TERAHERTZ SPECTROSCOPY FOR PREDICTING STABILITY OF
AMORPHOUS DRUGS
Field of lnvention
5 The invention relates to a method and an apparatus for characterising
amorphous materials, and in particular to a method and an apparatus for
assessing the stability of amorphous materials, for example during storage.
Backqround of lnvention
10
Over the past decades; research and development activities in the
pharmaceutical industry have lead to the dsscovery of thousands of new
rnolecules and chemicai structure motifs that have a strong potential to be
used in the treatment of humart diseases: yet ortly a sn-tall proportion of these
15 lead candidates have made it to the market. increasingly, loin: solubility and
complex poly~worphism of lead moleciiles limit the suitability of these
molecules, and a number of products based on such n~oleculesa re failing just
before introduction to the market. At the same time, the number of recalis of
products on the n-tarket due to problems originating from their physico-chemical
20 properties is 017 the rise.
One very promising approach to increase the solubiiity of a pharmaceutical is
to formulate the ~woleculeso f the pharmaceutical into art amorphous phase,
iwhicl? is higher in energy than the crystalline state and hence intrinsically tends
25 to exhibit higher sol~~bilitlyt .is fairly straightfofivard to make drug molecules
amorphous and an associated increase in bioauailability for an ar~~orphous
drug con-tpared to its crystalline counterparts has been de~wonstrated.
t-iowever; the amorphous state is tl~ern~~dynamicaulnlyst able and currently it
is smpossible to predict whether or not a17 amorphous drug will be stable over
30 the shelf life of the drug product This problem means that the commercial
application of the strategy of making drug molecules amorphous is currently
extremely limited.
Similar problems arise in fieids other tt-ran pharmaceuticais, suct-r as in relation
to foods, cosmetics, consumer ci7emicaIs, paints and the like, in which
pedormance enhanceiwei-rts may be gained by iising molecules ii-r an
amorphous form but in which the stability of the amorphous form cannot be
5 predicted.
Sumn~aryo f Invention
The invention provides a rnett-rod: an apparatus and an ar~~orphouns~ ateriaal s
10 def ned irt the appended independent claitms, to which reference should rtow
be made. Preferred or advai-rtageous features ~f the invention are set out in
dependent subelaims.
References to an-rorphous materials in the following description should be
15 taken to ii-rclude partially aiworpi7ous !materials, and material compositions such
as mixtures in whicI7 only one or soiwe of the con1p~nei7tso f the material are
amorphous, as the skilled person would appreciate.
The invention in its various aspects may thus advantageously provide a
20 method and apparatus for the use or measurement of the terahertz dynamics
of an amorphous material to correlate with or predict the stability, or resistance
to crystallisation, or stabilising effect, or rigidity, of the amorphous material.
In a first aspect, the invention may therefore advantageously provide a method
25 for characterising an amorphous material, comprising the steps of: evaluating a
rate of change with temperature of an interaction of the amorphous material
with electromagnetic (EM) radiation, the interaction being at an energy
corresponding to EM radiation of frequency between 10 GHz and 10 THz, in a
range of temperatures below a glass transition temperature, T,, of the
30 amorphous material; and comparing the rate of change with a predetermined
value. In a preferred embodiment, the frequency range may have a lower limit
of 100 GHz and/or an upper limit of 3 THz.
The interaction is at an energy corresponding to an EM frequency in this range
so as to measure dynamics of the amorphous material in this energy, or EM
frequency, range (such as terahertz dynamics). In other words the interaction
for the amorphous material may be at an energy of between (6.6 x J and
5 6.6 x J), or in a preferred embodiment between 6.6 x J and
2.0 x J, these energies corresponding to the frequencies of EM radiation
mentioned above.
Thus, for example, the interaction may comprise, or relate to, a loss of EM
10 radiation in the specified frequency range on passing through the amorphous
material.
Alternatively, the interaction may comprise, or relate to, an intensity of radiation
scattered from the amorphous material, for example deriving from EM radiation
15 or other energy incident on the amorphous material. Such scattered EM
radiation may correspond to, or be derived from, a dynamic or characteristic of
the amorphous material in the desired 10 GHz to 10 THz frequency range.
The scattered EM radiation may thus itself have a frequency between 10 GHz
and 10 THz, or it may derive from an energy shift or frequency shift in the
20 amorphous material corresponding to this frequency range. Thus, for example,
a frequency shift in the range 10 GHz to 10 THz, or in the preferred range
100 GHz to 3 THz, or other preferred range described herein, may be a shift of
frequency between scattered EM radiation and incident (exciting) EM radiation
after interacting with the amorphous material.
25
In a further alternative, the interaction at an energy corresponding to an EM
frequency in the desired range may arise from other interactions such as
fluorescence, as may be measured, for example, by fluorescence
spectroscopy. A suitable technique may be time-resolved fluorescence
30 spectroscopy such as time-resolved fluorescent Stokes shift spectroscopy.
In preferred embodiments, the interaction may therefore be measured by
measurement of EM radiation loss or absorption, or by a frequency-shift
technique using scattering such as Raman, VIS (visible) light or neutron
spectroscopy, or using fluorescence, such as time-resolved fluorescent Stokes
shift spectroscopy.
Other methods may also be used to characterise or evaluate the interaction of
5 the amorphous material in the desired energy range, such as Fourier
Transform l nfra Red spectroscopy (FTI R), l nfra Red spectroscopy (I R), nearinfrared
spectroscopy (near-IR), or Nuclear Magnetic Resonance spectroscopy
(NMR).
10 The rate of change may advantageously be evaluated by measuring EM
radiation within a temperature range. The measurement range may fall both
above and below T,, or may fall below T,, or may fall below 1.2 T,. The rate of
change of the interaction of the amorphous material with EM radiation (such as
the rate of change of EM loss or the rate of change of the intensity of scattered
15 radiation or other suitable measurement, including the methods described
herein) with temperature in a desired temperature range below T, may be
evaluated using measurements made outside the desired temperature range,
such as above T,, or the evaluation of the rate of change of the interaction with
temperature in the desired temperature range may be made more accurate by
20 including measurements made outside the desired temperature range.
In a first embodiment of the invention the desired temperature range for
evaluation of the rate of change of loss of EM radiation may have a lower limit
falling between 0.4, 0.5 or 0.55 T,, and 0.8, 0.7 or 0.66 T,. A particularly
25 preferred lower limit may be about 0.6 T,. In an embodiment of the invention,
measurements may be made at a plurality of temperatures within the range.
A further aspect of the invention may advantageously involve the steps of;
evaluating a first value of the rate of change within a temperature range
30 between T, and a transition temperature below T,; evaluating a second value
of the rate of change within a temperature range below the transition
temperature; and evaluating a difference between the first and second rates of
change. The difference may then be compared with a predetermined
difference value in order to characterise the amorphous material. Preferably,
the lower the value of the difference, the greater the stability of the amorphous
material against crystallisation.
In a preferred embodiment, the second value of the rate of change, below the
5 transition temperature, may be used as the predetermined value, or threshold
value, to which the first value of the rate of change may be compared.
The transition temperature may, for example, be above a lower limit of 0.4, 0.5
or 0.55 T,, and/or below an upper limit of 0.8, 0.7 or 0.65 T,. The transition
10 temperature is preferably about 0.6 T,.
In the aspects of the invention described above, the interaction may
advantageously be measured, or in respect of energies corresponding to, at a
frequency or frequencies above 10 GHz, 100 GHz, 0.5 THz or 0.75 THz,
15 and/or below 10 THz, 3 THz, 2 THz or 1.5 THz. A preferred frequency is about
1 THz.
To provide the most effective or accurate output, the interaction may be
measured at more than one frequency (or corresponding energy) within a
20 range of frequencies (such as within a range of frequencies described herein).
The rate of change of the interaction with temperature may then
advantageously be evaluated for the measured EM frequency providing the
interaction data with the highest signal-to-noise ratio.
25 The inventors' understanding is that the method and apparatus of the invention
is sensitive to motion, or vibration, of molecules in amorphous materials. In
particular, the method may be sensitive to the vibration of hydrogen-bonded
molecules. Thus, in a preferred embodiment the amorphous material
comprises a hydrogen-bonded amorphous material. Thus, for example, the
30 amorphous material may comprise a polymeric material.
In view of this understanding the efficacy of the methods for characterising or
evaluating the interaction of the amorphous material may be better understood.
Techniques such as Terahertz spectroscopy may be used to excite directly two
or more hydrogen-bonded molecules. This is because the energy of vibration
of the hydrogen bond itself may be within the specified energy range of the
interaction of the amorphous material.
5 Alternative techniques may be responsive to the strength, or the energy of the
hydrogen bond without directly measuring that parameter. For example in a
hydrogen-bonded molecule a group such as an -OH or -NH or -H group may
be bonded to a carbon atom in the molecule and may be hydrogen-bonded to
an adjacent molecule. In that case the energy or vibration of the OH or NH or
10 CH bond may be affected by the hydrogen bond and so measurement of the
energy or vibration of the OH or NH or CH bond may allow characterisation or
evaluation of the hydrogen bond. This may be achieved, for example, by using
FTlR to measure stretching or other vibrational modes of the OH or NH or CH
bond.
15
In its various aspects, the invention may advantageously allow a step of using
the characterisation of the amorphous material to assess or predict the
resistance to crystallisation of the amorphous material, for example under
predetermined conditions, or during storage of the material, even over a long
20 time period before the amorphous material (such as a pharmaceutical or other
useful material) is used.
In aspects of the invention, the interaction of the amorphous material with EM
radiation may be expressed in various ways, including in terms of an
25 absorption coefficient of the amorphous material, a dielectric loss value for the
amorphous material, an extinction coefficient for the amorphous material, an
amplitude of transmittance, an amplitude of reflectance, an amplitude of timedomain
peak, or absorbance, an intensity or amplitude of scattered radiation,
or any combination of these.
3 0
The invention may thus advantageously provide a powerful new method to
characterise or predict the stability of amorphous materials, such as drug
molecules in amorphous form, based on their dielectric properties at terahertz
frequencies, for example as measured by terahertz time-domain spectroscopy.
In addition, the invention may advantageously provide a method and apparatus
for enabling the development of methods for stabilisation of amorphous
materials. For example, if an amorphous material shows inadequate stability
5 for a particular purpose, it may be possible to increase or enhance its stability
by various techniques, such as mixing it with another material such as a
polymer. By using a method or apparatus embodying the invention to
characterise the stability of such new formulations, formulations with improved
stability may be developed. Similarly, a method or apparatus embodying the
10 invention may thus be used to characterise the stabilising effect of components
in formulations, such as pharmaceutical formulations, in which an amorphous
component (such as a sugar-glass matrix) is used to stabilise another
component (such as a freeze-dried protein or nucleic acid).
15 A Biopharmaceuticals Classification System (BCS) is used in the
pharmaceutical industry to assess properties of pharmaceuticals. Solubility
plays an essential role in drug delivery: s117ceth e ;tmaximum rate of passive
drug transpart across a bialogical membrane, the main pathway for drug
absorptiort, is the product af permeability and solubility. Aqueous soiubility is a
20 cnicial ntolecular property for successfiil drug development as it is a key factor
governing drug access to b~ologicaml embranes.
The number of poorly wafer-soluble drug candidates has recerttly risen si?arpiy,
particularly with recent progress in contbinatorial cheinistry and high-
25 throughput screening. Development of oral forrn~rlationsfo r such compounds
can put faward significant challenges at all stages of drug developr~~enl.
Irtsufticiertt bioavailability of these co~gpoundsd ue to their low soiubiiity may
result ii7 delays in developinent or cause them to be dropped froin the pipeline.
30 The BCS is used in drug development to split pharmaceutical compounds into
four classes based on their bioavailability:
Class I - high permeability, high solubility. Those compounds are well absorbed
and their absorption rate is ~rs~~ahilglhye r that excretion.
Class 11 - high permeability, low solubility. The bioavailability of those products
is limited by their solvatiai-r rate. A correlation beiween the in \ i i v ~b iaauailability
and the 117 vitrs solvation can be found.
5
Class Ill - low permeability, high solubility. The absorption is limited by the
permeation rate but the drug is sslvated very fast. If the formiilation does nai
change the permeability or gastrs-intestinal dirratlon time then class 1 critena
can be appiied.
10
Class IV - low permeability; low solubility. Those campou17ds !-rave a poor
bioavailability. Usually they are not well absorbed over the 117testinarln ucosa
and a high variability is expected.
15 As can be seen in Fig. 1, 30% of currently-marketed drugs fall into BCS Class
II. The figure is much more dramatic for the drugs in development where
approximately 70% of the drugs suffer from poor solubility.
Several strategies may be utilized in order to improve Active Pharmaceutical
20 Ingredients' (APls) solubility. On a molecular level this includes usage of
prodrugs (a prodrug is a drug administered to the body as a precursor to the
intended drug) or a formation of salts. On the particulate level the particle size
can be mechanically reduced in order increase the surface area and thereby
improve the solubility. Common methods for particle size reduction are spray-
25 drying or milling techniques.
A different way to improve a drug's solubility is to prepare it into an amorphous
solid form (lacking a long-range molecular order, e.g. glass) instead of the
commonly-used crystalline solid form (where molecules are arranged in a
30 periodic cell). The amorphous materials generally have better solubility
properties. On the other hand it is very difficult to formulate an amorphous drug
into a sufficiently stable form as regulatory requirements dictate that a drug
product must not degrade chemically or mechanically over at least 1-2 years
after production. These requirements are also different for different types of
drug.
There are two main difficulties related to the determination of stability of
5 amorphous materials. First is a lack of understanding of amorphous matter. For
a long time scientists have suggested that the crucial parameter is the glasstransition
temperature, T,, i.e. the temperature where a liquid solidifies into an
amorphous form if the necessary criteria are met in order to avoid
crystallization of the liquid (such as imposition of sufficiently high cooling rate
10 etc.). This seems intuitively correct as it is at the glass-transition temperature
that the molecules become spatially arrested and their mobility is significantly
reduced, preventing a crystal seed from diffusing and growing. During the
current, conventional formulation of small-molecule amorphous drugs the focus
is therefore commonly given to shifting T, to high values by adding extra
15 components to the formulation (such as polymers). The aim is to achieve a T,
above room temperature (or more precisely, above the storage temperature of
the drug). This approach is based purely on the temperature difference
between storage temperature and T,. However this empirical method does not
work reliably and very often amorphous drugs crystallize even when stored
20 below T,.
The inventors' recent investigations give a much deeper insight and a new
solution to the problem of characterising or predicting the resistance to
crystallisation of amorphous materials. They have found that even at
25 temperatures below T, a part of the molecular mobility is preserved, which may
allow an onset of crystallization, and they have developed a method and
apparatus for assessing the amount of that molecular mobility.
The inventors have found that this is a property which can be used to predict or
30 characterise amorphous material stability, and the invention may
advantageously provide a method or apparatus for the measurement of this
molecular mobility of amorphous materials, such as amorphous drugs or
pharmaceuticals, below T,.
The inventors have found that information on the molecular mobility of
amorphous materials can be extracted from measurement of interactions with
the amorphous material at terahertz frequencies (10 GHz to 10 THz) or
involving energy shifts or transitions in the material corresponding to energies
5 of terahertz EM radiation (6.6 x J to 6.6 x J), such as the dielectric
losses of a sample of the material at terahertz frequencies (-loq2 Hz), as
described herein. Fig. 2 illustrates (without limiting the generality of the
invention) the inventors' current understanding that the overall measured
absorption of amorphous solids at terahertz frequencies in general originates
10 from factors including (i) the primary (a) dielectric relaxation, (ii) the slow
secondary (P) dielectric relaxation, (iii) fast secondary dielectric relaxation, (iv)
vibrational density of states (VDOS) and (v) ionic conductivity if ions are
present (e.g. in salts). Point (v) is not considered here as the materials in our
current focus do not contain ions.
15
The inventors' realisation leading to the invention is that the process
responsible for sub-T, molecular mobility is the secondary dielectric relaxation.
Therefore by extracting the contribution of the secondary dielectric relaxation to
the terahertz absorption spectrum of a material, it may be possible to
20 determine the level of molecular mobility in the material below T,. The VDOS
peak is clearly observable at very low temperatures (below 0.6 T,) and is
expected to be independent of temperature. The primary dielectric relaxation
changes dramatically with temperature, but contributes to losses at terahertz
frequencies only at temperatures above T,. Therefore any temperature-
25 dependent part of absorption at temperatures below T, is related to the slow
and/or fast secondary dielectric relaxation process. Its contribution commonly
vanishes from terahertz spectra at around 0.6 T,, while no such behaviour is
observed for the fast secondary dielectric relaxation.
30 This has two implications which underpin aspects or preferred features of the
method and apparatus of the present invention:
1) That the linear thermal coefficient B of absorption coefficient a from
equation a" = A + B. T/ T,, where T is temperature, provides a good metric for
characterization of remaining molecular mobility between a transition
temperature of about 0.6 T, and the glass transition temperature 1.0 T,, or a
slightly higher temperature up to about 1.2 T,, and thus the stability of an
amorphous material against crystallization. As alternatives to the absorption
5 coefficient, other parameters such as dielectric losses E", absorbance, kappa or
terahertz electric field may be used; these are all related parameters as the
skilled person would be aware. Corresponding measurements using scattering
techniques such as Raman spectroscopy or measurement using other
techniques such as FTlR may similarly be effective, as described herein.
10
a = Ald, where a is the absorption coefficient, A is absorbance and d is
thickness of a sample; K = acl(4rrv), where c is speed of light and n and K
(kappa) are the real and imaginary parts of the complex refractive index,
respectively; E" = 2 n ~w,h ere E" are the dielectric losses (imaginary part of the
15 complex dielectric function).
2) That for temperatures below the transition temperature of about 0.6 T,
the molecular mobility (and thus the glass, or amorphous-material, instability)
caused by the secondary dielectric relaxation substantially vanishes. It is the
20 inventors' understanding that the slow secondary relaxation is the main source
of molecular mobility responsible for crystallisation below T,.
The invention in its various aspects thus involves the use or measurement of
the terahertz dynamics of an amorphous material to correlate with the stability
25 of the amorphous phase of the material. The measurement of the terahertz
dynamics may allow observation of the molecular mobility at terahertz
frequencies.
In a preferred embodiment of the invention, such measurements may be made
30 using a terahertz time-domain spectroscopy (THz-TDS) method and apparatus
but the method is, in more general terms, not limited to this technology. It may
advantageously include a method and apparatus generally applicable to the
analysis of measurement data from any other technique that is currently
available or will be available in the future to measure the dielectric properties of
materials at these frequencies (energies). For example, synchrotron or freeelectron
lasers may be usable to measure dielectric losses at terahertz
frequencies, as well as interferometric techniques of dielectric spectroscopy.
Scattering techniques such as Raman spectroscopy may also be used.
5
The invention may thus, in particular, provide a game-changing tool for
pharmaceutical and biotechnology companies allowing them systematically to
evaluate and develop BCS Class II drugs into suitable physical forms, such as
oral solid-dosage forms. Based on the measurements from embodiments of
10 the invention, it may be possible to predict which drug molecules or
formulations can be successfully developed into tablets that will maintain
amorphous stability throughout the shelf life of a desired product. This may
advantageously allow the development of a significant proportion of candidate
drug molecules into drug products that would otherwise drop out of the
15 development pipeline due to solubility problems. The technology has a huge
potential economic impact. The size of the total pharmaceutical market is
currently approximately US$850bn with expected growth to over US$1100bn
by 2014. Traditional small-molecular drugs account for 70% (US$GOObn) and
biopharmaceuticals 15% (US$IOObn) of the market. Out of the small-molecular
20 drugs, currently about 30% fall into BCS Class II (US$180bn). The number of
drugs that are rejected during development due to poor solubility is even more
significant: approximately 40% of all lead compounds do not reach the market
due to their poor solubility.
25 The method may advantageously be applicable to all amorphous materials,
such as amorphous drug products, no matter how they are prepared (for
example by melt extrusion, melt quenching, milling, spray drying etc.). The
method of the invention is fundamentally different compared to any existing
technology.
3 0
The method and apparatus of the invention may additionally be applicable to
aid the formulation development of biopharmaceuticals for applications such as
protein formulation stabilisation of freeze-dried proteins or peptides.
However, it is important to note that this method may provide a substantially
universal approach to assess amorphous material stability and the commercial
applications of this technology reach far beyond the pharmaceutical industry
with a range of applications in the food industry (freeze-dried products,
5 amorphous confectionery, etc.), the cosmetic industry, paint industry and
others.
A further aspect of the invention provides an apparatus for characterising
amorphous materials. This aspect of the invention may thus advantageously
10 provide an apparatus for characterising an amorphous material, comprising:
a spectrometer for measuring an interaction between the amorphous material
and electromagnetic (EM) radiation at an energy corresponding to EM radiation
of frequency between 100GHz and 3 THz (6.6 x J to 6.6 x J), at
each of a plurality of temperatures, or over a range of temperatures, less than
15 or equal to a glass transition temperature, T,, of the amorphous material; and a
processor for evaluating a rate of change of the interaction with temperature
and for comparing the rate of change with a predetermined value.
The apparatus may thus advantageously be programmed for, or otherwise
20 capable of, measuring the interaction and evaluating the rate of change within
a temperature range between T, and a lower temperature and, preferably, of
comparing the result with a predetermined value. The apparatus may also, for
example, be capable of measuring the interaction and evaluating a first value
of the rate of change within a temperature range between T, and a transition
25 temperature below T,, measuring the interaction and evaluating a second
value of the rate of change within a temperature range below the transition
temperature, evaluating a difference between the first and second rates of
change, and comparing the difference with a predetermined difference value.
30 In a still further aspect, the invention may advantageously provide an
amorphous material produced using a characterisation method or apparatus
embodying the invention.
Specific Embodiments of the Invention
Specific embodiments of the invention will now be described by way of
example, with reference to the accompanying drawings, in which:
5
Figure 1 shows two pie charts illustrating proportions of pharmaceuticals and
candidate pharmaceuticals of different BCS Classes;
Figure 2 is a schematic diagram illustrating different molecular mechanisms
10 leading to absorption or scattering of electromagnetic (EM) radiation, in a very
broad frequency range. The plot is a generalised case of dielectric losses at
some fixed temperatures;
Figure 3 is a plot of the absorption coefficient for terahertz radiation (alcm-')
15 measured in transmission through amorphous paracetamol and indomethacin,
against normalised temperature (plotted as TIT,);
Figure 4 is a plot of the dielectric losses ~"(vo) f: (a) glycerol; (b) threitol; (c)
xylitol; and (d) sorbitol, at terahertz frequencies in the temperature range 80-
20 310 K with 10 K temperature increments. The filled and empty circles highlight
the losses in the proximity of 0.6Tg and T,, respectively. The sample of threitol
recrystallised above 250 K and only data below this temperature are shown in
this figure;
25 Figure 5 is is a plot for sorbitol of the dielectric losses E" (T IT, ) at four different
terahertz frequencies. The solid lines represent linear fits to the data in regions
(i), (ii) and (iii), as explained in the text below. The dashed vertical lines
highlight the temperatures 0.6Tg and T,, respectively. Tp and T, represent the
crossover points of the linear fits from region (i) to region (ii), and from region
30 (ii) to region (iii), respectively;
Figure 6 is a plot for four polyalcohols of the dielectric losses E" (T IT, ) at a
frequency v = 1 THz. The solid lines represent linear fits to the data in regions
(i), (ii) and (iii), as explained in the text below. The dashed vertical lines
highlight the temperatures 0.6Tg and T,, respectively. Tp and T, represent the
crossover points of the linear fits from region (i) to region (ii), and from region
(ii) to region (iii), respectively. The dielectric-loss data for sorbitol and glycerol
are offset vertically in the positive and negative directions by 0.1, respectively,
5 for clarity;
Figure 7 is a plot showing the absorption of naproxen:indomethacin in two
molar mixtures, 1 :2 (squares) and 1:l circles, at 1 THz plotted against the
rescaled temperature TIT,;
10
Figure 8 is a plot of the rescaled absorption coefficient a/ao.6Tofg t he
naproxen:indomethacin molar mixtures of Figure 7 against the rescaled
temperature TIT,; the black lines in the plot show linear fits of the data
a/ao.6T=g C + DT/Tgi n a given thermal region;
15
Figure 9 shows plots of terahertz absorption coefficient of amorphous
trehaloselglycerol mixtures; 9(a) shows temperature dependence of the
mixtures reduced absorption spectra a/ao.6Togn reduced temperature T/T,,;
9(b) shows the coefficient Bg obtained from linear fit a/ao.6T=g A + BT/Tgi n
20 thermal region (ii) 0.67-1.0 Tg as a function of glycerol concentration;
Figure 10 illustrates an apparatus embodying the invention, for measuring
absorption of EM radiation;
25 Figure 11 illustrates a second apparatus embodying the invention, for
measuring intensity of scattered EM radiation;
Figure 12 shows plots of infrared absorption spectra for sorbitol obtained in the
temperature range 113-31 3 K; and
3 0
Figure 13 shows plots derived from the data of Figure 12, plotting Voigt
function fitting parameters for (a) peak central frequency, (b) peak width, (c)
peak height and (d) peak area, as a function of reduced (normalised)
temperature TIT,.
To exemplify the efficacy of the invention, the inventors characterised two
5 representative glass-forming drugs: acetaminophen (paracetamol) and
indomethacin. These amorphous materials differ greatly in their stability. The
glass (amorphous phase) of paracetamol has poor stability, while the glass of
indomethacin has very good stability, as is known from direct measurements of
the crystallisation of these materials during storage.
10
Figure 3 plots the results of the characterisation of these materials. Figure 3
plots the absorption coefficient for terahertz radiation (alcm-') measured in
transmission through the material at 1 THz, against temperature (plotted as
TIT,) for each material. As set out in the Summary of the Invention, the rate of
15 change of the loss of EM radiation with temperature (the gradient of the graph
in Figure 3) may then be assessed, or measured, and as appropriate
compared with a predetermined value in order to achieve a quantitative, or
relative, characterisation of the stability of the amorphous material as
described below.
20
In Figure 3, the plotted results for indomethacin show two distinct linear
regions, firstly a small and constant rate of change, or gradient, for the
absorption of the radiation below T,, and secondly a marked change to a
higher rate of change, or gradient, above T,. By contrast the plotted results for
25 paracetamol show three different linear regions, namely a low rate of change
below a transition temperature of about 0.6 T,, a higher rate of change
between 0.6 T, and T,, and a still higher rate of change above T,.
In other words, Figure 3 shows that the thermal change in absorption of
30 terahertz radiation between 0.6 Tg - 1.0 Tg is well developed in paracetamol
but very low in indomethacin.
The implication of this is that below T,, the structure of the amorphous phase of
indomethacin shows little or no freedom for any molecular movement, whereas
the greater absorption of terahertz radiation by amorphous paracetamol
between 0.6 T, and T, indicates a much greater freedom for molecular
movement below T,. This correlates with, and predicts, the resistance to
crystallisation of these amorphous materials at temperatures below T,.
5 Amorphous paracetamol crystallises rather readily below T,, whereas
amorphous indomethacin is much more stable if stored below T,.
These results can be quantified by comparing the rates of change, or
gradients, of the linear sections of the measured data in Figure 3 with
10 appropriate predetermined values such as threshold values. For example, if a
developer of an amorphous pharmaceutical product wishes to characterise the
stability of amorphous paracetamol and indomethacin as being above or below
a predetermined or desired threshold level of stability, then the gradients of the
linear sections of the plots in Figure 3 may be compared with threshold
15 gradient levels (determined in accordance with the level of stability required),
and the stability of paracetamol, indomethacin and any other desired
pharmaceuticals compared with the desired threshold value(s). This may
either be assessed in terms of whether or not a particular amorphous material
falls above or below a predetermined threshold, or more quantitatively in terms
20 of how far above or below the threshold the material falls. The gradients of the
data in each of the regions in Figure 3 may be assessed with reference to
predetermined values, but to predict the stability of amorphous materials below
T,, it is believed that the gradient in the region 0.6 T, to T, is the most critical.
25 In addition to the consideration of the gradients, the changes of gradient for the
data for each material may be assessed and compared with predetermined
values. For example, the negligible change in gradient at the transition
temperature (0.6 T,) for indomethacin indicates that very little molecular
mobility develops as the temperature rises towards T,, whereas the much
30 greater change in gradient for paracetamol at the transition temperature
indicates that significant molecular mobility develops as the temperature rises
towards T,. The changes in gradient may be measured and compared with a
predetermined, or desired, threshold value of the change in gradient
corresponding to a desired level of stability of the amorphous material. A
quantitative assessment may be made with reference to how far above or
below the threshold the measured value falls.
In further embodiments or examples of the invention, a series of polyhydric
5 alcohols were studied. These examples show, using terahertz time-domain
spectroscopy (THz-TDS), dielectric losses in the frequency range 0.2 - 3 THz
and the temperature range 80 - 310 K (straddling the glass-transition
temperature), for a series of inter-molecular hydrogen-bonded polyalcohols,
Cn(OH)nHn+2g:l ycerol (n = 3), threitol (n = 4), xylitol (n = 5) and sorbitol (n = 6).
10
These glass-forming liquids show (as known from earlier investigations) a
systematic change in the fragility index, m = B log qlB (Tg/T)T=Tig.e, . in the
degree of the non-Arrhenius temperature dependence of the viscosity, q, m =
57 (glycerol), 79 (threitol), 94 (xylitol), 128 (sorbitol), indicative of a decreasing
15 extent of a hydrogen-bonded network. Moreover, these materials show
significant differences in their dielectric spectra. They can be ordered in terms
of the observation of Johari-Goldstein P (JG-P) relaxation, from a wing-type
scenario to a fully resolved JG-P relaxation peak, in the series glycerol,
threitol, xylitol and sorbitol. Both well below and above T,, only limited
20 experimental dielectric-loss spectra are available at near-terahertz
frequencies in the literature for these and other glass-formers obtained by
conventional methods. The inventors' THz-TDS data, using embodiments of
the invention, show a universal response amongst the studied polyalcohol
samples for the microscopic peak at terahertz frequencies, and the first
25 observation of the JG-P relaxation vanishing from terahertz spectra
universally at the temperature 0.6Tg.
In these examples, systematic THz-TDS study allows direct access to the
complex dielectric function for the frequency range of 0.1 - 3 THz, over a wide
30 range of temperatures. For these experiments, the samples were melted
(except glycerol, which is liquid at room temperature), loaded into a
continuous-flow cryostat and cooled at a rate of approximately 25 ~.min-to' 80
K, followed by subsequent heating by 10 K increments to 310 K. Spectra were
acquired using a THz-TDS setup operating in transmission geometry. All four
polyalcohols were purchased from Sigma-Aldrich with >99% purity. The
samples were used without further purification.
Figure 4 shows the measured dielectric losses ~"(vo) f: (a) glycerol; (b) threitol;
5 (c) xylitol; and (d) sorbitol, at terahertz frequencies in the temperature range
80-31 0 K measured at 10 K temperature increments. The filled and empty
circles highlight the losses in the proximity of 0.6Tg and T,, respectively. The
sample of threitol recrystallised above 250 K and only data below this
temperature are shown in this figure.
10
Figure 5 shows the dielectric losses E" (T IT, ) at four different frequencies for
sorbitol. The solid lines represent linear fits to the data in regions (i) below a
transition temperature of about 0.6 T,, (ii) between the transition temperature
and T,, and (iii), above T,. The dashed vertical lines highlight the temperatures
15 0.6Tg and T, , respectively. Tp and T, represent the crossover points (changes
in gradient) of the linear fits from region (i) to region (ii), and from region (ii) to
region (iii), respectively. As described for paracetamol above, the data for
sorbitol shows three distinct rates of change, or gradients, in regions (i), (ii) and
(iii). The relatively high gradient in region (ii) and the distinct changes in
20 gradient at the crossovers between the regions indicate relatively poor stability
in amorphous sorbitol. The inventors found that the highest signal-to-noise
ratio was provided by the data at 1 THz.
Figure 6 shows the dielectric losses E" (T IT, ) at a frequency v = 1 THz for all
25 four of the polyalcohols. The solid lines represent linear fits to the data in
regions (i), (ii) and (iii), as explained above. The dashed vertical lines highlight
the temperatures 0.6Tg and T, , respectively. Tp and T, represent the crossover
points of the linear fits from region (i) to region (ii), and from region (ii) to region
(iii), respectively. The dielectric-loss data for sorbitol and glycerol are offset
30 vertically in the positive and negative directions by 0.1, respectively, for clarity.
Three common features were observed in the dielectric losses, E", of the series
of polyhydric alcohols: at temperatures well below the glass transition, ~"(v)
comprises a temperature-independent microscopic peak, which persists also
into the liquid phase, and which the inventors identify as being due to
librational/torsionaI modes. For 0.6 T, < T < T, , additional thermally-dependent
contributions are observed and the inventors found strong evidence for its
relation to the Johari-Goldstein secondary p-relaxation process. Clear
5 spectroscopic evidence is found for a secondary P glass transition at 0.6T,. At
temperatures above T,, the losses become dominated by primary a-relaxation
processes.
The temperature dependence of ~"(va) t v = 1 THz is shown in Fig. 6 for all four
10 polyalcohol materials. Here, we use the rescaled temperature T/T, on the
abscissa to compare the common features of the glassy state between the
different polyalcohols. Three absorption regimes can be resolved in all
samples: (i) temperature-independent losses; ii) a weak temperature
dependence of losses below T, ; and iii) a strong temperature dependence of
15 losses above T,, as proposed previously. More detailed information was
extracted by fitting the data points with an empirical linear fit, viz. cl'(T/T,) = A
+ B T 4 , in each of the respective temperature regions. In Table I, we
summarize the crossover temperatures Tp and T, between regions (i)-(ii) and
(ii)-(iii), respectively, together with the respective gradients B1,2,o3b tained
20 separately for each region, (i), (ii) and (iii). For all samples, Ta corresponds to
T,, the temperature above which the temperature-dependent part of ~"(v)
becomes dominated by the primary dielectric relaxation.
Table 1
Glass-transition temperature, T,, together with parameters for the empirical
linear temperature-dependent behavior used to analyse the dielectric losses,
5 E" (T /Tg ) = A + BT4 ,as s hown in Fig. 6. n stands for the number of OH
groups per molecule. Tp and T, represent the crossover points of the linear
fits from region (i) to region (ii), and from region (ii) to region (iii), respectively.
B 1,2,3 are the linear coefficients obtained from fits in regions (i), (ii) and (iii),
respectively. The numbers in the brackets state the standard deviation at the
10 last decimal place.
Sample n T, [K] T, [K] Tp [K] Tp/Tg B I B2 B3
-sorbitol -6 268.3 265 150 0.56 0.02(2) 0.34(2) 1.92(5)
xylitol 5 247.8 248 167 0.68 0.06(1) 0.13(3) 0.82(4)
threitol 4 226.3 228 147 0.65 0.07(1) 0.09(1) 0.43(15)
glycerol 3 191.7 189 - - 0.03(1) 0.64(1)
The plotted data in Figure 6 reveal two striking features. First, they show that
15 the weak temperature dependence of losses (region (ii) in Fig. 6 for threitol,
xylitol and sorbitol emerges at a temperature of around 0.6Tg in all cases.
Considering that the thermal changes of E" originate from the secondary
relaxation, and most likely from the JG-P relaxation, this means that the
secondary relaxation decouples completely from the microscopic peak at
20 around 0.6Tg. This observation is in excellent qualitative agreement with
calorimetric studies of glass-forming liquids, where the P-glass-transition
temperature has been linked to spontaneous temperature drift rates in the
region of 0.5-0.7 T,. A correlation has been proposed between the fragility
index m and a "correlation index" c, defined as (1 - c) = Tg ,pT,/ From the
25 examples of the invention, it is apparent, however, that such a correlation does
not hold since these polyalcohols cover a range of different fragilities yet, in all
cases, the onset of secondary relaxation is observed in the range of 0.5-0.7 T,.
A striking observation in the THz data is that the temperature gradient, B2, of
30 the dielectric losses in region (ii) varies significantly between the samples
(see Table I). Based on the value of B2, the polyalcohols can be arranged in
the series, glycerol, threitol, xylitol to sorbitol, i.e. in increasing order of
fragility, in analogy with how well the JG-P relaxation peak is resolved from
the primary relaxation in the dielectric spectrum at lower frequencies, from an
excess wing in glycerol to the strong JG-P peak in sorbitol. A previous study
revealed that the number of -OH groups in polyhydric alcohols plays an
essential role in the slow dynamics of these materials. This hints that the H-
5 bonding character of molecules in these glasses plays a similar role in both
primary and secondary relaxation. One of the implications is that the
observations presented here may be characteristic of hydrogen-bonded
systems.
10 To characterise these amorphous materials, values of the gradients, and of
gradient B2 in region (ii) in particular, may be compared with predetermined
values corresponding to desired levels of amorphous material stability. For
example, if it has been determined, for example by experiment, that a
threshold value of B2 of 0.1 is acceptable for amorphous materials for a desired
15 application, then according to the data in Table 1, threitol and glycerol exhibit
stability above the threshold (i.e. a lower value of gradient B2). Alternatively, or
in addition, the changes in gradient between regions (i) and (ii), i.e. B2-B1, may
be compared with predetermined values corresponding to desired levels of
amorphous material stability. In other words, the value B1 may effectively be
20 used as the predetermined threshold value to which the value B2 (for the same
material) may be compared. In general, the lower the value of B2-B1, or the
closer the value of B2-B1 is to zero, the more stable the amorphous phase of
the material.
25 Predetermined threshold values may also, or in addition, be determined by
experiment, for example by measuring corresponding values for amorphous
materials known (for example from tests of stability against crystallisation at
predetermined usage or storage temperatures, or from accelerated tests at
elevated temperatures) to have acceptable and unacceptable stability for a
30 desired application of the materials.
The quantitative difference between a measured value and a predetermined
value may additionally indicate quantitatively the stability of an amorphous
material above or below a threshold level.
In conclusion, using terahertz time-domain spectroscopy, the inventors have
studied dielectric losses in the supercooled hydrogen-bonded polyalcohols,
glycerol, threitol, xylitol and sorbitol, at terahertz frequencies, at temperatures
5 both above and below T,. The results reveal several universal features
amongst the samples. At the lowest temperatures, the losses comprise the
microscopic peak due to librational/torsionaI modes. As the glasses are heated
above a transition temperature of about 0.6Tg, the dielectric losses increase
steadily with temperature. There is strong evidence that this feature originates
10 from the high-frequency tail of the JG-P relaxation. It is best observed in the
case of sorbitol, while it remains unobservable in the case of glycerol.
Temperatures in the proximity of 0.6Tg appear to be the universal region for the
secondary glass transition in several systems, but with no correlation to the
fragility, as has been proposed previously. When the glasses are heated above
15 T,, the dielectric losses become dominated by the high-frequency tail of the arelaxation
that shifts to higher frequencies. This observation offers a
microscopic interpretation of T, as being the temperature where the primary
dielectric relaxation decouples from the libration-vibration band. The
temperature variation of the losses, both above and below T,, that originate
20 from relaxation processes increases with the number of -OH groups per
molecule. This finding highlights the possibility that the character of intermolecular
bonding plays an important role in both primary and secondary
relaxations.
25 A further embodiment, illustrated with reference to Figs 7 and 8, considers
calibration for estimation of drug stability against crystallisation. Here the
inventors show an example of calibration of stability of amorphous drug system
based on the terahertz absorption coefficient. The drug system is naproxen /
indomethacin mixture with molar fractions NAP:IND = 1:2 and 1:l. The
30 NAP:IND 1:2 mixture started to recrystallise within 21 days when stored at
room temperature (298 K), while the NAP:IND 1:l mixture remained
amorphous for 35 days.
There is an absolute difference in the absorption coefficient, a, and glass
transition temperature, Tg, between the two molar fractions originating from
their different composition (Fig 7). In order to compare the two samples the
inventors therefore calculated a relative absorption coefficient, a/ao.6T, g
5 measuring the absorption level a(T) against the absorption at T=0.6Tg, a 0 . 6 ~ ~
(i.e. at the onset of the sub-Tg mobility responsible for the crystallisation, Fig.
8). The rescaled absorption coefficient shows a linear change with rescaled
temperature T/T,and can be fitted by a linear function a/ao.6T=g C + DT/Tg.
Here the parameter D describes the increase in the absorption, which
10 reflects on the level of sub-T, molecular mobility. The parameter Dl describes
the absorption below 0.6Tg, which may also originate from secondary
relaxations that are however not thought of being responsible for the
crystallisation of amorphous drugs. The parameter D2 describes the absorption
above 0.6Tg that is thought to originate from the same processes as Dl with
15 extra contribution of the secondary relaxations related to the sample
crystallisation. The change of the relative absorption above and below T=0.6Tg,
i.e. D2 - Dl, correlates to the stability of the amorphous phase: the lower
the value of D2 - Dl, the longer the drug is expected to stay amorphous.
For this particular case of the NAP:IND system outlined above the
20 sample with D2 - Dl < 0.1 8 showed greater stability than the system
with a D2 - Dl > 0.94. A calibration for multiple mixtures or formulations
can be made using this method (Table 2).
TABLE 2: Calibration of the sub-Tg terahertz losses in naproxen 1
indomethacin mixture system with molar fractions NAP:IND = 1 :2 and
1 : 1. The relative level of the subTg losses is expressed in coefficient D2
- D,, obtained from fit a/ao,GT=g C + DT/Tg in the thermal regions
5 between 0.2 - 0.6Tg (index 1) and 0.6-1.0 Tg (index 2).
Sample Tg [Kl ao.6~~ Dl D2 D2 - Dl Stability
[cm-' ] at 298 K
NAPIND12 305.16 18.0 0.25(3) 1 .I9( 3) 0.94(4) < 21
days
NAP IND 11 298.45 18.5 0.08(3) 0.26(5) 0.1 8(6) < 35
days
A further embodiment of the invention illustrates its use in the optimization of
glassy matrix formulation for protein stabilisation.
10
Sugars may be usable for protecting dried biological structures, such as lipid
membranes or proteins, even under complete desiccation, creating a
suspended state of biological activity in the dry state that can be recovered
almost miraculously upon hydration. This embodiment shows an example of
15 optimization of glassy matrix formulation for protein stabilisation, using a
mixture of trehalose and glycerol. Trehalose and glycerol glasses have been
studied by incoherent neutron scattering and it was found that glycerol might
make the trehalose glass more rigid on the inter-molecular level, despite its
plasticising effect. In particular, these experiments have suggested that a 2.5%
20 glycerol / 97.5% trehalose mass ratio is the most rigid.
In the embodiment, trehalose di-hydrate and glycerol were sourced from
Sigma-Aldrich, UK, and used as received. Three samples were studied: pure
trehalose, 2.5% glycerol / 97.5 % trehalose and 5% glycerol / 95% trehalose
25 (weight fraction). The glass transition temperatures of different samples are
summarized in Table 3.
TABLE 3: Glass transition temperature for trehalose 1 glycerol mixtures
Glycerol weight 0 % 2.5 % 5 % 100 %
concentration
Trehalose di-hydrate crystalline powder was first mixed with glycerol and then
melted (T, = 480 K). Particular care was given to take into account mass
change of trehalose after losing water and becoming anhydrous during
heating. The liquid melts were loaded in a cryostat sample cell, cooled to room
10 temperature, attached to a cryostat and then cooled down to 80 K before the
start of the measurement. The samples were then heated with 20 K step
increments between 80 - 480 K. At each temperature step, reference and
sample spectra were acquired.
The experimental results show that there is an absolute difference in the
15 absorption coefficient, a, and glass transition temperature, Tg, between the
different molar fractions originating from their different composition. In order to
compare the samples the inventors therefore calculated a relative absorption
coefficient, a/ao.6Tg,m easuring the absorption level a(T) against the
absorption at a 0 . 6 ~= ~a( 0.6Tg) (i.e. at the onset of the sub-T, mobility
20 responsible for the crystallisation). The dependence of a/ao.6Togn reduced
temperature T/T, is shown in Fig. 9(a).
The data in Fig. 9(a) are split into three thermal regions: (i) below 0.67 T,, (ii)
0.67-1.0 T, and (iii) above 1.0 T,. Each region can be fitted by a linear function
25 a/ao.6T=g A + BT/Tg. Here the parameter B describes the increase in the
absorption, which reflects on the level of molecular mobility. In particular,
coefficient B2 from the linear fit in the region (ii) can be associated with
secondary relaxations that are strongly correlated to the stability (rigidity) of the
glass at temperatures below T,. The parameter B2 obtained for different
30 mixtures is shown in Fig. 9(b) as a function of glycerol concentration.
From Fig. 9(b) it is clear that B2 is lowest at 2.5% glycerol concentration. This
means that the trehalose/glycerol glass has lowest inter-molecular mobility at
this concentration. In other words, the glass is most rigid in this case, which is
well in line with previous observations by neutron scattering mentioned above.
5
A further embodiment, with reference to Figures 12 and 13, illustrates the use
of FTlR to characterise or evaluate the interaction of the amorphous material in
a desired energy range.
10 Figure 12 plots FTlR spectra for sorbitol, in a temperature range between
113 K and 313 K, at a range of infrared (IR) frequencies between about 72 THz
and 100 THz (wavenumbers 2400 cm-I to 3600 cm-I). The vertical axis of the
plot represents infrared absorbance, in arbitrary units. In this IR frequency
range, it is understood that IR absorbance occurs due to stretching of C-H
15 bonds and 0-H bonds in the sorbitol. As described above, however, where the
-H and -OH species are hydrogen bonded to other molecules in the sorbitol,
the stretching of the C-H bonds and, in particular, of the 0-H bonds will be
affected. This may affect the fundamental vibrational modes of the bonds
and/or overtones thereof. Measurement of the IR absorbance using FTIR
20 therefore allows characterisation of the hydrogen bonds involved in
intermolecular bonding, which have an energy falling within the terahertz
energy range (e.g. 6.6 x J to 6.6 x J) involved in embodiments of the
present invention, even though the energy of the IR radiation itself falls outside
this range.
25
In general, as illustrated by this embodiment, the inventors expect 0-H bonds
to be more strongly affected by inter-molecular hydrogen bonding than N-H or
C-H bonds, and so the measurement of 0-H bonds by techniques such as
FTlR may provide the best characterisation of the hydrogen bonds. But
30 measurement of N-H and C-H and other bonds may also be effective.
Figure 13 shows four plots derived (by curve fitting, or function fitting) from the
measured data in Figure 12 for the absorbance peak corresponding to the 0-H
bonds in the sorbitol.
In Figure 13(a), the frequency (wavenumber) of the FTlR absorbance peak
measured at each temperature is plotted against reduced temperature, TIT,.
In Figure 13(b), the widths of the FTlR absorbance peaks are plotted against
5 reduced temperature. In Figure 13(c), the heights of the FTIR absorbance
peaks are plotted against reduced temperature. And in Figure 13(d), the areas
beneath the FTlR absorbance peaks are plotted against reduced temperature.
It is striking that the data in all four of the plots in Figure 13 show three linear
10 portions, of different gradients, corresponding to the temperature ranges below
0.67 T,, between 0.67 T, and T,, and above T,, with kinks or corners in the
plots at 0.67 T, and T,. This is the same as was seen in the terahertz radiation
adsorption data for sorbitol shown in Figures 5 and 6 and discussed above and
demonstrates that the FTlR technique is responsive to the same interaction of
15 the amorphous material (the sorbitol) as the terahertz adsorption technique.
The FTlR technique therefore provides an alternative way to characterize or
evaluate the desired interaction of the amorphous material, in the terahertz
energy range, embodying the invention.
20 In the same way as described above for the terahertz spectroscopy method,
FTlR data may therefore be used to evaluate the stability of amorphous
materials, and data derived from FTlR may be compared with predetermined
threshold values of gradient, or used to compare the relative stability of one
material compared to another.
25
Figure 10 illustrates an apparatus embodying the present invention. The
apparatus comprises a transmission terahertz spectrometer. It starts with a
laser system 2 comprising a continuous wave pump laser and a Ti:Sapphire
oscillator producing femtosecond pulses at central wavelength 800 nm. A
30 beam splitter splits the laser beam into terahertz-generating and terahertzsensing
parts 4, 6.
The terahertz-generating part comprises a photoconductive emitter 8. The
emitter is made from a semiconductor substrate (GaAs) and has two
electrodes of bow-tie structure separated by a narrow gap of a few hundred
microns. The laser beam generates conducting charge carriers (electrons and
holes) in the semiconductor that are accelerated by a voltage applied to the
electrodes of the emitter, resulting in a photocurrent. The decay of the
5 photocurrent produces terahertz radiation that is collected and focused by
parabolic mirrors 10, 12 onto a sample plane.
A sample of amorphous material 14 sits in the sample plane in a compartment
that allows transmission of terahertz radiation. This is commonly a sandwich
10 structure of two terahertz-transparent windows, transparent at terahertz
frequencies, separated by a spacer with a central aperture. The aperture is
filled with the sample and the sandwich structure is attached to a cold finger of
a cryostat that allows the sample to be controllably cooledlheated. Terahertz
radiation penetrates the sandwich structure and is collected and focused by
15 further parabolic mirrors 16, 18 onto a ZnTe crystal 20.
The sensing part 6 of the femtosecond beam is led from the beam splitter
through an optical delay stage 22 to the ZnTe crystal 20. The terahertz field
creates the Pockel's effect in the ZnTe crystal that changes the polarisation of
20 the sampling femtosecond beam. The change in the polarization of the optical
beam is analyzed by a quarter-wave plate 24, an analyser (Wollaston prism)
26 and two balanced photodiodes 28. The quarter-wave plate is used to
balance the signal on the photodiodes when no THz field is present in the
ZnTe. The analyser is used spatially to separate two orthogonal polarizations
25 of the femtosecond beam, which are detected by the balanced photodiodes.
The difference signal from the photodiodes is then collected and processed
electronically by a processor 30. The terahertz part of the setup sits in a box 32
that can be operated under vacuum or dry nitrogen atmosphere to eliminate
absorption of terahertz radiation by water vapour.
3 0
In this apparatus, a photoconductive antenna is used for terahertz radiation
emission and an optoelectronics approach is used for detection. Other
apparatus embodying the invention may differ in the terahertz generation (e.g.
different antenna type, usage of quantum cascade lasers, photomixing, or any
other suitable system), terahertz detection (e.g. using photoconductive
antenna, Gap crystal, bolometer or any other suitable system) as well as in the
way the terahertz beam is transmitted through the sample (e.g. using elliptical
mirrors instead of parabolic, using a different sample compartment, or
5 changing the geometry from transmission to reflection mode, where reflected
terahertz beam is collected).
The processor 30 is advantageously suitably programmed to control the
apparatus to generate the results required in embodiments of the invention, for
10 example to measure the absorption of radiation by the sample at a range of
temperatures, to evaluate the rate of change of absorption with temperature
and/or any discontinuity in the rate of change of absorption with temperature at
a transition temperature, so that these measured parameters can be compared
with predetermined values, or thresholds.
15
Figure 11 illustrates a further apparatus embodying the present invention.
This apparatus is for measuring interactions between an amorphous material
and EM radiation in the form of EM radiation scattered from a sample of the
amorphous material.
20
A sample of an amorphous material 56 is held in a cryostat to control its
temperature. A laser 51 generates a beam of EM radiation which is guided
and focused by mirrors 52, filters 53, a filterlbeam splitter 54 and focussing
optics 55 onto the sample. The frequency of the EM radiation is such as to
25 cause scattered radiation due to an energy change or transition in the
amorphous material corresponding to the energy of a frequency of EM
radiation between 10 GHz and 10 THz. Neither the laser radiation nor the
scattered radiation needs to be of a frequency in the range 10GHz to 10 THz
(though either or both of them may have such a frequency), as long as
30 measurement of the intensity of the scattered radiation provides a measure of
a transition in the amorphous material having an energy corresponding to a
desired frequency in the range 10GHz to 10 THz, or other preferred range
described herein.
The scattered radiation from the sample is focussed by the focussing optics 55
and passes back through the beam splitter 54, notch filters 57 and further
focussing optics 58 before entering a spectrometer 59, where the intensity of
the scattered radiation is measured.
5
Possible Molecular Mechanisms
The following text discusses potential mechanisms giving rise to the
experimental results observed in the Examples of the invention. These
10 possible mechanisms do not limit the scope of the claimed invention but
illustrate the experimental data by showing the inventors' current thinking
behind the invention.
In all four polyalcohol samples, the dielectric losses of the materials in the
15 glassy state at the lowest temperatures are almost independent of
temperature and comprise a microscopic peak at a frequency around 2-3 THz,
as seen in Fig. 4. The peak is still evident for T>T,, but the amplitude now
increases with increasing temperature. The inventors assert that the
microscopic peak observed in the THz-TDS data in Fig. 4 is a manifestation of
20 a peak in the vibrational density of states (VDOS) due to low-lying, opticallyactive
librational/torsionaI modes.
Calculations of the internal vibrational modes in the isolated glycerol molecule
show that the lowest (torsional) mode occurs at 2.01 THz. Moreover, lattice-
25 dynamics calculations of phonons in crystalline glycerol, used to generate the
orientationally averaged (powder) 'glass-like' dynamical structure factor in the
incoherent approximation, indicate a peak at -1.5 THz. The lowest-frequency
optical modes in crystalline glycerol are observed from RS to occur at 1.65
THz. These findings support our assertion that the microscopic peak in Fig. 4
30 is due to low-frequency librational/torsionaI modes in these materials.
The temperature-dependent contributions to the dielectric losses below T, are
most pronounced in the case of sorbitol. In order to elucidate what leads to
these additional losses, we subtracted the contribution of the microscopic peak
from the dielectric-loss spectra, as E"(v)-E"~~~(a~s( vsh) own in Fig. 5). It is
immediately clear that, above T, (shown as circles in Fig. 5), the dielectric
losses resemble the tail of a broad peak with a maximum at frequencies below
1 THz, which links the origin of this loss to the primary dielectric-relaxation
5 process commonly observed by dielectric spectroscopy. At T,, the primary
dielectric relaxation corresponds to relaxation times of around 100 seconds, or
characteristic frequencies of HZ, far too low to contribute to ~"(v)in the
terahertz regime. Upon heating above T,, the primary relaxation rapidly shifts
to higher frequencies, resulting in the observed increase in dielectric losses.
10 This gives the glass transition a new physical meaning. Very often, T, is
addressed on a macroscopic level as the temperature corresponding to a
given arbitrary value of the viscosity (e.g. loq2P a s) in the middle of the
thermal region where the viscosity increases by many orders of magnitude, or
as the temperature in the middle of a step in the enthalpy, as observed by
15 DSC. From the results presented here, it is possible to address T, on a
microscopic level as the temperature where the primary dielectric relaxation
decouples from the temperature-independent microscopic peak and no longer
contributes to the losses at THz frequencies.
20 In the case of sorbitol, the changes in dielectric losses below T, are observed
only down to 170 K. At lower temperatures, the losses are substantially
constant. The change in losses with temperature below T, are roughly one
order-of-magnitude weaker compared to the contribution of the a-relaxation to
the dielectric losses above T, . This suggests that the source of the losses
25 below T, no longer originates from the a-relaxation process. The contribution
of the losses below T, is not uniform across the spectrum but slightly higher
losses are detected at lower frequencies, which we attribute to the highfrequency
tail of a process, such as the secondary relaxation, shifting to lower
frequencies with decreasing temperature. Indeed, a change in E" of the order
30 of 1 0-2 with a 10 K increment was observed at GHz frequencies in dielectric
spectra of sorbitol below T, , and can be assigned to the JG-P relaxation.
A different possible molecular mechanism lies is the so-called fast-secondary
relaxation. This type of relaxation is often explained as a rattling of a molecule
in a cage of neighbouring molecules. The process is usually observed in GHz -
THz frequency range, or ns-ps time scale, and there is a growing evidence that
this fast movements play a role in the supercooled liquids above Tg. The fastsecondary
relaxation process has been also shown to be important in the
5 stabilisation of proteins in glassy matrices.

Claims
1. A method for characterising an amorphous material, comprising the
steps of:
5 evaluating a rate of change of an interaction of the amorphous material
with electromagnetic (EM) radiation with temperature, at an energy
corresponding to EM radiation of frequency between 10GHz and 10 THz, in a
temperature range below a glass transition temperature, T,; and
comparing the rate of change with a predetermined value.
10
2. A method according to claim 1, in which the energy of the interaction is
between 6.6 x J and 6.6 x J.
3. A method according to claim 1 or 2, in which the rate of change is
15 evaluated within a temperature range between T, and a lower temperature.
4. A method according to claim 3, in which the lower temperature is
between 0.4 and 0.8 T,, preferably between 0.5 and 0.7 T,, or between 0.55
and 0.65 T,, and is particularly preferably 0.6 T,.
20
5. A method according to any preceding claim, comprising the steps of;
evaluating a first value of the rate of change in a temperature range
between T, and a transition temperature below T,;
evaluating a second value of the rate of change in a temperature range
25 below the transition temperature; and
using the second value of the rate of change as the predetermined
value for comparison with the first rate of change.
6. A method according to claim 5, in which the transition temperature is
30 between 0.4 and 0.8 T,, preferably between 0.5 and 0.7 T, or between 0.55
and 0.65 T,, and is particularly preferably 0.6 T,.
7. A method according to any preceding claim, in which the interaction is
evaluated for an EM frequency or frequencies between 100 GHz and 3 THz,
between 0.5 THz and 2 THz, preferably between 0.75 THz and 1.5 THz, and
particularly preferably at 1 THz.
8. A method according to any preceding claim, in which the interaction is
5 measured at a plurality of frequencies within a range of frequencies, and the
rate of change of the interaction with temperature is evaluated at the EM
frequency within that range of frequencies which provides the interaction data
with the highest signal-to-noise ratio.
10 9. A method according to any of claims 1 to 7, in which the interaction is
measured and the rate of change of the interaction is evaluated using EM
radiation at a frequency or frequencies between 100 GHz and 3 THz, between
0.5 THz and 2 THz, preferably between 0.75 THz and 1.5 THz, and particularly
preferably at 1 THz.
15
10. A method according to any preceding claim, in which the evaluation of
the rate of change of the interaction of the amorphous material with EM
radiation comprises the evaluation of the rate of change of loss of EM radiation
of frequency between 10 GHz and 10 THz on passing through the amorphous
20 material.
11. A method according to claim 10, in which the loss of EM radiation is
expressed in terms of an absorption coefficient of the amorphous material, a
dielectric loss value for the amorphous material, an extinction coefficient for the
25 amorphous material, an amplitude of transmittance, an amplitude of
reflectance, an amplitude of time-domain peak, or absorbance, or any
combination of these.
12. A method according to any of claims 1 to 9, in which the evaluation of
30 the rate of change of the interaction of the amorphous material with EM
radiation comprises the evaluation of the rate of change of an intensity of
scattered EM radiation at a frequency or frequency shift of between 10 GHz
and 10 THz.
13. A method according to claim 12, in which the scattered radiation
derives from EM radiation interacting with the amorphous material.
14. A method according to claim 12 or 13, in which the scattered radiation
5 derives from Raman, VIS light or neutron spectroscopy or scattering.
15. A method according to any of claims 1 to 9, in which the evaluation of
the rate of change of the interaction of the amorphous material with EM
radiation comprises the evaluation of the rate of change of an intensity of
10 frequency-shifted EM radiation at a frequency or a frequency shift of between
10 GHz and 10 THz.
16. A method according to claim 15, in which the frequency-shifted
radiation is due to fluorescence, for example as measured using a time-
15 resolved fluorescence spectroscopy technique, such as time-resolved
fluorescent Stokes shift spectroscopy.
17. A method according to any of claims 1 to 9, in which the evaluation of
the rate of change of the interaction of the amorphous material comprises FTlR
20 spectroscopy, I R spectroscopy, near-I R spectroscopy or NMR spectroscopy.
18. A method according to any preceding claim, in which the amorphous
material comprises a hydrogen-bonded amorphous material.
25 19. A method according to any preceding claim, in which the amorphous
material comprises a pharmaceutically-active material or a candidate
pharmaceutical material.
20. A method according to any preceding claim, in which the amorphous
30 material comprises a polymeric material.
21. A method according to any preceding claim, comprising the step of
using the characterisation of the amorphous material to assess or predict the
resistance to crystallisation of the amorphous material.
22. A method according to any preceding claim, comprising the step of
using the characterisation of the amorphous material to assess or predict the
resistance to crystallisation of the amorphous material under predetermined
5 conditions.
23. A method according to any preceding claim, comprising the step of
using the characterisation of the amorphous material to assess or predict a
stabilising effect of the amorphous material.
10
24. An apparatus for characterising an amorphous material, comprising:
a spectrometer for measuring an interaction of the amorphous material
with electromagnetic (EM) radiation at an energy corresponding to EM
radiation of frequency between 10 GHz and 10 THz; and
15 a processor for evaluating a rate of change of the interaction with
temperature, in a temperature range below a glass transition temperature, T,,
of the amorphous material, and for comparing the rate of change with a
predetermined value.
20 25. An apparatus according to claim 24, in which the energy of the
interaction is between 6.6 x J and 6.6 x J.
26. An apparatus according to claim 24 or 25, evaluating the rate of change
within a temperature range between T, and a lower temperature.
25
27. An apparatus according to claim 26, in which the lower temperature is
between 0.4 and 0.8 T,, between 0.5 and 0.7 T,, preferably between 0.55 and
0.65 T,, and particularly preferably 0.6 T,.
30 28. An apparatus according to any of claims 24 to 27, for measuring the
interaction and evaluating a first value of the rate of change in a temperature
range between T, and a transition temperature below T,, measuring the
interaction and evaluating a second value of the rate of change in a
temperature range below the transition temperature, and using the second rate
of change as the predetermined value for comparison with the first rate of
change.
29. An apparatus according to claim 28, in which the transition temperature
5 is between 0.4 and 0.8 T,, between 0.5 and 0.7 T,, preferably between 0.55
and 0.65 T,, and particularly preferably 0.6 T,.
30. An apparatus according to any of claims 24 to 29, in which the
interaction is measured for a frequency or frequencies between 100 GHz and 3
10 THz, between 0.5 THz and 2 THz, preferably between 0.75 THz and 1.5 THz,
and particularly preferably at 1 THz.
31. An apparatus according to any of claims 24 to 30, in which the
interaction is measured within a range of frequencies of EM radiation, and the
15 rate of change of the interaction with temperature is evaluated at the EM
frequency within that range of frequencies providing the interaction data with
the highest signal-to-noise ratio.
32. An apparatus according to any of claims 24 to 31, in which the
20 interaction is measured and the rate of change is evaluated using EM radiation
of between 100 GHz and 3 THz, between 0.5 THz and 2 THz, preferably
between 0.75 THz and 1.5 THz, and particularly preferably at 1 THz.
33. An apparatus according to any of claims 24 to 32, in which the
25 measurement of the interaction of the amorphous material with EM radiation
comprises a measurement of a loss of EM radiation of frequency between
10 GHz and 10 THz on passing through the amorphous material.
34. An apparatus according to any of claims 24 to 33, in which the
30 measurement of the interaction of the amorphous material with EM radiation
comprises a measurement of an intensity of scattered EM radiation at a
frequency or frequency shift of between 10 GHz and 10 THz.
35. An apparatus according to claim 34, in which the scattered radiation
derives from EM radiation interacting with the amorphous material.
36. An apparatus according to any of claims 24 to 30, in which the
5 measurement of the interaction of the amorphous material with EM radiation
comprises a measurement of an intensity of frequency-shifted EM radiation at
a frequency or a frequency shift of between 10 GHz and 10 THz.
37. An apparatus according to any of claims 24 to 30, in which the
10 evaluation of the rate of change of the interaction of the amorphous material
comprises FTI R spectroscopy, I R spectroscopy, near-I R spectroscopy or NMR
spectroscopy.
38. An apparatus according to any of claims 24 to 37, in which the
15 amorphous material comprises a hydrogen-bonded amorphous material.
39. An apparatus according to any of claims 24 to 38, in which the
amorphous material comprises a pharmaceutically-active material or a
candidate pharmaceutical material.
20
40. An apparatus according to any of claims 24 to 39, in which the
amorphous material comprises a polymeric material.
41. A method for characterising an amorphous material, comprising the
25 steps of:
evaluating first and second values of a rate of change with temperature
of an interaction of the amorphous material with electromagnetic (EM)
radiation, at an energy corresponding to EM radiation of frequency between
10 GHz and 10 THz, in respective first and second temperature ranges, the
30 first temperature range being between a glass-transition temperature, T,, of the
amorphous material and a transition temperature below T,, and the second
temperature range being below the transition temperature; and
evaluating a difference between the first and second rate of change
values. 42. A method according to claim 41, in which the transition temperature is
between 0.4 and 0.8 Tg, preferably between 0.5 and 0.7 Tg, or between 0.55
and 0.65 Tg, and is particularly preferably about 0.6 Tg.
43. An apparatus for characterising an amorphous material, comprising;
a spectrometer for measuring an interaction of the amorphous material
with electromagnetic (EM) radiation, at an energy corresponding to EM
radiation of frequency between 10 GHz and 10 THz; and
a processor for evaluating first and second values of a rate of change of
the interaction with temperature, in respective first and second temperature
ranges, the first temperature range being between a glass-transition
temperature, Tg, of the amorphous material and a transition temperature below
Tg, and the second temperature range being below the transition temperature;
and
evaluating a difference between the first and second rate of change
values.
44. An apparatus according to claim 43, in which the transition temperature
is between 0.4 and 0.8 Tg, preferably between 0.5 and 0.7 Tg, or between 0.55
and 0.65 Tg, and is particularly preferably about 0.6 Tg.
45. An amorphous material produced using the characterisation method of
any of claims 1 to 23 or 41 to 42.
46. A method for characterising an amorphous material substantially as
described herein.
47. An apparatus for characterising an amorphous material substantially as
described herein.
48. An amorphous material substantially as described herein, or
characterised substantially as described herein.