Table of Contents

Related Titles

Title Page

Copyright

Preface

List of Contributors

Chapter 1: Emulsion Formation, Stability, and Rheology

1.1 Introduction

1.2 Industrial Applications of Emulsions

1.3 Physical Chemistry of Emulsion Systems

1.4 Thermodynamics of Emulsion Formation and Breakdown

1.5 Interaction Energies (Forces) between Emulsion Droplets and Their Combinations

1.6 Adsorption of Surfactants at the Liquid/Liquid Interface

1.7 Selection of Emulsifiers

1.8 Creaming or Sedimentation of Emulsions

1.9 Flocculation of Emulsions

1.10 Ostwald Ripening

1.11 Emulsion Coalescence

1.12 Rheology of Emulsions

1.13 Bulk Rheology of Emulsions

1.14 Experimental η_r − ϕ Curves

1.15 Viscoelastic Properties of Concentrated Emulsions

References

Chapter 2: Emulsion Formation in Membrane and Microfluidic Devices

2.1 Introduction

2.2 Membrane Emulsification (ME)

2.3 Microfluidic Junctions and Flow-Focusing Devices

2.4 Microfluidic Devices with Parallel Microchannel Arrays

2.5 Glass Capillary Microfluidic Devices

2.6 Application of Droplets Formed in Membrane and Microfluidic Devices

2.7 Conclusions

Acknowledgments

References

Chapter 3: Adsorption Characteristics of Ionic Surfactants at Water/Hexane Interface Obtained by PAT and ODBA

3.1 Introduction

3.2 Experimental Tools

3.3 Theory

3.4 Results

3.5 Summary

Acknowledgments

References

Chapter 4: Measurement Techniques Applicable to the Investigation of Emulsion Formation During Processing

4.1 Introduction

4.2 Online Droplet Size Measurement Techniques

4.3 Techniques Investigating Droplet Coalescence

4.4 Concluding Remarks

References

Chapter 5: Emulsification in Rotor–Stator Mixers

5.1 Introduction

5.2 Classification and Applications of Rotor–Stator Mixers

5.3 Engineering Description of Emulsification/Dispersion Processes

5.4 Advanced Analysis of Emulsification/Dispersion Processes in Rotor–Stator Mixers

5.5 Conclusion

5.6 Nomenclature

References

Chapter 6: Formulation, Characterization, and Property Control of Paraffin Emulsions

6.1 Introduction

6.2 Surfactant Systems Used in Formulation of Paraffin Emulsions

6.3 Formation and Characterization of Paraffin Emulsions

6.4 Control of Particle Size

6.5 Stability of Paraffin Emulsions

6.6 Conclusions

Acknowledgments

References

Chapter 7: Polymeric O/W Nano-emulsions Obtained by the Phase Inversion Composition (PIC) Method for Biomedical Nanoparticle Preparation

7.1 Introduction

7.2 Phase Inversion Emulsification Methods

7.3 Aspects on the Choice of the Components

7.4 Ethylcellulose Nano-Emulsions for Nanoparticle Preparation

7.5 Final Remarks

Acknowledgments

References

Chapter 8: Rheology and Stability of Sterically Stabilized Emulsions

8.1 Introduction

8.2 General Classification of Polymeric Surfactants

8.3 Interaction between Droplets Containing Adsorbed Polymeric Surfactant Layers: Steric Stabilization

8.4 Emulsions Stabilized by Polymeric Surfactants

8.5 Principles of Rheological Techniques

8.6 Rheology of Oil-in-Water (O/W) Emulsions Stabilized with Poly(Vinyl Alcohol)

References

Index

Related Titles

Tadros, T. F.

Dispersion of Powders

in Liquids and Stabilization of Suspensions

2012

ISBN: 978-3-527-32941-0

Tadros, T. F. (ed.)

Self-Organized Surfactant Structures

2010

ISBN: 978-3-527-31990-9

Tadros, T. F. (ed.)

Colloids and Interface Science Series

6 Volume Set

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ISBN: 978-3-527-31461-4

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ISBN: 978-3-527-32003-5

Wilkinson, K. J., Lead, J. R. (eds.)

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ISBN: 978-0-470-02432-4

The Editor

Prof. Dr. Tharwat F. Tadros

89 Nash Grove Lane

Wokingham

Berkshire RG40 4HE

United Kingdom

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Preface

This book is based on selection of some papers from the Fifth World Congress on Emulsions that was held in Lyon, in October 2010. These series of World congresses emphasize the importance of emulsions in industry, including food, cosmetics, pharmaceuticals, agrochemicals, and paints. Following each meeting, a number of topics were selected, the details of which were subsequently published in the journals, Colloids and Surfaces and Advances in Colloid and Interface Science. The selected papers of the fourth Congress (2006) were published by Wiley-VCH (Germany).

This book contains selected topics from the Fifth World Congress, the title of which “Emulsion Formation and Stability” reflects the importance of emulsification techniques, the production of nanoparticles for biomedical applications as well as the importance of application of rheological techniques for studying the interaction between the emulsion droplets.

Chapter 1 describes the principles of emulsion formation, selection of emulsifiers, and control of emulsion stability. A section is devoted to the rheology of emulsions, including both interfacial rheology as well as the bulk rheology of emulsions. Chapter 2 deals with emulsion formation using membrane and microfluidics devices. In membrane emulsification (ME), the system is produced by injection of a pure disperse phase or a premix of a coarse emulsion into the continuous phase through a microporous membrane. Hydrophobic membranes are used to produce water-in-oil (W/O) emulsions, whereas hydrophilic membranes are used to produce oil-in-water (O/W) emulsions. In microfluidics, the combined two-phase flow is forced through a small orifice that allows one to obtain monodisperse droplets. Chapter 3 deals with adsorption of ionic surfactants at the hexane/water interface using the profile analysis technique (PAT) and the oscillating drop and bubble analyzer (ODBA). Theoretical models were used to analyze the adsorption results. Chapter 4 describes the various techniques that can be applied to investigate emulsion formation during processing. The effect of different emulsion techniques on the droplet size distribution was investigated using various methods such as light diffraction and ultrasound. Particular attention was given to online droplet size measurements. Chapter 5 deals with emulsification using rotor–stator mixers that are commonly used in industry, both in laboratory and large-scale production of emulsions. The various types of rotor–stator mixers are described. The selection of a rotor–stator mixer for a specific end product depends on the required droplet size distribution and the scale of the process. Chapter 6 describes the formulation, characterization, and property control of paraffin emulsions. The industrial application of paraffin emulsions is described highlighting the property of paraffin and method of preparation. The surfactants used in formation of paraffin emulsions are described in terms of their phase behavior. The control of particle size and its distribution of the resulting emulsion are described at a fundamental level. Chapter 7 describes polymeric O/W nanoemulsions produced by the phase inversion composition (PIC) method with application of the resulting nanoparticles in biomedicine. A description of the PIC method is given with reference to the aspects of choice of the components. The production of ethyl cellulose nanoparticles is described. Chapter 8 gives a detailed analysis of the rheology and stability of sterically stabilized emulsions. A section is devoted to the general classification of polymeric surfactants followed by discussion of the theory of sterically stabilized emulsions. The application of block and graft copolymers for preparation of highly stable emulsions is described. The principles of the various rheological techniques that can be applied to study the interaction between droplets in an emulsion are described. Various types of sterically stabilized emulsions are described: O/W emulsions stabilized with an A-B-A block copolymer of poly(ethylene oxide) (PEO, A) and poly(propylene oxide) (PPO, B); partially hydrolyzed poly(vinyl acetate) (PVAc); and W/O emulsions stabilized with an A-B-A block copolymer of poly(hydroxyl stearic acid) (PHS, A) and PEO (B).

On the basis of the above descriptions and details, it is clear that this book covers a wide range of topics: both fundamental and applied. It also highlights the engineering aspects of emulsion production and their characterization, both in the laboratory and during manufacture. It is hoped that this book will be of great help to emulsion research scientists, in both academia and industry.

I would like to thank the organizers – and in particular Dr Jean-Erik Poirier and Dr Alain Le Coroller – for giving me the opportunity to attend the Fifth World Congress and to edit this book.

October 2012

Tharwat F. Tadros

List of Contributors

Goran T. Vladisavljevi

Loughborough University

Chemical Engineering Department

Ashby Road

Loughborough

Leicestershire

LE11 3TU

UK

Chapter 1

Emulsion Formation, Stability, and Rheology

Tharwat F. Tadros

1.1 Introduction

Emulsions are a class of disperse systems consisting of two immiscible liquids [1–3]. The liquid droplets (the disperse phase) are dispersed in a liquid medium (the continuous phase). Several classes may be distinguished: oil-in-water (O/W), water-in-oil (W/O), and oil-in-oil (O/O). The latter class may be exemplified by an emulsion consisting of a polar oil (e.g., propylene glycol) dispersed in a nonpolar oil (paraffinic oil) and vice versa. To disperse two immiscible liquids, one needs a third component, namely, the emulsifier. The choice of the emulsifier is crucial in the formation of the emulsion and its long-term stability [1–3].

Emulsions may be classified according to the nature of the emulsifier or the structure of the system. This is illustrated in Table 1.1.

Table 1.1 Classification of Emulsion Types

1.1.1 Nature of the Emulsifier

The simplest type is ions such as OH⁻ that can be specifically adsorbed on the emulsion droplet thus producing a charge. An electrical double layer can be produced, which provides electrostatic repulsion. This has been demonstrated with very dilute O/W emulsions by removing any acidity. Clearly that process is not practical. The most effective emulsifiers are nonionic surfactants that can be used to emulsify O/W or W/O. In addition, they can stabilize the emulsion against flocculation and coalescence. Ionic surfactants such as sodium dodecyl sulfate (SDS) can also be used as emulsifiers (for O/W), but the system is sensitive to the presence of electrolytes. Surfactant mixtures, for example, ionic and nonionic, or mixtures of nonionic surfactants can be more effective in emulsification and stabilization of the emulsion. Nonionic polymers, sometimes referred to as polymeric surfactants, for example, Pluronics, are more effective in stabilization of the emulsion, but they may suffer from the difficulty of emulsification (to produce small droplets) unless high energy is applied for the process. Polyelectrolytes such as poly(methacrylic acid) can also be applied as emulsifiers. Mixtures of polymers and surfactants are ideal in achieving ease of emulsification and stabilization of the emulsion. Lamellar liquid crystalline phases that can be produced using surfactant mixtures are very effective in emulsion stabilization. Solid particles that can accumulate at the O/W interface can also be used for emulsion stabilization. These are referred to as Pickering emulsions, whereby particles are made partially wetted by the oil phase and by the aqueous phase.

1.1.2 Structure of the System

Several breakdown processes may occur on storage depending on particle size distribution and density difference between the droplets and the medium. Magnitude of the attractive versus repulsive forces determines flocculation. Solubility of the disperse droplets and the particle size distribution determine Ostwald ripening. Stability of the liquid film between the droplets determines coalescence. The other process is phase inversion.

1.1.3 Breakdown Processes in Emulsions

The various breakdown processes are illustrated in Figure 1.1. The physical phenomena involved in each breakdown process are not simple, and it requires analysis of the various surface forces involved. In addition, the above-mentioned processes may take place simultaneously rather than consecutively and this complicates the analysis. Model emulsions, with monodisperse droplets, cannot be easily produced, and hence, any theoretical treatment must take into account the effect of droplet size distribution. Theories that take into account the polydispersity of the system are complex, and in many cases, only numerical solutions are possible. In addition, measurements of surfactant and polymer adsorption in an emulsion are not easy and one has to extract such information from measurement at a planer interface.

Figure 1.1 Schematic representation of the various breakdown processes in emulsions.

In the following sections, a summary of each of the above-mentioned breakdown processes and details of each process and methods of its prevention are given.

1.1.4 Creaming and Sedimentation

This process results from external forces usually gravitational or centrifugal. When such forces exceed the thermal motion of the droplets (Brownain motion), a concentration gradient builds up in the system with the larger droplets moving faster to the top (if their density is lower than that of the medium) or to the bottom (if their density is larger than that of the medium) of the container. In the limiting cases, the droplets may form a close-packed (random or ordered) array at the top or bottom of the system with the remainder of the volume occupied by the continuous liquid phase.

1.1.5 Flocculation

This process refers to aggregation of the droplets (without any change in primary droplet size) into larger units. It is the result of the van der Waals attraction that is universal with all disperse systems. Flocculation occurs when there is not sufficient repulsion to keep the droplets apart to distances where the van der Waals attraction is weak. Flocculation may be “strong” or “weak,” depending on the magnitude of the attractive energy involved.

1.1.6 Ostwald Ripening (Disproportionation)

This results from the finite solubility of the liquid phases. Liquids that are referred to as being immiscible often have mutual solubilities that are not negligible. With emulsions, which are usually polydisperse, the smaller droplets will have larger solubility when compared with the larger ones (due to curvature effects). With time, the smaller droplets disappear and their molecules diffuse to the bulk and become deposited on the larger droplets. With time, the droplet size distribution shifts to larger values.

1.1.7 Coalescence

This refers to the process of thinning and disruption of the liquid film between the droplets with the result of fusion of two or more droplets into larger ones. The limiting case for coalescence is the complete separation of the emulsion into two distinct liquid phases. The driving force for coalescence is the surface or film fluctuations which results in close approach of the droplets whereby the van der Waals forces is strong thus preventing their separation.

1.1.8 Phase Inversion

This refers to the process whereby there will be an exchange between the disperse phase and the medium. For example, an O/W emulsion may with time or change of conditions invert to a W/O emulsion. In many cases, phase inversion passes through a transition state whereby multiple emulsions are produced.

1.2 Industrial Applications of Emulsions

Several industrial systems consist of emulsions of which the following is worth mentioning: food emulsion, for example, mayonnaise, salad creams, deserts, and beverages; personal care and cosmetics, for example, hand creams, lotions, hair sprays, and sunscreens; agrochemicals, for example, self-emulsifiable oils which produce emulsions on dilution with water, emulsion concentrates (EWs), and crop oil sprays; pharmaceuticals, for example, anesthetics of O/W emulsions, lipid emulsions, and double and multiple emulsions; and paints, for example, emulsions of alkyd resins and latex emulsions. Dry cleaning formulations – this may contain water droplets emulsified in the dry cleaning oil which is necessary to remove soils and clays. Bitumen emulsions: these are emulsions prepared stable in the containers, but when applied the road chippings, they must coalesce to form a uniform film of bitumen. Emulsions in the oil industry: many crude oils contain water droplets (for example, the North sea oil) and these must be removed by coalescence followed by separation. Oil slick dispersions: the oil spilled from tankers must be emulsified and then separated. Emulsification of unwanted oil: this is an important process for pollution control.

The above importance of emulsion in industry justifies a great deal of basic research to understand the origin of instability and methods to prevent their break down. Unfortunately, fundamental research on emulsions is not easy because model systems (e.g., with monodisperse droplets) are difficult to produce. In many cases, theories on emulsion stability are not exact and semiempirical approaches are used.

1.3 Physical Chemistry of Emulsion Systems

1.3.1 The Interface (Gibbs Dividing Line)

An interface between two bulk phases, for example, liquid and air (or liquid/vapor), or two immiscible liquids (oil/water) may be defined provided that a dividing line is introduced (Figure 1.2). The interfacial region is not a layer that is one-molecule thick. It is a region with thickness δ with properties different from the two bulk phases α and β.

Figure 1.2 The Gibbs dividing line.

Using Gibbs model, it is possible to obtain a definition of the surface or interfacial tension γ.

The surface free energy dG^σ is made of three components: an entropy term S^σ dT, an interfacial energy term Adγ, and a composition term Σ n_idµ_i (n_i is the number of moles of component i with chemical potential μ_i). The Gibbs–Deuhem equation is

1.1

At constant temperature and composition

1.2

For a stable interface, γ is positive, that is, if the interfacial area increases G^σ increases. Note that γ is energy per unit area (mJ m⁻²), which is dimensionally equivalent to force per unit length (mN m⁻¹), the unit usually used to define surface or interfacial tension.

For a curved interface, one should consider the effect of the radius of curvature. Fortunately, γ for a curved interface is estimated to be very close to that of a planer surface, unless the droplets are very small (<10 nm). Curved interfaces produce some other important physical phenomena that affect emulsion properties, for example, the Laplace pressure Δp, which is determined by the radii of curvature of the droplets

1.3

where r₁ and r₂ are the two principal radii of curvature.

For a perfectly spherical droplet, r₁ = r₂ = r and

1.4

For a hydrocarbon droplet with radius 100 nm, and γ = 50 mN m⁻¹, Δp = 10⁶ Pa (10 atm).

1.4 Thermodynamics of Emulsion Formation and Breakdown

Consider a system in which an oil is represented by a large drop 2 of area A₁ immersed in a liquid 2, which is now subdivided into a large number of smaller droplets with total area A₂ (A₂ A₁) as shown in Figure 1.3. The interfacial tension γ₁₂ is the same for the large and smaller droplets because the latter are generally in the region of 0.1 to few micrometers.

Figure 1.3 Schematic representation of emulsion formation and breakdown.

The change in free energy in going from state I to state II is made from two contributions: A surface energy term (that is positive) that is equal to ΔAγ₁₂ (where ΔA = A₂ − A₁). An entropy of dispersions term that is also positive (since producing a large number of droplets is accompanied by an increase in configurational entropy), which is equal to TΔS ^conf.

From the second law of thermodynamics

1.5

In most cases, ΔAγ₁₂ − TΔS ^conf, which means that ΔG ^form is positive, that is, the formation of emulsions is nonspontaneous and the system is thermodynamically unstable. In the absence of any stabilization mechanism, the emulsion will break by flocculation, coalescence, Ostwald ripening, or combination of all these processes. This is illustrated in Figure 1.4 that shows several paths for emulsion breakdown processes.

Figure 1.4 Free energy path in emulsion breakdown – (straight line) Flocc. + coal.; (dashed line) Flocc. + coal. + Sed.; and (dotted line) Flocc. + coal. + sed. + Ostwald ripening.

In the presence of a stabilizer (surfactant and/or polymer), an energy barrier is created between the droplets, and therefore, the reversal from state II to state I becomes noncontinuous as a result of the presence of these energy barriers. This is illustrated in Figure 1.5. In the presence of the above energy barriers, the system becomes kinetically stable.

Figure 1.5 Schematic representation of free energy path for breakdown (flocculation and coalescence) for systems containing an energy barrier.

1.5 Interaction Energies (Forces) between Emulsion Droplets and Their Combinations

Generally speaking, there are three main interaction energies (forces) between emulsion droplets and these are discussed in the following sections.

1.5.1 van der Waals Attraction

The van der Waals attraction between atoms or molecules is of three different types: dipole–dipole (Keesom), dipole-induced dipole (Debye), and dispersion (London) interactions. The Keesom and Debye attraction forces are vectors, and although dipole–dipole or dipole-induced dipole attraction is large, they tend to cancel because of the different orientations of the dipoles. Thus, the most important are the London dispersion interactions that arise from charge fluctuations. With atoms or molecules consisting of a nucleus and electrons that are continuously rotating around the nucleus, a temporary dipole is created as a result of charge fluctuations. This temporary dipole induces another dipole in the adjacent atom or molecule. The interaction energy between two atoms or molecules G_a is short range and is inversely proportional to the sixth power of the separation distance r between the atoms or molecules

1.6

where β is the London dispersion constant that is determined by the polarizability of the atom or molecule.

Hamaker [4] suggested that the London dispersion interactions between atoms or molecules in macroscopic bodies (such as emulsion droplets) can be added resulting in strong van der Waals attraction, particularly at close distances of separation between the droplets. For two droplets with equal radii R, at a separation distance h, the van der Waals attraction G_A is given by the following equation (due to Hamaker)

1.7

where A is the effective Hamaker constant

1.8

where A₁₁ and A₂₂ are the Hamaker constants of droplets and dispersion medium, respectively.

The Hamaker constant of any material depends on the number of atoms or molecules per unit volume q and the London dispersion constant β

1.9 G_A increases very rapidly with decrease of h (at close approach). This is illustrated in Figure 1.6 that shows the van der Waals energy–distance curve for two emulsion droplets with separation distance h.

Figure 1.6 Variation of the van der Waals attraction energy with separation distance.

In the absence of any repulsion, flocculation is very fast producing large clusters. To counteract the van der Waals attraction, it is necessary to create a repulsive force. Two main types of repulsion can be distinguished depending on the nature of the emulsifier used: electrostatic (due to the creation of double layers) and steric (due to the presence of adsorbed surfactant or polymer layers.

1.5.2 Electrostatic Repulsion

This can be produced by adsorption of an ionic surfactant as shown in Figure 1.7, which shows a schematic picture of the structure of the double layer according to Gouy–Chapman and Stern pictures [3]. The surface potential ψ_o decreases linearly to ψ_d (Stern or zeta potential) and then exponentially with increase of distance x. The double-layer extension depends on electrolyte concentration and valency (the lower the electrolyte concentration and the lower the valency the more extended the double layer is).

Figure 1.7 Schematic representation of double layers produced by adsorption of an ionic surfactant.

When charged colloidal particles in a dispersion approach each other such that the double layer begins to overlap (particle separation becomes less than twice the double-layer extension), repulsion occurs. The individual double layers can no longer develop unrestrictedly because the limited space does not allow complete potential decay [3, 4]. This is illustrated in Figure 1.8 for two flat, which clearly shows that when the separation distance h between the emulsion droplets becomes smaller than twice the double-layer extension, the potential at the midplane between the surfaces is not equal to zero (which would be the case when h is larger than twice the double-layer extension) plates.

Figure 1.8 Schematic representation of double-layer overlap.

The repulsive interaction G_el is given by the following expression:

1.10

where ε _r is the relative permittivity and ε _o is the permittivity of free space. κ is the Debye–Hückel parameter; 1/κ is the extension of the double layer (double-layer thickness) that is given by the expression

1.11

where k is the Boltzmann constant, T is the absolute temperature, n_o is the number of ions per unit volume of each type present in bulk solution, Z_i is the valency of the ions, and e is the electronic charge.

Values of 1/κ at various 1 : 1 electrolyte concentrations are given below

The double-layer extension decreases with increase of electrolyte concentration. This means that the repulsion decreases with increase of electrolyte concentration as illustrated in Figure 1.9

1.12

A schematic representation of the force (energy)–distance curve according to the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory is given in Figure 1.10.

Figure 1.9 Variation of G_el with h at low and high electrolyte concentrations.

Figure 1.10 Total energy–distance curve according to the DLVO theory.

The above presentation is for a system at low electrolyte concentration. At large h, attraction prevails resulting in a shallow minimum (G_sec) of the order of few kilotesla units. At very short h, V_A G_el, resulting in a deep primary minimum (several hundred kilotesla units). At intermediate h, G_el > G_A, resulting in a maximum (energy barrier) whose height depends on ψ_o (or ζ) and electrolyte concentration and valency – the energy maximum is usually kept >25 kT units. The energy maximum prevents close approach of the droplets, and flocculation into the primary minimum is prevented. The higher the value of ψ_o and the lower the electrolyte concentration and valency, the higher the energy maximum. At intermediate electrolyte concentrations, weak flocculation into the secondary minimum may occur.

Combination of van der Waals attraction and double-layer repulsion results in the well-known theory of colloid stability due to DLVO theory [5, 6].

1.5.3 Steric Repulsion

This is produced by using nonionic surfactants or polymers, for example, alcohol ethoxylates, or A-B-A block copolymers PEO-PPO-PEO (where PEO refers to polyethylene oxide and PPO refers to polypropylene oxide), as illustrated in Figure 1.11.

Figure 1.11 Schematic representation of adsorbed layers.

The “thick” hydrophilic chains (PEO in water) produce repulsion as a result of two main effects [7]:

Combination of G_mix, G_el with G_A gives the total energy of interaction G_T (theory of steric stabilization)

1.14

A schematic representation of the variation of G_mix, G_el, and G_A with h is given in Figure 1.12. G_mix increases very sharply with decrease of h when the latter becomes less than 2δ. G_el increases very sharply with decrease of h when the latter becomes smaller than δ. G_T increases very sharply with decrease of h when the latter becomes less than 2δ.

Figure 1.12 Schematic representation of the energy–distance curve for a sterically stabilized emulsion.

Figure 1.12 shows that there is only one minimum (G_min) whose depth depends on R, δ, and A. At a given droplet size and Hamaker constant, the larger the adsorbed layer thickness, the smaller the depth of the minimum. If G_min is made sufficiently small (large δ and small R), one may approach thermodynamic stability. This is illustrated in Figure 1.13 that shows the energy–distance curves as a function of δ/R. The larger the value of δ/R, the smaller the value of G_min. In this case, the system may approach thermodynamic stability as is the case with nanodispersions.

Figure 1.13 Variation of G_T with h at various δ/R values.

1.6 Adsorption of Surfactants at the Liquid/Liquid Interface

Surfactants accumulate at interfaces, a process described as adsorption. The simplest interfaces are the air/water (A/W) and O/W. The surfactant molecule orients itself at the interface with the hydrophobic portion orienting toward the hydrophobic phase (air or oil) and the hydrophilic portion orienting at the hydrophilic phase (water). This is schematically illustrated in Figure 1.14. As a result of adsorption, the surface tension of water is reduced from its value of 72 mN m⁻¹ before adsorption to ∼ 30–40 mN m⁻¹ and the interfacial tension for the O/W system decreases from its value of 50 mN m⁻¹ (for an alkane oil) before adsorption to a value of 1–10 mN m⁻¹ depending on the nature of the surfactant.

Figure 1.14 Schematic representation of orientation of surfactant molecules.

Two approaches can be applied to treat surfactant adsorption at the A/L and L/L interface [3]: Gibbs approach treats the process as an equilibrium phenomenon. In this case, one can apply the second law of thermodynamics. Equation of state approach whereby the surfactant film is treated as a “two-dimensional” layer with a surface pressure π. The Gibbs approach allows one to obtain the surfactant adsorption from surface tension measurements. The equation of state approach allows one to study the surfactant orientation at the interface. In this section, only the Gibbs approach is described.

1.6.1 The Gibbs Adsorption Isotherm

Gibbs derived a thermodynamic relationship between the variation of surface or interfacial tension with concentration and the amount of surfactant adsorbed Γ (moles per unit area), referred to as the surface excess. At equilibrium, the Gibbs free energy dG^σ = 0 and the Gibbs–Deuhem equation becomes

1.15

At constant temperature

1.16

or

1.17

For a surfactant (component 2) adsorbed at the surface of a solvent (component 1)

1.18

If the Gibbs dividing surface is used and the assumption is made

1.19

The chemical potential of the surfactant μ₂ is given by the expression

1.20

where is the standard chemical potential and is the activity of surfactant that is equal to C₂f₂ ∼ x₂f₂ where C₂ is the concentration in moles per cubic decimeter and x₂ is the mole fraction that is equal to C₂/(C₂ + 55.5) for a dilute solution, and f₂ is the activity coefficient that is also ∼ 1 in dilute solutions.

Differentiating Eq. (1.20), one obtains

1.21

Combining Eqs. (1.19) and (1.21),

1.22

or

1.23

In dilute solutions, f₂ ∼ 1 and

1.24

Equations (1.23) and (1.24) are referred to as the Gibbs adsorption equations, which show that Γ₂ can be determined from the experimental results of variation of γ with log C₂ as illustrated in Figure 1.15 for the A/W and O/W interfaces.

Figure 1.15 Surface or interfacial tension – log C curves.

Γ₂ can be calculated from the linear portion of the γ − logC curve just before the critical micelle concentration (cmc)

1.25

From Γ₂, the area per molecule of surfactant (or ion) can be calculated

1.26 N_av is Avogadro's constant that is equal to 6.023 × 10²³.

The area per surfactant ion or molecule gives information on the orientation of the ion or molecule at the interface. The area depends on whether the molecules lie flat or vertical at the interface. It also depends on the length of the alkyl chain length (if the molecules lie flat) or the cross-sectional area of the head group (if the molecules lie vertical. For example, for an ionic surfactant such as SDS, the area per molecule depends on the orientation. If the molecule lies flat, the area is determined by the area occupied by the alkyl chain and that by the sulfate head group. In this case, the area per molecule increases with increase in the alkyl chain length and will be in the range of 1–2 nm². In contrast, for vertical orientation, the area per molecule is determined by the cross-sectional area of the sulfate group, which is ∼ 0.4 nm² and virtually independent of the alkyl chain length. Addition of electrolytes screens the charge on the head group and hence the area per molecule decreases. For nonionic surfactants such as alcohol ethoxylates, the area per molecule for flat orientation is determined by the length of the alkyl chain and the number of ethylene oxide (EO) units. For vertical orientation, the area per molecule is determined by the cross-sectional area of the PEO chain and this increases with increase in the number of EO units.

At concentrations just before the break point, the slope of the γ − logC curve is constant

1.27

This indicates that saturation of the interface occurs just below the cmc.

Above the break point (C > cmc), the slope is 0,

1.28

or

1.29

As γ remains constant above the cmc, then C₂ or a₂ of the monomer must remain constant.

Addition of surfactant molecules above the cmc must result in association to form micelles that have low activity, and hence, a₂ remains virtually constant.

The hydrophilic head group of the surfactant molecule can also affect its adsorption. These head groups can be unionized, for example, alcohol or PEO; weakly ionized, for example, COOH; or strongly ionized, for example, sulfates , sulfonates , or ammonium salts . The adsorption of the different surfactants at the A/W and O/W interface depends on the nature of the head group. With nonionic surfactants, repulsion between the head groups is smaller than with ionic head groups and adsorption occurs from dilute solutions; the cmc is low, typically 10⁻⁵ to 10⁻⁴ mol dm⁻³. Nonionic surfactants with medium PEO form closely packed layers at C < cmc. Adsorption is slightly affected by moderate addition of electrolytes or change in the pH. Nonionic surfactant adsorption is relatively simple and can be described by the Gibbs adsorption equation.

With ionic surfactants, adsorption is more complicated depending on the repulsion between the head groups and addition of indifferent electrolyte. The Gibbs adsorption equation has to be solved to take into account the adsorption of the counterions and any indifferent electrolyte ions.

For a strong surfactant electrolyte such as

1.30

The factor 2 in Eq. (1.30) arises because both surfactant ion and counterion must be adsorbed to maintain neutrality. (∂γ/dln a ± ) is twice as large for an unionized surfactant molecule.

For a nonadsorbed electrolyte such as NaCl, any increase in Na⁺·R⁻ concentration produces a negligible increase in Na⁺ concentration ( is also negligible.

1.31

which is identical to the case of nonionics.

The above analysis shows that many ionic surfactants may behave like nonionics in the presence of a large concentration of an indifferent electrolyte such as NaCl.

1.6.2 Mechanism of Emulsification

As mentioned before, to prepare an emulsions oil, water, surfactant, and energy are needed. This can be considered from a consideration of the energy required to expand the interface, ΔAγ(where ΔA is the increase in interfacial area when the bulk oil with area A₁ produces a large number of droplets with area A₂; A₂ A₁, γ is the interfacial tension). As γ is positive, the energy to expand the interface is large and positive; this energy term cannot be compensated by the small entropy of dispersion TΔS (which is also positive) and the total free energy of formation of an emulsion, ΔG given by Eq. (1.5) is positive. Thus, emulsion formation is nonspontaneous and energy is required to produce the droplets.

The formation of large droplets (few micrometers) as is the case for macroemulsions is fairly easy, and hence, high-speed stirrers such as the Ultraturrax or Silverson Mixer are sufficient to produce the emulsion. In contrast, the formation of small drops (submicrometer as is the case with nanoemulsions) is difficult and this requires a large amount of surfactant and/or energy. The high energy required for the formation of nanoemulsions can be understood from a consideration of the Laplace pressure Δp (the difference in pressure between inside and outside the droplet) as given by Eqs. (1.3) and (1.4).

To break up a drop into smaller ones, it must be strongly deformed and this deformation increases Δp. This is illustrated in Figure 1.16 that shows the situation when a spherical drop deforms into a prolate ellipsoid [8].

Figure 1.16 Illustration of increase in Laplace pressure when a spherical drop is deformed to a prolate ellipsoid.

Near 1, there is only one radius of curvature R_a, whereas near 2, there are two radii of curvature R_b,1 and R_b,2. Consequently, the stress needed to deform the drop is higher for a smaller drop – as the stress is generally transmitted by the surrounding liquid via agitation, higher stresses need more vigorous agitation, and hence more energy is needed to produce smaller drops.

Surfactants play major roles in the formation of emulsions: by lowering the interfacial tension, p is reduced and hence the stress needed to break up a drop is reduced. Surfactants also prevent coalescence of newly formed drops.

Figure 1.17 shows an illustration of the various processes occurring during emulsification, break up of droplets, adsorption of surfactants, and droplet collision (which may or may not lead to coalescence) [8].

Figure 1.17 Schematic representation of the various processes occurring during emulsion formation. The drops are depicted by thin lines and the surfactant by heavy lines and dots.

Each of the above processes occurs numerous times during emulsification and the timescale of each process is very short, typically a microsecond. This shows that the emulsification process is a dynamic process and events that occur in a microsecond range could be very important.

To describe emulsion formation, one has to consider two main factors: hydrodynamics and interfacial science. In hydrodynamics, one has to consider the type of flow: laminar flow and turbulent flow. This depends on the Raynolds number as is discussed later.

To assess emulsion formation, one usually measures the droplet size distribution using, for example, laser diffraction techniques. A useful average diameter d is

1.32

In most cases, d₃₂ (the volume/surface average or Sauter mean) is used. The width of the size distribution can be given as the variation coefficient c_m, which is the standard deviation of the distribution weighted with d^m divided by the corresponding average d. Generally, C₂ is used that corresponds to d₃₂.

An alternative way to describe the emulsion quality is to use the specific surface area A (surface area of all emulsion droplets per unit volume of emulsion)

1.33

1.6.3 Methods of Emulsification

Several procedures may be applied for emulsion preparation, and these range from simple pipe flow (low agitation energy L); static mixers and general stirrers (low to medium energy, L–M); high-speed mixers such as the Ultraturrex (M); colloid mills and high-pressure homogenizers (high energy, H); and ultrasound generators (M–H). The method of preparation can be continuous (C) or batch-wise (B): pipe flow and static mixers – C; stirrers and Ultraturrax – B,C; colloid mill and high-pressure homogenizers – C; and ultrasound – B,C.

In all methods, there is liquid flow; unbounded and strongly confined flow. In the unbounded flow, any droplets are surrounded by a large amount of flowing liquid (the confining walls of the apparatus are far away from most of the droplets). The forces can be frictional (mostly viscous) or inertial. Viscous forces cause shear stresses to act on the interface between the droplets and the continuous phase (primarily in the direction of the interface). The shear stresses can be generated by laminar flow (LV) or turbulent flow (TV); this depends on the Reynolds number Re

1.34

where v is the linear liquid velocity, ρ is the liquid density, and η is its viscosity. l is a characteristic length that is given by the diameter of flow through a cylindrical tube and by twice the slit width in a narrow slit.

For laminar flow, Re 1000, whereas for turbulent flow, Re 2000. Thus, whether the regime is linear or turbulent depends on the scale of the apparatus, the flow rate, and the liquid viscosity [9–12].

If the turbulent eddies are much larger than the droplets, they exert shear stresses on the droplets. If the turbulent eddies are much smaller than the droplets, inertial forces will cause disruption.

In bounded flow, other relations hold. If the smallest dimension of the part of the apparatus in which the droplets are disrupted (say a slit) is comparable to droplet size, other relations hold (the flow is always laminar). A different regime prevails if the droplets are directly injected through a narrow capillary into the continuous phase (injection regime), that is, membrane emulsification.

Within each regime, an essential variable is the intensity of the forces acting; the viscous stress during laminar flow σ_{viscous is given by}

1.35

where G is the velocity gradient.

The intensity in turbulent flow is expressed by the power density ε (the amount of energy dissipated per unit volume per unit time); for laminar flow,

1.36

The most important regimes are laminar/viscous (LV), turbulent/viscous (TV), and turbulent/inertial (TI). For water as the continuous phase, the regime is always TI. For higher viscosity of the continuous phase (η_C = 0.1 Pa s), the regime is TV. For still higher viscosity or a small apparatus (small l), the regime is LV. For very small apparatus (as is the case with most laboratory homogenizers), the regime is nearly always LV.

For the above regimes, a semiquantitative theory is available that can give the timescale and magnitude of the local stress σ_ext, the droplet diameter d, timescale of droplets deformation τ_def, timescale of surfactant adsorption τ_ads, and mutual collision of droplets.

An important parameter that describes droplet deformation is the Weber number We (which gives the ratio of the external stress over the Laplace pressure)

1.37

The viscosity of the oil plays an important role in the breakup of droplets; the higher the viscosity, the longer it will take to deform a drop. The deformation time τ_def is given by the ratio of oil viscosity to the external stress acting on the drop

1.38

The viscosity of the continuous phase η_C plays an important role in some regimes: for TI regime, η_C has no effect on droplet size. For turbulent viscous regime, larger η_C leads to smaller droplets. For laminar viscous, the effect is even stronger.

1.6.4 Role of Surfactants in Emulsion Formation

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