:[Jalvmarnhismin
`Pharmaceutical
`Salins/
`
`‘
`
`edited by
`Harry G. Brittain
`Discovery Laboratories, Inc.
`Milford, New Jersey
`
`MAREEL
`
`fl MARCEL DEKKER, INC.
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`DEKKER
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`APR 2 0 2000
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`135
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`145
`155
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`161
`162
`163
`
`125
`
`4 S
`
`tructural Aspects of Hydrates
`and Solvates
`
`Kenneth R. Morris
`
`Purdue University
`West Lafayette, Indiana
`
`1. PHARMACEUTICAL IMPORTANCE OF CRYSTALLINE
`-HYDRATES
`
`II. HYDRATE THERMODYNAMICS
`
`A. Classical Higuchil’Grant Treatment
`B.
`Similarities and Differences Between Polymorphs and
`Hydrates
`C. Hydrogen Bonding in Hydrates
`
`HI. CLASSIFICATION OF HYDRATES
`
`A. Class 1: Isolated Site Hydratcs
`B. Class 2: Channel Hydrates
`C. Class 3: Ion Associated Hydrates
`
`IV. DEHYDRATIONIHYDRATION KINETICS
`
`A. Dehydration and Hydrate Class
`B.
`Impact of Particle Size and Morphology
`
`
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`126
`
`'
`
`Morris
`
`V. BEHAVIOR OF HYDRAT'ES DURING PROCES SING
`HANDLING, AND STORAGE
`A. Processing Induced Transitions
`B. Transitions in the Final Product
`C. Kinetics of Transformation
`VI. SUMMARY
`
`REFERENCES
`
`167
`167
`173
`177
`178
`
`179
`
`l.
`
`PHARMACEUTICAL IMPORTANCE OF
`CRYSTALLINE HYDRATES
`
`The potential pharmaceutical impact of changes in hydration state of
`crystalline drug substances and excipients exists throughout the devel-
`opment process. The behavior of pharmaceutical hydrates has become
`the object of increasing attention over the last decade, primarily due
`(directly or indirectly) to the potential impact of hydrates on the devel-
`opment process and dosage form performance. Substances may
`hydrate/dehydrate in response to changes in environmental condi-
`tions, processing, or over time if in a metastable thermodynamic. state
`[1].
`
`It may not be practical or possible to maintain the same hydrate
`isolated at the discovery bench scale synthesis during scale-up activities
`for a hydrated compound. The choice of counterions to produce a more
`soluble salt form may also be dictated by the extent and type of hydra-
`tion observed for a given salt and/or by the moisture level that may
`be safely accommodated by the dosage form [2].
`The physicochemical stability of the compound may raise issues
`during preformulation. Some hydrated compounds may convert to an
`amorphous form upon dehydration and some may become chemically
`labile. This is true of cephradinedihydrate that dehydrates to become
`amorphOus and undergoes subsequent oxidation. Other compounds
`may convert from a lower to a higher state of hydration yielding
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`Structural Aspects of Hydrates and Solvates
`
`127
`
`forms with lower solubility. In any case, the resulting “new” forms
`would represent unique entities that, depending on the dosage form,
`might have to be maintained throughout the manufacturing process and
`in the clinic and would impact on the regulatory status of the com«
`pound. Most often this demands that the form (usually crystalline) be
`identified and characterized with respect to handling conditions during
`the early pro-IND stage of the development process.
`As dosage form development proceeds, changes in hydration state
`can result in variable potencies depending on handling conditions dur-
`ing weighing steps, the kinetics of the hydration!dehydration process,
`and the envirorirnental conditions during processing. Differences in
`powder flow can result from changes in crystal form and/or morphol-
`ogy that may accompany the hydrationfdehydration process. This can
`affect content uniformity in solid processing either in the mixing pro-
`cess or during transfer to other processing equipment such as tablet
`presses. Aqueous granulation, particle size reduction, film coating, and
`tablet compression all provide opportunities to “trap" a compound in
`a metastable form that may “relax” to a more stable form at some
`unpredicted point in the life of a dosage form. Alternately, a kinetically
`favored but themodynarnically unstable form may be convened during
`these processes to a more stable and less soluble form.
`‘
`During and after manufacturing, moisture from the environment
`or that sealed in the package may redistribute throughout the dosage
`form and change the hydration state(s). These changes can, in turn.
`visit the negative consequences discussed above for the bulk drug on
`the dosage form. These can be manifest as changes in tablet/capsule
`dissolution rates (and perhaps bioavailability), changes in lyophile re-
`constitution times, tablet capping, chemical instability, discoloration,
`and more. Of course, the potential for changes in hydration state also
`exists for many pharmaceutical excipients (such as lactose or magne—'
`siurn stearate).
`Such problems are typically magnified as both synthetic and dos-
`age form production is scaled up. This may be caused by solvent limita-
`tions, heat transfer differences in production equipment, changes in raw
`materials and/or raw material suppliers, changes in processing times,
`and time and control constraints on product storage, to name a few.
`
`
`
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`~
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`128
`
`-
`
`Morris
`
`The arguments just provided detail the potential issues around
`hydrates in the development process. The other consideration is the
`frequency with which hydrates are encountered in real life. Focusing
`on active drug substances, it is estimated that approximately one-third
`of the pharmaceutical actives are capable of forming crystalline hy-
`drates [3]. A search of the Cambridge Structural Database (CSD) shows
`that approximately 11% of all the reported crystal structures contain
`molecular water [4]. This represents over 16,000 compounds. If organ-
`ometallic compounds are excluded, this number drops to approximately
`6,000 [3.8%], and the breakdowu of these according to hydration num-
`ber is shown in Fig. 1. This shows the expected trend in which monohy-
`drates are most frequently encountered, and where the frequency de—
`creases almost exponentially as the hydration number increases. The
`hemihydratc stoichiometry occurs approximately as frequently as the
`Irihydrate, which should serve as a caution to explore fully the occur-
`rence of fractional hydration. That is, an apparent stoichiometry of 0.6
`water molecules could be a‘rpartially dehydrated monohydrate, or it
`
`3500
`
`SD00
`
`33%
`NUMBEROFOCCURENCES S
`
`cm
`
`
`
`
`HYDFlA‘I'iDN HUME ER
`
`Fig. 1 Occurrence of various crystalline hydrate stoichiometries.
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`Structural Aspects of Hydrates and Solvales
`
`129
`
`could be a hernihydrate with additional sorption due to defects or amor-
`phous material.
`.
`The symmetry of these hydrate crystals follows fairly closely with
`that reported for organic structures overall [5]. Table 1 shows the break—
`down for space groups, organized by crystal system, accounting for
`the top approximately 90% of the structures. leic (number 14) is the
`most common space group here as with the general population of or-
`ganic molecules contained in the CSD. It has been reported for inor-
`ganic species that hydrated structures are generally of lower symmetry
`than are their anhydrous counterparts [6]. This is attributed to the fact
`that the highest symmetry associated with the water molecule is C1,,
`and most inorganic structures are of higher symmetry. This is not obviw
`ously the case for organic structures. Regardless of the solvation state,
`organic molecules generally exhibit lower symmetry than do inorganic
`compounds, so the impact of the symmetry constraints imposed by wa-
`ter does not appear to be the controlling element. Further comparisons
`would he required to explore the phenomena fully.
`
`Space Groups for the Top 90% of Organic
`Table 1
`Crystalline Hydrates in the Cambridge Structural
`Database
`
`Percent
`
`Space group
`Crystal system
`occurrence
`
`-
`
`15.5
`Tricliuic
`P_.
`2.6
`Triclinic
`P1
`23.2
`Monoclinic
`PM
`l3.4
`Monoclinic
`P21
`53
`Monoclinic
`C are
`2.8
`Monoclinic
`C2
`17. 8
`OI'thOI'hOInb iC
`P2|2|21
`2.3
`Orlhorhombic
`PM
`1.8
`Orthorhombic
`PM;
`1.8
`Orthorhombic
`PM
`1.3
`Orthorhombic
`Puma
`
`UnknoWn 1 2
`
`
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`130
`
`Morris
`
`ll. HYDHATE THERMODYNAMICS
`
`The equilibrium thermodynamics of stoichiometric hydrates has been
`described by several authors. The overview presented here is intended
`both to review the basic thermodynamics of crystalline hydrate
`formationfstability and to highlight the intrinsic differences between
`polymorphic systems and hydrate systems (a discussion of the kinetics
`of dehydration)r hydration will be given in Section IV). The following
`description is a hybrid based on the work of Grant and Higuchi [7]
`and that of Carstensen [8].
`-
`
`A. Classical nguchiIGrant Treatment
`
`The equilibrium betWeen a hydrate and an anhydrous crystal (or be-
`tween levels of hydration) may be described by the following relation-
`ship.
`
`A(solid) + mHgO :A - mH10[solid)
`where
`
`(1)
`
`_ a[A - mHgO{SOLid)]
`Kh — ————
`a[A(solid)]a[H;O]’"
`
`Here tr represents the activity of the hydrate (aEA - mH20(solid)]} and
`anhydrate
`(a[A(solid)]),
`respectively.
`_ When the water
`activity
`(flU‘IzOD is greater than the ratio
`
`a[A - mH20(solid)]
`
`a [A (solidflifl ”a
`
`(2)
`
`then the hydrate species is the stable form. The anhydrate species will
`be stable if the water activity is less than the ratio in Eq. (2). If the
`pure solids are taken as the standard states for the hydrate and anhy-
`drous materials (i.e., as the states with unit activity),
`then K, =
`a[I-I20]"'" (and m = 1 for a monohydrate). So, clearly, the stability of
`a hydrate relative to the anhydrate (or lower hydrate) depends upon
`the activity of water in the vapor phase, or the partial vapor pressure
`or relative humidity (the ratio of the vapor pressure of water to the
`saturation vapor pressure at that temperature PIPO). This straightfor-
`ward thermodynamic description of hydrate equilibria is the key to un-
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`Structural Aspects of Hydrates and Solvates
`
`131
`
`derstanding not only the stability of hydrated forms but the inherent
`differences between hydrates and polymorphs.
`Just as the state of hydration depends upon the water vapor activ—
`ity, so will the water activity {relative humidity, RH) in a closed system
`depend upon the state of hydration of the solid phase. These microenvi-
`ronmental RH values can be of significance for the redistribution of
`moisture within a dosage form and! or package. An excellent illustra~
`tion of this was given by Carstensen for sodium phosphate [9]. Figure
`2 shows the relation between water vapor pressure (P) and the number
`of moies of water for the compound. Here it is seen that as water is
`added to a closed system, the compound takes it up until it no longer
`has any capacity in a given form (i.e., all of the solid is converted to
`a given hydrate). During this time, however, the RH of the system is
`constant. As more water is added, the RH rises until the critical value
`is reached that is sufficient to initiate the formation of the next higher
`
`hydration state. This cycle repeats as long as there are more states to
`be attained. Ultimately, the RH drifts up if the compound dciiquesces.
`One would not, therefore, expect to maintain a constant RH with differ-
`ences in water content in a system unless it contains hydratable compo-
`nents to buffer the changes. The type of behavior shown here is most
`common with inorganic compounds, but the principle is the same for
`
`(in! a
`
`
`
`MO
`
`.5O %Water(9water/0.019Solid)
`
`ll
`
`20
`
`40
`
`SD
`
`30
`
`100
`
`'56 Relative Humidity
`
`Fig. 2 Vapor pressure—hydration state diagram of sodium phosphate (repro-
`duced with permission).
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`132
`
`Morris
`
`organic molecules even though the number of stable hydrates that form
`may be less.
`
`B. Similarities and Differences Between Polymorphs '
`and Hydrates
`
`Hydrates and polymorphs are typically discussed together (as in this
`volume), and there are good reasons for this. In the scope of character—
`ization of pharmaceuticals, many of the behaviors of polymorphic sys-
`tems are at least apparently shared by compounds that can exist in vari-
`ous crystalline states of hydration. For the purposes of this chapter,
`such systems (including the anhydrous) will be referred to simply as
`hydrates. Members of both polymorphic and hydrate systems have dif—
`ferent crystal structures and exhibit different x-ray powder diffraction
`patterns (XRPD), thermograms (DSC or TGA), infrared spectra, disso«
`lution rates, hygroscopicity, etc. luterconversion between polymorphs
`or hydrates may occur as a‘function of temperature andt'or pressure or
`be solution mediated. The potential for interconversion during pro-
`cessing, stability testing, and storage is,
`therefore, present for both
`polymorphs and hydrates. Given this long list of similar behaviors, it
`is generally proper mat polymorphs and hydrates be addressed in the
`same general area of the pharmaceutical development process (for both .
`technical and regulatory concerns).
`The differences between polymorphs and hydrates are significant.
`The basis for all these differences is that polymorphs are different crys-
`tal structures of the same moleculcs(s) while hydrates are crystals of the
`drug molecule with different numbers of water molecules. As discussed
`above, the hydration state (and therefore the structure) of a crystalline
`hydrate is a function of the water vapor pressure (water activity) above
`the solid. Polymorphs, however, are typically only affected by changes
`in water vapor pressure if water sorption allows molecular motion,
`which in turn allows a reorganization into a different polymorph (Le,
`a solution mediated transformation). This distinction is particularly im-
`portant in defining the relative free energy of hydrates. A simple (only
`one molecule) anhydrous crystalline form is a one component system,
`and the free energy is, practically, specified by temperature and pres—
`sure. A crystalline hydrate is a two—component system and is specified
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`Structural Aspects of Hydrates and Solvates
`
`133
`
`by temperature, pressure, and water activity. In both cases it is assumed
`that the activity of the pure solid is unity.
`Consider the thermodynamic stability of a phase that crystallizes
`from water. If the phase is anhydrous (assuming no specific interaction
`between the molecule and the water), when the phase is removed from
`the solvent it is usually stable at that temperature (i.e., the free energy
`of the phase is independent of the solvent of origin). If the phase is
`hydrated, when it is removed from the solvent the situation changes
`completely. All that can be known is that the phase was thermodynami-
`cally stable at a water activity of approximately unity. Although it is
`a rule of thumb that the higher the hydration state that forms at a tem-
`perature the more thermodynamically stable, Grant et a1. [10] have re-
`ported the opposite behavior. Once removed from the water, the activity
`of water needed to maintain the form (the critical activity) had to be
`determined by other methods. These may include water vapor sorption
`data or a titration of the amount of water in a cosolvent system [111.
`A typical constant pressure G—T diagram (free energy vs. temperature,
`recalling that SGIST = #5) for a polymorphic system is really analo-
`gous to a logarithm solubility vs. reciprocal temperature plot (in X vs.
`1/2“) for a system of hydrates (Figs. 3a and h). Alternatively, a 6—1"
`plot for a hydrate system at constant water activity is analogous. The
`relationship between free energy and the ideal solubility of a solid is
`seen from the following equation.
`
`AG=rRT1nX
`
`(3)
`
`or
`
`mx=m_mt
`R
`R
`T
`
`where ASf and um are the entropy and enthalpy of fusion at the melting
`point, respectively, and R is the gas constant. A plot of in X against
`If T should yield a straight line with a negative slope equal to —AHfr’R'
`and an intercept of ASffR for each phase. This conclusion assumes that
`the enthalpy of solution is equal to the enthalpy of melting at the melt-
`ing point. A more general expression may be derived, but the reciprocal
`dependence of solubility and temperature is preserved. Just as with a
`
`
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`134
`
`Morris
`
`(0}
`
`Temperature
`
`
`ANHYDROUS
`
` %
` 0 w
`
`TRIHYDRATE
`
`
`
`LOGD.R.,ngmIJrninJcm.1x1!]2 D
` O N
`
`D
`
`(b)
`
`3.2
`
`3.3
`1IT>< 101
`
`3.4
`
`(a) G-T diagram, two polymorphs. temperature plot. (b) Log dissolu-
`Fig. 3
`tion vs. reciprocal temperature plot for ampiciliin anhydrate and trihydrate
`(reproduced with permission).
`
`G—T plot, the intersection of curves generated for two' different crystal-
`line phases represents a point of equal free energy and a transition tem-
`perature.
`
`There are many implications of the relatively more complex struc-
`ture of hydrates. As water is included or lost from the crystal structure,
`there must be a change in the volume of the unit cell [corrected for Z,
`the number of molecules per unit cell) at least as large as the volume
`
`
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`Structural Aspects of Hydrates and Solvates
`
`135
`
`of the water molecule (15—40 21.3) [12]. Although there is no study
`known to the author comparing the relative volume change between
`polymorphic pairs vs. hydrate pairs, it must be assumed that the trend
`would be that the volume change is larger for hydrates, which have to
`accommodate the additional volume occupied by the water molecules.
`The obvious problem for pharmaceutical development is that the
`water activity can vary throughout the lifetime of the compound, and _
`it is for this reason that knowledge of the water sorption behavior of
`active substances and excipients is so critical.
`
`C. Hydrogen Bonding in Hydrates
`The ability of water to form hydrogen bonds and hydrogen bonding
`networks gives it unique behavior with respect to colligative properties
`such as boiling and melting points. Similarly, hydrogen bonding be-
`tween water molecules and drug molecules in the solid state dictates
`its role in the structure of all classes of crystalline hydrates lie, the
`ability of water to form cocrystals with the drug molecule). Water will,
`of course, be hydrogen bonded whenever physically possible. This may
`take the form of hydrogen bonding to other water molecules, with func-
`tional groups on other molecules, or to anions. Hydrogen bonding to
`other water molecules is common both in the crystal lattice and in inter-
`stitial cavities or channels. Hydrogen bonding to other moieties and
`anions in crystalline hydrates is primarily within the lattice. In addition,
`the lone pair electrons of the water oxygen may be associated with
`metallic cations present in many salts. This interaction is largely elec-
`trostatic in nature for the metal cations common to pharmaceutics (Na,
`Ca, K, Mg). These main-group metal ions lack the d-orbitals of suitable
`energy that are necessary to form coordinate covalent or coordination
`bonds that ions of the transition series form with oxygen. It is often
`stated that MgGI) has a coordination number of 4, but this is a result of
`packing (or geometric) restrictions arising when fitting water molecules
`around the cation in response to the electrostatic attraction. Since these
`“bonds" are mostly electrostatic in nature, they are not properly de-
`scribed hy a molecular orbital but are best defined by classical electro-
`statics [13]. These “bonds” are often stronger than hydrogen bonds
`but exist with less directional dependence. A typical water hydrogen
`
`
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`

`136
`
`Morris
`
`bond is on the order of 4.5 kcalirnol, whereas a sodium—oxygen lone
`pair electrostatic interaction can be four to five times stronger. These
`bonds also exert their influence through hydrogen bonds in the form
`of cooperative effects. The specific characteristics of the hydrogen bond
`are presented here in the formalism of Falk and Knop [6].
`The ubiquitous hydrogen bonding of water is largely a result of
`its being both a hydrogen bond donor and acceptor. It may participate
`in as many as four hydrogen bonds, one from each hydrogen and one
`for each lone pair on the oxygen. Classification schemes based solely
`on the type of coordination of the water oxygen have been proposed
`{6]. As each bond is formed, it makes the other sites more attractive
`as partners for additional bonds. Hydrogen bond acceptors must be
`electronegative and include one of the following: oxygen atoms from
`other water molecules, oxygen and nitrogen atoms from other func-
`tional groups, and chlorine atoms. Hydrogen bond donors include pro-
`tons on nitrogen, oxygen,. and sulfur, of the types usually found on
`water, alcohols, amines, and‘the like.
`..
`'
`Free water (vapor) has an OH bond length of 0.957 A and an
`HOH angle of 10452". As soon as the molecule starts interacting with
`other molecules through hydrogen bonds, coordination, or other elec-
`trostatic “bonds", the molecule is distorted from its free conformation.
`The formation of hydrogen bonds weakens the OH bond, usually re;
`sulting in an increase in its length. This increase can be up to 0.01 A
`for an exceptionally strong hydrogen bond, but it is more typically on
`the order of 0.01 to 0302 A for organic hydrates with hydrogen bond
`lengths of 2.7 to 2.9 A (0—0 distance).
`The limits of length of a hydrogen bond are defined at the lower
`end by the van tier Waais radii of the two atoms and at the upper end
`arbitrarily by the length of the weakest hydrogen bond observed. This
`can be seen more quantitatively by expressing the hydrogen bond dis-
`tances showu in Fig. 4 in terms of the van der Waals radii.
`
`R(H—Y) < r(H) + r(Y) — 0.20 .31
`
`'
`
`(4)
`
`and since r(H") = 1.2 11,
`
`R(H——Y) < r(Y) — 1.00 A
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`Structural Aspects of Hydrates and Solvates
`
`137
`
`H
`
`\ r(O-H)
`
`0.“ ‘
`
`H gr
`
`rot?)
`
`K‘ Y
`
`Fig. 4 Formalism used in the discussion of hydrogen bond strength and
`length. (From Ref. 6.)
`
`The factor of 0.2 represents the combined experimental and statistical
`uncertainty. The compounds studied by Fallc and Knop were inorganic
`and small organic hydrates [6]. 0f the 129 compounds studied, only
`one failed this criterion. Often the hydrogen bond lengths are given as
`the O—Y (e.g., oxygenuoxygen or oxygen—chlorine) distances, be-
`cause in x-ray diffraction studies it is often difficult or impossible to
`locate accurately the hydrogen atoms due to their inherently low scat-
`tering and their relatively high mobility. Because of the large cross
`sections, hydrogen atoms are often located by neutron diffraction stud-
`ies. Under these circumstances. crystallographers will report the O—Y
`distance they know to be reliable, and geometric constraints may also
`be applied to such data.
`
`R[0r~Y) s ROI—Y) + r(OH)
`
`(5)
`
`substituting above, then setting r(OH) = 0.98 13.,
`
`R(O—Y) 5 r{Y) + 1.93 it
`
`As the electrostatic bond strength of the donor to the water oxygen (X)
`increases, the length of the H—Y bond decreases. This cooperative
`effect is also seen as the number of hydrogen bonds per water molecule
`increases. Hydrogen bonds prefer to be linear but may adopt a range
`of angles at the expense of the strength of the bond [6,15].
`All of these aspects of water hydrogen bonding are evident in
`the infrared spectra of crystalline hydrates. When a molecule absorbs
`
`
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`138
`
`Morris
`
`infrared radiation, this energy is used to excite the molecule into higher
`vibrational energy level states. The occupancy of these higher states
`manifests itself in greater degrees of molecular Vibration. The frequen-
`cies at which the molecule absorbs are a function of the mass of the
`bonded atoms, the geometry of the molecule, and the force constant
`(strength) of the bond. This relationship can be described by analogy
`to classical mechanics through Hooke‘s law, which states that the fre—
`quency of motion (v) for a harmonic oscillator is inversely proportional
`to the square root of the reduced mass of the system (it). The force
`constant (f, in units of dynr'cm) is the proportionality constant. Thus
`
`
`1
`
`V = one) (El
`
`f
`
`If:
`
`(6)
`
`where c is the velocity of light in units of cm/s. As illustrated in Fig.
`5, Water in crystalline hydrates has nine potential degrees of freedom:
`two stretching modes (symmetric and asymmetric), one bending mode,
`three vibrational modes (hindered rotation), and three hindered transla-
`
`ii
`;
`\0/
`i
`a
`
`\H
`H;
`\0/
`i
`b
`
`H;
`\H
`\/
`#0
`C
`
`+
`H
`
`+
`H
`
`+
`H
`
`.
`H
`
`I
`H
`
`1-!
`
`Fig. 5 Vibrational modes of water. Shown are the internal modes: (a) sym-
`metric stretch, (b) bending, (c) asymmetric stretch. and the librational modes
`(d) wag, (e) twist, and (f) rock. Not shown are the three hindered translational
`modes.
`
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`Structural Aspects of Hydrates and Sotva’tes
`
`139
`
`tional modes. These vibrational modes and their characteristic absorp-
`tion frequencies are presented in Table 2 and contrasted with those of
`water vapor.
`The dominant feature in the infrared Spectrum of a hydrate is band
`system associated with the OH stretching frequencies between 4000
`and 3000 cm“. These peaks are unusually intense due to the effect of
`hydrogen bonding on the changes in dipole moment that are associated
`with the wave functions describing the molecular motion. If an O—H
`stretching band is not observed, then no water is associated with the.
`compound. When present, the contributing OH groups must be properly
`assigned to distinguish water from alcoholic, phenolic, hydroxide, or
`other interfering absorptions. This is accomplished by first assigning
`energy values to the known structure of the molecule from tables. If
`resolved, the presence of an H20 bending frequency around 1600 cm“
`is proof that the sample contains water. Comparing this to the IR spec-
`trum of the anhydrous material or the dehydrated sample shows which
`peaks in the region are due only to water. The IR spectra of ampicillin
`before and after dehydration exhibits such behavior.
`Table 2 also shows that the OH stretching frequency of water
`occurs at lower wave numbers (longer wavelength and lower energy)
`in the crystal than in the vapor. This is due to the reduction of the force
`constant (f) by interaction of the water with neighboring groups, in
`particular hydrogen bonding and lone pair interactions involving the
`water oxygen. The weakening of the bond results ip a Slight elongation
`of the bond length, in the range of 0.01 to 0.02 A [15}. This shift in
`
`Table 2 Vibrational Modes of Water in Various Phases
`_____—_—_.__——-—————-
`
`Frequency in
`vapor phase
`[cm'l]
`
`3755.8 (synunetrlc)
`365 5.7 (asymmetric)
`1594.6
`
`Frequency in
`solid phase
`(cm‘l)
`
`2850—3625
`
`Vibrational mode
`
`Stretching
`
`1498—1732
`Bending
`355—1080
`Rotationfllibration
`'
`200—490
`Translation
`__—__,__._.——-——-——-—
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`140
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`-
`
`Morris
`
`the OH stretching frequency of water can be used to evaluate the inter-
`action energy between water and the other molecules. Specifically, the
`higher is the degree of water hydrogen bonding,
`the lower the. fre-
`quency will be of the OH stretch. In fact, good correlation between
`OH stretching frequency and the length of hydrogen bonds is available
`for inorganics and very small organic crystals [14]. While repulsive
`lattice energy tends to increase this frequency, it typically yields only
`a very small shift. In large molecular crystals, however, the energetics
`become more complicated and the correlation is not as good. Adventi-
`tious adsorbed water tends to have broad peaks in the lower part of
`the frequency range. The broadening is due to the vibrational coupling
`between water molecules. and the lower frequencies are due to the mul—
`tiple hydrogen bonds. This “dispersion of stretching frequencies" is
`analogous to the broadening of DSC peaks due to the multiple energetic
`environment that adventitious water can experience. If the water occu—
`pies only one type of crystal site, the DSC and IR peaks should be
`sharp relative to those of adventitious water. This is seen in the ampicil-
`lin example of the classification section. The 0—H stretching peaks
`from water in the crystal lattice will occur at various frequencies de
`pending upon the strength of the hydrogen bonding.
`In addition to shifts in frequency and peak shape, peaks may be-
`come split owing to the interaction of the two water hydrogens if they
`participate in different hydrogen bonds. Therefore in some crystalline
`hydrates there may be two or more peaks associated with the OH
`stretching mode.
`Metal cations affect the infrared absorption behavior in several
`ways. First, if the water oxygen is bound at the inner hydration sphere
`of the cation, polarization of the electron density causes stronger hydro-
`gen honds to be formed. This effect will lower the OH stretching fre-
`quency in a manner proportionate to the degree of bond strengthening,
`a decrease that can be up to 640 cm“1 in inorganic compounds [6,15].
`Second, cation—water interaction can increase the bending frequencies
`(which are observed in the 1600 cm‘1 region) by as much as 50 cm“.
`Finally, the bonds formed betWeen the cation and the atoms in its inner
`
`coordination sphere will be observed as low-frequency modes below
`400 cm".
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`Structural Aspects of Hydrates and Solvates
`
`141
`
`III. CLASSIFICATION OF HYDRATES
`
`The combination of the vibrational mode information, the hydrogen
`bonding characteristics, and the thermodynamic relationships serves to
`form a clear picture as to why water can and does participate in hydrate
`formation with drug molecules. The possible structures that may result
`from such interactions are quite diverse. For practical purposes, an
`identification of types or classes of possible resulting structures is use-
`ful. Water is small enough to fill many commonly occurring periodic
`“voids" formed when larger molecules are packed, and it interacts
`through hydrogen bonds to overcome some of the entropy of mixing.
`The ability of the water molecules to self-associate. combined with the
`small size, allows them to fill larger periodic spaces conforming to
`different shapes. The characteristics give water a chameleon-like qual-
`ity (also seen in protein hydration). which gives rise to “motifs” of
`water arrangements in crystal structures.
`Crystalline hydrates have been classified by either structure or
`energetics [6]. The idea of the structural classification scheme presented
`here is to divide the hydrates into three classes that are discernible
`by the commonly available analytical techniques. The classification of
`crystalline hydrates of pharmaceutical interest by their structural char-
`acteristics is the most common, intuitive, and usefui approach. A good
`classification system should direct the prefonnulation/formulation sci—
`entist to the characteristics of the particular class that will help in identi-
`fying a new s