Determination of the Glass Properties of D-Mannitol Using Sorbitol as
`an Impurity
`
`LIAN YU,* DINESH S. MISHRA, AND DANIEL R. RIGSBEE
`
`Contribution from Eli Lilly and Company, Lilly Research Laboratories, Indianapolis, Indiana 46285.
`
`Received June 6, 1997. Accepted for publication March 9, 1998.
`
`Abstract 0 Due to its strong tendency to crystallize,
`the glass
`properties of mannitol cannot be measured directly. However, because
`mannitol can exist in a fully or partially amorphous state in drug
`formulations,
`it
`is important
`to determine the glass properties of
`mannitol. We obtained the glass properties of mannitol by introducing
`a small amount of sorbitol, an isomer of mannitol, to delay the onset
`of crystallization. Extrapolation to zero sorbitol concentration yielded
`the following properties for the mannitol glass: Tg onset ) 10.7 oC,
`Tg midpoint) 12.6 oC, Tg end ) 18.4 (cid:176)C and ¢Cp ) 1.27 J/g/K.
`In
`addition, we estimated the following parameters of the mannitol glass
`from the width of glass transition using the results of Moynihan (J.
`Am. Ceram. Soc. 1993, 76, 1081) and Angell (J. Phys. Chem. 1994,
`98, 13780): ¢H* (at Tg onset) ) 103 kcal/mol, D ) 11, and T0 ) 222
`K. The value of T0 is consistent with the Kauzmann temperature TK
`(236 K) obtained calorimetrically. The properties of the mannitol glass
`may be useful for predicting the behavior of amorphous mixtures
`containing mannitol.
`
`Introduction
`Pharmaceuticals are often formulated with excipients
`into glassy solid mixtures. Understanding the nature of
`these glasses (e.g., the glass transition temperature, Tg,
`the strength or fragility,1 and the phase homogeneity) is
`important for developing formulations that are physically
`and chemically stable. Theoretical models have been
`developed for predicting the Tg of a mixture from the
`component properties (Tg, heat capacity change at Tg,
`volume expansion coefficients before and after Tg, etc.).2-4
`To test and apply these models for pharmaceutical systems,
`it is necessary to determine the glass properties of common
`excipients.
`D-Mannitol is a common excipient in freeze- and spray-
`drying. Its chief advantage is good chemical stability. For
`example, unlike many disaccharides, mannitol does not
`undergo hydrolysis at low or high pH. Despite its strong
`tendency to crystallize, mannitol exists in fully or partially
`amorphous state in certain formulations.
`The glass transition of mannitol cannot be measured
`directly using the standard melt-quench method, because
`of its strong tendency to crystallize. In a typical melt-
`quench sequence, mannitol is melted (curve A, Figure 1),
`vitrified by quenching, and then reheated (curve B). Curve
`B shows no well-defined glass transition. Although a Cp
`increase is discernible (event 1, inset), which may be
`associated with a glass transition, the exotherm that
`immediately follows (event 2) makes the assignment
`ambiguous and the measurement of ¢Cp and the width of
`glass transition impossible. Events 2 and 3 are due to the
`crystallization of mannitol, possibly into different poly-
`morphs.
`
`* Corresponding author. Tel.: (317) 276 1448. Fax: (317) 277 5519.
`E-mail: yu_lian@lilly.com.
`
`Figure 1sDSC characteristics of pure mannitol. Curve A:
`first heating to
`remove crystallinity. Curve B: second heating after quenching. The exothermic
`events 2 and 3 are due to the crystallization of mannitol from the supercooled
`melt, possibly into different polymorphs.
`
`There has been a previous report on the glass-transition
`properties of mannitol (Tg ) 9 °C, ¢Cp ) 1.14 J/g/K).5
`Unfortunately, no experimental details are given in this
`report on the technique used and how the problem of
`crystallization was solved. The Tg of mannitol can be
`estimated from the melting point (Tm) using a variety of
`scaling rules.6 However, the crudeness of these rules, along
`with the problem of polymorphism (mannitol polymorphs
`melt at 158, 166.0, and 166.5 °C),7 makes such predictions
`inadequate for precise work. It is also possible to back-
`calculate the Tg of mannitol from the Tg of an amorphous
`mixture containing mannitol. To do so, however, one must
`assume that one of the several Tg-composition models2-4
`correctly applies to the mixtures because they cannot all
`apply at the same time.8
`A well-known technique for measuring the glass proper-
`ties of “poor glass formers” (materials with strong tendency
`to crystallize) is by introducing a small amount of melt-
`miscible impurity to delay the onset of crystallization.9 If
`the glass transition is successfully observed, one then
`extrapolates to the zero impurity concentration to obtain
`the glass properties of the pure material.
`This technique was adopted in this study to measure the
`glass properties of mannitol. For several reasons we
`selected sorbitol, a stereoisomer of mannitol, as the impu-
`rity. Because of their structural similarity, sorbitol and
`mannitol were expected to be melt-miscible and form a
`nearly ideal solution. In addition, the properties of the
`sorbitol glass are known5,10-12 and can serve as a reference
`point.
`We report here a set of parameters characterizing the
`mannitol glass (Tg, the width of glass transition, ¢Cp, D,
`T0, and ¢H*). The first three parameters were obtained
`by extrapolation. The last three parameters were esti-
`
`774 / Journal of Pharmaceutical Sciences
`Vol. 87, No. 6, June 1998
`
`S0022-3549(97)00224-4 CCC: $15.00
`Published on Web 04/21/1998
`
`© 1998, American Chemical Society and
`American Pharmaceutical Association
`
`Amneal v. Cubist
`IPR2020-00193
`Cubist Ex. 2005
`
`

`

`a
`
`0
`0.743
`
`0.821
`
`Table 1sGlass Transition Characteristics of Mannitol- Sorbitol Mixtures
`Tg end - Tg onset, (cid:176) C
`Tg midpoint - Tg onset, (cid:176) C
`Tg end,oC
`xm
`Tg onset,oC
`Tg midpoint,oC
`- 3.4 – 0.2b
`7.6 – 0.2b
`4.2 – 0.2b
`- 1.6 – 0.2b
`1.81 – 0.05b
`7.72
`14.08
`6.36
`8.36
`2.00
`7.52
`13.88
`6.36
`8.33
`1.97
`7.55
`15.17
`7.62
`9.58
`1.96
`8.06
`15.88
`7.82
`9.87
`2.05
`7.54
`16.14
`8.60
`10.48
`1.88
`7.80
`16.30
`8.50
`10.34
`1.84
`7.72c
`17.69c
`9.97
`11.86c
`1.89c
`9.72
`11.60c
`7.52c
`17.24c
`1.88c
`1.27 – 0.03e
`7.7 – 0.2d
`18.4 – 0.2d
`10.7 – 0.1d
`12.6 – 0.1d
`1.84 – 0.04d
`1.000
`a Mole fraction of mannitol. b Average – standard deviation from four measurements. c Estimated from data in which the glass transition and mannitol crystallization
`are not completely separated (see the text). d Extrapolated (average – standard deviation). e Estimated by averaging the ¢Cp values of mannitol- sorbitol mixtures.
`
`¢Cp, J/g/K
`1.17 – 0.02b
`1.29
`1.27
`1.29
`1.28
`1.24c
`1.23c
`s
`
`0.869
`
`0.949
`
`mated from the width of glass transition using the results
`of several previous studies.1,5,13-15
`
`Experimental Section
`MaterialssD-Mannitol (99+%, mp 167-170 °C) and D-sorbitol
`(99+%, mp 98-100 °C) were obtained from Aldrich Chemical Co.
`and used without further purification. In preparing the mannitol-
`sorbitol mixtures, we took precautions to ensure low moisture
`(because of the strong plasticizing effect of water) and thorough
`mixing (because of the high viscosity of molten mannitol and
`sorbitol). The mannitol-sorbitol mixtures were prepared as
`follows: (1) mix the two components, each accurately weighed, by
`grinding; (2) melt the physical mixtures and mix by swirling; (3)
`cool the mixtures to room temperature under dry nitrogen; (4)
`grind the solidified mixtures; (5) vacuum-dry the mixtures at 40
`°C for 2 days; and (6) store the mixtures in freeze-drying vials
`sealed with Teflon-coated stoppers until use. Karl Fischer titra-
`tion showed that the mixtures thus produced contain 0.1-0.2%
`moisture. The melt-miscibility of mannitol and sorbitol was
`confirmed both visually and with the aid of hot-stage microscopy.
`DSC MeasurementsDSC measurement was conducted using
`a Perkin-Elmer DSC 7. Temperature was calibrated using indium
`and water (ice melting) and checked against the NaCl-water
`eutectic point. Heat-flow was calibrated using indium. The
`sample (8-12 mg) was pressed into a pellet using a custom-made
`stainless steel tool and sealed in an Al pan. The sample prepara-
`tion was carried out in a glovebox purged with dry nitrogen (RH
`< 1%). DSC conditions were as follows: (1) heat the sample to
`just above the melting point, (2) quench the sample by contact
`with a -80 to -85 °C metal block (the DSC 7 heat-sink) for
`approximately 30 s, and (3) scan for Tg from -30 °C at 7 °C/min.
`
`Results and Discussion
`Figure 2 shows the effect of adding sorbitol on the DSC
`characteristics of mannitol. As the sorbitol concentration
`increased, the crystallization exotherm (event 2) was
`increasingly delayed from event 1. With enough separa-
`tion, event 1 was recognized as a glass transition. The
`glass transition of sorbitol was recorded under the same
`conditions for comparison (curve 6).
`From a well-defined glass transition (curves 4-6 in
`Figure 2), we measured three temperatures (defined on
`curve 6): Tg onset (point a), Tg midpoint (point b), and Tg end
`(point c). The heat capacity change upon glass transition
`(¢Cp) was also measured. If the post-Tg baseline was not
`well-defined but the end of the glass transition was
`discernible (curves 3 and 4), we measured only Tg onset and
`Tg midpoint and estimated Tg end and ¢Cp by drawing a post-
`Tg baseline, starting from the maximum of the endothermic
`“overshoot” (due to enthalpy relaxation, see later discus-
`sion), that matched the post-Tg baseline of a well-defined
`glass transition (e.g., curve 5). We made no attempt to
`measure curve 1 (pure mannitol). The glass transition data
`are summarized in Table 1.
`
`Figure 2sDSC characteristics of mannitol- sorbitol mixtures as a function of
`the mannitol mole fraction (xm): xm ) (1) 1, (2) 0.949, (3) 0.869, (4) 0.821,
`(5) 0.743, (6) 0. On curve 6, the different temperatures characterizing a glass
`transition are defined:
`(a) Tg onset, (b) Tg midpoint, (c) Tg end.
`
`Figure 3sDetermination of the Tg of mannitol by extrapolation:
`(a) Tg onset,
`(b) Tg midpoint, (c) Tg end, (b - a) Tg midpoint
`- Tg onset; (c - a) Tg end - Tg onset.
`
`In the concentration range studied (xm ) 0.743-1, where
`xm is the mole fraction of mannitol), the Tg-xm data were
`well-fitted by straight lines (Figure 3). Extrapolating these
`lines to xm ) 1 yielded Tg onset ) 10.7 ( 0.1 °C (r ) 0.998),
`and Tg midpoint ) 12.6 ( 0.1 °C (r ) 0.996), and Tg end ) 18.4
`( 0.2 °C (r ) 0.985). These temperatures were assigned
`to the glass transition of mannitol. The extrapolated Tg onset
`matched the start of event 1 in Figure 1, indicating that
`event 1 is indeed the onset of glass transition.
`
`Journal of Pharmaceutical Sciences / 775
`Vol. 87, No. 6, June 1998
`
`

`

`The quantities (Tg midpoint - Tg onset) and (Tg end - Tg onset),
`the “half and full widths” of the glass transition, were
`essentially independent of concentration (Table 1). Ex-
`trapolating the lines that best fit the ¢Tg - xm data to xm
`) 1 yielded (Tg midpoint - Tg onset) ) 1.84 ( 0.04 °C and (Tg end
`- Tg onset) ) 7.7 ( 0.2 °C (Figure 3). These values were,
`within experimental error, identical with those of sorbitol
`(Table 1).
`Because a good post-Tg baseline is necessary for a
`reliable measurement of ¢Cp, we had less data for extrapo-
`lation. However, Table 1 shows that ¢Cp does not change
`significantly with concentration in the xm range studied
`(Table 1). Therefore we estimated the ¢Cp of mannitol by
`averaging over the ¢Cp’s of the mixtures, which gave ¢Cp
`) 1.27 ( 0.03 J/g/K.
`From the measured Tg onset and Tg end, we were able to
`calculate additional properties of the mannitol glass using
`the results of Moynihan13 and Angell.14 Moynihan finds
`that for structurally similar glasses the following function
`is approximately constant:13
`¢H*/R (1/Tg onset - 1/Tg end) ) C
`
`(1)
`
`where ¢H* is the activation energy for enthalpy relaxation,
`a parameter describing the temperature dependence of the
`structural relaxation time ((cid:244)).1 For a group of high-Tg
`inorganic glasses, Moynihan finds C ) 4.8. For sorbitol,
`we calculated C from Tg onset and Tg end (Table 1) and ¢H*
`) 93 kcal/mol.11 This gave C ) 4.75, which is in surpris-
`ingly good agreement with Moynihan’s value. Assuming
`C(mannitol) ) C(sorbitol), which seemed reasonable for the
`two structurally similar glasses, we obtained ¢H* ) 103
`kcal/mol for mannitol.
`Next, we estimated the strength parameter (D) and the
`temperature of “zero mobility” (T0). These parameters
`describe the temperature dependence of structural relax-
`ation time ((cid:244)) through the VTF equation:1
`(cid:244) ) (cid:244)0 exp[DT0/(T - T0)]
`
`(2)
`
`One can estimate D and T0 from Tg onset and Tg end using
`eq 1 and the assumption14 that there exists a 17 order of
`magnitude difference between (cid:244) at Tg and (cid:244) 0 (the high-
`temperature limit of (cid:244)). Pikal has given a procedure
`(unpublished) on how to carry out the estimation.15 Pikal
`and co-workers recently investigated the general ap-
`plicability of this estimation procedure and concluded that
`the Moynihan constant C is not a “universal” constant for
`the pharmaceutical materials studied, but can be regarded
`as such within a “subclass” of materials.16 Hatley has used
`Pikal’s procedure to estimate D and T0 for sucrose and
`trehalose.17
`To carry out this estimation, one first obtains the
`relationship between ¢H* and the VTF parameters in eq
`2 using the definition ¢H* ) d(ln (cid:244))/d(1/T). This yields
`eq 3:
`
`¢H*/(RT) ) D(T/T0)/(T/T0
`
`-1)2
`
`(3)
`
`The “17-order of magnitude” assumption14 and eq 2 lead
`to
`
`Tg onset/T0 ) 1 + D/39.1
`
`(4)
`
`Substituting eqs 1 and 4 into eq 3 yields
`1/D ) 0.000653C/(1 - Tg onset/Tg end) - 0.0255 (5)
`
`Equations 4 and 5 allow the calculation of D and T0 from
`
`776 / Journal of Pharmaceutical Sciences
`Vol. 87, No. 6, June 1998
`
`Tg onset and Tg end, provided that the Moynihan constant is
`known (e.g., from structurally similar compounds).
`Applying eqs 4 and 5 to sorbitol and using C ) 4.75 (see
`above), we obtained D ) 11 and T0 ) 209 K. These values
`agree with those obtained from the combined fit of viscosity
`and DSC data (D ) 8 and T0 ) 215 K)11 and from the
`constrained fit of the dielectric relaxation data (D ) 12.7
`(constraint) and T0 ) 208 K).5 This agreement provided
`some confidence in the calculation procedure.
`Next, we applied the procedure to mannitol (assuming
`C ) 4.75) and obtained D ) 11 and T0 ) 222 K. Angell
`and Smith have reported the Kauzmann temperature TK
`of mannitol to be 236 ( 10 K,5 which is considered identical
`with T0.1 Therefore, the agreement between T0 and TK also
`indicates some internal consistency.
`A potential error in the above calculations may originate
`from the thermal gradients in DSC samples (“thermal
`lag”).18 To assess the effect of this error, let us retrace the
`steps of the calculation. The thermal lag should not
`significantly affect Tg onset nor therefore the ¢H* of sorbitol
`derived from Tg onset vs heating rate q.11 However, this
`effect can affect Tg end and, in turn, C(sorbitol) calculated
`by eq 1. If we assume that the observed width of glass
`transition ¢Tg ) (Tg end - Tg onset) differs from the true
`width by a factor f, i.e., ¢Tg obs ) f¢Tg, then eq 1 gives an
`apparent C that differs from its true value by approxi-
`mately the same factor: Capp (cid:25) fC. Now it is likely that
`mannitol will experience the same thermal lag as sorbitol
`(same f). Therefore if we use Capp and the observed Tg to
`calculate the ¢H* of mannitol (eq 1), the errors in the two
`parameters approximately cancel out. As a result, the ¢H*
`of mannitol is essentially free of the error from thermal
`lag. Similarly, the calculation of D (eq 5) is also essentially
`unaffected by thermal lag. The subsequent calculation of
`T0 (eq 4) does not involve Tg end and therefore is not
`influenced either.
`The validity of these arguments is supported by the
`agreement between the calculated and independently
`measured parameters (see above). In the case of sorbitol,
`the ¢H*’s obtained from both the Tg onset-q data and the
`Tg end-q data can be combined smoothly with the high-
`temperature viscosity data.11 This may suggest that the
`thermal lag does not cause a significant error in the Tg end
`for sorbitol and the structurally similar mannitol.
`On the basis of the D parameters, the sorbitol and
`mannitol glasses can be classified as “fragile to intermedi-
`ate” in the fragility/strength spectrum.1 On the other hand,
`one would expect high fragility on the basis of the large
`¢Cp upon glass transition in these glasses (Cp liquid/Cp glass
`(cid:25) 2).12 These implications are reconciled if one recognizes
`the H-bonded nature of polyol glasses.1 The need to
`rupture intermolecular H bonds for molecules to undergo
`rearrangement perhaps makes the liquid to appear less
`fragile than the large ¢Cp would indicate.
`One utility of the parameter ¢H* is to estimate the effect
`of heating rate (q) on the observed Tg through eq 6:19
`
`d(ln q)/d(1/Tg) ) -¢H*/R
`
`(6)
`
`Using eq 6, we estimated that increasing q from 7 to 10
`°C /min would increase the Tg onset by 0.6 °C and decreasing
`q from 7 to 2.5 °C/min would decrease the Tg onset by 1.6
`°C. This dependence is the same as that for sorbitol,11
`which is expected because of their structural similarity.
`The Tg of sorbitol obtained by this work (Table 1) is
`consistent with a previous report (Tg ) -2.0 °C), which is
`obtained under similar conditions (quenching by liquid N2
`vapor to -60 °C, heating at 10 °C/min).10 Our result,
`however, is considerably higher than those of another group
`(Tg onset ) -7 °C5 and -8 °C12). Several factors may explain
`
`

`

`this difference. First, the sorbitol sample in the previous
`work has slightly more moisture (0.61%)5 than ours (0.1-
`0.2%). Second, the difference may result from the different
`heating rate, q. The previous value Tg onset ) -8 °C is
`obtained at q ) 2.5 °C/min.12 Changing q from 7 to 2.5
`°C/min will lower the Tg by approximately 1.6 °C.11 Finally,
`the cooling rate of the vitrification step may play a role.
`The previous work uses the same cooling rates as the
`heating rates, whereas we employed a much faster cooling
`rate to prevent mannitol crystallization.
`In principle,
`different cooling rates lead to glasses that are “relaxed” to
`different extents,6 which, on reheating, yield different Tg’s.
`However, as long as the heating rate is constant and the
`cooling rate/heating rate ratio is within a reasonable range
`(0.2-5), the Tg is not significantly affected by the initial
`cooling rate.13 For sorbitol, the endothermic “overshoot”,
`which is due to enthalpy relaxation, does not change
`significantly with cooling rates; for example, the “over-
`shoot” observed in this study (fast cooling) was not signifi-
`cantly different from that observed after much slower
`cooling.11,12 Therefore, the sorbitol glass seems to relax so
`rapidly that the cooling rate has little influence on Tg.
`The Tg onset and ¢Cp for mannitol (Table 1) are in
`reasonable agreement with the previous values (9 °C and
`1.14 J/g/K, respectively).5 The difference in Tg may result
`from similar causes as enumerated above for sorbitol.
`However, the lack of experimental details in ref 5 precludes
`more detailed comparisons.
`The Tg onset/Tm ratio was 0.64 for mannitol and 0.73 for
`sorbitol.
`(In both cases, the Tm of the highest melting
`polymorph was used in the calculation: 167.5 °C for
`mannitol7 and 98 °C for sorbitol.20) Although both values
`are reasonable according to the Tg - Tm scaling rules,6 the
`significant difference between the two structurally similar
`molecules warrants some attention.
`The use of linear extrapolation, instead of extrapolations
`based on well-known Tg-composition models,2-4 may re-
`quire some discussion. First we note that linear extrapola-
`tion was sufficient for our purpose because there was no
`indication of nonlinearity in the xm region considered.
`Second, it was impossible to decide a priori which model
`best describes the mannitol-sorbitol system, for the dif-
`ferent models cannot be correct for the same system
`simultaneously.8 The linear extrapolation, on the other
`hand, does not depend on the validity of any theoretical
`model, for all models are reduced to a linear Tg-xm
`relationship as xm approaches unity. We intend to inves-
`tigate the question as to which model best fits the man-
`nitol-sorbitol system in a future study.
`
`Conclusions
`We have obtained the glass-transition properties of
`mannitol using sorbitol as an impurity, including Tg onset,
`Tg midpoint, Tg end, and ¢Cp. We have estimated additional
`parameters (¢H*, D, and T0) from the width of glass
`transition using the results of Moynihan13 and Angell.14
`These properties should be useful
`for predicting the
`properties of mannitol-containing glassy mixtures.3 The
`question as to how the fragility changes when mannitol is
`mixed with “strong” glasses (e.g., proteins14) seems par-
`ticularly interesting. We are currently investigating the
`
`Tg-composition behavior over the full concentration range
`for the mannitol-sorbitol system and other binary polyol
`mixtures.
`
`Acknowledgments
`We thank Professor M. Pikal of University of Connecticut for
`helpful discussions and one of the reviewers for pointing out a
`previous report on the Tg of mannitol.
`
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