Multiple Solid Phases and Crystal Polymorphism in Pharmaceuticals PDF

Multiple Solid Phases and Crystal Polymorphism in Pharmaceuticals Many pharmaceutical compounds can exist in multiple crystalline solid-state forms, which are referred to as crystal polymorphs. These different polymorphs can have distinct...

Multiple Solid Phases and Crystal Polymorphism in Pharmaceuticals Many pharmaceutical compounds can exist in multiple crystalline solid-state forms, which are referred to as crystal polymorphs. These different polymorphs can have distinct physical properties, such as solubility, stability, and bioavailability. Example: Paracetamol has at least three known polymorphs, each with different properties that can influence the drug’s effectiveness and shelf life. The stability of a polymorph can change with temperature, as different forms may be more stable at specific temperatures or humidity levels. In addition to crystalline forms, pharmaceutical compounds can also exist as amorphous (non-crystalline) solids. Amorphous forms typically have higher solubility than their crystalline counterparts but are more prone to instability, such as recrystallization over time. Control of the crystal form is critical in drug formulation. The polymorph selected for the final drug product (medicine) will influence key pharmaceutical properties like solubility, dissolution rate, stability, and ultimately bioavailability. Phase Diagram for a Compound with Two Crystal Forms A phase diagram for a compound with two crystal forms is similar to the basic one-component phase diagram, but with the addition of two distinct solid regions, denoted S₁ and S₂. o S₁ and S₂ correspond to the two different crystal polymorphs of the compound. o These polymorphs are crystalline forms of the compound that differ in their molecular arrangement, which affects their physical properties like solubility, stability, and melting point.  Temperature and pressure conditions dictate which polymorph (S₁ or S₂) will be the more stable form under specific environmental conditions: o One polymorph may be more stable at low temperatures, while the other may be more stable at higher temperatures. o The stability of the polymorphs can also depend on pressure, where a particular polymorph could be favored at higher or lower pressures. The phase diagram for such a compound typically has: o A solid-liquid boundary line, representing the conditions under which the substance is either a liquid or solid. o A solid-solid boundary line, separating the two crystal forms (S₁ and S₂), which indicates at what conditions one polymorph transforms into the other. Polymorph stability is important in the pharmaceutical industry, as the most stable form may have better shelf life and consistent performance. In contrast, less stable polymorphs may be more soluble and thus have faster onset of action, but they may be more prone to degradation or change into a more stable form over time. Dealing with Non-Ideality in Thermodynamics Thermodynamic functions like ΔU (internal energy), ΔH (enthalpy), ΔS (entropy), and ΔG (Gibbs free energy) are typically defined for ideal gas systems, where molecules are assumed to have no interactions with each other, and the system behaves in a predictable way. Real (non-ideal) systems, however, often involve solids, liquids, and especially solutions, where intermolecular forces and interactions are significant, making the system deviate from ideal behavior. For these systems, adjustments must be made in the thermodynamic equations to account for non-ideality. For any system, the Gibbs free energy (G) is a function of the pressure (P), volume (V), and temperature (T): Consider a system with three components, A, B, and C. For an ideal system, where the components do not interact, the total Gibbs free energy is simply the sum of the individual Gibbs free energies of each component: This is based on the assumption that each component behaves independently and does not influence the others in terms of energy changes.  However, for a non-ideal system (such as a mixture of liquids or a solution), the total Gibbs free energy will not just be the sum of individual components' free energies. The components interact with each other, and these interactions must be considered. For example: These interaction terms represent deviations from ideal behavior, such as activity coefficients or excess enthalpy. In non-ideal systems, the activity coefficient of each component reflects how much the behavior of that component deviates from ideality. The activity coefficient depends on the concentration and the interactions between the components in the mixture. The chemical potential for each component is adjusted by these coefficients: In summary, when dealing with non-ideal systems, it is essential to consider the interactions between components, which influence the overall thermodynamic behavior. For solid and liquid systems, and particularly solutions, the ideal assumptions no longer hold, and adjustments using activity coefficients, excess enthalpy, and modified forms of Gibbs free energy are necessary. Chemical Potential (μ) and Free Energy (G) in Real Systems In an ideal system, the total Gibbs free energy (GtotalG_{\text{total}}Gtotal) is the sum of the Gibbs free energies of the individual components: However, this is not true for real systems, where interactions between components must be considered. In real systems, the total free energy depends on the mutual interactions of all components, and any change in composition, temperature, or pressure affects the system based on these interactions. For example, in a solution, the solute and solvent interact, influencing the free energy of the system. The chemical potential (μ) represents the contribution of each component to the overall free energy in a real system. It reflects how the energy of a system changes with the addition of an infinitesimal amount of a component, keeping other factors constant (such as temperature and pressure). In a mixture, the chemical potential varies for each component depending on its concentration and  interactions. Free Energy in a Real System Key Points about Chemical Potential: Chemical potential and free energy: The chemical potential helps us understand how the total Gibbs free energy is distributed among the components in a system, and how it changes when the composition of the system changes. For real systems, unlike ideal systems, the chemical potential of each component is influenced by its concentration, interactions with other components, and the thermodynamic conditions (such as temperature and pressure). Real systems with mixtures: The total free energy is not simply additive because the interactions between components contribute to the overall free energy. This is why the chemical potentials are essential in understanding the behavior of real systems. In summary, for a real system, the total Gibbs free energy is the sum of the contributions from each component, where each contribution is weighted by its chemical potential, reflecting how the component's concentration and interactions affect the system's overall energy. Free Energy Changes in Real Systems and the Ideal Gas Equation In a real system, the free energy change (ΔG) is related to the equilibrium constant (Keq ) for the reaction, but this is slightly more complicated in systems where interactions exist between components. However, we can look at a similar equation for an ideal gas system. Gibbs Free Energy and Pressure in an Ideal Gas Relationship Between Free Energy and Concentration/Partial Pressure Connection to Free Energy Change Summary Free Energy Changes in Real Systems (e.g., Solutions) Activity and Activity Coefficients Key Concepts: Final Expression for Free Energy in Real Systems: Summary Free Energy Change and Equilibrium Constant in Real Systems Equilibrium Constant in Terms of Activities Activities vs. Concentrations Summary