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Stability properties of surfactant free thin films at different ionic strengths: Measurements and modelling Frederik Jürgen Lech, Peter A. Wierenga, Harry Gruppen, and Marcel B.J. Meinders Langmuir, Just Accepted Manuscript • DOI: 10.1021/la504933e • Publication Date (Web): 17 Feb 2015 Downloaded from http://pubs.acs.org on February 18, 2015
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Langmuir
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Stability properties of surfactant free thin films at different ionic strengths:
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Measurements and modelling
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Frederik J. Lecha,b, Peter A. Wierengaa,b, Harry Gruppenb, Marcel B.J. Meindersa,c*
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a
Top Institute Food and Nutrition, Wageningen, the Netherlands
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b
Wageningen University, Laboratory of Food Chemistry, Wageningen, the Netherlands
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c
Wageningen UR, Food and Biobased Research, Wageningen, the Netherlands
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*Corresponding author
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[email protected] 11
P.O. Box 17, 6700 AA, Wageningen, The Netherlands
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Telephone: +31 317 480165
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Abstract
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Foam lamellae are the smallest structural elements in foam. Such lamellae can experimentally be
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studied by analysis of thin liquid films in glass cells. These thin liquid films usually have to be
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stabilized against rupture by surface active substances, like proteins or low molecular weight
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surfactants. However, horizontal thin liquid films of pure water with a radius of 100 µm also show
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remarkable stability when created in closed Sheludko cells. To understand thin film stability of
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surfactant free films, the drainage behaviour and rupture times of films of water and NaCl solutions
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were determined. The drainage was modelled with an extended DLVO model, which combines DLVO
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and hydrophobic contributions. Good correspondence between experiment and theory is observed,
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when hydrophobic interactions are included, with fitted values for surface potential (ψ0, water) of −60 ±5
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mV, hydrophobic strength (Bhb,water) of 0.22 ±0.02 mJ/m2 and a range of the hydrophobic interaction
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(λhb, water) of 15 ±1 nm in thin liquid films.
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In addition, Vrij’s rupture criterion was successfully applied to model the stability regions and rupture
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times of the films. The films of pure water are stable over long time scales (hours) and drain to final
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thickness > 40 nm if the concentration of electrolytes is low (resistivity 18.2 MQ). With increasing
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amounts of ions (NaCl) the thin films drain to < 40nm thickness and the rupture stability of the films is
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reduced from hours to seconds.
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Keywords
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Surfactant free air water interface, surface potential, extended DLVO theory, foam stability
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Introduction
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An important aspect in the stability of foams is the life time of the thin liquid films that separate the
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gas bubbles in the foam.1 Usually, surface active materials, like proteins and low-molecular weight
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surfactants (LMW), are used to stabilize the films. The stability of LMW surfactant stabilized films
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has been studied extensively and was recently reviewed.2 Thin films of LMW can quantitatively be
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described by the DLVO.3 In addition, Vrij developed a criterion to describe how the growth of small
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surface perturbations leads to spontaneous rupture of the film.4 This criterion was used by others to
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determine the critical thickness in foam films.5
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Because it is impossible to make foam of pure water, it is expected that thin liquid water films are
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unstable. Still, horizontal thin liquid films of pure water and dilute NaCl solutions in closed Sheludko
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cells have been described by several authors.6-8 The films described are usually very unstable since
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90% of the films ruptured immediately after creation.6 However, stable, free standing (vertical) thin
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water films in small glass capillaries are also observed. The stability of the films is ascribed to ionizing
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x-ray photons, thereby inducing some charge between the two interfaces.8 Wang and Yoon showed the
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possibility to create horizontal thin films of dilute NaCl solutions that were stable for minutes.7 They
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argue that the stability of the films originates from equilibrium between hydrophobic and electrostatic
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forces that is mediated by the electrolytes in solution.
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The electrostatic forces in the thin films are considered the result of a surface wall potential of the air-
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water interface. This surface wall potential was for instance shown using experiments where the
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electrophoretic mobility of air bubbles in an electric field was measured.9 The origin, polarity and
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magnitude of the charge, however, is still under heavy debate. Several studies proposed the structuring
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of water layers close the hydrophobic interface as a source of the charge.10,
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however, would only be possible on short length scales up to 20 nm.12 The ordering of water over 40
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nm is far shorter than the equilibrium thickness (120 nm) of the films reported.
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explain the stability of the films by itself. For the stabilization of the films by structured water, the
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ordered layers should overlap to create repulsion. Other studies suggest that the surface charge of
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water could be due to the preferred adsorption of hydroxide ions to the interface.13-15 Typical values
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for this surface potential, obtained by different experimental techniques (i.e. Volta potential difference
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measurements or calomel electrodes) and simulations, were recently summarized, and showed values
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ranging from -1.1 V to +0.5 V.16
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Next to the surface charge of the water interfaces, the repulsive hydration interaction has been
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suggested to attribute to the stabilization of a thin film of clean water.17, 18 Whether or not hydrophobic
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forces play a role in the stability of thin liquid films is still under debate. 19, 20
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The aim of this study is to gain a generic understanding of the drainage and stability of surfactant free
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thin liquid films. To achieve this, drainage behaviour and rupture times of surfactant free thin films,
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created in Sheludko cells, were described with a model using extended DLVO (including hydrophobic
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interactions) and the stability criterion of thin films. 4
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Experimental Section
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Materials
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Ultra-pure water (Millipore, EMD Millipore Corp., Billerica, MA, USA) with a surface tension of 72.6
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± 0.3 mN/m at 20 °C stable over 1 h, a resistivity of 18.6 MΩ*cm and residual total organic carbon of
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3 ppb was used as is to make the films and the NaCl solutions. NaCl was purchased from Sigma
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Aldrich (Zwijndrecht, The Netherlands) and roasted at 700 °C for three days to eliminate possible
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7
This structuring,
Hence, it cannot
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organic contaminants. A stock solution of 0.1 M NaCl was prepared and diluted to make solutions for
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the thin film experiments. The solutions were prepared on the day of the experiment and kept at the
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same temperature (20°C) as the experimental set up before making the thin film. All glassware was
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soaked in dilute (0.1 M) NaOH solution, thoroughly rinsed with ultra-pure water and dried in an oven
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at 60°C before use.
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The total ionic strength of water and NaCl solutions is given by (equation 1)
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= ∑
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with the sum of all ions i in the solution, ρi∞ is the molar concentration of the ion in bulk at infinite
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distance from the interface and z is the valence of the ions. Note that this includes the OH- and H+ ions
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determining the pH of the water films, which was measured to be pH 5.6, for all experiments. The
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total ionic strength (INaCl + IpH 5.6) of a 0.700 mM NaCl solution is 0.703 mM.
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Methods
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Thin liquid films (radius = 100 µm) were made in a modified Scheludko cell as described elsewhere.1
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A schematic drawing, including relevant dimensions of the setup is depicted in figure 1. The Sheludko
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cell is encased in glass, closed with a glass cover. The casing has a reservoir of water at the bottom to
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ensure a relative humidity of 100 % in the cell during the experiments.
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The thickness of the thin films was determined by image analysis obtained by micro-interferometry
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using a microscope (Axio plan 01, Zeiss, Jena, Germany), in reflected light mode, equipped with a
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five mega pixel CCD camera (Mightex Systems, Pleasanton, CA, USA). Images of the thin films,
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recorded with the CCD camera, were processed by a software script (developed at the Laboratory of
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Food Chemistry) for Matlab (Software version 2013b, MathWorks. Natick, MA, USA). It calculated
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the average intensity of light in a defined area (at the centre) of the thin film. The area is typically
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1963 µm², which is ~6 % of total area of the thin film. The thickness was calculated according to
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equation (2):
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(1)
ℎ = ± √Δ
(2)
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with λ as the wavelength of the light (546 nm), n the refractive index of water, l the order of
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interference and ∆ as (I-Imin)/(Imax-Imin) where is I is the average of the light intensity at each time
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point, Imin, the minimum intensity (which is measured in the Sheludko cell without a water film
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present) and Imax as the maximum intensity.
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The film thickness was measured from the moment it reaches a radius of 100 µm up to 1 hour of
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lifetime. If a film did not break within one hour, it was considered stable. In this case, the life time will
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be given as one hour.
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If the thin films ruptured during this time, at least 20 repetitions were used to calculate the average and
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standard deviation of the rupture time and thickness at which rupture occurred. The rupture time is the
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time from reaching a 200 µm wide film until the film breaks. In case of stable films, solutions were
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measured 4 times, in case of rupturing films; the experiment was repeated at least 20 times.
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The whole setup, thin film cell, pure water and salt solution were equilibrated to room temperature (20
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°C) on the microscope table for at least 1 hour prior to the measurement. Liquid was drawn into the
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capillary by a syringe (500 µL, Hamilton, Reno, NV, USA) and left to equilibrate for 10 minutes
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before a thin film was made by drawing more solution into the capillary.
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Modelling and theoretical background
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Surface forces
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When two bubbles come into contact, the thin liquid film between the bubbles will drain due to the
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capillary pressure, caused by the difference in curvature of the thin film and the adjacent meniscus (or
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Plateau border in foam). When the film thickness becomes smaller than about 100 nm, attractive and
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repulsive interactions between the interfaces of the film become important and determine the stability
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of the thin liquid film. Attractive interactions, enhancing film thinning and destabilizing the film,
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include long range dispersion forces summarized as van der Waals (vdW) forces. Repulsive
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interactions, acting against film thinning and thereby stabilizing the film, include electrostatic
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interactions (ES) between two similarly charged surfaces and steric interactions. The vdW and ES
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interactions are described quantitatively by the DLVO theory. Besides these DLVO forces, other
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interactions are recognized that might play a role in film stability. The interactions include steric
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repulsion (excluded volume), hydration, repulsive and attractive hydrophobic forces as well as
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oscillatory solvation forces.2, 11, 18 The sum of these surface forces determine the disjoining pressure
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Π(h), which depends on the film thickness h.
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The van der Waals contribution is calculated from (equation 3)
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Πvw = − " #! $
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with AH as the compound Hamaker constant of a water film in air AH = 4*10-20 J. 18, 21
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The contribution of the electrostatic interaction to the disjoining pressure is approximated by equation
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(4)18
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Πel = 64)* + , e-.#
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with
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, = tanh 378 6:;
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and
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? @AB 4
(6)
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C6 CD 89:
*
hb
#
(7)
hb
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The theoretical individual attractive and repulsive contributions for an air water interface as well as the
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resulting disjoining pressure as function of film thickness are calculated (figure 2).
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Film drainage
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The drainage of the film is modelled by considering the flow between two circular plane-parallel
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plates. 23, 24 The change of the film thickness h with time t was described by (equation 8)
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d# dL
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where cf is a factor that accounts for the interaction of the fluid with the interface. For an immobile
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interface, as we will consider here, cf = 1. Furthermore, µ = 10-3 kg/m/s is the viscosity of the water
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phase, Rf is the radius of the film (in our experimental set-up Rf = 100 µm), and
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ΔS = Q − Π
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is the driving capillary pressure, with γ is the surface tension of the water-air interface (in the
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calculation we used γ= 72 mN/m), 1/Rm is the (mean) curvature of the meniscus and Π is the total
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disjoining pressure (Π= ΠVW+Πel+Πhb). Rm~1.25 mm, assuming complete wetting of the inner wall of
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the Sheludko cell. (see figure 1).
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Starting from an initial thick film with thickness h0, the film will drain. Depending on the precise
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shape of Π(h), the film can drain to a stable equilibrium thickness where the disjoining pressure equals
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the capillary pressure (figure 2 B). If the disjoining pressure is smaller than the capillary pressure the
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thin film can rupture spontaneously.
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Film rupture
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Film rupture of surfactant stabilized films has successfully been described by the theory developed by
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Sheludko and Vrij.4,
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curve. In these regions of instability, small spontaneous surface perturbations grow in time until both
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interfaces touch each other and the film ruptures. The unstable regions are given by the Vrij criterion
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(10)
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VW V#
M # $
= − OPN QR ΔS
(8)
N
T
(9)
U
