Several methods for controlling polymerizations have been mentioned before. In order to obtain defined materials it is important to determine whether the polymerization was conducted in a controlled fashion. The most important feature of controlled polymerizations is the possibility to make polymers with predefined molecular weights. For a successful polymerization, the molecular weight can be predicted from the conversion and the ratio of the catalyst, initiator or transfer agent to the monomer. The molecular weight and the conversion must be monitored during the polymerization in order to
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determine the controlled fashion of the reaction. By NMR-spectroscopy the conversion can be monitored and monomer ratios in case of copolymerizations can be monitored. In some cases it is even possible to determine the degree of polymerization by end group analysis.
Other techniques like IR-spectroscopy, which can be used for insitu monitoring, or gas chromatography can also be used to determine the conversion. SEC can be used to determine the molecular weight evolution by analyzing samples at different time intervals and kinetics of polymerization can be studied. The shape of the molecular weight distribution in SEC can be indicative of side-reactions. A broad distribution is the result of bad control and low- or high-molecular weight shoulders have their origin in unwanted transfer and termination reactions. For polymerizations with macroinitiators SEC is a reliable technique that can discern between the growth of a second block and the formation of homopolymers. After the conversion and the molecular weight are determined a linear relationship between both parameters must be observed with a slope which is proportional to ratio of the catalyst, initiator or transfer agent to the monomer, otherwise side reactions occurred and the control was lost.3
Complex polymer structures can be obtained by polymer analogous reactions of functionalized polymers. Here, the reactions of end and side groups have to be monitored.
For small molecules IR-spectroscopy in combination with NMR can be easily applied for this task. This combination can also be used to quantify the grafting of small molecule side chains to a polymer backbone.156 End groups on the other hand can be more difficult to characterize quantitatively due to the high dilution. MALDI-ToF can be used to identify end groups more accurately by the appearance of different peak series. The assessment of click conjugations of polymers and the formation of block/brush copolymers is often not straightforward. SEC can provide important information but is often misinterpreted. After the conjugation of two polymers a new copolymer should be obtained. In SEC a new distribution at lower elution values can be observed and also unreacted fractions of the precursor polymers. Low/high molecular weight shoulders or multimodal distributions are signs of an incomplete reaction or unwanted side reactions. This is only true if both polymers have truly narrow distributions. Barner-Kowollik showed that the quantitative
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conjugation of polymers with broad distributions can lead to products with bimodal distributions.157
2.2 X-ray Diffraction
Structure and structure formation has great influence on the electronical properties of organic semiconductors and the performance of devices made from these materials.158,159 A very versatile and reliable characterization technique for polymers is X-ray scattering.160 In contrast to microscopy techniques, which only give information about a small area at a surface (atomic force microscopy - AFM) or thin cut of a material (transmission electron microscopy - TEM), X-ray scattering can measure average bulk properties over a larger volume.
X-rays interact with the electrons in a material. The excited electrons start to oscillate and scatter X-rays. If this scattering of X-rays occurs at multiple positions in an ordered lattice, the scattered wave will form constructive and destructive interferences depending on the distance of the lattice planes d, which results in distinct diffraction patterns. The Bragg equation161 gives the condition for constructive interference (Fig. 11 a):
𝑛𝜆 = 2𝑑𝑠𝑖𝑛𝜃 (4) where = 0.154 nm-1 (CuKα radiation) is the wave length of the X-ray and is the angle of incidence.
Depending on the incidence angle of the X-rays θ, different size ranges can be analyzed. In the wide-angle X-ray scattering range (WAXS) sizes smaller than 5 nm can be analyzed (Fig. 11 b). Therefore, the crystalline lattice and crystal sizes and π-π distances can be analyzed.162 Temperature-dependent measurements in this region allow the observation of phase transitions between crystalline phases, meso-phases and amorphous melts. At smaller angles (SAXS), structures with a size of up to 100 nm can be measured.
This is especially useful to detect microphase separation in BCPs and the lamellar long period in crystallites 163
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The characterization of thin films is possible by grazing incidence X-ray scattering at small (GISAXS) as well as wide angles (GIWAXS) and allows for the characterization of inner morphology of the film.164 By GISAXS/GIWAXS it is possible to measure the orientation of the nanostructure and crystals within the film. This information is crucial for understanding the performance of these polymers in organic electronics. The crystal orientation, for example, has a profound influence on the charge carrier transport in a device due to the high anisotropy of the charge carrier mobility in polymeric semiconductors.165 GISAXS/GIWAXS has become an important method to understand the material properties of organic semiconductors in thin films.166,167 Only the necessity of a strong X-ray source such as a synchrotron due to the small measured volume and the low scattering contrast of organic materials prevents even wider application.166
Fig. 11 a) Scheme of the diffraction of rays at a lattice. b) Accessible length scale in SAXS and WAXS. The X-ray scattering of a microphase-separated diblock copolymer with a crystalline block is shown. In the SAXS region the microphase-separated domain can be observed. In the WAXS region the lamellar distance (a ~ 1.9 nm) and the π-π-stacking of the crystalline block are visible.
b) a)
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2.3 Charge Transport in Organic Semiconductors
The performance of devices incorporating organic semiconductors, such as organic photovoltaics (OPV), organic light emitting diodes (OLEDs) or organic field-effect transistors (OFETs), is coupled mainly to the efficiency of the charge transport. Organic semiconductors are disordered materials and, therefore, relatively low charge carrier mobilities are obtained in comparison to inorganic semiconductors.168 Several techniques are available for measuring this property. Two of them, space-charge limited current (SCLC) measurements and organic field-effect transistors (OFETs), were used in this thesis. Both methods will be discussed briefly.
After the generation of charge carriers, either electrons or holes, their movement is either driven by an electric field F or a gradient of the charge concentration. The charge carrier mobility µ is the motion of the charge carriers and is defined as the charge’s effective drift velocity ν per unit electric field:169
µ = 𝜈𝐹−1 (5)
The drift velocity is often not proportional to the electric field leading to a field dependence of the mobility µ. By Ohm’s law the current j is given by the materials conductivity σc and the electrical field as j = σcF. The current can also be described by j = enν = enµF (n is the number of charge carriers and e is the elementary charge) and we can therefore, relate the mobility and conductivity by:
𝜎𝑐 = 𝑒𝑛µ (6) Organic semiconductors are predominantly disordered materials (amorphous glasses, or semi-crystalline materials). In contrast to inorganic semiconductors, where band-transport can be observed169, the transport in organic semiconductors is usually described by disorder-controlled transport or hopping transport. The disorder in form of chemical or structural defects is the reason for localized states in the organic semiconductor and the transport of charges can only occur by a non-coherent transfer of electrons. This hopping process is thermally activated and the mobility µ becomes depended on the temperature T and the electrical field F. Additionally, in each method, the charge carrier concentration varies and the charge density influences the charge carrier mobility.170 Therefore, the mobility values determined by two different methods can vary orders of magnitude.
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Additional parameters that influence the measured charge carrier mobility are the preferential orientation of the polymer chains depending on molecular weight, processing conditions and nature of substrate.