Understanding Physicochemical Properties for Pharmaceutical ...

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the product lifecycle. Product development work provides much of the information in the product and process design stage, including active pharmaceutical ...
Deliang Zhou

Understanding Physicochemical Properties for Pharmaceutical Product Development and Manufacturing—Dissociation, Distribution/Partition, and Solubility Deliang Zhou

Welcome to “Product and Process Design.” “Product and Process Design” discusses scientific and technical principles associated with pharmaceutical product development useful to practitioners in validation and compliance. We intend this column to be a useful resource for daily work applications. The primary objective for this feature: Useful information. Information developed during product and process design is fundamental to drug and product development and all subsequent activities throughout the product lifecycle. The quality-bydesign (QbD) initiative encourages understanding of product and process characteristics and process control based on risk analysis. Process design is the first stage of pharmaceutical process validation as described in the recent US Food and Drug Administration process validation draft guidance. This stage comprises activities that support product and process knowledge leading to a consistent manufacturing process throughout the product lifecycle. Product development work provides much of the information in the product and process design stage, including active pharmaceutical ingredient information, dosage

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form characteristics, quality attributes, and so on. Work conducted in development supporting product and process design stage must be based on scientific and technical principles. Disciplines supporting this work include basic chemistry and pharmaceutics; pharamcokinetics including drug absorption, metabolism, distribution, and excretion; biopharmaceutics information, and so on. The principles associated with these areas are broad and complex. Also, the technical language and mathematics associated therein may be esoteric and intimidating. This column addresses topics relevant to product and process design with these difficulties in mind. It is our challenge to present these topics clearly and in a meaningful way so that our readers will be able to understand and apply the principles in their daily work applications. Reader comments, questions, and suggestions are needed to help us fulfill our objective for this column. Please send your comments and suggestions to column coordinator Yihong Qiu at [email protected] or to journal coordinating editor Susan Haigney at [email protected]



Deliang Zhou, Ph.D., is an associated research investigator in Global Formulation Sciences, Global Pharmaceutical R&D at Abbott Laboratories. He may be reached at [email protected] Yihong Qiu, Ph.D., is the column coordinator of “Product and Process Design.” Dr. Qiu is a research fellow and associate director in Global Pharmaceutical Regulatory Affairs CMC, Global Pharmaceutical R&D at Abbott Laboratories. He may be reached at [email protected] PROCESS VALIDATION – Process Design 19

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KEY POINTS The following are key points addressed in this discussion: t6OEFSTUBOEJOHUIFQIZTJDPDIFNJDBMQSPQFSUJFT of the active pharmaceutical ingredient (API) is fundamental to pharmaceutical product development, manufacturing, and stability t.PTUQIBSNBDFVUJDBMTBSFPSHBOJDNPMFDVMFT  many of which are weak acids or weak bases that partially dissociate in aqueous solution t%JTTPDJBUJPONBZCFDIBSBDUFSJ[FECZ acidity dissociation constant (K a) or basicity dissociation constant (K b), and their corresponding pK a and pKb t#VGGFSTZTUFNTTVDIBTDJUSBUFBOEQIPTQIBUF buffers that resist pH changes upon the addition of small quantities of acid or base are based on dissociation behavior or weak acids and weak bases t"DJECBTFEJTTPDJBUJPOIBTTJHOJGJDBOUJOGMVFODF on almost all other physicochemical properties including salt formation, API purification, formulation, processibility, solubility, stability, mechanical properties, and biopharmaceutical performance t%JTUSJCVUJPOPSQBSUJUJPOSFGFSTUPUIFSFMBUJWF solubility of a drug between aqueous and nonaqueous immiscible liquids t%JTUSJCVUJPOPSQBSUJUJPOJTDIBSBDUFSJ[FECZ logD or logP t5IFEJTUSJCVUJPOQBSUJUJPOQIFOPNFOPOJT important in manufacturing and laboratory extraction processes to separate organic and inorganic compounds. Partition is the foundation underlying various chromatographic techniques t%JTUSJCVUJPOQBSUJUJPOJTJNQPSUBOUJO determining the biological, pharmacological, pharmaceutical, and toxicological activities of a drug molecule. It is widely used in designing drug candidates to possess appropriate absorption, distribution, metabolism, and excretion (ADME) properties tn-Octanol/water is the most commonly used system to characterize drug partitioning t"TPMVUJPOJTBTJOHMFQIBTFNJYUVSFDPOTJTUJOH of two or more components, usually solute and solvent t"TPMVUJPOJOXIJDIUIFTPMVUFJTBCPWF the solubility limit (supersaturated) is not thermodynamically stable and will ultimately lead to solute crystallization t5IF6OJUFE4UBUFT1IBSNBDPQFJBIBTEFGJOFE solubility definitions such as very soluble, freely soluble, slightly soluble, and other terms



t.PMFDVMBSJOUFSBDUJPOTJNQPSUBOUJOUIF solution process include Van der Waals forces, hydrogen bonds, and ionic interactions t5FNQFSBUVSFHSFBUMZJOGMVFODFTUIFTPMVCJMJUZ of a drug molecule and is always noted when solubility values are reported t5IFTPMVCJMJUZQSPEVDUPGBOJOTPMVCMF compound is the basis for applications of the common ion effect t5IFBRVFPVTTPMVCJMJUZPGBXFBLBDJEPSCBTFJT strongly pH-dependent due to relative species abundances at different pH t5IFTPMVCJMJUZPGQPMZNPSQITDBOCF significantly different because they have different free energies. The metastable polymorph can convert to the more stable polymorphs through solution-mediated transformation. The solubility difference among various solid forms is one of the driving forces responsible for phase changes during pharmaceutical processing. t4PMVCJMJUZQMBZTBDFOUSBMSPMFJOBOVNCFSPG issues related to drug dissolution, absorption, formulation and process development and manufacture, as well as stability t4PMVCJMJUZJTPGQBSBNPVOUTJHOJGJDBODFUPUIF biological performance of a drug molecule. The physiology of the gastrointestinal (GI) tract plays an important role in drug solubilization, including the pH environment and solubilization by bile salts. pH change is particularly relevant for weakly acidic or basic drugs. Solubility changes along the GI tract could also cause changes such as formation of salt, free acid or base, and hydrate, amorphous, and polymorph conversion. t4PMVCJMJUZJTFYUFOTJWFMZVUJMJ[FEJO crystallization and purification of active pharmaceutical ingredients and intermediates. Experimental conditions, such as pH, solvent, antisolvent, temperature, and other factors may be modified to optimize processes, control solid forms, and maximize yields. t4PMVCJMJUZJTPOFPGUIFVOEFSMZJOHSFBTPOT during many process-induced phase transformations such as hydrate formation during wet granulation and amorphous transition during drying.

INTRODUCTION Physicochemical properties are the foundation for pharmaceutical product development, manufacturing, and stability. They also provide insights to the biopharmaceutical performance of a drug molecule. A general appreciation of these

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subjects is important for scientists and engineers involved in pharmaceutical product development and manufacturing. This column discusses basic physical properties including: Dissociation of weak acids and bases, distribution and partitioning between aqueous and non-aqueous liquids, and solubility. This column starts with basic definitions, follows with important considerations, and completes each discussion with practical relevance. Particular attention is given to the contributions of dissociation to distribution and solubility. The significance of these basic properties is highlighted in the contexts of biopharmaceutics, pharmaceutical development, manufacturing, and stability.

DISSOCIATION AND THE DISSOCIATION CONSTANT The vast majority of pharmaceuticals are essentially organic molecules, a large fraction of which are weak acids or weak bases. Typical acidic groups include carboxylic acid (–COOH), sulfonic acid (–SO3H), sulfonamide (–SO2–NH–), and phenols (C6H5–OH). Primary, secondary, and tertiary amines, as well as pyridines and other aromatic amines, are the most frequently encountered basic groups. These molecules tend to dissociate partially in aqueous solutions, where equilibrium exists between the various ionized and unionized species.

The Ionization Equilibrium The dissociation of a monoprotic weak acid, HA, can be represented as follows: H+ + A– HA Similar to chemical equilibrium, the dissociation equilibrium is defined as follows: [H+][A–] Ka = [HA] Where Ka is known as the acidity dissociation constant or simply as the ionization constant, and the bracket [ ] represents concentration of a particular species at equilibrium. The concentrations, instead of activities, are used throughout because of their simplicity, and appropriateness for the purpose of this general discussion. Similarly to the notion of “pH”, pKa is more commonly used to denote the negative logarithm of the acidity dissociation constant. The pKa value, often a small positive number, is more convenient because most Ka values are so small. It is obvious that the acidity decreases with pKa. A typical organic carboxylic acid has pKa ~ 5, while phenols and sulfonamides are weaker, with typical pKa values of 8-10.

Similar treatments can be applied to a weak base: BH+ + OH– B + H 2O In this case, the proton is transferred from the water to the base, generating a hydroxyl ion. The basicity dissociation constant is then as follows: [BH+][OH–] Kb = [B] By convention, the concentration term of water is dropped because it is in large excess and its concentration does not change appreciably. It is also well known that water itself is very weakly dissociable to produce a proton and a hydroxyl ion as follows: H+ + OH– H 2O The self-dissociation constant of water is often designated as Kw = [H+] [OH–], which equals to 1 × 10 –14 at 25°C. Substituting the Kw in the previous equation, one obtains the following: Kw Kw[BH+] = Kb = [H+][B] Ka where Ka is the acidity constant of BH+, the conjugate acid of the base B, as shown below: H+ + B BH+ Ka =

[H+][B] [BH+]

Therefore, the basicity constant of a weak base can be represented by the acidity constant of its conjugate acid as: pKa = pKw – pKb, as is conventionally done. Basicity increases with increasing pK a, contrary to the acidity. Acids and bases can be categorized as monoprotic, diprotic, or polyprotic based on the number of protons they can accept or donate. Multiple ion equilibriums exist simultaneously for a polyprotic electrolyte, and each has its own dissociation equilibrium. For example, phosphoric acid dissociates in the following three steps: H 3PO4

H 2 PO4



H+ + H 2 PO4 –


H+ + HPO42–


H+ + PO43–

These stepwise pKas for phosphoric acid are 2.21, 7.21, and 12.7, respectively. The acid becomes progressively weaker.

PROCESS VALIDATION – Process Design 21

Deliang Zhou Figure 1: Species distribution as a function of pH for succinic acid.

For example, consider the following equation for a weak acid:


pH = pKa + log

H2 Suc 0.8

H Suc

( ) [A–] [HA]

= pKa + log

[base form] [acid form]



Suc 0.6



0 0



6 pH




Species distribution and buffer capacity are direct results from dissociation and are discussed next.

Species Distribution In Solution In an aqueous solution of a weak electrolyte various species, such as the unionized parent, the proton, and the ion, coexist. The relative fraction of each species depends on its pKa value and the solution pH, which can be calculated based on the dissociation equilibrium. For example, consider a monoprotic acid HA:

( )

[A–] log [HA]

β = d[base]/dpH = 2.303 Ctot =

[H+]Ka ([H+]Ka)2

This is the exact reason that most buffers are used around their pKa values in order to achieve their intended function. Unlike the strong acid and base buffers, a weak acid and base buffer allows the buffering pH to be maintained while adjusting the buffer capacity by changing the total buffer concentration, Ctot.

Significance Of Dissociation = pH - pKa

Therefore, the ionized species will dominate at pH > pKa, while the unionized neutral molecule will dominate at pH < pKa. To preferably target a certain species, either ionized or unionized, we often follow the rule of two pH units from pKa, because the ratio is either 100 to 1 or 1 to 100. This is particularly useful in separation science such as high performance liquid chromatography (HPLC), because mixed mode partition can cause peak broadening or even shouldering. Similar equations can be worked out for bases. An example species distribution is shown in Figure 1 for succinic acid. The hydrogen succinate displays a maximum around pH of 5.

Buffer Capacity Of Weak Electrolyte Solutions Weak acids and bases are often used as buffering agents (e.g., citrate buffer, phosphate buffer). A buffered solution, namely, refers to its ability to resist pH changes upon the addition of small quantities of acid or base. Quantitatively, buffer capacity, β, is the ratio the added strong base (or acid) to the resulted pH change. 22

This equation is known as the buffer equation or the Henderson-Hasselbalch equation, which describes how pH changes with the ratio of its species concentrations. The right most part of the equation is more general as it also applies to a weak base. It can be demonstrated that the maximum buffer capacity occurs at pH = pK a, where concentrations of the acid and base forms are equal. The exact buffer capacity can be obtained by differentiating the Henderson-Hasselbalch equation:


Acid/base dissociation is a simple concept, yet has significant influences on almost all other physicochemical properties. Salt formation is well built upon the dissociation concept, which has been extensively exploited during active pharmaceutical ingredient (API) manufacture for purpose of purification, processibility, and other aspects of pharmaceutical development such as solubility, stability, mechanical properties, and biopharmaceutical performance. A general rule of thumb for salt formation is that the difference in pK a between the drug and the counter ion should be at least three to increase the chance of success. Dissociation can also significantly impact stability, because the ionized and unionized species usually have different intrinsic reactivity—their respective rates of degradation may be significantly different. The more stable form of the API can thus be selected for product development. One or both of these forms can be catalyzed by the proton or hydroxyl ions, as evidence from the pH-stability profiles. Buffering agents have been frequently used to maintain a formulation at the desired pH for optimal stability, which is particularly important for parenteral and other liquid formulations.

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where C o and Cw are the equilibrium concentration of molecule in the oil and in the water, respectively. The distribution coefficient can also be approximated as the solubility ratio. Because distribution coefficients are usually large for organic molecules, they are often converted to logarithms, known as “LogD”. Following the convention, the natures of the partitioning phases are often noted, such as LogD n-octanol / water or LogD n-octanol / pH 7.4 buffer . The partition coefficient, LogP, is usually reserved to the partitioning of the neutral or unionized species, which can be deemed as the intrinsic distribution coefficient of a molecule (as to be shown, LogD is pH-dependent with ionizable molecules). Another term, called cLogP, refers to calculated LogP value based on molecular fragmentation algorithms.

LogD For Weak Electrolytes An ionized species has much less affinity to the oil phase than the corresponding neutral species. It could be well assumed that only the unionized species distributes in both phases while the ionized species is concentrated in the aqueous phase. The pH-distribution relationship can then be derived. For example, the following equation holds for a monoprotic weak base: LogD = LogP + log


Ka [H+] + Ka


Figure 2 shows such a plot for a weak organic base with a LogP of 4 and a pK a of 9. LogD decreases linearly with pH with a slope of negative unity at pH < pK a. It even becomes negative below pH 5, which renders itself practically not extractable by oil phase and can be utilized in separation.

Applications Of Distribution/Partition The distribution/partition phenomenon is common and has been utilized to a great extent by various industrial and laboratory extraction processes. Organic compounds can be readily separated

Figure 2: Example pH - LogD profile for a weak base with pK a of 9.




DISTRIBUTION AND PARTITION When an immiscible liquid, such as hexane or n-octanol, is added to an aqueous drug solution, the drug molecules will distribute themselves in each of the two immiscible phases. This phenomenon is known as distribution or partition. At equilibrium, the ratio of the concentrations in each phase is constant, which is a characteristic of the drug molecule itself and the nature of the two phases. This ratio is called the distribution coefficient of the drug as follows: D = CO/CW



-4 0








from inorganics by extracting with an immiscible solvent. Separation of organic mixtures can be possible if their LogD values are sufficiently different, or by manipulating their LogD values via pH modification. Partition is the foundation underlying various chromatographic techniques. In HPLC, a solute molecule is repeatedly partitioned between the stationary (column) and the mobile (eluent) phases. The number of equivalent partitioning process is so large that minute differences in the solute molecules can be magnified and thus successfully separated. The pH of the mobile phase is an important factor to optimize the interactions between solute and the stationary phase and between the solute and the mobile phase, because ionized and unionized species have enormously different LogD values. Both single mode and mixed mode elution have been utilized in modern HPLC development. Distribution/partition also plays an important role in determining the biological, pharmacological, pharmaceutical, and toxicological activities of a drug molecule. The distribution/partition characteristics are directly related to the lipophilicity of a molecule. Lipophicility characterizes the affinity of a molecule to lipid, fat, or oil. It is well known that the cell membrane has the phospholipid bilayer structure, which consists of various phosphoglycerides. There is a similarity between water/oil partitioning of a molecule and its ability to penetrate cell membrane. As a perquisite for a molecule to function biologically, the molecule itself has to be able to pass the cell membrane and penetrate into the cell. Indeed, Hansch et al. (1) established a correlation between n-octanol PROCESS VALIDATION – Process Design 23

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and water partition coeffienct and biological activities in the era of quantitative structure activity relationship (QSAR). Since then, the n-octanol/ water distribution/partition coefficient has been well established in the pharmaceutical industry and other related fields. In pharmaceutical sciences, distribution/ partition coefficient is now widely used in designing drug candidates to possess appropriate absorption, distribution, metabolism, and excretion (ADME) properties. The majority and the most convenient route of oral administration of a drug requires the drug molecule to be able to cross the gut wall membrane and get absorbed into the blood stream, and similar requirements hold true for routes of administration other than intravenous applications. In the absence of carrier mediated absorption (nutrients or nutrient-like molecules) or paracelluar diffusion (small hydrophilic molecules), passive diffusion in which the drug crosses the bilayer of the intestinal epithelium remains the primary mechanism for most drug absorption. A molecule needs to be sufficiently lipophilic to be able to cross the gastrointestinal (GI) membrane. Therefore, an appropriate LogD value is required for passive permeability in the GI epithelium. After a drug gets absorbed into the blood stream, the drug molecules are then carried to the various tissues and distributed throughout the body. This process can be deemed similarly as partition. It is generally true that a hydrophilic drug is distributed primarily in the plasma, while a lipophilic molecule is more extensively distributed in peripheral tissues and organs. It has been well known that sufficient lipophilicity is necessary for a drug molecule to pass the thick lipid bilayer called blood-brain-barrier (BBB), a tight layer of glial cells surrounding the capillary endothelial cells in the brain and spinal cord. Therefore, the distribution coefficient is of vast importance in designing molecules to have pharmacological activities in the brain. A recent survey (2) on drug metabolism has also suggested that lipophilic molecules are usually more extensively metabolized in the body, while hydrophilic ones are often excreted unchanged in the urine or bile, relating to its ability to access the enzymes responsible for metabolism. Therefore, the LogD/LogP values can provide tremendous insight on the drug’s relevant fates in the body. Distribution/partition has also been useful in environmental sciences. Hydrophobic chemicals tend to stay in the environment longer and are more difficult to clean up. They also tend to preferably get into various living species. Hence, the partition coefficient is an important consideration in environmental regulations. 24


Partitioning Systems For historical reasons, the n-octanol/water partition coefficient has prevailed compared to other solvent systems in the pharmaceutical fields. The octanol/ water system was initially thought to model essential properties of typical biological membrane. However, a thorough literature review has not resulted in compelling arguments. Partition between water and other immiscible solvents, such as hexane, cyclohexane, heptane, isooctane, dodecane, hexadecane, and chloroform have also appeared in the research literature, but far less frequently. From a physicochemical property point of view, the n-octanol molecule is characterized by a hydrophobic backbone (i.e., the C8 group) and a hydrophilic hydroxyl head. The hydroxyl group can be both a hydrogen-bond donor and a hydrogenbond acceptor. In addition, water-saturated octanol has ~25 mol % water, that has led to the suggestion of the 1:4 tetrameric structure. However, it was later determined by X-ray diffraction analysis that a cluster structure is more evident where ~16 octanol molecules point their hydroxyl groups to the water cluster by forming an extensive hydrogen-bonding network (3). Therefore, a cluster structure’s interaction with a drug molecule can be complicated and may not capture all the lipid permeation characteristics of a molecule. The proposition of using multiple systems to better characterize biological membrane modeling has also appeared, such as the “critical quartet” system (4). However, there has not been much development in this area. The quartet system is composed of n-octanol (a hydrogen-bond acceptor and donor), chloroform (a hydrogen-bond donor), alkane (an inert medium), and propylene glycol dipelargonate (a hydrogen-bond acceptor).

SOLUBILITY A solution is a single-phase mixture consisting of two or more components. A binary solution is composed of only two components, while a ternary solution is composed of three components. The liquid component is usually called the solvent, and the dissolved component is the solute. But the distinction is not absolute and becomes vague when two liquid components are concerned. A drug may not be dissolved in a solvent at any concentration. Indeed, above the solubility limit, a solution will not be thermodynamically stable. Still widely employed today as the most reliable method, solubility can be determined by equilibrating excess solids with a solvent. Equilibrium is deemed reached when the solution concentration reaches an asymptote—the dissolving

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Table: USP designations on solubility. Part of solvent required for 1 part of solute

Solubility in mg solute per mL of solvent

USP terminology

Less than 1 part

>1 g/mL

Very soluble

1-10 parts

100-1000 mg/mL

Freely soluble

10-30 parts

33.3-100 mg/mL


30-100 parts

10-33.3 mg/mL

Sparingly soluble

100-1000 parts

1-10 mg/mL

Slightly soluble

1000-10,000 parts

0.1-1 mg/mL

Very slightly soluble

More than 10,000 parts

<0.1 mg/mL

Practically insoluble

solvent contains the maximum amount of solute. At this point, the solution is said to be saturated with the solute and the solution is known as a saturated solution. The solution concentration equals the solubility in a saturated solution. In the language of thermodynamics, the free energy of the solute in solution equals that of the solid solute. A solution is unsaturated when concentration is less than the solubility, while a supersaturated solution refers to one whose concentration is higher than the solubility. One might be curious as how a solution could become supersaturated because macroscopic dissolution ceases once its concentration reaches the solubility. Well, there are many scenarios where this could happen. For example, temperature can significantly affect solubility. Therefore, one can purposely create an unsaturated or supersaturated solution by merely adjusting the temperature of the solution. A supersaturated solution is thermodynamically unstable and will lead to solute crystallization when adequate time is given. The reason is that the free energy of solute molecules in a supersaturated solution is always higher than those in the solid phase, and the crystallization process is spontaneous by going from a higher free energy state to a lower free energy state. However, rate of crystallization (kinetics) could vary. Crystallization needs to start with nucleation, a process where nuclei are formed, that serves as the sites for crystal growth. A supersaturated solution may be kinetically stable for a long duration without crystallization. Parent crystals, dusts, and other exogenous materials can in many cases serve as the nucleation sites and are often utilized in laboratory and industrial crystallization processes. Solubility is often reported in units such as weight by volume (w/v, e.g., mg/mL), weight-byweight (w/w), molar fraction, molarity, or molarlity. These units can be inter-converted when adequate information is given. The most frequently used

units for drugs are mg/mL or μg/mL, because solubility usually falls in these concentration ranges. It should also be noted that the United States Pharmacopeia (USP) has a special solubility designation system, as shown in the Table.

Solubility And Molecular Interactions Let’s take a look at schematic solution formation process at the microscopic level. According to Hess’s law, energy change of a process is path independent, only the initial and final states being of importance. This path independence is true for all state functions, such as enthalpy, free energy, and entropy. Therefore, the solution formation can be deemed to be composed of the following three essential steps: tStep 1. A solute molecule is liberated from its crystal lattice. Work is needed to overcome the lattice energy. This process could be approximated as the melting of the solute crystal. A high melting temperature and melting enthalpy usually imply high lattice energy.


tStep 2. A solvent cavity is created, large enough to hold the solute molecule. This process needs to overcome the cohesive attractions among solvent molecules.

tStep 3. Finally, a solution is formed by placing the solute molecule into the solvent cavity created in step 2. Energy is released resulting from PROCESS VALIDATION – Process Design 25

Deliang Zhou Figure 3: A pH-solubility profile for a weak acid with pKa of 4 and intrinsic solubility of 1 μg/mL.









1.E+00 0







solvent-solute interaction. Hopefully this energy is large enough to compensate the work needed in the previous two steps. It should be pointed out, though, that the energy in the first two steps need not be entirely compensated, because the entropy gained after mixing is also favorable, and can negate part of the energy consumed during steps 1 and 2.


Tremendous insight can be gained on solubility by just considering these processes. The solubility of a compound can be low due to: high melting point; high melting enthalpy; lack of solutesolvent interaction; and too strong solvent-solvent cohesion. For a specific compound and a specific solid form, the melting temperature and enthalpy is given and can not be changed. However, the solvent-solute interaction and solvent-solvent cohesion can be modulated and an appropriate solvent system may be designed to achieve desired solubility. For this reason, the following molecular interactions are important: tVan der Waals forces. Van der Waals forces include both dipole-dipole, dipole-induced dipole, as well as induced dipole-induced dipole interactions. A molecule having permanent dipole tends to interact with another dipole by pointing to opposite pole and this interaction is known as dipole-dipole or Keesom forces. Permanent dipoles are also able to induce an electric dipole in nonpolar but polarizable neighboring molecules, and this interaction 26


is called the dipole-induced dipole or Debye force. Finally, transient polarization exists in nonpolar molecules because of the electronic cloud movements in the molecule. This induced dipole-induced dipole interaction is called the dispersion or London force. All these van der Waals forces decrease quickly with distance (1/ r6) and are usually in the magnitude of 1 – 10 kcal/mol. On an individual basis, they are weak and follow the rank order Keesom force > Debye force > dispersion force. However, they cannot be ignored for a collection of molecules. Even the weakest dispersion force is sufficient to cause the condensation of nonpolar gas molecules and crystallization of nonpolar liquids. tHydrogen bonds. Hydrogen bonds refer to the interaction between a hydrogen atom and a strongly electronegative atom such as fluorine, oxygen, and nitrogen. The nature of hydrogen-bond is largely electrostatic interaction between the small size and large electrostatic field of the hydrogen atom, and the strong electronegativity of the acceptor atoms. Hydrogen bond requires certain direction, is a fairly strong intermolecular interaction (2-7 kcal/mol), and is always in addition to the van der Waals forces. It exists in water, hydrogen fluoride, and ammonium, and is responsible for their abnormally high boiling points and high melting points in their corresponding homologous series. tIonic interactions. Ionic interaction is the electrostatic interaction (attraction and repulsion) between ions of the opposite or same charges. They are the primary interactions responsible for ionic crystals. Solubility of ionizable molecules also depends partially on the ion-dipole and ion-induced dipole interactions between the solute and solvent. A polar solvent has high dielectric constant (e.g., water) that can reduce the ion-ion interaction. Therefore, ionizable compounds such as salts usually are more soluble in polar solvents than in non-polar solvents. The empirical rule on solubility states “like dissolves like.” The rule itself is a bit vague; however, one may make judgment calls by examining the interactions stated previously. A polar molecule is likely more soluble in polar solvents. When a drug molecule is capable of forming hydrogen bonding, a solvent capable of satisfying such requirements is likely to provide improved solubility. In the absence of any polar group, a drug molecule is probably more soluble in a nonpolar solvent such as alkanes and benzene.

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A drug molecule that contains both polar and nonpolar groups may require a solvent or a mixed solvent capable of providing simultaneous interactions to both parts of the molecule.

Effect Of Temperature Temperature greatly influences the solubility of a drug molecule; therefore, the temperature is always noted when solubility values are reported. The influence of temperature on solubility depends on the heat of solution. Solubility decreases with temperature when the heat of solution is negative (i.e., when the dissolution is an exothermic process). Solubility increases with temperature if the solution process absorbs heat (endothermic). This observation is consistent with the Le Chatelier’s principle on equilibrium. The magnitude of the heat of solution determines the steepness of solubility change when temperature is altered. The quantitative relationship is well captured by the Van’t Hoff equation. Some molecules have a more complicated temperature-solubility relationship. For example, phenol shows an upper consolute temperature (UCP) of 66.8°C, above which it can be mixed with water at any ratio. Triethylamine demonstrates a lower consolute temperature (LCT) in water of ~18°, below which the two are miscible in all portions. Nicotine-water system shows both an UCP and LCT. The existence of UCP and LCT has something to do with the solute-solvent interactions and their temperature dependences. For example, the hydrogen-bonding interaction could be destroyed at higher temperature; therefore, an LCT could form. Sometimes solute can form complexes with solvent called solvates. It is then the solvated form that controls the equilibrium solubility. A solvate is usually less soluble in the same solvent than the unsolvated form due to thermodynamic reasons. A solvate may become unstable and dissociate above a certain temperature. Therefore, the temperaturesolubility line may break its trend. Sodium sulfate is an example of this type of interaction.

Solubility Product And The Common Ion Effect When a salt is dissolved, it dissociates into the respective anion and cation. At equilibrium, the product of the concentrations of these ions is constant. This is known as the solubility product, often represented as K sp. For example, the dissolution of silver chloride is as follows: Ag+ (aq.) + Cl– (aq.) AgCl(s)

where s and aq. represent solids and aqueous, respectively. Its solubility product is as follows: Ksp = [Ag+][Cl–] Therefore, the solubility of silver chloride can be reduced if additional chloride (e.g., NaCl) or silver (e.g., silver nitrate) ions are introduced into the solution. This phenomenon is known as the common ion effect.

pH-Solubility Profile The aqueous solubility of a weak acid or base is strongly pH-dependent due to relative species abundances at different pH. The concentration ratio between the ionized and unionized species is related via the Henderson-Hasselbalch equation, as discussed previously. The overall solubility can then be derived for a weak acid or base, noting that the unionized species is in equilibrium with the excess solid (i.e., at the intrinsic solubility S0). For example, the total solubility of a weak acid is as follows: S = S 0 (1 + 10pH–pKa) A typical pH-solubility plot is shown in Figure 3 for a weak acid with pK a of 4 and intrinsic solubility of 10 μg/mL. Below pH 4, solubility is essentially constant and is equal to the intrinsic solubility. However, above pH 4, the solubility increases exponentially with pH. The solubility will not, however, increase monotonically without a limit. Salt formation could also take place; therefore, the solubility reaches a plateau (shown in Figure 3 as the blue dash line), the value of which is determined by the solubility product of the salt. The broken red line is just an extension of the pH-solubility profile if a salt is not formed.

Solubility Of Polymorphs And Solvates Polymorphism is the existence of multiple crystal forms by the same chemical entity. They exist as different molecular packings in the crystal lattice. The reasons leading to polymorphism are complex but are related to the ability of a molecule to efficiently pack itself in a unit cell with different conformation, orientation, or hydrogen-bonding motifs. Crystal hydrate is the incorporation of water molecules in a drug crystal unit cell. Similarly, a solvate could be formed. In addition, amorphous form refers to the non-crystalline solid when the long-range order in a crystal is destroyed. All these can be collectively called the solid forms of a drug molecule. The solubility of polymorphs can be significantly different because they have different free energies.

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For example, the solubility of ritonavir Form II is about 1/4 of that of Form I at 5°C (5). The most stable form has the least free energy and lowest solubility. The free energy difference between two polymorphs is related to the following solubility ratio: ΔG(I – II) = RT ln(SI/SII) The metastable polymorph can convert to the more stable polymorphs through solution-mediated transformation, where the solution concentration is higher than the solubility of more stable form thus providing the thermodynamic driving force for conversion. The ritonavir Form I to Form II transition in the liquid-filled capsules is such an example. Still, the amorphous form, being the most energetic, has the highest solubility. Solvates usually have less solubility in the same solvent than the unsolvated form because equilibrium dictates so due to the large excess of solvent. Therefore, a solvated form is often discovered during the crystallization in a particular solvent. There also exists a critical solvent activity, above which the solvate is more stable while below which the unsolvated form is more stable. Specifically for hydrates, the critical relative humidity (RH) or water activity comes to play a significant role, because moisture is ubiquitous during storage and because water is the most frequently used solvent in wet granulation. It should also be noted that a solvate has higher solubility in other miscible solvents, because the dissociated solvent molecules drag the drug molecules into solution. The solubility difference among various solid forms is one of the driving forces responsible for phase changes during pharmaceutical processing.

Significance Of Solubility Solubility plays a central role in a number of issues related to drug dissolution, absorption, formulation and process development and manufacture, as well as stability. Solubility is of paramount significance to the biological performance of a drug molecule. Drug molecules, when presented as oral solid dosage forms, need first to dissolve in the GI fluid before absorption can take place. The dissolution rate of a solid is proportional to its solubility, diffusivity, and surface area. Therefore, the higher the solubility, the faster a molecule can get into solution, and the higher its concentration in the GI fluid. In turn, this leads to a higher rate of absorption, because the passive diffusion is driven by the concentration gradient across the GI membrane.

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The physiology of the GI tract plays an important role in drug solubilization, including the pH environment and the solubilization by various bile salts. For example, the human stomach is characterized by a low pH of 1.5-2 under fed conditions and pH 2-6 under fasted conditions. The pH increases going down to duodenum (pH 4.5-5.5), small intestine (pH 6-6.5), ileum (pH 7-8), and colon (pH~5.5-7). The small intestine is also characterized by a high concentration of bile salts and the large surface area attributing to its villi and micro-villi structures. The small intestine serves as the primary site of drug absorption. On the contrary, the large intestine does not possess the villi structure. It also lacks the fluid to solubilize a drug and is challenging for drug absorption, except for certain highly soluble and highly permeable molecules. The change in pH, bile salt concentration, fluid contents, motility, as well as the residence time, all affect the solubility and in vivo dissolution of a drug molecule, and influences its oral absorption. The pH change is particularly relevant for weakly acidic or basic drugs. Solubility changes along the GI tract could also cause solid form changes, such as salt formation, parent formation, hydrate formation, as well as polymorphic conversion, all complicating the drug absorption process. Appropriate solubility and solvent system are also required to develop other formulations such as parenteral, subcutaneous, transdermal, and aerosol formulations. Solubility is extensively utilized in crystallization and purification of active pharmaceutical ingredients and/or their intermediates. Experimental conditions, such as pH, solvent, antisolvent, temperature, and other factors may be modified individually or in combination in order to optimize the process. Solubility plays an important role in controlling the solid forms as well as the yields. Amorphous forms have been extensively utilized to improve drug bioavailability because they have higher apparent solubility (6). Solubility is one of the underlying reasons for many process-induced phase transformations (7). For example, hydrate formation can occur during wet granulation. The hydrate may then partially or fully dehydrate during drying, resulting in formations of partially amorphous or less ordered molecular form. A highly water-soluble, low dose drug may completely dissolve during wet granulation and turn into amorphous upon drying. All these changes can have profound effects on product attributes such as stability, dissolution, and in vivo performance. These phase changes can be

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scale, time, and equipment dependent due to their kinetic nature, which is worrisome from the quality control point of view. The solubility and solubility differences among the various solid forms are responsible for, and are the keys to, understanding and resolving these transformations as they provide the thermodynamic driving forces for change.

SUMMARY Dissociation, distribution/partition, and solubility constitute the fundamental physical properties of a drug molecule. They influence, directly or indirectly, almost every aspect in drug development: Absorption, distribution, metabolism and excretion, formulation development, processing development, stability, product manufacture, and regulatory concerns. Many issues during pharmaceutical development can be related to characteristics in these basic properties in one way or another. Awareness and knowledge of these subjects is important to understand and solve various issues during pharmaceutical development, manufacturing, and stability.

REFERENCES 1. Hansc h, C. and L eo, A. Substituent Constants for Correlation Analysis in Chemistry and Biolog y, WileyInterscience, New York, 1979. 2. Custodio, J. M.; Wu, C.Y. and Benet, L. Z., “Predicting Drug Disposition, Absorption/Elimination/Transporter Interplay and the Role of Food on Drug Absorption,” Advanced Drug Delivery Reviews 60, 717-733, 2008. 3. Franks, N. P., Abraham, M. H., and Lieb, W. R ., “Molecular Organization of Liquid n-Octanol: An X-ray Diffraction Analysis,” Journal of Pharmaceutical Sciences, 82, 707-712, 1993.

4. Leahy, D. E.; Morris, J. J.; Taylor, P. J. and Wait, A. R., “Membranes and Their Models: Towards a Rational Choice of Partitioning System,” Pharmacochem. Libr. 16, 75-82, 1991. 5. Bauer, J.; Spanton, S.; Henry, R.; Quick, J.; Dziki, W.; Porter, W. and Morris, J., “Ritonavir: An Extraordinary E x a mple of C on for m at ion a l Pol y mor ph i sm ,” Pharmaceutical Research, 18, 859-866, 2001. 6. Law, D.; Schmitt, E. A.; Marsh, K. C.; et al., “RitonavirPEG 8000 Amorphous Solid Dispersions: In vitro and in vivo Evaluations,” Journal of Pharmaceutical Sciences, 93, 563-570, 2004. 7. Zhang, G. G. Z.; Law, D.; Schmitt, E. A. and Qiu, Y., “Phase Transformation Considerations During Process Development and Manufacture of Solid Oral Dosage Forms,” Advanced Drug Delivery Reviews, 56, 371-390, 2004. JVT

ARTICLE ACRONYM LISTING ADME Absorption, Distribution, Metabolism, Excretion API Active Pharmaceutical Ingredient BBB Blood-Brain-Barrier FDA US Food and Drug Administration GI Gastrointestinal HPLC High Performance Liquid Chromatography Ka Acidity Dissociation Constant Kb Basicity Dissociation Constant LCT Lower Consolute Temperature QSAR Quantitative Structure Activity Relationship RH Relative Humidity UCP Upper Consolute Temperature USP United States Pharmacopeia

Originally published in the Spring 2009 issue of The Journal of Validation Technology

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