Impact of Local Stiffness on Entropy Driven Microscopic Dynamics of Polythiophene
Sudipta Gupta, Sourav Chatterjee, Piotr Zolnierczuk, Evgueni E. Nesterov, Gerald J. Schneider
EEntropy Driven Molecular Motion of Semiconducting Polymers in Solution
Sudipta Gupta*, Sourav Chatterjee, Piotr Zolnierczuk, Evgueni E. Nesterov*, and Gerald J. Schneider*
1, 3 Department of Chemistry, Louisiana State University, Baton Rouge, LA 70803, USA J¨ulich Centre for Neutron Science, Forschungszentrum J¨ulich GmbH Outstation at SNS,1 Bethel Valley Road, Oak Ridge, TN 37831, USA Department of Physics, Louisiana State University, Baton Rouge, LA 70803, USA (Dated: November 8, 2018)We investigate the entropy driven large-scale dynamics of semiconducting conjugated polymersin solution. Neutron spin echo spectroscopy reveals a finite dynamical stiffness that reduces withincreasing temperature and molecular weight. The Zimm mode analysis confirms the existence ofbeads with a finite length that corresponds to a reduced number of segmental modes in semi-flexiblechains. More flexible chains show thermochromic blue-shift in the absorption spectra.
PACS numbers: 61.25.he, 61.05.fg, 71.20.Rv, 81.05.Fb
The mechanical, optical, and electrical properties ofsemiconducting polymers are determined by their molec-ular interactions. Delocalized π -electron system in suchpolymers determines their optoelectronic properties andis related to the increased chain stiffness. Although thereis a wealth of studies on the effect of chain conforma-tion on optoelectronic properties of conjugated polymers[1–5], the impact of chain dynamics is still poorly un-derstood. In a step toward better understanding of thechain conformation, chain dynamics and optical responsein conjugated polymers, we want to exploit the high tem-poral and spatial resolution of neutron spin echo spec-troscopy (NSE). The point of interest is to determine aunique set of physical parameters that can quantify theimpact of the chain stiffness on the large scale polymerdynamics.In general, with increasing temperature, the energybarriers associated with conformational changes of thepolymer backbone are reduced. Twisting can lead tothe breakdown of π -electron conjugation, which causesthe thermochromic blue-shift in the absorption spec-tra [6–11]. A recent small angle neutron scattering(SANS) study on poly(3-alkylthiophene) (P3AT) semi-conducting polymers reported a direct relationship be-tween the conjugated polymer conformation and solva-tochromic/thermochromic phenomena [10, 12].The same thermal fluctuations that cause the confor-mational changes determine the degree of overlap of the π -orbitals [13]. Quasi-elastic neutron spectroscopy in-vestigations highlighted that the reduced conductivity ofsemiconducting polymers is associated with the local re-laxation of the alkyl side chains [14]. However, the effectsof entropic forces and solvent-mediated interactions onthe large-scale chain dynamics are still unexplored.Depending on the solvent quality and temperature,long flexible polymers in dilute solution can assume aswollen coil, a Gaussian chain, or collapse to a globuleconformation. On the contrary, semi-flexible polymerscan exhibit random coil to rod-like conformation. Theirinherent rigidity reduces the segmental mobility and canlead to a partially frozen or glassy state. De Gennessuggested that these effects the mode spectrum of single chains [18]. NSE spectroscopy demonstrated the exis-tence of such single chain glassy (SCG) states in semi-flexible polymers [16, 17]. However, the occurrence ofSCG states has not been verified in semiconducting con-jugated polymers. In addition, chemical defects [2] insemiconducting polymers cause dynamic disorder [14, 19]that can lead to structural and dynamical heterogeneity.As such, it can be an ideal model system to investigatein comparison to glassy materials [20–22].In this letter, we report a comprehensive studyof the temperature-dependent single chain confor-mation and dynamics of amorphous regioregularpoly(3-hexylthiophene) (P3HT) in deuterated 1,2-dichlorobenzene (DCB) solvent using SANS and NSE.P3HT was chosen as a well-studied representative of con-jugated polymers that has proven to be an archetypicalmaterial for electronic and optoelectronic applications[23]. We carried out experiments on two P3HT sam-ples of different molecular weights, which had close to100% regioregularity (Table I). Experiments were con-ducted at elevated temperatures and a low concentration( φ = 0.75% ) to reduce inter-chain aggregation [24].We determined the unperturbed chain dimensions inSANS experiments. Fig. 1 displays the Kratky plot [25]for two different molecular weights and temperatures inDCB. The plateau at intermediate momentum transfer, Q , is a signature of a Gaussian coil and indicates a scalingrelationship, I ∼ Q − /ν = Q − , with the Flory exponent, ν = 0.5 (Θ solvent) [25]. A fit with the Debye function,2 /u [ u − − u )], with u = Q R g , shows an in-creasing radius of gyration R g , with increasing molecularweight and a slight variation with temperature (TableI). The persistence length, (cid:96) P ∼ Q ’s are due to the incoherent background thatincreases the noise level, but do not change our findings.NSE spectroscopy measures the normalized dynamicstructure factor S ( Q, t ) /S ( Q ) as a function of Fouriertime, t at a given momentum transfer, Q (cf. SI [42]for details). At the intermediate length scale the center a r X i v : . [ c ond - m a t . s o f t ] O c t T Q / f Q2I/ f (×10-2Å-2cm-1) Q ( Å - 1 ) I n c r e a s e i n R g P 3 H T i n D C B
FIG. 1: Kratky plots for P3HT of two different molecularweights and temperatures in DCB, determined from SANS.The data are normalized by their volume fraction, φ . Thelines represent the fit with Debye model. of mass diffusion and segmental relaxation of a polymermelt is well described by the Rouse model. The molecularmotion originates from the balance between entropic andfrictional forces caused by the surrounding heat bath andis best described by its spectrum of relaxation modes [27].For polymers in solution, the hydrodynamic interactionsbecome important, and the dynamic structure factor canbe formulated within the framework of the Zimm model[28]: S Zimm ( Q, t ) = exp (cid:2) − Q D Z t (cid:3) S chain ( Q ) × exp (cid:40) − R ee Q π (cid:88) p p ν +1 cos (cid:16) pπmN (cid:17) × cos (cid:16) pπnN (cid:17) (cid:18) − exp (cid:18) − tp ν τ Z (cid:19)(cid:19) (cid:41) (1)with S chain ( Q ) = 1 N (cid:88) n,m exp (cid:40) − | n − m | ν Q (cid:96) (cid:41) (2)Here n , m are the polymer segment numbers wherethe summation runs over the total number of segments(beads), N . The statistical segment length is givenby (cid:96) and is obtained from, (cid:10) R ee (cid:11) = (cid:96) N ν = 6 (cid:10) R g (cid:11) [29]. The first part in Eq. (1) describes the Zimm cen-ter of mass diffusion with a diffusion coefficient, D Z = α D k B T / ( η s R ee ), where η s is the solvent viscosity and α D = 0.196, a constant pre-factor (Θ solvent) [30]. Thethird term represents the more local dynamics. It is rep-resented by a sum over relaxation modes of the poly-mer chain with mode number p , and characteristic time τ p = τ Z p − ν . The corresponding Zimm segmental relax-ation time is given by τ Z = 0 . η s R ee / ( k B T ) [30], fora thermal energy k B T , where k B is the Boltzmann con-stant. S chain ( Q ) represents the static structure factor ofthe chain (Eq. (2)). Figure 2 illustrates S ( Q, t ) /S ( Q ) obtained by NSE ex-periments over a Q -range from 0.062 to 0.124 ˚A − , forP3HT samples of two different molecular weights, at 313and 353 K. The incoherent and coherent contributionswere determined by polarization analysis in the diffrac-tion mode of the spectrometer. The elastic incoherentscattering from the background, including the solvent,the scattering that results from empty cell, sample en-vironment and instrument, were subtracted accordingly(cf. SI [42] for details) to obtain the coherent dynamicstructure factor.First, we used a rigid polymer model, calculated D Z , τ Z , with R ee coming from our SANS experiment. How-ever, it does not suffice to describe the measured data(cf. Figs. S3 (a) and (b), SI [42]). The much fasterdecay of our experimental data indicates a substantialcontribution of another relaxation mechanism.In the next step, we considered P3HT in solution asa rigid wormlike chain as proposed by McCulloch et al .[10], which requires to add the rotational diffusion ( p =1). The comparison with the experimental data (cf. Figs.S3 (c) and (d), SI [42]) shows that this is still not suf-ficient. Hence, we improve the model by considering apolymer coil with mobile segments, that requires to in-clude the segmental relaxation ( p > p = 1, 2 . . . , P (cf. Figs. S4(a) and (b), SI, [42]). The number of modes needed issurprisingly low, with P = 15 to 27.The parameter P represents the number of modes nec-essary to describe the experimental S ( Q, t ) /S ( Q ) at dif-ferent temperatures and molecular weights simultane-ously for all Q ’s. We would like to emphasize that thistheoretical description of the experimental NSE data in-volves no free parameters, except P .However, limiting the analysis to a finite number ofmodes neglects a substantial part of the mode spectrumand seems to be unjustified. On the other hand, theincreased stiffness caused by the delocalized π -electronsystem introduces a finite correlation length (dynamicKuhn segment), which can be taken into account byadding a fourth-order term, p + αp , to the entropicspring constant ( k = 3 k B T /(cid:96) ∝ p − ), with the dy-namic stiffness parameter α [16, 31]. The modified Zimmscattering model (Eq. (1)) is obtained by replacing themode dependence p ν by p ν + αp − ν , and 1 / (cid:0) p ν +1 (cid:1) by1 / (cid:0) p ν +1 + αp (cid:1) . Unlike limiting the number of modes,we now exploit the fact that by increasing the momen-tum transfer Q , the dynamic structure factor becomesmore sensitive to higher modes. In addition, for a given Q , the calculated S ( Q, t ) /S ( Q ) becomes independent of p , beyond a certain threshold ( p > p min ). This uses thefact that 2 π/Q probes a certain finite length, which limitsthe number of modes required to theoretically describethe experimental data. As a consequence, the stiffnessparameter α is unaffected by the maximum Q .The solid lines in Figs. 2 (a) and (b) compare the re- TABLE I: Sample labels, molecular weight M n , polydispersity M w /M n , radius of gyration R g , the chain end-to-end distance R ee , Zimm diffusion D Z , Zimm time τ Z , the Zimm modes p min , the stiffness parameter α and the size of the bead R rigid .P3HT M n T R g (˚A) R ee D Z × − τ Z p min α R rigid Label (kg / mol) M w /M n ( K ) (nm) (nm) (nm ns − ) (ns) (nm)63k 63.1 1.51 313 15 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± S( Q,t )/S( Q ) ( b ) a S t i f f n e s s a S( Q,t )/S( Q ) t ( n s ) ( a ) FIG. 2: The normalized dynamic structure factor S ( Q, t ) /S ( Q ) of P3HT in DCB for two molecular weights ((a)90 and (b) 63 kg/mol) at temperatures, 313 (red symbols )and 353 K (cyan symbols). Symbols represent Q = 0.062 ( (cid:3) ),0.087 ( (cid:13) ) and 0.124 ˚A − ( (cid:52) ). Solid lines represent the bestfit summing over a large number of modes p min , and a finitedynamical stiffness α . sult of our analysis with the experimental dynamic struc-ture factor. We can accurately describe our experimen-tal data by simultaneously fitting all the Q s. We obtainthe stiffness parameter α that decreases with increasingmolecular weight and/or temperature, cf. Table I.Based on this result, we can now estimate the mini-mum number of modes, p min , that are required to theo-retically describe the experimental S ( Q, t ) within the Q -range of our NSE experiments by solving S ( Q, t, α, N = p min ) = S ( Q, t, α, N = ∞ ) [33]. We find considerablygreater values of p min than in the case of simple assump-tion of a finite number of modes P , without taking into account the finite stiffness α (cf. Table I). The absence ofhigher order modes elucidates the fact that the chain dy-namics is partially frozen. Therefore, this is the first ex-perimental evidence of the existence of single chain glass(SCG) state in a conjugated polymer.If we compare the quality of the fits based on the stiff-ness parameter (Fig. 2) with those calculated assuminga low number of modes (Fig. S4 in SI [42]), we observea similarly good description irrespective of their physi-cal origins. The description of the relaxation of a chainby its mode spectrum assumes a certain number of sta-tistically independent segments, connected by entropicsprings. Numerous experiments justified the assumptionof an infinite number of modes in case of flexible poly-mers like poly(ethylene- alt -propylene) or poly(ethyleneglycol) (with α = 0) [34, 35]. In the present case, theincreased stiffness caused by the delocalized π -electronsystem introduces a finite correlation length, which de-creases the number of statistically independent beads.Thus, the calculation of S ( Q, t ) /S ( Q ) using a reducednumber of modes is formally equivalent to the calcula-tion using a stiffness parameter. However, the highest Q is limited in experiments. Hence, limiting the number ofmodes does not represent the full mode spectrum.This explanation can be rationalized by a simple es-timation. For semi-flexible polymer the number ofmodes, p min in Eq. (1), limits the displacement,cos( p min πm/N ), over m = N/p min segments. There-fore, we can estimate the size of the bead R rigid , inour bead spring approach. For distances less than R rigid , the segments are correlated. It is given by: R rigid = (cid:96) ( N/p min ) ν = R ee N − ν ( N/p min ) ν = R ee p − νmin [16]. From Table I it is evident that the effects of temper-ature and molecular weight are negligible, and we obtain (cid:104) R rigid (cid:105) = 4.7 ± α and a finite size of thebead, R rigid . The parameter α describes the damping ofthe mode relaxation. In the Rouse or Zimm approach,normal coordinates are introduced to solve the Langevinequation by simple exponential functions. The orthogo-nality of these normal coordinates follows from the uncor-related random forces. This assumption corresponds tothe freely jointed chain model that neglects correlationsbetween bond vectors. In a good approximation, those - 5 - 4 - 3 - 2 - 1 a P N B a t T = 2 9 3 K , 3 5 0 , 6 0 0 & 4 0 0 k a (cid:181) R - 8 (cid:1) e e T a(cid:215) c R (cid:1) e e ( Å ) FIG. 3: Generalized scaling behavior, α ∝ R − νee , of thepolymer stiffness α as a function of the chain dimension R ee of P3HT (two molecular weights and two temperatures)and polynorbornene (PNB) samples (three molecular weights,[16]). Here, α is vertically scaled by a factor c . finite correlations in a real polymer can be neglected ifgreater distances along the chain contour are considered.This leads to the introduction of R rigid and similarly to α .In order to investigate the scaling behavior betweenthe chain end-to-end distance and the dynamical chainstiffness α , we systematically varied R ee . The resultsare illustrated in Fig. 3. In addition to our results, wehave included the stiffness parameter α P NB of polynor-bornene (PNB) of different molecular weights in a goodsolvent [16]. For a better comparison, we rescaled α P NB by a factor ∼
7. Irrespective of the polymer, molecularweight and temperature, we observe a generic power-lawscaling, α ∝ R − νee . As a consequence, the molecularweight dependence of α is attributed to the increase inGaussian coil dimension, R ee by a factor ∼ R rigid ,is independent of molecular weight and temperature. (ii)The renormalized stiffness ¯ α = α/R − νee , decreases withincreasing temperature. (iii) The absorption spectra ofP3HT in DCB are independent of the molecular weight,but show a thermochromic blue-shift with increasingtemperature, cf. Fig. S5, SI [42]. These results agree with those found earlier for regioregular P3HT and seemto be common for semiconducting polymers [36–40].The constant bead size excludes a correlation with theobserved changes in the absorption spectra. The reducedrenormalized stiffness ¯ α . The associated breakdown ofthe π -electron conjugation can lead to the thermochromicblue-shift in the absorption spectra.To understand the temperature dependence of thestiffness, we now want to explore its relationshipto chain end-to-end distance, α (353 K ) /α (313 K ) =( R ee (353 K ) /R ee (313 K )) − ν ≈ .
7. The thermal expan-sion of P3HT, accounts only for a ratio of 0 .
9, which aloneis not sufficient to explain the reduction of the stiffness[41]. This highlights the fact that the static chain end-to-end distance is not associated with the conjugationlength or the thermochromic blue-shift, and more atten-tion needs to be paid to the large-scale chain dynamics.To summarize, we studied the large-scale dynamics ofP3HT in DCB by neutron spin echo spectroscopy. Weused a coarse-grained approach based on the Zimm modelto understand our experimental data. We introduced twoparameters, namely the bead size R rigid , and the stiffness α , that represent the mode spectrum. The effect of globalstiffness is exhibited clearly on the chain dynamics, eitherby the limited number of modes p min or by the introduc-tion of α as a damping term. We derived a renormal-ized stiffness ¯ α from the generic scaling of the stiffness α ∝ R − νee , and the molecular weight. We observe thatchains with higher flexibilty show a thermochromic blue-shift in the absorption spectra. The first observation ofthe existence of single chain glass modes in P3HT couldopen a new pathway to understand semiconducting poly-mers by models developed for colloidal glasses.We acknowledge the support of Louisiana Consortiumfor Neutron Scattering (LaCNS). The neutron scatter-ing work is supported by the U.S. Department of Energy(DoE) under EPSCoR Grant No. DE-SC0012432 withadditional support from the Louisiana Board of Regents.Research conducted at ORNL’s High Flux Isotope Re-actor (HFIR) and at Spallation Neutron Source (SNS)was sponsored by the Scientific User Facilities Division,Office of Basic Energy Sciences, U.S. Department of En-ergy (DoE). We thank Lilin He (HFIR), Marius Hofmann(LSU), Stefan Otto Huber (LSU) and Christopher VanLeeuwen (LSU) for helping us with the scattering exper-iments. [1] B. J. Schwartz, Annu. Rev. Phys. Chem. , 141 (2003).[2] D. Hu et al., Nature , 1030 (2000).[3] R. H. Friend et al., Nature , 121 (1999).[4] B. J. Sirringhaus et al., Appl. Phys. Lett. , 406 (2000).[5] P. M. Beaujuge, J. Am. Chem. Soc. , 20009 (2011).[6] J. Choi et al., Macromolecules , 1964 (2010).[7] F. Brustolin et al., Macromolecules , 1054 (2012).[8] K. Iwasaki et al., Synth. Met. , 101 (1994). [9] G. Petekidis et al., Macromolecules , 8948 (1996).[10] B. McCulloch et al., Macromolecules , 1899 (2013).[11] W. R. Salaneck et al., J. Chem. Phys. , 4613 (1988).[12] G. M. Newbloom et al., Langmuir , 458 (2015).[13] D. P. McMahon et al., J. Phys. Chem. C , 19386(2011).[14] J. Obrzut and K. A. Page, Phys. Rev. B , 195211(2009). [15] Y. A. Kuznetsov et al., J. Chem. Phys. , 3744 (1999).[16] M. Monkenbusch et al., Macromolecules , 9473 (2006).[17] Y. Mi, G. Xue and X. Lu, Macromolecules , 7560(2003).[18] P. G. De Gennes, Macromolecules , 587 (1976).[19] D. Djurado et al., Phys. Chem. Chem. Phys. , 1235(2005).[20] S. Gupta et al., Phys. Rev. Lett. , 128302 (2015).[21] S. Gupta et al., Sci. Reports , 35034 (2016).[22] V. A. Harmandaris et al., Phys. Rev. Lett. , 165701(2013).[23] S. Ludwigs P3HT Revisited from Molecular Scale to So-lar Cell Devices , Advances in Polymer Science, SpringerBerlin, Heidelberg, (2014).[24] D. E. Johnston et al., Nano , 243(2014).[25] P. Lindner and Th. Zemb, Neutron, X-rays and Light.Scattering Methods Applied to Soft Condensed Matter ,Elsevier Science, Amsterdam (2002).[26] H. Thienpont et al., Phys. Rev. Lett. , 2141 (1990).[27] D. Richter et al., Phys. Rev. Lett. , 2140 (1989).[28] M. E. Doi and S. F. Edwards, The Theory of PolymerDynamics , Oxford University Press, Oxford (2007).[29] For the sake of simplicity we define, R ee = (cid:113) (cid:10) R g (cid:11) .[30] B. Ewen and D. Richter, Adv. Poly. Sci., , 1 (1997).[31] D. Richter et al., J. Chem. Phys. , 6107 (1999).[32] S. Br¨uckner, Macromolecules , 449 (1981).[33] To calculate mode independent parameter α , above the threshold, p > p min , we summed over p = 1 . . . , 178001 (2013).[35] G. J. Schneider, et al., Soft Matter , 4336 (2013).[36] J. L. Bredas et al., J. Am. Chem. Soc. , 6555 (1983).[37] S. A. Jenekhe, Nature , 345 (1986).[38] J. Clark et al., Phys. Rev. Lett. , 206406 (2007).[39] N. Hosaka et al., Phys. Rev. Lett. , 1672 (1999).[40] T. Miteva et al., Macromolecules , 652 (2000).[41] T. Agostinelli et al., Adv. Func. Materials , 1701(2011).[42] See Supplemental Material, URL , which includes Ref. [24,44–50][43] C. A. Chavez et al., Macromolecules , 506 (2012).[44] W. H. Haynes, CRC Handbook of Chemistry and Physics ,Boca Raton, FL, 93 edn (2012).[45] K. D. Berry et al., Nucl. Instr. Meth. Phys. Res. Sec. A , 179 (2012).[46] M. Ohl et al., Nucl. Instr. Meth. Phys. Res. Sec. A ,85 (2012).[47] F. Mezei, C. Pappas, and T. Gutberlet,
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