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Surfactant interactions and organisation at the gas-water interface (CTAB with added salt) Pavel Yazhgur, Sampsa Vierros, Delphine Hannoy, Maria Sammalkorpi, and Anniina Salonen Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b03560 • Publication Date (Web): 08 Jan 2018 Downloaded from http://pubs.acs.org on January 8, 2018

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Langmuir

Surfactant interactions and organisation at the gas-water interface (CTAB with added salt) ∗,†,¶

Pavel Yazhgur,

‡

Sampsa Vierros,

Delphine Hannoy,

†

Maria Sammalkorpi,

‡

and

∗,†

Anniina Salonen

†Laboratoire

de Physique des Solides, CNRS UMR 8502, Université Paris Sud, 91405 Orsay, France

‡Department

of Chemistry and Materials Science, School of Chemical Engineering, Aalto University, P.O. Box 16100, 00076 Aalto, Finland

¶Current

address: Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland

E-mail: [email protected]; [email protected]

Abstract We have studied adsorbed layers of cetyltrimethylammonium bromide (CTAB) at air-water interfaces in the presence of added electrolyte. Fast bubble compression/expansion measurements were used to obtain the surface equation of state, i.e. the surface tension vs CTAB surface concentration dependence. We show that while a simple model where the surfactant molecules are assumed to be non-interacting is insucient to describe the measured response of the surfactant layer, a modied Frumkin equation where the local interactions between the molecular components depend on their surface concentration captures the response. The variation of the eective interactions in 1

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the surfactant layer in the model shows that the interactions in the surfactant layer change from eectively repulsive to attractive with increasing surface concentration. Molecular dynamics simulations are performed to probe the origins of the change in the interactions. The simulations indicate that already at low surface concentrations the surfactants aggregate as highly dynamic rafts with surfactant orientation parallel to the interface. Increasing the concentration leads to a change in the assembly morphology at the interface: the surfactant layer thickens and the surfactants sample a range of tilted orientations with respect to the interfacial plane. The change from transient raft-like assemblies to dynamical aggregates at the interface involves a clear increase in the degree of counterion binding: we speculate that the ip of the eective interaction parameter in the model used to interpret the experimental results could result from this. The work here presents basic steps toward a proper understanding of the molecular organisation and interactions of surfactants at an air-water interface. This is crucially important in understanding macroscopic properties of surfactant stabilized systems such as foams, emulsions, and colloidal dispersions.

Introduction Surfactant covered uid interfaces are present in almost every aspect of our daily lives. For example, surfactants adsorbed onto the surfaces of bubbles or oil droplets stabilise foams and emulsions

1,2

. Foams and emulsions are ubiquitous in chemical technology, pharmaceutics,

alimentary industry, cosmetics, and materials science but also in basic biology surfactants ensure the functioning of many vital processes allow us to breathe cellular tracking

7

6,8

5,6

3,4

. Biological

. For example, lung surfactants

and surfactant based tracking and solubilization have a key role in .

9

Surfactants are also instrumental in cleaning and detergency .

All

these uses of surfactants rely on the ability of surfactants to adsorb onto surfaces and interfaces. Here, we examine surfactant interactions and organisation at the gas-water interface for a very typical ionic surfactant, cetyltrimethylammonium bromide (CTAB) to resolve the

2


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basic assembly characteristics at interfaces. Very commonly, the eect of surfactants at uid interfaces and their adsorption at the interfaces is measured and described in terms of surface tension face concentration

Γ.

γ

and the surfactant sur-

The inuence of interfacial surfactant adsorption on surface tension

has been extensively studied by experiments and by theoretical work since the works of Gibbs

10,11

.

In order to describe dynamic macroscopic systems driven by surface tension

and its gradients, assumptions about the inuence of surfactant concentration are made to accurately describe interfacial rheology of surfactant systems dependent on it, such as soap lm formation

13

12

and physical phenomena

or Marangoni ow

14,15

.

The structure of

surfactant layers at interfaces has been mainly studied using neutron reectivity other spectroscopic methods are also able to probe surfactant organisation

16

17,18

, although

. In partic-

ular neutron scattering can be used to measure the surfactant concentration perpendicular to the surface to obtain the surface excess

16

. The partial deuteration of surfactant chains

has been used to obtain a more detailed description of the organisation of many surfactants at interfaces. For example the CTAB chains have been shown to have considerable tilt at the air-water surface, which decreases as the surface concentration increases

16,19,20

. Despite

the extent of the current comprehension, linking the macroscopic measurements of surface tension with the microscopic structure and interactions of the surfactants at the interfaces remains a challenge. Various adsorption models provide the rst step to linking the macroscopic level measurements to microstructure, i.e. surface tension of a surfactant coated air-water interface with the molecular organisation in the surfactant coating, see e.g. Ref. 10. Adsorption models aim at reproducing and predicting the evolution of the surface tension with the surfactant surface concentration.

Many of the theoretical equations of state used for such purposes

require several assumptions which are not rigorously valid.

For example, the Langmuir

isotherm models the surface adsorption response of ideal, non-interating surfactants based on mixing entropy of the components and the Frumkin isotherm is based on an assump-

3


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Page 4 of 34

tion that the interaction energy between adsorbed surfactant molecules is pairwise and thus independent of the surface coverage

10

. These are, of course, very rough approximations of

the surfactant interactions at the interface. More complicated and sophisticated models for surfactant adsorption and its eect on the surface tension exist. These account for, e.g. the interactions between the surfactants in the monolayer and in the bulk solution. For ionic surfactants, the double layer can be accounted for which leads to an increased description capability.

Classical examples of such theories include, for example, the Davies and the

Frumkin-Davies isotherms. An overview of these and several other surface equations of state to model surfactant adsorption at the interface are given in Refs. 10,2123. At a more detailed level than the adsorption models, molecular modelling has been employed to bridge the macroscopic surface tension measurements and the microstructure of the surfactant interfaces. Although molecular dynamics connect directly surface tension, surface concentration and assembly morphology, challenges lie in limitations in describable system sizes, timescales involved in surfactant adsorption and assembly equilibration, as well as, potential imbalances in the modelled interactions. Very recently, Sresht et al. advanced toward breaching these challenges via proposing a surface tension model that combines molecular thermodynamic theory and molecular modelling

24

. Besides that, most molecular modelling

approaches to surfactant monolayer formation and resulting surface tension have been on various lung surfactant and other lipid based monolayer assemblies because of the biological relevance, see e.g. SDS monolayers biosurfactants

33

31

Refs. 2530. , Phan et al.

Martinez et al.

have examined via molecular modelling

MIBC/CTAB mixtures

32

, and Kong et al.

more simple

at dierent surface concentrations and connected the ndings with surface

tension. The surface coverage dependency of surfactant aggregate morphologies at the interface has also received some molecular modelling attention for various surfactants, see e.g. Refs. 3436. Here, we combine an experimental measurements based empirical surface equation of state with theoretical adsorption models, and detailed molecular dynamics simulations to

4


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Langmuir

generate understanding of the adsorbed surfactant layer, and the governing interactions in the layer in a model system of CTAB with added NaBr at the air-water interface. In particular, we extract both from the measurement and the molecular modelling data consistent, eective surfactant-surfactant interaction parameters as the function of surfactant concentration based on a modied Frumkin adsorption model.

We show that the value of this

parameter varies with the surfactant surface concentration. We connect the change of the eective parameter value from repulsive to attractive to an assembly morphology change in molecular simulations of similar surface concentrations. We analyse possible causes for the change in the eective interactions between the surfactant assemblies in the experiments based on the molecular simulations and discuss the signicance of the ndings for understanding surfactant layers at air-water interface.

Materials and methods Experimental methods. We examine cetyltrimethylammonium bromide (CTAB) at

concentration in an aqueous solution. Sodium bromide (NaBr) at

0.1

10−5 M

M is added to enable

treating the system as a non-ionic one in the analysis (in the presence of excess salt the electrical double layer equilibrates very fast and does not strongly inuence the surface tension, see Supporting Information). CTAB concentration in the solution is below CMC at the given salt concentration (3

· 10−5

M)

37

which means that no micelles are present in the solution.

An ionic surfactant system is chosen because a high purity, which is extremely important in the study of the surface properties, can be achieved simply by multiple recrystallisations. To experimentally measure the surface equation of state, the dynamic surface tension is measured by a bubble shape analysis method using a commercial tensiometer Tracker (Teclis, France). To gain access to a large set of data we use fast compression/expansion method suggested by Pan et al.

38

. Previously, we have used this technique successfully to

study the kinetics of adsorption and desorption of the surfactant system under investiga-

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tion

37,39

Page 6 of 34

.

In the fast compression/expansion experiment, a bubble is created and after some ageing time it is rapidly compressed or expanded. If the deformation rate is suciently high, the total number of surfactant molecules on the bubble surface area A does not change and constant. Via known reference surface concentration tension

γref

this gives access to the product

reference values

Γref

and

γref

ΓA,

Γref

that is

ΓA =

corresponding to a certain surface

ΓA = Γref Aref .

In this work, the

are determined from the isotherm obtained using equilibrium

surface tension vs bulk concentration dependencies as explained in Ref. 37. Figure 1 shows an example of the measured surface tension and bubble area as a function of time during the fast compression experiment. Using this reference point the surface tension dependency on the air-water interface area equation of state

γ(A) can be converted to the experimentally determined surface

γ(Γ).

The assumption that the total quantity of surfactant molecules at the bubble interface stays constant fails if surfactants desorb from the interface. Figure 1 shows that increasing compression leads to a minimum value of surface tension that corresponds to the onset of surfactant desorption. The system reaches the maximum packing and any further compression leads only to the surfactant desorption. The limiting surface tension can be attributed to the maximum packing density of molecules at the interface,

Γ∞ = 4.07 · 10−6

2 mol/m , and

the points of higher compression are not used for calculating the surface equation of state. In our previous work

37

we have shown that the surface equation of state (γ(Γ) dependence)

for CTAB+0.1M NaBr system obtained in our experiments is in good agreement with results obtained by the same method by other authors and by classical analysis of the equilibrium surface tension isotherm as the function of bulk surfactant concentration.

0.2

are tested.

For each degree of compression, the experiment is repeated at least 3 times.

Taylor et

Dierent degrees of compression where

al.

∆A/A

varies between

0.03

and

have shown for the bubble shape method that surfactant adsorption during bubble

compression/expansion can signicantly inuence the results if the surface dilatation rate

6


Page 7 of 34



end of compression

70

30 25 20

70

 (mN/m)

50 40

60 50 40 30

15

1.5 L/s 2 L/s 4 L/s

1,0x10-6 2,0x10-6 3,0x10-6 4,0x10-6

30 49

start of compression

51

52

53

t (s)

10

A

 (mol/m2)

50

54

55

Figure 1: The top panel presents variation of surface tension surface area

A

2

60



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

γ

56

(black squares) and bubble

(red circles) with time during the bubble compression experiments.

inset shows the surface tension as a function of the calculated surface concentration

The

Γ

at

various compression rates. The bottom panel shows an initial conguration of the molecular 2 dynamics simulations at surface concentration of 1.17 nm /surfactant.

is not high enough account for this

40

.

40

. Specic corrections to the measured surface tension can be used to

Indeed, in our previous work, smaller compression rates have resulted

in deviation of the measured values which indicates the inuence of adsorption/desorption during the bubble dilatation

37

. To examine whether this is a concern in the current setup,

dierent dilatation rates ranging between

1.5 µl/s and 4 µl/s were tested.

The inset of Figure

1 shows superpositioning of the data for the dierent compression rates. This indicates that our experimental setup can be considered to have negligible surfactant exchange between the

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Page 8 of 34

interface and the aqueous phase. In the following, all other presented bubble compression data is the average data corresponding to compression experiments at

4 µl/s.

The temperature of the solution is controlled by using a water bath. Experiments are carried out at

25

◦

C.

Simulation methods. Molecular modeling of the system was performed utilizing em-

pirical CHARMM force eld

41

and GROMACS 5.0 simulation software

42,43

.

Parameters

for cetyltrimethylammonium cation and octyltrimethylammonium cation were adapted from CHARMM36 saturated lipid model

44

.

Parameters for octanol were taken from the com-

patible CHARMM General Force Field were utilized for the counterion.

45

.

Bromide ion parameters by Horinek et al.

46

The employed bromine parameters are not part of the

CHARMM distribution, and may suer from imbalances. The modied TIP3P water model of CHARMM was utilized as the water model

41,47

.

The simulations system was set up as a periodic rectangular 3D simulation box in which a slab of water is separated from a vacuum region that represents the air environment by a surfactant layer. Initial congurations were constructed by placing molecules into two regular

128

(or

288)

surfactant

8 × 8 (or 12 × 12) planar grids where the surfactants were oriented

perpendicular to the grid plane. Surfactant spacing in the grid was set to match the mean area per surfactant under the targeted experimental conditions. The two surfactant grids were placed at opposite orientations to each other, i.e., surfactant heads face each other and the two planes corresponding to the surfactant heads are at other. Counterions and salt corresponding to

100

8

nm distance from each

mM NaBr was then added between the

surfactant layers and the region between the surfactants lled with water while leaving the rest of the simulation box as vacuum to describe the air. The coordinate system is set so that the air-water interface plane coincides with the

xy -plane and the z -axis is perpendicular

to the interface. The box length in the direction perpendicular to the interface, was adjusted to be three times the water slab thickness, i.e. system setup.

8


24

z -direction,

nm. Figure 1 illustrates the

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Langmuir

Molecular dynamics simulations were run at either at constant temperature and surface tension (Nγ T ensemble) or at constant temperature and volume (NVT ensemble) conditions. Temperature coupling was achieved by the thermostat of Bussi et al.

T = 25◦ C

and coupling constant

τT = 0.5

ps.

48

with temperature

For controlling the pressure to obtain the

constant surface tension conditions, the semi-isotropic Parrinello-Rahman barostat utilized.

For this, compressibility

the interface plane) and employed.

κz = 0

κxy = 4.5 · 10−5

bar

−1

0.8

τP = 2 1.2

nm and

a smooth particle mesh Ewald method

−1 bar for the water slab (i.e., along

50

ps.

Lennard-Jones interactions were

nm, while electrostatics were treated using

. For this,

1.2

nm cuto,

order splines and a correction term for the slab geometry

2

motion were integrated in

100

lation. The surface tension

γ

Pii

nm grid spacing,

were employed.

4th

Equations of

52

and LINCS algorithms

53

.

mM NaBr solution was determined with a 20 ns NVT simu-

was obtained from the pressure tensor as

Lz γ= 2 The

51

0.12

fs time steps, and bonds involving hydrogen were constrained

to their equilibrium lengths using SETTLE The surface tension of

was

in the direction perpendicular to the interface were

The barostat coupling constant

smoothly shifted to zero between

49

Pxx + Pyy Pzz − 2

are the diagonal components of the pressure tensor and

(1)

Lz

is the length of the simu-

lation box in the direction perpendicular to the interface. For calculating via simulations the surface tension as the function of surfactant surface concentration, tions where the average surface tension

γ

γ (Γ) isotherm, congura-

is xed at desired level were generated by varying

the barostat algorithm reference pressure and equilibrating the system: with the anisotropic compressibility tensor setup this leads to the interface area, as well as, the average surface tension uctuating around a xed mean value through equilibration of the simulation box and

y

dimensions (Lx and

Ly )

while maintaining the non-compressible dimension

Lz .

x

Simu-

lations were run for 40-70 ns and the rst 20 ns was discarded from the analysis as the initial

9


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relaxation period.

Page 10 of 34

Equilibration was measured by the levelling of the area per surfactant

which took 5-20 ns depending on the system. Counterion binding was estimated by calculating the number of bromide ions closer than

0.56

nm (direct binding) and within a sphere shell dened by

0.56

nm and

0.84

nm (sol-

vent separated) distance to the nitrogen atoms in the CTAB headgroups. The cutos were determined from the rst and second local minima in the N-Br

−

radial distribution function.

Surface equation of state If the air-water interface is in chemical and thermal equilibrium with the subphase (here aqueous solution of surfactants), the adsorption of surfactants at the interface can be described by Gibbs equation

dγ = −

X

Γi dµi .

(2)

i This connects the surface tension tentials

µi

γ

to the surface concentrations

Γi

and the chemical po-

of dierent species i. If we consider the surface as an individual 2D phase, which

is generally valid for surfactant monolayers, a concept of the surface chemical potential can be introduced.

The surface equation of state that relates the surface tension

the surfactant surface concentration

Γ

γ

µs

and

can be obtained by integrating the Gibbs adsorption

equation 2 using an appropriate expression for the surface chemical potential. Determining the surface chemical potential can be extremely complex. To estimate it, various simple models for surfactant adsorption at the air-water interface exist. One of the rst is by Irving Langmuir who proposed a surfactant adsorption model for ideal surfactant solutions and ideal interfaces

54

. In the Langmuir model, the surfactants are assumed

to form a monolayer at the interface.

The adsorbed surfactant monolayer is viewed as a

simple two-dimensional lattice in which the total number of lattice sites corresponds to the maximum number of adsorbed surfactant molecules and corresponds to maximum surfactant surface concentration

Γ∞ .

In the model, all interactions between the surfactant molecules

10


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Langmuir

are neglected, that is, both the 2D phase of the surfactants at the interface and their bulk solution are assumed to be ideal. For the ideal surfactant monolayer of the Langmuir model, the surface chemical potential is based only on the mixing entropy, see Ref. 55, and becomes

s

s0

µ = µ + RT ln

Here

T

µs

0

Γ/Γ∞ 1 − Γ/Γ∞

is the chemical potential of a reference state,

temperature.

R

.

(3)

is the molar gas constant, and

Introducing the chemical potential from Equation 3 to Equation 2 gives

via integrating an estimate for the surface equation of state. Specically, this obtained link between the surface tension and surface concentration is known as the Szyszkowski equation of state

56

γ = γ0 + RT Γ∞ ln(1 − Γ/Γ∞ ). Here

γ0

(4)

is the surface tension of the bare interface without surfactant. It is worth noting

that Equation 4 does not assume equilibrium between the surface layer and the bulk phase; its only requirement is that the surface is in equilibrium with itself. The Langmuir model is often used for its simplicity and it can qualitatively describe the behaviour of the system, for example to describe the kinetics of surfactant adsorption/desorption

57

. However it does not take into account the molecular interactions of the

surfactants in the monolayer or between the surfactants in the monolayer and in the bulk solution. A more appropriate description of the system can be achieved by using the Frumkin model which incorporates either net attractive or net repulsive interactions between the adsorbed surfactant molecules. The model follows the setup of the Langmuir model but in the Frumkin model the surfactants are assumed to interact pair-wise with their neighbouring surfactant molecules on the lattice. This leads to the surface chemical potential following

11


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Page 12 of 34

Equation 3 but augmented by a surfactant-surfactant interaction energy term

s0

s

µ = µ + RT ln

where

w22

Γ/Γ∞ 1 − Γ/Γ∞

w22 Γ/Γ∞

+ w22 Γ/Γ∞ ,

(5)

is the total pair-wise interaction with no assumptions on its origin.

Following the formalism taken to obtain Equation 4, the Frumkin model leads to the equation of state

γ = γ0 + RT Γ∞

where the interaction parameter

AF

Γ ln 1 − Γ∞

AF

AF − 2

Γ Γ∞

2 ! ,

(6)

is

AF =

The interaction parameter

w22 . RT

(7)

captures the eective energy of interaction between the

adsorbed surfactant molecules modelled as residing on a simple lattice normalized by the thermal energy

RT .

Positive

AF

values reect net repulsive interactions and negative values

net attractive interactions between the surfactants. from, e.g.

Net repulsive interactions may result

charged surfactant head groups or steric interactions, while attraction can rise

due to hydrophobic interactions, van der Waals interactions, or enhanced condensation of counterions. At

AF = 0, the Frumkin equation of state, Equation 6, reduces to the Langmuir

equation of state, Equation 4, and thus corresponds to non-interacting surfactants. Rigorously, Equations 3-6 are valid only for non-ionic surfactant solutions. generally, the equations perform well for presence of

1 : 1

1 : 1

However

ionic surfactants (such as CTAB) in the

excess salt where the surfactant counterion is one of the salt ions (e.g.

NaBr) (see Supplementary Materials). In excess salt, the surfactants are pseudo-nonionic as the double layer is very thin and the charge of the ions does not play a big role

12


10

.

Page 13 of 34

Results and discussion Figure 2 shows the CTAB and tension

γ

0.1

M NaBr system equation of state in terms of the surface

vs. the surfactant surface concentration

Γ

as measured by the bubble expansion

experiments and the t by Frumkin model, Equation 6, which is the simplest theoretical model to take into account inter-molecular interactions. A comparison of the experimental data curve and the Frumkin model, labeled as classical Frumkin model in the gure, reveals that the model provides a poor t with the measurement data and cannot capture the system response. Consequently, the Langmuir model, Equation 4, that is a particular case of Equation 6 with

AF = 0

cannot provide a t to the data either. The Frumkin model is

based on constant nearest neighbour-based pairwise interactions and an assumption that the surfactants reside on a simple lattice the deviation of the experimental data of the model reveals that these assumptions do not capture the system response at a sucient level.

7 0 6 0

γ(m N /m )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

5 0 4 0 e x p e r im e n ta l d a ta " c la s s ic a l" F r u m k in e q u a tio n " lo c a l" F r u m k in e q u a tio n

3 0 1 ,0 x 1 0

-6

Figure 2: Equation of state

2 ,0 x 1 0

-6

3 ,0 x 1 0

Γ( m o l/m

modied Frumkin equation 9 with variable

Π−A

4 ,0 x 1 0

-6

)

γ(Γ) obtained by the bubble expansion experiments.

red line shows the best t by Frumkin equation 6. is plotted in a

2

-6

AF (Γ).

The solid red line shows the t by a T = 25◦ C. The same data

Temperature

representation in the Supporting Information.

13

The dashed


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Page 14 of 34

To gain more insight to the interface molecular structure and interactions there, we turn to molecular dynamics simulations. In comparing the computational and experimental results, the surface pressure-surface concentration (Π−Γ) isotherms are employed, see Figure 3. The surface pressure

Π

is dened

Π = γ0 − γ

where

γ0 is the surface tension of the surfactant-free solution.

(8)

This quantity is used instead of

the surface tension for the simulation results because the TIP3P water model that is employed in the simulations here underestimates signicantly the surface tension of water interfaces (a value of

48.3 mN/m) obtained for the 100 mM NaBr solution in comparison to experimental

values (about

72

mN/m). Figure 3 presents the simulated and the measured

γ

value based

Π−Γ isotherms at 25◦ C. The data reveals that the overall shape of the isotherm as measured by the bubble expansion experiments is relatively well reproduced by our simulations, a discrepancy can be observed only for high surface concentrations. In the simulations, the surfactant layer becomes unstable at surface pressures above

30

mN/m: rapid desorption

of surfactants from the interface is observed. Since the isotherms measured experimentally in this work extend to higher surface pressures, the instability of the surfactant lm in the simulations is likely due to slight imbalance in the intermolecular interaction strengths in the computational model. However, the simulations appear to capture the system response in terms of the

Π − Γ isotherms relatively well at pressures below this critical destabilization

pressure of the lm in the model. The main reason for the failure of the Frumkin model to capture the measured system response is that the interactions between the surfactant molecules in the surface layer are not constant, as assumed by Frumkin, but rather depend on the surface coverage and local environment in a non-trivial way. To better capture the interactions between the surfactants, dierent expressions have been proposed for the dependency of the interaction parameter

14


AF

Page 15 of 34

S im u la tio n 6 4 S im u la tio n 1 4 4 E x p e r im e n t

4 0 3 0

Π(m N /m )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

3

2 0 1

1 0

1 ,0 x 1 0

Figure 3:

-6

2

2 ,0 x 1 0

-6

3 ,0 x 1 0

Γ( m o l/m

2

-6

4 ,0 x 1 0

-6

)

Comparison of simulational and experimental pressure-surface concentration

isotherms (Π

−Γ

isotherms). Red circles represent experimental data calculated from the

surface tension measured by the bubble expansion technique while black squares indicate simulated data (64 surfactants per interface). Open squares represent comparison data from the larger simulations (144 surfactants per interface). snapshots shown in Figure 5.

The numbered arrows refer to the

The same data is plotted in a

Supporting Information.

15


Π−A

representation in the

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

on the surface density of the surfactants,

AF (Γ).

Page 16 of 34

For example, a power-law dependence has

been proposed in the empirical generalised Frumkin equation instead of assuming a certain form for the

AF (Γ)

58,59

. However, in this article,

dependence, we extract

AF (Γ)

from the

experimental data with the purpose of using the apparent eective interaction strength in interpretating the interface physically. For this purpose, Equation 5 can still be assumed to be valid locally, in a narrow range of surfactant surface concentrations over which be considered constant. In the vicinity of a certain surface concentration

˜, Γ

AF

can

this assumption

leads to the "local" Frumkin equation of state

˜ const(Γ)

z



˜ − RT Γ∞ ln 1 − γ(Γ) = γ(Γ)

}| ! ˜ Γ Γ∞

−

˜ AF (Γ) 2

+ RT Γ∞

˜ Γ Γ∞

{ !2   

! ˜ Γ 2 Γ AF (Γ) ln 1 − − . Γ∞ 2 Γ∞

(9)

By dividing the experimental data into small regions and tting Equation 9 to the experimental and simulational data points corresponding to each region independently, an

AF (Γ)

dependence can be obtained both for the experimental and simulation data. Figure 4 shows that the calculated

AF (Γ)

values for the experimental and the simulated surface tension

isotherms are qualitatively comparable to each other. This agreement can be taken as another indication that the simulated surfactant layer follows at a reasonable level the real system response. The data of Figure 4 shows that

AF

indeed varies strongly with

Γ.

At small surface cov-

erages, and consequently, large surfactant-surfactant inter-molecule distances, the surfactant molecules in the surface layer do not interact (AF repulsion and

AF < 0

= 0). AF > 0

corresponds to eective

to attraction between the surfactants: With increasing surface con-

centration, eective repulsion between the surfactants rst becomes stronger, then levels out and decreases. At a high-enough surface concentration, intermolecular attraction arises and the attraction increases rather steeply. A perplexing feature in our

16


AF

results is the high ef-

Page 17 of 34

R e p u ls io n

1 0 5 F

0

A

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

A ttr a c tio n

-5

s im u la tio n s e x p e r im e n t

-1 0 1 .0 x 1 0

-6

2 .0 x 1 0

-6

Γ( m o l/m

Figure 4: Local Frumkin interaction parameter

AF

3 .0 x 1 0 2

-6

4 .0 x 1 0

-6

)

as a function of surface concentration

Γ.

Black squares correspond to experimental data from the fast bubble compression/expansion measurements, while red triangles correspond to data from the computer simulations.

fective repulsion between the surfactant molecules at medium surface concentrations: in the Frumkin theory, the surfactant-surfactant eective interactions have been considered to be attractive. A strong repulsive interaction between surfactant molecules has previously been reported in Ref. 60.

The repulsion was then explained by formation of surfactant aggre-

gates in the adsorption layer

60

. Furthermore, a varying interaction parameter

AF

has been

reported previously in Refs. 61,62 but the origin of this variation has not been discussed. Our experimental measurements are insucient to draw conclusions about the origins of the varying interaction parameter values, or interprete the eective repulsion at intermediate coverage.

However, the molecular simulations which provided good agreement with the

experiments in terms of both the

Π−Γ

isotherm and the calculated

AF

values enable

additional insight. Figure 5 presents snapshots of the surfactant monolayers at three dierent surface concentrations in the simulations. These correspond to sparse, intermediate, and densely packed

17


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Page 18 of 34

monolayers and correspondingly, low, intermediate and elevated surface pressure. 4 shows the corresponding

Π−Γ

Figure

isotherm data points. Even at low surface concentration

−6 2 (1.42·10 mol/m ), the surfactant molecules cluster to a very high degree and form highly dynamical, transient planar rafts. This is similar to other ionic, straight-chain surfactants Additional simulation of a system containing

35,63

.

0.28·10−6 mol/m2 of CTAB (see Figure S4 of the

Supporting Information) indicates that rafting takes place well below the measured concentration range. The clustering persists when the lm is compressed (the surface concentration increases), but the aggregation morphology changes such that the surfactant layer visually thickens in the direction perpendicular to the interface. Since the packing of surfactants at the interface is uneven at all surface concentrations, the simulations show clearly that the interaction parameter

AF

extracted from them is an eective one.

Since the morphology and surface tension in the simulations may suer from the nite size of the simulation box in the

xy -direction and the imposed periodic boundary conditions

especially at the high surface concentrations, a set of simulations with larger interfacial areas and

144 surfactants at each interface were examined.

Neither the average surface area,

stability of the lm, nor the observed microstructure were aected by the increase in the simulated system size to any signicant degree. To quantify the transition in the microstructure of the adsorbed monolayer, the distribution of tail angles with respect to the normal of the interface is presented in Figure 6. The gure shows that the surfactant tail orientation evolves from being dominantly parallel to the interface (at along the interface plane) to being dominantly normal to the interface as the surfactant surface concentration increases. This is in agreement with neutron reectivity measurements on salt free CTAB solutions where the average chain tilt away from the interface was found to decrease from creased

16

68◦

to

54◦

as the surfactant surface concentration in-

. However, even at elevated surface concentrations, a portion of the surfactant tails

remains parallel to the surface. This indicates tendency toward surface aggregation, but also points towards a signicantly disordered lm morphology. Indeed, deuterium order param-

18


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Langmuir

−6 2 −6 Figure 5: Final simulation congurations corresponding to 1) 1.42·10 mol/m , 2) 2.66·10 2 −6 2 mol/m , and 3) 3.51 · 10 mol/m surfactant surface concentrations. For the highest surface concentration, in which the assembly morphology is most prone to system size dependencies, also the conguration at a larger system size is presented. In the visualization, bromine is in mauve and sodium in lime color. The size of the trimethylammonium nitrogen has been exaggerated. All images follow the same scale (see scalebar), periodic images are included in the visualization, and bottom leaets, as well as, all water molecules have been omitted.

eter proles calculated from the simulations (see Figure S2 in the Supporting Information) show considerably lower degrees of order in comparison to experimental proles obtained from CTAC micelles

64

. Although surface aggregates composed of conventional surfactants

have not been observed at air/water interfaces, prior simulations tions

66

35,65

and theoretical calcula-

suggest that disordered CTAB hemiaggregates could exist at the interface. However,

19


Langmuir

we do not have evidence of the formation of surface micelles, the aggregates are disordered structures and no characteristic size is measured. In Figure 6, the cross-over from dominantly planar rafts to more perpendicular surfactant orientation preference occurs approximately at surfactant surface concentration

2.91 · 10−6

2 mol/m . Incidentally, this coincides with the surface concentration where the eective interaction parameter

AF

starts to decrease substantially in Figure 4 both in the experimental

and the simulational data set.

This is an indication that a change in the morphology of

the adsorbed monolayer could be connected with the eective interaction turning to strong attraction at high surface coverages.

0.20

Γ (10−6 mol m−2):

1.42 1.68 2.13 2.40

0.15

Probability

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 34

0.10

2.66 2.91 3.09 3.29

3.51 3.65

0.05 0.00

0

10

20

30

40 50

60

70

80

90

Tail angle (°) Figure 6: Surfactant tail angle with respect to the air-water interface normal at varying −6 surface concentrations in the simulations. The surface concentration varies between 1.42·10 2 −6 2 mol/m and 3.65 · 10 mol/m , see gure legend. A tail perfectly at along the interface ◦ plane has a 90 angle and a tail oriented perpendicular to the interface corresponds to a ◦ 0 angle.

In order for the

AF

to change signs at high surface concentration, the interactions be-

tween surfactants must be composed of a repulsive and attractive part of approximately same order of magnitude. The attractive part is commonly attributed to the van der Waals

20


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Langmuir

attraction of the surfactant tails. As dispersive interactions decay

r−6 , at low surface concen-

tration surfactants can be considered to be essentially isolated and the aliphatic tails interact only with the bulk solution immediately below the adsorbed molecule. In denser lms, tails gain dispersive energy through interactions with neighbouring surfactants in the air phase. This could explain the strong attraction at high surface concentrations.

To quantify this

response, Figure 7 shows the change in dispersive, i.e. van der Waals, energy per surfactant calculated from the simulations compared with values obtained for a hexagonal array of hexadecane molecules arranged perpendicular to the interface, as well as, a at monolayer at the interface at corresponding surface coverages.

The data shows that van der Waals

energies of neither the at monolayer nor the hexagonal array can reproduce the energies from the CTAB simulations. This means that the change in the surface morphology and tail tilt are required to capture the energetic response of the interface. Furthermore, the data shows that the van der Waals energy increases quite rapidly even at surface concentrations below the lowest experimental data point.

This results from the formation of surfactant

rafts and indicates that there may be a balancing long-range contribution to the interaction potential such as long-range electrostatic repulsion or loss of congurational entropy as the rafts form. To probe the relative importance of these contributions and the eect of alkyl tail length we examined also octyltrimethylammonium bromide (OTAB) and octanol at low

−6 2 surface concentration (1.4 · 10 mol/m ) via the simulations, see Figure S3 of the Supporting Information. The simulations show that OTAB does not form rafts contrary to CTAB but octanol does. This indicates that electrostatic repulsion is the dominant repulsive contribution to the interaction parameter while van der Waals attraction between the surfactant tails is responsible for the attraction. Unfortunately due to the varying system compositions and salt, water, and surfactants all contributing to the electrostatics of the system, electrostatic repulsion between the surfactants cannot be directly extracted from the simulations.

The simulations do, however,

allow us to estimate the surface charge to evaluate if the electrostatic eects are important.

21


Langmuir

10 0

AF (RT)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 34

−10 −20 −30 −40

0

1×10

−6

2×10

−6

3×10

−6

4×10

Γ (mol/m2)

−6

Figure 7: Van der Waals energy per molecule calculated for the CTAB molecules in the simulations (+-symbols, dashed line) and hexadecane embedded 1) in an ideal hexagonal array (red line) or 2) in a at monolayer (blue line) at varying surface coverages.

Figure 8 shows how the degree of counterion binding evolves in the system with the surface concentration. Three dierent parameters are shown: a fraction of counterions in the rst binding shell

β1 ,

in the second binding shell

values of total counterion binding micelles

6771

β

β2 ,

and the sum of these

compare well with values

β = β1 + β2 .

The

0.71 − 0.89 reported for CTAB

. The counterion binding data shows that although the total counterion bind-

ing increases with

Γ,

it never reaches 1. This means that the interface remains positively

charged at all coverages. This, of course, creates a double layer in the subphase. Because of the excess salt concentration in the solution, the double layer does not sigicantly change the interaction potential prole, see Supplementary Materials. The presence of the uncompensated charged surfactant molecules at the interface, however, can induce an electrostatic repulsion between them through the air phase which thus is not eectively screened by the salt in the aqueous bulk. An order of magnitude estimation of electrostatic repulsion eect

Ael

on the interaction parameter

22


AF

can be obtained by

Page 23 of 34

0 ,8

0 ,6

β

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

c o n ta c t p a ir s s e c o n d s h e ll to ta l c o u n te r io n b in d in g

0 ,4

-6

1 ,0 x 1 0

-6

2 ,0 x 1 0

3 ,0 x 1 0

Γ( m o l/m β

Figure 8: Degree of counterion binding centration

2

-6

4 ,0 x 1 0

-6

)

at the interface as a function of the surface con-

Γ.

describing the interface simply as a charged surface. This means assuming a at interface, pairwise counterion binding and a homogenuous distribution of charges:

Ael ∼

where

e

is the electron charge,

NA

e2

p (1 − β1 )3 ΓNA , 4πε0 kT

is the Avogadro's number and

(10)

ε0

is the permittivity of

vacuum. Equation 10 allows us to estimate the elecrostatic part of the interaction parameter to be about

10 − 30kT .

Thus,

interaction parameter

Ael

AF

is comparable in magnitude with the experimentally measured

and the van der Waals energies extracted from the simulations.

This signies that both the van der Waals and the electrostatic interactions need to be considered for a proper understanding of the system. Also, Equation 10 points toward

Ael

decreasing with the surfactant concentration. This

is simply related with the surface charge and consequently total electrostatic energy staying

23


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Page 24 of 34

almost constant as the surfactant surface concentration increases. The interaction parameter

AF

represents an average value per one surfactant molecule at interface and therefore its

electrostatic part

Ael

decreases. Together with the van der Waals forces, the decrease of elec-

trostatic repulsion with increasing concentration can partially explain the strong attraction between surfactant molecules at high surface concentrations. The observed strong repulsion, on the other hand, is mainly attributed to electrostatic repulsion between surfactants and rafts. The electrostatics considerations presented here are of course oversimplied as they do not take into account many crucially important factors. For example, the change in surface aggregate morphology moves some of the head groups deeper in the water, making them inequivalent and increasing the eective dielectric constant. This eect enhances the decrease of the electrostatic part of the interaction parameter as the surface concentration increases. Obviously all of these eects together, and coupled with the change in the surface aggregation morphology, inuence the interaction parameter in a non-trivial way.

Conclusion Here, we measured the interfacial equation of state that connects the surface tension with the surface surfactant concentration for CTAB in

0.1

M NaBr aqueous solution using a fast

bubble compression/expansion method and extracted insight on the molecular level interactions via molecular simulations of the surfactant layer and extracting an eective interaction parameter of the local Frumkin equation of state to understand the system response. The eective interaction parameter showed that the interfacial surfactant layer experiences rst an increasing repulsion which turns into a plateau and a decrease of repulsion followed by attraction with increasing surface coverage. The molecular simulations enabled associating the shape of the interaction parameter curve with the increasing coverage to a morphology change in the surfactant monolayer. This is associated with a change in surfactant orientation

24


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Langmuir

in the simulations: as the surface concentration increases, the surfactants shift continuously from planar congurations where the surfactants lie along the surface plane to a mixture of tilted orientations due to the surfactants adopting more perpendicular orientations with respect to the interface. Further analysis of the van der Waals interactions (attraction between surfactants) and electrostatic interactions (repulsion) in the system enables to deduce that the response is dominated by a competition of these two interactions. Namely, packing density and morphology dictate the van der Waals attraction magnitude while for the ionic surfactant system, electrostatic repulsion rises to dominate when the charged surfactant heads interact via the air phase. The strength of the electrostatic interaction is dominated by the counterion binding, as well as, the morphology change which moves the surfactant heads further from the interface and results to increase of charge screening. As the results show indications that the van der Waals contributions and electrostatic interactions form the key contributions to the system response, we suggest that a detailed model of the surfactant layer at an air-water interface should include electrostatic eects in the surfactant layer, as well as, the inhomogeneity and changes in monolayer morphology for the proper description of the interface. The current study associated changes in eective surfactant interactions with adsorbed monolayer morphologies and showed indications that the response is dictated by van der Waals interactions and electrostatics in the system. Our research lays way for further studies of interfacial interactions between surfactants.

The ndings on relation of aggregate

morphology, surface tension, and eective interactions of the surfactants at the air-water interface are important as surface concentration and organisation inuences the permeability of the interfaces and their ability to sustain surface tension gradients. These phenomena are critical in the mechanical properties of all surfactant interfaces specically, the mechanical properties of surfactant assemblies at the air-water interfaces, i.e. the structure and dynamics of surfactants at the air-water interface is essential towards predicting foam and emulsion stability from molecular structure.

25


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Acknowledgement We are grateful to Dominique Langevin for many interesting conversations and useful comments.

The authors thank the Centre National des Etudes Spatiales (CNES Hydrody-

namique des Mousses Humides) (P.Y., D.H., A.S.), Academy of Finland (S.V., M.S.), and Aalto University School of Chemical Engineering doctoral programme (S.V.) for nancing this research. Computational resources by CSC IT Centre for Science, Finland, are gratefully acknowledged.

Supporting Information Available Double layer eect on the interaction parameter, CTAB deuterium order parameters calculated from the simulations, charting the eect of surfactant tail length on the clustering via comparison of CTAB, OTAB and octanol simulations, as well as, the data of Figures 2 and 3 in a surface pressure vs surface area presentation.

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CTAB with added salt - American Chemical Society

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