Open access peer-reviewed chapter

Pseudophase Model in Microemulsions

Written By

Antonio Cid, Aangel Acuña, Manuel Alonso-Ferrer, Gonzalo Astray, Luis García-Río, Jesus Simal-Gándara and Juan C. Mejuto

Submitted: May 22nd, 2018 Reviewed: January 10th, 2019 Published: April 11th, 2019

DOI: 10.5772/intechopen.84295

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Abstract

The kinetic behaviours in microemulsions can be easily modelled using an extension of the pseudophase model previously developed for micellar catalysis. This model considers that the microheterogeneous media can be considered as the sum of different conventional reaction media, where the reagents are distributed and in which the reaction can occur simultaneously. The reaction rate observed in the microheterogeneous system will be the sum of the velocities in each one of the pseudophases. This use can be considered as an extension of the pseudophase model, which has been developed for the quantitative analysis of nitrosation reactions in AOT/isooctane/water microemulsions and has been applied successfully in the literature in a large variety of chemical reactions.

Keywords

  • microemulsions
  • reverse micelles
  • kinetic model
  • pseudophase model

1. Introduction

The use of microemulsions, in particular, colloidal self-aggregates, and in general, as reaction media [1] makes the application of kinetic models necessary for the quantitative interpretation of the observed results. In this sense, a simple thermodynamic model was developed for its application in micelles [2] and it was called the pseudophase model [3]. This model was successfully applied through extensions to different microheterogeneous systems over the last 50 years [4, 5, 6, 7, 8, 9, 10].

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2. The pseudophase model

This model considers that the micellar system can be considered as the sum of two conventional reaction media, the continuous pseudophase and the micellar pseudophase, where the reagents are distributed and in which the reaction can occur simultaneously (see Figure 1).

Figure 1.

Pseudophase model applied to micellar aggregates as reaction media.

In this figure, Aand Bare the reagents, kis the kinetic constant and the subscripts wand mdenotes the reaction loci(wcorresponds to the continuous pseudophase and mis the micellar pseudophase). Finally, KAand KBare the distribution coefficients of both reactants between different pseudophases.

The model considers that the reaction rate observed in the microheterogeneous system will be the sum of the velocities in each one of the pseudophases, and it can be expressed as shown in the following equations assuming a first-order reaction for each reactant:

vT=vw+vmE1
vT=kobsATBTE2
vw=kwAwBwE3
vm=kmAmBmE4
k2ATBT=kwAwBw+kmAmBmE5

The mass balance on both pseudophases and the consideration of the distribution coefficients between them allow us to establish the existing relationship between the total concentrations of the reactants and the concentrations in each of the pseudophases considered.

AT=Aw+AmE6
BT=Bw+BmE7
KA=AmAwDnE8
KB=BmBwDnE9

In Eqs. (8) and (9), Dndenotes the concentration of surfactant micellized and [Dn] = [D]-CMC (where Dis the total surfactant concentration and CMCis the critical micellar concentration). Using Eqs. (8) and (9), the following equations can be written:

Am=KAAwDnE10
Bm=KBBwDnE11
AT=Aw+KAAwDnE12
BT=Bw+KBBwDnE13
Aw=AT1+KADnE14
Bw=BT1+KBDnE15
Am=ATKADn1+KADnE16
Bm=BTKBDn1+KBDnE17

Using Eqs. (14)(17) on Eq. (5), the following expressions can be deduced (Eq. (18)(21)):

k2ATBT=kwAT1+KADnBT1+KBDn+kmATKADn1+KADnBTKBDn1+KBDnE18
k2ATBT=kw11+KADn11+KBDnATBT+kmKADn1+KADnKBDn1+KBDnATBTE19
k2=kw11+KADn11+KBDn+kmKADn1+KADnKBDn1+KBDnE20
k2=kw11+KADn1+KBDn+kmKAKBDn21+KBDn1+KADnE21

According to the pseudophase model, each pseudophase is evenly distributed in the total micellar dispersion volume. The value of rate constanst must be corrected taking into account the molar volume of each pseudophase to compare de intrinsic reactivity in the two different domains due to this reactants distribution between both pseudophases [10].

Equation (21) can be simplified according to the distributions of A and B, and the presence of chemical reaction in one or both pseudophases. This model predicts the catalysis or inhibition processes with success due to the compartmentalising effect of these colloidal aggregates [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28]. However, this model must be expanded to take into account possible ion exchange processes between the continuous medium and the micelle, which give rise to more complicated expressions [29]. In some cases, it is necessary to resort to Poisson-Boltzmann distribution to evaluate the concentration of the different ions in the Stern and Gouy-Chapman layers to be able to model the ion exchange process between the continuous medium and the micellar electric double layer [30].

The pseudophase model applied to micelles has also been satisfactory for the analysis of the kinetic results in more complex micellar systems such as mixed micellar-cyclodextrin systems [31, 32, 33, 34, 35, 36, 37] or pseudo-micellar humic acids aggregates [38, 39, 40, 41, 42].

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3. The pseudophase model in microemulsions

The pseudophase model was first extended by our research group in order to quantitatively analyse the kinetic behaviour of nitrosation reactions in microemulsions based on AOT [43, 44]. Afterwards, this extended model, with minor corrections, has been satisfactorily tested on microemulsions covering all possible cases [45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55] such as: (i) different chemical reactions (ionic or non-ionic), (ii) reactants distributed throughout the different hydrophobic domains or (iii) with different reaction loci.

Unlike in normal micelles, where we recognised two different domains (micelles and bulk water), in a microemulsion system three domains can be found: (i) the microdroplets of the dispersed phase, (ii) the continuous phase and (iii) the surfactant film (or surfactant + cosurfactant) that stabilises the system. Due to this, in this case, three pseudophases will be considered, taking into account the same proposed considerations for the micellar model.

We will assume that the reactants can be located in each of these three pseudophases, and their distribution will be governed by the distribution coefficients defined in an analogous way to that proposed in micelles. The chemical reaction can take place in each of the three pseudophases. In this way, the model can be explained according to Figure 2, where Aand Bare the reagents, kcorresponds to the kinetic constant and the subscripts d, iand cdenotes the loci (ccorresponds to the continuous pseudophase, dwith the dispersed pseudophase and iwith the surfactant film -or interphase-). KA,idand KB,idare the distribution coefficients of both reactants between the interphase and the dispersed phase. KA,icand KB,iccorrespond to distribution coefficients of both reactants between the interphase and the continuous phase.

Figure 2.

Pseudophase model applied to microemulsions reaction media.

As in the case of micelles, the reaction rate observed in the microemulsions will be the sum of the velocities in each one of the pseudophases as it shown in the following equations (as in the case of micelles -vide supra-, assuming a first order reaction for each reactant):

vT=vc+vi+vdE22
vT=kobsATBTE23
vd=kdAdBdE24
vi=kiAiBiE25
vc=kcAcBcE26
k2ATBT=kdAdBd+kiAiBi+kcAcBcE27

As quoted above, the mass balance on the three pseudophases and the consideration of the distribution coefficients between them allow us to establish the existing relationship between the total concentrations of the reactants and the concentrations in each of the pseudophases considered

AT=Ac+Ai+AdE28
BT=Bc+Bi+BdE29
KA,id=AiDisAdDnE30
KB,ic=BiCBwDnE31

where [C] is the continuous phase concentration and [Dn] corresponds to the concentration of surfactant in the microemulsion. In the case of micelles, [Dn] is obtained as [Dn] = [D]-CMC; but in the case of microemulsions, CMC = 0. It means that the surfactant concentration in the microemulsion is equal to the total surfactant concentration. Similar expressions can be obtained for the partition coefficients between the dispersed pseudophase and the interphase. In this case, [Dis] corresponds to the dispersed phase concentration.

KA,id=AiDisAdDnE32
KB,id=BiDisBdDnE33

The previous equations (Eqs. (30)(33)) can be rewritten using the characteristic parameters of microemulsions: zand w. Both of them are mole ratios related with the microemulsion geometry. The w ratio is the molar ratio between the disperse phase concentration and the surfactant concentration, and z is the molar ratio between continuous phase concentration and the surfactant concentration (Eqs. (34) and (35)). The w ratio is directly proportional to the droplet radius and z is inversely proportional to the number of microdroplets of the dispersed phase in the microemulsion.

w=DisDnE34
z=CDnE35

Hence,

KA,id=AiAdwE36
KB,id=BiBdwE37
KA,ic=AiAczE38
KB,ic=BiBczE39

Using Eqs. (28), (29) and (36)(39), the following equations can be written:

Ad=AiwKA,idE40
Bd=BiwKB,idE41
Ac=AizKA,icE42
Bc=BizKB,icE43
AT=Ai+AiwKA,id+AizKA,icE44
BT=Bi+BiwKB,id+BizKB,icE45
Ai=AT1+wKA,id+zKA,icE46
Bi=BT1+wKB,id+zKB,icE47
Ad=wKA,idAT1+wKA,id+zKA,icE48
Bd=wKB,idBT1+wKB,id+zKB,icE49
Ac=zKA,icAT1+wKA,id+zKA,icE50
Bc=zKB,icBT1+wKB,id+zKB,icE51

Then, using Eqs. (46)(51), the following expressions are obtained:

k2ATBT=kdwKA,idAT1+wKA,id+zKA,icwKB,idBT1+wKB,id+zKB,ic+
+ kiAT1+wKA,id+zKA,icBT1+wKB,id+zKB,ic+
+ kczKA,icAT1+wKA,id+zKA,iczKB,icBT1+wKB,id+zKB,icE52
k2=kdwKA,id11+wKA,id+zKA,icwKB,id11+wKB,id+zKB,ic+
+ ki11+wKA,id+zKA,ic11+wKB,id+zKB,ic+
+ kczKA,ic11+wKA,id+zKA,iczKB,ic11+wKB,id+zKB,icE53
k2=kdw2KA,idKB,id11+wKA,id+zKA,ic11+wKB,id+zKB,ic+
+ ki11+wKA,id+zKA,ic11+wKB,id+zKB,ic+
+ kcz2KA,icKB,ic11+wKA,id+zKA,ic11+wKB,id+zKB,icE54
k2=KA,icKB,icw2kdKA,idKA,ic+KA,icw+KA,idzKB,idKB,ic+KB,icw+KB,idz+
+KA,idKA,icKB,idKB,ickiKA,idKA,ic+KA,icw+KA,idzKB,idKB,ic+KB,icw+KB,idz+
+KA,idKB,idz2kcKA,idKA,ic+KA,icw+KA,idzKB,idKB,ic+KB,icw+KB,idzE55
k2=KA,icKB,icw2kd+KA,idKA,icKB,idKB,icki+KA,idKB,idz2kcKA,idKA,ic+KA,icw+KA,idzKB,idKB,ic+KB,icw+KB,idzE56

This expression (Eq. (56)) can be simplified considering pseudo-first order conditions, and, of course, taking into account the reagents partitions and the loci of reaction (see Table 1).

ReactionA PartitionB PartitionReaction LociRef.
DICDICDIC
HydrolysisNitrophenyl Acetate (A) + OH (B)[56]
Cristal Violet (A) + OH (B)[57]
Malachite Green (A) + OH (B)[57]
Sodium nitroprusside (A) + OH (B)[58]
Carbofuran (A) + OH (B)[46]
3-hydroxy-carbofuran (A) + OH (B)[46]
3-keto-carbofuran (A) + OH (B)[46]
NitrosationPiperazine (A) + N-Methyl-N-nitroso-p-toluene sulfonamide (B)[43]
N-Methyl-benzyl amine (A) + N-Methyl-N-nitroso-p-toluene sulfonamide (B)[43]
Methyl-ethyl amine (A) + N-Methyl-N-nitroso-p-toluene sulfonamide (B)[48]
Methly-butyl amine (A) + N-Methyl-N-nitroso-p-toluene sulfonamide (B)[48]
Methyl-hexyl amine (A) + N-Methyl-N-nitroso-p-toluene sulfonamide (B)[48]
Methyl-octyl amine (A) + N-Methyl-N-nitroso-p-toluene sulfonamide (B)[48]
Methyl-dodecil amine (A) + N-Methyl-N-nitroso-p-toluene sulfonamide (B)[48]
N-Methyl-benzyl amine (A) + Ethoxy-ethyl nitrite (B)[44]
N-Methyl-benzyl amine (A) + Bromo-ethyl nitrite (B)[44]
Piperidine (A) + N-Methyl-N-nitroso-p-toluene sulfonamide (B)[43]
NitrosationDimiethylamine (A) + N-Methyl-N-nitroso-p-toluene sulfonamide (B)[43]
Morphonile (A) + N-Methyl-N-nitroso-p-toluene sulfonamide (B)[43]
Pyrrolidine (A) + N-Methyl-N-nitroso-p-toluene sulfonamide (B)[43]
Piperazine (A) + Ethoxy-ethyl nitrite (B)[44]
Piperazine (A) + Bromo-ethyl nitrite (B)[44]
Morpholine (A) + Ethoxy-ethyl nitrite (B)[44]
Morpholine (A) + Bromo-ethyl nitrite (B)[44]
AminolysisSarcosine (A) + Nitrophenyl Acetate (B)[49]
Piperazine (A) + Nitrophenyl Acetate (B)[49]
Glycine (A) + Nitrophenyl Acetate (B)[50]
N-decyl amine (A) + + Nitrophenyl Acetate (B)[49]
N-methyl-benzyl amine (A) + Nitrophenyl Acetate (B)[51]
Morpholine (A) + Nitrophenyl Acetate (B)[59]
N-butylamine (A) + Nitrophenyl caprate (B)[60]
Michael additionPiperazine (A) + N-ethylmaleimide (B)[51]
SolvólisisBenzoyl chloride (A) + H2O (B)[53]
4-Methoxy-benzoyl chloride (A) + H2O (B)[53]
Diphenylmethyl chloride (A) + H2O (B)[53]

Table 1.

Examples of reactions in microemulsions satisfactorily modelled with the pseudophase model.

Dand Ccorrespond to the dispersed or the continuous phase, respectively, Idenotes the surfactant film. Reactions in w/o microemulsions of AOT/isooctane/water.

Finally, to compare the obtained results, as quoted above for micelles model -vide supra-, the rate constant values must be corrected taking into account each pseudophase molar volume because the pseudophase model considers that each pseudophase is evenly distributed in the total microemulsion volume [47].

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4. Conclusions

The presented model is capable of modelling, as shown in Table 1, all the possible circumstances that can occur when the microemulsion is used as a chemical nanoreactor. In all the cases, the adjustment of the experimental data to the model is satisfactory, which shows us that despite its simplicity it presents a great versatility.

We must also indicate that it has not only been applied to micellar systems and microemulsions but also, with satisfactory results, to kinetic processes in other colloidal aggregates such as vesicles [61, 62].

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Acknowledgments

Financial support from Xunta de Galicia is gratefully acknowledged. Astray G. would like to give his warm thanks to Xunta de Galicia, Consellería de Cultura, Educación e Ordenación Universitaria for the post-doctoral grant B, POS-B/2016/001, which he received from them. Cid A acknowledges the post-doctoral grant SFRH/BD/78849/2011 granted to Requimte and UID/MULTI/04378/2013 granted to Unidade de Cien̂cias Biomoleculares Aplicadas (UCIBIO), both from the Portuguese Foundation for Science and Technology.

This chapter is dedicated to Professor Julio Casado Linarejos (sit tivi terra levis) who taught us chemistry and, what really matters, to be better people.

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Written By

Antonio Cid, Aangel Acuña, Manuel Alonso-Ferrer, Gonzalo Astray, Luis García-Río, Jesus Simal-Gándara and Juan C. Mejuto

Submitted: May 22nd, 2018 Reviewed: January 10th, 2019 Published: April 11th, 2019