Nonionic Surfactant Mixtures at

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Temperature Resistant Binary SLES/Nonionic Surfactant Mixtures at the Air/Water Interface Charles Smith, Jian Ren Lu, Ian M. Tucker, David Grainger, Peixun Li, John Robert Peter Webster, and Robert K. Thomas Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b01093 • Publication Date (Web): 16 Jul 2018 Downloaded from http://pubs.acs.org on July 16, 2018

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Temperature Resistant Binary SLES/Nonionic Surfactant Mixtures at the Air/Water Interface

Charles Smith1, Jian R. Lu1,* Ian M, Tucker2, David Grainger2, Peixun Li3, John R.P. Webster3, and Robert K. Thomas4

1 Biological Physics Laboratory, School of Physics and Astronomy, University of Manchester, Schuster Building, Brunswick Street, Manchester M13 9PL, U.K. 2 Unilever Research and Development Port Sunlight Laboratory, Quarry Road East, Bebington, Wirral CH63 3JW, U.K. 3 STFC, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, U.K. 4 Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, U.K.

*Corresponding author: Jian R Lu (email: [email protected]; Tel: +44 161 2003926)

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Abstract Surface compositions of adsorbed monolayers at the air/water interface, formed from binary surfactant mixtures in equilibrium, have been studied using neutron reflectivity at three discrete temperatures: 10 oC, 25 oC, and 40 o

C. The binary compositions studied are SLES EO3/C12En, where n = 6 and 8, at

a fixed concentration of 2mM with and without the addition of 0.1M NaCl. Without NaCl, the nonionic surfactant dominates at the interface and nonideal mixing behaviour is observed. This is modelled using the pseudophase approximation with a quadratic expansion of the free energy of mixing. The addition of 0.1M NaCl screens the charge interaction between the surfactants and drives the surface composition of each system closer to that of the bulk composition. However, model fits to both the micelles and surface layers suggest that non-ideal mixing is still taking place, although it is difficult to establish the extent of non-ideality due to the limited data quality. The effect of temperature changes on the surface adsorption and composition of the surfactant mixtures is minimal and within error, with and without NaCl, but the CMCs are significantly affected. This indicates the dominant influence of steric hindrances and surfactant charge interaction in determining interfacial behaviour for these surfactants, relative to the temperature changes. The study also highlights the delicate impact of a relatively small change in the number of EO groups on mixing behaviour.

Keywords: Surfactant mixture, binary system, non-ideal mixing, neutron reflection, free energy of mixing, surface adsorption

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Introduction Surfactants are available in a variety of molecular structures, each with their own characteristic features.1 Commercial formulations combine various surfactant types to take advantage of synergistic mixing.2 Surfactant performance in products can be dictated by temperature, notably affecting solubility and hydration of surfactant molecules and in the extremes, resulting in phase separation and inability to aggregate.3 However, it is often difficult to predict surfactant mixing behaviour, necessitating extensive physicochemical studies into properties at various interfaces and aggregation in solution, with due consideration of impact of structure and composition of surfactants under different environmental conditions.1-5 It is therefore useful to determine patterns in mixing behaviour and to predict how a given set of conditions affects a system, and this has generally been the focus of surfactant research to date.6 The pseudophase approximation, PPA, has been successfully applied to model non-ideal mixtures in previous publications.7-9 Theoretical descriptions of surfactant mixing tend to focus on the thermodynamic properties of the system with the implicit assumption that such information can be obtained reliably.10 The treatment and terminology adopted in this paper is similar to that of recent studies by Li

11

and Liley

12

with reference to the free energy

upon mixing, GE, defined in terms of entropy and enthalpy. A system driven purely by entropy is said to be ideally mixed, and any deviation from this is a result of a non-zero enthalpy contribution causing non-ideal mixing. The latter has been successfully modelled under the assumption that surfactant monomers, aggregates, and adsorbed surface layers form separate phases in solution and this approach, formally labelled as PPA, is often coupled with the 3


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regular solution theory approximation, RST, which further requires that the contribution to enthalpy can be characterized by a single interaction parameter.1, 11-14 Alternatives to the PPA method have been developed, most notably by Nagarajan and Blankschtein et al., based on molecular thermodynamics,10, 15, 16 as well as Markov chain models by Georgiev et al.17, 18 Non-ideality is often exhibited in mixtures of dissimilar surfactants, particularly with charged head groups.19 This work is concerned with studying binary ionic/nonionic mixtures of sodium lauryl dodecylether sulfate (SLES EO3)/ hexaethylene glycol monododecyl ether (C12E6) and SLES EO3/octaethylene glycol monododecyl ether (C12E8), using neutron reflectometry, at three distinct temperatures of 10 oC, 25 oC, and 40 oC. These surfactants are currently used in commercial products,20 there are studies into similar surfactant mixtures for corroboration, and some limited work is also available on their temperature dependent behaviour.12,

21-24

However, there is currently very

little information on surfactant mixing behaviour below ambient temperatures. Studies that look at low temperatures tend to focus on individual surfactants, rather than mixtures.25 Decreasing the temperature reduces the energy available to a surfactant mixture in solution, altering competition at the surface and in the aggregate. Penfold et al. found that changes in temperature on nonionics mainly affected the hydration of the EO groups and the solubility of the alkyl chains.25 This work seeks to understand how temperature changes between 10 oC and 40 oC affects surfactant mixing at the air/water interface and whether EO groups play a significant role in this. It also examines the interplay between temperature and charge effects, specifically by examining if there are any changes in temperature-dependent behaviour as a result of screening the charge interaction on the anionic head group by using NaCl. The aim is to compare the relative strength of both factors and how they relate to 4


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mixing behaviour. As the PPA model has been utilized in several previous studies, the results in this work are analysed similarly in order to test its validity over the temperature range. Experimental details Materials C12E6 and C12E8 are abbreviations of hexaethylene glycol monododecyl ether and octaethylene glycol monododecyl ether, respectively. They are linear nonionic surfactants with an alkyl chain length of 12 carbon atoms and a headgroup consisting of 6 and 8 ethylene oxide groups. The protonated components were obtained commercially from Nikkol and used as supplied; the deuterated components by the Deuteration Laboratory Facility, ISIS, Rutherford Appleton Laboratory. Their production consisted initially of mixing deuterated dodecanol with potassium tert-butoxide, adding hexaethylene glycol or polyethylene glycol for either C12E6 or C12E8. The samples were purified using a silica column and a 2-1 ether-acetone mixture. The D-C12E8 sample contained trace amounts of C12E7 and C12E9, but the EO number was definitely above C12E6. The deuteration facility also produced the protonated and deuterated components of sodium lauryl dodecylether sulfate, SLES EO3, a linear anionic surfactant with the same alkyl chain length as the nonionics and a polar sulfate headgroup with 3 ethylene oxide group spacers. The production method is described by Xu: sulfonation of synthesised polyethylene glycol monododecyl ethers, followed by recrystallization in propanol/ethanol mixtures.26 The solvents used in sample preparation were H2O and D2O: the former was MilliQ ultrapure water and the latter was obtained from SigmaAldritch (99.9% purity). Any glassware used in the experiment was cleaned with a dilute Decon 90 solution and thoroughly rinsed with deionised water. 5


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Surface tension Surface tension measurements were undertaken using a Krüss K11 digital tensiometer and a flame sterilised Wilhelmy plate. A glass vessel of diameter 45 mm and depth 30 mm held a sample solution of 10 ml, and the equipment was calibrated prior to each data set via a comparison of pure water measurements against values given in literature.27 Sample temperature was regulated using a HAAKE K20 water bath and DC3 moderator pump connected to a thermostattable sample jacket. Each composition was measured over 3 discrete temperatures of 10 oC, 25 oC and 40 oC, with an approximate equilibration time of 10 min. The force associated with pulling the plate out of the sample was recorded for successive dilutions from an initially high concentration, above CMC, to a low concentration, below CMC. The CMC was determined from the inflection point in the ln(concentration) plot against surface tension. There are alternative methods of determining the CMC, including conductivity measurements, dynamic light scattering, and small angle neutron scattering. However, conductivity measurements are, by their very nature, difficult to perform for nonionic (and partially nonionic) systems. Surface tension was chosen primarily as it provides the surface pressure of a system. It is also consistent with relevant literature on the application of the PPA model, which favours the technique.7-9, 25 Neutron reflectometry Neutron reflectometry, NR, measurements were primarily performed on the SURF reflectometer at the ISIS neutron spallation source at the Rutherford Appleton Laboratory; a few select measurements were also completed on a

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second reflectometer, INTER. The incident neutron beam struck the sample at an angle of 1.5o, resulting in a wave vector transfer range between 0.05 - 0.35 Å-1 for the reflected beam. A more complete description of neutron scattering theory and its application for practical usage is described elsewhere.28,

29

Fundamentally, neutron scattering techniques have been invaluable in studying surfactant behaviour, particularly adsorption at the air/water interface.30 Its success in this field is attributed to the large difference and opposite sign in the scattering lengths of hydrogen, -3.75 × 10-5 Å, and deuterium, 6.67 × 10-5 Å. NR measurements for the mixed surfactant systems were performed in null reflecting water, NRW, a 92:8 ratio mix of H2O and D2O providing a total scattering length of zero (same as air). Selective deuteration of the surfactant's alkyl chains enabled decoupling of each component from the binary mixture; isotopic combinations for the two alkyl chains of DD, HD, and DH produced significantly different scattering profiles while retaining near identical interfacial behaviour. This method has been employed on numerous counts for similar systems with remarkable success.7, 11, 19, 30, 31 Neutron attenuation and background radiation were accounted for via sample measurements of pure D2O and direct transmission runs, in line with the ISIS protocol. Reflectivity profiles for each measurement were fitted using the standard optical matrix technique 32 applied to a monolayer and allowing for two variable parameters: the scattering length density of the adsorbed surfactant layer and its thickness.29 This paper is concerned with mixed surfactant coverage and composition at the interface rather than the structure of the adsorbed layer. Coverage was determined from the product of the scattering length density and layer 7


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thickness involved in the fitting process.33 Hence, surface coverage is dependent on the product of the pair, not their individual values, with an absolute minimum accuracy of 7%.30 Sample environment consisted of hermetically sealed, Teflon coated steel troughs with an approximate sample volume of 20 ml and illumination area of 30 mm × 150 mm. Sample temperature was regulated by a pipe network connected to a Julabo waterbath that ran underneath each trough. The trough holder itself was set to be a few degrees hotter via Eurotherms and Peltier strips; each trough was the coldest point in the sealed system and thereby minimised evaporation of the liquid sample. An external probe was used to measure sample temperature throughout the experiment, and temperature variation was no more than 2 oC. Each sample was allowed to equilibrate for 10 min once it had reached the desired temperature. More information plus pictures of the trough setup are available in Liley’s thesis.24 Thermodynamics The PPA model treats the formation of micelles and adsorbed surface layers as separate phases and, hence, they are assigned chemical potentials. The surfactant systems studied in this paper were all in thermodynamic equilibrium and therefore all chemical potentials were equal. Examining the case for a dilute bulk solution, which is appropriate for this work, the bulk activity coefficient reduces to 1 and we have the following equation for the composition in a micelle, x , with i representing either component 1 or 2 in a binary mixture:

x =

c

f c

(1).

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Superscript µ denotes elements specific to the micellar phase, fi the activity coefficient, ci the CMC of component i, and cimon the monomer concentration of component i in solution. At the mixed CMC, cimon is equal to the product of the bulk composition, αi, and the total concentration, ctotal. If there is no dissociation of the surfactants in solution, then mass conservation states that xi and αi must both sum to 1 over all i. Combined with Equation 1, the mixed critical micellar concentration for a binary system is,

1

c

=

α

f c

+

α

f c

(2).

In this paper, the subscript 1 is used to denote the nonionic component in the binary mixture and, by extension, 2 the ionic. If ci and the activity coefficients over the whole composition range are known, then cmix is given over the composition range from Equation 2; the biggest problem lies in finding fi, which in turn requires determining GE. The PPA method adopted in this paper is similar to that by Li et al.11 and uses a quadratic expansion of the free energy,

G = x x B

(3),

where B is a constant value representing the deviation from ideal mixing. A negative B value implies negative free energy upon mixing or synergism. Note that the linear term of the expansion is excluded based on the requirement for GE to satisfy the Gibbs-Duhem equation.12 The activity coefficients are equal to the partial derivative of GE and hence, from Equation 3, are

lnf = B x

(4)

lnf = B x with units RT, the gas constant and temperature. Values of x1 and x2 cannot be found directly from experiments, necessitating a coarser approach to find the 9


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activity coefficients. The approach described by Liley et al. was adopted, as summarised in the following steps. An iterative fit of Equation 2 to a set of CMC data obtained from surface tension measurements, coupled with the solution of a Redlich-Kister function based on Equation 4, gives the following:

f ln = B x − x f

(5).

x c α = ln x c α Equation 5 was solved using the Newton-Raphson method, with the function converging on a suitable xi value within approximately 6 iterations. The situation is complicated in applying the previous procedure to concentrations exceeding the CMC: the monomer concentration shifts significantly, such that the PPA model for a mixed system is no longer valid.34 The following equation to calculate cimon above the CMC is derived from mass balance and Equation 1,

x =

α c − f x c

c −

f x c

−

f x c

(6).

The necessary calculations to find micellar compositions from a set of CMC measurements can equally be applied to find compositions of the adsorbed layer at the interface. It is achieved by swapping CMC values for concentrations of surfactant mixtures required to meet a fixed pressure, cπ. A correction to Equation 1 is required in order to find the surface composition because the chemical potential now relies on the surface pressure of the system. Following through with the same procedure, the final equation used to determine surface composition is given below, with a full derivation described elsewhere,12

10


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B

!" x

x c# α − x − ln # + ω %& − &'( ) x c α

(7),

−ω %& − &'( ) = 0

where ω is the area per molecule, π the pressure terms, and the subscripts refer to either the individual components or the equilibrium, eq, when mixed. The micellar and surface interaction parameters will often be different 11, 12 and in this paper, the latter are identified via the superscript sur. Results Surface tension measurements of binary surfactant mixtures C12E6/SLES EO3 and C12E8/SLES EO3, with and without 0.1 M NaCl, were undertaken at 3 different temperatures of 10 oC, 25 oC and 40 oC, with the raw surface tension changes shown in the Supporting Information. The CMCs determined from the surface tension plots, as a function of solution composition, are shown in Figures 1, 2, and 3. Figure 1 shows the variation in CMC for C12E8/SLES EO3 compositions at 25 oC, fitted using the ideal and single parameter non-ideal model. The ideal line is produced from Equation 2, where B is taken to be zero

resulting in f = f = 1, and the equation for the mixed CMC reduces to what is

commonly called the Clint equation.35 The CMC of SLES3 in pure water, at 25 o

C, is determined to be 2.31 ± 0.14 mM, which is in line with literature.36

Equally, the determined CMC for C12E6 and C12E8, at 25 oC, are 0.07 ± 0.02 mM and 0.09 ± 0.02 mM, respectively, both in line with values reported in literature.37 It is evident from the figure that the two surfactants are mixing

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Figure 1: CMC variation with solution composition of C12E8/SLES EO3 at 25 oC, portrayed by left filled, red circular markers. The blue dash dot line represents ideal mixing (B = 0) for the system, and the black dashed line is the regular solution fit to the data with an interaction parameter B = -2.3 ± 1.0. non-ideally and the deviation implies synergism, with micellar composition dominated by the nonionic; this is to be expected due to the relatively strong charge repulsion between SLES EO3 head groups. The data also imply that the errors may be overestimated, but this is not the case for all of the binary mixtures. An upper error of 5% and a minimum systematic error of 0.02 mM is assigned, in line with the manufacturing guidelines and error propagation. Figures 2a) and 3a) show CMC variation with solution composition for C12E8/SLES EO3 and C12E6/SLES EO3 in pure water. Data for all 3 temperatures are shown in each figure with their corresponding PPA fits, calculated using Equations 2 and 5. The PPA fits to the CMC data all imply synergistic mixing of the binary surfactant systems for all temperatures and all compositions, as demonstrated by negative free energies upon mixing. Micellar composition heavily favours the nonionic C12E8 and C12E6 over the

12


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Figure 2: CMC variation with solution composition of a) C12E8/SLES EO3 and b) C12E8/SLES EO3 with 0.1 M NaCl at 10 oC, 25 oC and 40 oC. The black lines are the best fits of the pseudo phase approximation model, using a quadratic expansion of GE, to each of the three data sets. ionic SLES EO3 in the mixture, explaining the relatively low mixed CMCs; this is in line with previous findings.11, 12, 30, 31 Free energy of mixing depends on the micellar composition and not the bulk solution composition, as shown in Equation 3. In Figure 3 a), the mixed CMC value of 0.6 mM corresponds to a bulk composition α2 = 0.95, which in turn translates into a micellar composition of roughly x2μ = 0.25 (subscript 2 represents SLES). Therefore, only a quarter of the free energy curve is measured through the CMC data points, leaving the rest of the curve to be 13


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Figure 3: CMC variation with solution composition of a) C12E6/SLES EO3 and b) C12E6/SLES EO3 with 0.1M NaCl at 10 oC, 25 oC and 40 oC, represented by empty, left filled, and filled purple square markers, respectively. The black lines are the best fits of the pseudo phase approximation model, using a quadratic expansion of GE to each of the three data sets. extrapolated. The limited micellar composition range also affects the determination of B by reducing the fit sensitivity to the data. Changing the B value in Figure 3 a) by ±1 shifts the predicted CMC at α = 0.75 by no more than the size of the marker. The situation is not much better when NaCl is added, but for different reasons. The corresponding micellar composition values determined from the CMC plots encompass more of the GE curve. However, the associated error on the CMCs is weighted towards lower values which, coupled with the smaller variation over composition relative to the 14


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Figure 4: NR profiles for binary mixtures of deuterated C12E8 and hydrogenated SLES EO3 at 25 oC. The solvent was NRW and the surfactant concentration was fixed at 2mM. Each curve represents a different ratio of dC12E8:h-SLES EO3 of 1:0, 4:1, 1:1, and 1:4, respectively. Each profile is flitted with a line obtained from application of the optical matrix method systems without salt, allows for the same range of possible B values as before. Both CMC and surface composition plots were fitted in conjunction, constraining the possible interaction parameter values, and the assigned errors are discussed later in relation to the surface fittings. The nonionic systems show significant temperature dependent effects, with a corresponding drop in CMC as the temperature increases from 10 oC to 40 oC. This is in line with observations by Chen et al. who, over this temperature range, found a decrease in CMC for the individual surfactants C12E 4, 6, and 8: a minimum in CMC was reached at roughly 50 oC.22 The C12E8 system appears to show greater temperature sensitivity, with differences in CMC values

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Figure 5: Adsorption of C12E8/SLES EO3 + 0.1M NaCl at the air/water interface as a function of bulk solution composition at 10 oC, 25 oC and 40 oC, represented by empty, left filled and filled markers. The nonionic and ionic data points are distinguished by blue and green markers respectively, and the total concentration of the system was fixed at 2mM. between the two temperatures reaching in excess of 35%. In contrast, changes in CMC for the C12E6 system are no greater than 25% and often less than the associated errors. Penfold et al. observed similar behaviour, attributing the difference to significant deviations in conformation and hydrogen bonding of the nonionic EO groups with temperature.25 This could also explain the large change in CMC of the pure SLES EO3, which decreases from 2.70 ± 0.16 mM to 1.74 ± 0.11 mM. The addition of 0.1 M NaCl screens the charge interaction on the SLES EO3 head group,36 lowering its CMC by an order of magnitude. As shown in Figures 2 b) and 3 b), the CMC values of the ionic surfactant are comparable to the nonionics. The same patterns in CMC variation with temperature occurs as before. Some of the mixed CMC values now drop below the CMC of pure C12E8, as expected for two surfactants of comparable CMCs

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Figure 6: Surface composition of adsorbed C12E6/SLES EO3 against bulk solution composition at 25 oC, portrayed by left filled purple circular markers. The dashed line represents ideal mixing in the adsorbed surface layer, using micellar interaction parameter Bμ obtained from the CMC fittings. The solid line is the PPA model fit with interaction parameters Bμ and Bsur; as before, the micellar interaction parameters are taken from the CMC data fittings and the surface parameters represent the best fit to the data. mixing synergistically.1 The differences between B values at different temperatures are minimal and within error. Binary mixtures of C12E8/SLES EO3 and C12E6/SLES EO3 in various ratios were studied at the air/water interface using neutron reflectometry, at a fixed concentration of 2 mM, to determine the effects of temperature and salt on surface composition as a function of its bulk composition. The concentration was deemed appropriate as it satisfied the 3 main requirements for this study: the concentration was above the mixed CMC (achieving surface saturation of the adsorbed layer), while simultaneously low enough to minimise bulk 17


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aggregate interaction with the interfacial layer, and is of a comparable concentration to similar studies into binary surfactant mixtures.8, 19, 25, 36 Reflectivity profiles of the C12E8/SLES EO3 system at 25 oC, with the corresponding isotopic combination of D/H, are shown in Figure 4 for the following ratios: 1:0, 4:1, 1:1, and 1:4. A calculation of the scattering length densities for D-C12E8 compared to H-SLES EO3 suggests that the deuterated surfactant will dominate the scattering profile; the hydrogenated ionic one is expected to contribute approximately 10% to the total scattering. The following physical interpretation of the profiles proceeds with the approximation that the nonionic is the sole scattering agent: the decrease in the absolute mean reflectivity alongside the decrease in the ratio of D-C12E8 is consistent with a reduction in C12E8 adsorption at the interface, and the near identical gradient for each of the profiles suggests the thickness of the total adsorbed layer does not change significantly.29, 32 Full details of data analysis and surface excess plots for each surfactant mixture are available in the Supporting Information. Broadly speaking, an adsorbed monolayer of thickness 20 Å forms at the interface and the total surface excess is approximately 3 × 10-10 mol cm-2, in line with values reported in the

literature.8, 19, 38, 39 The nonionic surfactants are more surface active than SLES

and so, in a similar fashion to the CMC data, they dominate at the surface. The addition of 0.1M NaCl reduces the dominance of the nonionic at the interface and results in near equivalent behaviour of the two components, as shown in Figure 5. Temperature effects on surface composition are less pronounced than on the CMC data; an increase in temperature appears to

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Figure 7: Surface composition at 10 oC, 25 oC, and 40 oC of adsorbed C12E8/SLES EO3 and C12E8/SLES EO3 + 0.1M NaCl against bulk solution composition at a fixed concentration of 2mM: represented by red and blue markers respectively. The black lines are the best fits of the full PPA model, with interaction parameters Bμ and Bsur; micellar interaction parameters are taken from the CMC data fittings and the surface parameters represent the best fit to the surface composition data at 25 oC. have a mildly adverse effect on adsorption, particularly for SLES EO3. However, this effect is not as predominant for adsorption of the individual surfactants. Penfold et al. noticed that an increase in temperature on an adsorbed monolayer of C12E8 above CMC, while not necessarily changing the amount adsorbed, did affect the associated roughness of the surface layer.25 Theoretical surface compositions of the surfactant systems were calculated, as mentioned previously, using the PPA approach in combination with experimental NR measurements.11, 12, 40 The process is defined here in several

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System

Temp

Phase

Page 20 of 37

B

o

C

RT

±2 oC C12E8/SLES EO3

C12E8/SLES EO3

C12E8/SLES EO3

C12E8/SLES EO3

10

25

40

10

+ 0.1M NaCl C12E8/SLES EO3

25

+ 0.1M NaCl C12E8/SLES EO3 + 0.1M NaCl

40

GE,min

±1.0

±0.2

micelle

-2.3

-0.6

surface

-0.9

-0.3

micelle

-2.3

-0.6

surface

-0.6

-0.2

micelle

-2.3

-0.6

surface

-0.8

-0.2

micelle

-2.0

-0.5

surface

-2.0

-0.5

micelle

-1.5

-0.4

surface

-1.6

-0.4

micelle

-1.6

-0.4

surface

-1.6

-0.4

Table 1: Interaction parameters and corresponding minimum free energies for interfacial PPA fits to binary C12E8/SLES EO3 systems. stages, starting with the calculation of xiμ values from CMC data, which forms the foundation of the approach.12,

41

Huang et al. observed a shift in the

monomer concentration above CMC large enough to invalidate PPA calculations: there is a significant change in the number of free surfactant molecules able to adsorb at the interface with changes in concentration above CMC 34. Equation 6 and the calculated xiμ values were used to obtain corrected monomer concentrations. While it is a tentative basis to proceed with modified but unverified monomer concentrations, previous studies have

20


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Figure 8: Surface composition at 10 oC, 25 oC, and 40 oC of adsorbed C12E6/SLES EO3 and C12E6/SLES EO3 + 0.1M NaCl against bulk solution composition at a fixed concentration of 2mM: represented by purple circles and black diamonds respectively. The black lines are the best fits of the full PPA model, with interaction parameters Bμ and Bsur; micellar interaction parameters are taken from the CMC data fittings and the surface parameters represent the best fit to the surface composition data at 25 oC. shown good agreement between monomer concentrations determined in this fashion.1, 11, 12 The final step is similar to the first, using the new α values and Equation 7 to determine surface composition values. The limiting values of area per molecule for C12E8, C12E6, and SLES EO3 were derived from NR measurements and at 25 oC, are 60, 45, and 40 Å2 respectively; variation in area either with temperature or addition of electrolyte is minimal and was factored into calculations. The necessary surface pressure terms were taken from their respective surface tension measurements and, for the C12E8/SLES

21


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EO3 system at 25 oC in pure water, were π1 = 38.8, π2 = 28.0, and πeq = 36.0 mN/m. Figure 6 compares surface composition measurements obtained from NR experiments, as a function of bulk composition, to two theoretical fits: ideal, and PPA. The non-ideal model expects, based on the CMC data, the C12E6 to dominate the surface composition over the entire bulk composition range. Data from a recent publication for a comparable system, C12E8/SLES EO2 (at a higher pH), supports this analysis.12 A means of checking if the model implementation is correct involves determining the intersection between the ideal and PPA curves in Figure 6. When x1 = x2 = 0.5, Equation 5 tends to zero and implies f1 = f2. For ideal mixing, the activity coefficients are always equal to each other. Therefore the two models should intersect at this point and, from Figure 6, do so within error. The PPA fit itself is not perfect and this could, in part, be due to error propagation accumulating at each stage in the calculations. The largest error contributions must derive from the surface pressure terms and the concentrations required for each component to reach a fixed surface pressure, ciπ. There is an order of magnitude difference in the CMCs between the ionic and nonionic components without salt. This effectively places greater weight on the ciπ values, compared to other terms involved in the PPA analysis, such that even a small change results in a significant deviation in the predicted surface composition. Each value is directly inferred from surface tension plots, but because the lowest possible surface tension for SLES is high relative to the nonionics, their ciπ values are much lower than their CMC’s. For this particular concentration range, the associated errors are roughly 20% which, coupled with the sensitivity to ciπ, introduces huge uncertainty. It is likely that 22


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System

Temp

Phase

B

o

C

RT

±2 oC C12E6/SLES EO3

C12E6/SLES EO3

C12E6/SLES EO3

C12E6/SLES EO3

10

25

40

10

+ 0.1M NaCl C12E6/SLES EO3

25

+ 0.1M NaCl C12E6/SLES EO3 + 0.1M NaCl

40

GE,min

±1.0

±0.1

micelle

-1.7

-0.4

surface

-0.5

-0.2

micelle

-2.0

-0.5

surface

-1.0

-0.3

micelle

-2.5

-0.6

surface

-1.5

-0.4

micelle

-1.2

-0.3

surface

-1.1

-0.3

micelle

-1.8

-0.5

surface

-1.5

-0.4

micelle

-1.7

-0.4

surface

-1.2

-0.3

Table 2: Interaction parameters and corresponding minimum free energies for interfacial PPA fits to binary C12E6/SLES EO3 systems. the application of the PPA model to any system with a large difference in CMCs and ciπ values would face similar problems to those found here. For this particular data set, all three models run through the error bars. This is in part because the interaction parameters for the surface are not much greater than zero. As a rough guide, the upper and lower error bars can be reached by altering individual interaction parameters by approximately ± 1.5, although altering all parameters simultaneously can increase the range of potential values. However, the greatest restriction on parameter values is due to the requirement for Bμ to fit both the CMC and corresponding surface plots at the 23


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same time. As such, model fitting parameters can typically be changed by no more than ± 1.0. Figure 7 displays the surface composition versus bulk composition of C12E8 when mixed with SLES EO3, with and without NaCl. It is evident from the information provided that NaCl significantly aids SLES adsorption at the interface. Without it, C12E8 dominates the surface molar fraction; it occupies 40% of the surface when it constitutes 20% of the bulk composition. A similar pattern is observed in the C12E6 system, shown in Figure 8, although to a lesser extent; at a high C12E6 composition, the surface and bulk fractions are equal, regardless of salt. Also, the differences between surface compositions with and without salt are smaller for C12E6 than C12E8 by approximately 10%. Studies into nonionic mixtures note that interfacial competitiveness is dependent on the EO number.8, 25 Ultimately, SLES is better able to compete with C12E6 over the entire composition range, shown by a higher adsorption levels (see Supporting Information). Table 1 shows the PPA model applied to both the micellar and surface phases in the system, with and without 0.1M NaCl, over the aforementioned temperature range. Without salt, the minimum free energy of mixing, GE, for the micellar phase is lower than the surface phase: -0.6 ± 0.2 versus -0.2 ± 0.2 RT, regardless of temperature. Therefore the bulk has more free energy available than the surface phase to perform work. The addition of 0.1M NaCl raises GE,min for the micellar phase by 0.2 and lowers it by 0.2 for the surface phase. The difference in the free energy between the surface and micelle phase is now within error, implying that the energy available in both pseudophases is roughly equal. The impact of temperature on the system is relatively small and, for the most part, changes in GE,min are within error. The 24


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C12E8 system is not particularly dissimilar to the C12E6, as shown in Table 2, although changes in GE,min values with salt are smaller and within error. It is reasonable to conclude that the addition of salt balances the competitive forces between the surfactant components and results in roughly equal surface to bulk compositions. Temperature effects on composition and free energy are minimal and typically within error, particularly for the systems containing salt. The fitted interaction parameters range from -2.5 to -0.5 or twice their associated error, which is a significant difference. However, the average value is -1.5 and the fitted B values for all systems are within error. Hence there is little difference in the free energies of mixing between the systems. Large differences in B values are possibly the result of errors and limitations in modelling the experimental data.

Discussion Negative free energy values correspond to energetically favourable mixing and can be inferred from the sign of fitted interaction parameters, where a negative value corresponds to a negative GE value. The fitted B parameters are consistently negative for all systems in this paper, implying all binary compositions mix favourably. The magnitude of B is generally low and often close to zero, within error: as a comparison, highly non-ideal interfacial mixing between DHDAB and C12E6 has associated Bμ and Bsur values of – 4.0.42 Without NaCl, the surface interaction parameters for both nonionic systems are

typically

smaller than

their

respective

micellar

counterparts,

implying adsorption at the interface is closer to ideal mixing. This is not an altogether uncommon finding, and Negm et al. explained it through molecular packing

arguments: one

would

expect

to

see

a

destabilised

interaction between molecules at the curved surface of a micelle compared 25


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with those same molecules organised in a planar geometry at the interface, particularly if there is a charge interaction.43 A similar line of reasoning based on molecular constraints has been employed in understanding surfactant aggregation as a function of its chain length, most notably by Israelachvili, Mitchell, and Ninham.44 The ratio of the tail length to the average area occupied by the head group offers a broad means of predicting surface curvature and hence, the particular type of aggregate a surfactant will form. Kahn et al. extended this to look at the role of chain length on mixing between different surfactant species, leading to the conclusion that a synergistic relationship is driven by the enthalpy of the system.45 Furthermore, packing arguments in combination with the PPA model were applied to a comparable study looking at SDS, an anionic surfactant close in structure to SLES. Similar to the observation by Negm et al., the area per molecule at the surface was low suggesting efficient packing in the aggregate. It was shown that synergistic mixing was dominated by the surfactant tail packing in the micellar core, with close agreement between experimental data and PPA predictions.46 It was claimed that differences in the free energy of mixing between the surface and aggregate phases was due to desorption of surfactant monomers from the interface. The broad assumption that the interaction parameters are constants have been validated in comparable systems by Hague and Staples et al., both showing strong agreement between fitted PPA models.47,

48

Various models accounting for a shift in B with

composition have been tried, notably by Hines, with little to no significant difference between them and the conventional model.38 The addition of NaCl raises the surface interaction parameter values and implies an increase in synergistic mixing at the interface. This is counter26


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intuitive: once the charge interaction is screened, it is expected that the surfactants would behave more like a nonionic mixture. It should be noted that the changes in B are small and typically within error. Therefore, the NaCl systems are mixing non-ideally but changes in mixing between the systems with and without salt are not significant. Liley et al. observed slightly different behaviour for C12E8/SLES EO2, where NaCl drove the system closer to ideal mixing

23

. The difference between the two findings stems from the different

CMC data fittings. As has already been mentioned, the CMC data for this system has large errors associated with them and are few in number. The model fits in this paper all point towards an approximate value of Bμ = -1.5 ± 1.0, but it is possible the errors are underestimated and, if so, it is not unreasonable to assume Bμ could be closer to zero. A smaller micelle interaction parameter would also lower the corresponding surface interaction parameter. This paper highlights the need, in order to provide more confidence in discussing changes in non-ideality between different systems, to improve CMC data plots and hence reduce the spread of potential interaction parameters that can fit the system. Further work in applying the PPA model should clearly outline the limitations of the model, as well as the uniqueness of the fitted parameters for a given data set. A more in-depth analysis of the PPA model and its limitations has been undertaken by Penfold et al.6 As indicated in the Results section, the CMC for each individual surfactant is in line with the values reported in literature. Since surface tension measurements are especially sensitive to any surface active impurities, the determined CMCs indicate that the samples used were of high purity. Despite the possible errors in the CMC data, the measurements were made under identical conditions. Therefore, while the absolute accuracy of an individual CMC point may suffer from error, 27


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any trend in CMC variation should be reliable. Thus, the trend of decrease in CMC over all compositions with temperature must be reliable, regardless of the limitations inherent in the surface tension method. The monomer corrections involved in the PPA analysis suggest that the number of free nonionic molecules available to adsorb at the interface at 2 mM is significantly reduced above the mixed CMC. This is largely expected and has been studied by Staples et al.: increasing the concentration of a mixed surfactant solution above CMC reduces the more surface active component in solution as they are more prone to aggregate. However, Staples et al. found this monomer shift ultimately invalidated the use of a single interaction parameter model (one interaction parameter for both the surface and aggregate),

arguing that

the

discrepancies

arose

from

intrusive

entropic factors.47 Monomer corrections are therefore paramount, and the correction procedure was adopted from Huang.34 Another failing of RST has been explored by Penfold et al. for an SDS mixture displaying antagonistic mixing. The model was incapable of matching the shape of the data trend, which is thought to be the result of inefficient packing conformations. An extension to multiple parameters was necessary for consistency between theoretical predictions and experimental data.49 The question then turns to the provision of a reasonable physical justification for the additional parameters. Holland and Rubingh initially defined the free energy of mixing as a series expansion, and the constants associated with each term have subsequently been relabelled as the interaction parameters.13,

50

A single B parameter

quantitatively defines the deviation of a system from ideal mixing, while the introduction of a second C parameter allows for asymmetry in the free energy curve about the equimolar position.11 However, the large errors and lack of data points, particularly for the surface compositions, do not justify the use of 28


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C. As such, two interaction parameters, one for the micelle and one for the surface, have been adopted to account for differences in mixing between phases. Asymmetry is not wholly unexpected in mixed systems, with Hines et al. observing a strong link between asymmetry arising as a result of electrostatic interactions and changes in hydration upon mixing.19 The relatively low B values for the SLES/C12En systems, as compared to those for cationic/nonionic mixtures,42 are thought to be caused by weak interactions between the two different head groups, as well as a high micellar curvature which would increase the average area per molecule. The interaction parameter is sometimes seen to vary with micellar concentration and is understood to be the result of increased intermicellar interactions.51 A variable interaction parameter invalidates the RST approximation: the model is too simple to account for all of the competing forces in the mixture. Higher order terms in the free energy expansion can be used to account for the discrepancies and provide a more accurate model, as demonstrated by Li et al.11 The fact that the data in this paper can be modelled using a single parameter suggests intermicellar interactions are too weak to affect mixing. This could be due to the relatively low surfactant concentration in solution of 2mM or the nature of the surfactants used. D-C12E8 contains trace amounts of E7 and E9 and it is useful to assess its impact on the outcome. This work has already shown that there is a very small difference, if any, between C12E6 and C12E8 behaviour in their respective binary mixtures. This point towards the view that, if there is a minor amount of E7 and E9 present in C12E8, then their impact would be negligible. This verdict is supported by previous observations by Penfold et al.25 29


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RST predicts the micellar composition to evolve towards the solution composition with an increasing concentration. This occurred for binary SDS/C12E6 and SDS/C12E8 mixtures at 25 mM, well above the concentration used in this study.7 This does not apply to the surface composition due to its dependency on the monomer concentration, a value which could be vastly different to the bulk solution composition.25, 31 The total surface excess of a surfactant system at its mixed CMC can be calculated from fits to surface tension plots as a function of concentration. While surface excesses for individual components cannot be determined in this way, it offers an apparently independent measure to compare against NR measurements. This has not been explored in this paper due to the primary interest in individual component excesses. Furthermore, as stated by Xu and Li et al., this method is vastly inferior to NR in this instance and it is not necessary to compare surface excesses calculated using these two methods.31, 52 Temperature changes, such that no phase transformation takes place, are thought to chiefly affect hydration and solubility of surfactant molecules; these factors often compete against each other.25 The surface compositions shown in this paper show little to no temperature sensitivity. A broad order ranking the relative strength of factors impacting adsorption, from strongest to weakest, is as follows: molecular constraints, electrostatic repulsion, hydration, and solubility of the alkyl chain in solution.21, 25, 53 Whilst this list is by no means comprehensive or accurate under all given circumstances, it does provide a general framework from which the results can be interpreted. It could be that, once

saturation

of

the

surface is

reached,

charge

repulsion

and

molecular constraints determine the packing and molar ratio of the surfactants at the interface, and energy changes arising from temperature shifts are too weak to compete. 30


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Without electrolyte, the surface is dominated by the nonionic component, as is the micellar composition and hence the CMC. The addition of the monovalent electrolyte screens the charge interaction on the SLES head groups,36 allowing tighter packing at the interface as well as increasing its molar fraction at the interface and in the bulk aggregate. The end result is a near equivalent fraction of SLES and nonionic at the surface. There are limitations in applying the PPA model to systems containing electrolyte, particularly when more complex bulk aggregates and multilayering at the surface come into play.8 There did not appear to be any occurrence of this happening in this study and the model fits imply little to no change in the mixing free energies.

Conclusion Surface composition data for the two binary ionic/nonionic systems has been obtained, through neutron reflectometry experiments, and compared to the predictions from the theoretical models based on surface tension measurements. The single parameter PPA model is appropriate and points towards non-ideal mixing for both C12EO 6 and 8 mixtures with SLES EO3. Differences between the SLES EO3/C12E6 and SLES EO3/C12E8 systems, e.g., the difference in GE between the surface and micelle phases, are minor but measurable, and mostly manifested via the hydration and dehydration of the EO groups with temperature changes. The model predicts mild synergism with the minimum free energies of mixing ranging from -0.2 to -0.6 RT. Addition of 0.1M NaCl drives the surface composition to equal the bulk composition and lowers the CMC of SLES EO3 by an order of magnitude. Temperature changes between 10 oC and 40 oC have little effect on the surface compositions but significantly lower the CMCs of the surfactant systems. This highlights the relative strength of steric hindrances and the charge interaction in determining 31


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interfacial behaviour at concentrations exceeding CMC in relation to the temperature variations.

Supporting Information The Supporting Information is available free of charge on the ACS Publications website, covering raw and adsorption plots containing the information used for each of the corresponding surface composition figures.

Funding CS is funded by a joint PhD studentship grant from STFC, Unilever and University of Manchester (P120094).

Notes The authors declare no competing financial interest.

Acknowledgements We thank the ISIS Neutron Facilities, STFC for the award of Neutron Reflection beam-time. We are grateful to STFC, Unilever and University of Manchester and EPSRC (EP/F062966/1) for support and provision of resources and materials.

References 1. Rubingh, D. N.; Mittal, K. L., Solution Chemistry of Surfactants. Plenum Press: 1979; p 337-354. 2. Ogino, K.; Abe, M., Mixed Surfactant Systems. Surfactant Science Series 1992. 3. Laughlin, R. G., The Aqueous Phase Behaviour of Surfactants. 13 ed.; Academic Press: 1996. 4. Shiloach, A.; Blankschtein, D., Measurement and Prediction of Ionic/Nonionic Mixed Micelle Formation and Growth. Langmuir 1998, 14, 7166–7182. 32


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5. Hamley, I., Introduction to Soft Matter: Polymers, Colloids, Amphphiles and Liquid Crystals. Wiley: 2000. 6. Penfold, J.; Thomas, R. K., Mixed Surfactants at the Air/Water Interface. Annu. Rep. Prog. Chem. Sect.C 2010, 106, 14-35. 7. Penfold, J.; Tucker, I. M.; Thomas, R. K.; Staples, E.; Schuermann, R., Structure of Mixed Anionic/Nonionic Surfactant Micelles: Experimental Observations Relating to the Role of Headgroup Electrostatic and Steric Effects and the Effects of Added Electrolyte. J. Phys. Chem. B 2005, 109, 10760-10770. 8. Penfold, J.; Thomas, R. K.; Dong, C. C.; Tucker, I. M.; Metcalfe, K.; Golding, S.; Grillo, I., Equilibrium Surface Adsorption Behavior in Complex Anionic/Nonionic Surfactant Mixtures. Langmuir 2007, 23, 10140-10149. 9. Penfold, J.; Thomas, R. K.; Dong, C. C.; Tucker, I. M.; Metcalfe, K. L.; Golding, S.; Grillo, I., Equilibrium Surface Adsorption Behaviour in Complex Anionic Nonionic Surfactant Mixtures. Langmuir 2007, 23, 10140-10149. 10. Nagarajan, R., Micellization, Mixed Micellization, and Solubilization: the Role of Interfacial Interactions. Adv. Colloid Interface Sci. 1986, (26), 205-264. 11. Li, P. X.; Ma, K.; Thomas, R. K.; Penfold, J., Analysis of the Asymmetric Synergy in the Adsorption of Zwitterionic Ionic Surfactant Mixtures at the AirWater Interface below and above the Critical Micelle Concentration. J. Phys. Chem. B 2016, 120, 3677-3691. 12. Liley, J. R.; Thomas, R. K.; Penfold, J.; Tucker, I. M.; Petkov, J. T.; Stevenson, P.; Webster, J. R. P., Surface Adsorption in Ternary Surfactant Mixtures above the Critical Micelle Concentration: Effects of Asymmetry on the Composition Dependence of the Excess Free Energy. J. Phys. Chem. B 2017, 121, 2825-2838. 13. Holland, P. M.; Rubingh, D. N., Non-ideal Multicomponent Mixed Micelle Model. J. Phys. Chem. B 1983, 87, 1984-1990. 14. Holland, P. M., Non-ideal Mixed Micellar Solutions. Adv. Colloid and Interface Sci. 1986, 26, 111-129. 15. Sarmoria, C.; Puwada, S.; Blankschtein, D., Prediction of Critical Micelle Concentrations of Nonideal Binary Surfactant Mixtures. Langmuir 1992, 8, 2690-2697. 16. Shiloach, A.; Blankschtein, D., Predicting Micellar Solution Properties of Binary Surfactant Mixtures. Langmuir 1998, 14, 1618-1636. 17. Georgiev, G. S., Markov chain model of mixed surfactant systems I, New expression for the non-ideal interaction parameter. Colloid Polym Sci 1996, 274(1), 49-58. 18. Slavchov, R. I.; Georgiev, G. S., Markov Chain Model for the Critical Micelle Concentration of Surfactant Mixtures. Colloid Polym Sci 2014, 292, 2927–2937. 33


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19. Hines, J. D.; Thomas, R. K.; Garrett, P. R.; Rennie, G. K.; Penfold, J., Investigation of Mixing in Binary Surfactant Solutions by Surface Tension and Neutron Reflection: Strongly Interacting Anionic/Zwitterionic Mixtures. J. Phys. Chem. B 1998, 102, 8834-8846. 20. Zoller, U.; Sosis, P., Handbook of Detergents, Part F: Production. CRC Press: 2009. 21. Lu, J. R.; Li, P. X.; Thomas, R. K.; Staples, E. J.; Thompson, L.; Tucker, I. M.; Penfold, J., Neutron Reflection from a Layer of Monododecyl Octaethylene Glycol Adsorbed at the Air-Liquid Interface: The Structure of the Layer and the Effects of Temperature. J. Phys. Chem. 1994, 98, 6559-6567. 22. Chen, L.; Lin, S.; Huang, C.; Chen, E., Temperature Dependence of Critical Micelle Concentration of Polyoxyethylenated Non-ionic Surfactants. Colloids Surfaces 1998, 135, 175-181. 23. Liley, J. R.; Thomas, R. K.; Penfold, J.; Tucker, I. M.; Petkov, J. T.; Stevenson, P.; Webster, J. R. P., Impact of Electrolyte on Adsorption at the Air– Water Interface for Ternary Surfactant Mixtures above the Critical Micelle Concentration. Langmuir 2017, 33, 4301-4312. 24. Liley, J. R. Optimising the Blending of Biosurfactants with Conventional Home and Personal Care Components: A Surface and Solution Study. University of Oxford, 2014. 25. Penfold, J.; Staples, E.; Tucker, I. M.; Thompson, L.; Thomas, R. K., Adsorption of Nonionic Mixtures at the Air-Water Interface: Effects of Temperature and Electrolyte. J. Colloid Interface Sci. 2002, 247, 404-411. 26. Xu, H. D.Phil. Thesis. University of Oxford, 2013. 27. Vargaftik, N. B.; Volkov, B. N.; Voljak, L. D., International Tables of the Surface Tension of Water. J. Phys. Chem. Ref. Data 1983, 12, 817-820. 28. Lu, J. R.; Su, T. J.; Li, Z. X.; Thomas, R. K.; Staples, E. J.; Tucker, I. M.; Penfold, J., Structure of Monolayers of Monododecyl Dodecaethylene Glycol at the Air-Water Interface Studied by Neutron Reflection. J. Phys. Chem. B 1997, 101, 10332-10339. 29. Webster, J. R. P.; Langridge, S.; Dalgliesh, R. M.; Charlton, T. R., Reflectometry techniques on the Second Target Station at ISIS: Methods and Science. Eur. Phys. J. Plus 2011, 126, 112-117. 30. Lu, J. R.; Thomas, R. K.; Penfold, J., Surfactant Layers at the Air/Water Interface: Structure and Composition. Adv. Colloid Interface Sci. 2000, 84, 143304. 31. Li, P. X.; Li, Z. X.; Shen, H. H.; Thomas, R. K.; Penfold, J.; Lu, J. R., Application of the Gibbs Equation to the Adsorption of Nonionic Surfactants and Polymers at the Air/Water Interface: Comparison with Surface Excesses Determined Directly using Neutron Reflectivity. Langmuir 2013, 29, 9324-9334. 34


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Nonionic Surfactant Mixtures at

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