ENVIRONMENTAL ENGINEERING SCIENCE
Volume 19, Number 6, 2002
© Mary Ann Liebert, Inc.
Membrane–Colloid Interactions: Comparison of Extended
DLVO Predictions with AFM Force Measurements
Jonathan A. Brant and Amy E. Childress*
Department of Civil Engineering
University of Nevada, Reno
Reno, NV 89557-0152
ABSTRACT
Theoretical predictions of interaction energies for several membrane–colloid pairs were made using the
classical DLVO theory and an extended DLVO (XDLVO) approach. The XDLVO approach accounts for
acid-base (polar) interactions that are not considered in the classical DLVO theory. For all membranecolloid pairs studied, DLVO interactions were similar. However, inclusion of acid-base interactions resulted in substantially different predictions of short-range (separation distance ,10 nm) interaction energies for several of the membrane–colloid pairs investigated. Predicted interaction energies were compared
with atomic force microscopy (AFM) force measurements. The colloid probe technique was used to directly measure the force of interaction between a single colloid and a membrane surface. It was found
that for strongly hydrophilic systems where the XDLVO approach predicts substantially different interaction energies than the DLVO theory, the measured force curves agree with the interaction sequence predicted by the XDLVO approach. For strongly hydrophobic systems where the XDLVO approach predicts
an interaction similar to that predicted by the DLVO theory, the measured force curves agree with the interaction sequence seen in both DLVO and XDLVO predictions. It was also found that because the membranes have much higher surface energies (primarily due to the acid-base component) than the colloids
investigated, the membranes control the general behavior of the interactions.
Key words: reverse osmosis; polar interactions; XDLVO approach; DLVO theory; AFM force curves;
colloid probe interactions
INTRODUCTION
T
leading to colloidal membrane fouling are traditionally described
using the classical DLVO (Derjaguin-Landau-VerweyOverbeek) theory, which characterizes total interaction
energy as the sum of the electrostatic double layer (EL)
and Lifshitz-van der Waals (LW) interaction energies.
HE THERMODYNAMIC INTERACTIO NS
However, the DLVO theory alone often fails to accurately describe membrane–colloid interactions, particularly when the separation distance is small (approximately 6 nm) (Butt et al., 1995; Bhattacharjee et al.,
1996; Meagher et al., 1996; Craig et al., 1998; Cho et
al., 1999; Molina-Bolivar et al., 1999; Chin et al., 2002).
Discrepancies between DLVO predictions and experimental observations have been attributed to various sur-
*Corresponding author: Department of Civil Engineering, University of Nevada, Reno, Reno, NV 89557-0152. Phone: 775784-6942; Fax: 775-784-1390; E-mail: amyec@unr.edu
413
414
face properties and additional interactions including surface
roughness, chemical and morphologic heterogeneities, and
short-range non-DLVO forces (e.g., hydrophobic effects
and hydration pressure) (Ducker et al., 1991; Butt et al.,
1995; Bhattacharjee et al., 1998; Pashley et al., 1998;
Bowen et al., 1999c; Brant and Childress, 2002; Chin et
al., 2002).
Hydrophobic and hydration effects are considered to
play a significant role in surface interactions in polar media (van Oss, 1994; Butt et al., 1995; Christenson and
Claesson, 2001). The combined effects of both interactions are often loosely characterized in terms of membrane hydrophobicity (Bouchard et al., 1997; Nabe et al.,
1997; Cho et al., 1999; Combe et al., 1999). A more precise theoretical and quantitative description of these polar interactions was put forth by van Oss (1986, 1994)
who referred to them as Lewis acid-base (AB) interactions. These AB interactions are based on electron-acceptor/electron-donor interactions between polar moieties in polar media (e.g., water). Consideration of these
additional interactions has resulted in an extended DLVO
(XDLVO) approach for characterizing surface interactions (van Oss, 1993). In the XDLVO approach, AB interactions are accounted for in addition to EL and LW
interactions. Although AB interactions are commonly
thought of as short-range interactions they may be up to
two orders of magnitude greater than EL and LW interactions (van Oss et al., 1988; van Oss, 1994; Butt et al.,
1995).
AB interactions have been shown to be a major contributor in colloidal deposition and aggregation processes
(Yotsumoto and Yoon, 1993; Yoon and Ravishankar,
1994; Durán et al., 1998; Ohki and Ohshima, 1999;
Wu et al., 1999; Aston and Berg, 2000; Brant and Childress, 2002; Grasso et al., 2002); however, their role in
membrane–colloid interactions is still relatively unclear.
Previously, it was shown that incorporating AB interactions into the DLVO theory results in substantially different short-range interfacial interaction predictions for
membrane–colloid systems (Brant and Childress, 2002).
Further, XDLVO predictions were in closer qualitative
agreement with actual membrane fouling experiments
than DLVO predictions. However, membrane fouling results from both thermodynamic and hydrodynamic interactions. Therefore, comparison of XDLVO predictions
with fouling results provides only a qualitative assessment
of the XDLVO model. To gain a more quantitative understanding, the thermodynamic (colloidal) interactions
must be isolated from the hydrodynamic interactions. The
colloidal interactions can be evaluated through the use of
an atomic force microscope.
A dramatic advancement in membrane research is the
ability to directly measure the interfacial interaction and
BRANT AND CHILDRESS
adhesion force between a colloid and membrane surface
using atomic force microscopy (AFM) (Senden, 2001).
AFM was originally developed as an imaging tool with
atomic level resolution; however, its operating principle
has always been based on force measurement (Lee and
Sigmund, 2001; Senden, 2001). AFM is capable of measuring the force profile (i.e., force as a function of separation distance) and the force of adhesion between two
interacting surfaces (Bowen et al., 1997, 1999a, 1999c).
Both measurements are significant to membrane research, as they describe colloid transport to and adhesion
with the membrane surface, both of which are critical
concerns for characterizing membrane fouling propensity.
Use of the AFM to quantify membrane–colloid interactions has been limited. Bowen et al. (1997) studied EL
interactions between a silicon tip and polymeric ultrafilitration (UF) and microfiltration (MF) membranes. Ionic
strength was varied to determine optimum surface imaging conditions. It was concluded that imaging was best
performed at a high ionic strength, as this allowed the tip
to get closer to the actual surface due to compression of
the electric double layer. Bowen et al. (1998) developed
a “colloid probe” to quantify the force of adhesion between a polystyrene sphere and two ultrafiltration membranes. Use of a colloid probe instead of a silicon nitride
tip is advantageous because the geometry and surface
chemistry of the colloid are known (Butt et al., 1995).
Other investigations have demonstrated the ability of the
AFM to measure forces of interaction between a colloid
and a surface other than a membrane (Butt et al., 1995;
Milling et al., 1996; Bowen et al., 1998, 1999a, 1999b;
Craig et al., 1998; Hook et al., 1999; Lee and Sigmund,
2001; Chin et al., 2002). Milling et al. (1996) used a colloid probe to measure forces of interaction between gold
spheres and a flat poly (tetrafluorethylene) surface. Theoretical predictions for repulsive dispersion forces were
compared to measured values and agreement was found in
apolar systems. However, in polar environments an attractive force was detected that could not be accounted for.
It was concluded that in polar systems, additional shortrange interactions must be considered. Bowen et al.
(1999b) studied adhesive interactions between a silica
sphere and a silica surface. DLVO predictions for adhesion were generally found to agree with measured values
when EL interactions were insignificant; however, it was
concluded that non-DLVO forces were likely to be significant. Chin et al. (2002) used AFM to study colloidal
surface forces between a silica particle and a smooth glass
plate in the presence and absence of copper ions. Agreement was found between DLVO predictions and measured
forces except at small separation distances where nonDLVO forces were not accounted for.
MEMBRANE–COLLOID INTERACTIONS
415
The goal of the current investigation was to quantitatively demonstrate the significance of polar interactions
in membrane–colloid interactions. The significance of
AB interactions was assessed through comparisons of
DLVO and XDLVO predictions with AFM direct force
measurements. The XDLVO approach required that the
surface energetics for several membranes and colloids be
determined using the Lifshitz-van der Waals acid-base
theory. From this, the force profile and adhesion energy
for membrane–colloid pairs were predicted. These results
were compared to the force profile measurements determined using AFM.
THEORY
Interfacial interactions between membrane
surfaces and colloidal particles
The total interaction energy between a spherical colloid and a membrane surface immersed in an aqueous
medium can be described as the sum of three interaction
energies according to the XDLVO approach: electrostatic (EL), Lifshitz van der Waals (LW), and acid-base
(AB) interactions (van Oss, 1994). The total free energy
of interaction may then be written as:
XDLVO 5 UEL 1 ULW 1 UAB
Umlc
mlc
mlc
mlc
(1)
where U XDLVO is the total interaction energy between
the membrane and colloid immersed in water, U EL is
the electrostatic interaction term, ULW is the Lifshitzvan der Waals interaction term, and UAB is the acidbase interaction term. The subscripts m, l, and c correspond to the membrane, bulk feed solution, and colloid,
respectively. From a thermodynamic standpoint, attraction or adhesion between two interacting surfaces
occurs when UXD LV O is negative; repulsion occurs
when U XD LVO is positive.
The total interaction energy, UXDLVO , is often evaluated as a function of separation distance (h) between the
interacting surfaces using interaction energy profiles. Interaction energy profiles illustrate the type of interaction
(attractive or repulsive) occurring as a colloid approaches
a membrane surface and the separation distance at which
the individual interaction energies are dominant.
Application of the XDLVO approach requires that the
surface energy parameters of the membrane and colloid
be determined experimentally. The surface tension components of a solid surface (i.e., gLW , g1 , and g2 ) can
be determined by performing contact angle measurements using three well-characterized probe liquids. Using the known surface tension properties of the probe
liquids and the measured contact angles, the surface tension components of the solid surface may be calculated
according to the extended Young equation (van Oss,
1993):
(1 1 cos u) gTOT
l
1
2
5 2 ÏgLW
gLW
1 Ïg1sg2l 1 Ïg2s g1l
s
l
(2)
where u is the contact angle; gTOT is the total surface tension; gLW is the Lifshitz-van der Waals component; and
g1 and g2 are the electron-acceptor and electron-donor
components, respectively. The subscripts s and l correspond to the solid surface and the liquid, respectively.
Surface tension components for membranes and colloids calculated using the Lifshitz-van der Waals acidbase approach can be used to evaluate the free energy
AB
components per unit area, DGLW
y 0 and DG y 0 , between
these surfaces. Expressions for the LW and AB adhesion energies per unit area are, respectively (van Oss,
1993),
1
21
2
(3)
2
(4)
LW 2 Ï g LW Ï g LW 2 Ïg LW
DG LW
y 5 2 Ïgl
m
c
l
0
and
1
DG yAB 5 2 Ïg1l Ïg2m 1 Ïg2c 2 Ïg2l
0
1
2
1 2Ïg2l Ïg1m 1 Ïg1c 2 Ïg1l
1
2 2Ïg1m g2c 2 2 Ïg2
mgc
(4)
The free energy of adhesion per unit area signifies the
interaction energy per unit area between two planar surfaces (bearing the properties of the membrane and the
colloid) that are brought into contact. The minimum equilibrium cutoff distance, y0 , was assigned a value of 0.157
nm (6 0.009 nm) (van Oss et al., 1988, 1999; Bhattacharjee et al., 1996) for this investigation.
As the separation distance between two surfaces increases, the LW and AB interaction energy components
diminish from their corresponding adhesion energy.
Equations showing the unique decay pattern for each interaction energy can be found elsewhere (van Oss, 1993;
Brant and Childress, 2002). Derjaguin’s technique (Derjaguin, 1934) can then be used to scale the interaction
energy between two infinite flat surfaces to the corresponding energy between a flat sheet (membrane) and a
sphere (colloid). Applying this technique, and using
Equation (3), the LW interaction energy between a sphere
and a planar surface as a function of separation distance
may be calculated according to:
2
LW y0 ac
ULW
mlc (h) 5 2p DG y 0 }
h
(5)
where ac is the radius of the colloid. Similarly, applying
Derjaguin’s technique and using Equation (4), the AB interaction energy between a sphere and a planar surface
ENVIRON ENG SCI, VOL. 19, NO. 6, 2002
416
BRANT AND CHILDRESS
as a function of separation distance is calculated according to:
AB
UAB
mlc (h) 5 2pac l DG y exp
0
y0 2 h
l
3}
4
(6)
where l is the characteristic decay length of AB interactions in water. A value of 0.6 nm (van Oss, 1994) was
used in the current investigation. Electrostatic interactions in aqueous media decay exponentially according to
(Brant and Childress, 2002):
1
1
1 1 e2kh
}
UEL
mlc (h) 5 p«r«0 ac 2zc zm ln 1 2 e2kh
1
2
2
2
1 zc2 1 z2m ln(1 2 e22kh ) (7)
where «r«0 is the dielectric permittivity of the suspending
fluid; zc and zm are the surface potentials of the colloid and
membrane, respectively; and k is the inverse Debye screening length. In the current investigation, surface potentials
were assumed to be the same as the measured zeta potentials of the surfaces involved. For both membranes and colloids, zeta potential values at pH 5.4 were used to determine the EL interaction energy term. In calculating the
inverse Debye screening length, a background electrolyte
concentration of 0.01 M NaCl was used.
MATERIALS AND METHODS
Representative membranes
The two RO membranes selected for this investigation
were the Desal CD and SG membranes (Osmonics, Minnetonka, MN). The CD membrane is a heat-treated cellulose triacetate/diacetate blend membrane, and the SG
membrane is a thin-film composite membrane. Both membranes were supplied as dry sheets and stored in ultrapure
water at 5°C. Selection of the CD and SG membranes was
based on their relative smoothness in comparison to the
radius of curvature of the colloids investigated. AFM images revealed that the CD membrane had a root-meansquare (RMS) roughness of 2 nm and a maximum peak to
valley distance of 25 nm, while the SG membrane had an
RMS roughness of 30.2 nm and a maximum peak to valley distance of 262 nm. Thus, both membranes appear
smooth when considered on a scale comparable to the radius of curvature of the colloid probe (minimum of 2.5
mm). This is necessary for accurate AFM force measurements on the membrane surface (Butt et al., 1995).
Representative colloids
The three colloids selected for this investigation were
silica colloids, alumina colloids, and polystyrene micros-
pheres. The silica colloids (SS05N, Bangs Laboratories,
Inc., Fishers, IN) were supplied dispersed in deionized water; the dispersion was stored at room temperature. According to the manufacturer, the silica colloids have an average particle diameter of 5 mm and a density of 1.96
g/cm3. The alumina colloids (D25, RSA Le Rubis SA, Jarrie, France) were supplied as a powder and stored at room
temperature. According to the manufacturer, the alumina
colloids have an average particle diameter of 25 mm and
a density of 2.0 g/cm3. The polystyrene spheres (PP-50100, Spherotech, Libertville, IL) were supplied dispersed
in deionized water; the dispersion was stored at room temperature. According to the manufacturer, the polystyrene
spheres have an average particle diameter of 5.26 mm and
a density of 1.05 g/cm3.
Electrokinetic measurements
Zeta potentials of the membranes were determined using a streaming potential analyzer (BI-EKA, Brookhaven
Instruments Corp., Holtsville, NY). Measurements were
conducted using a 10 mM NaCl solution at 25°C. Streaming potential was evaluated over the pH range of 3 to 11
for both membranes. Zeta potential was calculated from
the measured streaming potential using the HelmholtzSmoluchowski equation with the Fairbrother and Mastin
substitution. A detailed description of the measurement
procedure and zeta potential calculation can be found
elsewhere (Childress and Elimelech, 1996, 2000). Zeta
potentials of the colloids were determined using microelectrophoresis (Laser Zee Meter Model 500, Pen Kem,
Bedford Hills, NY). Electrophoretic mobility was evaluated with a background electrolyte of 0.01 M NaCl over
a pH range of 3 to 9. Zeta potential was calculated from
the measured electrophoretic mobility using the Smoluchowski equation.
Surface energy measurements
Automated goniometer. Contact angle measurements
were performed using an NRL Contact Angle Goniometer (Rame Hart, Mountain Lakes, NJ). The goniometer
has the capability of measuring contact angle using both
the sessile drop and captive bubble methods. In the sessile drop method, a drop of probe liquid is placed on a
dry surface; in the captive bubble method, the surface is
placed in a quartz cell, which contains the probe liquid,
and an air bubble is released onto the surface. The captive bubble method was used to measure membrane contact angle because of its numerous advantages over the
sessile drop technique (Kwok et al., 1996; Nabe et al.,
1997; Rosa and Pinho, 1997; Tröger et al., 1997; Palacio et al., 1999; Roudman and DiGiano, 2000; Brant and
Childress, 2002).
MEMBRANE–COLLOID INTERACTIONS
417
Probe liquids. The contact angle probe liquids selected
for this investigation were ultrapure water, glycerol, formamide, bromonaphthalene, and diiodomethane. The ultrapure water was obtained from a Millipore (Burlington,
MA) water purification system; the other probe liquids
were obtained from Fisher Scientific (Pittsburgh, PA).
Additionally, low energy alkanes (tetradecane, n-dodecane, decane, and heptane) were used to determine effective pore radius in the colloid thin-layer wicking measurements. The three surface tension components (gLW ,
g1 , and g2 ) as well as the polar energy component (gAB ),
the total free energy component (gTOT ), and the viscosity (h) of each probe liquid are shown in Table 1.
Measurement of membrane surface energy. A membrane coupon having the approximate dimensions of
1.0 3 0.25 in was cut from the membrane sample,
mounted on the sampling plate, and then lowered into the
probe liquid. A 10-mL air bubble was delivered to the
membrane surface and two contact angles (one on each
side of the bubble) were measured and averaged. A minimum of three coupons and three air bubbles per coupon
were used for each membrane. Additional details of the
membrane surface energy measurements can be found
elsewhere (Brant and Childress, 2002).
Measurement of colloid surface energy. Colloid contact angle was measured using the thin-layer wicking
technique (van Oss et al., 1992; Holysz and Chibowski,
1994; Liu et al., 1997; Teixeira et al., 1998; Norris et al.,
1999). The thin-layer wicking technique is based on the
Washburn equation, which describes capillary rise
through a packed colloidal bed (van Oss et al., 1992):
tRg1cosu
H2 5 }
2h
(8)
where t is the time required for the solvent to rise a distance H through the packed colloidal bed; R is the efTable 1.
fective interstitial pore radius of the colloid bed; gl is the
total surface tension of the solvent; u is the contact angle between the colloid and the solvent; and h is the viscosity of the solvent. For the Washburn equation to be
applied to a system, a linear relationship between H 2 and
t must be observed (van Oss et al., 1992; Holysz and Chibowski, 1994). Applying the Washburn equation results
in two unknowns, R and u. To determine R, several perfectly wetting liquids (i.e., liquids for which cos u 5 1)
must be wicked through the colloid bed (van Oss et al.,
1992; Norris et al., 1999). The spreading liquids used in
this investigation were tetradecane, n-dodecane, decane,
and heptane. R is calculated as the slope of the regression line passing through the origin of a plot of 2hH 2 /t
vs. gl. Once R has been determined for a colloid, contact
angle is measured using water, formamide, ethylene glycol, and bromonaphthalene.
Contact angles from the apolar probe liquids are used
to calculate the g LW component for a solid surface.
Bromonaphthalene and diiodomethane are the only two
apolar liquids that meet the criteria of g TOT . 40 mJ/m2
(van Oss, 1993). This is necessary to eliminate the need
to consider spreading pressure in Young’s equation for
calculating surface energetics from contact angle data.
However, polystyrene is known to be soluble in both
bromonaphthalene and diiodomethane (Busscher et al.,
1984; van Oss et al., 1992). Therefore, an alternate
method was used to estimate gLW for the polystyrene microspheres (van Oss et al., 1992). In this method, g LW
is the value of gl at the intersection of the linear plots of
2hH 2/t vs. gl for all spreading and nonspreading probe
liquids.
To create the thin layer for the wicking measurements,
a 5% (w/v) colloidal dispersion was deposited onto a precleaned glass slide (25 3 100 mm) (Fisher Scientific),
which had a graduated scale attached to the back. The
dispersion was left to dry on the slide overnight under
ambient conditions. The slides were then placed in an
Surface energy properties (mJ/m2) and viscosity (poise) of probe liquuids at 20°C.
Heptane
Decane
n-Dodecane
Tetradecane
Water
Ethylene glycol
Formamide
Glycerol
Bromonaphthalene
Diiodomethane
gTOT
gLW
g1
g2
gAB
h
20.1
23.8
25.35
26.6
72.8
48.0
58.0
64.0
44.4
50.8
20.1
23.8
25.35
26.6
21.8
29.0
39.0
34.0
44.4
50.8
0
0
0
0
25.5
1.92
2.28
3.92
0
0
0
0
0
0
25.5
47.0
39.6
5.74
0
0
0
0
0
0
51.0
19.0
19.0
9.5
0
0
0.00409
0.00920
0.01493
0.02180
0.01000
0.19900
0.04550
14.9000
0.04890
0.02800
Ref. (van Oss et al., 1992)
ENVIRON ENG SCI, VOL. 19, NO. 6, 2002
418
oven at 110°C overnight to remove any residual pore water that would dilute the probe liquid and possibly change
the probe liquid’s surface tension and viscosity (van Oss
et al., 1992). Following oven drying, the slides were
stored in a dessicator until wicking measurements were
made.
The first step in the thin-layer wicking measurements
was to equilibrate the colloid-coated glass slides with each
of the organic solvents used. To do this, the coated slide
and probe liquid were housed in a cylindrical glass container fitted with an airtight ground glass stopper (Fisher
Scientific). Equilibrating the coated slide with the organic
vapors for 1 h prevented excessive evaporation, and hence,
a depressed rate of capillary rise, during the wicking process (van Oss et al., 1992). After equilibration, the coated
slides were vertically immersed to a depth of 5 mm in a
probe liquid. Then, the vertical movement of the liquid
through the colloidal bed was measured using a stopwatch
and the graduated scale attached to the back of the glass
slide. The measurement stopped once the liquid had traversed a distance of approximately 40 mm.
AFM measurements
AFM force measurements were made using a Nanoscope
IIIa multimode atomic force microscope (Digital Instruments, Santa Barbara, CA) and the colloid probe technique
(Butt et al., 1995; Bowen et al., 1998). Measurements were
conducted in a fluid cell with 10 mM NaCl at pH 5.4 and
at room temperature. Measurements were made at three
separate locations on a membrane sample. Twenty measurements were performed at each location to calculate
an average force vs. scanner position plot. Additionally,
a single scan was also performed for each of the membrane–colloid pairs.
Figure 1. Penetration time of alkanes in thin-layer wicking
experiments for the silica colloid.
BRANT AND CHILDRESS
Table 2. Free energy of cohesion (mJ/m2) for membranes
and colloids.
Surface
DGsws
CD
SG
Alumina
Silica
Polystyrene
219.38
214.50
22.83
0.34
22.48
Colloid probes were prepared by attaching a single colloid to the end of a tipless cantilever following the method
developed by Ducker et al. (1991). Tipless silicon nitride
cantilevers (Digital Instruments) were used. The thermal
noise method (Hutter and Bechhoefer, 1993) was used to
determine the spring constant of the colloid-tipped cantilever.
RESULTS AND DISCUSSION
Surface characterization
Streaming potential measurements for the CD and SG
membranes showed that both have a weak negative zeta
potential (22.5 and 26.6 mV, respectively) at pH 5.4.
Electrophoretic mobility measurements for the alumina,
polystyrene, and silica colloids revealed more substantial
zeta potentials (23, 259, and 247 mV, respectively) at
pH 5.4. Thus, the colloid zeta potentials were substantially larger in magnitude than the membrane zeta potentials at pH 5.4. Therefore, the electrostatic double layer
interactions between the membranes and colloids involve
highly asymmetric surfaces with very different potentials.
Representative thin layer wicking plots for the silica colloid and spreading liquids decane, n-dodecane, tetradecane, and heptane are shown in Fig. 1. The effective interstitial pore radius was calculated from the linear plots
of H 2 vs. t. Results from similar experiments for nonspreading liquids (i.e., water, formamide, and bromonaphthalene), together with the pore radius values, were
used in Equation (8) to calculate contact angle for each
nonspreading liquid on silica. The linear (R2 . 0.9) behavior represented in Fig. 1 was characteristic of thin-layer
wicking plots for all of the colloids investigated, thereby
validating the use of the Washburn equation (van Oss et
al., 1992).
Contact angle results from the thin-layer wicking measurements (for the colloids) and from the captive bubble
method (for the membranes) were used in combination
with zeta potential measurements to determine cohesive
and adhesive free energies. Table 2 shows the free en-
MEMBRANE–COLLOID INTERACTIONS
419
ergy of cohesion per unit area (DGsws ) for each of the
membranes and colloids studied. The free energy of cohesion is the interaction free energy per unit area when
two surfaces of the same material are immersed in a solvent (in this case, water) and brought into contact. These
values provide quantitative insight into the hydrophobicity/hydrophilicity of the membranes and colloids. Positive values of the cohesive energy imply hydrophilic surfaces, while negative values indicate hydrophobic surfaces
(van Oss et al., 1988; van Oss, 1993). Based on this, the
CD membrane is strongly hydrophilic, the SG membrane
is strongly hydrophobic, the alumina and polystyrene colloids are weakly hydrophobic, and the silica colloid cannot be said to be hydrophobic or hydrophilic with DGsws
approximately equal to zero. It is important to note that
the free energy of cohesion may provide some qualitative
insight into potential interactions between membranes and
colloids, however; it is unable to provide a quantitative assessment of the adhesive energy between the two surfaces
(Brant and Childress, 2002).
Table 3 shows DLVO and XDLVO predictions of the
free energy of adhesion per unit area (DGmlc ) for each of
the membrane–colloid pairs studied. The DLVO theory
predicts a weak attraction ranging from 22.50 to 25.57
mJ/m2 for each of the membrane–colloid pairs. The
XDLVO predictions show that inclusion of AB interactions results in a substantially different prediction for the
free energy of adhesion for the membrane–colloid pairs.
For the CD membrane, the XDLVO approach predicts a
repulsive interaction at contact for each of the colloids
due to the hydrophilic nature of the CD membrane. This
is completely opposite of the attractive interaction predicted by the DLVO theory. For the SG membrane, the
XDLVO approach predicts a much stronger attraction
than was predicted by the DLVO theory due to the hydrophobic nature of the SG membrane.
Quality of AFM forces curves and determination
of surface contact
The overall quality of a measured force curve can be
assessed by the scatter in the data following contact beTable 3. DLVO and XDLVO predictions for interaction
energy at contact (mJ/m2).
DLVO
CD
SG
XDLVO
CD
SG
Alumina
Silica
Polystyrene
22.50
23.25
25.57
25.08
23.10
21.29
9.75
26.86
5.19
210.18
9.05
24.99
Figure 2.
Representative force vs. piezo scanner position plot.
tween the probe and surface (Senden, 2001). Figure 2
shows a representative force vs. scanner position plot
illustrating both approach and retraction curves for a
membrane–colloid pair. The minimal scatter between the
approach and retraction curves demonstrates that no detectable deformation is occurring upon contact and retraction of the colloid probe from the membrane surface.
The presence of a substantial amount of deformation
upon contact would make it very difficult to isolate repulsive interactions from the elastic properties of the
membrane (Cappella and Dietler, 1999). Figure 2 is representative of all measured force curves examined in this
investigation. This investigation focused only on the
force of interaction upon approach between the membranes and colloids; therefore, retraction curves are not
included in subsequent measured force profiles.
In addition to the averaged force profiles presented for
each membrane–colloid pair, single scans were also measured. Single scans, using fresh probes, were performed
to assess the possible contamination of the colloid probes
during multiple approach and retraction cycles. For each
of the membrane–colloid pairs tested it was found that
the averaged force profiles were similar to those measured for the single scans.
To accurately analyze AFM force plots it is important
to determine the contact point, or point of zero separation, between the colloid probe and the membrane surface (Freitas and Sharma, 2001). This is especially important when investigating short-range forces, which may
be misinterpreted if the contact point is not accurately defined. In AFM force plots, the colloid and membrane are
said to be in contact once cantilever deflection becomes
a linear function of piezo scanner position (compliance)
(Milling et al., 1996; Freitas and Sharma, 2001). Figure
3 shows the normalized force, or interaction force divided
ENVIRON ENG SCI, VOL. 19, NO. 6, 2002
420
BRANT AND CHILDRESS
amination reveals a point where the line deviates from a
strictly linear behavior. The point that separates the linear compliance region from the almost linear pseudocompliance region is roughly determined as the contact
point. For this reason, it remains difficult to compare separation distances for theoretical predictions and AFM
force measurements without an error of several nanometers (Butt et al., 1995). Determining separation distance
is further complicated by the presence of surface roughness (Cappella and Dietler, 1999) and friction between
the two surfaces (Hoh and Engel, 1993), which are not
accounted for in the theoretical calculations. Therefore,
approach curves are shown as normalized force as a function of piezo scanner position instead of as a function of
separation distance.
Figure 3. Method for determining the point of contact between the colloid probe and membrane surface for (a) attractive and (b) repulsive interaction.
by colloid radius, as a function of scanner position for
two different membrane–colloid pairs. The location on
the force plots where contact occurs has been magnified
to illustrate how the contact point was determined. In Figure 3(a) the interaction between the colloid probe and the
membrane surface is completely attractive. Because no
repulsion exists, the contact between the colloid and the
membrane surface creates an obvious minimum that
makes the point of contact easy to define. In cases where
a steep repulsive force profile exists [Fig. 3(b)], the point
of contact is not as easily determined (Milling et al.,
1996). In these cases, cantilever deflection during the
measurement is nearly linear and the system is therefore
said to be in pseudocompliance (Milling et al., 1996).
Figure 3(b) shows a pseudocompliance region where the
short-range interaction between the colloid probe and
membrane is strongly repulsive. In this case, close ex-
Figure 4. (a) DLVO and XDLVO interaction energy profiles
for the CD membrane and alumina colloid; I 5 10 mM NaCl,
pH 5 5.4. (b) Normalized force vs. piezo scanner position for
the CD membrane and an alumina colloid-tipped cantilever; I 5
10 mM NaCl, pH 5 5.4.
MEMBRANE–COLLOID INTERACTIONS
421
Force curve analysis
Figures 4, 5, and 6 show the predicted (a) and measured (b) force profiles for the CD membrane and alumina, polystyrene, and silica colloids, respectively. Figures 7, 8, and 9 show the predicted (a) and measured (b)
force profiles for the SG membrane and alumina, polystyrene, and silica colloids, respectively. For the theoretically predicted force profile, the normalized force is plotted against separation distance on a semi logarithmic
scale to illustrate the differences in the predicted force
curves at short separations. The measured force profile
represents the interaction force measured upon approach
of the colloid probe to the membrane surface.
In Fig. 4(a), both the DLVO and XDLVO predictions
are similar at large separations (.10 nm). Upon close approach, the DLVO theory demonstrates a completely at-
Figure 6. (a) DLVO and XDLVO interaction energy profiles
for the CD membrane and silica colloid; I 5 10 mM NaCl, pH 5
5.4. (b) Normalized force vs. piezo scanner position for the CD
membrane and a silica colloid-tipped cantilever; I 5 10 mM
NaCl, pH 5 5.4.
Figure 5. (a) DLVO and XDLVO interaction energy profiles
for the CD membrane and polystyrene colloid; I 5 10 mM
NaCl, pH 5 5.4. (b) Normalized force vs. piezo scanner position for the CD membrane and a polystyrene colloid-tipped cantilever; I 5 10 mM NaCl, pH 5 5.4.
tractive regime. This is due to the opposite charges (22.5
mV for the CD membrane and 23 mV for the alumina
colloid) of the two interacting surfaces, which result in
an attractive EL component. The XDLVO approach predicts a shallow attractive secondary minimum prior to entering a strongly repulsive region. The repulsion results
from the hydrophilic character of the CD membrane
(DGsws 5 19.4 mJ/m2 ). This illustrates that inclusion of
AB interactions results in a dramatically different predicted interaction profile for the CD-alumina pair.
In Fig. 4(b) the measured force vs. scanner position
curve is shown for the CD–alumina pair. Upon approach,
the colloid probe detects a slight repulsion, which is likely
due to instrument noise, prior to encountering a strong
repulsive force. The repulsive force produces an almost
linearly increasing force with scanner position before
ENVIRON ENG SCI, VOL. 19, NO. 6, 2002
422
BRANT AND CHILDRESS
dicts a weak repulsion prior to entering a strong attractive primary minimum. Although the CD membrane and
polystyrene colloid are similarly charged, the polystyrene
colloid charge (258 mV) is much greater in magnitude
than the CD membrane charge (22.5 mV). This asymmetry results in a mild attraction (Hunter, 1986; Brant
and Childress, 2002). The XDLVO approach predicts a
larger attractive secondary minimum than was observed
for the CD–alumina system prior to interacting with a
strong repulsion.
In Fig. 5(b), the measured force vs. scanner position
curve is shown for the CD–polystyrene pair. Interaction
between the colloid and membrane is attractive before
becoming repulsive at close separation. The attractive
secondary minimum seen in the measured force curve is
predicted by XDLVO theory. Upon approach, the DLVO
Figure 7. (a) DLVO and XDLVO interaction energy profiles
for the SG membrane and alumina colloid; I 5 10 mM NaCl,
pH 5 5.4. (b) Normalized force vs. piezo scanner position for
the SG membrane and an alumina colloid-tipped cantilever; I 5
10 mM NaCl, pH 5 5.4.
contact with the membrane. The nearly linear behavior
of the approach curve prior to contact suggests that a
strong repulsive interaction exists between the two surfaces upon close approach. The measured force curve for
the CD–alumina system agrees with the interaction sequence predicted by the XDLVO approach, which considers short-range AB interactions. The atomic force microscope detects the repulsive hydrophilic interactions
that are predicted by the XDLVO approach just prior to
contact. It is possible that because the attractive secondary minimum (seen in Fig. 4a) was shallow and acted
over a relatively short range, it was not detected by the
AFM at the scan rate used (9.3 Hz).
Figure 5 represents the predicted and measured force
profiles for the CD membrane and polystyrene colloid.
Similar to the CD–alumina system, the DLVO theory pre-
Figure 8. (a) DLVO and XDLVO interaction energy profiles
for the SG membrane and polystyrene colloid; I 5 10 mM NaCl,
pH 5 5.4. (b) Normalized force vs. piezo scanner position for
the SG membrane and a polystyrene colloid-tipped cantilever;
I 5 10 mM NaCl, pH 5 5.4.
MEMBRANE–COLLOID INTERACTIONS
Figure 9. (a) DLVO and XDLVO interaction energy profiles
for the SG membrane and silica colloid; I 5 10 mM NaCl,
pH 5 5.4. (b) Normalized force vs. piezo scanner position for
the SG membrane and a silica colloid-tipped cantilever; I 5 10
mM NaCl, pH 5 5.4.
theory predicts attraction until contact is reached,
whereas the XDLVO approach predicts a strong repulsion, following the attractive secondary minimum, prior
to contact. Indeed, it is the latter trend that is seen in the
measured force curve.
Figure 6(a) shows the theoretical force vs. separation
distance curves for the CD membrane and silica colloid.
Again, the DLVO theory predicts a completely attractive
regime, which is likely due to the asymmetric surface
charges of the silica colloid (247 mV) and the CD membrane (22.5 mV). The XDLVO approach predicts a shallow attractive secondary minimum prior to entering a
strongly repulsive region. When comparing this to the
measured force vs. scanner position curve [Fig. 6(b)], the
measured force curve again agrees with the interaction
sequence predicted by the XDLVO approach.
423
Figure 7 shows the theoretically predicted and measured
force profiles for the SG membrane and polystyrene colloid. In Fig. 8(a), both the DLVO and XDLVO theories
predict attraction for the SG membrane and alumina colloid. The hydrophobic nature of the SG membrane
(DGsws 5 214.5 mJ/m2 ) results in the XDLVO approach
predicting a substantially different interaction than that for
the hydrophilic CD membrane (DGsws 5 19.4 mJ/m2).
Therefore, because the AB interactions for the SG membrane are attractive, both the DLVO and XDLVO predictions are similar and only differ in magnitude. The
XDLVO approach predicts a steeper slope than the DLVO
theory. This is due to the fact that the XDLVO approach
accounts for the hydrophobic attraction between the SG
membrane and alumina colloid.
In Fig. 7(b), the measured force vs. scanner position
curve is shown for the SG–alumina pair. Upon approach,
the colloid probe detects no repulsion before encountering a strong, short-range attractive force. The nearly linear character of the approach curve indicates that the attraction is strong. As was predicted by both the DLVO
theory and the XDLVO approach, there was no repulsion
prior to contact. Comparing Fig. 8(b) to Figs. 5–7 there
is a noticeable difference in the slopes of the measured
repulsive and attractive approach curves. The difference
in slopes for the measured attractive and repulsive curves
results from the mechanical operation of the cantilever
(Cappella and Dietler, 1999; Heinz and Hoh, 1999). As
the colloid probe approaches the membrane surface, an
instability occurs when the force gradient becomes larger
than the elastic spring constant of the cantilever (Cappella and Dietler, 1999). If the interaction force is attractive then the colloid will jump into contact with the
membrane as long as no short-range repulsive interactions are present, resulting in an approach curve with a
steep slope. On the other hand, if the interaction force is
repulsive, the approach curve will have a smooth, continually increasing slope as no jump event occurs.
Figure 8(a) shows theoretical force vs. separation distance curves for the SG membrane and polystyrene colloid. Like the CD–alumina system, the DLVO and
XDLVO predictions are similar. However, in this case, a
repulsive barrier exists prior to the attractive primary minimum. When comparing this to the measured force versus
scanner position curve [Fig. 8(b)], upon approach the colloid probe detects essentially no repulsion before encountering a strong, short-range attractive force. It is possible
that the repulsive interaction could not be clearly discerned
from the approach curve due to deviation of the approach
curve from the zero force line at large separation distances.
This deviation may be the result of the colloid probe deflecting due to viscous drag on the colloid probe (Hoh and
Engel, 1993; Butt et al., 1995; Cappella and Dietler, 1999),
ENVIRON ENG SCI, VOL. 19, NO. 6, 2002
424
or it may be the result of optical interference by reflections
of the diode laser from both the cantilever and membrane
(Cappella and Dietler, 1999; Heinz and Hoh, 1999).
Figure 9 shows the theoretically predicted and measured force profiles for the SG membrane and silica
colloid. As seen in Fig. 9(a), the DLVO and XDLVO
predictions are similar to the SG–polystyrene predictions. However, the measured force vs. scanner position curve [Fig. 9(b)] does not resemble the measurements for the SG–polystyrene system. Instead, the
SG–silica curve exhibits a step-wise attraction. These
steps were detected in all force curves for the SG–silica pair. This type of behavior has been observed in
previous investigations (Hoh et al., 1992; Israelachvili,
1992; Bowen et al., 1999b) that used AFM to measure
interaction forces. Several possibilities have been proposed to explain the observed force steps. Israelachvilli
(1992) concluded that layers of ordered water molecules (i.e., structuring of water molecules or hydration)
at a mica surface caused oscillations in the approach
curve using an AFM tip. Similar behavior was observed
by Hoh et al. (1992) upon retraction of a silicon nitride
tip from a glass surface. Here it was proposed that the
step-wise character of the retraction curve resulted
from the tip pulling away from different force minima
generated by ordered layers of water molecules at the
glass surface. In the current investigation, hydration of
the silica surface could occur as a result of hydrogen
bonds being formed between surface silanol groups and
surrounding water molecules (Vigil et al., 1994; Pashley et al., 1998). Hydration of the SG membrane surface is expected to be minimal due to its hydrophobic
character (DGsws 5 214.5 mJ/m2 ). Therefore, the force
steps seen in Fig. 9(b) could result from the breaking
of the hydrogen bonds between the water molecules,
and the subsequent displacement of the ordered water
layers from the silica surface.
A second possible explanation for the step-wise attraction is contamination of the colloid probe by longchained polymers or functional groups. The colloid probe
can be contaminated with these structures as it is repeatedly brought towards and away from the membrane surface during multiple approach and retraction cycles
(Bowen et al., 1999c). To determine if the step behavior
is due to contamination of the colloid probe, a single scan
was performed on the SG membrane using a fresh silica
probe. Similar to the force curves developed from repeated measurements, the step behavior was observed in
the single force measurement curve. This indicates that
hydration, and the subsequent displacement of ordered
water molecules at contact, may be the more likely of the
two possibilities.
BRANT AND CHILDRESS
Surface roughness considerations
The theoretical predictions for surface interactions
used in this study were based on the assumption that all
surfaces were perfectly smooth. AFM analysis of the
membrane samples showed that both membranes posses
a certain degree of surface roughness (as described earlier). Further, scanning electron microscope (SEM) images of the colloids revealed that each of the colloids possessed some asperities on their surfaces, although exact
roughness dimensions were not determined. Models have
shown that force profiles derived for rough surfaces deviate significantly from those derived assuming smooth
surfaces (Suresh and Walz, 1996, 1997; Bowen and
Doneva, 2000; Shellenberger and Logan, 2002). Suresh
and Walz (1996, 1997) demonstrated that surface roughness extends the range and depth of the secondary minimum while decreasing the magnitude of the potential energy barrier. A similar conclusion was reached by Bowen
and Doneva (2000), who found that repulsive interactions
were greater in magnitude on flat sections than for peaks
on a membrane surface. Therefore, surface roughness
may result in a longer-ranged attraction than might be expected from theory. The CD membrane was relatively
smooth (RMS roughness of 2 nm) and most likely was
minimally affected by surface roughness effects. Conversely, the SG membrane was considerably rougher
(RMS roughness of 30.2 nm), especially when compared
to the scale over which the measured forces were found
to act (approximately 10–20 nm). Consequently, it is possible that the surface roughness of the SG membrane
masked some repulsive interactions that may have been
present (Suresh and Walz, 1996, 1997). This may explain
the lack of a measurable energy barrier for the SG–polystyrene pair (Fig. 8), although it was predicted by both
the DLVO and XDLVO theories.
Implications for membrane processes
The results presented in this study have a number of
implications for membrane fouling and performance. Previously, it was shown that inclusion of AB interactions
into the DLVO theory results in more accurate predictions of colloidal fouling tendencies of membrane surfaces during RO bench scale testing (Brant and Childress,
2002). Knowledge of the presence and strength of these
additional interactions is thus critical in determining the
overall fouling propensity of a membrane for a particular feed stream chemistry. For instance, the short-range
repulsive interactions predicted by the XDLVO approach
and later measured using AFM may reduce contact between membranes and colloids during treatment processes. This may be of particular interest in determining
MEMBRANE–COLLOID INTERACTIONS
425
the maximum critical flux for a membrane process
(Bowen et al., 1999a). Critical flux represents a condition where hydrodynamic drag forces, which transport
colloids from the bulk to the membrane surface, are
roughly balanced by repulsive interaction forces (Field et
al., 1995; Howell, 1995; Bowen et al., 1999a). Operating a membrane process at the critical flux is therefore
desirable, as it results in reduced membrane fouling. Accurate assessment and characterization of membrane–
colloid interactions may allow for optimization of repulsive membrane-colloid interactions in order to operate at
greater critical flux values.
sistance with streaming potential measurements. The authors would also like to thank Steve Kloos at Osmonics
for supplying membranes.
CONCLUSION
BHATTACHARJEE, S., SHARMA, A., and BHATTACHARYA, P.K. (1996). Estimation and influence of long
range solute. Membrane interactions in ultrafiltration. Ind.
Eng. Chem. Res. 35(9), 3108–3121.
By comparing the force profiles for all of the membrane–
colloid pairs, it is clear that the membranes generally control the behavior of the membrane–colloid system. In other
words, regardless of what colloid the membrane was paired
with, the predicted and measured force curves were quite
similar for each membrane. The primary reason for this
behavior is the considerably higher surface energies, principally the AB component, of the membranes compared
to the colloids. This same conclusion was reached in a previous study where the membrane–colloid interactions were
controlled by the surfaces having the greater surface energies (Brant and Childress, 2002).
Furthermore, for strongly hydrophilic systems (i.e., the
CD membrane pairs), the XDLVO approach (which considers AB interactions) predicted substantially different
interaction energies than the DLVO theory. When comparing the DLVO and XDLVO predictions with the measured force profiles, the measured force curves agreed
with the interaction sequence predicted by the XDLVO
approach. For strongly hydrophobic systems (i.e., the SG
membrane pairs), the XDLVO approach predicted an attractive interaction, similar to the DLVO theory although
greater in magnitude. In this case, the measured force
curves agreed with the interaction sequence seen in both
DLVO and XDLVO predictions.
ACKNOWLEDGMENTS
The authors would like to acknowledge the support of
the National Science Foundation, Division of Chemical
and Transport Systems under CAREER grant CTS0093617, and the U.S. Bureau of Reclamation, Water
Treatment Engineering and Research Group under research grant 98-FC-81-0057. The authors thank Seungkwan Hong at the University of Central Florida for his as-
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