Physical Properties of Polymers

Double screw-sense inversions of helical chiral-achiral random copolymers of fluorene derivatives in phase separating solutions


The addition of methanol to dilute THF solutions of chiral-achiral random copolymers of fluorene derivatives and the chiral homopolymer showed thermo-reversible circular dichroism (CD) induction in the main-chain fluorene absorption region. This finding demonstrated the uneven population of the right- and left-handed helical conformations in the polymer chains. From the sign of the induced CD, two helical screw-sense inversions were found by changing the chiral monomer content. The Ising model for chirally interacting chiral-achiral random copolymers can explain the double screw-sense inversions.


Recently, π- and σ-conjugated polymers, which possess interesting electrical and optical properties, have attracted much interest as candidates for organic light-emitting diodes1, 2, 3 and chemical sensors.4 Chiroptical properties, such as circular dichroism (CD), optical rotation, and circular polarized luminescence, enrich the applications of these organic semiconductors as optical devices or sensors.5, 6, 7, 8, 9 Optically active side chains may introduce chiroptical properties into conjugated polymers, but some polymers exhibit these properties only in films or phase separating solutions,10, 11, 12, 13 which indicates that intermolecular chiral interactions are necessary to induce the chiroptical properties in such conjugated polymers.

Polyfluorene derivatives are π-conjugated polymers. From electron and X-ray diffraction,14, 15 as well as molecular modeling,14, 16 these polymers are known to take a helical conformation, but chirality introduced to the side chain of the polymers was not found to induce circular dichroism (CD) on their backbone chain in dilute solution. This finding probably results from weak intramolecular chiral interactions that cannot discriminate against the handedness of the backbone helical conformation.

In a previous study,17 the CD induction of an optically active homopolymer of fluorene derivative, poly(2,7-[9,9-bis((S)-citronellyl)]fluorene) (PCF), in dilute THF solutions was found by the addition of a non-solvent methanol. Although the methanol-added solutions were almost transparent because of low polymer concentrations (10−6 g cm−3), static light scattering measurements indicated a liquid-liquid phase separation to form concentrated droplet phases, and it was concluded that this induction arises from the intermolecular chiral interaction of polyfluorene chains in the concentrated droplet phases separated from the dilute solution.

Helical chiral-achiral random copolymers often exhibit interesting chiroptical properties, for example, sergeants-and-soldiers behavior,18, 19, 20 composition-driven helical screw-sense inversion,21, 22 and so on. Therefore, the CD induction study in phase separating solution was recently extended to a helical chiral-achiral random copolymer of fluorene derivatives, poly(2,7-[9,9-bis((S)-citronellyl)]fluorene-random-9,9-di-n-octyl fluorene), as shown in Scheme 1, and double screw-sense inversions were found by changing the chiral monomer content x. To the best of our knowledge, this is the first observation of composition-driven double sense inversions in helical chiral-achiral random copolymers. In this paper, this finding is reported along with the theoretical argument of its origin.

Experimental procedure


Mixtures of the chiral and achiral dibromofluorene monomers of different compositions were copolymerized in a hot mixture of toluene and N,N-dimethylformamide (DMF) using a zero-valent nickel reagent by the Yamamoto coupling reaction.7 Each copolymer sample was divided into three fractions by fractional precipitation using THF as the solvent and methanol as the precipitant, and the middle main fraction was chosen for the following experiments.

The chiral monomer content x of five middle copolymer fractions was estimated from the ratio of the integrated intensities of the proton signals of the chiral side chains and aromatic rings. The results, listed in Table 1, are very close to the initial compositions fed at the copolymerization (the numbers in the parentheses in the second column of Table 1). The weight average molecular weights, Mw, and the ratios of Mw to the number average, Mn, of the five fractions were determined by size-exclusion chromatography with a multi-angle light scattering detector (SEC-MALS).23 Table 1 lists the results and weight average degree of polymerization N0,w calculated from the Mw determined. The values of Mw/Mn indicate the relatively narrow molecular weight distributions of the fractions used in this study. One fraction of the chiral homopolymer PCF prepared in the previous study was added to the copolymer fractions for the following CD induction study, and its Mw was determined by static light scattering (SLS).17 The values of N0,w of all the fractions were within the range of ca. 100–300.

Table 1 Characteristics of polymer fractions used in this study and of concentrated droplet phases in methanol-added THF solutions of fractions PC5O5 and PCF


Each fraction was first dissolved in THF (8 × 10−7 g cm−3), and then, methanol was added to the THF solution at room temperature. The methanol volume fraction φMeOH in the mixed solvent and the final polymer concentration c in the THF-methanol solution were adjusted to 0.5 and 4 × 10−7 g cm−3, respectively. CD and SLS measurements were conducted using the THF-methanol solutions prepared using a JASCO J-720WO spectropolarimeter and a Fica 50 light scattering photogoniometer with 546 nm incident light, respectively, at 40 and 15 °C.


Static light scattering

Figure 1 shows the light scattering profiles of THF-methanol solutions of fractions PC5O5 (x=0.50) and PCF (x=1) at 40 °C and 15 °C (300 min after quenching from 40 °C). Here, K is the optical constant, c is the polymer mass concentration, Rθ is the excess Rayleigh ratio at the scattering angle θ, and k2 is the square of the scattering vector. All of the profiles exhibit very strong angular dependences, demonstrating the existence of large particles in the solutions. The phase diagram obtained previously17 for the methanol-added THF solution of PCF indicates that the solutions may be in the biphasic region, and the large particles are the concentrated droplet phases separated from the dilute solutions.

Figure 1

Berry plots for methanol-added THF solutions of fractions PC5O5 (x=0.50) and PCF (x=1) at 40 °C and 15 °C (300 min after quenching from 40 °C); φMeOH=0.5 and c=4 × 10−6 g cm−3. Solid and dotted curves, theoretical values for polydisperse spheres fitted to the data at 15 and 40 °C, respectively (see the main text).

For dilute solutions of polydisperse spheres, (Kc/Rθ)1/2 can be calculated by17

where R is the radius of the sphere, w(R) is the weight fraction of a sphere of radius R, cc is the polymer mass concentration in the spherical concentrated phase, and NA is the Avogadro constant. Assuming that the size distribution w(R) obeys the log-normal distribution,17 equation (1) was fitted to the experimental results to obtain the weight-average radius Rw, the ratio of Rw to the number-average Rn of the droplet phase and cc. The solid and dotted curves in Figure 1 show the fitting results, and the parameters obtained are listed in columns 5–8 in Table 1. Droplet sizes are on order of 100 nm. The concentrations of the droplet phases are as high as 0.6 g cm−3 for both fractions and almost independent of temperature. The results of cc for fractions PC5O5 and PCF indicate the similar affinities of the chiral and achiral monomer units to the mixed solvent.

Circular dichroism induction

None of the copolymer fractions exhibited CD in dilute THF solution, as in the case of the chiral homopolymer PCF,17 which indicates that the intramolecular chiral interaction between the main and side chains of the copolymers is too weak to energetically discriminate the right- and left-handed helical conformations in the fluorene main chain.

Figure 2 shows UV-visible absorption and CD spectra of the phase separating solution of PC5O5 quenched from 40 to 15 °C. In Panel a, the main peak of the UV-visible absorption, arising from the π–π* transition in the fluorene main chain, is essentially unchanged over time since quenching, but the peak height decreases, the peak wavelength slightly increases, and a new side-peak appears at 426 nm. On the other hand, a bisign CD signal is induced in the fluorene main-chain absorption region by quenching in Panel b, just as in the case of fraction PCF reported previously.17 The induced CD disappeared upon heating to 40 °C and reappeared by quenched again to 15 °C, which is similar to PCF and demonstrates the thermal reversibility of the CD induction. The phase-separating solutions were verified to have no optical anisotropy,17 which means that the induced CD does not arise from a liquid crystal phase. The polyfluorene chain is known to take 5/2 or 5/1 helical conformations favorably14, 16 so that the CD induction indicates uneven population of the right- and left-handed helical conformations of the copolymer main-chain. The Kuhn dissymmetry factor gc≡Δɛ/ɛ at 410 nm (the CD peak position) reaches the asymptotic value at approximately 60 min (cf. Insert of Figure 1), which is slightly faster than gc of the PCF solution.17

Figure 2

Spectra of the molar circular dichroism Δɛ (a) and the average molar extinction coefficient ɛ (b) for methanol-added THF solution of fraction PC5O5; inset in Panel b: time dependence of the Kuhn dissymmetry factor at 410 nm. A full color version of this figure is available at Polymer Journal online.

The new side peak at 426 nm in Panel a corresponds to the so-called ‘β-phase’ observed for poly(9,9-di-n-octylfluorene) films,24, 25 which is assigned to an almost planar conformation of the fluorene main chain with the torsional angle ≈160° stabilized by the n-octyl side chains.26 A more pronounced side-peak was observed in the methanol-added THF solution of fraction PC2O8, indicating that some of achiral monomer units take similar planer conformations in the concentrated droplet phase. Interestingly, a side-peak also grows in the CD spectrum (Panel b) at the same wavelength, which may arise from the achiral monomer unit in the copolymer chain taking the ‘β-phase’ conformation.

In the methanol-added THF solution with the same φMeOH and c, a similar CD induction was observed for PC6O4 quenched from 40 to 15 °C, but a CD signal appeared for PC2O8 even at 40 °C and did not change with time after quenching to 15 °C. The CD induction experiments were examined twice for fraction PC2O8, and nearly the same CD spectra were obtained, confirming the reproducibility of the CD induction for this fraction.

Figure 3 shows the asymptotic CD absorption spectra for all chiral-achiral random copolymers and the chiral homopolymer PCF in methanol-added THF solutions (φMeOH=0.5, c=4 × 10−7 g cm−3). The bisign CD main signals induced in PCF and PC2O8 solutions are positive in the longer wavelength region but opposite in PC6O4 and PC5O5 solutions, and PC8O2 exhibits almost no CD. The sign of the side peak of PC2O8 (at 429 nm) is also opposite to that of PC5O5 (at 426 nm). The insert in Figure 3 shows the x dependence of the Kuhn dissymmetry factor at the CD peak in the region of 400–420 nm. These results demonstrate that the helical screw sense of the chiral-achiral random copolymer is inverted twice with changing x. To the best of our knowledge, this is the first observation of the double sense inversions in helical chiral-achiral random copolymers.

Figure 3

Asymptotic CD absorption spectra for all chiral-achiral random copolymers and the chiral homopolymer PCF in methanol-added THF solutions; inset: the x dependence of the Kuhn dissymmetry factor at the CD peak in the region of 400–420 nm. A full color version of this figure is available at Polymer Journal online.


Consider the origin of the double sense inversions in helical chiral-achiral random copolymers. For simplicity, assume that the main-chain bond (for example the internal rotation angle) of the helical polymer chain takes P- or M-states (a two-state model). The P-helix (M-helix) means the sequence of main-chain bonds taking the P-state (M-state). In a concentrated solution, a bond taking the P-state (M-state) feels the chiral molecular field *(P) (*(M)) generated by neighboring polymer molecules.27 If the solution contains P- and M-state bonds of fractions fP and fM, respectively, the molecular fields, *(P) and *(M), may be given by

where w*PP, w*MM, and w*PM are the chiral interactions between two pairs of adjacent monomer units connected by the bonds both taking the P-state, both taking the M-state, and taking the P- and M-states, respectively. Because the molecular field may include both enthalpic and entropic contributions, *(P) −*(M) can be regarded as the free energy difference 2ΔGh of a bond when taking the P-state and M-state in the concentrated solution. From equation (2), ΔGh is a linear function of the enantiomer excess 2fP−1, for example, ΔGh=κ(2fP−1) + λ where κ and λ are parameters related to the chiral interactions. In the previous study,17 it was assumed that λ=0, but w*PP and w*MM are not necessarily identical unless the interacting monomer units are both achiral.

In the case of a chiral-achiral random copolymer solution, ΔGh may depend on the kinds of adjacent monomer units connected by the bond under consideration:28

where the subscripts C and A denote the chiral and achiral monomer units, respectively. Because the achiral homopolymer should be racemic at 2fP−1=0, λAA must be zero. Helical polymers must have long sequences of the one-sense helical state along the main chain, or the helix reversal must be a rare event. Thus, the free energy ΔGr of the helix reversal, where the adjacent bonds take the opposite helical state, must be quite high.29 In what follows, the dependence of ΔGr on the kinds of adjacent monomer units connected by the bond under consideration is not considered, which should have a minor effect on the helical screw sense inversion.

The enantiomer excess 2fP−1 of the chiral-achiral random copolymer chain can be calculated by the matrix method for the Ising model.28, 30, 31 The matrix includes the statistical weights of the P- and M-states and the helix reversal, which are respectively written as

where the subscripts i(k) (1 k N), taking C (the chiral monomer unit)) or A (the achiral monomer unit), specify the copolymer sequence and RT is the gas constant multiplied by the absolute temperature. (This R should be distinguished from the radius R in equation (1)) Generating 100 sequences of chiral-achiral random copolymers with a given N and mole fraction x of the chiral unit on a computer, 2fP−1 can be calculated numerically for the given values of ΔGh,CC, ΔGh,CA, ΔGh,AA, and ΔGr in the routine procedure.

The calculated 2fP−1 must fulfill equation (3) for ΔGh,CC, ΔGh,CA, and ΔGh,AA. This self-consistent calculation can be performed as follows. From equation (3), the relations among ΔGh,CC, ΔGh,CA, and ΔGh,AA are obtained:

A trial value of ΔGh,CC is chosen first, and ΔGh,CA and ΔGh,AA are calculated from equation (5) using a given set of the parameters κCACC, κAACC, λCC, and λCA. Then, 2fP−1 is calculated by the matrix method using those values of ΔGh and a given value of ΔGr, and the resulting 2fP−1 is substituted into the first equation of equation (3) to check the equality. The self-consistent value of ΔGh,CC that fulfills the equation is sought.

The previous result indicated that 2fP−1 for PCF in the phase-separating solution is close to zero at 40 °C but takes a positive finite value at 15 °C.17 To reproduce these results, κCC=40 J mol−1 and λCC=2 J mol−1 were selected (using these parameters, 2fP−1 for PCF becomes 0.09 at 40 °C and 0.38 at 15 °C). Furthermore, N=220 (the average value of our five polymer fractions) and ΔGr=10 kJ mol−1 (a typical value for helical polymers such as polyacetylene or polyisocyanate derivatives32, 33). The remaining parameters in equation (2), κCA, κAA, and λCA, were taken as adjustable parameters. (The κ and λ parameters may depend on the polymer concentration cc in the concentrated phase, but here it is assumed that these parameters are independent of x because cc may be insensitive to x due to similar affinities of the chiral and achiral monomer units to the mixed solvent, mentioned above.).

Figure 4 shows the results of 2fP−1 at 15 °C as a function of ΔGh,CC and x for κCACC=−2.5, κAACC=3.5, λCC=2 J mol−1, and λCA=−4 J mol−1. Slight fluctuations in the calculated 2fP−1 values arise from statistical errors in the chiral monomer content generated. The straight line in Figure 4 represents the linear relation of 2fP−1=(ΔGhλCC)CC with κCC=40 J mol−1. The intersecting point of this line and the curve for each x fulfills equation (3). At large x, the curve intersects with the line once, but, in the small x region, there are three intersecting points.

Figure 4

Enantiomer excess as a function of ΔGh,CC and x, calculated by the matrix method for the Ising model of the random copolymer with κCACC=−2.5, κAACC=3.5, λCC=2 J mol−1, λCA=−4 J mol−1, ΔGr=10 kJ mol−1, N=220, and T=288 K (15 °C).

Figure 5 shows the self-consistent solution of 2fP−1 at 15 °C, obtained from Figure 4, as a function of x. At large x (> 0.227), the calculation gives the unique self-consistent solution of 2fP−1. When x decreases from unity, 2fP−1 changes from positive to negative (the solution of branch 1), corresponding to the first helical screw sense inversion. However, one negative and two positive solutions appear at x <0.227. Among these solutions, the positive one reaching the origin (labeled as the branch 2) should be the real solution because the achiral homopolymer must be racemic. Therefore, a transition from branch 1 to 2 is expected with decreasing x, which corresponds to the second helical screw sense inversion. This discontinuous transition is an interesting phenomenon. The CD induction at x between 0.2 and 0.5 will be studied experimentally in more detail in the near future.

Figure 5

Self-consistent solutions of the enantiomer excess 2fP−1 as a function of x for the parameters listed in the text.


Methanol-added THF solutions of chiral-achiral random copolymers of fluorene derivatives with different chiral monomer content x were studied. The addition of methanol to dilute THF solutions of the copolymers and the chiral homopolymer induced a liquid-liquid phase separation that produced concentrated phase droplets with a polymer concentration as high as 0.6 g cm−3 and a size of the order of 100 nm. In the concentrated phase, the copolymers and homopolymer exhibited mostly thermo-reversible circular dichroism (CD) induction after quenching in the main-chain fluorene absorption region, demonstrating the uneven population of the right- and left-handed helical conformation in the polymer chains. From the sign of the induced CD, two helical screw-sense inversions were found by changing x. The Ising model for chirally interacting chiral-achiral random copolymers can explain the double screw-sense inversions.


Chemical structure of the chiral-achiral random copolymer studied.


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Y Sanada thanks the Global Center of Excellence Program, the ‘Global Education and Research Center for Bio-Environmental Chemistry’ of Osaka University. This work was partly supported by a Grant in Aid for Scientific Research on Priority Area ‘Soft Matter Physics.’

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Correspondence to Takahiro Sato.

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Sanada, Y., Terao, K. & Sato, T. Double screw-sense inversions of helical chiral-achiral random copolymers of fluorene derivatives in phase separating solutions. Polym J 43, 832–837 (2011).

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  • chiral-achiral random copolymer
  • circular dichroism induction
  • helical screw-sense inversion
  • phase separation
  • polyfluorene

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