Glass transitions in native silk fibres studied by Dynamic Mechanical Thermal Analysis

Silks are a family of semi-crystalline structural materials, spun naturally by insects, spiders and even crustaceans. Compared to the characteristic β -sheet crystalline structure in silks, the non-crystalline structure and its composition deserves more attention as it is equally critical to the filaments’ high toughness and strength. Here we further unravel the structure-property relationship in silks using Dynamic Mechanical Thermal Analysis (DMTA). This technique allows us to examine the most important structural relaxation event of the disordered structure in native silk fibres, the glass transition (GT) in the lepidopteran insects Bombyx mori and Antheraea pernyi and the spider Nephila edulis . The measured glass transition temperature T g , loss tangent Tan δ and dynamic storage modulus are quantitatively modelled based on Group Interaction Modelling (GIM). The “variability” issue in native silks can be conveniently explained by the different degrees of structural disorder as revealed by DMTA. The new insights will facilitate a more comprehensive understanding of the structure-property relations for a wide range of biopolymers.


Introduction
The Glass Transition (GT) is the reversible process occuring in a material when its amorphous components convert between hard (glassy) and soft (rubbery) states. This paper primarily focuses on the structural changes during this process, hence we use the term GT instead of the commonly known T g , which specifically refers to changes in temperature. GT is among the most important structural relaxation events of materials, even though aspects of its physical basis are still under discussion and conventional thermodynamics does not consider the glassy state of polymers an equilibrium state. 1-3 Yet it is important to understand GT for any successful application of such amorphous materials simply because during this transition the engineering modulus experiences a dramatic drop by two orders of magnitude (from GPa to MPa) while viscosity decreases by up to 10 12 Pa. For any vitreous (glassy) polymer, GT causes the characteristic relaxation time of the backbone segments to become short enough for increased molecular mobility (minutes/seconds) to be captured under ordinary experimental conditions.
Porter, using the framework of Group Interaction Modelling (GIM), fundamentally assigned this increased molecular mobility, along with the change in stiffness, to the activation of polymer backbone freedoms. 4 Volumetric, entropic and enthalpic property changes occur during GT, which allows its detection using techniques such as dilatometry and Differential Scanning Calorimetry (DSC). Additionally, Dynamic Mechanical Thermal Analysis (DMTA) is a standard technique used by industry (and less so in academia) to measure the change in viscoelasticity of polymeric materials during structural relaxation events. [5][6][7] Since DMTA principally measures the stiffness (energy storage) and molecular mobility (energy dissipation), it provides arguably the most sensitive technique for GT measurements. However, to date extensive DMTA studies are still rare in the examination of biopolymer structural transitions at levels of sufficient detail to truly elucidate underlying structureproperty relations. Principally this is due to practical difficulties such as the handling and control of biological samples. Nevertheless, the term GT has long been introduced to the field of biomaterials, and importantly protein-water GT has been experimentally and theoretically demonstrated for various types of globular proteins. [8][9][10] Silks are biopolymers that bridge biology and physics and have for centuries provided great utility for both commerce and science communities. 11 Nature's silks are spun by a wide range of invertebrate animals and consist mostly of fibrous proteins. 12 Silks have independently evolved numerous times to perform a wide range of functions from providing a lifeline for spiders to protecting pupae during metamorphosis for silkmoth caterpillars.
commercial textile Bombyx mori (B. mori) mulberry silk and high performance spider dragline spider silk (often of Nephila spp), however recently other 'wild' silks such as the silkmoth Antheraea pernyi have offered key comparative insights concerning variation in both mechanical and structural properties. Silk structural variability is a result of numerous intrinsic and extrinsic factors such as genetic differences, as well as variable processing conditions (e.g. diet, spinning speed) and environmental effects (e.g. temperature and humidity) during production and storage. [15][16][17][18] Importantly the micro-and nanoscale structural variability in silk is reflected in highly sensitive macroscopic properties such as tensile mechanical properties and super-contraction capacities of spider dragline silks. 19,20 Furthermore, associated spectroscopic evidence 21,22 suggests that water content and changing microstructure contributes to the variability in mechanical properties of silk. Many silks possess a semi-crystalline, hierarchical structure and morphology. A simplified perception of a silk consists of sub-micron sized fibrils and nano-structural domains within the fibril. 23 At the nano-scale, β-sheets, the characteristic crystalline structure of many silks, are believed to contribute directly to stiffness and strength [24][25][26] whereas the noncrystalline/amorphous phase contributes significantly to fibre extensibility and toughness. [27][28][29][30][31][32] The distribution of these structures has been identified to some extent, i.e. native B. mori silk possesses 49-57% βsheets [33][34][35] and native Nephila spider dragline silk possesses 36-46% 33,36 . Details of the composition of the non-crystalline structure is still under debate due to silks' high degree of structural heterogeneity shown by techniques such as Nuclear Magnetic Resonance (NMR) 37,38 where silks demonstrate highly oriented molecular structures but lack well-defined βsheet or α-helix structures (long-range order). Therefore the concept of the non-periodic lattice structure, proposed by Guinier and others [39][40][41] , could be an alternative solution for the complex conformational structures of silks, let alone an orientation effect in the conformation complexity 42 . Clearly it is important to acknowledge different conformational forms in silks as they differentiate energetically on the nano-scale. In response to the issues surrounding the categorisation of the semi-crystalline morphology in silk, Vollrath and Porter [43][44][45] proposed the case for a distinction between Ordered and Disordered regions (as opposed to crystalline/non-crystalline fractions). This approach has the benefit that complex structural morphology can be reduced to a few fundamental structural parameters that reflect quantitative relationships and allow useful predictions via an established methodology developed from traditional polymer physics.
The Order-Disorder approach seeks to explain the molecular scale structural origins of macroscopic properties in silks and enables prediction of changes in properties induced by environmental conditions. GT in silk has been studied previously [46][47][48] and the effect of different environmental conditions on GT has also been evaluated 49 . To date DMTA has been applied to reconstituted silk fibroin (RSF) and its derived products to examine the GT behaviours, thermo-mechanical property and T g . 50 For native spider silks, the GT phenomenon has been shown to occur in a thermo-hydro cycle, and humidity-induced GT directly contributes to the property changes in spider silks. 49 Finally a recent study has shown that the GT temperature (T g ) is 200 o C for N. edulis spider silks and 220 o C for B. mori silkworm silks. 51 However, despite many specific studies, the generic GT behaviour, its structural origin, and the induced property changes in silk are yet to see a comprehensive analysis. Importantly, the high degree of order and the high density of hydrogen-bonding in silks (which sets them apart from conventional polymers) makes the quantitative analysis of GT behaviours technically and theoretically challenging and calls for new approaches in order to understand the non-crystalline structures in silks.
In this paper we provide experimental evidence of GT patterns in native silks using DMTA on single fibres. This data leads the development of a structural model based on the Vollrath/Porter Order-Disorder proposition and Group Interaction Modelling (GIM).
The main results will be presented in two sections: firstly the major GT behaviour of three native silks (B. mori, A. pernyi and N. edulis) and secondly the effect of intra-and inter-individual variability, commercial silk quality and processing conditions on the GT behaviour of silk.

The major glass transition in silk
We use a temperature-ramp DMTA experiment to dynamically deform the fibre samples as a function of temperature at a frequency of 1 Hz. The recorded raw signals of stress and strain wave forms allow the calculation of the storage modulus E' (energy storage) and Tanδ (energy dissipation). At GT the storage modulus experiences a steeper decrease as Tanδ increases and forms a Gaussian-shape peak. The transition temperature T g , defined by the peak temperature of Tanδ, the mathematical integrated peak area of Tanδ (cumulative peak Tanδ) and the storage modulus are the three quantities for our quantitative analysis and the subsequent modelling of the structure-property relations of native silk fibres. Figure 1 shows the profiles of both storage modulus and Tanδ during GT for two synthetic polymers and three types of silks in a DMTA temperature-ramp experiment. The data in Figure 1 (a) demonstrate that the amorphous polystyrene film displays a large Gaussian-shape Tanδ peak (peak value = 3.6) in a narrow temperature range (from 90 o C to 120 o C). This stands in contrast to a nylon 6,6 fibre shown in the enlarged inserted graph whose Tanδ peak shows a low peak value of 0.10 and a very broad temperature range (from 60 o C to 150 o C). This much broader span and lower peak in Tanδ may imply that the amorphous structure in semi-crystalline nylons has more diffused and less intense molecular motions during GT. In Figure 1 (b), (c) and (d), the three silks show GT behaviours similar to that of nylon 6,6 in terms of Tanδ magnitude and temperature range. Comparing the three silks, Please do not adjust margins Please do not adjust margins A. pernyi silk has a much greater Tanδ peak than silk of B. mori, which indicates a larger fraction of molecular motions in this wild silkworm silk. N. edulis spider dragline silk shows the Tanδ peak at a lower temperature (194 o C) than both silkworm silks. Common to other semi-crystalline polymers, low peakvalue and broad span of the Tanδ peak are the two features of GT behaviour patterns that suggest less intense and more diffused motions of the segmental molecular structures in the silks. The data in Figure 1 allow us to calculate the fractional changes of E' before and after GT for the three silks, which are 40% loss for B. mori; 66% loss for A. pernyi and 58% loss for N. edulis.

T g : Observations and predictions
The physical nature of the thermally induced glass transition of silk fibroin is proposed to derive from the cooperative or non-cooperative motions of backbone segments in the noncrystalline or disordered regions of silk when the intermolecular forces go through a maximum, or the intermolecular stiffness tends to zero. 52 The transition condition is known as Born's elastic instability criterion, which concentrates on bond stiffness/mobility (perpendicular to the interaction axis) instead of bond strength (along the interaction axis). Quantitatively, Porter's Group Interaction Modelling (GIM) theory offers a satisfying relationship between the structure and properties of polymers, and the expression between T g and the structural parameters is shown in Equation (1).
N. edulis 32.0 7 Table 2. GIM paramitization and calculations for T g and the degree of structural disorder f dis .
Silk name Group H-bonds ‫ܧ‬ The number of H-bonds per peptide group is 1 or 2; cohesive energy E coh is the sum of that from hydrogen bonds and the peptide base; N is the degrees of freedom; ܶܽ݊ ∆ and ܶܽ݊ ∆ e are respectively the theoretical and experimental cumulative Tanδ through GT; and f dis is the predicted degree of structural disorder by GIM. Theta temperature θ 1 is taken to be 153 o C for all cases.
The structural parameters of a representative interacting structural unit include theta temperature θ 1 , cohesive energy E coh and degrees of backbone freedom N, which for common polymers can be found in van Krevelen's book Properties of Polymers. The degrees of freedom, N, in the GIM framework are defined as the number of skeletal modes of vibration normal to the polymer main chain axis. If a total number of 3 vibrational modes is taken, for each main chain atomic group, e.g. -CO-in the peptide base, N is 2 (subtracting 1 along the main chain axis from the 3 vibrational modes); for each middle side chain group, e.g. -CH 2 -in serine, N is 1 (subtracting 1 along the main chain axis and another 1 along the side chain axis); for each terminal side group, N is 2 although in some cases when two side groups coexist (e.g. -CH 3 in Leucine) N is 1 for each. The experimental T g e is defined as the peak temperature of Tanδ Gaussian peak through GT, as indicated in Figure 1 and shown in Table 2. Using the GIM methods and the structural parameters (E coh =125 kJ/mol, N=28, θ 1 =241 o C), the T g of nylon 6,6 is modelled to be 71 o C without considering the contribution from hydrogen-bonding, which is lower than our DMTA observation. If an average of 6 hydrogen bonds is added to the group cohesive energy, the resultant T g becomes 82 o C, closer to the temperature at peak Tanδ. In silks, the hydrogen-bonds among amide groups are easier to form from the highly oriented molecular structure and the number of hydrogen bonds directly impact on the cohesive energy, as shown in Table 2  responsible for GT in silk do not have a singular form, but a probability spectrum with several favoured forms, e.g. of one or two hydrogen bonds per peptide. The experimental T g of 217 o C in Figure 1(b) thus is the result of the averaged hydrogen-bonding density contributed by hydrogen-bonding forms with different probabilities. If one or two hydrogen bonds are adopted, the molecular structure in native B. mori silk would have a 70% chance of two hydrogen bonds. In comparison, the hydrogen-bonding density in the reconstituted silk films (T g =177 o C 50 ) would have 23% of probable structures possessing two hydrogen bond per peptide. For A. pernyi silks, the representative group is taken as G 0.33 A 0.53 S 0.14 , whose total molar fraction accounts for 82% of the whole fibroin sequence. The average cohesive energy per peptide is 48.2 kJ/mol if 2 H-bonds are taken into account, and the predicted high-bound T g for A. pernyi silk is 234.5 o C. The observed T g of 232 o C for A. pernyi silk implies the great majority of the non-crystalline molecular structures is highly hydrogen-bonded (close to 2 H-bonds per peptide). For N. edulis spider silk, detailed modelling parameterization based on N. edulis dragline Spidroin I can be found in reference 43 . Different from the two silkworm silks, spider dragline silk sequence has a number of peptides with bulky side groups (e.g. Glutamine), the motions of which are restricted until the backbone chain segments become free to move. The increase in the degrees of freedom of the side -R groups needs to be taken into account together with that of the backbone to infer the overall degrees of freedom, which brings N from 6 to 7. Alternatively, the observed T g might, as we believe, be contributed by an average number of hydrogen bonds in the structure. Figure 2(a) more directly translates Equation (1) into a linear relationship between T g and E coh . Calculation tells the spider silk possesses an average of 1.87 hydrogen bonds per peptide group in the non-crystalline region, in comparison to 1.70 for B. mori and 1.97 for A. pernyi. Additionally, the Tanδ profiles for the three silks are fitted by single Gaussian peaks as found in Figure 2(b), which confirms the segmental motions of native silks through GT are in a Gaussian probability form.
So far the broad temperature span of GT seems sufficiently explained as the predicted T g has a limited number of "favoured" values whereas the observed T g is a probability function of different predicted T g s according to the variations in hydrogen-bonding and degrees of freedom. The higher the observed T g is, the non-crystalline structure in the silk molecular structure is more tightly hydrogen bonded. We note that the structural model of two hydrogen bonds per peptide group for an "amorphous" disordered phase may be confused with the crystalline β-sheet phase as both possess similar density of hydrogen-bonding on average. According to the most recent series of NMR studies 53 , the liquid Silk I structure prior to the native solid silk formation has been identified to be type II β-turns with both inter-and intramolecular hydrogen-bonding, which is a form with a high energy density. Our results further suggest that the noncrystalline structure in native solid silks is highly hydrogenbonded, although this structural form (e.g. β-turns) is different from long-range order of β-sheet. This will add evidence to the understanding of the non-crystalline structural regions of native silks from the perspective of macroscopic property measurements.
Cumulative Tanδ δ δ δ and the degree of structural disorder How can the Tanδ profiles through GT in the DMTA measurement be interpreted for structural analysis of native silks? As previsouly introduced, the Order-Disorder proposition avoids the complicated assignments of secondary structures and yet still can be correlated effectively with the macroscopic properties of silks. Firstly, a structural parameter is defined as the degree of structural disorder, f dis , which is the molar fraction of the non-crystalline structures that are responsible for GT. Arguably the degree of structural disorder approximates an averaged structural parameter of heterogeneous nano-structures in a mean-field homogeneous micro-and macroscopic morphology. For the three silks, the following f dis values are referenced from amino acid sequence analysis 54  shows that ܶܽ݊ ∆ is in the numerical range of 51-70 (shown in Table 2), which appears much greater than the experimental values. For semi-crystalline native silks, it is straightforward to introduce the degree of structural disorder f dis to the equation, and adapt a new form, as presented in Equation (3). The factor f dis is easy to understand as only the motions of the disordered structure can be activated in GT and contribute to the experimentally measured Tanδ.
Regarding the other coefficient (2/3) in Equation (3), it is introduced to correct for the experimental effect of the uniaxial tensile mode in DMTA measurement because the molecular structures subjected to the static stress of the tensile direction cannot be relaxed as the motions along this direction are restrained. As a result, the probability of molecular motions of the overall disordered structure through GT is reduced by one dimention, or a factor of 2/3.
Equation (3) opens two avenues: firstly it allows the prediction of the cumulative loss tangent with a known degree of structural disorder and secondly it allows the calculation of the degree of structural disorder from the experimentally measured ܶܽ݊ ∆ e . The integration temperature limits are taken as 100 o C and 250 o C as shown in Figure 1, and the integration curves are shown in the later Figure 3 for a variety of silks. As shown in Table 3, from referenced f dis we have succeeded to explain the apparent discrepancy of the experimental cumulative ܶܽ݊ ∆ e and the theoretical ܶܽ݊ ∆ (100% disorder) through GT in native silks using the GIM framework and an order-disorder structural model without bringing in detailed effects. Moreover, by using the experimentally measured ܶܽ݊ ∆ e , the resultant f dis for the three silks lie in the frame of the reported values from other techniques 55 , e.g. FTIR measurements report 0.40-0.61 for A.
The Tanδ profile through GT enabled us to conveniently obtain the degree of structural disorder, or the fraction of the disordered structure that is responsible for GT. Nevertheless, without understanding the forms of "order" and "disorder", a simple Order-Disorder structural model cannot sufficiently explain the properties of certain silks, for example the supercontraction in spider silks. As discussed previously 56 , N.
edulis silk contains some inter-phase structural components, meta-order and meta-disorder. The complete resolution of the structural composition requires extra information on the structural relaxations of the intermediate structures between crystalline order and the GT-responsible disorder, e.g. from thermal analysis (DSC) or mechanical property analysis (tensile testing), which cannot be acquired using DMTA.

Understanding storage modulus changes through GT
Experimentally measured Tanδ profiles and ܶܽ݊ ∆ e through GT can reveal the structural disorder for the three native silk examples using GIM. Nevertheless, correlations between the loss events and the changes in mechanical properties are also fundamentally useful and have practical importance. Since GIM combines a cell or lattice model and the mean-field theory, we first introduce the fundamentally important "elastic" parameter of bulk modulus, B, which is a ratio of pressure to volumetric strain in a 'material' cell. The B expression from GIM 55 considers the contributions from the cohesive energy, the van der Waals volume of the unit group and the relative interaction distance between groups. B changes as the relative interaction distance r/r 0 changes over temperature or pressure especially through a change in "state" (crystalline, glassy or rubbery amorphous).
Here we conveniently extract the expressions of B for the three "states" or phases of polymer from GIM as shown in Equation (4). For silks, we could thus establish the correlation between the state theory and the order-disorder structural model: the crystalline phase corresponds to the ordered structure, the glassy amorphous to the disordered structure below T g , and the rubbery amorphous to the disordered structure above T g . We assume that silks transit from a "(amorphous glass)+(crystal)" state to a "(amorphous rubber)+(crystal)" state through GT.
To solve the problem of structure-property relations of multi-phase polymer systems, the B of the system ensemble can be approximated using a simple additivity rule (see Equation 5) if homogeneous volumetric distributions of the different phases can be assumed. It is important to mention that each phase is responding to thermal energy independently and energy sharing between phases is excluded when the additivity rule is applied. Using this rule and the previously modelled f dis , the average B of the two "states" of silk below T g and above T g can be estimated. As shown in Table 3, the predicted B after GT for the three silks is: 15   Note: Van der Waal's volume V w of the peptide group can be found in 43 and the average V w for each silk is calculated from molar fractions listed in Table 1; bulk modulus B is presented in the three states of polymer which are abbreviated as (C) for crystalline, (G) for glassy amorphous and (R) for rubbery amorphous; f dis is the structural disorder and ܶܽ݊ ∆ is the experimental cumulative Tanδ.
Next we calculate the engineering tensile modulus, E, from the above calculated reference parameters. Equation (6) consists of two parts: firstly B(T) contributes a volumetric energetic parameter and the second part comes from the contribution of loss events that reduce the stiffness of polymer chains significantly. After all, both the binding energy density and the molecular movements (reducing the energy through dissipation to thermal energy) would determine the polymer's mechanical properties.
The ensemble loss parameter ‫‬ tan ߜ݀ܶ uses experimental ܶܽ݊ ∆ e , contributed by the molecular mobility of the disordered fraction in the tensile experimental mode.
The proportionality constant A is determined by structural parameters of the characteristic group unit, and most polymers have A in the range 1-2 GPa -1 . Here a generic A for all silks takes 1.5 GPa -1 in line with the literature 43 . Table 3 summarises the model parameters and the calculated quantities based on the above equations. The predicted complex tensile moduli E at T>T g are 6.9 GPa, 1.0 GPa and 6.1 GPa respectively for B. mori, A. pernyi and N. edulis in comparison with the experimental observed storage modulus E', 4.1 GPa, 1.5 GPa and 3.3 GPa. Note that the complex moduli are the result of both the storage moduli and the loss moduli, therefore the values of E tend to be greater than E'. Oddly, for A. pernyi silk the modelled value is smaller and divergent from the experimental data. Structurally, the disordered regions of A. pernyi silk are in such a large fraction that the energy storage and dissipation mechanism between the order/disorder might be different.
An alternative explanation may arise from the experimental control. As the modulus was reduced greatly after GT, the applied static force became so great as to induce work-hardening of the disordered structure, which results in higher observed modulus. Given the explanations, the present set of methods proved to be able to predict the property changes of silks through GT, which closely resembled the experimental observations.

Variability in GT of silks
As discussed in the introduction, variability is an important issue when studying natural materials such as silk. Silk structures can vary highly between species and even individuals, and for this reason it is not surprising to observe a variety of GT behaviours in silk materials. The library of silk fibres is expanded in this section to include some of the "unnaturally" manipulated silks from the native dope by forced-reeling. Hence the goal of this section is to give clear visions of the structural origin of the variability of properties in silks.
Previous work showed that A. pernyi silks had an inherent, relatively large variability among individuals in the tensile mechanical properties and DMTA profiles. 57 As shown in Figure 3 (a) and (b), DMTA results show that silks from different representative individuals have more variability in T g (at major peak Tanδ) and ܶܽ݊ ∆ e through GT than that from the same individual. The shift in T g suggests the average cohesive energy varies due to different hydrogen-bonding densities; and the difference in Tanδ suggests varying degrees of structural disorder changing from 0.40 to 0.65, as calculated by Porter and confirmed by FTIR 15 . The structural differences in this particular case of A. pernyi silks may originate from the forced-reeling process, which has been shown to have a dramatic impact on the structure of B. mori silks 58 . It is also noticed that silks from the same individual show a consistent major GT peak with several minor peaks, which may be the relaxation of the locked-in low-ordered structures due to the coagulation during spinning. B. mori silks from commercially graded cocoons show traits comparable to the inter-individual A. pernyi silks in Figure 3(c). Shifts in major T g and changes in ܶܽ݊ ∆ are apparent between different grades. This has implications for the commercial value of silks as poor grade cocoons of small size and defects consist of poor silks with a high degree of structural disorder, which could directly impact performance (reeling, weaving and so on) in the industrial processing.
The introduction of forced-reeling could induce more variability and undesirable structural disorder as discussed for A. pernyi silks and shown for B. mori silks in Figure 3(d). The manipulation of the natural spinning process -including forced-reeling w/wo post-drawing treatment -perturbs the formation of native structures under natural conditions and may lock in more disorder during the liquid-solid transformation 58 .  Table 1), among silks of intra-and inter-individual differences, of various commercial grades and of conditioned forced-reeling. It infers that the intrinsic reason for silk variability is the different forms of hydrogen-bonding in the non-crystalline structure. Note that there is a Tanδ baseline of 0.008 through our temperature range (brown lines in Figure 3a-d) and the integration is subtracted. Importantly, this quantitative analysis of ܶܽ݊ ∆ can be used to compare the delicate structural differences in silks, and to develop quality control methods for silk processing.

Protein-water GT and denaturation in silk
As mentioned earlier, peptide-water glass transition and denaturation are the two structural change mechanisms at temperatures below the major GT. Peptide-water glass transition is a relaxation process of the peptide-water complex, whereas denaturation involves both evaporation of volatile water and reformation of hydrogen-bonding from water-amide to amide-amide. Figure 4 shows the three structure change mechanisms and the contributing group interactions in the representative Tanδ profile of B. mori silk from -100 o C to 250 o C. The water-amide (in "wet" silk) and amide-amide (in "dry" silk) interactions are separated at T=120 o C.
The first lower relaxation temperature lies in a temperature range from -80 o C to -30 o C with Tanδ peaks at -60 o C; and the second relaxation lies in a temperature range from 30 o C to 90 o C with Tanδ peaks at about 60 o C. Different from the major GT, both lower relaxations disappear when the silk has gone through thermal annealing up to 120 o C, which confirms that the presence of water is the prerequisite of these two mechanisms. For the native silk fibres studied, the water content is about 6%, as reported previously 48 .
Porter 59 emphasised the importance of the two lowertemperature structure change mechanisms in understanding the properties and functions of proteins that perform in vivo (although it is noted that our silk model material has long evolved to perform ex vivo). For proteins such as enzymes, which have a key-and-lock structure-property-function relationship, the molecular structure and the peptide-water interactions are expected to be more sensitive to external stimuli. Therefore the question arises: can we follow the protocol of detecting GT in silks to study the structureproperty relationships, especially peptide-water interactions, of more functionalised proteins in living organisms? Here the standard approaches for property measurements in polymer science such as thermal analysis and dielectric analysis, complemented by other means, may help to get the complete picture of protein structure-property-function relations.

Experimental Materials
B. mori cocoon fibres were first unravelled carefully with as minimal force possible from the cocoon middle layer, and then single fibres were mounted loosely onto paper frames that are specifically designed to fit in the tension clamps of the DMTA Q800 (TA Instruments, Delaware). Furthermore, graded B. mori cocoon fibres were also prepared from the commercially graded B. mori cocoons in the silk production region (Jiangsu Province) in China, for more details refer to 48,60 . N. edulis spider dragline major ampullate silk was collected directly from live spiders under ambient conditions at a reeling speed of 10 mm s -1 as previously described 61 . Synthetic polymer examples include highly amorphous polystyrene thin film and nylon 6,6 fibre. Polystyrene thin sheet was prepared using a simple hot-press technique. Medium tenacity Nylon 6,6 fibres were purchased from GoodFellows UK and the diameter of the fibres was supplied as 25 µm and verified using SEM (JEOL Neoscope) in the lab.
The presence of minerals and sericin makes A. pernyi silk fibres very difficult to be unravelled directly from the cocoon, and during unravelling it was inevitable that the fibres may be taken under tension. Therefore A. pernyi fibres were mostly obtained through forced-reeling of A. pernyi silkworms, and fibres from three different individuals were characterised for the variability of the GT behaviour (for more information refer to 57 ). Similarly, B. mori fibres were also obtained through forced-reeling under varied conditions: without post-stretch treatment and with post-stretch treatment (for more details refer to 58 ). Methods Cross-sectional area characterisation for fibres. N. edulis spider silk fibres were characterised under SEM, and a circular cross-section was observed. The diameter of the above two fibres as measured directly using the SEM measure function when the micrograph was taken.
A. pernyi and B. mori silk fibres have irregular cross-sections. For A. pernyi and B. mori cocoon silk fibres, a bundle of silk fibres were held tightly together through a thin tube, and then short tubular sections were cut (see examples inset to Figure  1). An average cross-sectional area was calculated from over 30 measurements of the individual cross-sectional areas. For A. pernyi and B. mori forced-reeled silk fibres, the crosssectional area of the adjacent section of silk to that being used for DMTA was applied. The adjacent silk fibre was embedded in epoxy resin and sectioned to expose cross-sections. The measurement of the cross-sectional area was through the software ImageJ after the SEM micrographs being taken. Temperature calibration of the DMTA instrument. There are two temperature sensors in the Q800 DMTA instrument, one for the sample temperature and the other as an environmental reference temperature. The instrument automatically compares the two temperatures, and if the temperatures show discrepancy it will report an error. Temperature calibration includes 1) absolute and 2) dynamic temperature calibration of the thermocouple. 1) Absolute temperature was calibrated using two reference points (ice's melting point, 0 o C, and indium's melting point, 156.6 o C) by performing a lowstress creep experiment in a temperature range through the melting transition of the reference sample. 2) Dynamic temperature was calibrated using indium wire and provided reference sample (PET film) at a heating rate of 3 o C min -1 .
Single fibre Dynamic Mechanical Thermal Analysis. Single fibre specimens mounted onto paper frames were loaded and clamped tight into the tension film clamps. Before testing, the paper frame was carefully cut open to leave the silk fibre specimen between the drive and the fixed clamps. The gauge length was re-measured with a preload stress of ~50 MPa to straighten but not yield the fibre and the preload stress was applied throughout the temperature ramp experiment. The full range temperature experiment was from -120 o C to 250 o C, where the subambient temperature was obtained using the gas cooling accessory and liquid nitrogen. Dynamic mechanical thermal experiments were set up with the following parameters: temperature ramp rate 3 o C min -1 ; dynamic frequency 1 Hz; dynamic oscillation strain 0.2%.

Conclusions
We have shown that the disordered phase in native silks is a critical structural component that affects the mechanical properties of silks and is of equal importance to the ordered phase. Here we deployed Dynamic Mechanical Thermal Analysis (DMTA) to examine the structural relaxation of the disordered phase of native silks and focus on the Glass Transition. The observed high T g of the disordered structure of three native silks suggests a hydrogen-bonding density of nearly 2 hydrogen bonds per peptide group. Based on GIM and the Order-Disorder argument, the key structural parameter of silk, f dis , can be successfully deduced from the model parameters and the experimental cumulative Tanδ during GT. We were also able to provide a quantitative analysis on the observed dynamic storage modulus and to make predictions on the modulus changes through GT, which would be useful for engineering applications and practical uses of silk materials. The developed theory and methods is intended to explain obverved variability in a variety of native and manipulated silks. In addition to protein structure, processing and posttreatments also contribute to the final structure and properties of silk fibres.
Moreover, two lower-temperature structural relaxations of native silks, namely peptide-water GT at -60 o C and "denaturation" (water evaporation and change of amide-water interaction to amide-amide interaction) at 60 o C, are briefly introduced to complete the overall thermo-mechanical property graph for native silks.
The experimental data and theoretical modelling presented in this paper provide not only new insights on the microstructural picture of native silks, but also new possibilities on understanding the molecular interactions and structure-property-function relationships for other biological polymers.