Determination of Silkworm Silk Fibroin Compressibility Using High

Article pubs.acs.org/Macromolecules

Determination of Silkworm Silk Fibroin Compressibility Using High Hydrostatic Pressure with in Situ X‑ray Microdiffraction Christina Krywka,*,†,∥ Igor Krasnov,†,∥ Roxana Figuli,‡ Manfred Burghammer,§ and Martin Müller∥ †

Institute for Applied and Experimental Physics, Universität Kiel, Leibnizstr. 19, D-24098 Kiel, Germnay Institute for Experimental Physics, Universität Leipzig, Linnéstraße 5, D-04103 Leipzig, Germnay § European Synchrotron Radiation Facility (ESRF), 6 Rue Jules Horowitz, F-38043 Grenoble, France ∥ Helmholtz Zentrum Geesthacht, Max-Planck-Straße 1, D-21502 Geesthacht, Germnay ‡

ABSTRACT: A hydrostatic high pressure cell is used to record pressure resolved wideangle X-ray microdiffraction data (WAXS) from Bombyx mori silkworm silk fibers with in situ pressurization in the range of 0.01−0.5 GPa (0.1−5 kbar). From the pressure dependent peak positions of (002), (020), (200), and (210) Bragg reflections the (anisotropic) elastic moduli of compression were determined for the different unit cell axes of the crystalline fraction of silk fibroin, comprising of stacked polyalanine β-sheets. The data are compared with X-ray diffraction results previously obtained from silkworm silk at tensile load and spider silk data at high hydrostatic pressure and indicate a different response of the silk fibroin structure to pressure versus tensile load. The response of the unit cell of silkworm silk fibroin to the applied pressure is discussed and modeled taking into account the weak van der Waals bonds between protein β-sheets. Differences are pointed out between the responses of silk’s nanostructure to unidirectional (tensile) load versus the undirected pressure load. Next to the direct determination of the elastic moduli for the different crystal lattice parameters, the pressure response of what is usually referred to as the amorphous phase is also considered.

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It is widely accepted that most silk fibers share a composite structure with crystalline and noncrystalline compounds3,7−9 and that a significant degree of interlinking between these two fractions is required to account for the viscoelastic properties of silks.10 The crystalline fraction is mainly composed of the small side chain amino acids alanine and glycine (>70% overall fraction7) in a repetitive sequence, arranged into nanocrystals of stacked, pleated β-sheets interlinked by van der Waals interactions. Hydrogen bonds connect the parallel polypeptide chain within the β-sheets while the amino acid sequence within a chain is bound covalently. Reported repetition distances in Bombyx mori silk are 0.695−0.698 nm for the covalent bonds, 0.936−0.97 nm for the hydrogen bonds, and 0.93−0.949 nm for the van der Waals bonds in dry silk.7,11−13 The nanocrystals act as rigid and purely elastically deforming nodes in an amorphous network of noncrystalline protein chains, together creating a semicrystalline biopolymer. Although a wide range of typical dimensions for the nanocrystals has been reported, a lower limit for the dimensions is assumed to be 5 × 2 × 7 nm3 (van der Waals bond, hydrogen bond, and chain directions, respectively)7,8 derived from diffraction data and assuming perfect crystals. Recent studies9 indicate the existence of small fractions of crystalline material and potentially nonstacked β-sheets dispersed in the

INTRODUCTION Natural silk fibers, as spun by silkworms and spiders, are extraordinary materials. Despite the similarities the silks from both species share, their main functions are entirely different. While fulfilling their natural function, spider silks absorb a large amount of kinetic energy in order to decelerate an insect from full speed flight in such a way that it is not catapulted back.1 For the cocoon silk produced by silkworms, on the other hand, such precisely optimized mechanical properties do not play an essential role. The cocoon’s primary function is to protect and thermally insulate the developing silk moth. Nevertheless, silkworm and spider silk are remarkably similar. They share the same nanoscopic morphology; they are chemically and rheologically closely related and have very similar mechanical properties. Although silkworm silk is presumed to be weaker and less extensible than spider silk, it was shown that the mechanical parameters of silkworm silks can approach those of spider dragline silk when reeled under forced silking conditions, i.e., with a steady and increased reeling speed,2 introducing in this way a substantial amount of prestress. In spider silk, this residual stress is released when wet spider silk supercontracts.3 Native silkworm silk is spun with only low prestress applied, and no significant humidity induced supercontraction effects have been reported.1,4,5 High relative humidity or even a liquid surrounding does have, however, a distinct impact on the mechanical properties of silk which is apparent through the different elastic moduli for dry and wet fibers.5,6 © 2014 American Chemical Society

Received: September 10, 2014 Revised: October 2, 2014 Published: October 16, 2014 7187

dx.doi.org/10.1021/ma501880h | Macromolecules 2014, 47, 7187−7193

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Figure 1. (a) Schematic cross section of the hydrostatic high-pressure cell showing how the sample is pressurized via a surrounding fluid (water) using hydrostatic pressure. (b) Assembly of the actual hydrostatic high-pressure sample cell, as used in the experiments. Beam passage is enabled through two flat diamond windows. The inset shows the sample holder with an actual silk bundle.

Figure 2. Schematic of the data treatment: After the normalization and background subtraction, regions of interest (ROI) are selected from the 2D data around the various Bragg peaks and the diffraction ring (d.r.). These are integrated azimuthally to obtain 1D intensity profiles and fitted with an adequate sum of Gaussians (dotted curves) to account for both the Bragg peaks and the “amorphous” halos (A1, A2). The horizontal white line in the 2D pattern indicates the orientation of the silk fibers. the course of sample preparation, uniform bundles were made, each containing about 6−10 twisted fiber bundles (i.e., 60−100 individual fibers). At the time of the experiment, the previously prepared silk bundles were inserted into special sample holders, where they were axially restrained, i.e., oriented parallel and fixed at a very barely stretched, dry state. Immediately prior to the experiment, the holder was introduced into the water bath of the hydrostatic pressure cell, which was kept at a constant ambient temperature. Experimental Setup. In order to study changes of the molecular structure as a function of the applied pressure, we have combined synchrotron WAXS diffraction experiments with in situ hydrostatic pressure. The experiment took place at the beamline ID13 of ESRF (European Synchrotron Radiation Facility) using a microfocused X-ray beam with an incident photon energy of 22.98 keV (wavelength 0.053 96 nm). At this wavelength the geometry of the sample cell limited the maximum accessible wave vector transfer q to about 20 nm−1. The total flux in the focal spot was between 108 and 109 photons/s, and the focal spot size was ca. 30 × 30 μm2. The used detector was a MarCCD 165, and calibration measurements using Al2O3 and LaB6 standards were performed to determine the geometrical parameters of the setup. The samples, mounted into holders as described above, were inserted into a home-built hydrostatic high-pressure cell, and in situ isotropic pressure of up to 5 kbar (0.5 GPa) was applied during X-ray diffraction data acquisition. The design of the sample cell and the concept of pressurization are shown in Figure 1 and are described elsewhere.17 For beam passage the high-pressure sample cell has two diamond windows, each 1 mm thick and with a clear aperture of 2 mm. Water was used as pressurizing medium; i.e., the sample was embedded into a water bath which was put under pressure externally by means of a high-pressure pump. The hydrostatic pressure was continuously measured using piezo-based high-pressure sensors installed in the water piping. Data Acquisition. Diffraction images were recorded at a pressure range of 0.01−0.5 GPa (0.1−5 kbar), starting at the lowest pressure and increasing in steps of 1 kbar. Upon reaching peak pressure, the pressure was released stepwise, and diffraction data were again recorded in order to determine whether the samples return to their

amorphous phase. NMR measurements, as well as atomistic simulations, show that the amorphous regions are composed of β-turns, 31-helices, and random structures. Still, the interplay of these structural features is a matter of debate, and synthetically manufactured silk fibers remain to be inferior to the natural ones. Specifically, a better understanding of the interplay between the crystalline and the amorphous phase is essential. Despite the large amount of studies on mechanical properties of silk, a precise understanding of how mechanical load modifies its structure is incomplete. The vast majority of studies employed tensile tests methods where the fibers were only exposed to directed, uniaxial stress. In order to study the role of the amorphous matrix on the mechanical properties and the way nanocrystals are interconnected, it is desirable that undirected stress or pressure is applied, so that crystal and external stress are equal, regardless of the details of the nanostructure. This demand, however, has not yet been met experimentally. There have been only few attempts to employ pressure.14,15 None of them, however, investigated native silk samples but only silk fibroin solutions. To close this gap, this work employs wide-angle X-ray scattering (WAXS) with in situ hydrostatic pressurization, studying in this way the response of the polyalanine nanocrystals to hydrostatic pressure, i.e., a force applied with no preferential direction, and complementing our similar data recorded from spider silk.16

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EXPERIMENTAL SECTION

Sample Preparation. Degummed silkworm silk from Bombyx mori was provided by the “Museé de la soie”, F-30170 St-Hippolytedu-Fort, France. In order to remove the wax-like sericine layer, the raw silk had been unreeled in warm soap water. The silk samples, as obtained, consist of a twisted pair of fiber bundles, with a typical overall diameter of ca. 50 μm. One fiber bundle in turn consists of ca. 10 individual single fibers, each with a typical diameter of 10 μm. In 7188


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initial state. All measurements were started at a reference pressure of 0.01 GPa in order to ensure that the X-ray path was completely free of any microscopic gas bubbles that could have been trapped within the silk fiber bunches. Data were recorded with exposure times of 20−30 s. For every sample, both the actual data and the data from the empty pressure cell (i.e., water only) were recorded at each individual pressure. The relatively long exposure times were required in order compensate for the strong absorption of the pressure cell (diamond windows + water), the weak scattering power of silk, and the relatively low incident photon flux (reflecting a nonoptimal undulator setting, chosen in order to obtain the high energy of 23 keV). From the comparison of diffraction patterns recorded at the beginning and at the end of a pressure run it was evident that no radiation damage effects could be observed at the given, accumulated dose in a pressure run. Data Analysis. The recorded data were normalized for the incident flux, which was integrated over each exposure using an ionization chamber upstream of the sample cell. Following the normalization of the data, corrections were applied to account for the pressuredependent water absorption, and a background subtraction was performed in order to remove the strong and pressure-dependent parasitic scattering caused by the diamond windows and the pressurizing medium. Finally, selected regions of interest were integrated azimuthally using the Fit2D software package,18 controlled through a MATLAB script in order to automatically process the huge amount of data. The resulting intensity profiles were each fitted by a series of Gaussian curves whose positions were then evaluated as a function of pressure. This is shown conceptually in Figure 2. Silkworm fibroin diffraction patterns have also been simulated6 for a comparison with the experimental data, and the simulated data are shown in Figure 3.

Figure 4. Pressure-dependent positions of the 002, 020, 200, and 021 peaks, the diffraction ring (d.r.), and the broad amorphous halos (A1 and A2) accompanying the 020 and 021 reflections, respectively. The peak positions were derived from Gaussian fits to the integrated data, as shown schematically in Figure 2. Data acquisition started at the lowest pressure, and duplicate markers at 0.01 and 0.1 GPa denote data recorded after returning from high pressure.

shown are the positions of the broad amorphous halos, accompanying the 020 and 021 peaks, denoted “A1” and “A2”, respectively. As mentioned above, the nanostructure of silk comprises fibroin nanocrystals embedded into a more or less disordered amorphous matrix. Although aligned with the fiber axis, the fibroin nanocrystals are very small (typically 10−20 nm) and exhibit a notable range of misalignment angles relative to the fiber axis which is why the observed Bragg reflections occur as broad and azimuthally widened peaks. The presence of the isotropic diffraction ring indicates thatlike spider silk silkworm silk also contains a fraction of randomly oriented, repetitive structures in its amorphous phase. The q-values of the diffraction ring and the 200 peak are indistinguishable within their error bounds, speaking in favor of the hydrogen-bonded repetition distance (between chains within a β-sheet) being their common cause. The positions of the 020 peak, the relatively weak 200 peak, and the diffraction ring shift to larger q-values when pressure is applied, indicating a compression of the corresponding lattice spacing. The pressure response observed for the 200 peak and the diffraction ring is comparable within error bounds, indicating a structural affinity. The 002 reflection, on the other hand, remains constant within the entire pressure range. The strongest response to the applied pressure is evident for the positions of “A1” and “A2”, suggesting that these are caused

Figure 3. (a) Computed 2D diffraction pattern for silkworm silk fibroin6 using lattice parameters (a, b, c) = (0.947 nm, 0.87 nm, 0.699 nm) with 7, 9, and 28 repetitive units in a, b, and c direction, respectively. The angular misalignment of the nanocrystallites around the fiber axis is 12°, and the fiber axis is tilted 8° against the beam directionhence the asymmetric 002 reflection. (b) Experimentally derived, background subtracted data.

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RESULTS For the pseudo-orthorhombic unit cell of polyalanine nanocrystallites in silkworm silk, the lattice parameter convention as in ref 7 is used: a corresponds to the distance between chains within a β-sheet (hydrogen bonds), b is assigned to the distance between stacked β-sheets (van der Waals bonds), and c is related to the repetitive distance within the peptide chain (covalent bonds). The indices for the peaks found in the diffraction patterns are consistent with the P21 space group, as reported in ref 13. Shown in Figure 4 are the pressure-dependent q-values of the 002, 020, 200, and 021 peaks and the diffraction ring, as derived from Gaussian fits to the azimuthally integrated portions of the 2D data (refer to Figure 2 for the used regions of interest). Also 7189


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0.863 ± 0.002 nm, and c = 0.7006 ± 0.001 nm. Despite the elevated pressure and the samples being saturated with water, the values of a and c correspond well with lattice constants reported for dry or humid silk at ambient pressure.11,12,7,13 The value for b, on the other hand, is significantly smaller than the typical values of 0.93−0.95 nm. The elastic modulus Ex for an individual lattice parameter x of the unit cell can be determined from the relative, negative strain εx at a given pressure p:

by less rigid (and less ordered) fractions, assumingly to be found in what is usually referred to as the amorphous matrix. The intensities of the peaks and of the diffraction ring remain either constant or exhibit a slight decrease throughout the pressure range (in data corrected for the pressure-induced elevation of absorption), indicating that the amount of crystallinity does not increase upon applied pressure. This is in part contrary to our findings in spider silk16 where the intensity of the diffraction ring significantly (and reversibly) increased upon pressure elevation. All pressure-induced peak shifts in silkworm silk appear to be fully reversible; i.e., the peak positions return to their original values when pressure is released, and no hysteresis is visible within the error bounds of the data. From previous studies of wet silkworm silk and spider silk samples it is known that water only affects the noncrystalline amorphous parts.5,19,20 It can therefore be assumed that the pressurizing water does not directly alter the structure of the crystallites, and so the obtained peak positions can be used to calculate the lattice constants a, b, and c of the pseudoorthorhombic unit cell13 of the β-sheet polyalanine crystallites21 as for dry silk, i.e., using the equation d = 1/

h2 k2 l2 + + a2 b2 c2

Ex = −p /εx = −px /Δx

with x ∈ [a, b, c] being the undisturbed lattice parameter and Δx its change at the given pressure. In the representation of Figure 5, the elastic modulus Ex can be determined from the slope m = Δx/p of a linear fit, yielding Ex = x/m. Table 1 shows the elastic moduli determined in this way from our data. Despite isotropic pressure acting on the sample, the recorded data exhibit a highly anisotropic response of the nanocrystalite structure to the applied force. Obviously, the most rigid lattice parameter is c, which is associated with the peptide chain direction and its covalent bonds (no compression was detected). Maximum compression (i.e., lowest E) occurs for the lattice parameter b, associated with the weaker van der Waals bonds between stacked β-sheets. A higher rigidity is evident for the lattice parameter a, which is associated with the hydrogen bonds between the peptide chains in a β-sheet. Here no detectable compression was observed within our data’s error bounds. Notably, in order for any actual compression to be contained within the scatter of our data, the hypothetical modulus needs to be of the order of Ec = 103 GPa, which is much higher than the theoretical limit of the elastic modulus for a crystal of silk fibroin.36 For the diffraction ring a similar pressure dependence is found. If assumed that the amorphous peaks (A1, A2) denote a mean distance in the low order phase, the same calculation can be performed using their peak positions, leading to elastic moduli of the underlying, relatively soft structure. These values are also shown in Table 1 and compared with what has been calculated in ref 10 as the elastic modulus of the intracrystalline matrix from tensile test data. The relatively large errors for Ea and Ed.r. reflect the adverse combination of a near-zero slope and the uncertainties in the position determination of the very weak 200 peak and the diffraction ring. van der Waals Bond Length Compression. As shown with a higher level of detail in Figure 6, the lattice parameter b responds to applied pressure in a nonlinear way; that is, the compressibility coefficient depends on the pressure itself. Because of the small relative error, this relationship can be modeled more thoroughly than with the application of a linear fit. The direction of the lattice parameter b in the nanocrystals corresponds to van der Waals bonds, i.e., noncovalent and nonionic, pairwise attractive interparticle interactions, for which the van der Waals equation of state can be assumed to be applicable. Indeed, modified versions of this equation have been used for modeling polymer melts under high pressure (see e.g. refs 22 and 23). The equation of state, initially stated to describe the behavior of real gases and simple fluids, is

(1)

and the reciprocity relation

d = 2π /qhkl

(2)

where d denotes the real space distance between the lattice planes defined by the Miller indices (hkl) and the corresponding reflection qhkl in reciprocal space. As the lattice constants a, b, and c are associated with the 200, 020, and 002 directions, respectively, the corresponding peak positions can be used to directly derive the lattice parameters: a = 4π /q200 ;

b = 4π /q020 ;

c = 4π /q002

(4)

(3)

Figure 5 shows the pressure-dependent lattice parameters, calculated from the Bragg peak positions. The values at the lowest pressure of 0.01 GPa are a = 0.939 ± 0.007 nm, b =

Figure 5. Pressure-dependent lattice parameters a, b, and c of the pseudo-orthorombhic unit cell in the poly alanine crystals of silkworm silk fibroin, derived from the q-values of the recorded 002, 020, and 200 peak positions. The linear fits are used to derive the elastic moduli. The fit for b is dashed because it does not take into account the nonlinearity of the peak shift (which is considered in Figure 6). The left and right axes are shifted with respect to each other but show the same interval, so the slopes of the three fits are to scale.

(p + α /v 2)(v − β) = kBT

(5)

where p, v, and T are the pressure, specific volume, and temperature, kB is the Boltzmann constant, and α and β are measures of attractive forces between the particles and their 7190


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Table 1. Elastic Modulus of the Crystalline Unit Cell of Bombyx mori Silkworm Silk Calculated from the Positions of the 002, 020, and 200 Peaks (Ea,b,c) and Elastic Moduli of the Structures Causing the Diffraction Ring (Ed.r.) and the Amorphous Peaks A1, A2 (EA1,A2)a pressure load (GPa) tensile load (GPa)

Ea

Eb

Ec

EA1

63.4 ± 41.1

33.0 ± 5.7

(n.d.) 26.5

6.7 ± 0.4

EA2

Ed.r.

7.7 ± 1.7

56.7 ± 35.9

6.3

A high value represents a rigid structure, and so “n.d.” reflects the nondetectable compression of the lattice parameter c. The data from this work are in the first row, while tensile load data from our previous work10 are shown in the second row. a

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DISCUSSION The results indicate that, as the β-sheet planes are aligned mostly parallel to the fiber axis, the polyalanine nanocrystallites are squeezed only in the directions perpendicular to the fiber axis when pressure is applied. The structure most susceptible to compression isexpectedlythe relatively weak van der Waals interlink between β-sheets (lattice parameter b) while the hydrogen bond distance between the peptide chains within a βsheet (lattice parameter a) experiences a smaller but significant compression. The repeat distance along the covalently bonded peptide chains (lattice parameter c) exposes no detectable compression, which is not surprising because covalent bond lengths are not expected to be impaired at pressures below 2 GPa.26 However, an unlikely high compression modulus on the order of Ec = 103 GPa would be required for any compression to be contained within the scatter of our datathat is, of course, unless there are other processes (like rotation of bond angles) contributing to the dissipation of the load that is applied via pressure. When compared to tensile stress data, a notable finding there is that tensile load leads to a most exclusive elongation in the 002 direction;10 i.e., the nanocrystals appear to be most extensible in the direction corresponding to the lattice parameter ccontrary to what is observed in pressure load conditions and in agreement with our previous spider silk study.16 The remarkably huge deviation found for Ec speaks strictly against the comparability of modulus data obtained from tensile versus (isotropic) compressive load, and it must be assumed that different structural changes are triggered by the different types of load. In other previous studies27,28 we found that tensile load applied on silkworm silk results in a “kinked” stress−strain curve, similar to that in spider silk and it is accepted that both silk species share the same underlying process: upon initial tensile load an untangling and rearrangement of the polypeptide chains in the amorphous regions accounts for most of the elongation of the material. At the same time the nanocrystals increasingly take up the external load, leading to an elastic elongation. Such process does not, however, require an elongation of the covalent bonds in the nanocrystalites but merely a change of the involved bond angles or dihedral angles. The gradual shift of force-induced structural changes (from untangling of the amorphous phase to the elastic elongation of the crystalline phase) is reflected by the yield-point-like “kink” in a stress−strain curve, typically found around 0.3 GPa. When silk is exposed to (inherently undirected) pressure, on the other hand, the applied load cannot be sequentially dissipated through the untangling of the amorphous phase and the elastic deformation of the crystalline phase. Instead, a simultaneous compression of both phases must be assumed under these conditions. It is therefore surprising that a nonlinear response is nevertheless observed in high-pressure data, even though it occurs for a different lattice parameter (b). We have

Figure 6. Pressure-dependent lattice parameter b (spacing between βsheets) of the pseudo-orthorhombic unit cell in the polyalanine crystals of silkworm silk fibroin, derived from the q values of the recorded (020) peak. The solid line represents a fit to the simplified van der Waals equation of state (see text).

specific excluded volume, respectively. Using the proportionality of the specific volume to the unit cell volume (i.e., v ∼ abc), neglecting the variation of a and c (i.e., β = ab0c), and assuming the change in specific volume to be small, the equation of state can be simplified to (p + p0 )(b − b0) =

kB T ac

(6)

Following the concept proposed in ref 24, the parameter p0 represents a measure for the attractive forces between the βsheets (“internal pressure”) and b0 is the smallest possible distance (“excluded distance”) between the pleated sheets at infinite pressure. Equation 6 can be regarded as a pseudo 1D equation of state, connecting the variation of the β-sheet spacing with pressure, in the sense of the thermodynamics of small systems25 or, simpler, as an equation of state of the ensemble of crystallites in the fiber. The solid line in Figure 6 represents the fit of eq 6 to our experimental data. The derived fit parameters are for the internal pressure p0 = 0.3 ± 0.04 GPa and for the excluded distance b0 = 0.843 ± 0.005 nm. It appears tempting to associate them with physical meaning, although of course the high level of simplification involved in the model must be kept in mind. Nevertheless, b0 can be assigned to the shortest distance possible between the stacked polyalanine β-sheets with intact van der Waals bonds, and p0 can be assigned the amount of strain (i.e., negative pressure) required to overcome the attractive forces in the bond. 7191


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changes are considered to be caused mostly by the incorporation of additional water molecules into the hydrogen-bond-interlinked amorphous matrix. Our data support that the limited accessibility of water into the silk microstructure (i.e., its inability to penetrate the crystalline fraction) also holds true for elevated pressure. This statement is based on the finding that the lattice parameters a and c retrieved at the lowest pressure (0.01 GPa) correspond well with values derived at ambient pressure (0.1 MPa) and that the only observed response to pressure is a compression of the lattice constants. For the lattice parameter b we found a value that is 8% smaller (at zero pressure) than what is reported for dry silk. It appears very unlikely, however, that this is a result of water penetrating into the crystallite fraction. With the other lattice parameters unchanged, any expansion of the crystallites due to adopted water molecules would lead to an increase of the lattice parameter. A similar effect, i.e., the anisotropic decrease of the lattice parameters upon hydration, is observed in the cellulose crystallites in plant cell walls. It is hypothesized that humidity-induced swelling of its amorphous phase34 or the capillary condensation of water into the nanoporous amorphous matrix35 exert sufficiently high compressive forces onto the crystallites. The same process can be applied to silkworm silk, which is also known to contain nanopores33 and is therefore susceptible to compress the weakest bonds in its nanocrystals (van der Waals bonds) upon sufficient amount of hydration. However, the amount of humidity-induced lattice deformation observed in cellulose (1−2%) is significantly smaller. At the same time, the compressive pressure required to account for the 8% deviation is about 0.2 GPa (extrapolated from eq 6 for the smallest reported value of b = 0.93 nm). Although this value remains below the tensile strength of silk, it appears unlikely for the swollen amorphous phase and the capillary pressure to induce this level of compressive strain. We have to assume, therefore, that there is at least one further contribution that is currently unknown to us.

successfully modeled the pressure dependence of the lattice parameter using a simplified equation of state for the van der Waals forces comprising the bonds in this direction. The model has provided a value of p0 = 0.3 ± 0.04 GPa. Being the “internal pressure”, this value is a measure of the attractive forces acting in the system without any external pressure, and it correlates well with the strain at which the aforementioned kink is found in tensile stress data. Shifts of what is assumed to be peaks from amorphous structure support the three-phase model of silk in which next to the well-oriented crystalline phase there is a more and a less ordered amorphous fraction. The elastic modulus calculated from these peak shifts exhibits a striking accordance with the corresponding value that was indirectly derived from previous tensile test data.10 It is also noteworthy that the intensity of the silkworm diffraction ring remains constant throughout the entire pressure range (intensity data not shown here). On the contrary, our data previously recorded from spider silk16 exhibit a distinct, pressure-induced intensity increase of the diffraction ring in supercontracted spider silk and a less pronounced increase in non-supercontracted samples. It was assumed that the intensity increase in spider silk was due to the pressureinduced formation of (randomly oriented) β-sheet stacks from the individual β-sheets dispersed in the amorphous phase. As no such intensity increment was observed from silkworm silk data, it must be assumed that if dispersed β-sheet structures are present in silkworm silk, they do not serve as a crystallization precursor within the applied pressure range. The strong correlation of the diffraction ring with the 200 peak in terms of both q-value and pressure response, nevertheless, indicates that the randomly oriented fraction is structurally closely related to the crystalline phase. It is possible that the diffraction ring is caused by nanocrystalites that, for whatever reason, have not been aligned with the fiber axis during the spinning process. At random orientation, diffraction rings for 020 and 002 would easily become too weak to detect and only the relatively strongest 200 repetition distance would contribute to a powder diffraction ring. Another possible explanation is the presence of randomly oriented isolated βsheets, i.e., β-sheets that did not develop into stacked crystals, therefore lacking a stack repetition distance. In a nonrelated Xray diffraction study on single carbon fibers29 the twodimensionality of the randomly oriented graphite sheets was found to be the reason for the diffraction ring superimposing the corresponding Bragg peak.30 To our knowledge isolated βsheets have not been reported to exist in silk; however, flat βsheets were in principle shown to be stable at ambient conditions31 and were proven to exist without a hydrophobic core.32 During the experiment the silk samples were immersed in fluid water, which of course was a prerequisite to isotropic pressure transfer onto the fibers. The potential impact of the aqueous environment on the microstructure of silk needs to be addressed: To our best knowledge there is no evidence from studies on humid silk that absorbed water has a significant impact on silk’s crystalline structure. It has been demonstrated that silks immersed in boiled water for an extended period of time do not exhibit coarsening of the microstructure or a change of the volume fraction of ordered material.20 It is wellknown, though, that adsorbed humidity significantly modifies the noncrystalline (amorphous) phase, which is evident through swelling of the fibers by 10−18%33,5 and through an associated change in their mechanical properties.5 These

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CONCLUSION We have employed wide-angle X-ray diffraction with in situ hydrostatic pressurization in order to determine the anisotropic moduli of compression of the polyalanine nanocrystallites in Bombyx mori silkworm silk. The pressure-dependent data with peak pressures of 0.5 GPa (5 kbar) have yielded the elastic moduli for the directions of the three lattice parameters a, b, c and for the semiordered fraction in the noncrystalline phase of the fiber. To our knowledge, this is the first attempt to determine the elastic parameters for silk in a way where the different mechanical properties of the crystalline and the amorphous phases do not interfere with each other (as it is inherently the case in tensile tests). No compression of the lattice parameter c (intrachain covalent bond direction) was detected, contrary to what is usually observed in tensile test experiments with comparable (negative) load. This has been accounted to the inherently different nanoscopic mechanisms acting upon application of tensile (i.e., anisotropic) or hydrostatic compressive (i.e., isotropic) load, which is discussed in detail. The values found for the moduli of the lattice parameters b and a correspond well with the relative strengths of the involved bonds (van der Waals bonds and hydrogen bonds, respectively). While the pressure response data for a did not allow a closer examination of any potential nonlinearities, we were able to model the distinct nonlinear response of the 7192


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lattice parameter b (van der Waals bond direction) using a modified equation of state. In order to exclude a potential influence of the pressurizing water onto the lattice parameter b, similar experiments need to be performed with a water-free pressurizing medium (e.g., silicone oil).

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected], Ph +49-40-8998-6903 (C.K.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Prof. Roland Winter, Christoph Jeworrek, Sebastian Grobelny, and Martin Schroer of the Technical University of Dortmund (Germany) for sharing high pressure equipment components. Thanks also go out Emanuela Di Cola, Lionel Lardiere, and Michael Reynolds of ESRF for excellent support at the beamline ID13. Special thanks go out to Christian Sternemann and Michael Paulus for enabling initial test studies at the beamline BL9 of DELTA Synchrotron (Dortmund, Germany). The authors also acknowledge financial support by the German Federal Ministry of Education and Research (BMBF project 05KS7FK3). We acknowledge funding by the Deutsche Forschungsgemeinschaft to the Collaborative Research Center (SFB) 677 (“Function by Switching”).

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REFERENCES

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