Distribution of Surfactants in Latex Films: A Rutherford

Uneven distribution of surfactant in dried latex films can affect the final film .... Four different types of surfactants were used, sodium dodecyl su...
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Langmuir 2006, 22, 5314-5320

Distribution of Surfactants in Latex Films: A Rutherford Backscattering Study Wai Peng Lee,† Venkata R. Gundabala,† Belinda S. Akpa,‡ Michael L. Johns,‡ Chris Jeynes,§ and Alexander F. Routh*,†,+ Department of Chemical Engineering, UniVersity of Sheffield, Mappin Street, Sheffield, S1 3JD, U.K., Department of Chemical Engineering, UniVersity of Cambridge, Pembroke Street, Cambridge CB2 3RA, U.K., and UniVersity of Surrey Ion Beam Centre, Guildford, Surrey, GU2 7XH, UK ReceiVed January 18, 2006. In Final Form: March 23, 2006 Uneven distribution of surfactant in dried latex films can affect the final film properties such as its water-resistance, gloss, and adhesiveness. Therefore, it is important to understand the driving force for surfactant transport during drying. In this paper, the accumulation of surfactant on the surface of poly(styrene-co-butyl acrylate) latex is studied using Rutherford Backscattering (RBS) and compared with results from a model that is based on the diffusive transport of particles and surfactant. Experimentally, a 30-50 nm thick surface layer, rich in surfactant, is seen and the concentration in the bulk of the film, obtained from RBS, agrees, at least qualitatively, with the model predictions for two of the surfactants tested.

Introduction Latex consists of a suspension of polymer particles in water from which waterborne coatings can be prepared. Surfactants are usually added during the polymerization process to produce high-solid-content latices and to aid stability, with the surfactants adsorbed at the surface of the latex particles, as well as being dispersed in the aqueous phase. Addition of surfactant modifies the final properties of the latex, such as its particle packing,1 wetting ability,2 water permeability,3 and adhesion properties.4 Depending on the compatibility between surfactant and particles, surfactant will dissolve into the polymer, remain in the interfaces between particles, or phase-separate from the polymeric solution and migrate to the interfaces.5 Hence, the distribution of surfactants after coalescence of latex films is important in determining the performance of the film. Excess of surfactant at the film/air interface will reduce the gloss of the latex film, while accumulation of surfactant at the film/substrate interface will reduce the adhesion and peel strength. Excess surfactant, present between particles during film formation will hinder coalescence of particles,6 resulting in porous films. The rates of desorption and migration of the surfactants varies with the chemical composition of the surfactants and conditions of film formation.7 * To whom correspondence should be addressed. E-mail: [email protected]. † University of Sheffield. ‡ University of Cambridge. § University of Surrey Ion Beam Centre. + Present address: Dept of Chemical Engineering and BP Institute, University of Cambridge, Madingley Rise, Madingley Road, Cambridge, CB3 0EZ, U.K. (1) Wang, Y.; Kats, A.; Juhue, D.; Winnik, M. A. Freeze-fracture studied of latex films formed in the absence and presence of surfactant. Langmuir 1992, 8, 1435. (2) Mulvihill, J.; Toussaint, A.; De Wilde, M. Onset, follow up and assessment of coalescence. Prog. Org. Coat. 1997, 30, 127. (3) Bindschaedler, C., Gurny, R.; Doelker, E. Influence of emulsifiers on film formation from cellulose acetate latexes: Experimental study of phase separation phenomena due to sodium dodecyl sulphate I. J. Appl. Polym. Sci. 1987, 34, 2631. (4) Charmeau, J. Y.; Berthet, R.; Gringreau, C.; Holl, Y.; Kientz, E. Effects of film structure on mechanical and adhesion properties of latex films. Int. J. Adhes. Adhes. 1996, 17, 169. (5) Kientz, E.; Holl, Y. Distribution of surfactants in latex films. Colloids Surf., A 1993, 78, 255. (6) Keddie J. L. Film formation of latex. Mater. Sci. Eng. 1997, 3, 101.

Wheeler et al8 first noticed the effect of nonuniform surfactant arrangements on film properties. They reported that emulsifiers form an interface between particles, hindering coalescence and resulting in weak films. This effect of surfactant on coalescence was supported by Voyutskii et al.9 Since then, researchers have used various instruments such as polarized attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR), X-ray photoelectron spectroscopy (XPS), secondary ion mass spectrometry (SIMS), and Rutherford Backscattering (RBS) to study the accumulation of surfactants on film interfaces. Zhao et al10 studied surfactant enrichment at the film/air and film/ substrate interfaces using XPS, SIMS, and ATR-FTIR spectroscopy. They observed higher surfactant concentration at the interfaces and concluded that initial enrichment is due to migration of surfactants to the interfaces to minimize surface tension. The more pronounced enrichment at the air side is due to transportation of nonadsorbed surfactant by a water flux during drying. In the solid state, surfactant-polymer incompatibility provides the driving force for surfactant migration. This conclusion was also supported by Kunkel and Urban11 in their observations using ATR-FTIR spectroscopy on styrene/n-butyl acrylate copolymer latex and styrene/n-butyl acrylate latex blends. They observed higher enrichment of surfactant at the film/substrate interface on latex films with higher film/substrate interfacial energy. This theory is later contradicted by Amalvy and Soria,12 who argue that the difference in film/substrate surface energy is insufficient to account for the preferred interface accumulation. They argue (7) Aramendia, E.; Mallegol, J.; Jeynes, C.; Barandiaran, M. J.; Keddie, J. L.; Asua, J. M. Distribution of surfactants near acrylic latex film surfaces: A comparison of conventional and reactive surfactants (surfmers). Langmuir 2003, 19, 3212. (8) Wheeler, O. L.; Jaffe, H. L.; Wellman, N. Mechanism Of Film Formation Of Polyvinyl Acetate Emulsions. Off. Dig. 1954, 26, 1239. (9) Voyutskii, S. S. Amendment to the papers of Bradford, Brown and coworkers: Concerning mechanism of film formation from high polymer dispersions. J. Polym. Sci. 1958, 32, 528. (10) Zhao, C. L.; Dobler, F.; Pith, T.; Holl, Y.; Lambla, M. Surface composition of coalesced acrylic latex films studied by XPS and SIMS. J. Colloid Interface Sci. 1989, 128, 437. (11) Kunkel, J. P.; Urban, M. W. Surface and interfacial FT-IR spectroscopic studies of latexes. VIII. The effect of particle and copolymer composition on surfactant exudation in styrene-n-butyl acrylate copolymer latex films. J. Appl. Polym. Sci. 1993, 50, 1217. (12) Amalvy, J. I.; Soria, D. B. Vibrational spectroscopic studies of distribution of sodium dodecyl sulfate in latex films. Prog. Org. Coat. 1996, 28, 279.

10.1021/la0601760 CCC: $33.50 © 2006 American Chemical Society Published on Web 05/06/2006

Distribution of Surfactants in Latex Films

that hydrophilicity and the glass transition of the latex particles play an important role as well. The majority of work on surfactant distribution had concentrated on anionic surfactants. Kientz and Holl5 studied the distribution of incompatible anionic, cationic, and nonionic surfactants in poly(2-ethylhexylmethacrylate) films. They found that the surfactant distribution is well established during drying of the latex and evolves very slowly in the dry film. This view is later supported by Belaroui et al.13 Kientz and Holl5 indicated that the distribution of surfactant depends on three parameters: initial surfactant distribution at the interfaces, surfactant desorption during drying, and the mobility of surfactant in the drying film. They also note that desorption and mobility of a surfactant is dependent on the polymer-surfactant interaction. Belaroui et al.13,28 in their study on core-shell latices using confocal Raman spectroscopy agree that surfactant desorption is important in determining surfactant distributions. However, they also argue that the distribution of water and extent of coalescence of latex particles during drying are also important in determining enrichment/depletion at the interfaces. Mallegol et al.14 reported similar observations using magnetic resonance profiling and RBS, where stabilization of particles by surfactants creates capillaries between particles, thereby creating a pathway for the transport of water-soluble species to the film/air interface by capillary pressure during drying. Tzitzinou et al.15 have a different explanation for surfactant excess on the film/air interface. They suggested that surfactants at the water/air interface adsorb onto the particle surface as the water level drops below the particle and that surfactant is enhanced at the latex surfaces immediately upon film formation. Recently, Gundabala et al.16 modeled surfactant transport in latex films based on similar views. They propose that removal of water during drying increases the surfactant and particle concentration at the surface of the drying film. The higher surfactant and particle concentrations prompt higher adsorption of surfactant onto the particles to re-establish equilibrium. Surfactant enrichment/depletion at the interface depends on the mobility of the surfactant and the adsorption isotherm for that surfactant-particle system only. In this paper, we have used RBS to obtain a quantitative value of surfactant excess on the surface of poly(styrene-co-butyl acrylate) latex films. Four different types of surfactants were used, sodium dodecyl sulfate (SDS), sodium octyl sulfate (SOS), lithium dodecyl sulfate (LiDS), and sodium triflate (ST). The amount of enrichment obtained is compared to the values obtained from the model by Gundabala et al.16

Review of Surfactant Transport Model It is assumed that latex dries uniformly from the top surface. Since the sample area is large compared to the film thickness and is far from the edges, lateral drying fronts are neglected.17 The distribution of particles is determined by the Peclet number, (13) Belaroui, F.; Cabane, B.; Dorget, M.; Grohens, Y.; Marie, P.; Holl, Y. Small-angle neutron scattering study of particle coalescence and SDS desorption during film formation from carboxylated acrylic latices. J. Colloid Interface Sci. 2003, 262, 409. (14) Mallegol, J.; Gorce, J. P.; Dupont, O.; Jeynes, C.; McDonald, P. J.; Keddie, J. L. Origins and effects of a surfactant excess near the surface of waterborne acrylic pressure sensitive adhesives. Langmuir 2002, 18, 4478. (15) Tzitzinou, A.; Jenneson, P. M.; Clough, A. S.; Keddie, J. L.; Lu, J. R.; Zhdan, P.; Treacher, K. E.; Satguru, R. Surfactant concentration and morphology at the surfaces of acrylic latex films. Prog. Org. Coat. 1999, 35, 89. (16) Gundabala, V. R.; Zimmerman, W. B.; Routh, A. F. A model for surfactant distribution in latex coatings. Langmuir 2004, 20, 8721. (17) Routh, A. F.; Russel, W. B. Horizontal drying fronts during solvent evaporation from latex films. AIChE J. 1998, 44, 2088.

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Figure 1. High particle Peclet number leads to accumulation of particles at the top surface.

which is the ratio of the rates of evaporation and diffusion. The definition is Pe ) HE˙ /Do where H is film thickness E˙ is evaporation rate and Do is the Stokes-Einstein diffusion coefficient. This particle distribution is the subject of previous publications.18,19 Here a high particle Peclet number is assumed, where accumulation of particles occurs near the top surface, as shown in Figure 1. This is a common observation in drying latex films.20 For a given concentration of surfactant, the amount adsorbed onto the particles and the amount present in the bulk solvent, at equilibrium, depends on the adsorption isotherm. A high surfactant concentration in solution induces large surfactant adsorption onto particles. Evaporation of water from the top surface causes the film-air interface to recede, capturing any particles and watersoluble species, thereby increasing the concentration of surfactant and particles at the top of the film. Hence, more surfactant will be adsorbed onto the surface of the particles to re-establish equilibrium. We assume that any surfactant distribution is established during this evaporating stage and evolves very little thereafter. This is supported by the observations of Kientz and Holl.5 The adsorption of surfactant onto particles can be described by an adsorption isotherm. Here a Langmuir expression Γ ) Γ∞Cs/A + Cs is used, where Γ∞ is the maximum surface adsorption onto the particles and A represents the concentration at which half the maximum surface adsorption occurs. The transport equations take into account the diffusion of surfactant and the scaled Langmuir isotherm parameters A h and k. A h A is defined as A/Cso, which is the critical concentration scaled to the initial bulk concentration, and k is defined as 3Γ∞/RCso, representing the maximum surface adsorption on the particles scaled to the initial bulk concentration, Cso, and particle radius, R. The surfactant Peclet number depends on the molecular weight of the surfactant and determines the ability of the surfactant accumulated at the surface, due to the flux of water, to redistribute itself into the bulk solution. The surfactant Peclet number is defined as Pes ) HE˙ /Ds where Ds is the surfactant diffusion coefficient. The concentration of surfactant in the bulk, C h s and concentration of surfactant on the particles, Γ h , at a distance from the substrate, ξ, is solved from the following equation:16 (18) Routh, A. F.; Russel, W. B. Deformation mechanisms during latex film formation: Experimental evidence. Ind. Eng. Chem. Res. 2001, 40, 4302. (19) Routh, A. F.; Zimmerman, W. B. Distribution of particles during solvent evaporation from films. Chem. Eng. Sci. 2004, 14, 2961. (20) Eckersley S. T., Rudin A. Drying behaviour of acrylic latexes. Prog. Org. Coat. 1994, 23, 387.

5316 Langmuir, Vol. 22, No. 12, 2006

(

)( (

)

hs hs dΓ h ∂C ξ ∂C + dC h s ∂τ 1 - τ ∂ξ ∂C hs ∂ (1 - Φ) (Γ h -C h s)Φm ∂ξ 1 δ(ξ - ξp) ) 0 + 2 ∂ξ (1 - τ) Pes(1 - τ) (1)

1-Φ+Φ

)

where

Γ h)

kC hs A h +C hs

The first term represents an increase in concentration due to evaporation. The second term is the diffusion of material, and the third term is a source due to a packed particle front passing through the film. A full derivation of this equation is given in a previous publication.16 Experimental Section Materials. Latices used were surfactant free 50/50 wt% poly(butyl acrylate-co-styrene). They were prepared via emulsion polymerization21 at 80 °C using 4,4-azobis-cyanovaleric acid as the initiator at pH 9. The particles were made as follows. Styrene monomer (Acros Organics) was filtered through aluminum oxide, and butyl acrylate monomer (Acros Organics) was vacuum distilled to remove inhibitors. Distilled water was placed in a four-neck roundbottom glass reactor fitted with a stirrer and reflux condenser and heated under nitrogen in a water bath. The initiator was dissolved in sodium hydroxide solution and added to the water in the reaction vessel with half the monomers to produce a seed for the polymerization process. The pH was then adjusted to a value of 9 by dissolving more sodium hydroxide tablets in the solution. Fianlly, the rest of the monomers were added and the reaction was allowed to proceed overnight to ensure complete conversion. The latices were cleaned in dialysis tubing for a week, with two changes of water per day. Particle sizes were determined by dynamic light scattering (Brookhaven’s ZetaPALS). Particle weight percent was determined from the dry mass of the sample; a known mass of sample was dried at 60 °C overnight and the remaining mass of sample determined. In this work, surfactants were added after the polymerization process to ensure the exact amount of surfactant in solution is known. Four types of surfactant were used, SDS, SOS, LiDS, and ST (all from Sigma Aldrich, used as received). Film Preparation. Samples were made by mixing surfactant with latex at a known concentration and shaking overnight to ensure a good mixing. Each latex solution was spread onto aluminum foil as a 1 mm thick wet film and dried in an oven at about 60 °C for 20 min to obtain a transparent, homogeneous film. After film formation, a representative and uniform area of about 0.5 cm2 was cut from the film and stuck onto the target plate with carbon tape to increase conductivity and to prevent excess build up of charges during analysis. The samples were also held with metal fingers to further increase conductivity. Adsorption Isotherm. Adsorption isotherms for SOS, SDS, and LiDS were obtained by contact angle measurements of solution droplets on cover glass slips. Initially, calibration curves were obtained for each surfactant using a range of surfactant solutions in distilled water by placing 0.2 mL of liquid on a cover glass slip using a micrometer syringe and measuring the contact angle. Samples were prepared by adding a known amount of surfactant to a known mass of latex. The samples were shaken for several hours and left overnight to equilibrate. The samples were then used in contact angle measurements. It was assumed that surfactants adsorbed onto the particle surface have a negligible contribution to the surface tension (21) Goodwin, W.; Hearn, J.; Ho, C. C.; Ottewill, R. H. The preparation and characterisation of polymer latices formed in the absence of surface active agents. J Polym. 1973, 5, 347.

Lee et al. of the solution and any change in contact angle is only attributed to the free surfactants in the water phase. Using the calibration curve, the amount of surfactant in the water phase is calculated. A Langmuir-type adsorption is then fitted to the experimental data. It was not possible to obtain an adsorption isotherm for ST using this method. Nuclear Magnetic Resonance (NMR). The diffusion coefficients were measured with a standard pulsed field gradient (PFG) NMR technique using a 10 mm i.d. 1H r.f. coil on a 7 T vertical-bore NMR spectrometer. Chemical shift differences were used to selectively detect the surfactant resonance peaks. The samples were diluted such that minimal change was observed in the diffusion coefficient with further dilution. Rutherford Backscattering (RBS). RBS is a thin-film depth profiling technique with advantages over other techniques such as Fourier transform infrared (FTIR) spectroscopy and XPS because it gives a quantitative result directly (unlike FTIR) and nondestructive depth profiles of the elements present in a given sample (unlike XPS, although the incident beam always modifies the sample to some degree). RBS measures the energy of the incident fast ion, in this case 1.5 MeV 4He+, elastically scattered from the atomic nuclei in the film. The scattered energy, E1, is a function of the ratio of the incident and target nuclei masses, m and M: for direct backscattering, this is E1 ) E0 [(1 - r)/(1 + r)]2 where E0 is the incident energy and r ≡ m/M, and the electronic energy loss is approximately proportional to the depth of the scattering event in the film. The Rutherford scattering cross-section (given by the Coulomb potential) is proportional to Z2 (where Z is the atomic number), and therefore, this method is particularly suitable for obtaining the depth profile of a heavy element in a matrix of lighter elements. In this experiment, RBS was used to obtain the distribution of sulfur on the surface of latex films. Since sulfur is only found in the surfactants, it is representative of the distribution of the respective surfactants. The experiment was carried out using the 2 MV Tandetron accelerator at University of Surrey Ion Beam Centre (www.surreyibc.ac.uk and ref 22). The experiment was carried out with 1.5 MeV 4He+ at normal beam incidence using a detector with a solid angle of 3.1 msr and a scattering angle of 147.7°, a beam current of about 5 nA, and a spot size of about 1 mm diameter. Best-fit elemental depth profiles were extracted from the spectra using the automatic global minimization code DataFurnace (NDFv8.0b: see www.surreyibc.ac.uk/ndf), which implements the simulated annealing algorithm.23 The spectra obtained from films containing surfactant are potentially highly ambiguous (see the discussion in ref 24), and it is necessary to impose some assumptions about valid depth profiles to exclude unphysical solutions. The spectra were fitted using an assumption that only two molecules (the latex and the surfactant) were present in the sample. We assume further that the film is uniform in depth except near the surface and that the resulting depth profile is from a film thick enough to give S counts at the lowest detected energy. With these assumptions, the total yield in the low-energy part of the spectrum is fully determined by the composition and the charge.solid-angle product. However, the H content of the film is only determined indirectly (through the energy loss from the spectrum height, since He cannot scatter at backward angles from H), and therefore, the calculated spectrum can fit the data if the charge.solidangle product is allowed to be a free parameter. This is also true in the presence of the expected beam-induced H loss, which will affect only the height of the spectrum provided the H loss occurs equally throughout the depth probed. (22) Simon, A.; Jeynes, C.; Webb, R. P.; Finnis, R.; Tabatabian, Z.; Sellin, P. J.; Breese, M. B. H.; Fellows, D. F.; van den Broek, R.; Gwilliam, R. M. The new Surrey ion beam analysis facility. Nucl. Instrum. Methods 2004, B219, 405409. (23) Barradas, N. P.; Jeynes, C.; Webb, R. P. Simulated annealing analysis of Rutherford backscattering data. Appl. Phys. Lett. 1997, 71, 291. (24) Jeynes, C.; Barradas, N. P.; Marriott, P. K.; Boudreault, G.; Jenkin, M.; Wendler, E.; Webb, R. P. Elemental thin film depth profiles by ion beam analysis using simulated annealing - a new tool. J. Phys. 2003, R97, 36.

Distribution of Surfactants in Latex Films

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Table 1. Sample Compositions and the Langmuir Parameters for Surfactants sample

surfactant

mass of surfactant (g)

mass of wet latex (g)

surfactant wt%

Γ∞ (mol/m2)

A (mol/m3)

1 2 3 4

SDS SOS LiDS ST

0.0273 0.0211 0.0223 0.0216

3.0315 3.0331 3.0847 3.1073

0.89 0.69 0.72 0.69

2.00 × 10-5 8.00 × 10-5 3.00 × 10-5

2.1 8.0 1.2

Results Samples. Five different samples were prepared for this experiment, four with surfactants SDS, SOS, LiDS, and ST and the last sample consisting of the pure poly(styrene-co-butyl acrylate) latex. Table 1 lists the different samples with concentrations of the respective surfactants. The same latex was used for all the samples, with solid content of 13.47 wt% and particle diameter of 200 nm. Adsorption Isotherm. The Langmuir isotherm parameters, Γ∞ and A, were obtained from the adsorption isotherm graphs, as shown in Figure 2a, b, and c. Γ∞ represents the maximum surface adsorption onto the particles, and A represents the concentration at which about half the maximum surface adsorption occurs. The Langmuir isotherm parameters for each surfactant are shown in Table 1. It is clear from Figure 2 that a Langmuir fit is not ideal for the data and a more complicated adsorption mechanism is occurring. We, however, persist in using the best Langmuir fit to our data. RBS Results. Many spectra were obtained from a matrix of points on each sample each with 1 µC collected charge. All the samples displayed a large lateral inhomogeneity. The summed spectra are shown in Figures 3-7. The relatively low collected charge per spectrum is to reduce beam damage to the sample. We have demonstrated that beam damage does not significantly distort the spectra with cumulated data of 13 µC on one spot of the SOS sample. On the y axis, the number of backscattered helium ions detected is plotted on a linear scale. On the x axis, the channel number (linearly proportional to the energy of the backscattered ions) is displayed. The highest number of counts corresponds to the most common elements in the film, namely C and O. These lighter elements will appear at the lower channel number (lower energies). Channels that correspond to the energy backscattered from the various elements at the sample surface are labeled on the axis in Figures 3 and 4. Points to the left of the label for each of the element correspond to the backscattered energy from the element found below the film surface, since 4He+ loses energy while travelling through the material. The element of greatest interest here is S since it represents the distribution of surfactants. The analyzed depth is about 3 µm The data were fitted using IBA DataFurnace to obtain the elemental depth profiles, and this was done in a two-stage process: First, spectra from the bare latex were fitted. The elastic scattering cross-section for C was adjusted with a fixed cubic polynomial to get a good fit over the whole energy range.25 This corrects for double scattering and other effects and does not influence the analysis. The composition of the latex is known from the recipe and this is close to the composition obtained, assuming a single latex “molecule” with the composition obtained shown in Table 2. It is noticeable that there are significant amounts of sodium and silicon in the latex. The sodium is likely to be from the sodium hydroxide added to increase the pH and dissolve the initiator. The silica is likely to be leaching from the glassware (25) Barradas, N. P.; Jeynes, C.; Jackson, S. M. RBS/simulated annealing analysis of buried SiCOx layers formed by implanation of O onto cubic silicon carbide. Nucl. Instrum. Methods Phys. Res., Sect. B 1998, 137, 1168-1171.

Figure 2. Adsorption isotherm of (a) SDS, (b) SOS, and (c) LiDS where the adsorption on the particles is plotted against the concentration in solution.

used in the experiments.26 The spectrum from the base latex and the corresponding fit are shown in Figure 3. Once the latex (26) Routh, A. F.; Vincent, B. Some anomalous effects of sodium ions on the electrophoretic mobility and heteroaggregation of microgel particles. J. Colloid Interface Sci. 2004, 273, 435.

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Lee et al.

Figure 3. Pure poly(styrene-co-butyl acrylate) film. Note the excess Na in this spectrum.

Figure 6. Averaged RBS spectra for film containing 0.72 wt% LiDS and the resulting fit with calculated depth profile of surfactant (heavy line). The light line shows the complementary profile for the latex in this fit assuming only two phases.

Figure 4. Averaged RBS spectra for film containing 0.89 wt% SDS and the resulting fit with calculated depth profile of surfactant (heavy line). The light line shows the complementary profile for the latex in this fit assuming only two phases.

Figure 7. Averaged RBS spectra for film containing 0.69 wt% ST and the resulting fit with calculated depth profile of surfactant (heavy line). The light line shows the complementary profile for the latex in this fit assuming only two phases. Table 2. Atomic Compositions of Components Used in Fitting of RBS Data

Figure 5. Averaged RBS spectra for film containing 0.69 wt% SOS and the resulting fit with calculated depth profile of surfactant (heavy line). The light line shows the complementary profile for the latex in this fit assuming only two phases.

composition is obtained, a second molecule is added to mimic the surfactant. Starting from the nominal composition of these molecules, the composition is allowed to float to obtain a good fit. All the compositions obtained are shown in Table 2. It is noticeable that SDS seems to contain slightly less sulfur than anticipated and LiDS contains significant quantities of sodium. The RBS spectra show a large accumulation of surfactant at the surface with a decreasing concentration into the bulk. To obtain the bulk S concentration, the spectra are fitted by assuming there to be five layers of fixed thickness but varying proportions of the two molecules. The final layer represents the bulk of the film and the four layers above a surface accumulation of surfactant. It was necessary to impose this model on the data only to ensure

sample

C

SDS SOS LiDS ST bare latex

12 8 12 1 39

SDS SOS LiDS ST bare latex

12 8 12 1 39

latex + SDS latex + SOS latex + LiDS latex + ST

39 39 39 39

Nominal Composition H O S Li 25 17 25 52

4 4 4 3 5.2

1 1 1 1

4.6 4.6 4.6 4.6

Si

F

1 1 1

Actual Composition Used 25 4 0.9 17 4 1 25 4 1 1 3 1 52 4.6 52 52 52 52

Na

1

3

1 1 1.3 1.6 0.27

0.35

0.27 0.27 0.27 0.27

0.6 0.6 0.35 0.6

3

that the model has a total thickness sufficient to make the S signal extend down to the lowest analyzed energies. We use the relative height of the spectrum at the low energies to determine the contribution of S at those depths to the signal. This is a small effect, and the S content at depth is not well determined unless the conditions of the fit are sufficiently constrained. However,

Distribution of Surfactants in Latex Films

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Table 3. Results from Fitting Average Spectra, Showing Bulk Surfactant Concentration and the Equivalent Thickness of the Surfactant Layer Calculated from the S Signala

sample

bulk surfactant (atomic %)

surface surfactant equivalent thickness (nm)

bulk surfactant concentration (mol/m3)

Peclet number

predicted sulfur excess (mol/m3)

SDS SOS LiDS ST

3.5 0.2 3.2 1.3

41 31 52 54

56 3 51 21

0.13 0.06 0.19 -

73 108 112 -

a The measurement uncertainty of the first column is about 10%, and at least 0.1 atomic %. The final two columns show the numerical results showing the predicted sulfur excess at the top surface.

with these constraints, the S content at depth is determined with an uncertainty of about 10%. The values obtained can be seen in Table 3. By assuming the latex and surfactants to all have densities of 1 g/cm3, it is possible to convert from thin film units (in units of atoms/cm2) to depth by using the atomic densities. The surfactant profile near the surface is fitted model-free (except for the strong assumption of only two phases) and is shown in Figures 4-7. The overall result from the average spectra fitting is shown in Table 3, detailing the depth of the surfactant layer and the bulk surfactant concentration. Although the two-phase assumption is a strong constraint the fit is very good, showing that the assumption is valid. This shows that any variation of composition with depth (apart from near the surface) is small. NMR Diffusometry. The diffusion coefficients for the three surfactants were obtained at 18 °C, which is lower than the temperature of the experiment, and this will affect the diffusion coefficients. The values obtained were 2.6 × 10-10 m2/s for SDS, 1.8 × 10-10 m2/s for LiDS, and 6.1 × 10-10 m2/s for SOS. As expected, the smaller SOS is more mobile than the longer SDS and LiDS. Why the diffusion coefficients for LiDS and SDS are so different is not clear. Numerical Predictions. The Langmuir parameters have been obtained experimentally. The only other parameter in the numerical model is the surfactant Peclet number. This is defined as Pes ) HE˙ /Ds where H is the film thickness, E˙ is evaporation rate, and Ds is the surfactant diffusion coefficient. The initial film thickness and evaporation rate at 60 °C are known, while the diffusion coefficient has been measured. We estimate the surfactant Peclet numbers, Pes, of 0.13 for SDS, 0.19 for LiDS, and 0.06 for SOS. This corresponds to a film thickness of 1 mm, evaporation rate of 0.3 cm/day, and the measured diffusion coefficients. With these estimates for the Peclet numbers, surfactant distributions at the end of drying are calculated. A characteristic distribution is shown in Figure 8. The predicted surfactant concentrations at the top surface are shown in the final column of Table 3. It should be noted that the transport model ignores adsorption of surfactant to the air-water interface and hence is not capturing the top layer of surfactant as seen in the RBS experiments. The films are initially 1000 µm thick and comprise particles at 13 wt%. Hence, the final film is likely to be in excess of 100 µm thick. The experimental measurements are down to a depth of 3 µm, and therefore, the “bulk” concentration obtained from the RBS measurement should be compared with the predictions for concentration at the top surface of the film. Because it was not possible to obtain an adsorption isotherm for the ST surfactant, no numerical predictions are made for this sample.

Figure 8. Predicted percentage excess/depletion of SDS across the film thickness using Pe ) 0.13 and the measured adsorption isotherm parameters.

a bulk concentration below. With the four samples examined, the SDS had the largest bulk concentration, followed by LiDS, ST, and finally SOS, which had a very low bulk concentration. While the SDS displayed the largest bulk concentration, the original amount present in the film was largest for SDS, and so we observe a greater accumulation for LiDS than for any other surfactant. (The bulk concentration divided by the original surfactant concentration is largest for LiDS). The very low bulk concentration of SOS is discussed in detail below. A monolayer of surfactant has a thickness of 1-2 nm,27 yet the RBS indicates a far thicker surfactant layer of 30-50 nm. If surfactant diffusion in the wet latex were negligible, then a large surface accumulation would be expected. For the cases considered here, where Pe ≈ 0.1, diffusion of surfactant is strong and hence such a large accumulation is a surprising result. In spite of this, the RBS results are clear in showing a thick (30-50 nm) layer of surfactant at the top surface of the films. The results from the transport model indicate a larger accumulation of LiDS at the top surface when compared to the other surfactants. The two competing factors are adsorption on particles, leading to accumulation at the top surface, and diffusion leading to a more uniform surfactant concentration profile. The Peclet number for LiDS is the highest of all the surfactants, implying a greater accumulation at the top surface and in addition LiDS has a higher binding to the particles than for SDS (higher Γ∞). In the early stages of drying, the particles accumulate at the top surface and this leads to an accumulation of surfactant. The particles finally consolidate throughout the film, but excess of surfactant at the top surface leads to a reduced bulk concentration in the lower part of the film and hence less surfactant on the

Discussion The RBS results indicate an accumulation of surfactant at the film-air interface. This surfactant layer is 30-50 nm thick with

(27) Penfold, J.; Tucker, I.; Thomas, R. L. Polyelectrolyte modified solid surfaces: the consequences for ionic and mixed ionic/nonionic surfactant adsorption. Langmuir 2005, 21(25), 11757.

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Lee et al.

Table 4. Variation in Sulfur Counts Across Samples and Standard Deviation in Count no. of points examined highest count lowest count average count standard deviation %

SDS

SOS

LiDS

ST

19 159 63 107 30

12 222 31 112 48

8 232 54 131 61

23 445 36 190 69

particles in this region. Hence, LiDS is predicted to display a larger accumulation at the top surface, and this is observed experimentally. For all the samples, there was a large lateral disparity in the surfactant concentration and the surfactant excess reported is the average concentration found from many measurements. Table 4 shows the range in sulfur counts obtained for each latex sample and the resulting standard deviation among the data. One reason for the lateral inhomogeneities is lateral flows created by disparities in surface tension. This Marangoni-type flow instability will also lead to nonuniform film height profiles and is the subject of a future publication. The experimental findings are of an SOS concentration close to zero in the bulk of the film. There are two possibilities as to the location of the added surfactant. The simplest explanation is of a large accumulation of surfactant at the film-air interface. Of the four surfactants tested, SOS has the largest amount of loading onto particles (Γ∞ is the largest), and this will lead to a large loading of surfactant at the film-air interface throughout the drying process. If the adsorption of surfactant at the waterair interface for SOS is sufficiently large, a depletion of SOS throughout the rest of the film will then be observed. If a simple monolayer of surfactant were forming at the top surface, the amount of surfactant involved would be too small to account for the “missing” surfactant. To see this, consider the following scaling argument: If the film-air adsorption isotherm, Γs, is included in the boundary condition to eq 1, a factor, R/H, where R is the particle radius and H is the film thickness appears from the scaling, and the boundary condition becomes

hs ∂C hs R ∂Γ 1 ) (1 - φ) - ((1 - φ)C h s + φΓ h) H ∂th Pe ∂yj If the term R/H is sufficiently small, the boundary condition reverts to the case without the film-air adsorption isotherm and no effect of the surfactant distribution will be seen. Physically the surface area available at the top surface is much smaller than the surface area of the particles, and this is the argument put forward by Kientz and Holl5 in their justification for ignoring the film-air adsorption isotherm. If, however, the amount of surfactant at the top surface is large enough, then a depletion in the bulk will ensue, and this seems to be the case here. For this argument to be valid, the total amount at the top surface must be large enough to counter the R/H scaling, i.e., R/H dΓ h /dth ) O(1) even though R/H ,1. In these cases, the boundary condition used to solve eq 1 is lacking the surface accumulation and, hence, the overestimation of the bulk concentrations. An alternative explanation for the lack of SOS is that lateral inhomogeneities in the SOS concentration are present and the areas of high SOS concentration have been missed by the RBS. The likely large accumulation at the film-air interface, because of the larger film-air adsorption isotherm, will enhance lateral flows and the subsequent segregation. Therefore, the surfactants with the largest film-air adsorption isotherm are most likely to display this lateral segregation. This, however, is not that satisfactory an explanation because all the surfactant samples

studied show a lower bulk concentration than expected. We therefore conclude that a large surface accumulation of surfactant into layers of 30-50 nm leads to a depletion of surfactant in the rest of the film. There are numerous assumptions in the numerical model that require discussion: Desorption of surfactant as the particles deform and interdiffusion occurs will lead to regions rich in surfactant, on a length scale comparable to that of the particle. By writing a particle volume fraction, we are volume-averaging in the film, and hence, this blurs out any local accumulation on such small length scales. However, any accumulation of surfactant into such regions will enhance a diffusive flux and hence minimize the surfactant accumulation. The temperature of film formation was 60 °C, well above the 18 °C used to measure the diffusion coefficients, and in addition, the evaporation rate of water was not that closely controlled. While these factors will all affect the Peclet number, it is important to recognize that any error in the Peclet number is constant between each of the surfactant samples. The largest source of error is in the adsorption isotherms and assuming a Langmuir fit to the measured data. This assumption is convenient numerically, and although the experimental points were determined using contact angle measurements, with an inherent error, the Langmuir isotherm assumption does not correlate very well with the measured isotherms. The experimental adsorption isotherm profiles for SDS and LiDS, in Figure 2, display two critical bulk concentrations: one to initiate loading onto particles and the second at the onset of saturation. This is more complex than a simple Langmuirian competition for adsorption sites. It is noticeable that SOS, the shortest chain surfactant, gives the most Langmuirian-type isotherm. While the surfactant concentration will equilibrate to some extent as the particles deform and the film ages, this level of diffusion through a continuous polymer is many orders of magnitude less than the mobility in the water phase.29 Hence, the initial condition on surfactant distribution, set up during the evaporation stage, remains even after complete film formation, and it is this that is being detected.

Conclusions Using RBS, the enrichment of surfactants on the surface of poly(styrene-co-butyl acrylate) latex films for four surfactants (SDS, SOS, LiDS, and ST) has been shown, together with the near-surface equilibrium concentration, which can be compared to the surface concentration of the numerical model. The near-surface concentration amounts of SDS and LiDS are predicted to be somewhat larger than measured, and very little near-surface concentration for SOS is observed. Overall, the model has adequately predicted the near-surface concentration of surfactant for two of the samples tested, although it has failed to capture the behavior of SOS. Acknowledgment. This work was supported by EPSRC through Grants No. GR/S05885/01 and GR/R50097/01. The authors are very grateful to Joe Keddie and Mike Hounslow for helpful advice and to Aliz Simon for help with RBS experiments. LA0601760 (28) Belaroui, F.; Hirn, M. P.; Grohens, Y.; Marie, P.; Holl, Y. Distribution of water-soluble and surface-active low-molecular-weight species in acrylic latex films. J. Colloid Interface Sci. 2003, 26, 1336. (29) Chainey, M.; Wilkinson, M. C.; Hearn, J. Permeation through homopolymer latex films. J. Polym. Sci., Part A: Polym. Chem. 1985, 23, 2947.