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Monitoring Nanoscale Deformations in a Drawn Polymer Melt with Single-Molecule Fluorescence Polarization Stefan Krause, Martin Neumann, Melanie Fröbe, Robert Magerle, and Christian von Borczyskowski ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.5b05729 • Publication Date (Web): 01 Feb 2016 Downloaded from http://pubs.acs.org on February 2, 2016
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Monitoring Nanoscale Deformations in a Drawn Polymer Melt with Single-Molecule Fluorescence Polarization
Stefan Krause,* Martin Neumann, Melanie Fröbe, Robert Magerle,* and Christian von Borczyskowski
Fakultät für Naturwissenschaften, Technische Universität Chemnitz, 09126 Chemnitz, Germany
Abstract Elongating a polymer melt causes polymer segments to align and polymer coils to deform along the drawing direction. Despite the importance of this molecular response for understanding the viscoelastic properties and relaxation behavior of polymeric materials, studies on the singlemolecule level are rare and were not performed in real time. Here we use single-molecule fluorescence polarization microscopy for monitoring the position and orientation of single fluorescent perylene diimide molecules embedded in a free-standing thin film of a polymethylacrylate (PMA) melt with a time resolution of 500 ms during the film drawing and the subsequent stress relaxation period. The orientation distribution of the perylene diimide molecules is quantitatively described with a model of rod-like objects embedded in a uniaxially elongated matrix. The orientation of the fluorescent probe molecules is directly coupled to the local deformation of the PMA melt, which we derive from the distances between individual dye molecules. In turn, the fluorescence polarization monitors the shape deformation of the polymer coils on a length scale of 5 nm. During stress relaxation, the coil shape relaxes four times more 1 ACS Paragon Plus Environment
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slowly than the mechanical stress. This shows that stress relaxation involves processes on length scales smaller than a polymer coil. Our work demonstrates how optical spectroscopy and microscopy can be used to study the coupling of individual fluorescent probe molecules to their embedding polymeric matrix and to an external mechanical stimulus on the single-molecule level.
Keywords: Single-molecule microscopy, fluorescence polarization, orientation dynamics, polymer melt, film drawing, stress relaxation
Single-molecule spectroscopy is the basis for super-resolved fluorescence microscopy, which finds widespread use in the life sciences.1 In seminal works, single molecules and their dynamics were studied in organic crystals.2,3 Since then, single-molecule spectroscopy has been used for probing local viscosities and local density fluctuations in glasses,4 liquids5 and polymers by rotational6-8 and translational9-14 diffusion processes. In addition, spectral15-18 and lifetime19,20 fluctuations reveal the dynamical processes of the polymer matrix embedding fluorescent probe molecules, for instance, spatial21 and temporal heterogeneities22 as well as cooperative effects, such as transitions among meta-basins.23,24 Single-molecule spectroscopy studies of polymers have been reviewed by Wöll et al.25 The orientation fluctuations of fluorescent single molecules, which can be measured by fluorescence polarization microscopy,26-28 couple strongly to the dynamics of the embedding polymer matrix6-8 and slow down significantly upon cooling towards the glass transition temperature.23 Drawing a polymer film causes the polymer chains as well as the embedded fluorescent molecules to align along the elongation direction. In polymer melts and glassy polymers, this alignment is due to the steric interaction between the polymer chains and the fluorescent molecules29 and can be utilized for polarizers30,31 and in sensing applications.32 2 ACS Paragon Plus Environment
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The long molecular axis of rod-like molecules aligns parallel to the direction of elongation, and the maximal degree of fluorescence polarization increases with the length of the fluorophore.33 In drawn semi-crystalline polyethylene,34-36 a different alignment mechanism has been proposed. The dyes adsorb on the surface of polymer crystals which align during film drawing.36 Recent work addresses the effects of elongation and other mechanical deformations on the conformation and the chemical reactivity of mechanophoric molecules.37,38 Although the response of the embedded fluorescent molecules to the mechanical deformation of the polymer matrix has been studied at the ensemble level,11,29 investigations on the single-molecule level are rare34-36,39,40 and have not included measurements taken during the drawing process. Photobleaching, strong sample drifts and fluorescent impurities in the polymers are reasons for this lack of investigations.
In particular, a detailed understanding of the coupling mechanism between the dye and polymer molecules is missing. Since a perfect alignment of all the probe molecules along the elongation direction has never been observed, two different explanations have been suggested:33,36 (i) Only a fraction of probe molecules orient along the elongation direction and contribute to the fluorescence polarization. (ii) All the molecules contribute to the fluorescence polarization, but the alignment exhibits a broad distribution of orientation angles. The latter may result from a dependency of the reorientation of each single dye molecule on its initial orientation. Distinguishing between these two cases is of fundamental interest in understanding the coupling between fluorescent dyes and the embedding polymer chains during a mechanical deformation of the specimen. In addition, the properties of the polymeric host matrix are expected to have a major impact on the type and the degree of the dye-to-polymer coupling. For example, Wirtz et al. observed an alignment of the probe molecules with the oriented crystallites 3 ACS Paragon Plus Environment
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in low-density polyethylene,36 a process which cannot be responsible for the dye orientation in polymer glasses and melts.
Here we use single-molecule fluorescence polarization microscopy for monitoring the position and orientation of a set of single fluorescent perylene diimide molecules embedded in a thin film of a polymethylacrylate (PMA) melt. This allows for a real-time observation of the local elongation of the PMA melt between the individual perylene diimide (PDI) molecules (Figure 1) and their orientation distribution function during the uniaxial elongation of the polymer melt and during the subsequent stress relaxation period. In PDI molecules, the optical transition moment is oriented parallel to the long molecular axis, analogous to the case of perylene,41 which avoids depolarization effects.18,25 A comparison of optical polarization and mechanical stress relaxation experiments reveals different time and length scales for the molecular and the mechanical stress relaxation processes.
Results and Discussion
Film Drawing and Single-Molecule Microscopy Setup. We use a microtensile testing setup as described by Franke et al.42 and observe the fluorescence polarization of single molecules of N,N′-di(hexadecyl)-perylene-3,4:9,10-tetracarboxylic diimide (PDI) embedded in a free-standing, approximately 2-µm-thick PMA film, using single-molecule fluorescence polarization microscopy with a wide-field microscope according to Schob et al.6 (Figure 1). The diffraction-limited fluorescence images are divided into a parallel polarization component and a perpendicular polarization component with a Wollaston prism in front of a CCD camera and are recorded with a frame rate of two frames per second. The centers of the imaged spots each 4 ACS Paragon Plus Environment
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correspond to the position (x, y) of an individual PDI molecule. From the intensity IP (parallel to the elongation direction) and IS (perpendicular to the elongation direction) of each fluorescent PDI molecule, the orientation angle of the in-plane projection of the transition dipole, = arctan ( / ), is calculated.43 The accuracy is ± 5°, depending on the signal-to-noise ratio of the detected fluorescent molecule (Figure S6b). Furthermore, the position data yield the distance (∆x, ∆y) between two PDI molecules as function of time (Figure 1b). The relative change of these distances is the local elongation , and , , respectively.
Figure 1. (a) Schematic of the experimental setup. A free-standing PMA film doped with PDI molecules is uniaxially elongated using a microtensile testing setup and observed with wide-field fluorescence polarization microscopy. The fluorescence signal is divided into a parallel
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polarization component and a perpendicular polarization component and imaged onto a CCD camera. (b) Sum of the fluorescence signal intensities IS and IP (the intensity scale is given in arbitrary units). Spots correspond to individual PDI molecules. The arrows correspond to the direction of polarization. (c) and (d) Molecular structures of PDI and PMA, respectively. The transition moment of PDI is marked by a red arrow in analogy to that of perylene.41
Single-Molecule Reorientation Dynamics. Figure 2a shows the positions and orientations of single PDI molecules in a PMA film at 285 K. This temperature is 3 K above the glass transition temperature TG of PMA and was chosen to minimize the rotational and translational diffusion due to Brownian motion.7,23 Our experiment allows for the direct measurement of the position and orientation of single PDI molecules during the film drawing process. Figure 2 shows the data for a PMA film at 285 K before (Figure 2a) and after (Figure 2b) the uniaxial elongation of the film to a global elongation εG = 1.7. The free-standing region of the PMA film was uniaxially elongated with a (global) strain rate = 0.01 s-1. After the film reached the maximal elongation εG = 1.7, the elongation was kept constant. The entire sequence of images taken during the film drawing process is shown in Movie M1 (see Supporting Information). The orientation of each molecule is indicated by a short bar, which reflects the orientation angle within the plane of the polymer film. An orientation angle of = 0° corresponds to an orientation parallel to the elongation direction. With increasing elongation of the film, the dye molecules orient more parallel to the elongation direction. This is interpreted as a steric interaction between the dye molecules and the polymer matrix, which causes the alignment of the rod-like dye molecules preferentially parallel to the stretched polymer
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chains.29,33,44-46 The distribution of orientation angles φ is shown in Figure 2c,d. The average orientation is initially = 46.3° and changes during the elongation to = 24.8°.
Figure 2. (a,b) Sum of the fluorescence signals IS and IP and the in-plane orientation of individual PDI molecules measured at εG = 0 (a) and εG = 1.7 (b). The circles/bars indicate the position/orientation of the molecules. (c,d) Distribution of the in-plane orientation angles φ derived from 25 consecutive frames at εG = 0 (c) and at εG = 1.7 (d).
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We analyzed the entire sequence of images shown in Movie M1 (see Supporting Information). The resulting distributions of orientation angles are shown in Figure 3. All the distributions were normalized with respect to their total area. The elongation period lasted 170 s. We divided the time interval into 5 equal subintervals of 34 s (68 frames) and determined the distributions of the orientation angles for each subinterval. The distributions are labelled according to the increment of the local elongation , . The first distribution shown for , = 1.3 is the time average over the first 34 s after the deformation finished. During the elongation of the film, the distribution of the orientation angles transforms continuously from a uniform distribution to a broad anisotropic distribution with a peak at ≈ 10°, which is close to a perfect alignment ( = 0°) (Figure S2). This continuous transition of the orientation angle distribution indicates that, on average, all molecules contribute to the increase in fluorescence polarization. We do not observe two distinctive fractions of individual probe molecules (one fraction taking part in orientation along the stretching direction and the other randomly oriented) as was proposed by Springer et al.
33
as a possible, alternative reorientation mechanism and was
experimentally observed in low density polyethylene by Wirtz et al.36
Finally, we compare the distribution of orientation angles at the end of the deformation process (t = 170 s) with that at the end (t = 470 s) of the whole experiment (Figure 3b). The two distributions differ only slightly from each other. The maximum of the distribution at the end of the measurement (blue bars) is shifted only 3° to higher orientation angles. In addition, after the 300 s relaxation period, only a few more molecules exhibit orientation angles greater than 45°. These small changes result in a shift of the average orientation angle from 23.7° to 27.5°.
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This shows that the relaxation of the molecular orientation is slow at a temperature of 3 K above TG. The details of this slow relaxation will be discussed later.
Figure 3. (a) Distributions of the measured (red) and simulated (grey) in-plane orientation angles φ and φS, respectively, for increasing elongation (from top to bottom). For each distribution, the data are integrated over 68 image frames corresponding to the indicated range of local 9 ACS Paragon Plus Environment
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elongations εy,loc. The red and grey dashed lines represent the arithmetic averages of φ and φS, respectively. The continuous temporal evolution of the orientation distribution is shown in Figure S2. (b) Comparison of the distributions of the in-plane orientation angles φ at the beginning (t = 170 s, red) and at the end (t = 470 s, blue) of the relaxation period. The dashed lines represent the arithmetic average of the in-plane orientation angles = 23.7° (red) and = 27.5° (blue).
Local Elongation. In addition to the orientation angles, our data yield the position coordinates (x, y) of each probe molecule as a function of time during the deformation process, which allows the local elongation , to be quantified for the investigated area of the film. This is important, since it differs from the global elongation of the specimen (Figure 4d). We attribute this difference to spatial variations of the thickness and the density of the polymer film and/or its coupling to the microtensile testing setup. Furthermore, the investigated area is not positioned exactly at the neutral line of the deformed film. This is evident from Figure 4a, where the y-coordinates of all the tracked PDI molecules are shown. During the elongation period, the polymer film moves (as indicated by the time-dependent y-coordinates) relative to the field of view. The direction of the motion changes at about 50 s. After reaching the maximal elongation at t = 170 s, the positions of the probe molecules do not change.
The translational and rotational diffusion of the probe molecules is negligible at a temperature of only 3 K above TG.23 The distances ∆#$ (%) = |#$ (%) − # (%)| between the probe molecules k and l are shown in Figure 4b. They have been determined from a sequence of 10 frames, corresponding to a time interval ∆% = 5 s, in order to determine the local strain rate ,$ (%) = [∆#$ (% + ∆%) − ∆#$ (%)]/[∆#$ (%) ∙ ∆%]. For each time t, the local strain rates 10 ACS Paragon Plus Environment
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were averaged over all pairs of PDI molecules, resulting in 〈,$ (%)〉. Both the local strain rates and their average are shown in Figure 4c. The local strain rate deviates from the constant global strain rate = 0.01s /0 . For t < 40 s, the local strain rate increases steadily and then drops to about 0.005 s/0 . We attribute this deviation to an interplay between the heterogeneities in the thin film and the viscoelastic properties of the PMA melt. At the end of the global elongation (at t = 170 s), the local deformation rate εy,loc drops to zero. Integrating the average local strain rate 4
〈,$ (%)〉 over the elapsed time gives the local elongation , (%) = 15 6〈,$ (%′)〉3%′, shown in Figure 4d (red curve). As mentioned above, the local elongation (red line) deviates from the global elongation (black line). We arrive at the important conclusion that after the whole elongation, the local elongation , is 0.4 smaller than the global elongation .
The local elongation is consistent with the number N of dye molecules that are visible within the field of view. Assuming a homogenous distribution of dye molecules and volume conservation of the polymer film, the local film thickness as well as N are proportional to (, + 1)/0. Indeed N decreases from 76 initially to 40 at t = 170 s, where , = 1.3 (see Figure S6a).
The arithmetic average of the orientation angles is shown in Figure 4e. Its temporal evolution closely follows the local elongation , . This indicates that the reorientation of the observed probe molecules couples directly to the local elongation (red curve in Figure 4c). In an analogous way, we determined the local elongations ,$ and the local contraction rate perpendicular to the stretching direction ,$ for all pairs of PDI molecules as well as the ensemble average for each time t (Figure 4f). The ensemble average reveals that the contraction 11 ACS Paragon Plus Environment
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perpendicular to the stretching direction is negligible. This is a consequence of the slit geometry, in which the film width (5 mm) is 50 times larger than the slit width (initially 95 µm), as shown in Figure 5a. Our data provide detailed information about the response of a set of single probe molecules in a drawn polymer melt. We obtain the temporal evolution of the orientation distributions as well as the local deformation parallel and perpendicular to the stretching direction. The temporal evolution of the orientation angle average and the temporal evolution of the local elongation , indicate that the reorientation of the probe molecules is proportional to the local deformation of their embedding matrix. This is the basis for our following model, which describes how the orientation distributions respond to the elongation of the polymer film.
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Figure 4. (a) Time evolution of the y-positions of the PDI molecules and (b) the distances ∆ykl between the PDI molecules k and l, parallel to the direction of global uniaxial elongation. (c) Local strain rate y,loc calculated from the slope of the ∆ykl distance curves shown in (b). The red curve represents the mean value at any given moment of time. (d) Global uniaxial elongation εG (black) and the integral εy,loc (red) of the mean local strain rate y,loc. (e) Arithmetic average of the in-plane orientation angles ϕ. Each value was averaged over 25 consecutive image frames. (f) Time evolution of the local contraction rate x,loc perpendicular to the direction of the global, uniaxial elongation.
Modelling. To establish a model for the orientation of dye molecules in a deformed polymer melt and to consider artefacts which arise, for example, from the numerical aperture of the microscopes objective, we followed Kratky’s work.47 The PDI dye molecules are modelled as rod-like objects embedded in a uniaxially elongated thin film (Figure 5). The optical transition moment is parallel to the rod axis and defines the diagonal of a small volume element with the dimensions b0, d0 and l0. Their ratio is determined by the initial orientation angles 5 and 75 of the rod. We assume an initially isotropic distribution of orientation angles, as shown in the spherical plot of Figure 5a. Upon a uniaxial elongation of the polymer film, the dimensions of the volume element change as indicated in Figure 5b. In particular, the width b0 of the volume element remains constant, since ,$ (%) is negligible. The length l0 increases by a factor of (, + 1), determined by the local elongation parallel to the stretching direction. We assume a volume conservation of the polymer film corresponding to a Poisson’s ratio 8 = 0.5. As a consequence, d0 decreases by a factor of (, + 1)/0. This assumption is corroborated by the observation of the area density of PDI molecules, which decreases with increasing elongation due 13 ACS Paragon Plus Environment
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to the thinning of the film. The polar coordinates of the diagonal of the deformed volume element correspond to the orientation (9 , 79 ) of the embedded rod (optical transition moment) in the elongated film. The exact relation between (5 , 75 ), , and (9 , 79 ) is given in the Supporting Information. The resulting distribution of the orientation angles for , = 1.3 is shown in the spherical plot in Figure 5b. The distributions of the orientation angles (5, 75 ) and (9 , 79 ) are shown in Figure S3.
Figure 5. Model for the change in orientation of PDI molecules in a uniaxially elongated thin film with conserved volume. The sketch (left and middle) shows an infinitely small volume element (white) of the polymer film (grey), with the diagonal corresponding to the direction of 14 ACS Paragon Plus Environment
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the transition moment of the PDI molecule. (a) For εy,loc = 0, an isotropic distribution of orientation angles φ0 and θ0 is assumed, as shown in the spherical plot on the right, where each red spot represents a pair of orientation angles φ0 and θ0. (b) Upon uniaxial elongation εy,loc in the y-direction, the volume element deforms as indicated, and the orientation angles φS and θS of its diagonal change accordingly. The spherical plot shows the resulting distribution of orientation angles for , = 1.3. The black arrows indicate the direction of the uniaxial elongation.
The measured distributions of the in-plane orientation angles are subject to imaging artefacts and limitations due to the finite signal-to-noise ratio.48 In particular, molecules with the transition moment oriented perpendicular to the film plane emit light preferentially perpendicular to the optical axis of our setup and cannot be detected against the background noise. Furthermore, molecules oriented perfectly parallel or perpendicular to the elongation direction experience a negligible torque and give no sufficient signal in the s-polarization channel or p-polarization channel, respectively. Due to noise and background corrections, the probability for observing an in-plane orientation angle close to 0° or 90° is very low (Figure 3). To take these effects into account, we simulated a sequence of images, starting with an initially isotropic distribution of orientation angles and calculating the response of each rod on the local elongation , (see Supporting Information for details). This image sequence was analysed using the same image processing algorithms as for the experimental data. We note that the model has no adjustable parameters. All input parameters, such as the local elongation as well as the optical image size on the detector and the noise level, are taken from the measured data.
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For comparison with the measured data, we integrated the resulting distributions over 68 frames. The simulated distributions are shown in Figure 3 (grey bars) and closely resemble the experimental data. From this, we conclude that our model of rod-like objects in a deformed continuum adequately reflects the average reorientation of single probe molecules in a drawn polymer melt. We note, however, that the reorientation trajectory of the individual molecules cannot be described with this model. A careful inspection of Movie M1 shows that some molecules do not change their orientation upon the elongation of the film. We attribute this to details of the molecular motion that cannot be captured with a continuum model.
Relaxation Behavior. We now turn to the stress relaxation period, which starts after the deformation period at t = 170 s. At this point of time, the deformation rate along the elongation direction and the rate perpendicular to it vanish within the time resolution of our experiment (0.5 s). During the 300 s of the stress relaxation period (Figure 3 b), we observe a decrease in the orientation angles parallel to the elongation direction, resulting in a small shift of the distribution maximum at ≈ 10°. This shift has only a small effect on the average in-plane orientation angle < > indicated by the vertical dashed lines. This small change in orientation angles on a timescale of 300 s agrees with extrapolations from temperature-dependent rotational diffusion measurements in non-deformed PMA films7 (Figure S7). In contrast, the relaxation time of the α process in PMA is 5 s at 3 K above TG (ref. 49, see also Figure S7).
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To address the slow reorientation, we studied the fluorescence polarization < = ( = − 9 )/( = − 9 ) on the single-molecule and on the ensemble level. The red curve in Figure 6a shows the normalized fluorescence polarization
