Result and Discussion

2.3.1 Aggregate Structure in DP6-PPV/Chloroform Solutions.

Figure 2-1 shows the room-temperature SANS profiles of DP6-PPV in the solutions with chloroform at different concentrations. The SANS intensities followed I(q) ~ q^-1 dependence in the high-q region (q > ~ 0.03 Å^-1) irrespective of the polymer concentration, indicating the presence of rod entity under large spatial resolution^14,15. The scattering intensity in this q region was dominated by the form factor of the rod entity, viz.¹⁵

I(q) = NΔρ²Vrod2Prod(q) (2)

where I(q) is the absolute intensity in the unit of cm^-1, N is the number density of rod particles, Δρ is the SLD contrast between the solvent and the particle, Vrod is the volume of the rod, and Prod(q) is the form factor function of rod particle. Let Vrod = zvu with z and vu being the number of monomer units in a rod and volume of a monomer unit, respectively, and N = cNav/(zMu) with c, Mu and Nav being the concentration in g/ml, molar mass of the monomer unit and the Avogardro’s number, respectively, then Eq. (1) can be reorganized to give

2 2

0.01 0.1 10^-3

10^-2 10^-1 10⁰

I(q) (cm

)

q (Å

)

0.1 wt%

0.5 wt%

1.0 wt%

fitted result

-2.7

-1.0

Figure2-1. The room-temperature SANS profiles in log-log plots of DP6-PPV in the solutions with chloroform at different concentrations. Two power-law regimes were identified in the scattering profiles irrespective of the concentration. The intensity exhibited a power law of I(q) ~ q^-2.7 in the middle- to low-region characterizing the mass fractal dimension of the network aggregates. The q-dependence transformed to another power law of I(q) ~ q^-1 at high q corresponding to the form factor of the rodlike sub-chains between the junction points in the networks. The solid curves are the fitted results using the unified equation.

where ML is the molar mass per unit length of the rod. Eq. (3) prescribes that the product of G(q) and q reaches an asymptotic value given by πML/Mu. Figure 2-2 displays the G(q)q vs. q plot for the 1.0 wt% DP6-PPV/chloroform solution. The plot was generated using the following parameter values: ρDP6-PPV = 1.321 x 10¹⁰ cm^-1, ρd-chloroform = 3.16 x 10¹⁰ cm^-2 and vu,DP6-PPV = 5.73 x 10^-22 cm³. ML determined from the plateau was 4.3 gmol^-1nm ^–1. This value closely agreed with the molar mass per unit length of the monomer unit of DP6-PPV (= 5.0 gmol^-1nm ^–1) calculated by dividing the molecular weight of the monomer unit (Mu = 338 g mol^-1) by the length of a monomer unit (= 6.7 Å)³⁵. This attested that the rod entity probed in the high-q region corresponded to the rodlike segments constituting DP6-PPV chains.

The conformation of semirigid polymers is usually described by the “worm-like chain” possessing relatively large persistent length, lps (lps < contour length)^36-39. In the low-q region (q < lps-1) where the global conformation is probed, the worm-like chain approaches the coil behavior and the corresponding form factor exhibits an asymptotic power law of I(q) ~ q^-ν with ν = 2.0 and 1.7 in θ and good solvent, respectively⁴⁰. Rodlike behavior corresponding to the rigid nature of the polymer chain on local scale emerges in the high-q region (q > lps-1). In principle, the persistent length of the worm-like chain may be determined from the crossover (qc) from the rodlike behavior to the coil behavior via lps = 3.5/qc,^37-39 provided that the scattering profile over the q range of interest represents the form factor of the single chain or the sub-chain that is long enough to manifest the worm-like behavior. Exact determination of lps was however implausible here because, as will be shown later, the scattering profiles at q < ~ 0.03 Å^-1 in Figure 1 were not dominated by the form factor of molecularly dissolved DP6-PPV chains. Nevertheless, the fact that the q^-1 power law extended to ca. 0.03 Å^-1 indicated that lps of the chain was larger than 3.5/0.03 Å^-1

=117 Å.

0.02 0.04 0.06 0.08 0.10 0.12 -2

0 2 4 6 8 10

G(q)q ( Å

)

q (Å

)

1.0 wt%

Figure 2-2. G(q)q vs. q plot of 1.0 wt% DP6-PPV/chloroform solution for the determination of the molar mass per unit length (ML) from the asymptotic value of the plot.

The scattering intensities of DP6-PPV/chloroform solutions exhibited obvious upturns at q < ~ 0.03 Å^-1, where the corresponding slope in the log-log plot became ca. –2.7 and was virtually independent of concentration. Therefore, the scattering profiles of the three concentrations shared essentially the same feature, namely, the intensities exhibited a power law of I(q) ~ q^-2.7 in the middle- to low-q region but this q-dependence transformed to I(q) ~ q^-1 at high q corresponding to the rodlike behavior of the chain segment. Since polymer chain conformation usually depends weakly on concentration, the observed SANS profiles may be ascribed intuitively to the form factor of the molecularly dissolved polymer chains in the solution. However, the power law exponent of 2.7 at low-q was not prescribed by the asymptotic scattering behavior of worm-like chain or other form factor models of linear polymer chains.

The attribution of the observed scattering pattern to single-chain form factor was further ruled out by the strong concentration dependence of the concentration-normalized intensity (I(q)/c), as shown in Figure 2-3. It can be seen that, instead of collapsing onto a single master curve, the concentration-normalized intensity in the low-q region increased with increasing overall polymer concentration.

The concentration dependence of I(q)/c was not prescribed by the dynamic network structure formed by the inter-chain overlap in the semidilute solution either, because in this case I(q)/c should decrease with increasing concentration in the low-q region (q < ξd-1 with ξd being the dynamic mesh size) as I(q)/c is proportional to the mesh size which decreases with the increase of concentration⁴⁰.

The larger I(q)/c at higher concentration was attributable to the significant aggregation of DP6-PPV chains in chloroform. We asserted that the observed SANS profiles were overwhelmed by the structure of the inter-chain aggregates. In this case, the power law of I(q) ~q^-2.7 signaled that over the length scale covered by the low-q region the structure of the aggregates was characterized by a mass fractal dimension of ca. 2.7 irrespective of polymer concentration. The proximity of the

observed fractal dimension to that (= 2.5) displayed by the percolation clusters suggested that the aggregates of DP6-PPV were networks generated by the segmental association of the polymer chains, as schematically illustrated in Figure 4. The sites of the segmental association acted as the (physical) junction points for the chains (with the average distance between the junction points denoted by ξs). Two structural levels of the aggregates were hence probed by the SANS profiles. At q

> ξs-1 the scattering behavior was dominated by the form factor of the sub-chains between the junction points in the networks. If ξs was smaller than the Kuhn length of the chain, these sub-chains were essentially rodlike and hence gave rise to the q^-1 power law in the high-q region in Figure 1. At Rg-1<< q < ξs-1(with Rg being the radius of gyration of the aggregates) where the structure at a more global length scale dominated the scattering behavior, the intensity displayed another power law of I(q) ~ q^-2.7 characterizing the fractal dimension of the networks. Consequently, the overall scattering profile exhibited a crossover from q^-1 to q^-2.7 with decreasing q. Similar crossover between the power law of q^-1 and q^-α with α lying between 2.0 and 3.0 has also been noted recently for the scattering patterns of the aggregates of carbon nanotubes in solution state.⁴¹

The fractal aggregates revealed here for DP6-PPV was in clear distinction with the compact plate aggregates formed by the rodlike PPE chains.^24,25 The latter was consider to posses a uniform density ^24,25 whereas the fractal aggregates of DP6-PPV had an opened structure as a significant fraction of the unassociated segments remained mixed with the solvent molecules contained within the aggregates (cf.

Figure 2-4).

It can be seen from Figure 2-1 that the crossover between the two power-law regimes (marked by the arrow) shifted to higher q with increasing polymer concentration (e.g. from 0.022 Ǻ^-1 at 0.1 % to 0.037 Ǻ^-1at 1.0 %), implying a smaller ξs at higher polymer concentration due to higher degree of segmental association. We

0.01 0.1 10⁰

10¹ 10²

I(q)/c (cm

g

ml)

q (Å

)

0.1 wt%

0.5 wt%

1.0 wt%

Figure 2-3 The concentration-normalized SANS profiles of DP6-PPV/chlororofm solutions. I(q)/c in the low-q region was found to increase with increasing overall polymer concentration, indicating that DP6-PPV exhibited significant inter-chain aggregation.

Figure 2-4 Schematic illustration of the network aggregates formed by DP6-PPV in the solution state. The networks were looser in chloroform but became highly compact in toluene.

attempted to deduce the quantitative value of ξs through fitting the SANS profile by the “unified equation” developed by Beaucage.^{42, 43} The unified equation describes the scattering profiles of fractal objects in terms of hierarchical levels of structure in the system. Each structural level is described by a Guinier’s law and a structurally-limited power law. The unified scattering function in terms of two structural levels is given by ^{42, 43}

⎪⎭ the volume of the particle, respectively. B and Bs are the prefactors specific to the types of power-law scattering characterized by the exponents P and Ps, respectively, they are given by

where Γ is the gamma function. For the present system, the first two terms in Eq. (5), which revealed the fractal feature of the aggregates, dominated the intensity at q < ξs-1. The last two terms, which dominated the intensity at q > ξs-1, captured the building block (i.e., the rodlike sub-chains between the junction points) with the characteristic radius of gyration of Rs of the networks.

Because the Guinier region prescribed by the Rg of the aggregates was not accessible over the q range of the present SANS experiment due to relatively large

aggregate size, the first term in Eq. (4) was omitted for the fitting. For the curve fitting we have fixed Ps = 1.0 (corresponding to the power-law exponent of the rodlike sub-chains), thereby leaving B, Gs, Bs, Rs and P as the fitting parameters. The fitted results were displayed by the solid curves in Figure 2-1 and the numerical values of the parameters and the error bar obtained from the fits were listed in Table 2-1. The fractal dimensions, P, obtained from the fits were close to those estimated directly from the slopes of the intensity profiles in log-log plots.

Rs corresponded to the radius of gyration of the rodlike sub-chains between the junction points, ξs was hence given by ξs ≈ (12Rs2)^1/2. The values of ξs thus calculated were 29.4, 22.1 and 15.2 nm for the concentration of 0.1%, 0.5% and 1.0%, respectively. The smaller ξs at higher polymer concentration signaled a higher degree of segmental association, as having also been manifested by the shift of the crossover between the two power-law regimes to higher q.

Table 2-1. The values of the parameters obtained from the unified equation fits for DP6-PPV/chloroform solutions.

0.1 wt% 0.5 wt% 1.0 wt%

Gs 0.014 ± 0.008 0.026 ± 0.09 0.02 ± 0.012 B^B_s (×10 ) ³ 7.7 ± 0.45 5.9 ± 0.05 11.6 ± 1.3

P 2.71 ± 0.43 2.65 ± 0.05 2.62 ± 0. 6 R_g (nm) 30.9 ± 4.2 25.3 ± 3.5 20.3 ± 0.4 Rs (nm) 8.5 ± 2.9 6.4 ± 1.1 4.4 ± 0.9

ξ_s (=12R_s²)^1/2 (nm) 29.4 22.1 15.2

Since the accessible q range in the present SANS experiment did not allow the Rgs of the aggregates to be determined, DLS experiment was conducted to reveal the hydrodynamic radii, Rh, of the aggregates. Figure 2-5 shows the distribution of Rh in the 1.0 wt% DP6-PPV/chloroform solution at 25 ^oC. The Rh profile displayed three peaks with each stemming from a characteristic relaxation mode in the system. The dynamics of DP6-PPV in the solution was hence characterized by three modes, namely, the fast, medium and slow modes. The largest Rh of 3.8 μm associated with the slow mode may be attributed to the average hydrodynamic radius of the aggregates in the solution. Consequently, the inter-chain aggregation of DP6-PPV in chloroform generated relatively large aggregates with μm in size; down to the nanometer length scale the internal structure of the aggregates could be described by a rather well-defined fractal dimension of ca.2.7. The physical range of mass fractal dimension dm is between 1.0 and 3.0.^14,15 In general, a small value of dm would imply that the structure of the fractal object is more opened or has a lower dimensionality. The rather large fractal dimension of DP6-PPV aggregates in chloroform indicated that these aggregates were quite dense in structure. It is noted that the value of the fractal dimension may also be useful for resolving the mechanism of the cluster growth from the aggregation of small subunits.⁴⁴ However, such an analysis becomes even more complex for the aggregation of long polymer chains, because the building block by itself is a fractal object.

The small peak at 72 nm (corresponding the medium mode) in the Rh profile was attributed to the internal relaxation mode of the networks, while the other peak with Rh ~ 8 nm was ascribed to the motions of the rodlike segments. It is noted that the Rh of a rod entity is usually smaller than its corresponding Rg.^{15, 45} However, as can be seen from Table 2-1, the radius of gyration of the rodlike subchains between the junction points (Rs = 4.4 nm) in the 1.0 wt% solution was smaller than the value of Rh

( ~ 8 nm) deduced from DLS. This discrepancy may be reconciled by the considering that Rh is related not only to the size of the object but also to its dynamics of motion.

In the aggregates, the motions of the rodlike subchains were indeed constrained by the

junction points; therefore, the corresponding Rh became larger than that of the freed rods.

10⁰ 10¹ 10² 10³ 10⁴ 10⁵ 10⁶ 10⁷

0.0 0.2 0.4 0.6 0.8 1.0 1.2

We ighting (a . u.)

Hydrodynamic Radius (nm)

DP6-PPV in CHCl

3

DP6-PPV in toluene

Figure 2-5 The distribution of hydrodynamic radius Rh in the 1.0 wt% chloroform and toluene solutions at 25 ^oC. The Rh profile displayed three peaks with each stemming from a characteristic relaxation mode in the system. The largest Rh was attributed to the average hydrodynamic radius of the aggregates in the solution, while the two small peaks were attributed to the internal relaxation mode of the networks and the motions of the rodlike segments.

2.3.2 Aggregate Structure in DP6-PPV/Toluene Solutions.

We now turn to the structure of DP6-PPV in the poorer solvent, toluene. Figure 2-6 displays the room-temperature SANS profiles of DP6-PPV in the solutions with toluene. In contrast to the two distinct power-law regimes observed for the chloroform solutions, only one asymptotic power law was identified here at q > ~ 0.02 Ǻ^-1. The corresponding slopes in the log-log plots were –2.2, -2.4 and -2.7 for the concentration of 0.1, 0.5 and 1.0 wt%, respectively. These power law exponents were again attributed to the mass fractal dimensions of the networks formed by the inter-chain aggregation of DP6-PPV in toluene. The absence of the q^-1 power-law regime in the scattering profiles implied that the networks were highly compact with very small ξs due to severe segmental association. In this case, the q^-1 regime was located at the region beyond the measurable q range of the SANS experiment. The smaller fractal dimensions (compared with that observed for the chloroform solutions) coupled with highly compact internal structure indicated that the aggregates in toluene tended to collapse into objects (such as disks) with lower dimensionality due to severe segmental association.

The distribution of Rh of 1.0 wt% DP6-PPV/toluene solution at 25 ^oC is also shown in Figure 2-5. The Rh profile also exhibited three peaks centering at 1.3 μm, 95 nm and 10 nm. The largest Rh of 1.3 μm was again attributable to the average hydrodynamic radius of the aggregates. Therefore, the aggregates in toluene were smaller than those in chloroform due to more compact internal structure. The other two peaks corresponded to the network internal relaxation mode and the motion of the rodlike segments. The Rh associated with the former was larger than that found for the chloroform solution, as the corresponding motion became more restricted due to higher degree of segmental association in the aggregates.

0.01 0.1 10^-3

10^-2 10^-1 10⁰ 10¹ 10²

I(q ) (cm

)

q (Å

)

0.1 wt%

0.5 wt%

1.0 wt%

Figure 2-6 The room-temperature SANS profiles in log-log plots of DP6-PPV in the solutions with toluene at different concentrations. Only one asymptotic power law was identified at q > ~ 0.02 Å^-1. The corresponding power law exponents were attributed to the mass fractal dimensions of the highly compact networks formed by the inter-chain aggregation of DP6-PPV in the solvent.

Owing to the higher boiling point of toluene, temperature-dependent SANS experiment was conducted to examine the effect of elevating temperature on the aggregation behavior of DP6-PPV in this solvent. Figure 2-7 displays the SANS profiles of 1.0 wt% toluene solution collected in-situ at different temperatures in the heating cycle. The low-q intensity depressed progressively with increasing temperature, signaling the occurrence of de-aggregation upon heating. Interestingly, the fractal dimension of the aggregates remaining in the solution was found to retain at ca. 2.7, as the low-q slope in the log-log plot was essentially unaffected by increasing temperature. Accompanied with the depression of the low-q intensity was the gradual emergence of the q^-1 power law in the high-q region (q > 0.04 Å^-1). The q^-1 power-law regime became clear at 85 ^oC, which was about the highest achievable temperature before the intervention of solvent boiling. In this case, the scattering pattern was characterized by two distinct power-law regimes and became nearly identical with the room-temperature SANS profile of the corresponding chloroform solution after normalized by the respective neutron contrast factors (cf. the inset in Figure 2-7).

The temperature-dependent SANS experiment hence revealed that heating the toluene solution tended to reduce the degree of segmental association in the network aggregates. The segmental dissociation loosened the networks and the increase of ξs

shifted the q^-1 power-law regime to the accessible q range. Although the aggregates became less compact at higher temperature, their fractal dimension remained essentially unperturbed. It is further noted that the inter-chain aggregation was never completely dissipated even by heating to 85 ^oC, at which the aggregate structure was analogous to that in chloroform at room temperature. The results suggested that two types of segmental association with distinct stability existed in the aggregates of

DP6-PPV. The first type was prevalent in the poorer toluene solvent and could be disrupted by moderate heating. The other type of segmental association was highly stable in the sense that they could neither be solvated by the good solvent such as choroform nor be dissipated thermally at 85 ^oC in toluene.

0.01 0.1

Figure 2-7 The temperature-dependent SANS profiles of 1.0 wt% DP6-PPV/toluene solution collected in a heating cycle. The low-q intensity depressed progressively with increasing temperature while largely retaining its slope.

Accompanied with this intensity depression was the gradual emergence of the q^-1 power law in the high-q region. The q^-1 regime became clear at 85

oC. The inset displays the SANS profiles normalized by the contrast factors for 1.0 wt% DP6-PPV/toluene solution at 85 ^oC and 1.0wt%

DP6-PPVchloroform solution at room temperature. It can be seen that the two scattering profiles were nearly identical.

2.3.3 The Nature of the Segmental Associations.

Here we attributed the highly stable segmental association to the π-π complex already present in the DP6-PPV powder used for the solution preparation. This kind of complex was formed by the in-plane stacking of the phenylene or phenyl moiety in DP6-PPV and the characteristic distance of ca. 3.0 Å between the aromatic groups forming the complex would lead to a peak at 2θ ≈ 29^o in the wide-angle X-ray scattering (WAXS) profile ⁴⁵. Figure 2-8 shows the WAXS scan of the DP6-PPV powder used for the solution preparations. The two peaks located at 18 and 22^o corresponding to the interplanar spacing of 4.9 and 4.0 Å , respectively, were associated with the packings of the aliphatic side chains of DP6-PPV.³⁵ A π-π complex peak was clearly discernible at 2θ = 29^o. This scattering peak was found to persist even after annealing the powder at 330 ^oC (cf. Figure 2-8), showing that the π-π complex was highly stable. The WAXS profile of a DP6-PPV film cast from chloroform solution with a very rapid solvent removal is also displayed in Figure 2-8.

It can be seen that the π-π complex peak still existed, which implied that the complex present in the powder remained unsolvated in chloroform, such that it was transferred into the film after solvent removal. Consequently, the WAXS results suggested the

It can be seen that the π-π complex peak still existed, which implied that the complex present in the powder remained unsolvated in chloroform, such that it was transferred into the film after solvent removal. Consequently, the WAXS results suggested the