curves measured in 5% C12E5 contain a significant contribution from micelles in solution as indicated by the unreasonably high value of the Debye length. This further indicates that our “Electrostatic” term may be dominated by surface interactions due to micelles in the solution than an actual electrostatic force. There does not seem to be a significant impact by surface roughness in the F108 solution. However the smaller ks values for F108 indicate that the polymeric surfactant is less densely packed than the monomeric surfactant C12E5. Surface roughness has a significant impact on the interactions between the polystyrene colloids in the ionic Joncryl 60 solution. The force curves measured in 0.2%, 1%, and 5% are different between pairs of PSS and PSR. In the case of 1% and 5% Joncryl 60 solutions the Felec term drops to zero due to high ionic strength. Series1 PSS in 5% F108 Series2 Fsteric Series3 Felec

100 F/R (µN/m)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Series4 Ftotal

10

0 1

20

40

60

80

100

Separation (nm)

Figure 6. Semi-logarithmic plots of colloidal force measurement and biexponential model fitting for PSS in 5% Pluronic F108 solution. The lines are model-based fitting curves.


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The adhesion measured by the pull-off force during retraction of PSS probe from PSS-covered substrate was reduced to zero by all three surfactants in 0.2% solution. But when the same force measurements were conducted between the PSR colloids, the adhesion was reduced to zero only in 0.2% solution of F108. The adhesion values in 0.2%, 1%, and 5% C12E5 are 2.0 ± 0.3 nN, 1.0 ± 0.4 nN, and 0.5 ± 0.1 nN, respectively. The adhesion values in 0.2%, 1%, and 5% Joncryl 60 solution are 46 ± 10 nN, 0.1 ± 0.03, and 0, respectively. The data show that surfactant performance in preventing colloidal adhesion could be impacted by surface roughness at the nanoscale.52 Higher amounts of surfactants may be necessary to achieve the same degree of colloidal stability when the colloids have a rougher surface. The surface roughness effect differs among the three surfactants. It has more significant effect on C12E5 and Joncryl 60 than on F108 as seen from the ks and ke values given in Table 2. This suggests that molecular packing in the adsorbed F108 layer is less disturbed by local topography of the adsorbed surface as well as by the pressure applied by surface asperities from an approaching colloid. It is also important to consider the molecular weight (Mw) and hence the Rg value difference among the three materials: F108 (Mw = 14,600), Joncryl 60 (Mw = 8,500), and C12E5 (Mw = 390). One possible reason for this observation is the closeness of the Rg value of single F108 chains to the dimensions of the asperities resulting in possible “masking”. It is also important to note that in our study, Joncryl 60 and C12E5 are at concentrations far above their CMC values containing association structures (micelles) with much larger dimensions than observed layer thickness values. This indicates that the surfactants used in this study do not adsorb as micelles on the polystyrene surface. The presence of micelles in solution also prevents accurate estimation of the Debye length using Eqn. 7; particularly, in the case of C12E5 and 5% F108, the model fitting gave unreasonable high Debye length values clearly indicating the failure of Eqn. 7 in concentrated solutions.


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PSS

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PSR

ks (nN)

λ (nm)

ke (nN)

ks (nN)

λ (nm)

ke (nN)

C12E5 0.2%

13.5

2.06

0.08

4.77

1.28

0.10

C12E5 1%

13.7

2.04

0.10

4.05

1.51

0.14

C12E5 5%

7.72

3.50

0.24

23.2

1.42

0.15

F108 0.2%

3.39

2.07

0.59

2.72

4.90

1.52

F108 1%

2.43

3.08

0.52

2.40

2.63

0.39

F108 5%

1.58

5.91

0.34

2.39

4.29

0.14

Joncryl 60 0.2%

0.34

1.52

1.50

39.2

1.16

0.32

Joncryl 60 1%

14.1

2.04

0

7.17

0.704

0

Joncryl 60 5%

15.9

2.48

0

1.26

1.42 S

0 R

Table 2. Fitting parameters of force curves using PS and PS in various surfactant solutions fitted to the biexponential model.

Surfactant adsorbed layer structure. It is commonly assumed that thicker and more rigid surfactant layers are more efficient in stabilizing colloid dispersions. The nanoindentation experiments provide direct measurements of two parameters: thickness (h) and Young’s modulus (E) of the adsorbed layer. Quantitative evaluation of both parameters can predict dispersant performance. Nanoindentation experiments were conducted to determine h and E of the adsorbed surfactant layer using normal AFM probes with a nominal radius of curvature of 10 nm and a spring constant of 0.1 N/m. The indentation force curves are shown in Figure 7. The thickness of the adsorbed layer was determined by the maximum indentation, for example, the layer thickness was determined to be 16 nm in the case of 5% F108 (Figure 7a). All the measured adsorbed layer thickness values are given in Table 1. The C12E5 adsorbed layer thickness was determined to be 2.5−3.1 nm in the concentration range of 0.2−5%, which is slightly less than the adsorption layer thickness reported by others.53 The elastic modulus of the C12E5 layer is in the range of 0.20−0.26 MPa. Since all the measurements were conducted in solutions with concentrations above the 22 ACS Paragon Plus Environment

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CMC the adsorbed layer structure of C12E5 did not vary in the measured concentration range. The Hertz model (Eqn. 9) is commonly used in nanoindentation experiments to determine the E value:54

F=

4 E R 3/2 δ 3(1 − σ 2 ) ,

Eqn. 9

where F is applied force, R is probe radius, σ is Poisson’s ratio, and δ is the indentation distance. Eqn. 9 is only valid for thick films. For thin physisorbed films a modified Hertz model (Eqn. 10 and 11) containing a correction term, β, is used:55 F=

(

4E

31−σ 2

1/ 2 3 / 2

)R

δ

β.

Eqn. 10

β = 1+ 0.884χ + 0.781χ 2 + 0.386χ 3 + 0.0048χ 4 with χ = Rδ / h .

Eqn.11

h is the adsorbed layer thickness. E was calculated from the slope of Eqn. 10 plot in which a Poisson’s ratio of 0.5 was used. An example of the data fitting is given in Figure 7b by fitting the nanoindentation curve measured in 0.2% Pluronic F108 with the modified Hertz model. The fitted E values are listed in Table 1. The standard deviation is as high as 0.05 MPa, as a result of the small thickness and low modulus, and was also reported by other researchers.55,

56

The

application of the Hertz model has been widely used to analyze AFM nanoindentation data on adsorbed polymer films both by others and our group.57,

58, 59, 60, 61

In particular, a similar

approach was used by others to determine the Young’s modulus of a thin polyethylene glycol (PEG) monolayer with thickness less than 20 nm.57 The Young’s modulus is comparable to the values measured for much thicker brush structure. In another work of AFM force measurements conducted on adsorbed surfactants at concentrations above the CMC,59 a modified Hertz model


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for thin films was applied and a direct correlation between variation in surfactant density and apparent elastic modulus was discussed. F108 shows a film thickness around 13 nm and a slight trend of thickness increase with concentration. The Young's modulus of the adsorbed F108 layer also shows a weak dependence on concentration consistent with pseudo adsorption plateau associated with polymer adsorption. In comparison, the moduli of adsorbed poly(N-isopropylacrylamide), polyethylene glycol (PEG, 20 kDa), and PEG (35 kDa) were reported to be 0.12−0.15 MPa,62 0.09 MPa,56 and 0.15 MPa,63 respectively. In the case of Joncryl 60 both the thickness and Young's modulus of the adsorbed layer increased with increasing concentration. The Young’s modulus of Joncryl 60 is higher than those of C12E5 and F108 due to the ionic nature of the surfactant. Our values are within the range reported for other surface-grafted acrylic acid layers.64 The increase in its concentration causes an increase in the ionic strength, which results in a reduction in the Debye length and increase in Joncryl 60 chain flexibility. This allows Joncryl 60 molecules to pack more closely on the surface. The increased adsorption and packing density result in an increased rigidity of the Joncryl 60 layer with increasing concentration. The nonionic surfactants, on the other hand, maintain similar adsorbed structure in different concentrations. It can be concluded that surfactant concentration has a stronger impact on adsorbed layer structure in ionic surfactant systems than nonionic surfactant systems.


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Series1 C12E5 0.2%

a) 1.6

Series2 C12E5 1% Series3 C12E5 5%

Force (nN)

1.2

Series7 Joncryl 60 0.2% Series8 Joncryl 60 1%

0.8

Series9 Joncryl 60 5% Series4 F108 0.2% Series5 F108 1%

0.4

Series6 F108 5%

Thickness≈16 nm

0 0

b)

4 8 12 Indentation (nm)

16

0.2 0.16

Force (nN)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.12 0.08 0.04 0 0

200 400 16 R1/2δ3/2β (nm2) 9

600

Figure 7. a) AFM force curves between an unmodified AFM probe and polystyrene particles immobilized on mica measured in various surfactant solutions. The line was drawn to give an example of how the adsorbed layer thickness was determined from the indentation curve. b) Determination of the apparent Young’s modulus in 0.2% Pluronic F108 using the modified Hertz model. The slope (= 0.46 MPa) of the fitted line is the apparent Young’s modulus.

The adsorbed layer thickness was also measured by DLS. For the DLS measurements we used 100 nm in diameter polystyrene particles instead of the 15 µm ones used in AFM force measurements. The thickness determined from the hydrodynamic radius, δH, of the adsorbed layer was calculated by subtracting the hydrodynamic diameter of the bare latex particle from that of the same particle in the presence of surfactant solution. Table 3 summarizes the 25 ACS Paragon Plus Environment

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hydrodynamic diameter and zeta potential values of 100 nm polystyrene in various surfactant solutions. The hydrodynamic thickness results agree with the AFM measurements for C12E5 and Joncryl 60 but not F108. F108 adsorbed layer structure has been extensively studied. In a study using photon correlation spectroscopy, the adsorption isotherm of F108 on polystyrene latex particles was determined.65 The adsorbed layer thickness was determined by hydrodynamic radius measurements on both bare and polymer-coated particles to be 10-14 nm in the pseudo adsorption plateau concentration range of (0.5-5)×10-4 g/ml. There is a slight increase in the adsorbed layer thickness with concentration. Another detailed study of F108 adsorption on latex reported similar adsorbed layer thickness of 11±1 nm.66 Our AFM values are within the range of these reported data but our DLS data do not match. The discrepancy may be caused by the difficulty of interpreting DLS data in the presence of surfactant micelles. It is likely that the microviscosity in the vicinity of the adsorbed layer is much higher in more concentrated polymer solution than the bulk value used in the hydrodynamic radius calculations. This leads to higher computed hydrodynamic radius values resulting from the use of lower viscosity values in Eqn. 2. The zeta potential of 100 nm polystyrene latex, -44 mV, is more negative than those values obtained from the CPM force curves on 15 µm latex. It is possible that different polystyrene particles exhibit different zeta potential values. In the presence of surfactants, the electrokinetic mobility equation of Smoluchowski, which was used here to extract the zeta potential values, does not take into account of complexities arising from particles covered by a soft shell of polymer brushes.67 To fit our data using the more accurate dynamic electrophoretic mobility equations is beyond the scope of this paper. We generally observed a decrease in the apparent zeta potential values with increasing surfactant concentration for nonionic C12E5 and F108 indicating the increasing importance of the Donnan potential and the surface potential at the


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boundary between the brush and the surrounding surfactant solution. However, in the case of polyelectrolyte Joncryl 60, the apparent zeta potential became more negative with increasing concentration, which is consistent with increasing surface charge with increasing Joncryl 60 surface adsorption. Surfactant

Zeta potential (mV)

Surfactant layer thickness δH (nm)

None

-44.5

0

C12E5 0.2%

-23

2.5

C12E5 1%

-10.4

2.6

C12E5 5%

-0.4

3.4

F108 0.2%

-21

7.8

F108 1%

-13.7

24.2

F108 5%

-4

46.5

Joncryl 60 0.2%

-23.4

8.5

Joncryl 60 1%

-31.6

10.4

Joncryl 60 5%

-58.6

11.6

Table 3. Zeta potential and layer thickness measured by the zetasizer on 100 nanometer polystyrene particles. The layer thickness was determined by the difference between the hydrodynamic radius in the presence of the surfactant and particle radius in the absence of the surfactant (= 54.4 nm).

CONCLUSIONS CPM was used to study the surface roughness effect on colloidal forces and colloidal stabilization by surfactant adsorption. We conducted CPM measurements between commercial polystyrene particles with a diameter of 15 µm and root-mean-square (RMS) surface roughness of 30 nm and heat-treated polystyrene particles with roughness reduced to 1 nm. Approaching and retracting force curves were measured in various salt and surfactant solutions. The surfactants used were: non-polymeric nonionic surfactant pentaethylene glycol monododecyl ether (C12E5), polymeric nonionic surfactant poly(ethylene oxide)x–poly(propylene oxide)y– 27 ACS Paragon Plus Environment

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poly(ethylene oxide)x (Pluronic F108), and polymeric ionic styrene/acrylic surfactant Joncryl 60. In the absence of the surfactants, nanometer surface roughness affects colloidal forces only in high salt conditions when the Debye length becomes smaller than the linear dimension of the surface roughness. On the other hand, the adhesion was found to be stronger between rougher colloids. The adhesion was reduced to zero by all three surfactants above a critical solution concentration. Under otherwise identical conditions, a higher surfactant concentration was necessary in order to eliminate the adhesion between PSR than PSS. We also found that surfactant concentration has a stronger influence on the adsorbed surfactant layer structure of ionic surfactants than that of the nonionic ones. The measured range of steric repulsion for the surfactants provides important information for designing formulations with targeted properties. Such information is valuable for polymeric dispersants, particularly, polyelectrolytes such as Joncryl 60 whose behavior is not readily amenable to interpretation by available theories. This study demonstrates that surface roughness even at the nanoscale can influence colloidal forces significantly and should be taken into account in colloidal dispersion formulations. It may be possible to select appropriate surfactant solutions in colloidal dispersion by direct particle/particle force measurements and by considering the relative scale of the surfactant molecular structure and surface roughness.

ACKNOWLEDGEMENTS We acknowledge the financial support from the National Science Foundation (CBET−0553533, CBET−0619528, and CBET−0755654) and BASF (Pigments and Dispersions Technology).


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Influence of Nanoscale Surface Roughness on Colloidal Force

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