Langmuir 1993,9, 257-262
257
Measuring Double Layer Repulsion Using Total Internal Reflection Microscopy Scott
G.Flicker and Stacy G. Bike*
Department of Chemical Engineering, The University of Michigan, Ann Arbor, Michigan 48109-2136 Received July 6,1992. In Final Form: September 28,1992 Total internal reflection microscopy has been developed as a new technique to measure the mean potential energy of interaction between a single colloidal particle and a flat plate. Based on the total internal reflection of light at an interface separating two media of different refractive indicestotal internal reflection microscopy (TIRM)provides an instantaneous measurement of the separation distance between the particle and the plate with the nanometer resolution of scanning electron microscopy. Unlike conventional scanning electron microscopy, however, TIRM can be used to observe noninvasively the dynamics of particle motion in situ. We have used TIRM to quantify double layer forces between a glass plate and polystyrene latex spheres of diameters 7,10, and 15 pm dispersed in aqueous solutions of varying ionic strength. The potential energy profiles agree very well with those predicted by a model of double layer and gravity forces which involves no adjustable parameters. The measured double layer potential energy is accurately described by a simple exponential model based on the linear superposition of potential profiles and Derjaguin's approximation, with the Debye length as the decay length. The double layer potential energy is also shown to scale with the first power of the particle size, as predicted by Derjaguin's approximation.
Introduction A fundamental problem in colloid science is understanding the mechanisms of colloidal interactions. While the manifestation of these interactions can often be seen at the macroscopic level, quantification of the interactions at the microscopic level is difficultto realize. For example, a loas in material strength of a ceramic can often be attributed to microheterogeneities resulting from incomplete dispersion of a ceramic powder prior to casting.l Measuring the forces between colloidal particles in situ is difficult, however, because of the submicrometer size of the particles and the small magnitudes of the interaction forces. Total internal reflection microscopy (TIRM) has recently been developed as a technique to measure the instantaneous separation distance between a single Brownian microscopic particle and a flat surface.2-s TIRM is baeed on the totalinternal reflection of light at an interface separatingtwo media of differentrefractive indices. When the light is incidenton the interfacefrom the more optically dense medium, total reflection of the light produces an evanescent electromagneticwave that penetrates into the lees optically dense medium. Any material of unmatched refractive index located in this wave will scatter light at an intensity which decays exponentially with the normal distance from the interface. Consequently,the scattered light intensity gives an exponentially-sensitivemeasure of the instantaneous distance at which the scatterer is located from the interface,with a spatial resolutionon the order of conventional scanning electron microscopy. Assuming that the distribution of separation distances is described by Boltzmann's distribution, potential energy profiles can then be derived from these distance mea(1)Lange, F. F. J. Am. Ceram. SOC.1989, 72, 3.
(2) Prieve, D. C.; Lanni, F.;Luo,F.Faraday Discuss. Chem. SOC.1987, 83,297. (3) Bike, 5.0.; Prieve, D. C. Znt. J . Multiphme Flow 1990, 16, 727. (4)Prieve, D. C.;Bike, S. G.; Frej, N.A. Faraday Discuss. Chem. SOC. 1990,90,209. (5) Prieve, D.C.;Frej, N. A. Langmuir 1990,6, 396. (6) Brown, M. A.; Smith, A. L.;Staples, E. J. Langmuir 1989,5,1319. (7) Brown, M. A,; Staples,E. J. Faraday Discuss. Chem. SOC.1990,90, 193. (8) Brown, M. A.; Staples, E. J. Langmuir 1990,6, 1260.
0743-7463/93/2409-0257$04.00/0
surements. With TIRM, the mean potential of the interaction force between a microscopic particle and a flat surface can thus be directly measured. TIRM has been used to measure gravity and weak double-layer forces acting on a micrometer-size polysmne latex sphere located near a flat glass plate.2+ In addition, TIRM has been used to measure hindered diffusion coefficients of micrometer-size spheres undergoing Brownian motion near a flat surfa~e.49~ Brown et al. have used TIRM together with radiation pressure to measure weak interaction By applying radiation pressure to a polystyrene latex sphere, they obtained the first measurements of absolute separation distance between the sphere and the reflecting interfa~e.'?~All of this work demonstratesthe potentialof TIRM to become an accepted analytical tool for measuring colloidal forces. TIRM differs from the well-known surface forces apparatusgJoin two respects. First, TIRM measures the mean potential of the interaction force, while the surface forces apparatus measures the potential of the mean interaction force. Second, TIRM permits the study of Brownian particles, while the surface forces apparatus measures the interaction forces between macroscopic crossed-cylindrical surfaceswith radii of curvature on the order of 1cm. While TIRM does not have the angstrom resolution of the surface forces apparatus, TIRM does allow one surface to be reduced to colloidal dimensions. In this paper, we describe the application of TIRM to quantify the electrostatic double layer forces between a glass microscope slide and polystyrene latex spheres of nominal diameters 7,10, and 15 pm dispersed in aqueous solutions of varying ionic strength. This work is the first systematic study of both the particle size dependence and the ionic strength dependence of double layer forces using TIRM. Distributions of separation distance between the plate and a single sphere are calculatedfrom the scattering intensity measurements. Assuming that these distributions can be represented by a Boltzmann distribution, potential energy profiles are then constructed. Not only ~~
(9) Israelachvili,J. N.; Adame, G. E. Nature, 1976,262,774. (10) Israelachvili,J. N.; Adams, G.E.J. Chem. SOC.,Faraday "a. 1 1978, 74, 975.
Q 1993 American Chemical Society
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268 Langmuir, Vol. 8, No.1, 1993
do the potential energy measurements demonstrate the influence of both double layer repulsion and gravity on the sphere's movement, but they also agree very well with potential energies predicted from models of these forces. By subtracting the known gravity potential energy from the total potential energy of interaction, the double layer potential energy as a function of separation distance is calculated. Thiedouble layer potentialenergy is accurately deecribed by a simple exponential model based on the linear superpodtion of potential profdes and Derjaguin's approximation,with the Debye length as the decay length. Background Total Internal Beflwtion M~croscopy. TIRM is baaed on the totalinternal reflection of light at an interface separating two transparent media of different refractive indices. When a beam of light is incident on such an interface, the light is partially refleeted back into the first mediumandpartiallytr~~~intothesecondmedium. The angle of refraction of the transmitted beam is given by Snell's law" sin 4 = nzl sin e (1) where B is the angle of incidence, Q is the angle of refraction, , ni is the refractiveindex of medium and n21 n d n ~where i. Internal reflection occurs when the light is incidentfrom the medium of greater refractive index (Le., n l > nz).In this case,the angle of incidence 8 is always lees than the angle of refraction 4. When 4 is equal to 90' the corresponding incident angle is designated as the critical angle 8,; for incident angles greater than the critical angle, 4 is imaginary and the light is totally reflected at the interface. While no visible light is propagated into the lese optically dense medium for 8 > e, an evanescent electromagnetic wave does penetrate a short distance into this medium. The intensity Z of the evanescent wave decays exponentially with distance h away from the interfacell
I = Z, exp( -
t)
Vn1 (3) d~ 4r(sin2 e - n 2 3 / 2 A,) is the wavelength of light in a vacuum. When an objectwhoee refractive index differsfrom that of medium 2 interacta with the evanescent wave, light of wavelength A,) is scattered by the object. Chew et al.I2 have &own that for spherical dielectric particles located in an evanescentwave, the intensity of thia scattered light decays exponentially with the distanceh from the interface
(- da>
V(h)= V*(h)+ V,(h) + V&h) (5) where VA(~), VR(~), and Vg(h)are the van der Waals, double layer, and gravitationalpotential energies, respectively. For the experimentalsystem that we have studied, the contributionfrom van der Waals attraction to the total potential is negligible.'q Thus, it is neceeaary to consider only the contributionsfrom doublelayer and gravity forces to the total potential energy. For thin, slightly overlapping counterion clouds, the doublelayer potential energy between a sphericalparticle and a flat plate is given by16
where cis the dielectricconstant of the fluid,a is the radius of the sphere, kT is the thermal energy, z is the ion valency (assuming a symmetric electrolyte), e is the protonic charge, and and #p are the surface potentials of the sphere and the plate, respectively. K is the inverse Debye length (7)
where ZO is the intensity of the evanescent wave at the interface(h * 0). d, is the characteristicpenetration depth of the evanescent wave
I(h,Q)= I(0,Q)exp
equationwas derived for particleslocated far enough away from the reflecting interface so that multiple reflections could be neglected, Walzand Prieve have shown that this exponential decay is valid for any separation distance for spherical particles less than approximately 30 pm in diameter.13 Consequently, we have used eq 4 to transform the measured scattering intensities into separation distances for spheres of diameters from 7 to 15 pm. Model for the Total Potential Energy. Using TIRM, we have measured the mean potential of interaction between a colloidal sphere and a flat plate. We have then used the following model for the total potential energy to compare with these experimental measurements.2 Consider a sphere dispersed in an electrolyte solution and located near a flat plate. The total potential energy V(h) can be written as follow8
(4)
where Z(0,Q) is the scattered light intensity for a sphere in contact with the reflecting interface (h = 0) and Q is a fmed angle over which the scattered light is collected. By measuring the scattered light intensity, we thus have an exponentially sensitivemethod to measure the separation distancebetween the sphere and the interface. While thia (11) L i p n , S. 0.;Lipon, H.Optical Phyuice, 2nd ed.; Cambridge Univenity R e a New York, 1981. (12) Chew, H.;W a g , D.S.;Kerker, M . Appl. Opt. 1979,18, 2679.
where C is the ionic strength. This model for the double layer potential energy, which is based on linear superposition of the potential profdes on opposing surfaces and Derjaguin's approximation, is valid for all potentials provided that Ka >> & >> 1. Note that thia model predicta a simple exponential dependence on the separation distance h. The gravitational potential energy is given by
Ap is the difference between the particle and the fluid densities and g is the gravitational acceleration. Since the particle sizes used in thie work are accurately known, we can subtract the contribution from the gravitational potential energy given by eq 8 from the measured total potential energy to yield the double layer potential energy. This will allow us to compare the measured double layer potential energy with that predicted by eq 6 to validate the applicability of linear superposition and Derjaguin's approximation for our experimental systems. The total potential energy can then be simply written as follow8 (13) Walz, J.; Prieve, D.C. Langmuir 1992,8, oo00. (14) Alexander, B. M.;H e w , D. C. Longmuir 1987,3, 788. (16) Verwey, E.J.; Overbeek, J. Th.Theory of Stability of Lyophobic Colloidu; Elsevier: Amsterdam, 1948.
Langmuir, Vol. 9, No. 1, 1993 269
Measuring Double Layer Repulsion
..
Amplifier
A D Board
uI.rBwln
figure^ 1. (a, top) Sketch of TIRM apparatua. (b, bottom)
Magnified view of acattering assembly.
V(h)= B exp(-Kh) + Gh where B and ct depend only on material properties and temperature
G = ra3Apg 4 At equilibrium,the sphere will locate at the position h m where the total potential energy is a minimum. From eq 9, thia position is given by
Experimental Section Apparatus. Shown in Figure l a ia a sketch of the TIRM apparatua which incorporatea a Nikon Microphot microacope located on a Newport vibration-hlation table. The light source uaed to generate the evaneacent wave ia a multiline 100-mW Ar ion laaer (Ion Laeer Technology) operating at a wavelength of 514.5 nm and a power of 5 mW. The light from the laser is directed to a dove prim uaingtwo fvstsurface aluminummirrors mounted on a beam steering apparatus. The upper mirror is attached to a rotating stage, which permits controlof the incident angle 6. The prism is mounted on a modified microecope stage that can translate in three directiona. As detailed in Figure lb, a g b microscope slide is o p t i d y coupled to the prism using index-matched immersion oil. Total internal reflection of the laaer beam then occura at the upper surface of the glaaa slide. A dilute diapersion ia placed in a glaaa well fuaed to the microecope elide. The slide is then translated to f m on one particle interacting with the glaaa slide. The light ecattered by the aelelectsdparticle is captured by a 40X water-
immersible objective (Zeiaa). After paaaing through an Omega bandpaaa filter (514.5 nm), the intensity of the acattered light ia monitoredby a HamamatauRllO4 photomultipliertube ("PMT") driven by a Bertan Model 215 high-voltage power supply and incorporating a uaer-made voltage divider circuit to auppreaa dark current. The PMT generates a current that ia linearly proportional to the intensity; thia current is amplified and converted to a voltage using a Keithley Model 470 current amplifier. The resulting analog signal ia aampled at a known rate by a Keithley Model 500 data acquiaition system, and the discrete output is stored on an IBM PS/2 Model 70 for later analysis. Materials. The colloidal particles studied were polystyrene latex spheres of diameters 7.04 f O.O4,9.87 f 0.06, and 15.00 f 0.09 pm from Duke Scientific. Hereafter, we will refer to these particles sizes by their nominal diameters of 7,10, and 15 pm, respectively. The particles were diaperaed in aqueoua aolutions prepared by adding a known amount of a filtered 0.1 M NaCl (FisherScientificACS grade) stocksolution to filtered deionized water containing0.05mM of the nonionic surfactant octaethylene glycol mono-n-decyl ether (Nikko Chemical Co., Ltd.). The nonionic surfactant waa used to prevent sticking of the particles to the glass slide during an experiment. The ionic strength of each dispersion was calculated from pH and conductivity meaaurementa. Four ionic strengths were wed in this work 0.07 mM, 0.14 mM, 0.30 mM, and 0.90 mM. Thew low ionic strengths enabled us to neglect van der Waala attraction and employ the potential energy model described in the previoua section. The corresponding Debye length calculated from the conductivity and pH meaaurementa are, in order of increaeingionic strength, 34.5, 24.4, 16.4, and 9.09 nm. Methods. Prior to each experiment,the h e r waa warmed up at full power for 30 min to ensure stable operation. After this warm-up period, the laser power was reduced to 5 mW. Approximately 0.5 mL of a selected diapersion waa placed in the glass well on the microacope slide. The objective waa carefully lowered into the dispersion, and the expoaed liquid surface waa covered with Parafih to prevent evaporationand a correaponding change in ionic strength. After focusing on particles near the bottom of the glaaa well, a single particle that waa aeparatedby at leaat 7 particlediameters from other particlea waa centered in the field of view of the microscope using the tranalating stages. A rectangular slit aperture in the microscope waa adjusted to allow the PMT to %e" an area of approximately 3 particle diameters aquare. This area waa sufficient to allow the particle to diffuse parallel to the glaaa slide surface during an experiment without leaving the aperture window. The laaer beam waa then focused directlyunder the particle aa determined by maximizing the detected acattering intensity. Each experiment consisted of recording at leaat 3000 measurementaof the acattering intensity at a aampling rate of 50 ma. Before each experiment, the particle waa moved juat outaide of the field of view and the background intensity recorded. Thia background intensity waa later subtracted from the meaaured scatteringintensity to give a true value of the scatteringintensity. Then, the particle waa moved back into the field of view and the scattering intensity recorded. Typically, 300+1oooO meaaurementa of intensity were recorded to ensure that an equilibrium hiatogram of intensities waa constructed. Data Analyais. Hietograms. The hiatograma of frequency, N ( 0 , aa a function of the acattering intensity, Z(h,Q),are constructed in the following manner. The mean background intensity is subtracted from each meaaurement of the acattering intensity to yield the true acattering intensity, aaauming that the angle Q is Constant. The time aeriea data for each experiment are then converted into a histogram, which in condensed by combining frequencies in the range I - Al to I + Af into une interval. Typically, AZranged from 60 to 200 (in arbitrary units) while Z ranged from 0 to M)o. The maximum in the histogram correspond0 to the ltratiw designated hz, which is not equivalent to the must-probable aeparation distance baaed on a balance of furoep, deniynwred h,,, (eq 12).* Instead, theehapeof the hintugram reprw~tuthe*hyo of the probability denaity function ftu inttuwy, f i t ) . 'I% probability p ( h ) dh of locating. a particle betwcw k wud h + CVr
Flicker and Bike
260 hngmuir, Vol. 9, No. 1, 1993
350
distance h, at which dpldh = 0. We denote the maximum frequency and the correspondingintensity aa N[Z(hz)land Z(hz), respectively. PotentialEnergy Profiles. The scatteringhistogramsare then converted into potential energy profiles as summarized be10w.~ From eq 4, the separation distance h relative to the moat frequently observed distance based on intensity measurements, hz, is given by
f
250
1 ,j 50
1
0 2500
3500
4500
5500
6500
We assume that the probabilityof findinga particleat one location relative to another is represented by a Boltzmann distribution. The potential energy V(h)relative to that at the moat probable location, V(hz),is then given by
7500
Scattering Intensity (a.u.)
Figure 2. Histogram of scattering intensity for one 15.00-pm polystyrene latex sphere dispersed in the 0.90 mM solution.
I-
_
j12 4
7
-
'
'
l
"
'
'
I
"
"
I
o
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o
0.14mM 0.30mM
'
1
"
* /
V(h)- WhJ = In ( N [ l ( h z ) l ~ ( h ~ ) ) (15) kT N[l(h)lZ(h) We can compare our experimental potential energy profiles with those predicted from our model. Combining eqs 9 and 12, the total potential relative to that at h, is given by exp[-rc(h - h,)l- 1
io
kT
8 -
4i 2
-25
25
0
75
50
h - h, (nm)
Figure 3. Potential energy profiles for four 15.00-pmpolystyrene latex spheres each dispersed in a solution of different ionic strength from 0.07 to 0.90 mM. The potential energy curves have been shifted vertically by 2 dimensionlessenergy units for ease of viewing. The symbols are the experimentaldata and the solid lines are the model predictions. 14.'
12
'
"
1
:
'
\
'
'
'
1
'
I
'
1
0.07 mM
0
0.14mM 0.30mM
o
\
'
0
'
'
"
I
"
"
_
0.90mM
L
4 1
0 -100
+ (h- h,))
(16)
Note that eq 16has no adjustable parameters: the inverseDebye length K is calculated from the measured solution conductivity and pH. In addition, the parameter B is not needed to evaluate eq 16;thia is fortuitous since the parameter B includesthe surface potentials of the sphere and the glass slide, which are difficult to evaluate in situ.
6-
-50
K
-50
0
50
100
150
h - hz (nm)
Figure 4. Potential energyprofdesfor four 9.87-pm polystyrene latex spheres each dispersed in a solution of different ionic s t r e n e from 0.07 to 0.90 mM. The potential energy curves have n shifted vertically by 2 dimensionlessenergy units for ease of viewing. The symbols are the experimentaldata and the solid lines are the model predictions. is related to P(Z) by (13) where P(Z)dl is the probability of observing a scatteringintensity between Z and Z + dz. Consequently, the separation distance h2 at which dP1d.l = 0 is not necessarily equal to the separation
Results and Discussion Histogramsof ScatteringIntensity. ShowninFigure 2 is a representative scattering histogram for one 16 pm diameter sphere dispersed in the 0.90 mM solution. Note that the histogram is not symmetric about the maximum. The slower decrease in frequencywith decreasing intensity for scattering intensities less than I(h$ r e f l a the influence of the gravitational potential which varies with the fmt power of the separation distance. Electrostatic repulsion dominates at smaller separation distances, or equivalentlyhigher scattering intensities. The expected exponential variation of the double layer potential with separation distance gives rise to a faster decrease in frequency with increasing intensity for scattering intensities greater than I(h& Such histograms were obtained for one particle of each size in the four different ionic strength solutions. Potential Energy Profiles. Potential energy profiles were derived from the histugrams of scattering intensity according to the algorithm outlined in the previous section and are shown in Figurea 3-6 for all three particle sizes. The dimensionleesrelative potentialenergy V(h)- V(h$l/ kT is plotted versus the relative separation distance h hi. Thespbols c o ~ ~ d t o t h e e ~ r i m e n t a l d a t a w h i l e the solid linea are predicted from the model given by eq 16 using the calculated Debye lengtha reported in the previous section. Note that the minimumin eachpotential energy profile should lie on the 1c axis, corresponding to a zero relative potential, for 8888 of viewing, however, adjacent potential energy profileg are shifted vertically by 2 dimensionless energy units. The potential energy profiles for the 16-pm particles are shown in Figure 3. Each potential energy profile corresponde to a single (but different) particle. The experimental data and the model predictions agree very well, while a slight deviation from the model is noted for h < hz in the 0.30 mM solution. As discussed later, thia deviationcorreepondeto a weaker thanexpectedrepdive
Langmuir, Val. 8, No. I, 1993 261
Measuring Double Layer Repulsion
' i
0
"
-100
"
A
-50
50
0
100
d 150
200
250
h . h2 (nn)
Figure 5. Potentialenergyprofiles for four 7.04-pm polystyrene latex spheres each dispersed in a solution of different ionic strength from 0.07 to 0.90 mM. The potential energy curves have been shifted vertically by 2 dimensionless energy units for ease of viewing. The symbols are the experimental data and the solid limes are the model predictions.
t
e0.14mM o 0.30mM
I
1.o
-40
-20
0
20
40
.
60
k (nm) (Relative)
Figure 6. Double layer potential energy as a function of relative separation distance corresponding to the 15.00-pm particles in Figure 3. Table I. Comparison of Debye Screening Lengths Calculated from Solution Conductivity and pH Mearurementr and from Double Layer Potential Energy Mearurementr ~ - (nm) 1 calculated from measured VR predicted 7.04pm 9.87 pm 16.00 pm I(mM) ~-1(nm) diameter diameter diameter 30.8 33.3 34.5 32.0 0.07 24.6 25.0 22.0 0.14 24.4 18.2 19.0 16.5 0.30 16.4 11.0 9.81 9.09 11.6 0.90
force between the sphere and the plate. For separation distancesmuch greater than h2,the slopes of the potential energy profilea become constant and kualtothe net weight of the particle. In thh region, the double layer force is negligible. For separation distances less than h2 the potential energy profiles display an increasing slope with increasingionic strength,reflecting the decreasein double layer repulsion with increasingionic strength. As expectad, the potential energy profiles become more narrow as the ionic strength increases. Note that the spatial resolution in the separation diatance is on the order of a few nanometers; of course,this resolution is dependent on the condensinginterval Alselected for the scattering intensity histopram. Figure 4 shows the corresponding potential energy profiles for the l0-pm particles. Again, good agreement
is generally seen between the experimental data and the model predictions. Note that the slope of the c w e s in the region h > h2 is lesa than that for the l b p m particles, which resulta from the smaller net weight of the 10-pm particles. Somedeviation is noted in the 0.30m M solution for h > hz. That the experimental potential energy values are greater than those predicted in this solution suggests that the particle is experiencing an additional attractive force that restricts ita motion. Such a force might result from the presence of a ytether",or extended polymer chain, on the particle that is attached to the glass slide.lB An alternate explanationis that the particle is located directly abovean asperity on the glassslidethat restricts the motion of the particle. The fmt explanation seems more likely, however, since the potential energy curve deviates from the model only at large separation distances. The potential energy profiles for the 7-pm particles are shown in Figure 5. Unlike the results shown for the 10and 15-pm particles, good agreement is not always seen between the experimentaldata and the model predictions. In the region h h2, however, the experimental data exhibit a systematic positive deviation from the model predictions. This positive deviation implies that the particle doee not sample separation distances greater than hz as frequently as expected. While such a deviation might result from an additional attractive force, as proposed for the 10-pm particle in the 0.30mM solution,we instead attribute thh deviation to a loss of resolution resulting from the smaller size of the 7-pm particles. At a given separation distance, the smaller '7-pm particles will generate a lower scattering intensity as compared to that generated by the larger 10pm and lbpm particles. Moreover, because of their smaller net weight the 7 pm diameter particles diffuse to greater distances above the glass slide; given the exponential decay in the evanescent wave intensity, the Scattering intensity for a sphere in this region is significantly lower. For example, we expect a 7-pm diameter polystyrene latex sphere to diffuse up to 6 times the penetration depth away from the glass slide. At this distance, the scattering intensity is 150 times lesa than that when the separation distance and penetration depth are equal, and the PMT is less able to detect this lower scattering intensity. In addition, since the intensity of the evanescent wave changes very slowly with distance in the region far from the reflecting interface, the PMT is then less able to resolve changes in scattering intensity and, correspondwly, changes in separation distance. Exponential h a y of the Double Layer Potential Energy. The double layer potential energy can be calculatedfrom the measured relative potential energy by subtracting the known gravitational potential energy. Shown in Figure 6 is a plot of the dimensionless double layer potential energy VdkT as a function of relative separation distance for the 15 pm diameter particles. T h e separation distancesreportad in Figure 6 do not correspond to actualseparationdistances above the glass slide;inatead, the range of separation distances shown corresponds to that sampled by the particle for which double layer repulsion acts on the particle. In fact, each data set has (16) van de Ven, T.G.;Dabroe, T.;Czamecki, J. J. Colloid Interface Sci. lW, 89,680.
Flicker and Bike
262 Langmuir, Vol. 9, No.1, 1993 2.5
v
2'ol
lpm lOpm
o
1
ISpm
-Pndiciion
I .5
0.5
nn
150
200
250
300
350
400
h (nm)
Figwe 7. Double layer potential energy waled by the particle size as a function of separation distance for all three particle sizes in the 0.14 m M solution.
been shifted horizontally for ease of viewing. Note that the range of separation distances for which double layer repuleion acta on the particledecreasesasthe ionic strength increases, demonstrating the weakening in double layer repulsion at higher ionic strengths. Similar trends were noted for the other particle sizes. The data for each ionic strength can be described by a straight line on a semilogarithmic plot, which indicates that the simpleexponentialmodel of doublelayer repulsion is applicable at these low ionic strengths. Further confirmation of the validity of the exponential model given by eq 6 is provided by the correspondence of the slope of each line with the calculated Debye length. Shown in Table I isacomparison Of K-l calculatedfrom the measured solution conductivity and pH and K - ~calculated from the slope of the double layer potential energy versus distance. Good agreement is noted between the Debye lengths calculated from the solution conductivity and pH measurements ('predicted") and those calculated from the experiments. Positive and negative deviations noted between the data and the model are reflected in similar deviationsbetween the 'predicted" and calculated Debye lengths. Note, however, that it is the slope of the data in the region h < h2 that is important. Often the slope of the data matches with the predicted Debye length while the model and the data may exhibit a deviation; for example, see the potential energy profile for the 10-pm sphere in the 0.30 mM solution. The deviation in the potential energiesobserved for h > h2 does not affect the estimation of K - ~ from the measured double layer potential energy, since at these distancesdouble layer repulsion is negligible. Particle Size Dependence of the Double Layer Potential Energy. Equation 6 predicts the double layer potentialenergy to be directly proportional to the particle size. This fmt-power dependence results from applying Derjaguin's approximation to the potential energy of interaction between two flat plates. We can determine the validity of Derjaguin's approximation for our experimental systems by scaling the measured double layer potential energies by the particle size. If Derjaguin's approximation is applicable, the double layer potential energiea scaled by particle size should yield a single master curve as a function of separation distance. Shown in Figure 7 is such a plot of the scaled double layer potential energy, VdkTu,as a function of separation distance for all three particle sizes in the 0.14 mM solution. The experimental data are given by the symbols and the prediction according to eq 6 is given by the solid line. To obtain the distance values for the *: axis, h, was estimated
from eq 12 assuming that both the particle and slide surfaces have equal surface potentials of 60 mV and that the surfacepotential of the particle is invariantwith respect to particle size for a given ionic strength. Note that the actual values chosen for the surface potentials are not relevant, in that different values will uniformly shift the scaled double layer potential profdes horizontally along the x axis but will not alter the correspondenceof potential energies for the three particle sizes. The scaled double layer potentialprofdes do yield a singlecurve independent of particle size. This confirms that the double layer potential energy is proportional to the particle radius to the first power, a result predicted by Derjaguin's approximation. Future Applications of TIRM. We have shown that TIRM is capable of measuring weak double layer forces acting between a colloidalsphere and a flat plate. We are now extending the TIRM technique to study nonspecific interactionsbetween cell-size lipid vesicles and either bare or lipid-coatedsubstrates. Biological colloids are subject to both specific and nonspecificinteraction forces." The short-range specific forces lead to cell adhesion through receptor-ligand attachments. The longer-rangenonspecific forces, which include van der Waals and double layer forces, control the approach of the particle to the surface. It has been suggestedthat the adhesionproceee isprimarily nonspecific and that the specific interaction forces are influenced by the nonspecific forces.l8Jg We are using TIRM to quantify nonspecific interactions in biological systems, thus providing fundamental insight into the process of cell-substrate adhesion and the mechanistice of nonspecific forces including steric, undulation, and hydration forces.
Summary We have shown that TIRM can be used to measure double layer forces between a single colloidal sphere and a flat plate. Based on the total reflection of light at an interface separating two media of different refractive indices, TIRM provides the capability to observe the dynamics of particle motion with the spatial resolution of scanning electron microscopy. Potential energy profiles were derived for polystyrene microspheres of nominal diameters 7,10, and 16 pm dispersed in aqueous solutions of low ionic strength. These profdes demonstrated the influence of gravity and double layer repulsion on the movement of the spheres. In addition, the experimental potential energy profiles agreed very well with those predicted from model of gravity and double layer forces which involved no adjustable parameters. The experimentally-derived double layer profiles confiied that a simple exponentialmodel of double layer repulsion based on linear superpoeitionof potentialprofdes and Derjaguin's approximationdescribes the data well. The demy length of the double layer profdes was found to be equivalent to the Debye length, and the double layer potential energy was directly proportionalto the fmt power of the particle size. Acknowledgment. We gratefully acknowledge the financial support of the National Science Foundation under Granta CTS-8907739 and CTS-9068078. S.G.F. thanksthe Amoco Foundation for a graduate fellowship. (17)Rutter, P. R.; Vincent, B. In Microbial Adheaion to Swfocea; Berkeley, R C. W., et al., W.; Ellin H o m d Chichater, ISSO;p 70. (18) Cingell, D.; Vice, S. In Cell A d h i o n and Motility; Curtir, A. 5.G., Pitte, J. D., Eda.;Cambridge Univenity F"E New York, 1980; P 1. (19) Cowley, A. C.; et al. Eiochemiatry 1978,17,3168.
