Colloidal Structures and Surfactants

Colloidal Structures in Surfactant Solutions

Association colloids: Aggregates of surfactants in solution due to physical interactions among amphipathic molecules. Includes micelles, reverse micelles, liquid crystals, bilayers, vesicles, and microemulsions.
Liposomes: Surfactant aggregates common in physiological systems, used as drug-delivery vehicles.
Micelle Formation:
- Representation of micellization: $nS \leftrightarrow Sn$ , where S is the amphipathic species and $Sn$ is the micelle with aggregation number n.
- Reversible reaction: Dilution shifts the equilibrium towards monomeric surfactant.
Surfactant Structure:
- General formula: RX, where R is a hydrocarbon chain and X is a polar group.
- Hydrocarbon chain (R):
 - Typically C8 or greater.
 - Saturated or unsaturated.
 - Linear or branched.
 - May contain an aromatic ring.
- Polar group (X):
 - Nonionic: short-chain polyoxyethylene moieties, $-(C2H4O)_x$ , where x ranges from 3-4 to 20 or more.
 - Anionic: sulfate $(−SO4^-)$ , sulfonate $(−SO3^-)$ , and carboxylate $(−CO_2^-)$ .
 - Cationic: quaternary ammonium groups $(−NR_3^+)$ .
 - Zwitterionic: combine both positively and negatively charged groups.
 - Example: Sodium dodecyl sulfate (SDS), $M^+ = Na^+$ and $S^- = C{12}H{25}SO_4^-$ .

Critical Micelle Concentration (CMC)

Definition: The threshold concentration at which micellization begins.
Identifying CMC: Decrease in the slopes of different properties indicates an increase in the average molecular weight of the solute.
Factors Affecting Aggregation Number (n):
- Increases with hydrocarbon chain length.
- Increases for sodium dodecyl sulfate with added indifferent electrolyte (NaCl).
- Fraction ionized $\alpha$ decreases with added electrolyte (0.1 to 0.4).
- Ion binding order to negative micelles: $Cs^+ > Rb^+ > Na^+ > Li^+$ .
- Ion binding order to positive micelles: $I^- > Br^- > Cl^-$ ; larger, more polarizable, less hydrated ions bind more effectively.
- For nonionics, increasing polyoxyethylene chain length decreases n.
Relationship between n and CMC: Factors that increase n tend to lower the CMC.
Micelle Shape at CMC: Roughly spherical and relatively monodisperse.
Factors Increasing Aggregation: Variations that increase the hydrophobic character of the surfactant:
- Increasing hydrocarbon chain length.
- Decreasing polyoxyethylene chain length.
- Increasing counterion binding.

Micelle Structure and Hydrophile-Lipophile Balance (HLB)

Micelle Core: Predominantly hydrocarbon.
Micelle Surface: Polar heads in water.
Hydrophile-Lipophile Balance (HLB): The relative sizes of the hydrophilic and hydrophobic groups of the surfactant molecules.
Packing Ratio (P):
- Definition: $P = \frac{Vt}{al l_t}$ , provides a measure of HLB.
- $V_t$ is the volume of the hydrophobic tail.
- $a$ is the optimal head group area.
- $l_t$ is the length of the hydrophobic tail.
- O/W structures: favored if the polar part is bulkier than the hydrophobic part ( $P < 1$ ), interface curves towards water (positive curvature).
- W/O structures: formed when the interface curves in the opposite direction ( $P > 1$ , negative curvature).
- Zero curvature: when HLB is balanced ( $P = 1$ ), either bicontinuous or lamellar structures may form depending on the film's rigidity.

HLB Values and Surfactant Blending

HLB Scale: 1-40
- High HLB = Hydrophilic.
- Low HLB = Lipophilic/Hydrophobic.
HLB ranges and Applications:
- 3-6: W/O emulsifiers.
- 8-13: O/W emulsifiers.
- 12-18: Detergents / Solubilizing agents.
Estimating HLB:
- $HLB = 7 + \sum HLB{hydrophiles} - \sum HLB{lipophiles}$
- Example: For $C{10}E{12}$
 - $HLB_{lipophile} = 10 \cdot 0.47 = 4.7$
 - $HLB_{hydrophile} = 12 \cdot 0.36 + 1.9 = 6.2$
 - $HLB = 7 + 6.2 - 4.7 = 8.5$
Surfactant Blending:
- Calculate the combined HLB: $f1 \cdot HLB1 + f2 \cdot HLB2$
 - Where $f1$ and $f2$ are the fractions of each surfactant in the blend.
- Example: Arlacel 60 (HLB = 4.7) and Tween 60 (HLB = 14.9) in a 3:1 ratio.
 - $0.75 \cdot 4.7 + 0.25 \cdot 14.9 = 3.525 + 3.725 = 7.25$
- Calculating amounts for a target HLB: Use a system of equations to determine the required volumes of each surfactant.

Minimum Amount of Surfactant

Formulas:
- Minimum amount of surfactant (O/W): $Qs = 6 \frac{\rhos}{\rho} \left[ \frac{4Q}{10 - 0.5 \cdot RHLB} + \frac{Q}{1000} \right]$
 - $\rho_s$ is the density of the surfactant mixture (g/cm³).
 - $\rho$ is the density of the dispersed phase (g/cm³).
 - Q is the percentage of the continuous phase.
- Minimum amount of surfactant (W/O): $6 \frac{\rho_s}{\rho} \left[ \frac{4Q}{10 - 0.5 \cdot RHLB} + \frac{Q}{1000} \right]$
Example calculation for O/W emulsion:
- Oil phase: Paraffin (60%, HLB 10.0), Beeswax (40%, HLB 9.0).
- Water: 60 g total.
- Densities: Water (1.00 g/mL), Oil (0.85 g/mL), and O/W (1.05 g/mL).
- $RHLB = 0.6 \cdot 10 + 0.4 \cdot 9 = 6.0 + 3.6 = 9.6$
- $Q_s = 6 \cdot \frac{1.05}{0.85} \left[ \frac{4 \cdot 60}{10 - 0.5 \cdot 9.6} + \frac{60}{1000} \right] = 51.665g$

HLB and Emulsion Formation

Importance of Surfactant Selection: Crucial for dispersing a liquid into another liquid to form a stable emulsion.
Emulsion Types:
- Water-in-oil (W/O): Water droplets dispersed in a continuous oil phase.
- Oil-in-water (O/W): Oil droplets dispersed in a continuous water phase.
HLB Values and Emulsion Type:
- High HLB (>10): favors O/W emulsions (e.g., PEG 400, Tween 85).
- Low HLB (<10): favors W/O emulsions (e.g., Glyceryl monostearate, Span 65).

Factors Affecting HLB and Micelle Structure

Temperature:
- Ionic surfactants: temperature rise increases positive curvature due to counter ion dissolution.
- Nonionic surfactants: hydration characteristics vary with temperature; temperature is crucial for effective head group size.
Oil Type: Short-chain oils penetrate tail group region more than long-chain alkanes, increasing negative curvature and reducing effective HLB.
Other Factors: pH, electrolyte concentration.
Head Group Area:
- Depends on attractive (hydrophobic attraction of hydrocarbon chains) and repulsive forces (hydrophilic, steric, and ionic repulsion between adjacent head groups).
Optimal Head Group Area: Determines the number of surfactants in an aggregate.
Micelle Radius (Rs) and Chain Length (lc): The ratio $\frac{Rs}{l{c.t}}$ must be less than or equal to 1 for a liquid-like core.
Changing Head Group Area:
- Ionic surfactants: alter electrolyte concentration or pH.
- Nonionic surfactants: change degree of ethoxylation or decrease temperature.
Changing Tail Volume: Increase alkyl chains, introduce branching, or use unsaturated hydrocarbon chains.

Packing Parameter and Micelle Shape

Packing Parameter (P) and Spherical Micelles:
- For spherical micelles, P must be less than 1/3.
- Derivation: For a spherical micelle of radius R and aggregation number n:
 - $n = \frac{\frac{4}{3} \pi R^3}{vt} = \frac{4 \pi R^2}{al}$
 - $\frac{vt}{al} = \frac{R}{3}$
 - $P = \frac{vt}{al lt} = \frac{R}{l{c.t}} \cdot \frac{1}{3}$
- Since $\frac{Rs}{lc}$ must be less than or equal to 1, P must be less than or equal to 1/3.
**Table of Packing Parameters and Aggregate Shapes: **
- P < 1/3: Cone shape, spherical micelles.
- 1/3 - 1/2: Truncated cone, cylindrical micelles.
- 1/2 - 1: Truncated cone, flexible bilayers, vesicles.
- ~1: Cylinder, planar bilayers.
- >1: Inverted truncated cone or wedge, inverted micelles.

Thermodynamics of Micelle Formation

Entropy: Positive values of $\Delta S_{mic}^0$ are primarily responsible for spontaneous micelle formation.
Water Entropy: Water must experience an increase in entropy.

Solubilization in Micelles

Definitions:
- Solubilizer: The surfactant.
- Solubilizate: The substance dissolved.
CMC Changes: Solubilizates can change the CMC.
Solubilization Limit: There is an upper limit to the amount of material that can be solubilized.
Location of Solubilizate:
- Example: Isopropyl benzene molecules orient with isopropyl groups in the micelle core and benzene ring in the hydrated palisade layer when hexadecyl pyridinium chloride is the surfactant.
- Core vs. Mantle: Depends on the polarity of the solubilizate.
Temperature Effects:
- Nonionics become more hydrophobic at higher temperatures, favoring dehydration of ether oxygens.
- Cloud Point: Solutions of nonionic surfactants undergo phase separation at the cloud point.
  - Nonpolar solubilizates: Solubilization increases as the cloud point is approached.
  - Polar solubilizates: Solubilization decreases due to dehydration of polyoxyethylene chains.
Location based on Polarity: Nonpolar compounds are solubilized in the core, while polar solubilizates are in the mantle.

Phase Diagrams and Microemulsions

Free Energy: Solubilizates decrease their free energy by entering micelles.
Pseudo-Ternary Phase Diagrams: Used to investigate planar sections of tetrahedron diagrams by keeping one component fixed or using a constant ratio for two components.
Cosurfactants: Non-ionic surfactants often don't need a cosurfactant for microemulsion formation.
Temperature Importance: Temperature is crucial for non-ionic systems as they become more lipophilic with increasing temperature.
*Typical pseudo-binary phase diagram of oil and water as a function of temperature with a fixed amount of nonionic surfactant:
*Single phase isotropic region at high and low water concentration
*Intermediate three-phase region, III represents a transition between o/w and w/o phases.
*The inversion temperature, PIT of the system is found in this region.
*Two-phase region in the lower part of the phase diagram II o/w, is composed of water with dissolved surfactant and oil.
*Il w/o upon mixing an o/w at higher temperature represents a two-phase region composed of water and oil with dissolved surfactant from which w/o macroemulsions is formed on mixing.
*Limitation of these phase diagrams is that these do not indicate the stability of the system formed.

Ternary Phase Diagrams and Winsor Phases

Three-Component Microemulsions: Systems with oil, water, and a double-chained surfactant (e.g., sodium bis-2 ethylhexylsulfosuccinate or DDAB) are studied as prototype models.
Ternary Diagram Representation: Phase behavior can be completely represented by a ternary diagram.
Winsor Phases:
- Winsor I: Two phases, lower (O/W) microemulsion phase in equilibrium with upper excess oil.
- Winsor II: Two phases, upper (W/O) microemulsion phase in equilibrium with excess water.
- Winsor III: Three phases, middle microemulsion phase (O/W + W/O, biocontinuous) in equilibrium with upper excess oil and lower excess water.
- Winsor IV: Single phase, oil, water, and surfactant homogeneously mixed.
- Winsor V: Simultaneous presence of two microemulsion phases, one in contact with water and the other in contact with oil.
Phase Rule: At constant temperature and pressure, one, two, or three phases can be present.
Tie Lines: Connect points having the compositions of equilibrium phases in two-phase regions.
Triangular Shapes: Three-phase regions have triangular shapes with corners indicating equilibrium phase compositions.

Types of Phases in Ternary Diagrams

Two Liquids: Two-phase region with two liquid solutions in equilibrium.
L1 and L2: Homogeneous, isotropic liquid solutions containing three components.
- L1: Acid solubilized in aqueous micelles.
- L2: Water solubilized in reverse micelles.
Liquid Crystal: Ordered yet fluid phase forming anisotropic structures.

Micelle Shape and Structure

Micelle Shape Transformation: Spheres distort into prolate or oblate ellipsoids, cylindrical rods, or lamellar disks as surfactant amount and solubilization increase.
Micelle Structures:
- Viscous isotropic phase (spherical).
- Middle phase (cylindrical).
- Neat phase (lamellar).
Amphipathic Molecule Orientation: Depends on the nature of the continuous and solubilized components.

Micellar and Enzyme Catalysis

Differences:
- Micelles enhance reaction rates less effectively than enzymes (rarely exceeding 100-fold).
- Micellar catalysts are less specific than enzymes.
Enzyme Catalysis: Lock-and-key model implies specific binding sites maintained by covalent bonds.

Micellar Catalysis: Example Reaction (F)

Reaction Rate Enhancement:
- Cationic micelles concentrate $\text{OH}^−$ reactant in the Stern layer.
- Cationic crystal violet is less stable in cationic micelles than the zwitterionic transition state.
- Electrostatic effects favor the transition state in the micelle compared to a non-solubilized species.
Rate Enhancement Comparison: The ratio of relative rates with and without surfactant is 241/17 for cationic micelles and 1/17 for anionic micelles.
Anion Inhibition: Other anions inhibit catalysis by competing with $\text{OH}^−$ for adsorption sites.
- Inhibition order: $\text{NO}_3^- > \text{Br}^- > \text{Cl}^- > \text{F}^-$ .
Cation Inhibition: For acid-catalyzed ester hydrolysis in anionic micelles, cations inhibit the reaction.
- Inhibition order: $\text{R}_4\text{N}^+ > \text{Cs}^+ > \text{Rb}^+ > \text{Na}^+ > \text{Li}^+$ .

Reverse Micelles

Formation: In nonaqueous media, amphipathic molecules cluster with polar heads together in the micellar core and tails in the organic continuous phase.
Core Solubilization: Water is solubilized in the core.
Examples: Aerosol OT, Triton X-100, and various Spans.
Size Differences: $\text{n}$ is about 50 or larger for aqueous micelles, while for many reverse micelles $\text{n}$ is about 10 or smaller.

Emulsions and Microemulsions

Coarse Emulsions: Look white when examined visually.
Thermodynamic Instability: Emulsions are two-phase systems thermodynamically unstable with respect to separation into oil and water layers because of the free energy associated with the oil-water interface.
Emulsion Types:
- O/W: Oil is the dispersed phase and water the continuous phase.
- W/O: Water is dispersed in oil.
Determining Continuous Phase: Compatibility with either oil or water on dilution.

Microemulsions

Definition: Systems prepared by emulsifying an oil in aqueous surfactant and adding a cosurfactant (generally an alcohol of intermediate chain length).
Cosurfactant Role: Addition of alcohol makes the usual milky emulsion transparent.
*Benzene, water, potassium oleate, and hexanol might be the components of a typical microemulsion formulation.

Differences Between Microemulsions and Coarse Emulsions

Particle Size: Microemulsions contain particles at least an order of magnitude smaller than those in coarse emulsions (10-100 nm).
Clarity: Microemulsions are clear, and coarse emulsions are cloudy.
Formation: Microemulsions form spontaneously while coarse emulsions require vigorous stirring.
Stability: Microemulsions are stable with respect to separation, while coarse emulsions may have kinetic stability but ultimately separate.

Nonionic Surfactants and Microemulsions

Cosurfactant Independence: Nonionic surfactants form microemulsions without requiring cosurfactants at certain temperatures (e.g., water-cyclohexane-polyoxyethylene-(8.6)-nonyl phenol ether).
Temperature Effects: The micellar phase changes from water-continuous to oil-continuous with increasing temperature.

Ionic Surfactants and Microemulsions

Example System: water-benzene-potassium oleate-pentanol.
Benzene Incorporation: Up to 50 wt% benzene can be incorporated into the system at equilibrium.

Applications of Microemulsions

Polymer synthesis.
Floor waxes.
Shaving lotions.
Beverage concentrates.
Pesticide preparations.
Cold creams.
Pharmaceutical and cosmetic products.
Tertiary oil recovery.