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Dynamic mechanical thermal analysis is the most widely and accessibly rheological test in laboratory and industry. According to the different specialties (e.g. engineering, chemistry, polymer physics), different market and purpose of analysis, this technique may be referred into a range of terms such as dynamic mechanical analysis (DMA), thermal mechanical analysis (TMA) and even dynamic mechanical rheological testing (Rheometer). By the time 1961, Ferry wrote the first book of Viscoelastic Properties of Polymers (Ferry, 1980) which gave the best development of the theory in polymer area. This term viscoelastic has been combined by two parts 'viscous' and 'elastic' properties in almost every material (Barnes et al., 1996), which are consisted of the complexity of ideal liquid and solid parts. The elastic extreme of the material may be defined as Hooke's behaviour while the liquid-like flow property may be defined by Newtonian model (Jones, 1999). Therefore, most materials existed in real world exhibit viscoelastic materials with a phase difference between these two extremes (0-90Â°) when a force is applied (Fig. 1). This is the stress strain diagram vs time as most of us often are used to see, which has been transferred from DMTA test
0Â° < Î´ < 90Â°
Figure . The viscoelasticity of material response (strain) following application of an oscillatory stress. Note: the phase angle between applied stress and resultant strain is Î´ (0Â° (ideal solid) < Î´ < 90Â° (ideal liquid))
at varying temperatures. By measuring the responded amplitude at the peak of sine wave and lag phase between the stress and strain, the information of material's stiffness (modulus) may be obtained from DMTA. In another simplification, this technique may be described as the analysis of material's response corresponding to the applied oscillations, which has be within the linearity viscoelastic region (LVR). Despite the varying strain versus time during the test, the interpretation of results would be relatively simple within the material's LVR (Jones, 1999; Craig et al., 1995).
The complex (stiffness) modulus E* may be defined as follow:
where E' is storage modulus, E'' is loss modulus and the relationship between E' and E'' may be defined in terms of phase angle and complex modulus as eq.(2) - (4):
A very good visually explanation of storage and loss modulus has shown in Fig.2. When the ball is dropped, the elastic response may be presented as how high this ball
Figure . Visualised storage modulus and loss modulus (Menard, 1999)
bounced while the height difference between bounced and dropped from may be attributed to the energy loss in the internal motions and frictions. Thereby, this sinusoidal wave oscillation in DMTA helps us to break down the force/energy distribution from one single modulus into two terms, one related to storage (real) modulus and another related to the loss (imaginary) modulus. This will help us to understand how a material responses upon temperature and/or frequency fluctuation. It is also very important to look at the tangent delta, which is the ratio of loss energy to storage energy (Eq. 4). This geometry independent ratio can help us to understand how efficiently the material loss energy due to the rearrangements and internal friction under stress.
DMTA provides an ability to explore the molecular structure characterisation via even a simple thermal scanning test, which gives a powerful consideration into the material behaviour. It is arguable that DMTA can provide enough detailed information just next to solid state NMR, dielectric analysis and electron spin resonance (Duncan, 2008). A wide applications of DMTA is in generation of modulus and damping factor (tan Î´) over a wide range of temperature (-150-500 Â°C), whilst, the frequency is less domain due to the limited range available in a single mechanical equipment (0.1-200Hz, TA Q800). Therefore, the use of this technique is preferred in the temperature change rather than frequency (Craig, 1995). Since it is mechanic equipment, the self-support sample geometry is necessary for detecting the quantitative modulus (stiffness) of the sample. For example the linearity viscoelastic region (LVR), which is the basic requirement of using DMTA, will highly depend on the geometry of the testing sample. Considering deforming a 1mm thick aluminium foil between your fingers, it is much easier than bending a 10*1mm stuck aluminium foil. This is exactly how DMTA performed in any sample. However, as most pharmaceutical sample of therapeutic interests are powder, a novel powder sample holder was developed recently to extend the limitation of using DMTA in pharmaceutical area (Royall et al., 2005; Mahlin et al., 2008). It is based on the cantilever geometry from DMTA with either a folding steel or rectangular pocket (with base and lid) as shown in Fig.3. The powdered sample was evenly split inside the holder, and the holder is packed into the cantilever clamp and tied by the clamp at certain pressure. The sample is tested by a vertical motion of the clamp in the middle or one edge of this holder. Since the damping factor (tanÎ´) is geometry independent, the structural information may be obtained by this accessory from DMTA is the relaxation temperature at tanÎ´ and the temperature related data interpretation. It is noted that the storage and loss modulus collected from powder pocket accessory is not suitable for quantitative analysis due to the natural random orientations of powder. Table 1 gives a general indication of the choice of sample geometry and dimensions as approximately to the modulus range being measured (TA Q800).
Table 1 Typical geometry sample and dimensions (suits force range 0.01-18N)
1-5 (mesh cover required )
Single/Dual cantilever (powder pocket)
Plate/ other irregular shape
0.5-10 height or thickness
* Sample length is the free length between two clamps; wide sample may not be uniform for a film and/or held uniformly under clamp, thereby, a narrow sample is recommended in film tension test.
Figure . The novel powder sample holder, left side is stainless steel dual cantilever pocket, consisted with a base and a lid, developed by TA Instruments; right side is the aluminium folding holder developed by Triton Technology.
It is very important to identify the most suitable geometry and understand that a small change in geometry may lead to a huge difference. The better choice of sample geometry may refer to a better generation of data from DMTA; nevertheless, small adjustments on the operating parameters are also essential for individual materials. It is always a good assessment to use Multi-Strain Mode (Strain Scan) to identify the suitable strain (amplitude) range that is within the material's linearity viscoelastic region (LVR) prior to a series measurements (as shown in Fig.4). For example: applying large amplitude in a thick and stiff sample may result in an excess amount of driving forces applied by the machine; large and thick sample usually takes longer time to equilibrate than a small and thin film, thereby, a slow heating rate or stepwise method may be required for better accuracy; film tension is the most sensitive testing geometry in DMTA, however it highly depends on the sample's quality (e.g. smooth edge, similar shape), loading position and amplitude (Menard, 1999). Extensive details about the operation parameters corresponding to geometries have been discussed in several books (Menard, 1999; Price, 2002; Duncan, 2008)
Figure Schematic of Multi-Strain Mode to identify the linearity viscoelastic region
Application of different DMTA Test Mode in Solid State of Pharmaceutical and Biomedical interested
Dynamic mechanical thermal analysis is not only a versatile and sensitive technique that offers a great number of advantages over other technique (Ferry 1980; Matsuoka 1992). It is also a sophisticated investigation approach to complement other techniques and generate a full imagine of the molecular structures and behaviours of sample (Chan et al., 2005; Wu et al., 2008). The author will be focus on some commonly used DMTA testing mode in the characterisation of solid state micro/macromolecular systems such as film packaging, coating, tableting process, scaffolds in tissue engineering, medical device and amorphous-crystalline sample in order to possibly provide a good understanding of using DMTA as a convenient yet critical analytical technique in pharmaceutical interested area.
Creep-Recovery & Stress-Relaxation Mode
Generally speaking, creep-recovery and stress-relaxation are inverse tests to each other. Creep-recovery involves a finite stress force applied into sample and records the response over time, then also monitors the recovery once the force is removed. In contrast, in stress-relaxation test, the sample will be held at a constant deformation (strain), the force required to maintain this strain will be monitored over time. Two simplest understanding of these behaviours may be described as Voigt-Kelvin alone and/or Maxwell and Voigt combined in series as shown in Fig5. The Maxwell model with the spring and dashpot in series has been used to show the sharp strain step of material's response under stress; while the Voigt-Kelvin model describes a time-dependent response as the dashpot slows down the spring due to the parallel connection between them (Akolins et al., 1983). A better four parameters expression Burger's model has been discussed by Nielsen and Landel later on (Nielsen et al., 1994). In this model the total strain Îµ can be described as:
Figure Simplified mathematic models for stress-relaxation and creep-recovery testing methods, E and Î· are the elastic and viscous component of respectively. Maxwell Model
where E1 and Î·1 are the elastic and viscous part of Maxwell model, E2 and Î·2 are the elastic and viscous components of Voigt-Kelvin model. Ïƒ is the applied force and t is the creep time. This testing model has been successfully employed in the characterisation of crosslinking-degree of gelatine film and plasticizer composition in coating polymer (Ceulemas et al., 1999; Lafferty et al., 2002; Martucci et al., 2006). Martucci et al. demonstrated that the creep analyzed by single Burger's model provided a great agreement between the degree of crosslinking, relaxation time and viscosity in Glutaraldehyde-gelatin crosslinked films. A significantly decrease of the creep response (strain at each corresponding time) was found in higher crosslinked film in comparison with low/non crosslinking film. This phenomenon may be explained perfectly by the Burger's model as shown in Fig.5. The increased crosslinking degree consequently increases the rigidity and elastic response from the film. Then the Voigt-Kelvin part was dominated by large viscous Î·2 results in a small and restricted response from elastic E2, thereby, the whole system exhibits mainly as an elastic response contributed from E1. The difference between elastic domain and viscous domain may be visually exhibited in terms of creep behaviour as shown in Fig.6, a high degree of crosslinking in the system leads to a big increase in the stiffness, and a long creep time may be observed as shown the 'c' curve in Fig.6. In contrast, the sample with low/non crosslink ('a, b' curve) may require shorter creep time until the dynamic equilibrium status was achieved due to the higher flowability in the system yet not pure liquid. Nevertheless, the solid system with high crosslinking may also consume more energy due to the elastic internal motions, which result in a lower % strain upon the same applied forces in comparison with a soft system.
Figure The schematic of creep behaviours of solid system with elastic dominated sample (c, stiff) and viscous dominated sample (a, soft) and somewhere between (b), upon the same stress, creep time t3 > t2 > t1
It is also noted that such experiment may be expanded into a time-temperature superposition model (TTS). This TTS model may be used to construct a 'master curve' which has been used for the prediction of shift-factor, viscosity in solid, material's life-time behaviours and coupling theories in the complexity, (Ngai, 2000a; Kasapis et al, 2003, 2008; Jiang et al., 2011). The author will be focused on this TTS model in section 3.3 later on.
Stress-relaxation was also a widely used testing mode from tableting industry, film coating to scaffolds evaluation in tissue engineering (Shlanta et al., 1964; Krycer et al., 1982; Casahoursat et al., 1988; Bashaiwoldu et al., 2004; Cespi et al., 2007; Hafeman et al., 2008). Just like creep-recovery testing, stress-relaxation can be used to probe the internal deformation of the compressed material and qualify the energy required for elastic and viscous deformation and hence to interpret the consolidation of different pharmaceutical compacts (Casahoursat et al., 1988). Ebba et al. successfully demonstrated that stress-relaxation can be used to identify the precise influences of different lubricants (Mg stearate, Preairol and Talc) and particle size (from 100-600 Âµm) in tablet capping during process (Ebba et al., 2001). Multi-Maxwell (spring and dashpot in series as shown in Fig.5) in parallel with isolated spring was generated by Ward et al. in order to describe the behaviour of a viscoelastic solid at a considerable simply yet precisely level (Ward et al., 1993). Moreover, the stress relaxation testing may also be used to evaluate the mechanical properties of biodegradable polyurethane scaffolds (PUR) at defined temperature (e.g. 37Â°C). A slow stress-relaxed PUR may maintain a good contact between the bone and implant, thereby, promotes the migration of local osteoprogenitor cells from the bone into the implant and enhance the bone regeneration (Hafeman et al., 2008).
Controlled Strain Temperature Scan
This test mode in DMTA is the easiest and most widely used technique in any area, which has be used alone for i) quantitative and qualitative modulus analysis (i.e. storage and loss modulus); ii) detecting primary and subtle relaxation (Î±, Î², Î³); iii) damping property (tanÎ´) to characterise the ratio of loss to storage modulus; iv) interaction and solubility/miscibility between polymeric components or between drug and polymer; v) complement with other thermal analysis technique. Generally speaking, th oscillation is performed on the sample at a controlled strain (within LVR) of interest temperature range scanning at 1-5 Â°C/min with defined frequency. In many cases, the great sensitivity for the detection of glass transition (Î± relaxation) has been reported. The measured data from this test mode show a dramatic change in tanÎ´ or loss modulus E'' when temperature approach to glass transition. Amorphous polymers such as polyvinyl chloride (PVC) or polystyrene (PS) exhibit a major glass transition due to the motions of carbon-carbon backbone, while secondary transitions (Î² or Î³) may also occur due to the side chain re-organisation or rotation. For a semi-crystalline polymer or sample with crystalline and amorphous components, DMTA may also be used to possess the amorphous content with a theoretical limit of detection of 2.8% (w/w) in the powder pocket accessory (Saha, et al., 2006). A typical semi-crystalline polymer sample polyethylene glycol (PEG) in powder pocket upon temperature scan is shown in Fig.7. The glass transition (-50Â°C) from PEG amorphous region is time dependent which shifts as a function of frequency, while the melting event (60Â°C) of crystalline region of PEG does not shifts due to the melting is only relating to the chemical potential of PEG.
- - - - Frequency 0.3 Hz
. . . . Frequency 1.0 Hz
Figure The DMTA temperature scan data of semi-crystalline sample PEG, frequencies 0.3 and 1 Hz were swept in order to differentiate the glass transition of amorphous region and melting event of the crystalline region
Yang et al. also demonstrated that the DMTA may be used as means of solubility of crystalline drug acetaminophen in PEO, with great sensitivity in determination of glass transition, the Tg increases as a function of drug loading from 1% to 10% in the solid dispersion of acetaminophen/PEO may be recorded and the dissolution of acetaminophen in PEO was plotted as temperature vs. drug loading (Yang et al., 2011). The construction of drug solubility in defined polymer system is believed to be one of the critical considerations in forming stable amorphous drug within polymeric solid dispersion system (Qian et al., 2009; Caron et al., 2011).
There are several awarenesses of using this testing mode as has been mentioned previous (Craig et al., 1995):
Sample preparation related such as the choice of testing method, shape and quality of sample and parameter setting.
Data interpretations, e.g. multi-thermo events and subtle transitions are overlaid, the distinctive of main chain relaxation (Î±) and the melting of lattice in a semi-solid system.
Great attentions may be worth to pay in order to achieve the reproducibility and sensitivity of DMTA, for example, the sample related errors may be overcame if a pre-test was carried out such as determination of LVR, track force or a smooth cutting of sample (for film) and also the novel powder pocket, which may be used as means of providing a great accuracy in the molecular relaxation temperature. Abkabori et al. successfully demonstrated that DMTA is capable of detecting the glass transition of an ultrathin polystyrene film as thin as 37nm by a single temperature scan (Abkabori et al., 2005). A varies accessories provided in DMTA also offers a wide range of applications. For example, Fadda et al. compared the glass transition temperatures of a group of acrylic polymers (Eudragit L and S) within the DMTA immersion apparatus (Fadda et al., 2010). The immersion tank was filled with 0.1M HCl buffer simulated to the pH of stomach fluid. The Tgs of Eudragit L and S film samples exhibit a drastically drop after immersing into this buffer indicated that the effects of water in plasticising acrylic polymer may result in an unexpected change within the gastrointestinal tract. Nevertheless, the new developed accessory powder pocket in DMTA also provides a great option to solve this sample caused limitations and especially useful for pharmaceutical powdered samples. A considerable amount of approaches were carried out with this sample holder (Royall et al., 2005; Mahlin et al., 2008; Wu et al., 2008; Gearing et al., 2010).
For the data interpretation, there is none one equipment can provide a straightforward result of any sample. One of the best ways to possibly solve the distinctive of glass transition and melting event would be to apply a small range of frequency during the temperature scan (as shown in Fig.7). This relaxation process involved in the molecular rearrangements in viscoelastic materials occur at defined temperature and time (frequencies). The frequency dependent event will be found in the primary or secondary relaxations (Î±, Î², Î³), whilst, the melting event generally only happens with chemical potential (time independent). Moreover, with some complements of other techniques such as differential scanning calorimetry (DSC), x-ray diffractometer (XRD), thermogravimetric analysis (TGA), atomic force microscopy (AFM) and hot-stage polarized microscopy, DMTA stands a strong position to produce the reliable results to help the understandings. Wu et al. developed that the hermetic aluminium DSC pan can be tested directly underneath the probe in the DMTA with sealed sample inside similar as powder pocket. With the advantages of wide range of temperature and great sensitivity provided in DMTA, the sample can be fast cooled to -60Â°C by liquid nitrogen, and then the molecular structural rearrangements upon the regular temperature scan may be recorded. This data was used to help the interpretation of DSC and AFM results on frozen aqueous trehalose solutions (Wu et al., 2008). Similar complementary experiments were also carried out; Gearing et al. used DMTA with powder pocket to determine the glass transition in the frozen state by applying multi-frequency temperature scan to differentiate the glass transition of excipient and the melting of water (Gearing et al., 2010). Studying the effect of mechanical stress supplemented with thermal stress was achieved in DMTA to identify the devitrification of amorphous xelecoxib (Gupta et al., 2005); the selection of different modifiers (Mw of PVP) for ethylcellulose composite film (Chan et al., 2005). These wide range application areas of this simple test from DMTA demonstrate the great utility of using this technique to capture the micro/macroscopic level structural rearrangements and/or relaxations of solid sample and provide a fully understanding of every sample.
Time-temperature superposition is 'the method of reduced variable' (Ferry, 1980) has been used for a very long time since 1955, Williams et al. correlated the reference temperature to the temperature obtained from creep analysis (Williams et al., 1955); later the WLF equation was derived by Doolittle et al. on the free volume theory of polymer above glass transition temperature (Doolittle et al., 1959); Adam and Gibbs also introduced the kinetic factor of molecular motions into the amorphous polymeric system and further developed by Matsuoka with a complete molecular relaxation model (Adam et al., 1965; Matsuka 1992). The most commonly used WLF equation for the shift factors is shown as:
where aT is the shift factors, C1 and C2 are material constants, Î· and Î·r are viscosity and reference viscosity respectively, T is temperature in degrees Kelvin and Tr is reference temperature in degrees Kelvin. For a time-temperature superposition data, the reference temperature is normally a 'rate-independent' glass transition temperature normally taken from slow ramp DSC result (Gao et al., 1996). If we plot the logat against 1/T, then the activation energy for glass transition may be calculation from the slope of the 'Angell plot' (Angell, 1991). Nevertheless, from the Angell plot, it may be useful to describe whether the glass transition of system is single mechanism or several mechanisms. It is noted that the Arrhenius and WLF may be only applicable for sample temperature below and above Tg respectively. Recently, the 'coupling theory' has been promoted in order to clarify the intermolecular interactions which have been suggested for better fundamentally understanding of the molecular dynamic factors in randomly packed amorphous samples (Ngai, 2000b). The coupling model provides a bridge between chemical monomers and macromolecular glassy behaviours with the coupling constant, n (0 < n < 1), which can be used to describe the weak or strong interaction system. A new interpretation of Kohlrausch, Williams and Watts (KWW) equation with the extent of neighbouring segments related relaxation time and stretched exponential function in terms of the TTS stress relaxation modulus was deviated from WLF equation as shown below (Ngai, 2000b):
where Ï„ are the relaxation time, Gg and Ge are the unrelaxed glassy modulus and relaxed modulus and t is the time after the application of fixed strain. The coupling constant, n (0 < n < 1), indicates the relaxation of original material and the physicochemical environment of surrounding materials. It is plausibly to see the demonstration of using WLF and KWW equations to calculate the free volume and coupling constant of polysaccharide/co-solute system (Jiang et al., 2011). It was also mentioned that the coupling constant of strongly interlinked chains of synthetic materials range appear between 0.66 and 0.77 (Ngai et al., 1995). However, based on the thermorheological simplicity, it is arguably to use short time stress relaxation method for a viscoelastic system. Caron et al. examined the relaxation time of amorphous phenobarbital and amorphous phenobarbital solid dispersion containing 5%PVP (Caron et al., 2010). The calculated coupling constants for amorphous phenobarbital alone was 0.67 which is within the strongly interlinked region (0.66-0.77), while for 5%PVP/phenobarbital solid dispersion system was 0.32 (poor interlinking). The experimental results indicated that the interactions within pure amorphous phenobarbital are much stronger than PVP/phenobarbital solid dispersion system. Interestedly, the crystallisation onset time for amorphous solid dispersion PVP/phenobarbital (>200days at 25Â°C, dry condition) is much longer than pure amorphous phenobarbital system (approximate 36days at 25Â°C, dry condition). Despite the different phenomenon in different cases, TTS constructed master curve exhibited a great approach in understanding the fundamental theory of molecular rearrangement, interaction, steric influences and phase separation in a pharmaceutical interested system.