Diffusion Enhancement in a Periodic Potential under High-Frequency Space-Dependent Forcing

We study the long-time behavior of underdamped Brownian particle moving through a viscous medium and in a systematic potential, when it is subjected to a space-dependent high-frequency periodic force. When the frequency is very large, much larger than all other relevant system-frequencies, there is a Kapitsa time-window wherein the effect of frequency dependent forcing can be replaced by a static effective potential. Our new analysis includes the case when the forcing, in addition to being frequency-dependent, is space-dependent as well. The results of the Kapitsa analysis then lead to additional contributions to the effective potential. These are applied to the numerical calculation of the diffusion coefficient (D) for a Brownian particle moving in a periodic potential. Presented are numerical results, which are in excellent agreement with theoretical predictions and which indicate a significant enhancement of D due to the space-dependent forcing terms. In addition we study the transport property (current) of underdamped Brownian particles in a ratchet potential.Comment: RevTex 6 pages, 5 figure

Echtzeit in-situ Untersuchung der Strukturentwicklung während der Filmbildung von Polymer-Fulleren Schichten für den Bulk-Heteroübergang

This thesis was devoted to investigate the real-time structural evolution of a polymer/fullerene blend from solution using in-situ x-ray diffraction. In this thesis, the structural evolution of the blend of electron-donor semiconducting polymer poly-(3-hexylthiophene) (P3HT) with the electron-acceptor semiconducting fullerene-derivative [6,6]-phenyl- C61-butyric-acid-methyl-ester (PCBM) in a solution in solvent 1,2-dichlorobenzene (DCB) during solvent drying has been studied in-situ using x-ray scattering. The effect that processing parameters play on the nanostructural evolution of the P3HT:PCBM blend is largely unknown. Real-time x-ray scattering study of P3HT:PCBM blends during drying gives novel insight into the crystallisation and the associated evolution of the elastic properties of the blend film during the film formation. The blend microstructure has been shown to emerge from smectic liquid crystal phase to solid phase as the solvent evaporates. The bulk modulus and the bending rigidity modulus of the blend film was calculated at different drying times using diffuse x-ray scattering analysis. This enabled for the first time direct evaluation of the material properties of the blend film as it was drying. Drying temperature has been seen to play a very important effect on the structural evolution of doctor-bladed P3HT:PCBM blends in the transition from wet to solid blend film. Drying the P3HT:PCBM active layer at a lower temperature of 10°C was seen to lead to a good P3HT interchain pi-pi stacking, broader orientational distribution of P3HT enabled by the slow crystallization kinetics and a restricted phase separation of P3HT and PCBM due to lower molecular mobility giving rise to better nanomorphology with finer interpenetrated network. It had been previously observed that lower drying temperature during processing of the photoactive blend created better performing solar cells; however the nanomorphological and nanostructural reason behind this empirical finding was not known. Based on the study carried out in this thesis, it can be proposed that lowering the substrate temperature during coating and drying is a simple route for optimization of device efficiency in doctor-bladed solar cells. The composition of P3HT:PCBM blend has been observed to be vital for good solar cell performance. The structural evolution of P3HT: PCBM blend film has been observed to depend on the blend composition ratio. The work in this thesis shows that the mosaicity of P3HT decreases with increasing loading of PCBM in the P3HT: PCBM blend suggesting that the interlayer ordering of P3HT improves with higher PCBM content in the blend film. However, the interchain pi-pi stacking of P3HT deteriorates with increased loading of PCBM. In the P3HT:PCBM blend film with high PCBM content, the formation of a complex P3HT-PCBM structure was observed for the first time. All the above investigations conducted during this thesis work exhibited delicate ordering of pi-pi interchain stacking in P3HT along the substrate that depends on drying temperature, composition ratio of P3HT:PCBM blend and the nature of solvent including additives in the solvent used to process the blend. On the other hand, structural ordering of P3HT along [100] direction, which is normal to the substrate surface, is found to be quite resilient. It forms in the early part of drying and improves with higher temperature processing and when P3HT phase segregates from PCBM in the P3HT:PCBM blend. However, this phase segregation of P3HT from PCBM deteriorates the nanophase mixing of their blend and hence photovoltaic efficiency. The resilience of P3HT out-of-plane ordering along [100] was studied here following concepts used in the diffuse scattering study of liquid crystalline phases. The results obtained in this thesis work clearly show that out-of-plane ordering of P3HT along [100] forms first in these films and in-plane interchain π-π P3HT ordering do not form in the initial phase of drying and P3HT:PCBM blend films behave like a liquid crystalline film having long range order in the out-of-plane direction without any ordering in the in-plane direction. In-plane P3HT interchain pi-pi ordering forms in the later part of drying exhibiting emergence of P3HT (020) peak only if blend ratio and processing temperature are proper. It has also been found here that nanophase mixing of P3HT and PCBM exhibiting higher mosaicity in P3HT (100) peaks and sharper in--plane P3HT (020) peaks provide the red-shift of the solid-state absorption band having vibronic side bands related to P3HT pi-pi interchain interaction that results in more efficient solar cell performance.In dieser Dissertation wurde die Nanomorphologie des Stoffsystems P3HT und PCBM mit einem für dieses System üblichen Lösungsmittel 1,2-Dichlorbenzol (DCB) während des Trocknungsvorgangs in-situ mittels Röntgenstreuung untersucht. Echtzeit Untersuchungen mittels Röntgenbeugung an P3HT:PCBM Schichten während der Trocknung dünner Schichten lieferten neuartige Einblicke in die Kristallisation und der damit verbundenen elastischen Eigenschaften des Films während der Film Formation. Die Mikrostruktur des Gemisches durchläuft einen flüssig kristallinen, smektischen Zustand während der Trocknung. Das Kompressionsmodul und die Biegesteifigkeit des Films wurden für verschiedene Zeitpunkte des Trocknungsvorgangs aus der Analyse diffuser Röntgenstreuung bestimmt. Dies ermöglichte erstmalig die direkte Bestimmung der Materialeigenschaften des Gemisches während der Trocknung. Diese Entdeckung eröffnet Möglichkeiten ein mikroskopisches Verständnis der nanoskaligen Anordnung von Polymer/Fulleren Schichten in "bulk-heterojunction" Solarzellen zu schaffen. In dem Zusammenhang wurde der Einfluss der Phasengleichgewichte und des Trocknungsverhaltens auf die Selbstanordnung untersucht, was eine Schlüsselrolle in der Kontrolle der nanoskaligen Struktur optimierter Solarzellen einnimmt. In all den im Rahmen dieser Dissertation durchgeführten Arbeiten, zeigte sich eine sehr sensible pi-pi Stapelung zwischen den P3HT Ketten entlang des Substrates. Diese ist von der Trocknungstemperatur, dem Mischungsverhältnis von P3HT und PCBM und der Art des verwendeten Lösungsmittels und der zusätzlichen Verwendung von Additiven abhängig. Andererseits ist die Anordnung der P3HT Ketten in [100] Richtung, senkrecht zur Substrat Oberfläche, vergleichsweise unbeeinflusst von den genannten Einflüssen. Die Kristallinität in diese Richtung bildet sich bereits in einer frühen Phase des Trocknungsprozesses aus und ist bei höheren Trocknungstemperaturen stärker ausgeprägt. Auch die Phasentrennung von P3HT und PCBM in deren Mischung begünstigt die Kristallinität dieser Richtung. Die Segregation des P3HT von PCBM bewirkt bei einer zu groβskaligen Phasenseparation einen Verlust der nanoskaligen Mischung und damit eine Verringerung des Wirkungsgrades der Solarzelle. Die Elastizität in [100] Richtung des P3HT senkrecht zum Substrat wurde hier nach den Konzepten diffuser Streuung flüssig kristalliner Phasen untersucht. Die Ergebnisse dieser Arbeit zeigen deutlich, dass während der Filmtrocknung die P3HT Kristallinität in [100] Richtung senkrecht zum Substrat zuerst gebildet wird, gefolgt von der zu einem späteren Zeitpunkt ausgebildeten π-π Ordnung des P3HT parallel zum Substrat. Die P3HT:PCBM Schichten verhalten sich wie flüssig kristalline Schichten mit einer weitreichenden Ordnung senkrecht und keiner Ordnung parallel zum Substrat. Die P3HT Ordnung in π-π Richtung entlang des Substrates bildet sich in einer späten Phase der Trocknung, wobei der (020) Bragg Peak nur auftritt, sofern das Mischungsverhältnis von P3HT: PCBM und die Trocknungstemperatur entsprechend gewählt wurden. Weiterhin wurde in dieser Arbeit für P3HT: PCBM Schichten mit höherer Mosaizität des P3HT (100) Peaks und schärferem (020) Peak eine Rotverschiebung des Absorptionsspektrums mit stärker ausgeprägten vibratorischen Schultern bewirkt. Es konnte gezeigt werden, dass diese Schultern mit den P3HT π-π Wechselwirkungen zusammen hängt, deren stärkere Ausprägung zu effizienteren Solarzellen führt

Gaining Further Insight into the Solvent Additive-Driven Crystallization of Bulk-Heterojunction Solar Cells by <i>in Situ</i> X‑ray Scattering and Optical Reflectometry

The use of solvent additives has become a successful strategy to control the structural evolution upon film formation in bulk-heterojunction (BHJ) solar cells. Nonetheless, a complete understanding of the additive’s role in the phase separation mechanisms and organization of donor and acceptor materials in BHJs is still lacking. In this work we gain further insight about the specific role that a widely used additive, 1,8-octanedithiol (ODT), has in the crystallization of both PCPDTBT and PC₇₁BM, directly after wet film deposition using blade-coating. By <i>in situ</i> X-ray scattering and optical reflectometry, we correlate the additive-driven crystallization with the evolution of film composition from the earliest time of solvent evaporation. It is shown that ODT influences the evolution of both PCPDTBT and PC₇₁BM. ODT leads to prolonged crystallization time during the ODT-drying dominated period corresponding to an overall solvent content (<i>x</i>) of 75 wt % > <i>x</i> > 15 wt % and delays the onset of PC₇₁BM aggregation to <i>x</i> < 20 wt %, being pushed out of the crystalline polymer domains

Structure Formation in Low-Bandgap Polymer:Fullerene Solar Cell Blends in the Course of Solvent Evaporation

The drying process of the bulk heterojunction (BHJ) layer has a strong impact on the solar cell performance for the well-investigated material system P3HT:PC₆₁BM. For higher performing low-bandgap polymers and C₇₁ fullerene derivatives, no comprehensive studies of the BHJ structure evolution during film drying are available. In this work we investigate the structure formation of the low-bandgap polymer poly­{[4,40-bis­(2-ethylhexyl)­dithieno­(3,2-<i>b</i>;20,30-<i>d</i>)­silole]-2,6-diyl-<i>alt</i>-(2,1,3-benzothidiazole)-4,7-diyl} (PSBTBT) and [6,6]-phenyl C₇₁-butyric acid methyl ester (PC₇₁BM) in the transition from wet to solid by in-situ grazing incidence X-ray diffraction (GIXD) and laser reflectometry simultaneously. The nucleation and crystallization of PSBTBT differs from the interface-induced crystallization of P3HT and occurs partially in the solution. It is shown that PSBTBT:PC₇₁BM blend nanomorphology and optoelectronic device properties are rather insensitive to the drying process in the investigated temperature range of 40–85 °C. This is beneficial for fast drying at elevated temperatures which enables high throughput fabrication of efficient organic photovoltaics