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`January 1997
`Volume 86, Number 1
`
`REVIEW ARTICLE
`
`Characteristics and Significance of the Amorphous State in Pharmaceutical
`Systems
`
`BRUNO C. HANCOCK*X AND GEORGE ZOGRAFI†
`Received April 26, 1996, from the *Merck Frosst Canada Inc., Pointe Claire-Dorval, Quebec, H9R 4P8, Canada, and †School of Pharmacy,
`University of WisconsinsMadison, Madison, WI 53706.
`Final revised manuscript received July 31, 1996.
`Accepted for
`publication August 1, 1996X.
`
`Abstract 0 The amorphous state is critical
`in determining the solid-
`state physical and chemical properties of many pharmaceutical dosage
`forms. This review describes the characteristics of the amorphous state
`and some of the most common methods that can be used to measure
`them. Examples of pharmaceutical situations where the presence of the
`amorphous state plays an important role are presented. The application
`of our current knowledge to pharmaceutical
`formulation problems is
`illustrated, and some strategies for working with amorphous character in
`pharmaceutical systems are provided.
`
`Introduction
`During the final stage of developing a synthetic procedure
`for a new drug entity, a great deal of emphasis is placed on
`obtaining material of high purity, and reproducibility in terms
`of its physical, chemical, and biological properties. Every
`effort is made to ensure a high degree of crystallinity, wherein
`the molecules have regular and well-defined molecular pack-
`ing, and emphasis is also placed on whether or not the
`compound can exist in polymorphic or solvated crystal forms.1
`These forms can have different thermodynamic properties
`(e.g., melting temperature, vapor pressure, solubility), and a
`knowledge of their existence is required to anticipate spon-
`taneous changes in the properties of the solid during storage
`and/or handling of the material. It is also possible that upon
`isolation the material will be obtained in a fully or partially
`amorphous state.2 The four most common means by which
`amorphous character is induced in a solid are shown in Figure
`1. These are condensation from the vapor state, supercooling
`of the melt, mechanical activation of a crystalline mass (e.g.,
`during milling), and rapid precipitation from solution (e.g.,
`during freeze-drying or spray drying). Amorphous character
`is common with polymeric molecules used as excipients, and
`
`X Abstract published in Advance ACS Abstracts, October 1, 1996.
`
`© 1997, American Chemical Society and
`American Pharmaceutical Association
`
`S0022-3549(96)00189-X CCC: $14.00
`
`Figure 1sSchematic diagram of the most common ways in which amorphous
`character is induced in a pharmaceutical system.
`
`large peptides and proteins used as therapeutic agents, and
`it can also occur with small organic and inorganic molecules.
`When a system consists of multiple components, as with
`pharmaceutical formulations, it is possible that amorphous
`solid-state solutions can form analogous to liquid solutions.
`Water vapor can also be absorbed by an amorphous solid to
`form an amorphous solid solution.
`The three-dimensional
`long-range order that normally
`exists in a crystalline material does not exist in the amorphous
`state, and the position of molecules relative to one another is
`more random as in the liquid state. Typically amorphous
`solids exhibit short-range order over a few molecular dimen-
`sions and have physical properties quite different from those
`of their corresponding crystalline states.
`In Figure 2 we
`schematically plot the enthalpy (H) or specific volume (V) of
`a solid substance as a function of its temperature. For a
`crystalline material at very low temperatures we see a small
`increase in enthalpy and volume with respect to temperature,
`indicative of a certain heat capacity (Cp) and thermal expan-
`sion coefficient (R). There is a discontinuity in both H and V
`at the melting temperature (Tm) representing the first-order
`phase transition to the liquid state. Upon rapid cooling of
`the melt the values of H and V may follow the equilibrium
`line for the liquid beyond the melting temperature into a
`Argentum EX1028
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`this state by considering its rate and extent of molecular
`motions. The average time scale of molecular motions within
`a supercooled liquid is usually less than 100 s, the viscosity
`is typically between 10-3 and 1012 Pa(cid:226)s (Figure 3), and both
`properties are strongly temperature dependent.6-10 Cooling
`the supercooled liquid even further appears to reduce the
`molecular mobility of the material to a point at which the
`material is kinetically unable to attain equilibrium in the time
`scale of the measurement as it loses its thermal energy,
`resulting in a change in the temperature dependence of the
`enthalpy and volume. The temperature at which this occurs
`is the experimentally observed glass transition temperature
`(Tg). Below Tg the material is “kinetically frozen” into a
`thermodynamically unstable glassy state with respect to both
`the equilibrium liquid and the crystalline phase, and any
`further reduction in temperature has only a small effect upon
`its structure. Molecular motions in glasses typically occur
`over a period in excess of 100 s, and viscosities are usually
`greater than 1012 Pa(cid:226)s.6-10 Many of the physical properties
`of glassy amorphous materials (e.g., thermal expansion coef-
`ficient) are different from those of the corresponding super-
`cooled liquid above Tg.
`The molecular processes which contribute to the glass
`transition are currently the subject of intensive research and
`debate. Whether the changes in thermodynamic properties
`(e.g., specific heat, volume) that are seen during cooling (or
`reheating) are due to a real thermodynamic phase transition
`or are of purely kinetic origin is a controversial issue, and no
`theory has yet been proposed which accounts for all the
`observed experimental features. Several excellent reviews
`which describe the current thinking in this field have been
`published.6-8,10,11 Models based on statistical mechanical or
`free volume theories are the simplest and most widely
`invoked. Polymer scientists, metallurgists, ceramists, etc.
`each have their preferred approaches with specific advantages
`for the materials and processes with which they are working.
`From Figure 2 it can be seen that the glass transition can be
`considered to be a thermodynamic requirement for a super-
`cooled liquid since without such a transition the amorphous
`material would attain a lower enthalpy than the crystalline
`state at some critical temperature and would eventually attain
`a negative enthalpy. This critical temperature is known as
`the Kauzmann temperature (TK) and is thought to mark the
`lower limit of the experimental glass transition (Tg) and to
`be the point at which the configurational entropy of the system
`reaches zero.9,10 Experimental studies of the glass transition
`are complicated by the existence of many different modes of
`molecular motion in most systems (e.g., rotational or trans-
`lational), changes in the scale and type of motions with
`temperature, and cooperativity or coupling of molecular
`motions. One can only say for certain that at Tg the mean
`molecular relaxation time ((cid:244)) associated with the predominant
`molecular motions is about 100 s and that Tg can be expected
`to vary with experimental heating and cooling rates, sample
`molecular mass,12,13 sample history, sample geometry,14,15 and
`sample purity.16 The experimental glass transition temper-
`ature is also influenced by the choice of technique used to
`measure it because of the varying sensitivities of available
`techniques to different types and speeds of molecular motions.
`The temperature dependence of molecular motions directly
`determines many important physical properties of amorphous
`materials,
`including the location of the glass transition
`temperature and the ease of glass formation. This tempera-
`ture dependence is most frequently described using the
`empirical Vogel-Tammann-Fulcher (VTF) equation:7,8,10
`(cid:244) ) (cid:244)0 exp(DT0/T-T0)
`
`(1)
`
`where (cid:244) is the mean molecular relaxation time, T is the
`
`Figure 2sSchematic depiction of
`temperature.
`
`the variation of enthalpy (or volume) with
`
`“supercooled liquid” region. On cooling further a change in
`slope is usually seen at a characteristic temperature known
`as the glass transition temperature (Tg). At Tg the properties
`of the glassy material deviate from those of the equilibrium
`supercooled liquid to give a nonequilibrium state having even
`higher H and V than the supercooled liquid. As a result of
`its higher internal energy (e.g., (cid:25)25 kJ(cid:226)mol-1 for cephalospor-
`ins3) the amorphous state should have enhanced thermody-
`namic properties relative to the crystalline state (e.g., solu-
`bility,4 vapor pressure) and greater molecular motion. We
`would also expect amorphous systems to exhibit greater
`chemical reactivity3 and to show some tendency to spontane-
`ously crystallize, possibly at different rates below and above
`Tg.5 From a pharmaceutical perspective we have an interest-
`ing situation. The high internal energy and specific volume
`of the amorphous state relative to the crystalline state can
`lead to enhanced dissolution and bioavailability,4 but can also
`create the possibility that during processing or storage the
`amorphous state may spontaneously convert back to the
`crystalline state.5
`In considering the importance of the amorphous state in
`pharmaceutical systems we must direct our attention to two
`main situations. In the first, a material may exist intrinsically
`in the amorphous state or it may be purposefully rendered
`amorphous and we would like to take advantage of its unique
`physical chemical properties. Under these circumstances we
`usually want to develop strategies to prevent physical and
`chemical instability of the amorphous sample. In the second
`case, we may be dealing with a crystalline material that has
`been inadvertently rendered amorphous during processing.
`This type of amorphous character usually exists predomi-
`nately at surfaces at levels not easily detected and has the
`potential to produce unwanted changes in the physical and
`chemical properties of the system. In this situation we usually
`want to process the system so that the amorphous portions
`of the solid are converted back to the most thermodynamically
`stable crystalline state.
`
`Definition and Description of the Amorphous State
`The rapid cooling of a liquid below its melting point (Tm)
`may lead to an amorphous state with the structural charac-
`teristics of a liquid, but with a much greater viscosity (Figures
`2 & 3). The enthalpy and volume changes immediately below
`Tm exhibit no discontinuity with those observed above Tm, so
`we consider this amorphous state to be an equilibrium
`“supercooled” liquid. This amorphous state is also called the
`“rubbery state” because of the macroscopic properties of
`amorphous solids in this region. We can further characterize
`
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`Figure 3sMolecular mobility (or viscosity) of amorphous materials as a function of normalized temperature above Tg.7,8 Reprinted with permission from ref 8. Copyright
`1995 American Association for the Advancement of Science.
`
`temperature, and (cid:244)0, D, and T0 are constants. The value of
`T0 in the VTF equation is believed to correspond to the
`theoretical Kauzmann temperature (TK), and (cid:244)0 can be related
`to the relaxation time constant of the unrestricted material.7,8
`When T0 is 0, the familiar Arrhenius equation is obtained,
`and D is directly proportional to the activation energy for
`molecular motion. When T0 is greater than 0, there is a
`temperature dependent apparent activation energy. The
`Williams-Landel-Ferry (WLF) equation17 describing the
`temperature dependence of viscosity (Ł) in polymers above Tg
`is a special case of the VTF equation:
`Ł ) Łg exp{C1(T - Tg)/(C2 + (T - Tg))}
`
`(2)
`
`where Łg is the mean viscosity at Tg and C1 and C2 are
`constants. This equation can be derived from first principles
`based on polymer free volume theories. The constants C1 and
`C2 are found to be quite universal for a range of polymers17
`and are equivalent to DT0/(Tg - T0) and (Tg - T0), respectively,
`in the VTF equation. The WLF equation has been shown to
`fit viscosity data for several small organic molecules using
`the universal constants,18-20 making it useful for predicting
`the relaxation behavior or molecular mobility of amorphous
`pharmaceutical solids. However, it is important to recognize
`that this is not always the case and such predictions cannot
`always be assumed to be accurate.
`Depending upon the magnitude and temperature depen-
`dence of the apparent activation energy for molecular motions
`near and above Tg in supercooled liquids, it is possible to
`classify them as either “strong” or “fragile” amorphous systems
`(Figure 3).7,8 A strong liquid typically exhibits Arrhenius-like
`changes in its molecular mobility with temperature and a
`relatively small change in heat capacity at Tg. Proteins are
`good examples of strong glass formers, with their changes in
`heat capacity at Tg often being so small that they cannot be
`detected using standard calorimetry techniques.21 A fragile
`
`supercooled liquid has a much stronger temperature depen-
`dence of molecular mobility near Tg and a relatively large
`change in heat capacity at Tg and will typically consist of
`nondirectionally, noncovalently bonded molecules (e.g., etha-
`nol). The constant D in the VTF equation is an indicator of
`fragility, with low values (<10) corresponding to very fragile
`glass formers and high values (>100) indicating strong glass-
`forming tendencies. The value of T0 in the VTF equation is
`also linked to the fragility of the system with (Tg - T0) > 50
`typical of strong glass formers and (Tg - T0) < 50 usual for
`fragile materials. A simple graphical means of ranking
`materials in terms of their strength/fragility is to plot the
`molecular mobility (or viscosity) as a function of the temper-
`ature normalized to the experimental glass transition tem-
`perature (e.g., Figure 3).7,8 A “rule of thumb” for determining
`fragility without relaxation time data has also been proposed
`based on the relative magnitudes of the melting and glass
`transition temperatures: strong, Tm/Tg (in K) >1.5; fragile,
`Tm/Tg (in K) < 1.5)7, 8 (Table 1). (See Note Added in Proof.)
`The extent of departure of a glass’s properties from equi-
`librium is determined by its formation conditions, so we can
`presume the existence of multiple metastable glasses below
`Tg (Figure 2),2,3 and even polyamorphic glasses that convert
`via first-order transitions.22-24 As a result of this, the tem-
`perature dependence of molecular motions below the glass
`transition temperature is highly dependent upon the condi-
`tions under which the glass was formed.12 This temperature
`dependence is generally less extreme than above Tg and more
`linear, with some authors proposing an Arrhenius-like rela-
`tionship. That molecular motions do occur below Tg is
`unquestionable, and the consequences of the relaxation or
`“aging” of glassy materials have been widely reported. For
`example, Guo et al.25 described effects upon the film-coat water
`permeability and dissolution rate of film coated tablets, and
`Byron and Dalby26 studied the effects of aging on the perme-
`ability of poly(vinyl alcohol) films to a model water soluble
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`Table 1sMeasured Physical Properties of Some Amorphous Pharmaceutical Materialsa
`
`Material
`
`Mw
`
`Tm (K)
`
`Tg (K)
`
`Tm/Tg
`
`Famorph (kg(cid:226)m-3)
`Fcrystal (kg(cid:226)m-3)
`¢Cp (J(cid:226)g-1(cid:226)K-1)
`1.32
`1.38
`0.466
`1.37
`320
`438
`358
`Indomethacin
`1.43
`1.59
`0.544
`1.30
`348
`453
`342
`Sucrose
`1.48
`1.60
`0.472
`1.27
`383
`486
`342
`Lactose (anhydrous)
`1.49
`1.58
`0.534
`1.24
`385
`476
`342
`Trehalose (anhydrous)
`(cid:25)5 · 105
`s
`s
`s
`Dextran
`0.92
`0.400
`498
`(cid:25)1 · 106
`s
`s
`s
`Poly(vinylpyrrolidone)
`1.25
`0.260
`458
`(cid:25)0.95
`Waterb
`<0.95
`0.100
`2.01
`136
`273
`18
`aMw ) molecular mass; Tg ) glass transition temperature; Tm ) melting temperature; ¢Cp ) heat capacity change at Tg; F ) density. b Reference 134.
`
`drug. The effects of aging are often detrimental, but they can
`also be used to improve a product’s performance with a
`deliberate “annealing” process. This strategy is particularly
`useful when small amounts of amorphous character have been
`unintentionally introduced into a system by high-energy
`processing (see later).27,28 The time scale of molecular motions
`in a glass is much longer than above Tg ((cid:244) . 100 s) and
`requires different experimental techniques for its study. In
`almost all cases the molecular relaxation processes that occur
`in glasses follow a nonexponential function. This nonexpo-
`nentiality has been widely studied and modeled29 and appears
`to be the result of a heterogeneous microstructure within
`glasses which leads to a distribution of types and rates of
`molecular motion under any given time and temperature
`conditions. The reader is referred to some excellent reviews
`for detailed information on the application of these models to
`glassy systems.12,29 The empirical Kohlrausch-Williams-
`Watts (KWW) stretched exponential function is most often
`used to describe the distribution of molecular motions:10
`(cid:30)(t) ) exp{-(t/(cid:244))(cid:226)}
`
`(3)
`
`where (cid:30)(t) is the extent of relaxation at time t, (cid:244) is the mean
`molecular relaxation time, and (cid:226) is a constant. A (cid:226) value of
`unity corresponds to a single relaxation time with exponential
`behavior. The smaller the value of (cid:226), the more the distribu-
`tion of molecular motions deviates from a single exponential.
`(cid:226) has been shown to correspond to the strength/fragility of
`the material above Tg, but no similar relationship has yet been
`established below Tg. By fitting data to the KWW function it
`is possible to determine the mean molecular relaxation time
`((cid:244)) and (cid:226) for any well-defined glass.30 A general means of
`ranking glasses in terms of the temperature dependence of
`molecular motions, similar to Angell’s strong/fragile classifica-
`tion system above Tg, would be of great use to pharmaceutical
`materials scientists but has not yet been developed because
`of the greater complexities of the glassy state.
`Perhaps the most important question relating to amorphous
`pharmaceutical systems is, At what temperature do the
`molecular motions responsible for physical and chemical
`instabilities cease to become likely over the lifetime of that
`particular system?30 It has been suggested that this lower
`temperature limit might correspond to the Kauzmann tem-
`perature (TK). Although this appears to be the case for some
`systems, there also appears to be an influence from the
`strength/fragility of the system, and also from whether or not
`the molecular motions that are responsible for the glass
`transition and any instabilities are identical.30 Mean molec-
`ular relaxation times have been reported for several pharma-
`ceutical glass formers as a function of temperature following
`enthalpy relaxation and thermomechanical relaxation experi-
`ments, and the temperature of negligible molecular mobility
`during a 3-year shelf life varied according to (i) the method
`used to assess the molecular motions and (ii) the identity of
`the glass former.30 As yet there is no reliable means of
`predicting the temperature of negligible molecular mobility
`in amorphous solids, and thus a conservative approach is
`
`4 / Journal of Pharmaceutical Sciences
`Vol. 86, No. 1, January 1997
`
`required when defining storage and processing conditions for
`amorphous pharmaceutical systems (see later).
`The behavior of amorphous systems as defined in Figure 2
`is dependent upon the assumption of constant pressure and
`composition. Pressure effects upon amorphous materials have
`not been widely studied but are likely to be significant with
`effects on molecular packing potentially modifying the glass
`transition temperature, the thermal expansion behavior, and
`the strength/fragility of a supercooled liquid.10,31,32 From a
`practical perspective the glass transition temperature of a
`system containing volatile components may only be experi-
`mentally accessible at elevated pressures. For example, the
`widespread and significant plasticizing effects of sorbed water
`vapor in high-Tg amorphous polymers have only recently been
`fully realized because of advances in sample-handling methods
`which allow samples of varying water content to be sealed at
`ambient temperature and then heated through Tg without loss
`of their sorbed water vapor.33 The properties of a glassy
`amorphous solution prepared by lyophilization are also likely
`to be significantly different from those of the same system
`prepared at ambient pressure since the reduced pressure
`within a lyophilization chamber will affect the structure of
`the amorphous cake that is formed and also the composition
`of the solution through the primary and secondary drying
`processes. Angell et al.34 have noted that for aqueous solutions
`the fragility of the supercooled solution is dependent upon the
`solute concentration in the solution. From the limited data
`available it can be concluded that some supercooled aqueous
`solutions become stronger as they become more dilute (e.g.,
`sugars), whereas others become more fragile (e.g., electrolytes,
`salts). The type of behavior observed appears to be linked to
`the extent of hydrogen bonding in the aqueous solution. The
`fragility of such mixed systems may also be related to the
`ideality of their mixing behavior. Simple mixing rules have
`been used by many authors35,36 to describe the variation of
`the glass transition temperature with blend composition;
`however, the effects of nonidealities (e.g., immiscibility, mo-
`lecular size differences, specific interactions, etc.) are often
`significant. The simplest and most reliable approach for use
`with amorphous pharmaceutical materials appears to be a
`modified Gordon-Taylor equation35,36 which is based on free
`volume theories with some simplifying assumptions. For
`simple two-component mixtures,
`Tgmix ) (w1Tg1 + Kw2Tg2 )/(w1 + Kw2)
`
`(4)
`
`where Tg is the glass transition temperature, w1 and w2 are
`the weight fractions of components 1 and 2, and K can be
`calculated from the densities (F) and glass transition temper-
`atures (Tg) of the components:
`K ) (Tg1F1)/(Tg2F2)
`
`(5)
`
`Similar equations can be readily derived for mixtures of more
`than two components. A perfecty miscible system will display
`a single sharp glass transition event. Immiscibility, incom-
`patibility, or nonideality is often indicated by a poor fit to the
`
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`theoretical equation, the appearance of more than one Tg, or
`“broadening” of the glass transition event. Deviations from
`ideal behavior can also be identified and their most likely
`causes assessed using the graphical approach of Schneider
`and co-workers.36,37 Deviations usually occur over discrete
`composition ranges and often can be explained in terms of
`molecular size effects and the disappearing free volume of the
`high-Tg component at lower temperatures and composi-
`tions.38,39 Such an approach is analogous to percolation
`theories and has considerable potential for describing mixed
`amorphous systems. Simple solution theories also can be used
`to describe such systems and to provide a qualitative under-
`standing of the important factors regulating the glass transi-
`tion in pharmaceutical systems. For example, it is likely that,
`when a macromolecule is mixed in small amounts with an
`amorphous small molecule, it will introduce a considerable
`excess free volume to the system because of its much larger
`molecular size. In this situation the glass transition temper-
`ature of the mixture probably will not be elevated as much
`as predicted by theory. The addition of low levels of a small
`molecule to an amorphous macromolecular system probably
`will be much less disruptive. Both materials will make near
`ideal contributions to the overall free volume of the mixture,
`and in this instance the predictions of the mixing equations
`are likely to be quite accurate for at least the first 50 K change
`in Tg. This is very important since the presence of very low
`levels of low molecular weight contaminants or additives
`(including water vapor) is predicted and observed to have
`significant plasticizing effects on pharmaceutical glasses,36
`whereas the addition of low levels of high molecular mass
`additives often has minimal antiplasticizing effect.39 It should
`be noted that the concept of a critical additive composition
`(Wg) at which a glassy macromolecular material is sufficiently
`plasticized by a low molecular weight penetrant that it
`transforms to a rubbery amorphous solid under ambient
`conditions has been described by several authors.33,40
`Pharmaceutical solids rarely exist as 100% crystalline or
`100% amorphous phases so it is necessary at this point to
`consider how partially crystalline or amorphous systems are
`likely to behave. The coexistence of two thermodynamically
`different states of a material will probably result in (i)
`significant and measurable structural heterogeneities and (ii)
`batch to batch variations in physical properties. The presence
`of one phase in another can act as a focal point for spontaneous
`phase transitions such as crystallization.28,41,42 In addition,
`as each phase is intimately dispersed in the other, there may
`not be complete independence of their behavior. For example,
`the dispersion of crystalline drug in an amorphous carrier has
`been reported to alter the observed glass transition temper-
`ature of the amorphous phase.43 For macromolecules there
`may even be molecules which are part of both crystalline and
`amorphous domains physically linking the two regions to-
`gether. Partially ordered systems have traditionally been
`described using either “one-state” or “two-state” models.4,28,41,42
`In the two-state model, domains of material are assumed to
`be either 100% amorphous or 100% crystalline and they
`coexist side by side in a molecular mixture. This type of
`system can be simulated to some extent by making physical
`mixtures of reference samples of crystalline and amorphous
`materials.3 The one-state model consists of domains which
`are truly partially crystalline and in which the molecules have
`formed a semiordered structure as a result of being restricted
`in their motion during crystallization, or following the disrup-
`tion of a more perfect crystalline state. The one-state model
`seems intuitively more likely than the two-state model but
`raises many questions which cannot be readily answered by
`studying mixtures of the reference crystalline and amorphous
`materials. In metallic systems there is also a state known as
`the “nanocrystalline phase” which has properties intermediate
`
`Figure 4sX-ray powder diffraction patterns for amorphous (bottom) and crystalline
`(top) lactose.
`
`to those of the amorphous and crystalline states,44 and the
`concept of “glassy” or “plastic” crystals has recently been
`described.45 Clearly the ability to distinguish between crys-
`talline and amorphous states of a material and to be able to
`quantify one phase in the presence of the other is critical to
`the successful design and production of amorphous pharma-
`ceutical systems.
`
`Characterization of the Amorphous State
`Upon passing into the supercooled liquid state or through
`the glass to rubber transition it is possible to observe changes
`in a multitude of material physical properties including
`density, viscosity, heat capacity, X-ray diffraction, and diffu-
`sion behavior. Techniques which measure these properties
`(directly or indirectly) can be used to detect the presence of
`an amorphous material (glass or rubber), and some of these
`methods are sensitive enough to allow quantification of the
`amount of molecular order or disorder (amorphous content)
`in a partially crystalline system.
`As there is no long-range three-dimensional molecular order
`associated with the amorphous state, the diffraction of
`electromagnetic radiation (e.g., X-rays) is irregular compared
`to that in the crystalline state (Figure 4). Diffraction tech-
`niques are perhaps the most definitive method of detecting
`and quantifying molecular order in any system, and conven-
`tional, wide-angle and small-angle diffraction techniques have
`all been used to study order in systems of pharmaceutical
`relevance.3,5,41 The specificity and accurate quantitative
`nature of these nondestructive techniques make them first
`line choices for studying partially crystalline pharmaceutical
`materials. Conventional X-ray powder diffraction measure-
`ments can be used to quantify non-crystalline material down
`to levels of about 5%41 and with temperature and environ-
`mental control can also be used to follow the kinetics of phase
`transformations, or to quantify the presence of a crystalline
`drug in an amorphous excipient matrix.46 Small-angle X-ray
`measurements have been used to study subtle structural
`(density) changes in polymers in the glassy state upon
`annealing,47 and neutron scattering is gaining wider use in
`the characterization of short-range two-dimensional order in
`amorphous materials.48 It should be remembered that dif-
`fraction techniques only “see” molecular order, and thus
`disorder is only implied.
`The irregular arrangement of molecules in the amorphous
`state usually causes them to be spaced further than in a
`crystal so that the specific volume is greater and the density
`lower than that of the crystal, and we say that there is a
`greater “free volume” (Figure 2). Highly accurate measure-
`
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`+
`
`ments of volume or density are difficult, and the magnitudes
`of differences involved are fairly small (Table 1), so such
`determinations are not a method of choice for characterizing
`amorphous pharmaceutical systems. The use of gas displace-
`ment pycnometry for quantifying the amorphous content of
`partially crystalline pharmaceutical systems has been de-
`scribed by Saleki-Gerhardt et al.,41 and the accuracy achieved
`was about (10%. Liquid displacement pycnometry has also
`been used to determine the crystallinity of several starch
`samples.49 This approach has proved useful for quantifying
`low levels of disorder in crystalline pharmaceutical samples.50
`Precise dilatometric techniques are widely used for the study
`of amorphous polymers,51 and these techniques could be useful
`for pharmaceutical systems; however, the methods are time-
`consuming and quite difficult to perform and so would not be
`suitable for routine use.
`The most characteristic property of the amorphous state is
`its viscosity (approximately <1012 Pa(cid:226)s above Tg and >1012
`Pa(cid:226)s below Tg). The greater free volume and molecular
`disorder of an amorphous material compared to its crystalline
`counterpart result in the mechanical properties of amorphous
`systems (viscosity, elastic modulus) being much more like
`those of a liquid than those of a solid. In some supercooled
`liquids a breakdown of the Stokes-Einstein relationship
`between the viscosity and the rate of diffusion (or molecular
`mobility) has been observed.52 It is thought that the break-
`down of this fundamental relationship may be due to the
`decoupling of certain modes of molecular motion in the
`amorphous state.52,53 Methods which are used to measure the
`viscosity of amorphous materials are quite specialized and
`include the bending of rods or curved fibers below Tg
`54 and
`the torsion pendulum and falling-sphere methods above Tg.19
`Experimental difficulties are often quite significant, and thus
`such measurements are usually feasible only in a specially
`equipped research laboratory.
`Diffusion-controlled processes (such as gas transport, self-
`diffusion, crystallization, and some chemical reactions) which
`are all closely linked to the viscosity of the amorphous matrix
`have been the subject of many studies of glassy and rubbery
`amorphous materials.23 As a consequence of the greater free
`volume in amorphous materials, diffusive transport processes
`are usually significantly more rapid and isotropic than in
`crystals. Often different diffusion rates are observed above
`and below Tg, with significantly faster diffusion occurring
`above Tg. This phenomenon can be used to identify the glass
`transition temperature in some amorphous systems. The
`sensitivity of transport processes to small fractions of crystal-
`line order has yet to be clearly defined, although it appears
`that ordered domains can slow down the rate of diffusion.
`There is an intuitive connection between the viscosity of an
`amorphous system and the rate of diffusion wit