5.1 Introduction
Solubility of a drug molecule in polar liquids, especially in water, is one of the most important factors that influence the drug use, formulation of the drug and its effectiveness. Equally important factor is the rate of dissolution of the drug molecule in physiologically relevant conditions (temperature, pH of aqueous medium, other ions or molecules that are present in the same solution etc.). Standardized methods of measuring the rate of dissolution is important to compare different drug molecules in terms of their use and effectiveness. Partitioning refers to the propensity of a solute molecule to get distributed in each of the phases in a two-phase liquid-liquid system. The drugs are often formulated in oils (topical formulations) or emulsions when the drug molecule does not have appreciable solubility in aqueous medium. Drug molecules from such formulations need to get distributed throughout the body through systemic circulation to reach the target tissue. Subsequently, drug molecules from systemic circulation has to reach the target tissue which are often hydrophobic (like adipose tissue, nervous tissue etc.).
This transfer of solute drug molecules from aqueous medium to lipid medium or vice versa happens at the interface where the two immiscible phases meet. This phenomenon is called partitioning. Knowledge of partitioning helps one to understand the transfer of molecules between two adjacent but immiscible phases in quantitative terms.
5.2 Solubility
Solubility of a solute molecule in a solvent refers to the concentration of the solute in that solvent. The solvent is water or aqueous in most situations in pharmaceutical sciences. The solubility of a molecule depends on many factors including the nature of the molecule itself, the nature, specifically the polarity, of the solvent, the temperature and also the pH of the aqueous solution if the solute is a weak electrolyte. We are mainly interested in the solubility of drug molecules in physiological conditions (i.e. in blood plasma, gastro-intestinal fluid, inter and intracellular fluid in body temperature 37.4 0C) and also in the environmental conditions in which the drug molecules remain in the formulation outside the body.
5.3 Solubility and temperature
Solubility refers to the mass of solute that gets dissolved per unit volume of solvent. When the solute and the solvent are both liquid in room temperature, (250C) the term miscibility is used instead of solubility. Miscibility refers to the mass or volume of solute (liquid) that is miscible per unit volume of solvent. Solubility and miscibility are both expressed in concentration terms of the solute. The relationship between solubility and temperature is explored in this section. The relationship is expressed through Arrhenius equation.
ΔHsoln<0 means solute molecules give off energy in the dissolution process, solution become hotter and the dissolution process is exothermic. When ΔHsoln<0, an increase in temperature results in decrease in solubility.
ΔHsoln>0 solute molecules absorb energy in the dissolution process and the solution becomes colder and the dissolution process is endothermic. When ΔHsoln>0, an increase in temperature results in increase in solubility.
ΔHsoln is a property of solute molecule. A more convenient common logarithmic form of the same equation is often used.
Sometimes the solubility of a drug molecule is required. This can easily be calculated if the solubilities of the drug molecules are determined in the same solvent or solvent system in two different temperatures. The modified form of Arrhenius Equation in logarithmic form with two temperatures is given below.
The heat of solution is easily determined from the following form of the equation by substituting for the solubilities ST1 and ST2 at temperatures T1 and T2. The heat of solution, thus determined, is the property of the molecule in the specific solvent system. The solubility of the said molecule for a third temperature can now be determined, if required, using the numerical value of heat of solution.
5.4 Solubility of weak electrolytes and pH
Most of the drug molecules are weak electrolytes i.e. weak acids and weak bases and their salts. As explained in the previous chapter (Ionic Equilibria and its Application), weak acids are almost completely unionized in pHs that are two log units below their respective pKas. The solubility of the weak acid at these low pHs are minimum and are called the molar solubility of the weak acid. Molar solubility is a property of the solute molecule/drug.
In those low pHs, unionized weak acids have limited solubility in aqueous medium. As the ionization increases exponentially with increase in pH within two log units of the pKa, so does the solubility. At a pH above two log units of pKa of the weak acid, almost all of the weak acid is ionized and maximum solubility of the weak acid is achieved at a pH that is above two log units of its pKa.
pHp is not a property of the molecule or drug. The pHp depends on the pKa and the total concentration of the drug is being dissolved.
Significance: pHp of S molar weak acid is 6.3. What does it mean?
It means pH=6.3 is the minimum pH at which all of S molar weak acid will remain in solution; if the pH is lowered any further, the weak acid will start precipitating.
The pH of precipitation of weak base:
Molar solubility-solubility of the unionized species: S0
Molar solubility is a property of the solute molecule/drug.
Total solubility of the weak base (ionized plus unionized): S
Solubility of the ionized weak base (conjugate acid): (S-S0)
Using Henderson Hasselbalch equation in case of weak bases;
Significance: pHp of S molar weak base is 6.3. What does it mean?
It means pH = 6.3 is the maximum pH at which all of S molar weak base will remain in solution; if the pH is increased any further, the weak base will start precipitating.
5.5 Influence of solvents on solubility: strong, weak and non-electrolytes
The nature of the solvent and the solutes and the interaction between them determines solubility of a solute in a solvent. In the area of pharmaceutical sciences, the solvent is primarily water. Sometimes, very little amount of miscible liquids like ethyl alcohol (C2H5OH) or glycerol (CH3OH-CHOH-CH3OH) are added to water for various practical reasons. These miscible liquids, often called co-solvents, often increase the solubility of solute (often drug) molecules. Co-solvents are also often used to minimize bacterial or fungal growth in aqueous environment. A solution is called aqueous when most of the solvent present in the solution is water. Water is called a universal solvent; most (drug) molecules have at least slight solubility in water. Most strong electrolytes are readily soluble in water. Weak electrolytes (weak acids, weak bases and their salts) have lower solubility in water.
Sometimes the nature of the solvent (water) is slightly modified using co-solvents or pH chemistry to suit the solubility needs of the particular solute. The solubility of weak electrolytes is dependent on the pH of the aqueous medium as the pH determines the percent ionized of weak electrolytes in water. Polar non-electrolytes (like glucose) have reasonable solubility in water. Reasonably non-polar molecules including non-electrolytes but also weak electrolytes have solubility limitation in water. If a drug is reasonably non-polar and a non-electrolyte, sometimes a suitable co-solvent like ethyl alcohol or glycerol is used to dissolve the solute in aqueous environment. Alternatively, the nature of the solute can also be changed slightly to fulfill the needs of the solvent. Sometimes a salt of a weak electrolyte drug is deliberately used in formulations to increase its solubility i.e. to keep the molecule in aqueous solution. Other techniques like formation of stable, aqueous-soluble complexes and micellar solubilization (by the use of surface-active molecules) are also regularly used in formulations.
5.6 Dissolution
The process in which a solid solute molecule becomes a part of solution in a solution is called dissolution. Drug molecules need to get dissolved in gastro-intestinal fluid to be absorbed in the blood stream and then reach the site of action through the same. Undissolved solid drug particles cannot be absorbed and cannot travel to the site of action. That is why dissolution and, more importantly, rate of dissolution of the drug molecule from the formulation is of paramount importance. It is the rate of dissolution of the drug molecules that determines how quickly the particular drug is absorbed in the blood stream to initiate the pharmacological action.
Rate of dissolution
Dissolution is a phenomenon by which solute molecules escape the matrix of the solute particles and evenly distributes themselves homogeneously in the solvent body. Dissolution and more importantly, the rate of dissolution is an important aspect of pharmaceutics. Solid oral dose forms undergo disintegration, which is the conversion of a tablet or capsule into a mass of individual solid particles. Disintegration usually happens in the upper parts of the gastro-intestinal tract (GIT, specifically esophagus). The drug molecules then undergo dissolution in stomach and small intestine. A fraction of the dissolved drug (a fraction of the local concentration) gets absorbed in to the blood stream through the intestinal wall, which contains a large surface area due to the presence of villi and microvilli. The rate of dissolution refers to the rate at which the drug molecules are transferred from the solute particles to the bulk of liquid. The rate of dissolution is measured in terms of mass or concentration change (from solid to dissolved state) per unit time. When the solute (drug) particles are surrounded by water ( or GIT fluid), there remains a thin layer of water ( or GIT fluid) that adheres to the particles tightly. This layer is called the diffusion layer
Figure 5.1:
Scheme 1. Dissolution of drug particles according to diffusion layer model
On the particle surface of the diffusion layer (with thickness h in the scheme), the concentration of the solute is the saturation concentration Cs, which is the property of the solute for that particular solvent. At the end of the diffusion layer, (at a distance h from the solute particle surface) the concentration is C, which is also the bulk concentration. The bulk concentration is zero at the beginning of the diffusion process and keeps on increasing as the time passes, with the highest possible concentration in bulk liquid being C = Cs. The solute concentration decreases sharply across the thickness of the diffusion layer. The following diffusion scheme is the basis of the Noyes-Whitney (proposed in1897) equation that quantitatively describes the dissolution process.
Noyes-Whitney equation
C= the bulk concentration of the solute
D = the diffusion coefficient of the solute. Diffusion coefficient is the property of the solute molecule for a specific solvent (water in this case) at a specific temperature. Hydrophilic (polar molecules) generally have higher diffusion coefficient in water which means that the molecules diffuse faster through water and the rate of dissolution is higher. Diffusion coefficient is measured by area per unit time.
S = the surface area of the solute particle that is dissolving.
V= the total volume of solvent in which the diffusion is taking place.
h = the thickness of the boundary layer or diffusion layer. A thin layer of liquid always remains attached to the solute particle/crystal whenever a particle is suspended or put into the liquid. This layer of liquid moves with the particle/crystal as the latter moves in the body of liquid. This thin layer of liquid is called boundary layer or diffusion layer. The concentration of the solute in dissolved form sharply decreases across the diffusion layer from saturation solubility (Cs ) at the surface of the solute particle to the instantaneous bulk concentration of dissolved solute (C) at any point of time. Diffusion layer thickness (measured by unit of length) is inversely proportional to the rate of dissolution.
K= dissolution rate constant =
the first form of the Noyes Whitney equation and is measured in the units of distance per unit time.
5.7 Significance of dissolution, Factors affecting dissolution, USP dissolution testing
Most drug molecules are in solid form in room temperature and most formulations (especially for oral use) are in solid form (tablets, capsules etc.) too. These formulations have to go through the processes of disintegration (into particles) and dissolution before the drug is absorbed to the blood stream and get distributed to the target tissue before they can have pharmacological activity. The time involved for these processes to be completed and pharmacological action to start indicates the delay of drug action from taking the drug. This time is sometimes referred to as ‘lag time’. A faster onset of action is almost always desirable. Sometimes, longer duration of action is also desirable in addition to faster onset of drug action. The rate of dissolution of the drug molecules from the formulation controls both the onset of action and duration of action. That is why the rate of dissolution of a particular drug molecule from a particular formulation has to be determined. This is achieved by dissolution testing of the formulation under standardized conditions of temperature, dissolution media (e.g. simulated gastro-intestinal fluid) and maintaining sink condition in all dissolution experiments. This standardization helps in comparing the rate of dissolution of different drug molecules and that of the same drug molecule in different formulations. The dissolution testing standards are specified in United States Pharmacopeia (USP) chapter (711). The following link provides further information regarding standardized conditions of dissolution testing and different dissolution apparatus etc.
5.8 Phases and Partitioning across two phases in contact with each other
Phase
A phase is a three-dimensional space occupied by molecules that are homogeneously distributed within that space. A phase can contain similar and/or dis-similar molecules. For example, pure water in a beaker constitutes a phase. Normal saline (0.9% w/v sodium chloride solution) constitute a phase also as the sodium chloride molecules and Na+ and Cl- ions along with water molecules are homogeneously distributed in the space of the solution. A liquid phase is always transparent (see through, light goes through) though a liquid phase can have color.
A two-phase system contains two completely separated phases that are in contact with each other, with each phase being homogeneous in terms of molecular distribution. When we mix two immiscible liquids like water and octanol, we get a two-phase system with both water and octanol (that are in contact with each other), constituting two separate homogeneous spaces in terms of their molecular compositions. When a two-phase system remains undisturbed, the phases are completely separated and are both transparent in case of liquids and gaseous phases. Sometimes, it is advantageous to make a formulation in a two-phase system because of various practical reasons including the limiting solubility of the drugs in water. It is important that in the two-phase pharmaceutical formulations both the phases are finely distributed in each other to ensure dose uniformity. For example, when a drug is formulated in an emulsion, the liquid phases consist of water and oil; with one phase being distributed as fine droplets surrounded by another phase. The two-phase systems are inherently unstable. The two phases tend to separate and exist as two distinct spaces lying next to each other. Such a condition, if it occurs in a formulation, is undesirable as it hampers dose uniformity. These formulations containing two-phase systems can be made quazi-stable using principles of physical pharmacy. A suspension of fine solid drug particles in liquid water is also a two-phase system in which one of the phases is the solid particles while the other phase is liquid. These two-phase system formulations are often opaque (light cannot pass through) or at least translucent (a fraction of the light passes through).
Partitioning
Partitioning refers to the distribution process of solute molecules among two immiscible liquid phases that are in contact with each other. When a solute molecule (e.g. a drug) is added to a two-phase system, almost always, the solute molecules get distributed in both the phases in different concentrations. The concentration in each phase is different from each other and depends on the polarity of the solute and that of the solvents constituting each phase. The ratio of concentrations of the solute molecules in the two phases remains constant for a specific solute and for a specific
set of immiscible
Where, Kd= Partition coefficient or Distribution coefficient and
C0-Concentration of solute in organic phase (for example octanol)
CW-Concentration of solute in water
The partition coefficient Kd is a property of the solute (often the drug molecule in the context of formulations) and its value is characteristic of the solute molecule for the set of immiscible solvents.
Water-octanol partition coefficient is traditionally used for partition coefficient data for pharmaceutical use. When the liquid phases are fixed to be water (polar, hydrophilic) and octanol (relatively non-polar, hydrophobic), the partition coefficient Kd represents the property of the solute/drug molecules and it becomes easier to compare the properties of different drug molecules in similar drugs of the same pharmacological families. The octanol-water partition coefficient can also be used to have an initial idea of where the drug molecule gets distributed once it is in the body. The drug that has a higher Kd, is more likely to get distributed to the hydrophobic part of the body (adipose tissue, brain, skin, skeletal muscle) compared to blood stream and well perfused cells. The concentration of the drug/solute in organic phase C0 is always in the numerator while the drug/solute concentration in water CW is always in the denominator in the Kd calculation. A higher value of Kd for a solute represents higher concentration in organic and lower concentration in aqueous phase (i.e. more hydrophobic, more lipophilic). A lower value of Kd for a solute represents lower concentration in organic and higher concentration in water (i.e. more hydrophilic, more lipophobic).
5.9 Partitioning of strong, weak and non-electrolytes between two phases
Strong electrolytes
Non-electrolytes
Non-electrolytes partition between aqueous and organic phases in varying degrees; their partition coefficient depends on the properties of the solutes (polarity, hydrophilicity etc.) for the chosen liquid phases.
The partitioning of the non-electrolytes is not affected by the pH of the aqueous phase, i.e.
Weak electrolytes
Weak electrolytes are the compounds that ionize in polar/aqueous phase but, only partially. Examples include weak acids, weak bases, salts of weak acids and weak bases.
Molar partition coefficient
-
- Molar partition coefficient- partition coefficient of the unionized species
- Molar partition coefficient –only applicable for weak electrolytes
- Molar partition coefficient; Kd
- For weak acids: Molar partition coefficient occurs at a pH that is at least two log units below the pKa of the solute
- For weak bases: Molar partition coefficient occurs at a pH that is at least two log units above the pKa of the solute
Apparent Partition Coefficient
The pH of the aqueous phase controls the extent of ionization in these cases and the partitioning is largely controlled by the pH of the aqueous phase; as the pH of the aqueous phase in the octanol-water two phase system is changed, the partitioning pattern also changes and so does the partition coefficient (Kd). In this partition coefficient of the weak electrolytes, the value of the said partition coefficient depends on the pH of the aqueous phase. This partition coefficient is called the apparent partition coefficient (Kd app). In summary:
- Apparent partition coefficient- (Kdapp): the actual partition coefficient of a weak electrolyte when the aqueous phase is maintained at a specific pH such that the weak electrolyte is ionized in a controlled manner based on the pH of the aqueous phase
- Apparent partition coefficient- Kdapp: depends on the pH of the aqueous phase and pKa of the solute
- Apparent partition coefficient is specified at certain pH; without the mention of the pH, apparent partition coefficient does not have any meaning
- Apparent partition coefficient of a solute is a property of the molecule that is specified for a specified set of liquid phases and at a specific pH
Apparent Partition Coefficient for weak acids
Apparent Partition Coefficient weak bases
Kd app = the apparent partition coefficient for the specific solute at that specific pH and for the specific organic phase
Kd = the molar partition coefficient for the specific solute irrespective of pH and for the specific organic phase
Ka = the ionization constant of the weak base converted from Kb to Ka
[H+]= the hydrogen ion concentration in the aqueous phase
It needs to be noted that the weak bases get more ionized as pH of the aqueous solution decreases. At a pH that is two log units above the specific pKa of the weak base, almost none of the weak base molecules are ionized, i.e. the aqueous solubility of the weak base is minimum and organic solubility of the weak base is maximum.
At that pH or above, the
is maximum.
5.10 Significance and application of partitioning
The principles of partitioning apply in many different levels in pharmaceutical sciences including in pharmaceutics, formulation science and pharmacokinetics. A significant number of formulations, both oral and especially topical preparations, are two-phase systems, mainly emulsions; both water-in-oil and oil-in-water types. In these formulations, the total solubility of the drug molecules and the excipients like coloring agents, preservatives etc. depend on the solubility of the solute molecules in each of the phases. Additionally, the aqueous solubility of the weak electrolytes (most drug molecules and preservatives are weak electrolytes) depend on the pH of the aqueous phase of the two-phase formulation. In depth knowledge of the principles of partitioning and application of the appropriate equations help the formulation scientists to assess the total solubility of the solutes (drug and excipients) in the chosen two-phase formulations. Preservatives are generally required to stop microorganism (bacteria, fungi etc.) growth in the aqueous phase of the two-phase formulations. A minimum preservative concentration in the aqueous phase of the two-phase formulation is necessary for adequate preservative action. Control of pH and relative phase volumes along with the application of this knowledge help scientists to achieve this goal.
Partition coefficient of a drug at physiological pH dictates the relative concentration of the same in different parts (compartments) of the body. For example, a drug that has a high apparent partition coefficient (Kd app), dictates that the concentration of the drug in hydrophobic tissue (e.g. adipose tissue, brain, nervous tissue, skin, skeletal muscle) is high. If the target tissue of the drug is in any of those hydrophobic tissues, lower blood concentrations can also achieve optimum therapy. In case the target site is in hydrophilic compartment of the body like blood cells, myocardial muscle, lung etc., higher concentration of the drug with higher apparent partition coefficient (Kd app) is necessary for optimum therapy as we know that most of such drug molecule partitions into the hydrophobic tissue. The converse is also equally true. Adequate knowledge of the topic is thus extremely important for the pharmaceutical scientists and practicing pharmacists.
