Polymorphic states and phase transitions in a comb-like polymer having a rigid polyester backbone and flexible side chains

Polymorphic states and phase transitions in a comb-like polymer having a rigid polyester backbone and flexible side chains

Thermochimica Acta 677 (2019) 162–168 Contents lists available at ScienceDirect Thermochimica Acta journal homepage: www.elsevier.com/locate/tca Po...

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Thermochimica Acta 677 (2019) 162–168

Contents lists available at ScienceDirect

Thermochimica Acta journal homepage: www.elsevier.com/locate/tca

Polymorphic states and phase transitions in a comb-like polymer having a rigid polyester backbone and flexible side chains Varun Dankea,b, Gaurav Guptaa,b, Heiko Hutha, Jürgen E.K. Schawec, Mario Beinera,b,

T



a

Fraunhofer Institute for Microstructure of Materials and Systems IMWS, Walter-Hülse-Straße 1, D-06120 Halle (Saale), Germany Faculty of Natural Sciences II, Martin-Luther-University Halle-Wittenberg, Heinrich-Damerow-Straße 4, D-06120 Halle (Saale), Germany c Mettler-Toledo GmbH, Heuwinkelstrasse 3, CH-8606 Nänikon, Switzerland b

ARTICLE INFO

ABSTRACT

Dedicated to Prof. Dr. Christoph Schick on the occasion of his 65th birthday.

Structure formation in an alkoxylated polyester having rigid backbone and flexible side chains composed of 10 alkyl carbons per side chain is studied using X-ray diffraction, conventional DSC and flash DSC techniques. Two crystalline states-modification B and modification A are observed with their occurrence depending on the thermal treatment. Additionally, a liquid crystalline phase is also detected above the melting temperature of modification A. While modification B is the thermodynamically preferred phase at low temperatures consisting of crystalline side chains, modification A is observed on heating above 120 °C and shows a disordered packing of the side chains. Rapid cooling using Fast Differential Scanning Calorimetry (FDSC) yields a liquid crystalline state wherein a long range ordered layered morphology exists, however, the π − π stacking of the backbones is absent. The molecular orientation of backbones under the influence of shear fields as well as on a glass fiber surface is also studied. Both modifications A and B show backbone orientation along the shear fields in an extruded sample while a preferential edge-on orientation is inferred on the glass fiber surface.

Keywords: Comb-like polymers Phase transition Molecular orientation

1. Introduction Comb-like polymers having a rigid backbone and flexible alkyl side chains often exhibit a layered arrangement on length scales of 1–3 nm [1–5]. The side chains typically self-assemble to form alkyl nano-domains resulting in long range ordered crystalline or liquid crystalline states [5,6]. While the side chains primarily improve processability [7], the ring-like sub-units in the backbone impart functional properties to the polymer having potential applications in the area of light weight composites [7], organic photovoltaics [8] and electrolyte fuel cells [9]. The functional properties of such materials often depend upon the crystalline packing of the rigid backbone in the form of π − π stacking which may in turn also be influenced by packing behavior of the side chains [10,11]. Side chain packing is known to depend upon a number of factors such as thermal treatment [12–14], backbone constitution [5], molecular weight [15,16], side chain position [17] and length [18,19]. Although both crystalline and amorphous packings of the side chains are possible, comb-like polymers predominantly exhibit long range ordered layered structures as seen in poly(3-alkyl thiophenes) (P3ATs) [20], poly(1,4-phenylene-2,5-n-dialkyloxy terephthalates) (PPAOTs) [10], alkoxylated polyimides [17] and poly(2,5-dialkyloxy1,4-phenylene vinylene) (AOPPV) [21]. The individual packing



tendencies of the components-rigid backbone and flexible side chains result in a competing effect giving rise to structural polymorphs having different thermodynamic stability [10]. Multiple phase transitions are commonly observed in alkoxylated polyesters upon thermal treatment highlighting the complex phase behavior of such systems [22–24]. Knowledge about these phase transitions could be beneficial to develop a better understanding of the factors affecting overall packing in comblike polymers, thereby allowing to fine tune functional properties. Apart from the native molecular packing, it is well-known that molecular orientation is an important factor influencing anisotropic properties. Conventional processing techniques such as extrusion [25], injection molding [26], and electrospinning [27] are known to induce orientation due to the presence of strong shear fields. Overall crystallinity [28], optical properties [29], charge transport [30] and mechanical properties [31] strongly depend on molecular orientation. Previous works on oriented PPAOT samples [32,33] have attempted to understand the influence of molecular orientation on mechanical properties in different structural polymorphs. Depending on the backbone constitution and side chain packing, shear oriented PPDOT (poly (1,4-phenylene 2,5-n-didecyloxy terephthalate)) and DOPPV (poly(2,5didecloxy-1,4-phenylene vinylene)) fibers show different in-plane orientations of the backbone along or perpendicular to the shear fields

Corresponding author at: Fraunhofer Institute for Microstructure of Materials and Systems IMWS, Walter-Hülse-Straße 1, D-06120 Halle (Saale), Germany. E-mail address: [email protected] (M. Beiner).

https://doi.org/10.1016/j.tca.2019.02.003 Received 30 November 2018; Received in revised form 4 February 2019; Accepted 5 February 2019 0040-6031/ © 2019 Elsevier B.V. All rights reserved.

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[34]. On the other hand, effects such as epitaxy [35], as well as high temperature rubbing and friction transfer [36], are also used to control molecular orientation in supported thin films on surfaces. Both “edgeon” and “flat-on” situations can be achieved depending on the substrate and the technology used [37,38] which may lead to different charge carrying properties. Investigations on molecular orientation of comblike polymers on surfaces such as endless fibers can also be used to develop high performance light weight composites. Moreover, mechanical contact between adjacent fibers can be improved by fine tuning side chain crystallization. In this work, we focus on different phases and their thermodynamic stability as well as temperature-dependent phase transitions in poly (1,4-phenylene-2,5-n-didecyloxy terephthalate) [PPDOT] using X-ray diffraction and differential scanning calorimetry. Additionally, Flash DSC is employed to improve the understanding of high temperature phase transitions and their significance on the overall packing. Extruded samples are used as a means to study effect of shear fields on molecular orientation as well as to elucidate the crystal structure. A PPDOT coated long glass fiber is prepared by a simple fiber pull-out method to study the molecular orientation on the fiber surface.

performed at room temperature 2 nm−1 ≤ q ≤ 29 nm−1.

3. Results and discussion 3.1. Phases in PPDOT Modifications B and A. Fig. 2(a) shows the temperature dependent Bragg spacings dhkl during the first heating of the pristine sample. Within the temperature range 60–110 °C the calculated d100 values increase from 13.6 Å to 19 Å. This transition can also be clearly seen in B the X-ray diffractogram Fig. 2(c). The intensity of the peak q100 seen at −1 reduces whereas an almost simultaneous increase of the q ≈ 4.6 nm B A q100 is seen within this temperature range. Above 120 °C the q100 peak disappears. The increase in interlamellar spacing between two backbone chains along the alkyl side chain or d100 has been attributed to a solid-solid transition from modification B to modification A. In addition, interesting changes also occur in the d020 spacing which corresponds to the distance between two backbones along the π − π stacking B direction. The q020 seen at q ≈ 14.2 nm−1 shifts to q ≈ 17.2 nm−1 above 110 °C as seen in Fig. 2(c). The corresponding Bragg spacing shows a decrease from 4.4 Å to 3.6 Å (Fig. 2(a)). It has been reported that the side chains in modification B tend to pack densely in a crystalline manner while in modification A they are disordered [10]. This was inferred on the basis of a complete crystallographic analysis and estimation of the volume occupied by CH2 unit VCH2 in the side chain. This solid-solid transition is also indicated in the DSC heating scan (see Fig. 2(b)). An endothermic bimodal peak is seen in the temperature range 50–120 °C which also indicates a solid-solid phase transition. The side chains which are originally crystalline in modification B undergo melting within this temperature range forming modification A. This change in side chain packing not only causes differences in the d100 but also along the π − π stacking direction. The latter effect has been interpreted as a consequence of constraints on the main chains introduced by crystalline methylene sequences present in case of modification B, which are absent in modification A [10]. It is therefore assumed that packing of the side chains strongly influences the crystalline packing of the backbones. Although the functional properties of comb-like polymers having a rigid backbone are primarily determined on the basis of the packing states of the backbones, the fact that side chain packing behavior plays a pivotal role in the backbone packing cannot be ignored. These competing effects and interrelations are of great significance and determine the overall packing behavior of the system. A Another phase transition is seen upon heating above 160 °C. The q100 reflection shifts marginally to smaller scattering vectors (see Fig. 2(d))

Temperature-dependent XRD measurements were performed in reflection mode using an Empyrean diffractometer (PANalytical) equipped with the temperature chamber TTK 450 (Anton Paar). The heating and cooling rate was kept at 10 K/min. The emitted CuKα radiation is parallelized and monochromatized using a parallel beam mirror (λ = 1.54 Å). The scattered beam passes a parallel plate collimator (0.27°) and is detected by a Pixel 3D detector with 19 channels of 0.055 μm size combined to be used as a receiving slit. The scan range with the magnitude of scattering vector q = 4π sin θ/λ was 1.5 nm−1 ≤ q ≤ 20.0 nm−1, with a counting time of 1 s per step. Further 2D X-ray diffraction experiments on the oriented samples were performed in transmission mode using a SAXSLAB laboratory setup (Retro-F) equipped with an AXO microfocus X-ray source with an AXO multilayer X-ray optic (ASTIX) as monochromator for Cu Kα radiation (λ = 0.154 nm). A DECTRIS PILATUS3 R 300 K detector was used to record the 2D diffraction patterns. As sample holders two millimeter thick aluminum discs with a central hole having a diameter of 1 mm were used. A twin slit system was used for the measurements with slits of diameter 0.9 mm and 0.4 mm. The measurements were

C 10H 21 O O

range

Extruded fibers were prepared by ram extrusion with a capillary die at 120 °C with a shear rate of 600 s−1 using the equipment described in Ref. [34]. Glass fibers were coated by pulling out a single fiber of diameter 150 μm obtained from Hilgenberg GmbH. through the polymer melt at a rate of 10 mm/min.

2.2. X-ray diffraction

C

the

2.4. Sample preparation

The investigated poly (1,4-phenylene-2,5-n-dialkyloxy terephthalate) with n = 10 carbons in the alkyl side chains belonging to the class of comb-like polymer having rigid backbone was synthesized as described in ref [6]. The repeating unit of the polymer is shown in Fig. 1

C

in

The DSC measurements on PPDOT were performed using a power compensated Perkin-Elmer DSC 7. The samples were cooled to −60 °C prior to measuring. The heating and cooling rates were 10 K/min. Samples with a mass between 5 and 8 mg were used. Fast DSC measurements were performed using the Mettler-Toledo Flash DSC 1. Before the measurements, a sample of PPDOT was molten onto the sensor to increase the thermal contact. The sample mass is estimated to be about 20 ng from the sample geometry and an approximate density of 71 g cm−3. The sample was cooled down at various rates ranging from 10 K/s to 20,000 K/s followed by heating at 1000 K/s.

2.1. Materials

O

vacuum

2.3. Differential scanning calorimetry

2. Experimental

O

in

O

O C10H21 Fig. 1. Chemical structure of the investigated PPDOT polymer. 163

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(a)

1

0 3

(c)

d100

d020 104.9 °C 174.1 °C

221.3 °C

80 120 160 200 Temperature (°C)

220

110

210

100

200

90

5

80

190 180

70

170

60

qA100 qB100 40

230

130 120

2 54.2 °C

1

T/°C

T/°C

d001

(b)

A-LC-iso

(d)

B-A

Intensity (a.u.)

Heat Capacity (J/gK)

dhkl (nm)

2

10

q (nm-1)

15

qA100 q A 001 q200 5

qA020 10

q (nm-1)

160

15

Fig. 2. (a) Temperature-dependent Bragg spacings dhkl as a function of temperature during the first heating of the pristine sample. Open symbols denote the Bragg spacings for modification B while closed symbols correspond to the Bragg spacings for modification A. (b) The corresponding DSC heating scan shows the different phase transitions. (c) Temperature-dependent XRD plots in the temperature window within which the solid-solid transition mod B-mod A occurs while (d) shows the temperature-dependent XRD plots showing the transition from modification A to liquid crystalline state to the isotropic melt state.

leading to a reduction in the calculated d100 spacings from 1.9 nm to A 1.78 (see Fig. 2(a)). Additionally, the q020 reflection disappears above 170 °C suggesting that the π-π stacking between the backbone rings is A lost at this stage. However, the sharp q100 reflection along with the A A higher orders q200 and q300 are still observed indicating that the polymer at this stage exhibits a long-range ordered layered structure. The backbones show no π − π interactions. In other words, the polymer no longer exhibits a truly crystalline state but a semi-ordered liquid-crystalline state. Such a liquid crystalline state has also been observed by Damman et al. in similar systems having a dodeclyoxy side chains (and was termed as a ‘layered mesophase’) [39]. Such a phase was also detected by Rodriguez-Parada et al. within the same temperature range in similar polymers having the same backbone but alkoxylated side chains attached at different positions (either hydroquinone or terephthalic acid moiety) [24] pointing to the fact that the associated transition is a backbone related effect. In some cases, the term nematic biaxial phase has been used to describe this thermotropic liquid crystalline phase [2]. Heating above 220 °C leads to transition to the isotropic state which is A indicated by the disappearance of the q100 reflection. A broad pre-peak or a halo-like feature is seen in the range 2 nm−1 ≤ q ≤ 5 nm−1 in addition to the conventional halo typically seen at wide angles. At this point the polymer is most likely in a short range ordered nanophaseseparated melt state [40]. Such a two halo feature of the diffraction pattern has also been noted for tetra substituted comb-like polyamides and polyesters [41]. The side chains remaining in the plane of the backbone and not randomly oriented about the backbone was reported to be probably reason for this feature. The modification A-liquid crystalline (A-LC) and liquid crystalline-isotropic (LC-iso) transitions are also seen the DSC heating curves in the form of two endothermic peaks at 174.1 °C and 221.3 °C respectively (see Fig. 2(b)). Further details about these high temperature transitions are considered in the last section. Molecular orientation in extruded fibers. In order to serve the dual purpose of understanding the effect of shear fields on lamellar morphology in PPDOT as well as to perform a complete crystallographic analysis of both modifications B and A, an oriented sample was prepared with the help of a home-made ram extruder as explained in Ref. [34]. Fig. 3(a) shows the 2D WAXD pattern of the extruded PPDOT fiber. The primary observation is that while lamellar morphology is preserved, reflections corresponding to both modification B and modification A are present, better seen in the integrated plot (see Fig. 3(b)). This is a bit surprising considering the processing temperature is above

the thermal stability range of modification B. It is however important to note that modification A is found to slowly transform back to modification B over time at room temperature leading to the inference that modification B is most likely the thermodynamically more stable polymorph at room temperature. Therefore, the modification B seen here is most probably the fraction which slowly converted back from modification A upon storage at ambient conditions. Secondly, both the B A and q100 corresponding to interlamellar spacing in reflections q100 modification A and B respectively show anisotropic intensity distribution with intensity maxima at the equatorial positions. Fig. 3(c) and (d) shows the anisotropic intensity distribution as a function of the azimuthal angle confirming that the (100) planes in modifications A and B show similar orientation with their surface normals perpendicular to B A the fiber axis. Additionally, the q020 and q020 also show intensity maxima at the equatorial positions implying that the (020) planes in both modification A and B have their surface normals perpendicular to the fiber axis. On the contrary, the (001) reflection shows intensity maxima at the meridional position indicating that the surface normals are preferentially oriented along the fiber axis. Based on the azimuthal positions of the intensity maxima of the (100), (001) and (020) reflections in both modification A and modification B, an orthorhombic unit cell was inferred. It is also clear that the polymer backbones tend to orient along the fiber axis and hence along the shear field. Moreover, it is also interesting to note that during the transformation from modification A to modification B at ambient conditions after shear treatment, the orientation was preserved. In other words, the solid-solid transition has almost a negligible effect on the shear induced orientation. It is a well known fact that orientation of molecular crystals has a strong impact on material properties such as optical, mechanical and charge transport which are highly application relevant. Phase transitions which allow the orientation to remain undisturbed could prove beneficial for improving properties by simple post processing operations. Molecular orientation on the glass fiber surface. In order to investigate the structure formation process on surfaces, samples were prepared by simply pulling out a glass fiber at a fixed speed through the polymer melt. A thin film of the polymer on the glass surface was obtained which was further studied using 2D X-ray diffraction in transmission. Fig. 4(a) and (b) show the 2D XRD pattern in the wide angle and the intermediate angle regime respectively. Reflections characteristic to both modification A and B are observed although the processing temperature in this case was 230 °C, better seen in (Fig. 5 (c)). Similar to the previous case, the polymer originally formed modification A on 164

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Fig. 3. (a) 2D WAXD pattern for an oriented PPDOT fiber while (b) shows the integrated pattern. The fiber axis is vertical in the plane of the detector. Parts (c) and B A (d) show the intensity distribution over the azimuthal angle for the q100 and q100 reflection respectively. (e) Schematic of the orientated PPDOT unit cells within the extruded fiber for both modifications A and B.

cooling and subsequently partially converted to modification B upon storage. A closer inspection of the intensity distribution in the 2D B A WAXD pattern, reveals that both q100 and q100 show anisotropic intensity distribution with intensity maxima at the equatorial position. The variation of the intensity as a function of the azimuthal angle is well seen in Fig. 5(d) and (e) for modifications A and B, respectively. Interestingly, the (001) reflection shows no preferential orientation. Moreover, it is also hard to separate the contributions from the glass fiber and the signal from the π − π reflections in the wide angle range. Irrespective to that, it is clear from the 2D XRD pattern that (100) planes in modifications A and B are oriented in such a way that their surface normals tend to orient perpendicular to the glass surface. On the other hand, there is no preferential in-plane orientation of the backbones inferred from the diffraction pattern. In other words, the backbones are oriented in an edge-on manner with a random in-plane orientation on the surface. To have such preferential orientations on endless glass fibers offers potentially, the possibility to improve the mechanical properties of fiber reinforced composites. Conventional thermoplastics could be replaced by high performance comb-like polymers as a matrix material which offer a good compromise between processability and mechanical strength for use in composites. It can be imagined that side chain crystallization in comb-like polymers coated on to a long glass fiber could promote better correlation between neighboring glass fibers, thereby improving the mechanical properties not only in the fiber

direction but also perpendicular to the fiber direction. Enhancing the properties of semi-finished composites or ’pre-pegs’ such as uni-directional tapes which can later be used for different high performance applications could be possible by using such simple processing methods and material systems. In addition to this, solid-solid transitions on the surface may further offer the possibility to tweak the crystal structure by simple downstream thermal treatments. 3.2. The liquid crystalline state The two high temperature phase transitions isotropic-liquid crystalline phase and the liquid crystalline phase-modification A can be followed while cooling the PPDOT sample from the melt. The first apA pearance of theq100 reflection is seen at T = 190 °C (see Fig. 5(c)) corresponding to a d100 spacing of 1.8 nm (see Fig. 5(a)) characteristic of the inter-lamellar spacing in the liquid crystalline state. The observations from X-ray diffraction are complimented by an exothermic transition seen in the DSC curve with peak temperature 185.9 °C (see Fig. 5(b)) indicating the isotropic phase-liquid crystalline phase tranA A sition. On further cooling, theq100 and q001 appear showing that the polymer undergoes a transition to the crystalline modification A from the liquid crystalline state. No additional phase transitions are seen during further cooling. In other words, modification B is not formed during cooling under the given experimental conditions. This is probably due to the fact that the individual sub-units, namely rigid 165

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Fig. 4. (a) and (b) show the 2D X-ray diffaction pattern for a glass fiber having a thin PPDOT coating in the wide angle and intermediate angle regime respectively while (c) shows the integrated pattern. The inset in (c) shows a light microscope image of the coated glass fibers. (d) and (e) show the intensity distribution as a B A function of the azimuthal angle for the q100 and q100 reflection respectively. The coating process together with the orientation of the chains on the glass fiber surface is shown in (f).

backbones and alkyl side chains retain their individual thermodynamic phase behavior and packing tendency. During cooling, the rigid backbones having a higher melting temperature tend to pack first forming π − π stacks. At these high temperatures, there is almost no driving force for the side chains to crystallize. At lower temperatures, the crystallization of the side chains is sterically hindered due to the formed π − π stacks, thereby preventing the formation of modification B. The formation of modification B in samples stored under ambient conditions

could be mainly due to the free energy difference between the amorphous and crystalline states in the alkyl side chains acting as a driving force for side chain crystallization. Flash DSC measurements were used to probe the two high temperature transitions modification A-liquid crystalline phase and liquid crystalline phase-isotropic phase. The focus was on understanding the influence of different cooling rates on structure formation in such nanolayered systems similar to that what has been done for several other

Fig. 5. (a) Temperature-dependent Bragg spacings dhkl as a function of temperature during the first cooling of the sample and (b) corresponding conventional DSC cooling scan showing the different phase transitions.(c) Temperature-dependent XRD plots in the temperature window within which the transition from isotropic state-liquid crystalline state-modification A occurs. The inset shows a schematic for the liquid crystalline state. (d) Heating curves in a Flash DSC after cooling at different rates. Two endothermic transitions A-LC and LC-iso are seen. The enthalpies are plotted as a function of the cooling rate in (e). 166

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polymers showing different polymorphs earlier [42,43]. Fig. 5(d) shows the heating scans in a Flash DSC at 1000 K/s after cooling at different rates. Note that fast heating rates discourage reorganization effects thereby allowing one to get information about the actual structure formed during cooling. The heating scans clearly show for samples cooled at different rates two transitions. The one in the range 150–175 °C corresponds to modification A-liquid crystalline phase transition while the other in the range 175–220 °C corresponds to the liquid crystalline phase-isotropic phase transition. As the cooling rate is increased, modification A-liquid crystalline phase transition becomes less prominent and almost disappears at 20,000 K/s whereas the liquid crystalline phase-isotropic phase transition seems to be present in all the curves. This is evident on looking at the enthalpy of both the phase transitions as a function of the cooling rate (e). While the modification A-liquid crystalline phase transition shows a consistent decrease in enthalpy with the cooling rate, the liquid crystalline phase-isotropic phase transition enthalpy is basically cooling rate independent. This suggests that during cooling the polymer undergoes the transformation from the isotropic to the liquid crystalline state and this process is fairly independent of the cooling rate. On the other hand, the transformation to modification A from the liquid crystalline state is hindered to a large extent at high cooling rates. The backbones remain in this state, do not show π − π stacking and most likely remain staggered even at lower temperature where the crystalline modifications A and B are thermodynamically preferred. Such a quenched liquid crystalline phase was also previously reported for rapidly cooled samples of a polymer having the same backbone and an alkoxylated side chain containing twelve carbon atoms [39]. However, the polymer still exhibits a layered structure which is most likely long range ordered. Although structural inhomogeneities may exist in the form of partially ordered backbones, the system seems to have a strong tendency to form layered structures. Comb-like polymers such as regio random (poly-3-alkyl thiophenes) and higher poly (n-alkyl methacrylates) despite having disordered backbones have also been known to show nanophase-separated long range ordered layered structures [44]. It is therefore more likely that phase separation on the nano-scale is a relatively fast process whereas the crystalline packing of the sub-units within their respective domains requires more time. The rigid backbones due to fast cooling, although packed in layers, do not get enough time to pack on their respective lattice to form π − π stacking arrangement. This situation in a certain sense can be compared with that of the A-B transition during cooling. During cooling in a conventional DSC, the backbones pack first and hinder the packing of the alkyl groups in the side chain. However, storing at room temperature conditions for a prolonged amount of time promotes side chain crystallization forming modification B. It seems therefore likely that the driving force for crystallization of the alkyl groups wins at the end affecting the backbone packing. Similarly it would be interesting to follow structural changes occurring in a stored sample previously quenched in to liquid crystalline phase. In which temperature range the polymer slowly converts to modification A or shows a direct transformation to modification B due to side chain crystallization would be an intriguing question to answer.

field. In case of PPDOT coated glass fibers, a predominantly edge-on orientation of the rings on the glass surface is observed. Interestingly, the solid-solid transition in both the extruded fiber and on the glass surface does not affect the molecular orientation. Acknowledgements The authors thank Prof. Dr. Christoph Schick for a longstanding and very fruitful collaboration in the field of innovative calorimetric methods, polymer crystallization and glass transition. Over the years he contributed with many helpful discussions, constructive comments and advice to the success of our research. We acknowledge support by Dr. Nasir Mahmood during the preparation of oriented PPDOT samples and coated glass fibres as well as Demet Acargil for supporting the DSC measurements. Funding by the Deutsche Forschungsgemeinschaft within the framework of Sonderforschungsbereich SFB/TRR 102 ‘Polymers under multiple constraints’ (Project B14) is highly appreciated. References [1] R. Duran, M. 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