SURFACE ENERGY CHARACTERIZATION AND COMPETITIVE SURFACE
EQUILIBRIA USING CONTACT ANGLE
By
Barrack Perez Stubbs

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirement
for the degree of
Chemistry – Master of Science
2017

ABSTRACT
SURFACE ENERGY CHARACTERIZATION AND COMPETITIVE SURFACE
EQUILIBRIA USING CONTACT ANGLE
By
Barrack Perez Stubbs
Surface energy measurements are usually difficult to assess when not considering a solidair or liquid-air interface. Contact angles was used as a method of obtaining the interfacial energy
of a silanol-water surface using carbon tetrachloride as a probing liquid. The theory for this work
operated under the assumption that the pKa of a silanol surface could be measured by obtaining a
titration like curve as a function of pH. A decrease in contact angle of about 7 o was observed at a
pH (pKa) of 3.5. This corresponds to an energy difference of 2 mN/m.
Additionally, the effect of competing equilibria was investigated using this technique. The
above result was see at an ionic strength of 0.1M NaCl but the effect was not observed at 0.01M.
This lead to the assertion that there is a competition between H+ and Na+ for the deprotonated
silanols. At these conditions the association constant for Na+ with the surface, KNa, was found to
be 7 x 10-3.

ACKNOWLEDGMENTS

Special thanks is given to my research group who helped with ideas and theory for this
work, to Jillian Mutcher whose question sparked this investigation, Scott Bankroff who helped
with modifying the substrates used, and to Dr. Gary Blanchard for the opportunity to work under
him throughout the project.

iii

TABLE OF CONTENTS

LIST OF TABLES

v

LIST OF FIGURES

vi

Chapter 1
Introduction
LITERATURE CITED

1
1
9

Chapter 2
Abstract
Introduction
Experimental Section
Results and Discussion
Conclusions
APPENDIX
LITERATURE CITED

11
11
11
13
14
19
21
28

Chapter 3
Conclusions and Future Directions
Future Work
LITERATURE CITED

31
31
32
35

iv

LIST OF TABLES

Table 1. Surface Energy. Surface energy values calculated from the contact angle
measurements and Wilhelmy plate measurements

v

22

LIST OF FIGURES

Figure 1. Dye Sensitized Solar Cell. A schematic of a dye (red line) sensitized solar cell that is
used for energy conversion. Titanium dioxide is used as the electron transfer material from
the dye to the electrode.
4
Figure 2. Representative Silica Surface. Example image of a silica surface. Q1 and Q2 silanols
are shown on the surface as well as siloxane bridges under the surface. These bridges can
also be above the surface.
5
Figure 3. Liquid Drop on Solid Surface. Schematic of a contact angle image. A liquid is placed
onto the surface and the balanced forces create the profile of the drop.
7
Figure 4. Young’s Equation. Relating contact angle (theta) to the balancing of forces where
𝛾SV is the solid-vapor energy, is the 𝛾SL solid-liquid energy, and 𝛾LV is the liquid-vapor energy. 8
Figure 5. Contact angle measurements. Contact angle measurements as a function of pH at
0.1M ionic strength (a) and 0.01M ionic strength (b).

23

Figure 6. Association Constant Model. The apparent pKa transition was modelled as a function
of association constant (a) and of sodium concentration (b). The contact angle is shown
as a function of pH.
24
Figure 7. Surface energy difference. The change in surface energy affects the magnitude
of the contact angle change. This model shows energy changes from 0 mN/m to 2 mN/m

25

Figure 8. Zisman Plot. Zisman plot approximation used to determine the surface energy of
silanol in air.

26

Figure 9. Ionic Strength on Buffer shape. The contact angle was measured at different pH
values under two different ionic strength. The image left shows the set-up of the experiment. 27
Figure 10. Phosphorylated surface data. pKa values are 7.2 and 12.3. The first proton,
pKa 2.2, is the one that is reacted when the phosphate group is attached to the surface.

vi

34

Chapter 1

Introduction
Interfaces are ubiquitous in chemical reactions and separations, and their physical and
chemical properties determine their utility. Interfaces are defined by the contact between two or
more immiscible phases of matter. Surfaces provide a wide variety of supports on which physical
and chemical processes can happen. Due to the wide variety and often complex nature of surfaces,
it is typically difficult to characterize them adequately. In this document, fundamental surface
characteristics are examined using chemical equilibria and contact angle measurements to address
questions that remain to be fully understood regarding silica surfaces.
Phospholipid membranes provide a medium for reactions to happen in biological systems
and exhibit a range of physical and chemical properties depending on the function(s) they are
specialized for.1 Such membranes show distinct reactivity and selectivity and this has been an
attractive target for scientists to replicate. Model lipid bilayer interfaces are typically formed on
planar supports, composed of a limited number of components, and placed on support surfaces that
are suited for the intended application (e.g. electrochemistry, spectroscopy). The interaction of the
lipid molecules with the surface (e.g. silica, mica, gold, ITO) has been examined previously.2
Bilayer fluid properties have been investigated for their potential utility as biomimetic systems. 3
Monolayers and bilayers can be placed on supports with metal ions that are used to modulate the
strength of the interaction with the surface. The identity, charge and ionic radius of these metal
ions affect their interaction not only with the surface but with the lipids through the phosphate
head group.

1

The interactions between metal ions with either surfaces or functional groups can be
characterized. These associations are characterized by their characteristic free energy, in the same
manner as covalent bonds. Bond strengths are well documented through quantities such as lattice
strength and solubility products, depending on the system. If we consider sodium chloride, the
body dissociation energy is about 411 kJ/mol.4-5 In solution there is an electrostatic interaction
that changes based on the distance between the molecules. This is similar to what would be
expected on the surface. The metal ions are attracted to the surface and as such have their own
attraction/association energies.

Among the differences between surface and solution phase

interactions between specific metal ions and complexing species is the difference in solvation
energies for the complexing species in bulk solution and surface environments. While difficult to
model owing to the complexity and transient nature of the solvation process, such interactions are
certainly amenable to experimental evaluation.
Ionic and other associative interactions depend on factors such as pH, temperature,
concentration, and charge. These system properties affect both the metal ion and the surface. The
groups with which metal ions can complex are characterized by acid dissociation constant(s),
rendering the complexation process pH-dependent.
Metal and conducting oxide surfaces are employed in experiments that require conductive
surfaces.

Insulating oxide surfaces, such as silicon dioxide or titanium dioxide, are used

extensively in energy storage and conversion, and separations, for example. Transition metal
oxides and semi-metal oxides have also been used in certain applications.6
Energy conversion and storage is an area of current and long-term interest. As the
population continues to grow and countries continue to develop technologically, fossil fuels will
at some point become depleted, and energy demands will rise. Solar energy is an attractive target

2

for energy generation. In the late-20th century, solar cells were used as a method to convert solar
radiation to electrical energy.
In a chemical separation technique such as high performance chromatography, silica serves
as the support material on which chemical functionality is attached to facilitate the separation. The
silica surface contains reactive silanols that can be modified to suit the proposed target analyte(s).7
The interaction of the analytes with the surfaces mediates the separation process but the molecularscale details of these processes remain to be understood fully.
Oxide surfaces such as silica or titania can exhibit a wide range of surface morphologies,
from microcrystalline to amorphous, and the bulk surface structural features can likewise vary
widely. Among the consequences of this structural variability over a range of length scales is the
non-uniform accessibility of surface chemically-active species. For example, surface hydroxyl
functionality will exhibit different dissociation behavior when on an open surface region versus
when located deep within a pore or crease. Such morphology-dependent chemical properties
further complicate attempts to characterize and model such materials.
Dye-sensitized solar cells take advantage of surface-adsorbed optical absorbers (dyes) to
effect carrier injection into the conduction band of the acceptor semiconductor (TiO2). The dye is
typically a transition metal complex such as Ru(bpy)32+. Titanium dioxide, as a mesoporous
material (pore diameter < 50 nm), can be coated with a usefully large amount of Ru(bpy)32+ due
to its relatively large surface area. Titania is capable of supporting electron diffusion across its
surface. Its band gap is also suitable for absorption of ultraviolet (UV) radiation. Incident UV
(solar) photons excite the chromophore on the TiO2 surface which then transfer electrons to the
semiconductor, with subsequent carrier diffusion within the bulk material. A better understanding
of electron injection at the semiconductor surface is essential, although the limiting factor to

3

efficiency in such solar cells is recombination, and it is not clear that the semiconductor surface is
capable of functioning to make electron transport asymmetric across the interface. Substantial
fundamental work remains to be done.

e
-

e

-

TiO2

e

Ru
*

I

Ru/Ru

I

TiO2

TiO2

+

-

Figure 1. Dye Sensitized Solar Cell. A schematic of a dye (red line) sensitized solar cell
that is used for energy conversion. Titanium dioxide is used as the electron transfer material from
the dye to the electrode.

The chemical nature of these surfaces can also vary from sample to sample and depending
on the method in which they are prepared. The terminal groups on a silica surface are hydroxyls,
but there can be more than one type of hydroxyl group. Silanol groups are classified as Q1 through
Q3, with the superscript indicating the number of hydroxyl groups bonded to a parent silicon atom.
Silicon atoms that are bonded exclusively to other Si-O functionalities are designated Q0. The
distribution of the groups Q1 through Q4 in silica depends on the morphology and porosity of the
bulk material.8-9

4

Characterizing and mapping the distribution of Q1 to Q3 surface functionalities has been
attempted by others based on the different pKas characteristic for each type of hydroxyl group. A
complicating factor, as indicated above, is that in addition to the structural differences in different
silanol functionalities (Q1 through Q3), the local environment of the silanols can serve to alter the
effective dissociation constant(s) for these groups. Effects such as hydrogen bonding with
neighboring silanols and access to bulk aqueous solvent can alter the effective pKa of a silanol
group significantly.
The spatial distribution of the different types of silanol groups is also not understood well
nor characterized easily. This is partly a matter of the length scales involved and partly because
of the wide morphological variability in silica. While there is limited data available indicating the
spatial variability in the distribution of surface silanol groups, making such a determination
requires significant surface modification chemistry to be observable.10

Figure 2. Representative Silica Surface. Example image of a silica surface. Q1 and Q2
silanols are shown on the surface as well as siloxane bridges under the surface. These bridges can
also be above the surface.

5

The pKas of these silanol groups are generally accepted to be between 4.5 and 8.5,11
depending on both structural form (Q1 – Q3) and local morphology. Hydrogen bonded silanols,
and Q2 and Q3 silanols are thought to have higher pKa values due to stabilizing effects such as
hydrogen bonding between neighboring OH groups. Due to the distribution of silanol pKa values,
the silica surface will exhibit partial dissociation, with the extent of the dissociation extending over
several pH units. It is well established that at neutral pH a silica surface is characterized by a net
negative charge.
The surface charge of silica is exploited effectively in electrophoretic separations. The
charge on the surface interacts with the overlaying solution.12 In the presence of a potential
gradient, the fixed charges on the inside of a silica capillary and mobile charge carriers in the
solution contained within the capillary give rise to electroosmotic and electrophoretic flow. In the
absence of fixed surface charges, electrophoretic flow would not proceed and only electroosmotic
flow of solution phase ions would occur. In practice, there are multiple charged components in
solutions that are analyzed using electrophoresis due to the use of buffer(s), and the cationic
solution phase species (e.g. H+, Na+, K+, etc.) will compete for the silica surface (anionic) siloxide
sites. The details of these competitive equilibria have not been considered in detail to this point,
and we present a means in this Thesis to evaluate these competing processes.
The experiments described in this thesis focus on two phenomena that operate at a silica
interface. First, the surface-charge interacts with cations in an overlaying media. Even though the
surface is protonated to some extent there remains associative interactions between solution phase
cations from the buffer and the negatively charged siloxide functionality. The solution phase ions
are attracted to the surface and form an electric double layer. The competitive equilibria between

6

protons and specific metal ions in solution and the surface determines the properties of the
interface.
Because the extent of surface charge varies with experimental conditions such as cation
concentration (i.e. ionic strength) and pH, the surface energy varies. Surface energies can be
challenging to quantitate and we use several techniques in concert to evaluate them for the systems
reported in this work. We employ a variant of contact angle measurement in conjunction with
Wilhelmy plate measurements to characterize the constituent surface energies of the systems we
study, and in particular, we monitor how the surface energy for the silica surface varies with
experimental conditions. Contact angle measurements are described using the same physics used
to describe meniscus phenomena, and is based on the balance of energies between three phases of
matter. In the case of contact angle measurements, the liquid drop, the solid surface, and the
overlying medium (usually air), interact with each other and achieve a balance of forces (surface
energies) that determines the contact angle of the drop with the (solid) surface as described by
Young’s Equation.13 In 1805 Thomas Young developed a qualitative theory to explain surface
tension and the rise of liquids in capillaries.

Figure 3. Liquid Drop on Solid Surface. Schematic of a contact angle image. A liquid is
placed onto the surface and the balanced forces create the profile of the drop.

7

Figure 4. Young’s Equation. Relating contact angle (theta) to the balancing of forces
where 𝛾SV is the solid-vapor energy, is the 𝛾SL solid-liquid energy, and 𝛾LV is the liquid-vapor
energy.
Young’s Equation relates the contact angle ( in Fig. 3) to the surface energies, , where
𝛾SV is the solid-vapor interface energy, is the 𝛾SL solid-liquid interface energy, and 𝛾LV is the
liquid-vapor interface energy.

13

Changes in one or more of these energies is manifested as a

change in the measured the contact angle. For a silica surface, there is a change in surface charge
associated with the chemical composition of the (aqueous) overlayer, and changes in ionic
interactions that involve the (silica) surface will produce changes in SV and SL. It is these changes
that we sense as a function of the chemical composition of the aqueous overlayer. The work
contained in this Thesis demonstrates a method for measuring and quantitating the interfacial
energy of a solid surface in an aqueous medium, with a specific focus on the competitive equilibria
that determine the effective properties of the (silica) interface. Such data have not been reported
widely and knowledge of this information can be of direct use in chemical sensing and separations
applications.

8

LITERATURE CITED

9

LITERATURE CITED

1. Alberts, B.; Johnson, A.; Lewis, J., Molecular Biology of the Cell. 4th ed.; Garland Science:
New York, 2002.
2. Langmuir-Blodgett Films. 1990.
3. Kijewska, K.; Blanchard, G. J., Using Diffusion To Characterize Interfacial Heterogeneity,
Langmuir 2017, 33 (5), 1155-1161.
4. CRC Handbook of Chemistry and Physics. 95th ed.; Boca Raton, FL, 2014.
5. Dean, J. A., Lange's Handbook of Chemistry. McGraw-Hill: 1992.
6. O'Regan, B.; Grätzel, M., A low-cost, high-efficiency solar cell based on dye-sensitized TiO2
films, Nature 1991, 353, 737-740.
7. Krupczyńska, K.; Buszewski, B.; Jandera, P. Characterizing HPLC Stationary Phases 2004, p.
227 - 234.
8. Zhuravlev, L. T., Concentration of Hydroxyl Groups on the Surface of Amorphous Silicas,
Langmuir 1987, 3, 316-318.
9. Zhuravlev, L. T., The Surface Chemistry of Amorphous Silica. Zhuravlev model, Colloids and
Surfaces 2000, (173), 1-38.
10. Horne, J. C.; Huang, Y.; Liu, G.-Y.; Blanchard, G. J., The Correspondence Between Layer
Morphology and Intralayer Excitation Transport in Zirconium-Phosphonate Monolayers, Journal
of the American Chemical Society 1999, 121, 4419-4426.
11. Sulpizi, M.; Gaigeot, M.; Sprik, M., The Silica-Water Interface: How the Silanols Determine
the Surface Acidity and Modulate Water Properties, Journal of Chemical Theory and Computation
2012, 8 (3), 1037-1047.
12. Gouy, M., On The Constitution of the Electric Charge On The Surface In An Electrolyte, J.
Phys. Theor. Appl. 1910, 9 (1), 457-468.
13. Young, T., An Essay on the Cohesion of Fluid, Philosophical Transactions of the Royal
Society of London 1805, 95, 65-87.

10

Chapter 2

Abstract
Characterizing the composition of an oxide surface is critical to a range of applications in
separations and reaction chemistry. For silica surfaces, among the key issues is the competition
for occupancy of the siloxide (SiO-) sites by H+ and other cations. We have studied the competition
between H+ and Na+ for surface siloxide occupancy as a function of the concentrations of each
cation using the contact angle of a droplet of CCl4 on a silica surface immersed in aqueous solution
as the probe of surface energy. We find the dissociation constant for SiONa to be larger than the
SiOH dissociation constant, and with knowledge of the surface energy for CCl 4 in contact with
H2O, we are able to determine the surface energies of the SiOH-water, SiONa-water and CCl4SiOX interfaces.

Introduction
Characterizing the composition of an oxide surface is critical to a range of applications in
separations and reaction chemistry. For silica surfaces, among the key issues is the competition
for occupancy of the siloxide (SiO-) sites by H+ and other cations. We have studied the competition
between H+ and Na+ for surface siloxide occupancy as a function of the concentrations of each
cation using the contact angle of a droplet of CCl4 on a silica surface immersed in aqueous solution
as the probe of surface energy. We find the dissociation constant for SiONa to be larger than the
SiOH dissociation constant, and with knowledge of the surface energy for CCl 4 in contact with
H2O, we are able to determine the surface energies of the SiOH-water, SiONa-water and CCl4SiOX interfaces.

11

Oxide interfaces are among the most widely used surfaces in the chemical sciences. Silica
and alumina, for example, have found wide use in chemical separations, ranging from plate
chromatography to electrophoresis.
heterogeneous catalysis applications.

Titania has found use in solar energy conversion and
These interfaces share the common challenge of

characterization owing to their complex, and for some systems, amorphous structure.
In many instances, a key parameter in the utilization of an oxide surface is the extent to
which its chemically (re)active –OH functionalities are dissociated and what chemical species are
present in the system for the -O- sites to interact with. For liquid phase measurements, it is a simple
matter to measure the pH of a solution, but for oxide surfaces, gauging the extent of protonation
and/or occupancy by other (cationic) species poses a much greater challenge.11 Among the reasons
for this challenge is the inability to use electrochemically-based techniques, and the fact that the
surface silanol functionalities can interact with multiple different chemical species.11, 14 It is for
these reasons that we have devised an experimentally simple means of evaluating competitive
equilibria at an oxide surface.
We focus on silica in this work as an illustrative oxide surface, and consider the competition
for its accessible silanol groups in aqueous solution under conditions of variable [H+] and [Na+].
We measure the contact angle of a droplet of CCl4 on a silica surface immersed in aqueous solution.
Our data show that the contact angle of the CCl4 droplet changes with the pH and the pNa of the
aqueous solution, with both equilibria contributing to the observed pH-dependence of the droplet
contact angle.15-17 We describe these data in the context of competing equilibria and based on the
contact angle data and the known surface energy of the H2O-CCl4 interface, we can determine the
surface energies for the SiOH-water, SiONa-water and CCl4-SiOX interfaces. These data are, to
our knowledge, the first reports of the surface energies of these systems.

12

Experimental Section
Chemicals and preparation: For all measurements, the silica surface used was fused silica
in the form of a cuvette (ThorLabs). The aqueous solutions were prepared using 18 M-cm water
(Milli-Q). Carbon tetrachloride (CCl4, 99.9%, Sigma-Aldrich), sodium chloride (J.T. Baker),
potassium chloride (Spectrum) and hydrochloric acid (CCI) were used in the highest purity grade
available, as received. The CCl4 droplets used were colored with 10-5 M Solvent Red 7335 dye
(Koch Colors) to provide contrast for the contact angle measurements. All glassware used in this
work, including the fused silica cuvette, was cleaned with Piranha solution (Caution! Strong
oxidizer!).
Contact angle measurements: Contact angle measurements were performed on a VCA
2000 Visual Contact Angle System. Dye-containing CCl4 drops were added to buffered solutions
using a micro-syringe. The volume of the drops was kept near 5L. With the drop resting on the
cuvette, a picture was taken using the camera and the contact angle was analyzed using commercial
software (VCA).
Surface energy measurements: The interfacial tension between CCl4 and water (ionic
strength 0.1M, pH 4.5) was measured using a platinum Wilhelmy plate. The plate was flamed
using a handheld propane torch and then submerged into CCl4. Aqueous solution was added slowly
to the crystallizing dish and the plate was slowly pulled through the interface until half of it was
in water and half remained in CCl4. Pressure readings were recorded using commercial software
(KSV NIMA).

13

Results and Discussion
The surfaces we are concerned with in this work are complex structures that are
characterized by irregular distributions of surface functionalities and a non-uniform, highly
featured physical structure. There are known to be multiple structural forms of silica, ranging from
Q0 through Q3, with the superscripted number referring to the number of silanol groups per silicon
atom. The compositional distribution of silica among the forms Q0 through Q3 depends on the
physical format and processing history of the material.8-9 For these reasons, the equilibria that
describe the chemical properties of such oxide surfaces are complex and in systems that contain
multiple associative species it is important to understand the competition between these processes.
We have focused on the competition between H+ and Na+ association with the (accessible) surface
siloxide functionalities in this work because of the importance of understanding the various
reactions that the surface experiences, and the many systems where this competition is operative.
The characterization of oxide surfaces is hampered by the intrinsic complexity of the
material, its inability to be addressed electrochemically and the small number of chemical
functionalities that determine the surface properties. A typical silica surface has a silanol density
of 4-8 µmol/m2 and the “molecular” surface area can vary widely relative to the geometric surface
area, depending on the physical form of the silica.9 The characterization of surface silanol groups
by NMR and other techniques has provided a great deal of insight, especially in terms of the pKas
that characterize the silica surface.18 Among the properties of surfaces that determine their utility
is their surface energy. We have chosen to examine changes in the surface energy of the silica
surface using contact angle measurements. Despite the outward simplicity of this measurement,
the results contain information on the relative surface energies of the interfaces involved in the

14

measurement and such measurements are amenable to being performed in situ, under ambient
conditions.
Initially, the goal of this work was to characterize the pKa(s) of a silica surface in situ, using
contact angle measurements of a CCl4 droplet immersed in aqueous solution of controlled pH.
Initial results of this work produced results that were not consistent with the known pKa values of
silica, and, the pH-dependence of the CCl4 contact angle data changed with the ionic strength of
the aqueous solution (Fig. 9).19-20 These inconsistencies required further examination.
As noted above, we interrogate the silica surface with a droplet of CCl4 where both the
droplet and the silica surface are immersed in an aqueous medium containing known amounts of
H+ and Na+. The contact angle of a droplet of a liquid on a surface is determined by the balance
of surface energies between all of the interfaces involved, as described by Young’s equation,

cos  

 SV   SL  SiOX  H O   SiOX CCl

 LV
 CCl  H O
2

4

4

[1]

2

Where the surface energies  are for the interfaces indicated. For the purposes of this work we
consider that the SiOX-CCl4 surface energy changes to a limited extent at most (i.e. SiOH-CCl4 ~
SiONa-CCl4, vide infra) and CCl4-H2O changes negligibly with changes in aqueous solution
composition. The dominant change in surface energy for this system is for the SiOX-H2O
interface, where X = H+, Na+. In order to maintain these conditions and vary the pH of the aqueous
solution, the ionic strength of the aqueous solutions is held constant, and for this situation to obtain
the ionic strength is determined by the lowest pH solution used. In other words, for a solution of
HCl at pH = 1, the [H+] = [Cl-] = 0.1 M, and [Na+] = 0.0 M. For the measurements reported here,
the ionic strength was maintained at either 0.1 M or 0.01 M.

15

For the system under consideration, where the silica surface is in equilibrium with an
aqueous solution containing, in general, both Na+ and H+, the competitive equilibria of interest are
given by
Ka

 SiO   H 
SiOH 


[2]

 SiO   Na 
SiONa 

K Na

The surface species of interest in this work are SiOH, SiO- and SiONa. We assert that the
association of H+ and Na+ with SiO- is sufficiently favorable (i.e. small Kdis) that the steady state
concentration of SiO- is small for our experimental conditions. In this case, the ratio of surface
coverage by SiOH to SiONa is given by
[ SiONa ] [ Na  ]K a

[ SiOH ] [ H  ]K Na

[3]

The ratio of siloxide sites associated with Na+ to those associated with H+ is directly
relevant to the surface energy of the macroscopic silica surface. As noted above, knowledge of
the exact density and distribution of silanol (and siloxide) sites is not known, and consequently the
evaluation of absolute surface concentrations of each species is not feasible. We can, however,
normalize the ratio to fractional monolayer coverage of each species, with [SiOH] =  and [SiONa]
= 1-. Substituting these quantities into Eq. 3,
K a [ Na  ] 1  

K Na [ H  ]


[4]

The surface energy of the silica surface is the weighted average of the surface energies for the
SiOH and SiONa components of the surface, and this expression of surface energy can be related
to the contact angle of a CCl4 droplet on the silica surface through Eq. 1, where

16

 SiOX H2O   SiOH H2O  (1   ) SiONaH2O

[5]

The quantities  and (1-) can be calculated as a function of [H+], [Na+], Ka and KNa, and all of
these quantities are known, save for KNa. Using Eq. 5 to determine the surface energy of the SiOXH2O interface as a function of pH, and with the assumptions provided above, we can model the
pH-dependence of the contact angle data for this system.
The experimental data show a change in contact angle between pH 3 and pH 4 for the CCl4
droplet on silica, immersed in an aqueous NaCl solution with ionic strength of 0.1 M (Fig. 5a).
When these measurements are performed using an aqueous NaCl solution with ionic strength of
0.01 M, there is no discernible pH dependence in the range of pH 2 to pH 5 (Fig. 5b). It is known
from NMR studies that the pKa for silanol is 4.5 (Ka = 3x10-5) and it is the Ka and KNa values that
determine the position of the change in contact angle.18 The experimental data are consistent with
a value of KNa = 7x10-3 and we report the calculated pH-dependence of the contact angle in Fig.
6a for a fixed [Na+] = 0.05 M as a function of KNa. The SiONa moiety thus dissociates more
readily than the SiOH moiety, and this is not a surprising result. The comparison is between a
polar bond with some covalent character (O-H) and an ionic association (O- - Na+). This model
predicts that the position of the change in contact angle should be pH dependent and we observe
this to be the case for measurements performed in 0.01 M NaCl (aq) (Fig. 5b). We show the
corresponding calculated results for KNa = 5x10-3 as a function of [Na+] (Eqs. 4 and 5) in Fig. 6b.
With the value of KNa established, and the predicted [Na+]-dependence verified
experimentally, we consider the information available from the contact angle data. The value of
 implies a negative value for cos, which obtains for SiOX-CCl4 > SiOX-H2O. The magnitude of the
difference between SiOH-H2O and SiONa-H2O determines the change in contact angle that we observe

17

(Fig. 7). Young’s equation (Eq. 1) involves the ratios of surface energies, and the pH-dependence
of the contact angle is not, by itself, sufficient to determine the surface energies of the interfaces
comprising the system. We have measured using a Wilhelmy plate balance that the surface energy
CCl4-H2O is 45 mN/m, and this value is in agreement with literature reports. 21 With this value and
the contact angle data, we can determine that the quantity (SiOX-H2O - SiOX-CCl4) ≈ 40 mN/m.
Without further information on either quantity separately, we are not able to further elucidate these
terms. There are two factors that allow us to determine these surface energies, however. The first
is through the use of a Zisman plot (Fig. 8), which yields an estimate of 23.3 mN/m for SiOX-air. (It
should be noted that SiOX-air was estimated by using several liquids whose contact angles on quartz
are known. A series of plots, each plot with a different combination of liquids, was used to estimate
the energies. These plots were averaged together. It is also well established in the literature that
the surface tension of water, H2O-air, is 72 mN/m. Taking the difference between these surface
energies yields SiOH-H20 ≈ 49 mN/m. The extraction of an interfacial energy by taking the
difference between two surface energies of surfaces with a common phase is justified based on the
finding that H2O-air - CCl4-air = (72 mN/m – 26.4 mN/m) = 45.6 mN/m, in excellent agreement with
experimental data. We note that, while it is feasible to estimate CCl4-H2O from CCl4-air and H2O-air,
because there is not a substantial chemical interaction between CCl4 and H2O, the use of this
approximation is slightly more open to question for the estimation of SiOX-H2O because silica and
water interact more strongly. It appears based on anecdotal information, however, that this means
of estimating SiOX-H2O does not give rise to large errors. Using these values for the several
interfaces, we find that the best agreement between experiment and data are for and SiOH-H2O and
SiONa-H2O are 48 mN/m and 50 mN/m, respectively, and CCl4-SiOX = 90 mN/m.21-23 These data are

18

summarized in Table 1. It is significant to note that SiOH-H2O is slightly smaller than SiONa-H2O.
Differences in the nature of aqueous solvation of these two species likely plays a role in
determining these values.
These findings are the result of competitive equilibria between H+ and Na+ for accessible
SiO- sites on the silica surface. It is useful to consider the competition between H+ and other
cations, such as K+. Our initial data were acquired using NaCl to maintain constant ionic strength.
Using KCl to maintain constant ionic strength allows for a comparison between two different
cations. Na (ionic radius 116 pm) and K (ionic radius 152 pm) were found to exhibit the transition
in contact angle at the same pH, to within the resolution of our measurements. This finding
suggests that KK and KNa are similar, which is not surprising.
Our experimental data show that the contact angles for the CCl4 droplet are the same for I
= 0.1 M, whether NaCl or KCl is used to establish the ionic strength. This finding suggests that
the identity of the cation (Na+ or K+) does not alter the solution phase charge screening of the silica
surface charge significantly. While it could be argued that the identity of the compensating cation
may influence the surface energy of the SiOx-H2O interface, the absence of a cation dependence
indicates that the density of surface silanol groups is sufficiently low to avoid contributions from
steric crowding or charge repulsion. This experimental finding also underscores that it is the
physical charge screening effect that is more important than ion-specific effects associated with
Na+ or K+.
Conclusions
We have reported on the existence of competitive equilibria exhibited by siloxide groups on a
silica surface for association with H+ and Na+ cations. We measure the contact angle of a carbon
tetrachloride droplet on the silica surface immersed in aqueous solution to gauge changes in the

19

surface energies of the SiOX-H2O interface, the SiOX-CCl4 interface and the CCl4-H2O interface,
and how these relative energies depend on pH and the ionic strength of the aqueous solution. Our
data demonstrate that the pH dependence of the CCl4 droplet contact angle does not correspond
simply to the measurement of the silica surface pKa, but depends on the competitive equilibria
between H+ and Na+ association. The pKa of the silanol groups in this pH region is known to be
4.5 (Ka = 3x10-5) and we find that KNa = 7x10-3 by fitting the experimental data to a competing
equilibria model.
In addition to measuring the effect of competitive equilibria, when our experimental contact
angle data are analysed in conjunction with Wilhelmy plate measurements of the CCl4-H2O surface
energy and the known values of SiOH-air and H2O-air surface energies, we can determine the
surface energies for both the SiOH-H2O and SiONa-H2O interfaces (Table 1). A significant piece
of information emerges from these data, that the surface energies of the SiOH-H2O and SiONaH2O interfaces differ by 2 mN/m, or ca. 5%. In order to elucidate this information measurement
of the CCl4 droplet contact angle has to be accurate and reproducible to ¹2°, a level that challenges
the capabilities of the instrumentation used for this work.
This approach to the characterization of competitive equilibria at oxide surfaces offers the
opportunity to examine a number of important materials as well as an opportunity to evaluate the
effect of surface modification chemistry (e.g. phosphorylation) on such surfaces.24 In such
experiments, the contact angle of a non-polar liquid droplet can be used to evaluate relative surface
energies and competitive equilibria, and contact angle hysteresis measurements can be used to
characterize the homogeneity of the surface modification chemistry applied to the interface.25-27
That work is presently underway.

20

APPENDIX

21

SiOH-H2O

48 mN/m

SiONa-H2O

50 mN/m

SiOX-CCl4 22

90 mN/m

CCl4-H2O 21

45 mN/m

Table 1. Surface Energy. Surface energy values calculated from the contact angle measurements
and Wilhelmy plate measurements.

22

Figure 5. Contact angle measurements. Contact angle measurements as a function of pH at 0.1M
ionic strength (a) and 0.01M ionic strength (b).

23

Figure 6. Association Constant Model. The apparent pKa transition was modelled as a function of
association constant (a) and of sodium concentration (b). The contact angle is shown as a function
of pH.

24

Figure 7. Surface energy difference. The change in surface energy affects the magnitude of the
contact angle change. This model shows energy changes from 0 mN/m to 2 mN/m

25

Figure 8. Zisman Plot. Zisman plot approximation used to determine the surface energy of
silanol in air.

26

Effect of Ionic Strength
contact angle

165
160

0.01M

155

0.1M

150
145
0

2

4

6

8

pH
Figure 9. Ionic Strength on Buffer shape. The contact angle was measured at different pH values
under two different ionic strength. The image left shows the set-up of the experiment.

27

LITERATURE CITED

28

LITERATURE CITED

1.
Sulpizi, M. G., M.
Sprik, M., The Silica-Water Interface: How the Silanols Determine the Surface Acidity and
Modulate Water Properties. Journal of Chemical Theory and Computation 2012, 8 (3), 1037-1047.
2.
Leung, K. N., M.B.
Criscenti, L.J., Elucidating the Bimodal Acid-Base Behavious of the Water-Silica InterfaceFrom
First Principals. Condensed Materials 2010.
3.
Bain, C. D. W., G.M., A Study by Contact Angle of Acid-Base Behavior of Monolayers
Containing ω-Mercaptocarboxylic Acids Adsorbed on Gold: An Example of Reactive Spreading.
Langmuir 1989, 5, 1370-1378.
4.
Holmes-Farley, S. R.; Reamey, R. H. M., T.J.
Deutch, J.
Whitesides, G.M., Acid-Base BEhaviour of Carboxylic Acid Groups COvalently Attached at the
Surface of Polyethylene: The USefulness of Contact Angle in Dollowing the Ionization of Surface
Functionality. Langmuir 1985, 1, 725-740.
5.
Young, T., An Essay on the Cohesion of Fluid. Physical Transactions of the Royal Society
of London
1805, (95), 65-87.
6.
Zhuravlev, L. T., Concentration of Hydroxyl Groups on the Surface of Amorphous Silicas.
Langmuir 1987, 3, 316-318.
7.
Zhuravlev, L. T., The Surface Chemistry of Amorphous Silica. Zhuravlev model. Colloids
and Surfaces 2000, (173), 1-38.
8.
Pfeiffer-Laplaud, M. G., M.
Sulpizi, M., pKa at Quartz/Electrolyte Interfaces. Journal of Physical Chemistry Letters 2016, 7
(16), 3229.
9.
Kennedy, C. D., Ionic Strength and the Dissociation of Acid. Biochemistry and Molecular
Biology Education 1990, 18 (1), 35-40.
10.
Seymour, M. D. F., Q., Effect of Ionic Strength on Equilibrium Constants. Journal of
Chemical Education 1977, 54 (4), 225.
11.

Adamson, A. W. G., A.P., Physical Chemistry of Surface. Sixth ed.; Wiley: 1997.

12.
Ethington, E. F., Interfacial Contact Angle Measurements of Water, Mercury, and 20
Organic Liquids on Quartz, Calcite, Biotite, and Ca-montmorillonite substrates. 1990.
13.

Troy, B. B.; Beringer, P., The Science and Practice of Pharmacy. Philadelphia, PA, 2006.

29

14.
Faucheux, N. S., R LĂźtzow, K Werner, C Groth, T, Self-assembled monolayers with
different terminating groups as model substrates for cell adhesion studies. Biomaterials 2004, 25
(14), 2721-2730.
15.
Davis, A. N. M. I., S.A., Counce, R.M., DePaoli, D.W.
Hu, M.Z.-C, Ionic strength effects on hexadecane contact angles on a gold-coated glass surface in
ionic surfactant solutions. Colloids and Surfaces 2003, 221 (1-3), 69-80.
16.
Jada, A. A. A., R; Douch, J., Surface charge and adsorption from water onto quartz sand
of humic acid. Chemosphere 2006, 64 (8), 1287-1295.
17.
Drelich, J. M., J.D., Good, R.J., The Effect of Drop (Bubble) SIze on Advancing and
Receding Contact Angles for Heterogeneous and Rough Surfaces as Observed with Sessile-Drop
and Captive-Bubble Techniques. Colloid and Interface Science 1996, 179 (1), 37-50.
18.
Baumler, G. B., G.J., The Influence of Metal Ions on the Dynamics of Supported
Phospholipid Langmuir Films. Langmuir 2017, 33 (12), 2986-2992.

30

Chapter 3

Conclusions and Future Directions
The competitive equilibria presented in this paper serves to show the inherently dynamic
system present at any charged interface. Driven but a tendency towards neutrality, a charged
surface will associate with counterions in solution. The strength of this interaction is driven by the
relative concentrations of any counterion species present in the buffer. We have established a
relationship between sodium concentration and proton concentration on the magnitude of contact
angle and the change on the interfacial surface energy. By relying on the fact that the dominate
interaction is that between the surface and the buffer we can establish the equilibrium constants
for cationic species on the silica surface. The KNa of this system is on the order of 7 x 10-3 and is
the first such reported value.
The ability to extract such constants from contact angle measurements is a useful tool as a
measure of finding association constant of various metal ions to functionalized surfaces. The
impact of this work could see applications in work that involves membrane stability on planer
substrates or any system that needs facile diffusion as well as reproducible binding data. By also
showing the relationship between apparent binding constant for metal with the surface as a
function of pH, greater control over the reactions occurring at the surface can be obtained.
We have also shown a method of determining the surface the magnitude of the interfacial
energy of the system. By knowing the contact angle of various liquids on the quartz surface and
by knowing the interfacial energy of those liquids in air, the energy of the quartz surface in water
can be known. Interfacial energy values are hard to come by for solid interfaces. Zisman plot
provide a method of estimating the energy of a surface in air but since this was only an estimate

31

and depends greatly on the contact angle of the liquids used, a more robust method was developed.
While still using a Zisman estimation, the energy of the silanol surface was water was found. This
was done taking into consideration that the difference between the interfacial energy surface A
and surface air and the interfacial energy between surface B with air gives the interfacial energy
between surface A and surface B. This was used to estimate the quartz-air interface and then
calculate the quartz-water interface. The original contact angle data was used to measure the
difference between silica-carbon tetrachloride and silica-buffer (~40mN/m).
By using both the Zisman approximation and the contact angle measurements, the value of
the silica-buffer interfacial energy was found in both pH regions. This was a value of 48mN/m at
low pH and 50mN/m at high pH. Care must be taken to remember that this result was seen at an
ionic strength of 0.1M and as such the sodium ions were able to outcompete the protons for the
surface. The change in contact angle is not apparent at ionic strength 0.01M.
Surface energy values are typically hard to come by as these values have not before been
reported to the best of our knowledge. These surface energy values are not often known and are
important in techniques that rely on changes in surface energies. It is also shown that the change
in surface energy with protonation, 2 mN/m, is small but has a noticeable effect on the contact
angle of the system.
Future Work
This work has laid the ground for a wide variety of experiments moving forward, some of
which has been investigated during the course of this work. It establishes not only equilibria
processes for surfaces and metal ions but also competitive equilibria between the metal ions and
protons for the surface. By modulating the ionic strength of the solution the equilibria of the surface
towards either the proton or the metal ion can be manipulated.19-20 This has implications in the

32

field of separations where the quality of the separation is dependent on the affinity of the analyte
for the surface. This means that factors such as pH, ionic strength, and ion identity play large role
in the separation. Refining such separations is possible knowing the equilibrium constants for the
analytes with the surface.28
More complicated surfaces can also be investigated with this technique. For example, since
a quartz surface has such a wide distribution of morphologies and reactivities, it would be good to
modify the surface in such a way that gives a more dependable surface. An exhaustive
phosphorylation was attempted and this the measurements were repeated. It was presumed that the
phosphate moiety would give two contact angle changes as there are two acidic protons. The
following data set was from a preliminary experiment with a modified surface. It was done before
the method was completely refined and as such will be revisited in the future. It is hard to draw
any conclusion from this data but there does seem to be a transition between pH 1 and pH 2 and
then again being pH 8 and pH 10. The nature of these equilibria are different than the initial
experiment and deserve more attention.

33

Phosphorylated
160

158

156

154

152
0

2

4

6

8

10

12

Figure 10. Phosphorylated surface data. pKa values are 7.2 and 12.3. The first proton,
pKa 2.2, is the one that is reacted when the phosphate group is attached to the surface.

In addition, bilayer dynamics could be investigated with this method. Complex systems
with different metal ions with multiple association constants could be investigated for change in
bilayer fluidity as a function of pH. It could be possible to change the identity of the metal ion
currently bound to the surface while the other is free to diffuse throughout the system.
These effects as seen provide insight into the fundamental nature of surfaces that has not
been dealt with in a thorough manner. The future experiments planned seeks to fill the apparent
hole in the literature.

34

LITERATURE CITED

35

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New York, 2002.
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Langmuir-Blodgett Films. 1990.

3.
Kijewska, K.; Blanchard, G. J., Using Diffusion To Characterize Interfacial Heterogeneity.
Langmuir 2017, 33 (5), 1155-1161.
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CRC Handbook of Chemistry and Physics. 95th ed.; Boca Raton, FL, 2014.

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Dean, J. A., Lange's Handbook of Chemistry. McGraw-Hill: 1992.

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O'Regan, B.; Grätzel, M., A low-cost, high-efficiency solar cell based on dye-sensitized
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2004, p. 227 - 234.
8.
Zhuravlev, L. T., Concentration of Hydroxyl Groups on the Surface of Amorphous Silicas.
Langmuir 1987, 3, 316-318.
9.
Zhuravlev, L. T., The Surface Chemistry of Amorphous Silica. Zhuravlev model. Colloids
and Surfaces 2000, (173), 1-38.
10.
Horne, J. C.; Huang, Y.; Liu, G.-Y.; Blanchard, G. J., The Correspondence Between Layer
Morphology and Intralayer Excitation Transport in Zirconium-Phosphonate Monolayers. Journal
of the American Chemical Society 1999, 121, 4419-4426.
11.
Sulpizi, M.; Gaigeot, M.; Sprik, M., The Silica-Water Interface: How the Silanols
Determine the Surface Acidity and Modulate Water Properties. Journal of Chemical Theory and
Computation 2012, 8 (3), 1037-1047.
12.
Gouy, M., On The Constitution of the Electric Charge On The Surface In An Electrolyte.
J. Phys. Theor. Appl. 1910, 9 (1), 457-468.
13.
Young, T., An Essay on the Cohesion of Fluid. Philosophical Transactions of the Royal
Society of London 1805, 95, 65-87.
14.
Leung, K.; Nielsen, M. B.; Criscenti, L. J., Elucidating the Bimodal Acid-Base Behavious
of the Water-Silica InterfaceFrom First Principals. Condensed Materials 2010.
15.
Bain, C. D.; Whiteside, G. M., A Study by Contact Angle of Acid-Base Behavior of
Monolayers Containing ω-Mercaptocarboxylic Acids Adsorbed on Gold: An Example of Reactive
Spreading. Langmuir 1989, 5, 1370-1378.

36

16.
Holmes-Farley, S. R.; Reamey, R. H.; McCarthy, T. J.; Deutch, J.; Whitesides, G. M.,
Acid-Base BEhaviour of Carboxylic Acid Groups COvalently Attached at the Surface of
Polyethylene: The USefulness of Contact Angle in Dollowing the Ionization of Surface
Functionality. Langmuir 1985, 1, 725-740.
17.
Young, T., An Essay on the Cohesion of Fluid. Physical Transactions of the Royal Society
of London
1805, (95), 65-87.
18.
Pfeiffer-Laplaud, M.; Gaigeot, M.; Sulpizi, M., pKa at Quartz/Electrolyte Interfaces.
Journal of Physical Chemistry Letters 2016, 7 (16), 3229.
19.
Kennedy, C. D., Ionic Strength and the Dissociation of Acid. Biochemistry and Molecular
Biology Education 1990, 18 (1), 35-40.
20.
Seymour, M. D.; Fernando, Q., Effect of Ionic Strength on Equilibrium Constants. Journal
of Chemical Education 1977, 54 (4), 225.
21.

Adamson, A. W.; Gast, A. P., Physical Chemistry of Surface. Sixth ed.; Wiley: 1997.

22.
Ethington, E. F., Interfacial Contact Angle Measurements of Water, Mercury, and 20
Organic Liquids on Quartz, Calcite, Biotite, and Ca-montmorillonite substrates. 1990.
23.

Troy, B. B.; Beringer, P., The Science and Practice of Pharmacy. Philadelphia, PA, 2006.

24.
Faucheux, N.; Schweiss, R.; LĂźtzow, K.; Werner, C.; Groth, T., Self-assembled
monolayers with different terminating groups as model substrates for cell adhesion studies.
Biomaterials 2004, 25 (14), 2721-2730.
25.
Davis, A. N.; Morton III, S. A.; Counce, R. M.; DePaoli, D. W.; Hu, M. Z.-C., Ionic
strength effects on hexadecane contact angles on a gold-coated glass surface in ionic surfactant
solutions. Colloids and Surfaces 2003, 221 (1-3), 69-80.
26.
Jada, A.; Ait Akbour, R.; Douch, J., Surface charge and adsorption from water onto quartz
sand of humic acid. Chemosphere 2006, 64 (8), 1287-1295.
27.
Drelich, J.; Miller, J. D.; Good, R. J., The Effect of Drop (Bubble) Size on Advancing and
Receding Contact Angles for Heterogeneous and Rough Surfaces as Observed with Sessile-Drop
and Captive-Bubble Techniques. Colloid and Interface Science 1996, 179 (1), 37-50.
28.
Baumler, G.; Blanchard, G. J., The Influence of Metal Ions on the Dynamics of Supported
Phospholipid Langmuir Films. Langmuir 2017, 33 (12), 2986-2992.

37