Physical Pharmacy 1 - State of Matter PDF

Physical Pharmacy 1 State of Matter ‫ محمد اياد البوريدي‬.‫م‬.‫م‬  Objectives To understand the application of quantitative and theoretical principles of the physical characters of matter to the practice of pharmacy. It helps the pharmacist to predict the solubil...

Physical Pharmacy 1 State of Matter ‫ محمد اياد البوريدي‬.‫م‬.‫م‬  Objectives To understand the application of quantitative and theoretical principles of the physical characters of matter to the practice of pharmacy. It helps the pharmacist to predict the solubility, compatibility and biological activity of drug products. As a result of this knowledge, it is helpful in the development of new drugs and dosage forms as well as in the improvement of various modes of administration. BINDING FORCES BETWEEN MOLECULES In order for molecules to exist in aggregates in gases, liquids, and solids, intermolecular forces must exist. *Cohesion, or the attraction of like molecules, and *adhesion, or/the attraction of unlike molecules, are manifestations of intermolecular forces.  RepUlsive and Attractive Forces. When molecules interact, both repulsive and attractive forces operate. Moelwyn-Hughes points to the analogy between human behavior and molecular phenomenon. 1. Van der Waals Forces Dipolar molecules frequently tend to align themselves with their neighbors, so that the negative pole of one molecule points toward the positive pole of the next. Types of Van der Waals Forces dipole-dipole or Keesom forces Force between two permanent dipoles dipole-induced dipole, or Debye, interactions Force between a permanent dipole and a corresponding induced dipole dispersion , (London dispersion force or Van der Waals-London force) weak electrostatic force  A-Dipole-Dipole /Keesom forces Are the forces that occur between two molecules with permanent dipoles. (Two polar molecules align so that δ+ and δ- are matched (electrostatic attraction) An example of this can be seen in: HCl ,fluromethane (CH3F) & KBr  B-Dipole-Induced Dipole A dipole can induce (cause) a temporary dipole to form in a non-polar molecule, the molecules then line up to match δ+ and δ- charges.  C-London Dispersion Forces A temporary dipole forms in a non-polar molecule…which leads to a temporary dipole to form in ANOTHER non-polar molecule. Dispersion is the ONLY intermolecular attraction that occurs between nonpolar molecules  Review Dipole – Dipole : between two polar molecules Dipole – Induced Dipole : b/w a polar & a non-polar molecule Dispersion : between two non-polar molecules  2-Ion Dipole Forces : The force of attraction between an ion and a polar molecule. NaCl breaks up because the ion dipole with water is stronger than the attraction of Na+ to Cl 3-Ion- Induced Dipole Forces : The force of attraction between an ion and weak dipole which are induced in non polar molecules. Example: 1. An ionic substance in anon polar solvent (NaCl in hexane) 2. Iodine with potassium iodide  4.Hydrogen Bonds The interaction between a molecule containing a hydrogen atom and a strongly electronegative atom such as fluorine, oxygen, or nitrogen is of particular interest.  Hydrogen bonding affects physical properties (mp, bp, solubility) of substance. About one sixth of the hydrogen bonds of ice are broken when ice convert to liquid state and all are destroyed when it vaporize Example: water, H-F------H-F, salicylic acid Bond Energy : Ionic 100-200 Kcal/mole Covalent 50-150 Kcal/mole H-bond 2-7 Kcal/mole Van der Waals forces 1-10 Kcal/mole  Hydrogen bonds are relatively weak, having a bond energy of about 2 to 8 kcaVmole as compared with a value of about 50 to 100kcal for the covalent bond and well over 100~ fer the ionic bond. The metallic bond, representing a third type of primary valence, will be mentioned in connection with crystalline solids.  Covalent bonding takes place between atoms with small differences in electronegativity which are close to each other in periodic table (between non-metals and non-metals). The covalent bonding is formed by sharing of electrons (i.e., s and p electrons) between atoms rather than by electron transfer. This bonding can be attained if the two atoms each share one of the other’s electrons.  Ionic bonding Ionic bonding is the electrostatic force of attraction between positively and negatively charged ions (between non-metals and metals). These ions have been produced as a result of a transfer of electrons between two atoms with a large difference in electro negativities. All ionic compounds are crystalline solids at room temperature. NaCl is a typical example of ionic bonding.  STATES OF MATTER Gases, liquids, and crystalline solids are the three states of matter. The molecules, atoms, and ions in the solid state are held in close proximity by intermolecular, interatomic, or ionic forces. Solids with high vapor pressures, such as iodine and camphor, can pass directly from the solid to the gaseous state without melting. This process is known as sublimation, and the reverse process, that is, recondensation to the solid state, may be referred to as deposition. mesophase (Greek, mesos, middle), which lies between the liquid and crystalline states. This so-called liquid crystalline state  Gases: The average kinetic energy of the gas molecules is much larger than the average energy of the attractions between them. Liquids: the intermolecular attractive forces are strong enough to hold the molecules close together, but without much order. Solids: the intermolecular attractive forces are strong enough to lock molecules in place (high order)  1.THE GASEOUS STATE Owing to vigorous and rapid motion, gas molecules travel in random paths, frequently colliding with one another and with the walls of the container in which they are confined. The temperature involved in gas equations is given in absolute or Kelvin degrees (K) Zero degrees on the centigrade scale is equal to 273.15° K. can be compressed exert pressure on whatever surrounds them expand into whatever volume is available mix completely one another can be described in terms of their temperature, pressure, the volume occupied, and the amount (number of moles) present P, V, T, n 1. The Ideal GAS law The student may recall from general chemistry that the gas laws were formulated by Boyle, Charles, and Gay- Lussac. Boyle's law. relates the volume and pressure of a given mass of gas at constant temperature. The law of Gay-Lussac and Charles states that the volume and absolute temperature of a given mass of gas at constant pressure are directly proportional,  MoIecular weight The approximate molecular weight of a gas can be determined by use of the ideal gas law. The number of moles of gas n is replaced by its equivalent g/M, in which g is the grams of gas and M is the molecular weight: The two methods most commonly used to determine the molecular weight of easily vaporized liquids such as alcohol and chloroform are the Regnault and Victor Meyer methods.  Kinetic Molecular theory. Some of the more important statements of the theory are the following : 1. Gases are composed of particles called molecules, This condition is approximated in actual gases only at low pressures and high temperatures, molecules of the gas are far apart. 2. The particles of the gas do not attract one another but rather move with complete independence; again, only at low pressures. 3. The particles exhibit continuous random motion owing to their kinetic energy. E = 3/2 RT. 4. The molecules exhibit perfect elasticity, that is, there is no net loss of speed after they collide with one another and with the walls of the confining vessel, which latter effect accounts for the gas pressure. Although the net velocity, and therefore the average kinetic energy, does not change on collision, the speed and energy of the individual molecules may differ widely at any instant. The van der Waals Equation for Real Gases. 2. Real Gases One of the assumptions of the kinetic molecular theory of gases is that the gas particles are separated by large distances. Under conditions of high pressure and low temperature Deviations Due to Low Temperature : Under conditions of low temperature gas particles are close enough together so that intermolecular attractive forces become significant. Deviations Due to High Pressure : At high pressure gas particles are close enough together to experience intermolecular attractive forces. This causes the volume of the gas to be less than that predicted by the ideal gas law.  Phase Changes Evaporation: Liquid → Gas Condensation: Gas → Liquid Melting: Solid → Liquid Freezing: Liquid → Solid Sublimation: Solid → Gas 2.THE LIQUID STATE intermediate state as the matter goes from solid state to the gaseous state. Liquefaction of Gases. When a gas is cooled, it loses some of its kinetic energy in the form of heat, and the velocity of the molecules decreases. This temperature, above which a liquid can no longer exist, is known as the critical temperature. The pressure required to liquefy a gas at its critical temperature is the critical pressure, which is also the highest vapor pressure that the liquid can have. 2 ways for Liquefaction of Gases: 1-When a gas is cooled, it loses some of its kinetic energy in the form of heat, and the velocity of the molecules decreases. 2-If pressure is applied to the gas; the molecules are brought within the sphere of the van der Waals interaction forces and pass into the liquid state. Because of these forces, liquids are considerably denser than gases and occupy a definite volume. Methods of Achieving Liquefaction. intense cold by the use of freezig mixtures. An adiabatic expansion, may be achieved by carrying out the process in a Dewar, or vacuum, flask, which effectively insulates the contents of the flask from the external environment. Joule- Thomson effect and differs from the cooling produced in adiabatic expansion,. in which the gas does external work. A cooling effect is also observed when a highly compressed nonideal gas expands into a region of low pressure.  Critical temperature : Is the temperature, above which a liquid can no longer exist irrespective to the pressure applied. Critical pressure: Is the pressure required to liquefy a gas at its critical temperature. The critical temperature of water is 374°C, or 647 K, and its critical pressure is 218 atm, whereas the corresponding values for helium are 5.2 K and 2.26 atm. The high critical values for water result from the strong dipolar forces between the molecules and particularly the hydrogen bonding that exists. Conversely, only the weak London force attracts helium molecules. Aerosols. As mentioned earlier, gases can be liquefied by increasing pressure, provided we work below the critical temperature. In such products, a drug is dissolved or suspended in a Propellant, a material that is liquid under the pressure. conditions existing inside the container but that forms a gas under normal atmospheric condition. Gases can be liquefied under high pressures in a closed chamber as long as the chamber is maintained below the critical temperature. When the pressure is reduced, the molecules expand and the liquid reverts to a gas. This reversible change of state is the basic principle involved in the preparation of pharmaceutical aerosols. Vapor Pressure of Liquids Translational energy of motion (kinetic energy) is not distributed evenly among molecules; some of the molecules have more energy and hence.higher velocities than others at any moment. The pressure of the saturated vapor* above the liquid is then known as the equilibrium vapor pressure  Evaporation is the name of the process by which a liquid becomes a gas. Evaporation takes place from the surface of a liquid. If we place a liquid in a sealed container with some empty space above the liquid initially there will be no vapor or gas above that liquid  Those molecules that have strong intermolecular attractive forces have lower vapor pressures than expected.  As we increase the temperature the vapor pressure of a liquid increases. This due to strong hydrogen bonds between water molecules. Clausius- Clapeyron Equation: Heat of Vaporization. The relationship between the vapor pressure and the absolute temperature of a liquid is expressed by the Clausius-Clapeyron equation. Molar heat of vaporization (ΔHvap) is the energy required to vaporize 1 mole of a liquid. Boiling Point. If a liquid is placed in an open container and heated until the vapor pressure equals the atmospheric pressure, the vapor is seen to form bubbles that rise rapidly through the liquid and escape into the gaseous state. These quantities of heat, known as latent heats of vaporization, are taken up when the liquids vaporize and are liberated when the vapors condense to liquids. Other properties of liquids, such as surface tension and viscosity The temperature at which the (equilibrium) vapor pressure of a liquid equals the external pressure (atmospheric pressure) is called the boiling point.  The normal boiling point is the temperature at which a liquid boils when the external pressure is 1 atm. Liquids with high vapor pressures (Volatile compounds) require relatively little energy (heat) to increase the vapor pressure to match the applied (atmospheric) pressure, and thus, boil, i.e. they have low boiling points. Liquids with low vapor pressures require considerably more energy to increase the vapor pressure to the point where it matches the applied pressure, thus, they have relatively high boiling points  Factors that affect boiling point: 1. Atmospheric pressure The boiling point of liquid increases with the increase of atmospheric pressure (at lower altitude) 2. Intermolecular forces: London dispersion forces < Dipole-Dipole interactions < Hydrogen bonds The stronger the attractive forces, the higher the boiling point.  3. Number of sites for intermolecular interactions (surface area): Larger surface (more electrons) → more sites for London → ↑ b.p. CH3 -CH2 -CH2 -CH2 -CH3 > CH3-CH2-CH3 4. Molecular shape: With the same molecular weight. Linear CH3-CH2-CH2-CH2-CH3 > branched 5. Boiling point of alcohol higher than hydrocarbons of the same molecular weight because the presence of hydrogen bonds between molecules of alcohol. CH3-CH2-OH > CH3-O-CH3 6. Boiling point of carboxylic acid is high because the presence of hydrogen bonds between 2 molecules (dimer). 3.SOLIDS AND THE CRYSTALLINE STATE Crystalline Solids. The structural units of crystalline solids, such as ice, sodium chloride, and menthol, are arranged in fixed geometric patterns or lattices. The various crystal forms are divided into six distinct crystal systems. They are, together with examples of each, cubic (sodium chloride), tetragonal (urea), hexagonal (iodoform), rhombic (iodine), monoclinic (sucrose), and triclinic (boric acid) The solids can be divided into two groups: Crystalline—particles are in highly ordered arrangement. ex, crystalline SiO2 Amorphous— no particular order in the arrangement of particles, not distinct melting point. Ex, amorphous SiO2, rubber, glass, nylon. Types of Bonding in Crystalline Solids Molecular solid – solids like ice that is held together by intermolecular forces. Covalent network – a solid consists of atoms held together in large networks or chains by covalent networks. Ionic solids – ionic bonds hold the solids in a regular three dimensional arrangement. Metallic – similar to covalent network except with metals. Provides high conductivity.  Metallic crystals are composed of positively charged ions in a field of freely moving electrons, sometimes called the electron gas. Metals are good conductors of electricity because of the free movement of the electrons in the lattice. Metals may be soft or hard and have low or high melting points. The hardness and strength of metals depend in part on the kind of imperfections, or lattice defects, in the crystals.  X-Ray Diffraction. X-rays are diffracted by crystals just as visible light is dispersed into a color spectrum by a ruled grating (i.e., a piece of glass with fine parallel lines of equal width drawn on it). Melting Point and Heat of Fusion. The temperature at which a liquid passes into the solid state is known as the freezing point. It is also the melting point of a pure crystalline compound. In practice, it is taken as the temperature of the equilibrium mixture at an external pressure of 1 atm; this is sometimes known as the normal freezing or melting point. the heat absorbed when gram of a solid melts or the heat liberated when it freezes is known as the latent heat of fusion, and for water at 0° C it is about 80 cal/g (1436 cal/mole)  This phenomenon can be rationalized in terms of Le Chatelier's principle, which states that a system at equilibrium readjusts so as to reduce the effect of an external stress. (When the ice-water equilibrium mixture is saturated with air under a total pressure of 1 atm, the temperature is lowered an additional 0.0023. Pressure has only a slight effect on the equilibrium temperature of condensed systems (i.e., of liquids and solids).  Changes of the freezing or melting point with pressure can be expressed by using a form of the Clapeyron equation where Vl and Vs are the molar volumes of the liquid and solid, respectively. Molar volume (volume in units of cm3 /mole) is computed by dividing the gram molecular weight by the density of the compound, and AT is the change of melting point brought about by a pressure change of AP. Molar heat of fusion (AHf) is the amount of heat absorbed when 1 mole of the solid changes into 1 mole of liquid.  Melting Point and Intermolecular Forces The heat of fusion may be considered as the heat required to increase the interatomic or intermolecular distances in crystals, thus allowing melting to occur. Paraffins crystaliZe as thin leaflets composed of zig-zag chains packed in a parallel arrangement. The melting points of the alkanes with an even number of carbon atoms are higher than those of the hydrocarbons with an odd number of carbon atoms.  A crystal that is bound together by weak forces generally has a low heat of fusion and a low melting point, whereas one bound together by strong forces has a high heat of fusion and a high melting point. The melting points and solubilities of the xanthines of pharmaceutical interest, determined by Guttman , further exemplify the relationship between melting point and molecular structure.  Then if there is compound of 2 polymorphic forms, polymorph A which is held by higher attractive forces than is polymorph B. lt is clear that more heat will be required to break down the attractive forces in polymorph A, and thus its melting temperature will be higher than that of polymorph B. The melting points of the alkanes with an even number of carbon atoms are higher than those of the hydrocarbons with an odd number of carbon atoms. This is because alkanes with an odd number of carbon atoms are packed in the crystal less efficiently. The crystal lattice is more stable (more arranged, more packed), the melting point is higher. There is inverse relationship between solubility and melting point. The Effect of intermolecular Forces on solubility Solubility Like melting points is strongly influenced by intermolecular forces. in general like dissolves like Non-polar solutes dissolve in non-polar solvents; Paraffin wax (C30H62) is a non-polar solute that will dissolve in non-polar solvents like oil, hexane (C6H14) or carbon tetrachloride (ccl4). Paraffin wax will NoT dissolve in polar solvents such as water (H2O) or ethanol (ethyl alcohol, C2H5OH).  polar solutes such as glucose (C6H12O6) will dissolve in polar solvents such as water (H20) or ethanol (ethyl alcohol, c2H5oH) as the partially positively charged atom of the solute molecule is attracted to the partially negatively charged atom of the solvent molecule, and the partially negatively charged atom of the solute molecule is attracted to the partially positively charged atom of the solvent molecule. Glucose will NOT dissolve in non-polar solvents such as oil, hexane (C6H14) or carbon tetrachloride (cc14). ionic solutes such as sodium chloride (NaCl) will generally dissolve in polar solvents but not in non-polar solvents, since the positive ion is attracted the partially negatively charged atom in the polar solvent molecule, and the negative ion of the solute is attracted to the partially positively charged atom on the solvent molecule. Polymorphism Some elemental substances, such as carbon and sulfur, may exist in more than one crystal line form and are said to be polymorphic. Nearly all long-chain organic compounds exhibit polymorphism. Theobroma oil or cacao butter is a polymorphous natural fat. Since it consists mainly of a single glyceride, it melts to a large degree over a narrow temperature range (34°_36 C) Theobroma oil is capable of existing in four polymorphic forms: the unstable gamma form melting at 18", the alpha form melting at 22 , the beta prime form melting at 28", and the stable beta form melting at 34.6° C.  Polymorphs and/or solvates of a pharmaceutical solid can have different physical properties such as melting point, apparent solubility, dissolution rate, optical and electrical properties, vapor pressure, and density. Numbers of methods have been employed for characterizing polymorphs in pharmaceutical solids. Polarizing optical microscopy and thermo microscopy have proven to be useful tools. Thermal analysis procedures, such as differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA), can be used to obtain additional information. Examples on polymorphism Theobroma oil is capable of existing in four polymorphic forms The polymorphic state of chloramphenicol palmitate has a significant influence on the biologic availability of the drug. Cortisone acetate exists in at least five different forms, four of which are unstable in the presence of water and change to a stable form Polymorphism has achieved significance- in recent years owing to the fact that different polymorphs exhibit different solubility's. Polymorphism can also be a factor in suspension technology. *The arrangement of the atoms in a particular stereoisomer gives the configuration of a molecule.  Amorphous Solids. Amorphous solids may be considered as super cooled liquids in which the molecules are arranged in a random manner somewhat as in the liquid state. This force, below which the body shows elastic properties, is known as the yield value. Amorphous substances, as well as cubic crystals, are usually isotropic, that is, they exhibit similar properties in all directions. Crystals other than cubic are an isotropic, showing different characteristics (electric conductance, refractive index, rate of solubility) in various directions along the crystal. Beeswax and paraffin, although they appear to be amorphous, assume crystalline arrangements when heated and then allowed to cool slowly,  Many pharmaceutical solids can exist in different physical forms. Polymorphism is the ability of a drug substance to exist as two or more crystalline phases that have different arrangements and/or conformations of the molecules in the crystal lattice. Amorphous solids consist of disordered arrangements of molecules and do not possess a distinguishable crystal lattice. Solvates are crystalline solid adducts containing amounts of a solvent incorporated within the crystal structure. If the incorporated solvent is water, the solvates are also commonly known as hydrates. 4.The Liquid Crystalline State or mesophase A fourth state of matter is the liquid crystalline state or mesophase. Materials in this state are intermediate between the liquid and solid states. For example, cholesterol myristate (a derivative of cholesterol) is a crystalline solid below 71"C. When the solid is warmed to 71C, it turns into a cloudy liquid. When the cloudy liquid is heated to 86'C, it becomes a clear liquid. Cholesterol myristate changes from the solid state to an intermediate state (cloudy liquid) at 71"C, and from the intermediate state to the liquid state at 86"C. Because the intermediate state exits between the crystalline solid state and the Iiquid state, it has been called the liquid crystal state.  According to the mobility and rotation direction, the Iiquid crystals are divided into: Structure of liquid Crystals 1- smectic (soaplike or greaselike) 2- nematic (threadlike) 3- (cholesteric) Properties and Significance of Liquid Crystals Because of their intermediate nature, liquid crystals have some of the properties of liquids and some of the properties of solids. For example, liquid crystals are mobile and thus can be considered to have the flow properties of liquids: At the same time they possess the property of being birefringent , a property associated with crystals. The liquid crystalline state is widespread in nature, with lipoidal forms found in nerves, brain tissue, and blood vessels. Finally, liquid crystals have structures that are believed to be similar to those in cell membranes.  Birefringence , the Light passing through a material is divided into two components with different velocities and hence different refractive indices. in general, molecules that form mesophases (a) are organic, (b) are elongated in shape , (c) are rigid, and (d) possess strong dipoles and easily polarizable groups. PHASE EQUILIBRIA AND THE PHASE RULE Phase Rule : a useful device for relating the effect of the least number of independent variables (e.g., temperature, pressure, and concentration) upon the various phases (solid, liquid, and gaseous) that can exist in an equilibrium system containing a given number of components. F=C-P+2 the number of components is the smallest number of constituents by which the composition of each phase in the system at equilibrium can be expressed in the form of a chemical formula or equation The number of degrees of freedom is the least number of intensive variables (temperature, pressure, concentration, refractive index, density, viscosity, ete.) that must be fixed to describe the system completely.  The greater the number of phases in equilibrium, however, the fewer the degrees of freedom. Thus: liquid water + vapor F=C-P+2 = 1-2+2 =1 UNIVARIANT liquid ethyl alcohol + vapor F=C-P+2 =1-2+2 = 1 UNIVARIANT liquid water + liquid ethyl alcohol + vapor mixture F=C-P+2 =2-2+2 =2 BIVARIANT (Note: Ethyl alcohol and water are completely miscible both as vapors and liquids.) liquid water + liquid benzyl alcohol + vapor mixture F=C-P+2 =2-3+2 = 1 UNIVARIANT  note: Benzyl alcohol and water form two separate liquid phases and one vapor phase. Gases are miscible all proportions; water and benzyl alcohol are only partially miscible. It is therefore necessary to define the two variables in the completely miscible [one-phase] ethyl alcohol-water system, but only one variable in the partially miscible [two-phase] benzyl alcohol-water system.)  Systems Containing One Component. the curve OA in Figure 2-13 is known as the vapor pressure curve. Its upper limit is at the critical temperature, 3740 C for water, and its lower end terminates at 0.00980 C, called the triple point. Along the vapor pressure curve, vapor and liquid coexist in equilibrium. This sequence, vapor -- ice -- liquid, is due to the fact that ice occupies a larger volume than liquid water below the triple point. Finally, at the triple point where the three phases ice, liquid water, and water vapor- are in equilibrium, we have seen that F = O.  condensed Systems. are systems in which the vapor phase is ignored and only solid and/or liquid phases are considered. We have seen from-the phase rule that in a single-component system, the maximum number of degrees of freedom is two. This situation arises when only one phase is present, that is, F =1 1 + 2 =2. In a two-component system, therefore, only two variables (temperature and concentration) remain, and we are able to portray the interaction of these variables by the use of planar figures on rectangular coordinate graph paper. Two-Component Systems Containing Liquid Phases We know from experience that ethyl alcohol and water are miscible in all proportions, whereas water and mercury are, for all practical purposes, completely immiscible regardless of the relative amounts of each present. Such a system is phenol and water  Figure 2-15 illustrates a liquid mixture that shows no upper consulate temperature but instead has a lower consolute temperature below which the components are miscible in all proportions. The example shown is the triethylamine- water system. Figure 2-16 shows the phase diagram for the nicotine-water system, which has both a lower and an upper consolute temperature. Lower consolute temperatures arise presumably because of that interaction between the components that brings about complete miscibility only at lower temperatures. Two- Component Systems Containing Solid and liquid Phases: Eutectic Mixtures: We shall restrict our discussion, in the main, to those solid-liquid mixtures in which the two components are completely miscible in the liquid state and completely immiscible as solids, that is, the solid phases that form consist of pure components. Examples of such systems are salol-thymol and salol-camphor. there are four regions: a single liquid phase; a region containing solid salol and a conjugate liquid phase; a region in which solid thymol is in equilibrium with a conjugate liquid phase; and a region in which both Components are present as pure solid phases.  Mixtures of salol and camphor show similar behavior. In this combination, the eutectic point occurs with a system containing 56% by weight of salol in camphor at a temperature of 60 C. Several other substances form eutectic mixtures (e.g., camphor, chloral hydrate, menthol, and betanaphthol). Lidocaine and prilocaine, two local anesthetic agents, form a 1:1 mixture having a eutectic temperature of 18 C. The mixture is therefore liquid at room temperature and forms a mixed local anesthetic that may be used for topical application. Further work showed that the liquid eutectic can be emulsified in water, opening the possibility for topical bio absorption of the two local anesthetics Solid Dispersions. Eutectic systems are one example of solid dispersions. The solid phases constituting the eutectic each contain only one component and the system may be regarded as an intimate crystalline mixture of one component in the other. A second major group of solid dispersions is the solid solution, in which each solid phase contains both components, that is, a solid solute is dissolved in a solid solvent to give a mixed crystal. Phase Equilibria in Three-Component Systems. in systems containing three components but only one phase, F = 3 - 1 + 2 = 4 for a non condensed system. The four degrees of freedom are temperature, pressure, and the concentrations of two of the three components. Rules Relating to Triangular Diagrams 1. Each of the three corners or apexes of the triangle represent 100% by weight of one component (A, B, or C). 2. The three lines joining the corner points represent two-component mixtures of the three possible combinations of A, B, and C. 3. The area within the triangle represent all the possible combinations of A, B, and C to give three component systems. 4. If a line is drawn through any apex to a point on the opposite side (e.g., line DC in Fig. 2-18), then all systems represented by points on such a line have a constant ratio of two components, in this case A and B. 5. Any line drawn parallel to one side of the triangle, for example, line HI in Figure 2-18, represents ternary systems in which the proportion (or percent by weight) of one component is constant. Ternary Systems with One Pair of Partially Miscible Liquids. Water and benzene are miscible only to a slight extent, and so a mixture of the two usually produces a two-phase system. The heavier of the two phases consists of water saturated with benzene, while the lighter phase is benzene saturated with water. On the other hand, alcohol is completely miscible with both benzene and water. Effect of Temperature Figure 2-19 shows the phase equilibria in a three-component system under isothermal conditions. Changes in temperature will cause the area of immiscibility, bounded by the binodal curve, to change. In general, the area of the binodal decreases as the temperature is raised and miscibility is promoted. Ternary Systemic with Two or Three Pairs of Partially Miscible Liquids  THERMAL ANALYSIS a number of physical and chemical effects can be produced by temperature changes, and methods for characterizing these alterations upon heating or cooling a sample of the material are referred to as thermal analysis. The most common types of thermal analysis are: differential scanning calorimetry (DSC), differential thermal analysis (DTA), thermogravimetric analysis (TGA), and thermomechanical analysis (TMA)  In general, thermal methods involve heating a sample under controlled conditions and observing the physical and chemical changes that occur. These methods measure a number of different properties, such as melting point, heat capacity, heats of reaction, kinetics of decomposition, and changes in the flow (rheologic) properties of biochemical, pharmaceutical, and agricultural materials and food. Differential Scanning Calorimetry. Differential Thermal Analysis.  Differential Thermal Analysis. Therefore, it is not possible to directly calculate energies of melting, sublimation, and decomposition, and DTA is used as a qualitative or semi quantitative method for calorimetric measurements. The DSC, although more expensive, is needed for accurate and precise results. Differential scanning calorimetry has found increasing use in standardization of the lyophilization process. Crystal changes and eutectic formation in the frozen state can be detected by DSC (and by DTA) when the i Thermogravimetric and Thermomechanical Analyses. changes in weight with temperature (thermogravimetric analysis, TGA) and changes in mechanical properties with temperature (thermomechanical analysis, TMA) are used in pharmaceutical engineering research and in industrial quality control. (TGA) also may be used to study drug stability and the kinetics of decomposition. (TMA) measures the expansion and extension of materials or changes in viscoelastic properties, and heat distortions·, such as shrinking, as a function of temperature. used TMA in studies on the mechanical and viscoelastic properties of hair and the stratum corneum of the skin.