Crystallinity, Solid State Manipulations, and Solubility

Influence of Crystallinity and Molecular Structure on Solubility

• Symmetry and Packing Efficiency:

  • Symmetrical molecules often exhibit lower solubility than unsymmetrical molecules because more work is required to separate the particles within the crystalline solute lattice.
  • Efficient packing in a crystal increases the stability of the solid state, requiring more energy to disrupt.
  • Comparative Example: Amino Acids:
    • Alanine (2-Amino-propionic acid): Forms a compact crystal due to its structure. It has a high melting point of $295\,^{\circ}\text{C}$ and a solubility of $1.66\,\text{mol/L}$.
    • 2-Amino-butyric acid: Molecules pack less efficiently in the crystal lattice. It has a lower melting point of $195\,^{\circ}\text{C}$ and a higher solubility of $1.8\,\text{mol/L}$.

• Amorphous vs. Crystalline Forms:

  • Drugs may exist in an amorphous (non-crystalline) form, which typically lacks a defined long-range lattice structure.
  • Amorphous materials generally have a faster dissolution rate and higher solubility than their corresponding crystalline forms because no lattice energy must be overcome.
  • This difference can significantly impact bioavailability.
  • Example: Novobiocin:
    • The crystalline form of this antibiotic is inactive because it dissolves too slowly for effective absorption.
    • The amorphous form is more soluble, dissolves rapidly, and is readily absorbed by the body.

Thermodynamics of Solubility: The Van’t Hoff Relationship

• Ideal Solutions and Solubility Theory:

  • The solubility of a solid in an ideal solution is governed by temperature ($T$), the melting point of the solute ($T_m$), and the molar heat of fusion ($\Delta H_f$).
  • In an ideal solution, the interactions between solute-solute, solvent-solvent, and solute-solvent are considered equal, resulting in no net energy change during the dissolution process.

• Key Parameters and Effects:

  • Temperature ($T$): Increasing the temperature generally leads to increased solubility.
  • Melting Point ($T_m$): A lower melting point for a solute typically results in increased solubility.

• Manipulating Melting Point ($T_m$):

  • The melting point can be altered by changing the compound itself or by forming a eutectic mixture.
  • Aqueous Solubility of Sulpha-compounds (Example):
    • S’thiazole: Melting Point $173\text{--}175\,^{\circ}\text{C}$; Solubility $0.588\,\text{mg/100 mL}$.
    • S’pyridine: Melting Point $191\text{--}193\,^{\circ}\text{C}$; Solubility $0.286\,\text{mg/100 mL}$.
    • S’merazine: Melting Point $234\text{--}238\,^{\circ}\text{C}$; Solubility $0.200\,\text{mg/100 mL}$.
    • S’diazine: Melting Point $252\text{--}256\,^{\circ}\text{C}$; Solubility $0.077\,\text{mg/100 mL}$.
    • General Rule: As melting point increases, aqueous solubility decreases.

Eutectic Mixtures and Solid State Manipulations

• Definition and Composition:

  • A eutectic mixture is formed when two crystalline solids are mixed together, resulting in a system with a lower melting point than either component individually.
  • The Eutectic Composition is the specific ratio of components that yields the lowest possible melting point.
  • In some cases, mixing two solids at room temperature can result in the formation of a liquid.

• Eutectic Phase Diagram Components:

  • One phase liquid mixture: Occurs at high temperatures above the melting points of components A and B.
  • Solid A plus liquid / Solid B plus liquid: Regions where one component remains solid while the other is in a liquid mixture.
  • Solid A plus solid B: Regions below the eutectic temperature where both components are solid.
  • E (Eutectic Point): The intersection where the liquid phase and both solid phases coexist at the minimum temperature.

• Pharmaceutical Significance:

  • Advantages: Eutectics can be used to produce liquids that enhance dissolution and absorption rates.
    • Example: EMLA (Eutectic Mixture of Local Anesthetics) containing lidocaine and prilocaine is a liquid at room temperature.
    • Example: Griseofulvin-Succinic Acid eutectics show significantly higher concentrations in solution over time compared to micronized or coarse drug forms.
  • Disadvantages: Eutectics can cause formulation problems in dry powders. For instance, adding lactose to a mixture of aspirin and paracetamol can produce a "gummy mass" due to melting point depression.

Prodrugs and Chemical Modifications

• Solubility can be improved by chemically modifying a drug to create a more water-soluble derivative, known as a prodrug.
• Example: Hydrocortisone:
  • Pure hydrocortisone is practically insoluble in water.
  • Hydrocortisone sodium phosphate is a chemically modified derivative that is freely soluble in water, facilitating easier administration in aqueous vehicles.

Cosolvents and Mixed Solvent Systems

• Mechanism:

  • Weak electrolytes and non-polar compounds often have poor aqueous solubility. Adding a water-miscible solvent in which the drug has high solubility alters the overall polarity of the solvent system.
  • The added vehicle is termed a Cosolvent.
  • The solubility in these mixed systems is often significantly higher than what would be predicted by the individual solubilities in each solvent separately.

• Selection and Practical Use:

  • Choice is limited by concerns regarding toxicity and irritancy, particularly for oral or parenteral routes.
  • Common Cosolvents: Ethanol (most widely used), sorbitol, glycerol, propylene glycol, polyethylene glycol, and isopropyl alcohol.
  • Formulation Examples:
    • Paracetamol elixir: Uses ethanol and propylene glycol.
    • Betnovate scalp application: Uses isopropyl alcohol.
    • Nitroglycerin Spray: Uses glycerol and ethanol.

• Mathematical Model for Cosolvency:

  • A simple model for solubility in a mixed solvent is given by:
  • $ln(S_f) = ln(S_0) + \sigma f$
  • $S_f$: Solubility in the mixed solvent.
  • $S_0$: Solubility in pure water.
  • $f$: Volume fraction of the cosolvent.
  • $\sigma$: System constant.
  • When $f = 1$, the equation describes solubility in the pure cosolvent ($S_c$).

Three-Component (Ternary) Phase Diagrams

• These diagrams represent the relationship between three components (e.g., Water, Isopropanol, and Methyl salicylate).
• System Dynamics:
  • One phase region: Where the components are fully miscible.
  • Two phase region: Where the mixture separates into distinct phases.
  • Solution A: Composed of $60\%$ Isopropanol (IPA), $30\%$ Methyl salicylate (MS), and $10\%$ Water exists as a single phase.
  • Solution B: Composed of $20\%$ IPA, $30\%$ MS, and $50\%$ Water falls into the two-phase region.
  • Dilution of a single-phase solution (e.g., $80\%$ IPA and $20\%$ MS) with water can cause the system to cross the boundary into the two-phase region, resulting in precipitation or separation.

Interactions Between Cosolvents, pKa, and pH

• The addition of a cosolvent like ethanol can change the $pK_a$ of a drug, which in turn affects its ionisation and solubility at different pH levels.
• Case Study: Phenobarbitone:
  • $pK_a$ in water = $7.41$.
  • $pK_a$ in $30\%$ ethanol = $7.92$.
  • Effect at pH 2–6: The drug is predominantly unionised. Solubility increases steadily as the percentage of ethanol increases.
  • Effect at pH 8: The drug is significantly ionised in pure water (high initial solubility). Adding ethanol increases the $pK_a$, which reduces ionisation, causing a slight initial drop in solubility before it begins to increase again due to the cosolvent effect.
  • Effect at pH 9–10: High initial water solubility due to high ionisation. Large initial falls in solubility occur as ethanol suppresses ionisation by shifting the $pK_a$.

Solubility Parameters and Solution Non-Ideality

• Most real-world solutions are non-ideal, meaning solute-solvent interactions differ from solute-solute or solvent-solvent interactions. This requires an activity correction.

• Solubility Parameter (SP):

  • This parameter estimates the activity of a substance. The closer the SP of the solute and solvent, the more likely the system is to behave ideally.
  • The principle "Like Dissolves Like" applies: polar solvents dissolve polar solutes, and non-polar solvents dissolve non-polar solutes.

• Example: Caffeine in Dioxan/Water Mixes:

  • Maximum solubility of caffeine occurs at a specific mixture of $28\%$ water and $72\%$ dioxan.
  • At this specific ratio, the system's solubility parameter is $13.8$, which is very close to caffeine's SP of $14.1$.

Solubilisation through Surface Active Agents (Surfactants)

• Mechanism of Micellisation:

  • Surfactants are amphiphilic, containing both hydrophobic and hydrophilic regions. They accumulate at phase boundaries.
  • At sufficient concentrations, they form colloidal aggregates called micelles.
  • Micelles can be spherical, cylindrical, or form complex structures like liposomes and liquid crystals.
  • In aqueous environments, micelles have a hydrophobic core. Non-polar (insoluble) drug molecules can dissolve within this interior, effectively increasing the drug's apparent solubility.

• Control and Risks:

  • Concentration: Must be strictly controlled.
  • Too Low: May fail to solubilise all the drug or lead to precipitation during storage/dilution.
  • Too High: Increases costs, may cause toxicity, and can decrease bioavailability if the drug is bound too tightly within the micelle.

• Pharmaceutical Applications:

  • Phytomenadione (Fat-soluble Vitamin K): Solubilised using polysorbates for co-administration with water-soluble vitamins.
  • Iodine: Solubilised using macrogol ethers to improve chemical stability.
  • Cresol: Aqueous solubility is normally $2\%$. By using potassium soaps of oleic, linoleic, and linolenic acids (Lysol), solubility increases to $50\%$.

Molecular Complexation and Cyclodextrins

• Complexation Principles:

  • Poorly soluble drugs can interact with soluble materials to form soluble macromolecule complexes.
  • Complexes must be reversible; if the drug remains bound to the macromolecule, it cannot cross biological membranes.
  • Examples:
    • Aqueous Iodine (KI3): Formed by reacting $I_2$ with $KI$.
    • Povidone Iodine (Betadine): A complex of iodine and polyvinylpyrrolidone.
  • Negative Impact: Some complexes are detrimental to bioavailability. For example, tetracycline forms an insoluble complex with calcium carbonate, leading to slower dissolution.

• Cyclodextrins:

  • These are cyclic glucose units forming a hollow cylindrical shape.
  • Types: $\alpha$-cyclodextrin ($6$ units), $\beta$-cyclodextrin ($7$ units), $\gamma$-cyclodextrin ($8$ units).
  • Inclusion Complexes: The drug molecule (or a portion of it) inserts into the hydrophobic hollow central cavity, while the hydrophilic exterior of the cyclodextrin maintains solubility in water.
  • Pharmaceutical Examples:
    • Sporanox: Itraconazole with hydroxypropyl-$\beta$-cyclodextrin.
    • Menagargle: Iodine with $\beta$-cyclodextrin.
    • Viridal: Alprostadil with $\alpha$-cyclodextrin.
    • Nicorette Microtab: Nicotine with $\beta$-cyclodextrin.

Temperature Effects on Solubility

• Endothermic Reactions: The dissolution process absorbs heat. Increasing temperature leads to increased solubility.
  • Example: Sodium Sulfate Decahydrate ($Na_2SO_4 \cdot 10H_2O$).
• Exothermic Reactions: The dissolution process releases heat. Increasing temperature leads to decreased solubility.
  • Example: Anhydrous Sodium Sulfate ($Na_2SO_4$).
• Transition Point: For sodium sulfate, the transition from decahydrate to anhydrous form occurs at $32.5\,^{\circ}\text{C}$, shifting the solubility behavior from increasing with temperature to decreasing with temperature.