ARTICLE pubs.acs.org/Langmuir
Lubrication, Adsorption, and Rheology of Aqueous Polysaccharide Solutions Jason R. Stokes,*,§,|| Lubica Macakova,§ Agnieszka Chojnicka-Paszun,†,‡ Cornelis G. de Kruif,‡,^ and Harmen H. J. de Jongh† †
TI Food & Nutrition, P.O. Box 557, 6700 AN Wageningen, The Netherlands Van’t Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands § Unilever Corporate Research, Unilever R&D Colworth, Colworth House, Sharnbrook MK44 ILQ, United Kingdom School of Chemical Engineering, University of Queensland, Brisbane, Queensland 4072, Australia ^ Texture Department, NIZO Food Research, Kernhemseweg 2, P.O. Box 20, 6710 BA Ede, The Netherlands
)
‡
ABSTRACT:
Aqueous lubrication is currently at the forefront of tribological research due to the desire to learn and potentially mimic how nature lubricates biotribological contacts. We focus here on understanding the lubrication properties of naturally occurring polysaccharides in aqueous solution using a combination of tribology, adsorption, and rheology. The polysaccharides include pectin, xanthan gum, gellan, and locus bean gum that are all widely used in food and nonfood applications. They form rheologically complex fluids in aqueous solution that are both shear thinning and elastic, and their normal stress differences at high shear rates are found to be characteristic of semiflexible/rigid molecules. Lubrication is studied using a ball-on-disk tribometer with hydrophobic elastomer surfaces, mimicking biotribological contacts, and the friction coefficient is measured as a function of speed across the boundary, mixed, and hydrodynamic lubrication regimes. The hydrodynamic regime, where the friction coefficient increases with increasing lubricant entrainment speed, is found to depend on the viscosity of the polysaccharide solutions at shear rates of around 104 s-1. The boundary regime, which occurs at the lowest entrainment speeds, depends on the adsorption of polymer to the substrate. In this regime, the friction coefficient for a rough substrate (400 nm rms roughness) is dependent on the dry mass of polymer adsorbed to the surface (obtained from surface plasmon resonance), while for a smooth substrate (10 nm rms roughness) the friction coefficient is strongly dependent on the hydrated wet mass of adsorbed polymer (obtained from quartz crystal microbalance, QCM-D). The mixed regime is dependent on both the adsorbed film properties and lubricant’s viscosity at high shear rates. In addition, the entrainment speed where the friction coefficient is a minimum, which corresponds to the transition between the hydrodynamic and mixed regime, correlates linearly with the ratio of the wet mass and viscosity at ∼104 s-1 for the smooth surface. These findings are independent of the different polysaccharides used in the study and their different viscoelastic flow properties.
1. INTRODUCTION Polysaccharides are high molecular weight polymers that are abundant in plants and animals. They are widely used in food and many other consumer products as water-soluble thickening and gelling agents for stabilization and texture control.1 They also modify the mouthfeel of foods and beverages, which is considered to be associated with their lubrication properties.2 Polysaccharides are used in many nonfood applications. For example, r 2011 American Chemical Society
they are used during oil recovery and drilling processes where the adsorption of polymers to pipe surfaces is considered to improve the lubricity characteristics of the drilling fluid.3,4 Polysaccharides can also be used to stabilize mineral dispersions, where their Received: October 7, 2010 Revised: February 1, 2011 Published: March 02, 2011 3474
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Langmuir adsorption and lubrication at particle surfaces are anticipated to influence their flow properties at high particle volume fractions.5 While the general rheological properties of polysaccharides have been extensively investigated,1 there are relatively few studies that evaluate their effectiveness as aqueous lubricants across the three lubrication regimes (boundary, mixed, hydrodynamic) in tribological contacts in combination with an evaluation of their adsorption properties and their rheological behavior under the high shear rate conditions present in tribological contacts. We show that anionic polysaccharides do enhance the lubrication of aqueous fluids across the three lubrication regimes present within low-pressure tribological contacts through both viscosity modification and by adsorbing to hydrophobic substrates. Our lubrication studies utilize low-pressure contact (i.e., softlubrication) that is typical for biotribological application so that the pressure in the contact does not affect the fluid's rheological properties. While our original motivation is in determining the physical basis for the mouthfeel of foods, where lubrication is a factor, the results of the study have elucidated new insights into the properties of polysaccharides in solution in general that has wider implications. The results highlight how aqueous lubrication depends on the molecular characteristics, rheology, and adsorbed film properties of the polymers. There are only a few studies that have investigated the influence of polysaccharides on the lubrication of aqueous solutions in soft-tribological contacts that have been primarily aimed toward applications in the food industry; these studies seek to probe the influence of the polymers on the three tribological regimes of boundary, mixed, and hydrodynamic lubrication due to their potential relevance on the behavior of foods during oral processing. For example, in studying sensory properties of foods, Malone et al.2 considered that “oral slipperiness” perception of guar solutions was related to the mixed-regime friction coefficient between a steel ball and rough-elastomeric plate. Using the same tribopair, Cassin et al.6 showed that increasing concentrations of guar polysaccharide and pig gastric mucin glycoprotein decreased the friction coefficient in the mixed regime due to adsorption and viscous effects. The measured friction coefficient was related to the adsorption properties of the polymers investigated with evanescence wave spectroscopy. The lower boundary friction coefficient observed for mucin solutions than water was attributed to the formation of a thin, adsorbed layer of mucin. In addition, guar showed similar boundary lubrication to water because it did not adsorb to the surface. However, in the mixed-lubrication regime (i.e., transition regime between boundary and hydrodynamic lubrication), guar reduced the friction coefficient.6 De Vicente et al.7 also observed a decrease in friction in the mixed regime with increasing concentration of the polysaccharides xanthan gum and guar, as well as for synthetic polyethylene oxide. It was concluded that this is caused primarily by hydrodynamic and viscous forces, and they used an effective viscosity to collapse the data to a single Stribeck curve whereby the friction coefficient is plotted as a function of entrainment speed multiplied by the effective viscosity in the contact. Furthermore, de Vicente et al.7 determined the shear rates present in the contact gap to be between 104 and 106 s-1. Both studies of Cassin et al.6 and de Vicente et al.7 demonstrated that high-shear viscosity plays an important role in determining the dynamics in the soft-tribological contact within the mixed regime, but neither study measured the actual viscosity at shear rates relevant to tribological studies of beyond 1000 s-1. However, to truly rationalize these previous results in terms of fluid (lubricant)
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material properties, it becomes necessary to decouple the relevant roles of the high-shear viscosity and adsorbed film properties on the friction coefficient measured within the mixed regime; this is one of the aims of our study. The boundary lubricating behavior of a few polysaccharides has been investigated using nanotribological configurations in the surface force apparatus (SFA) and atomic force microscope (AFM). For example, an anionic polysaccharide from algae was recently shown to be an effective aqueous lubricant in tribological contacts between ceramic tribopairs and steel-polyethylene tribopairs, and that it was a superior lubricant to hyaluronic acid that is often targeted as a biolubricant between human/artificial joints.8 Surprisingly, this anionic polysaccharide adsorbs to mica surfaces as a relatively mobile film that exhibits a low friction coefficient (0.015) when confined to less than 1 nm; this result is in contrast to studies on other polyelectrolytes and proteins that lubricate through the presence of thick “polymer brush” layers.9 Other studies on polysaccharides have investigated in detail the lubricating and adsorption properties of hyaluronic acid and chitosan.10-12 Hyaluronic acid is not a very effective lubricant when physiosorbed to surfaces, although it was somewhat more effective when cross-linked into a gel and confined in the SFA,10 while chitosan was effective when freely adsorbed under very low-pressure conditions but not when confined as a cross-linked gel. The effective boundary lubrication of physiosorbed chitosan was attributed to “weak interpenetration between the layers arising from steric effects and counterion osmotic pressures, together with the presence of hydration sheaths about the charged polyelectrolyte,”11 but no complementary adsorption studies were conducted to give additional information on the properties of the adsorbed layer. Another recent study combining tribological and adsorption studies involving polysaccharides showed that adsorbing numerous alternating layers of crosslinked chitosan and hyaluronic acid creates a very effective boundary film that is resistant to wear as well as resistant to biofouling from proteins that is necessary in biotribology applications such as coating of medical prostheses and implants, contact lenses, catheter tubes, and artificial joints.12 Adsorption studies using the quartz crystal microbalance showed that these were adsorbed and bound to the surface as hydrated viscoelastic film. It was concluded that the high charge density and electrostatic repulsion between opposing surfaces enabled the film to remain hydrated as well as provide an effective barrier to asperity contacts and wear under load.12 Multilayer adsorption of anionic mucin and cationic chitosan has also been characterized nanotribologically, but these were not as effective as single layers of either mucin or chitosan; this was due to interlayer bridging between the tribopair in the mixed layer that is not apparent for the individual polymers.13,14 It is generally considered that when a polymer is strongly bound through electrostatics or covalent bonding, the degree of hydration of the polymer as well as the presence of hydrated ions determines the boundary friction coefficient for aqueous systems.12,15-18 However, in studying the glycoprotein mucin, Lee and Spencer17 found that the mucin studied was more lubricating in the neutral state, which suggests that lubrication from macromolecules is also related to adsorption energy, polymer conformation, and dynamics (including wear) of the adsorbed film. In a study by Yakubov et al.,19 the boundary friction coefficient between relatively rough elastic surfaces lubricated by mucin solutions was dependent on polymer concentration, but no significant enhancement was found for smooth 3475
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Table 1. Description of the Polysaccharides Used in This Study ionic charge densitya
Mw (kDa)b
conc (%)c
strength (mS/cm)
pH
pectin
0.29
170
1.27
0.65
3.8
from fruit and vegetables, used in food as a gelling
xanthan gum
0.25
4200
1
0.3
6.9
bacterial polysaccharide, used in bakery products, beverages, sauces,
LBG
0
1500
0.48
0.15
6.9
galactomannan, extracted from the seed of the tree used in dressing, desserts cream, instant
gellan gum
0.25
1400
0.54
0.50
5.5
products, ketchup, pet food, cream filling, cream cheese bacterial polysaccharide, used as a emulsifier and stabilizer, thickener,
κ/ι-carrageenan
0.7
580
0.91
0.75
7.0
from the seaweeds, used as a gelling agent for jellies and puddings,
polymer
characteristic/application
agents, thickener, water binder, stabilizer emulgator, dressings-thickener, stabilizer, provides “fat-feel” in low/no-fat dairy products
in the jelly desserts, fruit preparations, dairy products thickening agent for soups and sauces, as stabilizer in ice cream, whipped cream, etc. a
Charge density in mol/mol monosaccharide; all charged polysaccharides given in this table carry negative charges, from de Jong and van de Velde.20 b Weight average molecular weight distribution as determined by SEC-MALLS from de Jong and van de Velde.20 c Concentrations used in this work.
surfaces. The effectiveness of mucin to lubricate rough surfaces was hypothesized to be due to a viscous boundary layer from mucin adsorbing to the surface, and this was supported by correlating the friction to the adsorbed film thickness measured using optical waveguide light spectroscopy in a separate experiment involving flow of mucin across a smooth hydrophobic surface. Collectively, these studies highlight the importance of hydration of adsorbed polymer films on lubrication. The objective of the present study is to probe the lubrication properties of various polysaccharide solutions within low-pressure tribological contacts using both smooth and rough substrates. We take the novel approach of decoupling the influence of fluid rheology and adsorbed film properties. This primarily involves characterization of their lubrication properties using a soft elastomeric sphere and a flat disk in a mixed sliding/rolling contact mimicking biotribological contacts. As opposed to previous tribological studies, we fully characterize the viscosity and normal stress differences (measuring fluid elasticity) up to shear rates of order 105 s-1. In addition, we utilize both quartz crystal microbalance and surface plasmon resonance to fully characterize the adsorbed polysaccharide film that allows the adsorbed mass, film thickness, hydration, and viscoelasticity to be determined.
2. MATERIALS AND METHODS Materials. Sugar syrup (67 Brix) was kindly provided by Cosun (Roosendaal, The Netherlands). Low acryl gellan gum (Kelcogel F), xanthan gum (Keltrol T), GSK-carrageenan (C-122, κ/ι-hybrid carrageenan extracted from Gigartina skottsbergii), locust bean gum (C-130, LBG), and high methyl ester (HM) pectin (H-6, 71% DE) were kindly donated by CP Kelco Inc. (Lille Skensved, Denmark). Chemical composition of these polysaccharides was previously reported by de Jong and van de Velde.20 All ingredients were used without further purification and without correction for their moisture content. The molecular weight and charge density of the biopolymers used in this study are listed in Table 1. Sample Preparation. Two types of solutions were used in this study: (i) Newtonian solution. The lubricants consist of aqueous sugar syrup or glycerol solutions. Newtonian fluids at various concentrations were obtained at ambient temperature by mixing the solutions with demineralized and filtered (Millipore) water. (ii) Shear thinning polysaccharide solution. We chose a range of biopolymers that varied in charge density, molecular weight, and
conformation, as listed in Table 1. In this way, we anticipated to obtain an understanding of the rheology, lubrication, and adsorption properties of commonly used food biopolymers. All polymer solutions were prepared at ambient temperature, by hydrating the appropriate amount of the material in demineralized and filtered (Millipore) water for approximately 3 h. Subsequently, solutions were heated at 80 C for 45 min under continuous stirring; these conditions are typical of those used in preparing polysaccharides within the food industry for optimizing degree of solvation. After heating, the polysaccharide solutions were cooled to room temperature, stored at 4 C, and used within 2 days after preparation. Table 1 lists the polysaccharides and their final concentrations used in this study. These concentrations were chosen based on a previous rheological study that considered them to possess the same viscosity at 50 s-1 at 20 C (Anke Janssen, personal communication). Note that this shear rate was chosen as a common basis for comparison because the viscosity obtained at 50 s-1 is often considered by food scientists to be appropriate for assessing oral thickness perception.21 Rheological Measurements. The rheological properties of all solutions investigated in this study were recorded at 25 C using a standard rheometer (AR 2000, TA Instruments, Leatherhead, U.K.). Aluminum parallel-plate geometry with 40 mm diameter was used to measure the viscosity and normal stress differences (i.e., fluid nonlinear elasticity) of the solutions at gap heights of 30 and 50 μm from low to high shear rates (beyond 105 s-1). Parallel-plate geometry was chosen in order to obtain flow curves up to extremely high shear rates with a similar accuracy to the more usually preferred cone-and-plate geometry, following the procedures of Davies and Stokes.22,23 To reduce the gap error that arises in parallel-plate measurements, the gap is zeroed at a load of 5 N. The gap error for this set of experiments was typically around 10 μm. Tribological Measurements. The lubrication properties of all aqueous solutions used in this study were measured at 25 C with a mini traction machine (MTM, PCS Instruments Ltd., U.K.). Following Bongaerts et al.,24 the MTM was modified using a compliant poly(dimethylsiloxane) (PDMS) ball and flat PDMS disk (PDMS was obtained from Dow Corning under the trade name Sylgard184). The radius of the PDMS sphere and disk was 9.5 mm and 23 mm, respectively, with the thickness of the latter element of 4 mm. Young’s modulus (E) of the PDMS material was 2.4 MPa.24 In order to investigate the effect of the surface roughness on the lubrication properties of polysaccharide solutions, two types of the PDMS disks were used that differed in roughness. The root-mean-square (rms) of asperities was equal to 8.6 and 382 nm for the smooth and rough PDMS disks, respectively. 3476
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Langmuir Prior to the experiments the PDMS surfaces were cleaned in an ultrasonic bath with isopropanol, followed by rinsing with demineralized filtered water (Millipore). After such treatment, the surface of the PDMS element retained its natural, hydrophobic characteristic. New PDMS surfaces were used for each measurement. The friction was determined as a function of the applied entrainment speed (U) in a range between 1 and 750 mm/s, while the applied load (W) was set to W = 1 N and the slide to roll ratio (SRR) equal to 50%. The SRR is defined as the ratio of the absolute value of sliding speed, |uball - udisk| to the entrainment speed, U = (uball - udisk)/2, where uball and udisk are the surface speeds of the ball and disk, respectively.25 Friction coefficient (μ) was measured at least three times for every speed and averaged. While data were measured starting from high-to-low speeds and followed by low-to-high speeds, only data obtained from decreasing speed are discussed here, since curves showed negligible hysteresis. This negligible hysteresis was also an indicator that no substantial wear of the PDMS took place. Our previous study on aqueous lubrication also indicated that the PDMS tribopairs were not susceptible to wear under the conditions studied.24 Stribeck master curves for aqueous Newtonian lubricants were obtained using water, corn-syrup-water and glycerol-water, and these are found to be similar to those previously obtained by Bongaerts et al.24 This is obtained by plotting the friction coefficient as a function of Uη and fitting the following equation to the data:24 ! hðUηÞl - gðUηÞn n ð1Þ μtot ¼ gðUηÞ þ 1 þ ðUη=BÞd h and l are a coefficient and power law index for the boundary regime, respectively; g and n are the coefficient and power law index for the elastohydrodynamic (EHL) regime, respectively; B is effectively the transition value of Uη between the boundary and mixed regimes, and d is another power law index; η is the viscosity in the contact zone. Using U in mm/s, the fitting values found for the smooth surface are n = 0.46, g = 0.0027, h = 4.73, l = 0.19, B = 0.035, and d = 2.06; and for the rough surface, these values are n = 0.46, g = 0.0028, h = 1.26, l = 0.0044, B = 0.24, and d = 2.35. These were similar to the values obtained by Bongaerts et al.24 for the same smooth and “medium-rough” surfaces, and hence, the data has not been shown for brevity. These master curves are included as a line on all subsequent plots of friction coefficient against the product of speed and viscosity. Adsorption Measurements. The properties of the adsorbed boundary films were determined using a combination of quartz crystal microbalance with dissipation function and surface plasmon resonance techniques. In order to mimic a surface chemistry that reflects the MTM experiments, Sylgard184 PDMS was spin coated from a 5% solution in toluene onto the gold working electrode of the Q-sense crystal or onto substrate of the SPR chip following the procedure detailed by Macakova et al.26 After coating for 15 s at 3000 rpm, the substrates were left to cure overnight in the oven set to 120 C and then cleaned in isopropanol and deionized water in the same way as MTM disks and spheres. The polysaccharides were allowed to adsorb at the substrate from their solutions for 25 min. This time equals the time between introducing the solutions into the MTM measuring chamber (i.e., starting the experiment) and reaching the boundary lubrication regime.
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recorded in the form of changes of a resonance frequency and a dissipation of the oscillation energy of the piezoelectric quartz resonator. Baseline corresponds to the values recorded in deionized water. The temperature of the measuring chamber was stabilized at 25 C, with the solution flow rate of 50 μL/min. The polysaccharide solution was left in contact with the substrate for 25 min, and then excess polymer was rinsed with deionized water. The relation between the change of detected signal and the properties of the adsorbed film is not straightforward, and a theoretical model has to be applied in order to resolve them. In an approach developed by Voinova et al.,28 the quartz resonator is assumed to be purely elastic and the adsorbed film is modeled as a Voigt viscoelastic element with a complex elasticity modulus Gf defined as Gf ¼ μf þ i2πf ηf ¼ Gf 0 þ iGf 00
where μf is the film shear elasticity modulus, f is the sensing frequency, ηf is the film viscosity, Gf0 is the apparent film storage modulus and Gf00 is the apparent film loss modulus. Beside the basic resonance frequency, odd overtones were also detected (3rd, 5th, 7th, 9th, and 11th). The data were numerically fitted to obtain the film thickness, shear elasticity modulus, and viscosity assuming a film density of Ff = 1100 kg/m3, using a commercially available program, Q-tools. The adsorbed mass was obtained as mVoigt ¼ hf Ff
ð3Þ
where hf is the thickness obtained from the fit to Voigt model and Ff is the input density. The Voigt mass and the adsorbed film’s shear elasticity modulus and viscosity are nearly independent of the choice of input density (in reasonable limits, e.g., between 1010 and 1500 kg/m3); however, the fitted film thickness is inversely proportional to the chosen density.28,29 Surface Plasmon Resonance (SPR). The Biacore 2000 (Biacore AB, Uppsala, Sweden) instrument was used, which is an SPR instrument operating in Kretchman configuration. The gold coated sensor chips were purchased from GE Healthcare (SIA kit Au). The main principles of SPR are explained in detail elsewhere.30,31 In brief, at the chip’s surface, the light is reflected under total internal reflection conditions. The angle of a minimum reflection, the SPR angle θ, is detected, which changes upon adsorption at the interface or change of the bulk solvent. The baseline was recorded in deionized water. During SPR experiments, the temperature was set to 25 C and the flow rate to 10 μL/min. The flow was stopped 5 min after polysaccharide solutions were introduced into the measuring chamber (when the onset of the adsorption plateau was observed) and was resumed during rinsing by deionized water after allowing 25 min for adsorption. Hydration of the Adsorbed Film. While SPR is sensitive to the “dry” mass of the film related to refractive index changes, QCM-D is sensitive to the hydrated “wet” mass of the film, since the water trapped within the film affects its viscoelastic properties. This water can be attributed to the “bound water” involved in hydration shells associated with the adsorbed molecules as well as to the “mechanically trapped water” within the topological irregularities of the film.32-34 The relative solvent content (w) in the film was calculated as w ¼ 100%
Quartz Crystal Microbalance with Dissipation Monitoring (QCM-D). The viscoelastic properties of the adsorbed film were probed by the quartz crystal microbalance with dissipation monitoring technique (QCM-D) using a Q-Sense instrument, model E4 (Q-Sense, Vastra Frolunda, Sweden) with a peristaltic pump maintaining the flow of the liquids through the measurement chamber. We used gold coated AT cut quartz sensors (Q-sense, QSX 301-standard gold) with a nominal resonance frequency of 5 MHz, which were spin coated by a thin hydrophobic layer of PDMS. The experimental setup and basic principles are explained in detail elsewhere.27 The QCM-D signal was
ð2Þ
ðmVoigt - mSPR Þ mVoigt
ð4Þ
where mVoigt and mSPR are the adsorbed masses determined by QCM-D and SPR, respectively.
3. RESULTS AND DISCUSSION Rheology. Figure 1 shows the flow curves of polysaccharide solutions and Newtonian sugar syrup obtained using the parallelplate geometry at a gap of 50 μm. While most studies on the 3477
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Figure 1. Measured viscosity as a function of shear rate of the polysaccharide solutions and 97% corn syrup at 25 C using parallel-plate geometry at gap height of 50 μm. Polymer concentrations are listed in Table 1.
rheology of polysaccharides focus on shear dependent viscosity up to shear rates of around 1000 s-1,1,35 we have obtained both the viscosity and the viscoelasticity (i.e., normal stresses) for shear rates up to 105 s-1 that are relevant to tribological studies. All polysaccharide solutions investigated show non-Newtonian shear thinning behavior that typically arises due to alignment and disentanglements of the long polymer chains. All solutions have essentially the same viscosity at a shear rate of around 100 s-1 (η ∼ 0.11 ( 0.03 Pas) at 25 C; this is a marginally higher shear rate than the expected consistency at 50 s-1 due to a lower temperature of 20 C being used in the preliminary studies. Figure 2 shows the elasticity of the polymer solutions in the form of normal stress differences (N1 - N2) obtained at high shear rates; note that N2 is generally regarded as zero for polymer solutions so that (N1 - N2) can be considered as equivalent to N1 (see Davies and Stokes22,23). The normal stresses were also measured for the Newtonian syrup and found to give scattered values about zero, thus providing confidence that the normal stresses for the polymer solutions are free from methodological or instrumental artifacts. While polysaccharides are generally regarded as semiflexible or semirigid molecules, at high shear rates they are considered to favor an ordered configuration.35 For example, xanthan gum is a particularly stiff molecule35 with a persistence length of order 1000 nm and diameter 2 nm,36 and this has previously been shown to display nonlinear viscoelastic and extensional properties characteristic of the rigid dumbbell model.36,37 We show here that all our polysaccharide solutions exhibit normal stress values with relatively low power law dependence (index < 1) at high shear rates, which is characteristic of rigid rodlike molecules;36-40 flexible polymers generally exhibit a quadratic dependence with shear rate, although this can decrease to a linear dependence at high shear rates.37 Therefore, a rigid dumbbell model suitable for high shear rates was fitted to the data:39 N1 ¼ 1:2nkTðλD γÞ2=3
ð5Þ
Figure 2. Measured normal stress differences (N1 - N2) of the polysaccharide solutions (Table 1) at 25 C with parallel-plate geometry at gap height of 50 μm, showing normal stress differences (N1 - N2). The lines are fits to rigid dumbbell model assuming N2 = 0 and fitting relaxation times λD (see listed relaxation times in Table 2).
Table 2. Relaxation Time (λD) of the Polysaccharide Solutions Calculated from the Rigid-Dumbbell Model polysaccharide pectin
λD (ms) 0.10
xanthan LBG
101.28 27.53
gellan gum
2.26
κ/ι-carrageenan
2.72
where relaxation time λD is the free parameter and n, k, T, and γ_ are the number density of molecules, Boltzmann’s constant, temperature, and shear rate, respectively. The model follows the data points reasonably well, with the fits shown in Figure 2 and corresponding relaxation times listed in Table 2. The longest relaxation time (and thus the most elastic fluid) was obtained for xanthan gum solution, which also had the lowest viscosity at high shear rates. Tribology. Smooth Substrates. Figure 3a displays the friction coefficient of the polysaccharide solution as a function of the entrainment speed measured using the smooth PDMS disk. The data show clear differences in measured Stribeck curves between the polysaccharide solutions. At increasing values of entrainment speed, the friction coefficient decreases to a minimum and then increases with increasing speed; this is indicative of the mixed and hydrodynamic regimes, respectively. At the lowest speed, LBG is the least lubricating while pectin is the most lubricating. However, at the highest speeds, the polysaccharides are difficult to distinguish. To decouple the influence of viscosity and surface effects on the Stribeck curves, the data is replotted in Figure 3b to show the friction coefficient as a function of Uηeff. An effective viscosity term ηeff is used as an estimate of the viscosity in the contact by fitting the hydrodynamic portion of the Stribeck curves to that of 3478
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Table 3. List of Parameters Determining the Friction Coefficient-Speed Relationship in the Hydrodynamic Regime between Smooth PDMS Tribopairs for the Polysaccharide Solutionsa smooth PDMS polysaccharide ηeff (Pa s) γ_ eff (1/s) min(Uηeff) (N/m) hm (nm) hc (nm) pectin
0.0197
14009
9.8 10-4
613
1261
xanthan
0.0064
11236
2.4 10-3
1101
2149
LBG
0.0059
32304
2.9 10-3
1262
2431
gellan
0.0070
9825
1.4 10-3
776
1562
carrageenan
0.0107
10392
2.1 10-3
1028
2018
ηeff is defined in Figure 3, and the effective shear rate γ_ eff is obtained from ηeff using Figure 1. min(Uηeff) corresponds to the value of Uηeff at the minimum friction coefficient in Figure 3b located at the transition between the mixed and hydrodynamic regimes. The minimum (hm) and central (hc) film thicknesses between surfaces were predicted at the values of min(Uηeff) using eq 6. a
Figure 3. Measured tribological properties of polysaccharide solutions between smooth hydrophobic PDMS tribopairs, showing apparent friction coefficient measured (a) as a function of entrainment speed and (b) as a function of Uηeff, the product of entrainment speed and an effective viscosity. The line is the Newtonian master curve (eq 1) for smooth PDMS surfaces. The effective viscosity (ηeff) is determined for the polysaccharide solutions by overlaying the data in hydrodynamic regime to that of the master curve. The error bars are indicated.
the Newtonian master curve. This is necessary because the exact shear rate in the contact is unknown due to the current inability to routinely measure film thickness directly in soft contacts, although this situation may soon be improved through some recent developments in the area.41-43 According to EHL theory and observations from our previous studies, the friction coefficient in the hydrodynamic regime depends solely on the product of the entrainment speed and the viscosity for constant load and substrate elasticity, and regardless of wetting or roughness.24 The effective viscosity in the contact using this approach is listed in Table 3. Figure 3b shows that the polysaccharides affect the transition point between the mixed and EHL regimes; pectin, gellan, and carrageenan promote full film lubrication at significantly lower values of Uηeff than xanthan gum and LBG. A similar result was previously observed for aqueous surfactant solutions (see Graca et al.44) that was considered to be a surface wetting effect. The transition point for each polymer is listed in Table 3 in terms of
Figure 4. Measured tribological properties of polysaccharide solutions between rough hydrophobic PDMS tribopairs, showing the apparent friction coefficient as a function of entrainment speed. The error bars are indicated.
min(Uηeff). Also listed is the shear rate required to obtain ηeff using the rheology data in Figure 1, which is around 104 s-1 for all samples. In addition, Table 3 presents the predicted “minimum” (hm) and “central” (hc) film thicknesses separating the surfaces at the junction beteen the mixed and elastohydrodynamic regime based on Uηeff and calculated using the model of de Vicente et al.45 that is given as follows: 0:6 W -0:14 0 Uη hc ¼ 3:3R E0 R 0 E0 R 02 hm ¼ 2:8R 0
Uη E0 R 0
0:66
W E0 R 02
-0:22
ð6Þ
E0 and R0 are the reduced elastic modulus and reduced radius defined by 2/E0 = (1 - ν12)/E1 þ (1 - ν22)/E2 and 1/R0 = 1/Rx1 þ 1/Rx2 respectively, where E, ν and, Rx are the elastic modulus, Poisson ratio, and radii in the entrainment direction ,respectively, for the two surfaces. For further discussion on this data, see the 3479
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Table 4. Interfacial Shear Strength (τi, MPa) Fitted to Data in Figure 5 for a Hertzian Contact with E0 = 1.6 MPa, R = 0.0095 m polysaccharide
τi
water
0.15
pectin
0.018
xanthan
0.048
LBG
0.13
gellan carrageenan
0.07 0.0065
Figure 5. Measured friction force versus applied load for polysaccharide solutions and water between rough PDMS surfaces at an entrainment speed of 5 mm/s and slide-to-roll ratio of 50%. Lines correspond to fits for the friction force to W2/3.
following section: Relating Interfacial Film Properties to Lubrication. Rough Substrate. Figure 4 shows the friction coefficient as a function of speed for the rough PDMS tribopair. The results indicate that only the boundary and mixed lubrication regime is observed for all samples. The friction data is approaching a plateau at low entrainment speeds, which is indicative of boundary lubrication; the hydrodynamic pressure is not enough to prevent contact between asperities of the rubber in the measured range of entrainment speeds. At low speeds, LBG and gellan are the poorest lubricants while carrageenan and pectin are the most lubricating; this largely mirrors the results for the smooth surface except that gellan is a poorer lubricant for the rougher contact. Since there is no hydrodynamic regime, there is no anchor in which to normalize the data, and hence an effective viscosity has not been determined. We probe the boundary regime for rough substrates by measuring the friction force as a function of applied load at a constant speed of 5 mm/s, as presented in Figure 5. When water is the lubricant, the friction forces depends on W2/3 across the loads studied, which is the scaling expected for highly compliant surfaces where the area of contact is determined by elastic conformity rather than from plastic deformation of asperities, as observed previously.24,46-49 Since the friction force in the boundary regime is considered to be proportional to contact area as F = τiAt, where τi is the interfacial shear strength between the materials,50 this load dependency is theoretically obtained using the Hertz equation that gives the true contact area for a circular contact as At = π(3WR/4E0 )2/3. While adhesive forces are likely to be present in a PDMS-PDMS contact, the contribution of this to these friction curves appears to be only very small as indicated by an intercept of only 0.2 N friction force for water as zero load is approached, which is within experimental error for the mini-traction machine.
Figure 6. Adsorbed “dry” mass of polysaccharides measured using SPR.
It is also observed that the friction force in the boundary regime for the polymer solutions also has the same W2/3 dependency as water, indicating that the polymers have modified the interfacial shear strength between the substrates, as listed in Table 4, which is likely to arise from an adsorbed polymer layer at the substrate surface. Adsorption, Hydration, and Viscoelasticity of Interfacial Films. To provide more insight into the origin of the lubrication of the polysaccharide solutions, SPR and QCM-D were employed to determine the effective thickness, hydration, and viscoelastic properties of the adsorbed interfacial films. The combination of these two techniques allows the “dry” mass and “wet” mass of the adsorbed film to be determined, and thus the degree of film hydration that has previously been considered influential to boundary lubrication.11 This is anticipated to be directly related to the properties of the thin film that contributes to the boundary and mixed lubrication in the contact zone. In this series of measurements, only four of the polymer solutions were examined at the same concentration as in the tribology and rheology studies: pectin, LBG, xanthan, and gellan gum. Figure 6 shows the adsorbed “dry” mass from SPR measurements. The data shows that a majority of the polymer is adsorbed within 5 min. The adsorbed mass can only be determined following rinsing, since the bulk refractive index contributes to the response. The samples were rinsed 25 min after the beginning of the measurement. This revealed the adsorbed amount of polymers that follows a sequence: pectin . xanthan > LBG, gellan, as listed in Table 5. 3480
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Table 5. Properties of the Adsorbed Polysaccharide Films Interpreted from SPR and QCM-D Measurements solvent/ polysaccharide
QCM (wet) mass (mg/m2)
SPR (dry) mass (mg/m2)
viscosity (mPa.s)
shear modulus (kPa)
hydration (%)
polymer mass ratio
adsorbed film thickness (nm)
pectin
38.67 ( 0.39
3.12 ( 0.31
1.38 ( 0.02
34.2 ( 7.2
92 ( 1
11.39
38.6
xanthan
14.59 ( 1.36
1.63 ( 0.16
1.36 ( 0.02
44.4 ( 1.3
89 ( 2
7.95
14.6
LBG
4.85 ( 0.02
1.01 ( 0.10
2.08 ( 0.02
105.1 ( 4.1
gellan
30.25 ( 0.44
1.01 ( 0.10
1.07 ( 0.01
22.6 ( 0.12
79 ( 2
3.8
4.9
97 ( 1
28.85
30.2
Figure 7. Measured change in frequency (normalized by the overtone number) and dissipation using the QCM-D technique. Different graphs correspond to four specimens: (a) gellan, (b) xanthan, (c) pectin, and (d) LBG.
The “viscoelastic” properties of the adsorbed polysaccharide films are reflected in the QCM-D results (see Figure 7). The baseline corresponds to resonance frequency and dissipation of the clean PDMS modified sensor crystal immersed into deionized water, and rinsing was typically performed at the 25 min time point, removing nonadsorbed polymers. Pectin displays a large variation in the frequency change between different overtones and large dissipation. This illustrates an adsorption of a highly viscoelastic, nonrigid layer. In contrast, the frequency changes sensed for different overtones are similar in the case of the LBG sample. Moreover dissipation of energy by the film is low, indicating that the adsorbed layer is rigid. While film properties were compared for films rinsed by water, it is also interesting to compare the results obtained for substrate in contact with bulk polymer solutions. An initial rapid increase in the dissipation of the oscillation energy is caused mainly by the exchange of the water to polysaccharide solution in the measurement chamber, and it is caused by an increase in the bulk liquid viscosity, elasticity, and density. In the case of gellan and LBG,
the actual adsorbed film formation is a much slower process. Even after 25 min of contact between solution and film, the measured values do not reach any plateau. On the other hand, the layer formation is rapid for pectin and xanthan and takes place on the same time scale as the exchange of water to polysaccharide solution in the QCM-D chamber. Table 5 summarizes the properties of the adsorbed film determined by combining the SPR and QCM-D results: the “wet” mass, “dry” mass, percent hydration, and solvent/polymer mass ratio. These results show that the adsorbed polysaccharide films are highly hydrated, comprising more than 70% water, and the effective density of hydrated films is very close to that of water. Thus, an “effective” thickness of the adsorbed films can be approximated as a ratio between wet mass and density of the water, and follows the order: pectin (38.6 nm) > gellan (30.2 nm) > xanthan (14.6 nm) . LBG (4.9 nm). However, while gellan forms a relatively thick film, it is the most fluidlike of all samples with the lowest apparent film viscosity and shear modulus as it contains 97% water. 3481
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Figure 8. Correlation shown between friction measurements on the smooth tribopair and adsorbed film properties obtained from QCM: (a) (Uη)min from Stribeck friction curve against adsorbed wet mass of polymer (the line has a gradient and intercept of -5.8 10-5 and 0.0032, respectively); (b) equivalent data represented in the form of minimum (hm) and central (hc) film thickness versus adsorbed hydrated film thickness (equivalent to wet mass) (the lines have gradients of -19.5 and -35, and intercepts of 1370 and 2630 nm). The data points from left-to-right correspond to locus bean gum, xanthan, gellan, and pectin.
Relating Interfacial Film Properties to Lubrication. We find that there is a direct relationship between the tribological properties and the effective hydrated film thickness of the adsorbed polymers obtained from QCM-D. Figure 8 shows that, for the smooth PDMS tribopair, the measured value of Uη at the minimum friction coefficient (i.e., the junction between the hydrodynamic and mixed regimes) linearly correlates (negatively) with the wet mass of adsorbed polymer obtained from QCM-D measurements. This is the first time such a connection has been shown between the regime transition points and adsorbed hydrated mass of polymer. To attempt to rationalize this unique correlation, we also plot that same data in the form of the predicted EHL film thickness (ie. gap between surfaces) at (Uη)min and adsorbed polymer film thickness; the correlation coefficient for the linear fits is r2 = 0.998 (it should be noted that the adsorbed film thickness is directly proportional to the wet mass of adsorbed polymer). However, it is noted from Figure 8b that these expected film and adsorbed layer thicknesses differ by 2 orders of magnitude so it is difficult to imagine why they would be related. The adsorbed film thickness though is of similar order to the roughness length scale (∼10 nm), and even small changes in roughness are known to have a substantial effect on this transition point.24,48 We thus currently consider that the adsorbed polymer films reduce the effective roughness of the substrates in combination with enhancing the wetting properties and hydration layer at the substrate surface; both of these effects promote full film lubrication to lower entrainment speeds. Further correlations were investigated between the friction measurements in the boundary-mixed lubrication regimes and the adsorbed film parameters obtained from QCM-D and SPR, although only relatively weak correlations are found (not shown for brevity): • For smooth surfaces, it is found that polysaccharides that formed viscous (low storage modulus) films that had a large thickness are more lubricating; the friction coefficients at each speed in the range of 1-100 mm/s correlate positively with the film storage modulus (average r2 = 0.94, linear correlation) and negatively with the hydrated film thickness
(or wet mass) in the speed range of 10-100 mm/s (average r2 = 0.94, power law correlation). • For rough surfaces, lubrication in the boundary-mixed regime (Figure 4) is governed by the dry mass of adsorbed polymer; the friction coefficients at each speed in the range of 1-200 mm/s and the interfacial shear strength (Table 4) correlate negatively with the dry mass of adsorbed polysaccharide (average r2 = 0.95 and r2 = 0.91, respectively, power law correlations). While these correlation coefficients are reasonable, with only four samples it is difficult to prove whether it is causal at this stage. However, we conclude that the viscoelasticity, hydrated mass, and film thickness, as well as quantity of adsorbed polymer are all very important for setting the lubrication properties of a polysaccharide solution during the transition in the mixed regime to the boundary regime. It is only through a combination of techniques that we can start elucidating the mechanisms of their observed lubricating properties.
4. CONCLUDING REMARKS We highlight here that the lubrication properties for aqueous solutions of polysaccharides (pectin, xanthan gum, carrageenan, locus bean gum, and gellan) in soft-tribological contacts between hydrophobic surfaces in relation to their rheological and adsorption properties. Distinct speed-dependent friction “Stribeck” curves are observed for each of the polysaccharide solutions on both smooth and rough substrates covering each of the three main lubrication regimes: boundary, mixed, and hydrodynamic. Rheology measurements show that while the polysaccharides have been formulated to have a similar rheology at low shear rates (
