Dodecane Interface

Article pubs.acs.org/JPCC

Kinetics of Triton-X100 Transfer Across the Water/Dodecane Interface: Analysis of the Interfacial Tension Variation Pierre-Marie Gassin,* Gaelle Martin-Gassin, Daniel Meyer, Jean-François Dufrêche, and Olivier Diat Institut de Chimie Séparative de Marcoule, UMR 5257 (CEA-CNRS-UM2-ENSCM), B.P. 17171, 30207 Bagnols sur Ceze Cedex, France S Supporting Information *

ABSTRACT: The interfacial tension of water/dodecane interface is investigated by the pendant drop technique during the transfer of a surfactant molecule, the Triton X-100. This molecule is initially present in one of the liquid phases, and the measurement of the interfacial tension as a function of time permits us to probe the dynamic incoming and outgoing surfactant at the interface and to deduce a rate of transfer. As a rule, after the contact of both solutions, the interfacial tension exhibits a steep initial decrease, passes through a minimum, and then levels off at a value that depends on the initial surfactant concentration in the drop. The time delay before reaching the equilibrium state is due to the limitant step of the surfactant crossing over the liquid/liquid interface. Moreover, the interfacial tension evolution depends strongly on the phase where the Triton-X100 is initially dispersed. Indeed, the global kinetics is found to be faster when Triton X100 transfers from dodecane toward water as compared to the reverse pathway. To quantify the limiting factors of the interfacial transfer mechanism, two theoretical models describing the time evolution of the system are presented and discussed. The first one is based on a diffusioncontrolled adsorption/desorption at the liquid/liquid interface, whereas the second one also takes into account an interfacial chemical adsorption/desorption reaction. This latter permits us to give an estimation of importance of the chemical processes, which occurs at the interface in the overall kinetics.

■

INTRODUCTION Liquid/liquid (L/L) interfaces have a great interest because of their applications in chemistry and their essential role in biological and biochemical processes.1 Nonmiscible liquid− liquid systems are often implemented in industrial applications such as phase-transfer catalysis,2 electrochemical processes,3 liquid chromatography,4 and solvent extraction.5 Over the thermodynamic aspects, the kinetics of species transfer at interfaces is an essential point to understand these processes' efficiencies. We are thinking that the interfacial behavior during the transfer of a neutral or an ionic species contains the energetical signature for understanding the various mechanisms or elementary steps that make up the global processes. At a first level, we can consider that the overall L/L transfer arises from the coupling of diffusion mechanisms of the species from the bulk onto the interface and vice versa with interfacial reactions. To study the rate of transfer at L/L interfaces, one can find in the literature different experimental systems that were developed to get information at the macroscopic level: constant interfacial cell with laminar flow,6,7 rotating membrane cell technique,8 and microfluidics channels.9,10 The development of nonlinear optical techniques gives complementary information about the structure at the molecular level of the L/L interface during the transfer.11,12 In this work, we proposed to get kinetics information of the phase-transfer process by studying the interfacial dynamics during the transfer of a surfactant molecule across a water/oil interface. The studies were performed by using the pendant © 2012 American Chemical Society

drop technique, which permits us to monitor the interfacial population evolution.13 Indeed, a surfactant, which has a strong affinity for the interfacial area, can transfer across a water/oil interface when it is soluble in both organic and aqueous phases.14 The driving force for this transfer is the chemical potential gradient, which will tend to partition the surfactant between both phases. The ratio between the surfactant concentration in the organic phase and in the aqueous phase under equilibrium conditions is known as the partition or distribution coefficient Kp. The dynamics and partition of surfactant at L/L interface was reviewed in detail by Ravera et al.,15 where they showed that for an initial fresh interface, the interfacial tension (IFT) evolution is not only controlled by the adsorption but also counterbalanced by the desorption on the other side of the interface. Both actions, adsorption and desorption, occur until an equilibrium state is reached, corresponding to the partition of the surfactant in the two phases. A nonionic surfactant, Triton X-100 (TX-100), soluble in both water and dodecane and extensively studied at air/ water16−19 and at the L/L interface,20−23 has been chosen for those studies. In particular, it was shown that adsorption of TX100 at air/water interface is essentially controlled by diffusion,18 while desorption is controlled by both diffusion and interfacial Received: March 15, 2012 Revised: May 21, 2012 Published: May 29, 2012 13152

dx.doi.org/10.1021/jp302514k | J. Phys. Chem. C 2012, 116, 13152−13160

The Journal of Physical Chemistry C

Article

processes.24 The original measurements described in this paper concern the comparison of the IFT variation for two different transfer pathway across the L/L interface: “configuration A” for a TX-100 transfer from oil to water and “configuration B” from water to oil. Measurements were performed over a large time range (104−105 s) to attempt to reach the equilibrium state and were performed for TX-100 at concentrations below the critical micellar concentration (CMC) in water.16 The experimental data are compared with two theoretical models, considering either diffusion or both diffusion and interfacial processes. The first model, developed in a finite spherical system, assumes that the adsorption/desorption is controlled by the diffusion process.25 The second model is based on the assumption that the adsorption/desorption is controlled by interfacial processes and is developed to be compatible with a Langmuir isotherm.26

were measured systematically using an Anton Paar density analyzer (model DSA 5000). For the measurement of the system in the equilibrium state, both aqueous and oil phases were equilibrated as described above. The IFT value is taken after 1000 s, the time required to have a stable IFT (see the Supporting Information for more details). For IFT measurements of a system out of equilibrium, a droplet of TX-100 dodecane solution was formed in a cell containing pure water (configuration A), or a droplet of TX-100 aqueous solution was done in a cell containing pure dodecane (configuration B).

■

RESULTS AND DISCUSSION A. Studies of the Equilibrium States. Before studying the dynamics of the water/dodecane interface with TX-100, the equilibrium states of the ternary system TX-100/dodecane/ water were explored. A first point has to be noted and concerns the phase diagram. A third phase appears in the system after emulsification and for an initial concentration of TX-100 in one phase above 3 × 10−4 mol/L. This third phase, which is a demixion of the organic phase into two different phases, is fully stable for more than 1 year. The demixion in the oil phase has already been observed in the polyethoxylated system31,32 and in several extractant systems.33 The driving force for this phase separation is related to an increase in the attraction potential between the reverse aggregates. The description of this phase behavior is off topic of this work, and the experiments presented here have been performed in the two phases regime. For all of the following studies, concentrations are taken below the threshold concentration, previously given, to prevent the third phase formation. The second point concerns the partitioning of TX-100 in two phases. Figure 1 gathers the TX-100 titration results in each

■

EXPERIMENTAL SECTION Materials. TX-100 or polyoxyethylene(10) octylphenyl ether (C34H62O11, M = 646.85 g/mol) was from Acros Organics and was used without further purification.The RNM spectra measurement, given in the Supporting Information, are consistent with those shown in ref 27. In particular, it shows that TX-100 has no distribution along the alkyl chain, and the variation of the oxethylation number is not detectable. The 99% n-dodecan was supplied by Aldrich, distilled in an all-glass apparatus, and passed seven times through an alumina column to remove any active impurities.28 Ultrapure water (Milli-Q Labo, Millipore) was used. All experiments were carried out at 295 ± 1 K. Preparation of Equilibrate Phases. For the measurement of the surfactant partitioning at the equilibrium state, a TX-100 aqueous phase of 10 mL was first brought in contact with the same volume of a dodecane phase. After a vigorous agitation (5 min in vortex), which drives to an emulsification of the system, the two phases were centrifuged (5000 rpm, during 20 min) and separated. We checked that the equilibrium state was completely reached after this treatement. TX-100 Titration. The concentration of TX-100 in each phase was determined by the UV−vis absorption measurement at 223 nm for the aqueous solution and absorption measurement at 225 nm for the dodecane phase. Those measurements were performed with a Cary 50 UV−visible spectrophotometer from Agilent. More details are given in the Supporting Information about the calibration of those measurements. IFT Measurements. The IFT measurements were carried out by the drop shape method using a Kruss tensiometer apparatus (model DSA-100). The size and shape of the drop formed at the tip of a needle fixed on a glass syringe were analyzed by the drop shape analysis software. The diameter of the needle was ϕ = 1.49 mm for a dodecane rising droplet in water (configuration A) and ϕ = 1.48 mm for a water hanging droplet in dodecane (configuration B). The size of the droplet depends on the experimental conditions but was around 20 μL, and the cell in which the droplet is formed is full of 5 mL of liquid. As IFT varies with time, the shape of the droplet will obviously change with time. The B shape parameter29,30 will, during all experiments, be in the range of 0.45−0.6, which means an absolute accuracy less than 1%.30 The value of γ0 obtained for a pure water/dodecane interface in both configurations (A or B) was found to be at 49 mN/m±1 mN/m. During experiments, the IFT of pure water/dodecane was repeated several times to check any contamination of the syringe. The densities of the organic and the aqueous phases

Figure 1. TX-100 concentration for the equilibrate system at 22 °C: the left axis is the TX-100 concentration in the dodecane phase, and the bottom axis corresponds to the concentration of TX-100 in the aqueous phase. The dashed line is the best fit obtained by using Kp = 0.75.

bulk phase when the system is at equilibrium. In this range of concentrations (below 150 μmol/L), the TX-100 concentration in the organic phase is linear with the concentration in the aqueous phase. It means that the partition coefficient is nearly constant in this concentration range. The calculations of the errors bars are detailed in the Supporting Information. The partition coefficient Kp, defined as the ratio of the TX-100 concentration in the organic phase over the TX-100 concentration in the aqueous phase, is evaluated at 0.75 ± 0.05 at 22 °C by fitting those results. This value agrees with the partition coefficient of TX-100 in the hexane−water system measured to 0.82 by Ravera34 at 20 °C and to 0.71 in heptane− water at 25 °C.35 The corresponding solvation free enthalpy 13153



Article

difference is −ln KP = 0.29 kBT, which is relatively low so that this system appears to be a good candidate for the study of the kinetics of reversible transfer. Figure 2 presents the IFT for equilibrated solutions of TX100. The results can be expressed in terms of the TX-100

Γ = Γm

[TX]dodecane adodecane + [TX]dodecane

(3a)

Γ = Γm

[TX]water a water + [TX]water

(3b)

[TX]water =

concentration in aqueous phase or in terms of TX-100 concentration in the dodecane phase. These data are satisfactorily fitted using the ideal Langmuir adsorption model.36 If the IFT is studied as a function of the TX-100 concentration in the water phase, the aqueous phase is referred as the “reference phase” with a corresponding isotherm described as:

(1)

where γ is the IFT, γ0 is the IFT value in the absence of surfactant, R is the gas law constant, T is the absolute temperature, Γm is the maximum adsorbed amount, and awater is the Langmuir−Szyszkowski constant. Symmetrically, if the IFT is studied as a function of the TX-100 concentration in the dodecane phase, the organic phase is referred as the “reference phase”, and the isotherm is in that case: ⎛ [TX]dodecane ⎞ γ = γ0 − RT Γm ln⎜1 + ⎟ adodecane ⎠ ⎝

(3c)

The main objective of this works consist in clarifying the significance of the various phenomena on the kinetics of the transfer: adsorption and desorption of the molecules at the interface, diffusion in the two phases, collective effects, etc. The L/L transport kinetic has been observed indirectly thanks to the measurement of the IFT as a function of time for nonequilibrated systems. The interpretation of this quantity depends on the way the kinetics of the transfer is modeled. For the sake of simplicity, we considered two limiting cases for the interpretation of the experiments. • The first theoretical model (sections B and C) only takes into account the diffusion of the molecules in the two phases, the interface itself being at local equilibrium at any time. This situation corresponds to a diffusioncontrolled reaction for which the interfacial transfer is very fast as compared to the diffusion of the species in the two phases. • On the other hand, the second theoretical model (sections D and E) supposes that the interfacial adsorption/desorption process mechanism is the limiting factor. The system is described in terms of reaction kinetics, which represents the mechanism of the molecule transfer. Both models were used to interpret in the best way the experimental data. Model 1 is the reference model, since in any case diffusion is necessary. Discrepancies between this model and the experimental curves are interpreted as specifically interfacial dynamical processes, and they are interpreted thanks to model 2. B. Model 1: Diffusion-Controlled Interface Dynamic. The model that we implemented has been proposed by Liggieri et al.18,25 It is assumed that the transfer is a diffusion-controlled phenomenon, all of the local interface transfer being infinitely fast. It considers that the droplet is isolated with the syringe needle. This latter hypothesis, applied in this work, is in a first way suitable, as shown by Yang et al.,37 who calculated the IFT variation with taking into account the whole system, that is, the droplet and the inside of the needle syringe. This first model assumes that the adsorption takes place at the interface of a sphere of radius R1, which represents the bulk 1, surrounded by a spherical shell of radius R2, which represents the bulk 2. Assuming a spherical coordinate system, the adsorption Γ varies under the flux balance at the interface, which leads to

Figure 2. IFT of TX-100 at the water/dodecane interface expressed as a function of the concentration in the aqueous phase (blue circle) or expressed as a function of the concentration in the dodecane phase (red triangle). The blue continuous line is the best fit obtained by using the Langmuir isotherm with the water as the reference phase, and the red dashed line is the best fit obtained with the dodecane as the reference phase: those parameters are given in Table 1.

⎛ [TX]water ⎞ γ = γ0 − RT Γm ln⎜1 + ⎟ a water ⎠ ⎝

[TX]dodecane Kp

(2)

Both eqs 1 and 2 are actually equivalent at the equilibrium state, if we assume that awater = adedecane/Kp. The TX-100 surfactant is present in the system in three different forms: TX-100 dissolved in water characterized by its concentration [TX]water, TX-100 adsorbed at the interface characterized by its surface excess Γ, and TX-100 dissolved in dodecane characterized by its concentration [TX]dodecane. An equilibrium state is thus fully described by one of these quantities; the others can be deduced by using two of the following equilibrium relationships:

∂c dΓ = −D1 ∂r dt

r = R1−

+ D2

∂c ∂r

r = R1+

(4)

where c = c(r, t) is the surfactant concentration at time t and at a distance r from the origin of the coordinates and D1 and D2 are the diffusion coefficients, respectively, in bulk 1 and bulk 2. The diffusion phenomena in the bulk phases are described by the Fick equations: 13154



Article

Figure 3. Dynamic IFT for a fresh droplet of dodecane with TX-100 at initially c0 = 2 × 10−4 mol/L (blue square), 7.5 × 10−5 mol/L (green triangle), and 3.375 × 10−5 mol/L (red circle) in an initially 5 mL pure water cell (configuration A). Continuous curves are theoretical models with the parameter given in Table 2.

⎛ ∂ 2c 2 ∂c ⎞ ∂c = D1⎜ 2 + ⎟ r ∂r ⎠ ∂t ⎝ ∂r ⎛ ∂ 2c 2 ∂c ⎞ ∂c = D2⎜ 2 + ⎟ r ∂r ⎠ ∂t ⎝ ∂r

Γ(t ) = Γm

for 0 < r < R1 (5)

c(R1− , t ) = k(12)c(R1+ , t )

c(r , 0) = 0

for R1 < r < R 2

(6)

Moreover, being a closed system, the boundary conditions are ∂c ∂r

=0 r = R 2−

and

∂c ∂r

=0 r=0

(7)

The model considers that the interface is at local equilibrium with both adjacent phases, that is, c(R1+ , t ) = k(21)c(R1− , t )

(8)

where k(21) in this model is the partition coefficient Kp if water represents the bulk 1 and dodecane the bulk 2. k(21) is Kp−1 if dodecane represents the bulk 1 and water the bulk 2. Finally, the relation used between the boundary concentration at interface and the adsorption is a Langmuir isotherm: Γ(t ) = Γm

c(R1− , t ) a− + c(R1− , t )

(11)

Those two ways to formulate the model are, of course, equivalent if k(12) = 1/k(21) and a+ = a−/k(12). A Fortran numerical code has been used to implement the model with the same scheme as detailed here.25 More information about the Fortran numerical code and its validation is given in the Supporting Information. In particular, this code has been tested with the same parameter given in this work25 and gives the same results. After those verifications, this code has been used to interpret experimental data. C. Comparison between the Model 1 and the Experimental Data. First, the studies of TX-100 transfer are presented in configuration A. The IFT evolution, after the creation of a fresh droplet, is monitored for several dodecane droplets of TX-100 in a cell containing pure water and for the nonequilibrated phase. These IFT evolutions are reported on Figure 3 and compared with the model 1. All theoretical and experimental parameters are given in Table 2. The only theoretical parameters adjusted with the experimental data are the diffusion coefficients D1 and D2, whereas all of the other parameters are constraints. Radii R1 and R2 are fixed to have the same volume than the experimental setup, and a, Γm, and Kp are fixed by the equilibrium states studies (part A).

The initial conditions are for 0 < r < R1

(10)

and similarly we have

for R1 < r < R 2

c(r , 0) = c0

c(R1+ , t ) a+ + c(R1+ , t )

(9)

−

where a is the Langmuir−Szyszkowski constant and Γm is the saturation adsorption. In these equations, the relations 8 and 9 are formulated as considering the phase 1 as the “reference phase”, simply because it supposes that the adsorption isotherm on that phase is known. Relations 8 and 9 can also be formulated, in the case where the phase 2 is considered as the “reference phase”. In that case, the adsorption isotherm of phase 2 is

Table 1. Adsorption Parameter Expressed in Terms of TX100 Concentration in Water or in Terms of TX-100 Concentration in Dodecane Γm (mol m−2) Langmuir isotherm water Langmuir isotherm dodecane 13155

−6

2.3 × 10 2.3 × 10−6

a (mol L−1) awater = 1.5 × 10−7 adodecane = 1.1 × 10−7



Article

Table 2. Experimental and Theoretical Parameters for a Dodecane Droplet of TX-100a experimental data

theoretical model

TX-100 conc in droplet (mol/L)

oil droplet volume (μL)

water volume (mL)

R1 (cm)

R2 (cm)

D1 (m2/s)

D2 (m2/s)

2 × 10−4 7.5 × 10−5 3.375 × 10−5

10 18 24

5 5 5

0.14 0.16 0.18

1 1 1

9 × 10−10 9 × 10−10 9 × 10−10

8 × 10−10 8 × 10−10 8 × 10−10

Phase 1 is dodecane and used as the reference phase and phase 2 is water: the adsorption parameters used in that case are a− = adodecane = 1.1 × 10−7 mol/L and k(12) = Kp−1 = 1.33. a

Figure 4. IFT vs time for a water droplet with TX-100 at initially c0 = 2 × 10−4 M (blue square), 7.5 × 10−5 M (green triangle), and 3.375 × 10−5 M (red circle) in an initially pure dodecane cell (configuration B). Line curves (D1 = 8 × 10−10 m2/s and D2 = 9 × 10−10 m2/s) and color dotted curves (D1 = 1 × 10−10 m2/s and D2 = 1 × 10−10 m2/s) are theoretical models with the parameters shown in Table 3.

Table 3. Experimental and Theoretical Parameters for a Water Droplet of TX-100a experimental data TX-100 conc in droplet (mol/L) 2 7.5 3.375 2 7.5 3.375

× × × × × ×

10−4 10−5 10−5 10−4 10−5 10−5

theoretical model

water droplet volume (μL)

dodecane volume (mL)

R1 (cm)

R2 (cm)

10 18 24 10 18 24

5 5 5 5 5 5

0.14 0.16 0.18 0.14 0.16 0.18

1 1 1 1 1 1

D1 (m2/s) 8 8 8 1 1 1

× × × × × ×

10−10 10−10 10−10 10−10 10−10 10−10

D2 (m2/s) 9 9 9 1 1 1

× × × × × ×

10−10 10−10 10−10 10−10 10−10 10−10

Phase 1 is water and is used as the reference phase, and phase 2 is dodecane: so the adsorption parameters used in that case are a− = awater = 1.5 × 10−7 mol/L and k(12) = Kp = 0.75. a

(CiEj), the presence of convection39 (e.g., thanks to the Marangoni effect40) makes the transfer faster. Thus, the value of the diffusion coefficient found in this model can be considered as an effective diffusion coefficient, which certainly takes in account convective contributions in the bulk phases. The second point concerns the final equilibrium state. Indeed, the experimental final IFT value is lower than expected with the model. Several interpretations can be argued. It may be explained by the limits of the “spherical drop model” because, for long time scales, the droplet is not totally isolated from the syringe needle and a small fraction of surfactants contained at the bottom of the needle is able to move into the droplet. The full quantity of surfactant is then more important than the only amount injected in the droplet. Another explanation can be that

The theoretical model 1 describes well the general behavior of the IFT evolution. It exhibits a steep initial decrease, because of the TX-100 adsorption at the L/L interface, passes through a minimum, and then increases because of the surfactant desorption and transfer in the other phase. Two points can nevertheless be discussed. First, the diffusion coefficients D1 and D2 obtained by fitting the model with the experimental results are higher than expected. Indeed, the TX-100 diffusion coefficient in water was measured to 1.5 × 10−10 m2/s with the Fourier transform pulsed field gradient NMR technique,38 whereas in the theoretical model, the TX-100 diffusion coefficient in dodecane and in water must be set to, respectively, 9 × 10−10 and 8 × 10−10 m2/s to fit correctly the experimental datas. As shown recently for related surfactant 13156



Article

where ka1 is the adsorption rate of TX-100 in phase 1, kd1 is the desorption rate of TX-100 in phase 1, ka2 is the adsorption rate of TX-100 in phase 2, and kd2 is the desorption rate of TX-100 in phase 2. The model, developed here, follows Langmuir kinetics where the adsorption rates are proportional to the surfactant concentrations and the number of vacant adsorption sites at the interface [1 − Γ(t)/Γm], and the desorption rate is proportional to Γ(t). The evolution of surface excess is then given by the equation

the adsorption of TX-100 at the interface is not totally reversible.24 Nevertheless, in this configuration A, the general IFT behavior is well reproduced, and model 1 gives a credible representation of the transfer in that case. The configuration B is performed to study the transfer in the reverse pathway; the TX-100 is dissolved in water and transfers in the organic phase. Experiments are performed for various TX-100 water solution droplets in a cell containing pure dodecane. The experimental and theoretical results from model 1 concerning the configuration B are presented in Figure 4, and parameters are given in Table 3. The time evolution of IFT is quite different in configuration B, especially for a long time range. The IFT increase at a long time scale is slower than in the configuration A. Indeed, for configuration A, the equilibrium state is reached in around 104 s, whereas in configuration B, the equilibrium state is not reached after more than 7 × 104 s. Moreover, the theoretical model 1 does not work with those data. Indeed, for a large class of diffusion coefficient, model 1 cannot fit the experimental data with values in the range from 8 to 1 × 10−10 m2/s (anyway lower than the true diffusion coefficient measured by NMR). Possible explanations could be that the desorption on the L/L interface is, in that case, not only controlled by the diffusion but rather than with a mixed of diffusion and interfacial processes. To go further in the comprehension of this interfacial dynamic, those data need to be interpreted with another theoretical model. Such a model is available for describing the adsorption at the L/L interface with a surfactant soluble in both phases but for the case of two infinite bulk phases.41 For the water to dodecane transfer (configuration B), diffusion has to be completed by an interfacial kinetics at the L/L interface. Thus, to interpret the experimental data, we proposed here a further model, based on the description of the interface transfer. This model is a basic first approach to validate the treatment of both aspects, the diffusion and interface located processes; furthermore, probably more rigorous models need to be developed including chemical aspects, especially for modeling metals phase transfers. The model uses a Langmuir isotherm description of the interfacial processes and a phenomenological description of the diffusion. D. Model 2: Interfacial Process-Controlled Dynamic. This second model adds a description of adsorption/desorption interfacial driven processes on both sides of the interface. The diffusion contribution on each side will be added in the model by introduction a characteristic time of diffusion, which will take into account the time delay to transport the surfactant from the droplet to the interface. A related model was recently proposed by Prpich26 to describe transfer across a gas/liquid interface in the case of infinite bulk phases. Here, this model is modified to describe the transfer across a L/L interface for finite bulk phases. The notation used is as follows: TX1 represents the TX-100 dissolved in phase 1 (which is dodecane in the configuration A or water in configuration B), TX2 represents TX-100 dissolved in phase 2, and TXint is TX-100 adsorbed at the interface. The following chemical equilibrium is now considered: k1a

→

⎛ Γ(t ) ⎞ dΓ = k1aC1(t )⎜1 − ⎟ − k1d Γ(t ) + k1aC2(t ) dt Γm ⎠ ⎝ ⎛ Γ(t ) ⎞ ⎟ − k 2d Γ(t ) ⎜1 − Γm ⎠ ⎝

The concept added, as compared to Prpich model,26 is to consider that the two bulks are a finite system, that is, the concentration of TX-100 in phase 1, C1, and in phase 2, C2, are time dependent and not constant. It means that the concentration evolution of surfactant is calculated for any time in each bulk phase. In that case, this evolution is given in each bulk phase by: ⎤S ⎡ ⎛ dCi Γ(t ) ⎞ = ⎢ −kiaCi(t )⎜1 − ⎟ + kid Γ(t )⎥ ⎥⎦ Vi dt Γm ⎠ ⎝ ⎣⎢

kia kid

=

Γm ai

(15)

where i = 1, 2 and ai and Γm are the constants defined above (eq 1 and 2) and with the value given in Table 1. The initial conditions are C1(0) = c0, Γ(0) = 0, and C2(0) = 0. To summarize the interfacial process part of the model, it consists of three equations (13 and 14 for i = 1, 2) with three unknown quantities Γ(t), C1(t), and C2(t). This model depends on the value of two independent parameters ka1 and ka2, whereas kd1 and kd2 are deduced using eq 15. An additional improvement is added to take into account phenomenologically some diffusional effect in the interfacial dynamic. When the surfactant transfers from phase 1 to phase 2, a diffusion contribution, which represents the time to transport the surfactant from the inside of the droplet to the interface, is added to ka1. Indeed, if τ1eff is defined as the characteristic time of adsorption/desorption of the surfactant in phase 1, we can suppose that τ1eff ≈ τ1 + τdiff, where τ1 is the kinetic characteristic time and τdiff is the diffusion characteristic time. Under those assumptions, the kinetic coefficient becomes ⎛a ⎞ 1 a k1eff =⎜ 1⎟ d ⎝ Γm ⎠ (1/k1 ) + τdiff

k 2d

TX1 d TX int a TX 2 k1 k2 ← ← transfer pathway: from bulk 1 to bulk 2

(14)

where i is the phase (1 or 2), S is the surface of the L/L interface, and Vi are the volume of each phase. For the present study, V1 represents the volume of droplet (typically 0.015 cm3), V2 is the volume of the cell (5 cm3), and S is the surface of the droplet (typically 0.3 cm2) To reach the same equilibrium state as define in section A, the following relation is needed between kai and kdi :

→

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→

(13)

(16)

ka2

and is not suppose to change. The diffusion time in the droplet is estimated to τdiff/droplet ≈ R2/4D ≈ 500 s, where R is the radius of the droplet (≈0.15 cm) and D is the diffusion coefficient. The value taken for D is around 10−9 m2/s and

(12) 13157



Article

Figure 5. (1) Dynamic IFT in configuration A (empty red point) and in configuration B (full red point) with TX-100 at initially c0 = 3.75 × 10−5 M. Black curves are the global fit in each case: line curve for the configuration A and dotted line for the configuration B. (2) Idem with TX-100 at initially c0 = 7.5 × 10−5 M.

formulation.42 This model 2 is nevertheless not totally satisfactory because the global fit, for configuration B, reproduced not well the IFT evolution at a long time range, as we can see in Figure 5. We think that a more accurate simulation with a proper treatment of the diffusion and of the interfacial processes would soften this drawback. In particular, the rapid increase at a long time is a clear signature of an exponential chemical mode, which is unavoidable for a model based on the kinetic equation. In a more accurate treatment, the desorption would probably be smoother because diffusion in the final phase is expected to slow down the process. Anyway, one point must be highlighted about this model 2. It can qualitatively explain the dissymmetry for the IFT evolution in the two cases A or B. Indeed, a gap between kawater and kadodecane is required to induce this dissymmetry in the IFT evolution. With this model, kawater must be higher than the kadodecane to give a faster evolution in configuration A than in configuration B. This difference in the kinetics rate can be interpreted by the presence of a potential energy barrier at the interface, which differs depending the direction of the mass transfer. When leaving the interface to the dodecane phase, it looks like the species need to pass over a higher energy barrier as going the reverse way from interface to the aqueous phase. The most likely explanation is probably a difference in the variation of the speciation depending on the direction. In the case of TX-100, such as a loss of water molecules of the hydrophilic part when going from water to oil can be the reason of this dissymmetrical behavior. Consequently, in configuration A (dodecane to

includes some convection/Marangoni effect (see part C). The new equation of the model is written with keff. The numerical resolution of this system is performed with mathematica software and specially using the NDSolve function. E. Comparison between the Model 2 and the Experimental Data. The experimental data are now compared with model 2. The two independent parameters of the model, kawater and kadodecane, were adjusted to reproduce the experimental data for all cases, configurations A and B. IFT calculated with model 2 is presented in Figure 5. The global fit gives the following values for the real adsorption and desorption rates (not the effective), kdwater = 0.0065 s−1, kawater = 0.0001 m s−1, kddodecane = 0.0014 s−1, and kadodecane =0.00003 m s−1. As this model does not take proper account of diffusion, those values have to be considered as an order of magnitude of the adsorption/desorption rates. Nevertheless, the range of acceptable adsorption and desorption rates, with regard to the experimental data, is very narrow, because it is a global fit considering two experimental very different set of data. Indeed, the values of those parameters are strongly constraint to explain simultaneously the two cases. For instance, if kddodecane is taken low to correctly adjust the configuration B, it cannot give a good fit in configuration A. Moreover, those rates can be compared with those of similar surfactant (CiEj) where ka and kd were deduced by applying a mixed kinetics and diffusion controlled dynamics at the air/ water interface.42,43 It was found in this case for C12E6 a kd to 1.4 × 10−5 m s −1 and ka to 1.4 × 10−4 s−1 in a Frumkin kinetic 13158



Article

Notes

water), the reaction is mainly controlled by diffusion, whereas in configuration B (water to dodecane), the interfacial dynamics is the predominant process. Those studies show that the TX-100 transfer across the liquid−liquid interface does not follow a simple mechanism, so the transition rates determined from this analysis must be consider only as effective parameter values.

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We thank J. J. Molina for help with Fortran numerical calculations. We are grateful to Thomas Zemb, Pierre Bauduin, and Pierre-François Brevet for stimulating discussions. This work was supported by the RBPCH project from the Nuclear Energy Division of CEA with partial financial support from the CNRS under the PACEN/GUTEC Programme.

■

CONCLUSION A first static study of the ternary system water/dodecane/TX100 system at equilibrium and for surfactant concentrations below the critical micellar concentration was carried out by exploring UV−visible and IFT measurements. When such a system is prepared out of equilibrium, the IFT measurements can monitor the interfacial population evolution during the transfer of TX-100 across the interface until equilibrium is reached. This evolution depends strongly on the phase where the TX-100 is initially dispersed. Indeed, the IFT evolution is faster when TX-100 is transferred from dodecane to water (configuration A) than when the TX-100 is transferred from water to dodecane (configuration B). The comparison between the experimental data and the theoretical model 1, based on diffusion-controlled adsorption/desorption, shows relatively good agreement in the configuration A. In the configuration B, this model 1 cannot explain the interfacial dynamic, which is slower than expected with this model. To interpret this difference in the IFT evolution, a second model where the adsorption/desorption is also controlled by the interfacial processes is applied. This model 2 permits us to extract the adsorption and desorption rates and can qualitatively reproduce this difference in the IFT behavior. Those studies demonstrate that IFT evolution depends on both diffusion and interfacial processes during transfer of surfactant across the L/L interface. In some cases, the interfacial processes can be ignored (configuration A) and diffusion can itself correctly explain the IFT variation. In other cases (configuration B), diffusion only is not sufficient to explain the interfacial activity, and important local effects such as interfacial molecular reorganizations or associations have to be taken into account. One main result of this work is that some systems can show a significant difference in the kinetics depending on the directions of the mass transfer. This dissymmetrical behavior finds probably its origin in a potential that can be assimilated to an activation energy, which is not the same when moving from dodecane to water and when moving from water to dodecane. To go to a more accurate description of the overall mass transfer kinetic, there is still a need to introduce chemical aspects in the description of the interfacial processes, leading to a more comprehensive characterization of the various mechanisms of the transfer at the molecular level.

■

■

(1) Volkov, A. G. Liquid Interfaces in Chemical, Biological, and Pharmaceutical Applications; Marcel Dekker: New York, 2001. (2) Fiamegos, Y. C.; Stalikas, C. D. Anal. Chim. Acta 2005, 550 (1− 2), 1−12. (3) Reymond, F.; Fermin, D.; Lee, H. J.; Girault, H. H. Electrochim. Acta 2000, 45 (15−16), 2647−2662. (4) Smith, R. D.; Loo, J. A.; Edmonds, C. G.; Barinaga, C. J.; Udseth, H. R. Anal. Chem. 1990, 62 (9), 882−899. (5) Rydberg, J.; Cox, M.; Musikas, C.; Choppin, G. R. Solvent Extraction Principles and Practice; Marcel Dekker: New York, 2004. (6) He, W. W.; Liao, W. P.; Wang, W. W.; Li, D. Q.; Niu, C. J. J. Chem. Technol. Biotechnol. 2008, 83 (9), 1314−1320. (7) Liu, J. J.; Wang, Y. L.; Li, D. Q. Sep. Sci. Technol. 2008, 43 (2), 431−445. (8) (a) Lewis, F. W.; Harwood, L. M.; Hudson, M. J.; Drew, M. G. B.; Desreux, J. F.; Vidick, G.; Bouslimani, N.; Modolo, G.; Wilden, A.; Sypula, M.; et al. J. Am. Chem. Soc. 2011, 133 (33), 13093−13102. (b) Simonin, J. P.; Hendrawan, H. Effect of a salt on the kinetics of solute transfer at a free liquid/liquid interface. J. Phys. Chem. B 2000, 104 (30), 7163−7170. (9) Chao, L.; Daniel, S. J. Am. Chem. Soc. 2011, 133 (39), 15635− 15643. (10) Nichols, K. P.; Pompano, R. R.; Li, L.; Gelis, A. V.; Ismagilov, R. F. J. Am. Chem. Soc. 2011, 133 (39), 15721−15729. (11) Haslam, S.; Croucher, S. G.; Hickman, C. G.; Frey, J. G. Phys. Chem. Chem. Phys. 2000, 2 (14), 3235−3245. (12) Martin-Gassin, G.; Gassin, P. M.; Couston, L.; Diat, O.; Benichou, E.; Brevet, P. F. Phys. Chem. Chem. Phys. 2011, 13 (43), 19580−19586. (13) Dukhin, S. S. Dynamics of Adsorption at Liquid Interfaces: Theory, Experiments, Application; Kretzschmar, G., Ed.; Elsevier: Amsterdam, 1995; Vol. 1. (14) Ferrari, M.; Liggieri, L.; Ravera, F.; Amodio, C.; Miller, R. J. Colloid Interface Sci. 1997, 186 (1), 40−45. (15) Ravera, F.; Ferrari, M.; Liggieri, L. Adv. Colloid Interface Sci. 2000, 88 (1−2), 129−177. (16) Janczuk, B.; Bruque, J. M.; Gonzalezmartin, M. L.; Doradocalasanz, C. Langmuir 1995, 11 (11), 4515−4518. (17) Fainerman, V. B.; Lylyk, S. V.; Aksenenko, E. V.; Makievski, A. V.; Petkov, J. T.; Yorke, J.; Miller, R. Colloids Surf., A 2009, 334 (1−3), 1−7. (18) Fainerman, V. B.; Lylyk, S. V.; Aksenenko, E. V.; Liggieri, L.; Makievski, A. V.; Petkov, J. T.; Yorke, J.; Miller, R. Colloids Surf., A 2009, 334 (1−3), 8−15. (19) Lin, S. Y.; McKeigue, K.; Maldarelli, C. Aiche J. 1990, 36 (12), 1785−1795. (20) Vanhunsel, J.; Joos, P. Colloids Surf. 1987, 24 (2−3), 139−158. (21) Horozov, T.; Arnaudov, L. J. Colloid Interface Sci. 2000, 222 (1), 146−155. (22) Fainerman, V. B.; Zholob, S. A.; Miller, R. Langmuir 1997, 13 (2), 283−289. (23) Zholob, S. A.; Fainerman, V. B.; Miller, R. J. Colloid Interface Sci. 1997, 186 (1), 149−159. (24) Fainennan, V. B.; Miller, R.; Ferri, J. K.; Watzke, H.; Leser, M. E.; Michel, M. Adv. Colloid Interface Sci. 2006, 123, 163−171.

ASSOCIATED CONTENT

* Supporting Information S

RNM spectra of TX-100, UV/visible calibration for the titration, IFT time evolution for equilibrate system, numerical resolution for the model 1, and the validation of the Fortran code. This material is available free of charge via the Internet at http://pubs.acs.org.

■

REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 13159



Article

(25) Liggieri, L.; Ravera, F.; Ferrari, M.; Passerone, A.; Miller, R. J. Colloid Interface Sci. 1997, 186 (1), 46−52. (26) Prpich, A. M.; Biswas, M. E.; Chen, P.. J. Phys. Chem. C 2008, 112 (7), 2522−2528. (27) Yuan, H. Z.; Miao, X. J.; Zhao, S.; Shen, L. F.; Yu, J. Y.; Du, Y. R. Magn. Reson. Chem. 2001, 39 (1), 33−37. (28) Zeppieri, S.; Rodríguez, J.; López de Ramos, A. L. J. Chem. Eng. Data 2001, 46 (5), 1086−1088. (29) Song, B. H.; Springer, J. J. Colloid Interface Sci. 1996, 184 (1), 64−76. (30) Song, B. H.; Springer, J. J. Colloid Interface Sci. 1996, 184 (1), 77−91. (31) Blin, J. L.; Grignard, J.; Zimny, K.; Stebe, M. J. Colloids Surf., A 2007, 308 (1−3), 71−78. (32) Blom, A.; Warr, G. G.; Wanless, E. J. Langmuir 2005, 21 (25), 11850−11855. (33) Bauduin, P.; Testard, F.; Berthon, L.; Zemb, T. Phys. Chem. Chem. Phys. 2007, 9 (28), 3776−3785. (34) Ravera, F.; Ferrari, M.; Liggieri, L.; Miller, R.; Passerone, A. Langmuir 1997, 13 (18), 4817−4820. (35) Gobel, J. G.; Joppien, G. R. J. Colloid Interface Sci. 1997, 191 (1), 30−37. (36) Chang, C. H.; Franses, E. I. Colloids Surf., A 1995, 100, 1−45. (37) Yang, C.; Gu, Y. Langmuir 2004, 20 (6), 2503−2511. (38) Fang, X. W.; Zhao, S.; Mao, S. Z.; Yu, J. Y.; Du, Y. R. Colloid Polym. Sci. 2003, 281 (5), 455−460. (39) Moorkanikkara, S. N.; Blankschtein, D. Langmuir 2009, 25 (3), 1434−1444. (40) Berg, S. Phys. Fluids 2009, 21 (3), 12. (41) Ravera, F.; Liggieri, L.; Passerone, A.; Steinchen, A. J. Colloid Interface Sci. 1994, 163 (2), 309−314. (42) Pan, R. N.; Green, J.; Maldarelli, C. J. Colloid Interface Sci. 1998, 205 (2), 213−230. (43) Moorkanikkara, S. N.; Blankschtein, D. J. Colloid Interface Sci. 2006, 302 (1), 1−19.

13160


Dodecane Interface

Recommend Documents