3.3 Results and Discussion
3.3.3 SANS with Perdeuterated Side-Chains – The Backbone Conformation Results
crystalline behavior in which the bottlebrushes have a parallel alignment in solution with spacing determined by the side-chain dimensions. These phenomena, however, are observed at much higher concentrations (5 to 16 wt%)[72-74]. Thus we can consider the RCS for the side-chains to be the unperturbed side-chain dimensions.
The RCS values in Table 3.5 are in remarkably good agreement with end-to-end distances estimated for free polystyrene chains with N=Ns. Using empirically fitted equations for Rg(Mw)[75] and converting from Rgto Re-e[16] we calculate Re-e for PS-25 to be 4.3nm in THF and 3.3nm in cyclohexane. For PS-65 the values are 7.2nm in THF and 5.3nm in cyclohexane. These values deviate from the RCS determined for the corresponding bottlebrushes by less than the experimental uncertainty. This indicates that both the radii of the side-chains and the molecular weight dependence are the same as those of free polystyrene chains. Although data on the Rg of free PtBA chains was not available for comparison, the scaling of RCS with Ns of ν~.6 is consistent with that of a linear polymer chain in good solvent. From these results we can conclude that the side- chain conformation does not appear to be significantly distorted by being grafted to the backbone.
3.3.3 SANS with Perdeuterated Side-Chains – The Backbone Conformation
1130-dPS-25 in dTHF with 0.3wt% solutions of linear polynorbornene with N=660 and N=1370 serving as the control. The resulting radially averaged and solvent subtracted scattering patterns are shown in Figure 3.8.
Figure 3.8: Radially averaged SANS patterns for PNB-g-dPS bottlebrushes (left, taken at NIST) and linear polynorbornene (right, taken at ORNL). All samples are in deuterated THF which is an almost exact contrast match for the deuterated polystyrene side chains, leaving only the scattering from the backbone for the brushes and providing good contrast for the linear PNB. The scattering curves for both the 1130-dPS-25 and PNB-1370 were offset for clarity (done by multiplying the intensity by 4.0).
Qualitatively the scattering curves I(q) for the bottlebrush backbones are remarkably similar to those of linear polynorbornene. All of the curves in Figure 3.8 have power law scattering I(q) ~ q-m in the mid q region (0.02Å-1 < q < 0.1Å-1) with a q independent plateau at lower q. This is the behavior expected of a linear polymer coil in dilute solution and is typically fitted using a generalization of the Debye scattering function[54] allowing for values of the power law other than the m=2 expected for a gaussian polymer. The resulting expression characterizes the scattering from polymers with scaling ν =1/m [76]:
𝐼(𝑞 ) =
𝜈U11 2𝜈�𝛾 �
2𝜈1, U� −
𝜈U11 𝜈�𝛾 �
1𝜈, U�
(3.6)Here γ(x,U) is the incomplete gamma function and U is given by
𝑈 =
𝑞2𝑅𝑔2(2𝜈+1)(2𝜈+2)6 (3.7)
The expression is valid over the range 1/3 < ν < 1 but is most reliable in the excluded volume polymer region with ν~0.6. This model was fit to the data by setting the background to zero and then determining the rest of the parameters by nonlinear least squares fitting. The resulting Rg and ν values are presented in Table 3.7.
Table 3.7: Radii and scaling exponents for the backbones of bottlebrushes with deuterium labeled side- chains and linear polynorbornene obtained by fitting polymer excluded volume I(q) to Figure 3.8.
The polymer excluded volume expression perfectly characterizes the scattering of both the bottlebrush backbones and linear polynorbornene. The similar sizes and scaling exponents reinforce the similarity that was evident from inspection of the scattering curves. The scaling exponent ν for the backbones is slightly larger for the backbones than the linear polynorbornene, indicating that they are somewhat stretched. The Rg values for the bottlebrush polymer backbones are much smaller than those determined for the bottlebrushes by MALLS. This is consistent with the bottlebrushes being above the overlap concentration and the measured radius corresponding to Rc-c rather than the backbone Rg.
In order to determine the side-chain dimensions perpendicular to the backbone contour, SANS scattering patterns were taken for the same bottlebrushes (dPS-25) in a
partially deuterated THF solvent (described in section 3.2.4), providing equal contrast for the side-chains and the backbone. The resulting radially averaged and solvent subtracted scattering patterns are shown in Figure 3.9.
Figure 3.9: Radially averaged SANS patterns for PNB-g-PS bottlebrushes in a mixed THF solvent (54.8%
deuterated) providing equal contrast for the backbone and the side-chains.
The scattering patterns are similar to those of ordinary unlabeled PS bottlebrushes in deuterated THF. The noise level is much greater due to the significant incoherent scattering caused by the greater hydrogen content of the solvent, drowning out much of the monomer level scattering at high q and obscuring the differences between the different Nb at low q. The cross-sectional size was determined to be RCS = 4.8nm using a Beaucage fitting function.
SANS experiments on 1wt% solutions of 820-dPS-65 were attempted, but the very low concentration of backbone (0.04wt%) resulted in unacceptably poor signal to noise ratios. It was not possible to acquire a usable pattern even after 3 hours of acquisition time. Raising the bottlebrush concentration to 5wt% allowed a pattern to be
acquired although the low-q region (q<0.01Å-1) was still too noisy to use. A peak was observed in the scattering for a 5wt% solution that was not present at 1wt% and so the 1wt% data was subtracted from the 5wt% in order to isolate this feature, shown in Figure 3.10.
Figure 3.10: Radially averaged SANS pattern (taken at NIST) for 820-dPS-65 in deuterated THF (contrast matched to the side chains) isolating the scattering due to the backbone. This sample is at 5wt%
concentration with a 1wt% sample used as the background (subtracted from the data). The solid black line is a Lorentzian fit to the peak which is centered on q = 0.064Å-1 corresponding to a length scale of 9.8nm.
At 5wt% the scattering for 820-dPS-25 shows a peak in the mid q range (0.02Å-1 < q < 0.2 Å-1). Fitting a Lorentzian to this peak allowed the center position to be determined as qpeak = 0.064 Å-1, corresponding to a length scale of 9.8nm, which is of the same order of magnitude but somewhat larger than the side-chain size RCS of PS-65 bottlebrushes (7.1nm).
Discussion
Small Angle Neutron Scattering patterns for the backbones of bottlebrush polymers are remarkably similar to those of linear polynorbornenes of N~Nb. The
intensity trends and the turnover from power law to q independent scattering is located at a similar position in q. The scaling exponent ν is lower for 1130-dPS-25 than for 670- dPS-25 and this drop of ν with Nb is consistent with a contour length L > lk, but not yet at its asymptotic limit L ≫ lk. The lk calculated from light scattering data for a linear polynorbornene is 3.4nm while that for dPS-25 based bottlebrushes is 37nm, meaning that the asymptotic limit of scaling is reached for a bottlebrush with Nb ten times greater than expected for PNB.
Based on this similarity between the linear polynorbornene and the bottlebrush backbone, we conclude that the backbone conformation is not significantly perturbed, although the Kuhn length lk is presumed to be larger than that of PNB. The very low number of data points precludes the determination of lk for the backbone without further scattering experiments on bottlebrushes with differing Nb. The Rg of the backbones may not be reliable due to the overlap issue discussed in section 3.3.2, which would explain the very small difference in Rg between 1130-dPS-25 and 670-dPS-25. Reducing the sample concentration and using samples with shorter backbones should resolve this issue.
Through the use of selective labeling we have been able to isolate the scattering from the backbone of a bottlebrush polymer. However, this proved to be possible only for relatively short side-chain lengths (Ns < 65) and required more than 2 hours of acquisition time per sample. Further study will require careful planning and may benefit from the use of sample cells with much longer path length (2mm path length cells were used in experiments at NIST).
Although it was not possible to obtain I(q) over the entire range for 820-dPS-65, a very interesting feature was seen in the 5wt% scattering pattern, a peak corresponding to
a feature with a 9.8nm length scale. Since the side-chains are contrast matched to the solvent, this must be due to a backbone-backbone correlation length. Polymer mass fractals do not give rise to scattering peaks and this length scale is not explained by the overlap scaling shown in Figure 3.7. Thus we hypothesize that this peak is direct evidence of a lyotropic liquid crystalline phase with the 9.8nm corresponding to the characteristic intermolecular spacing. Lyotropic phases have been observed for bottlebrush polymers in solution [72-74], but to the best of our knowledge this is the first molecular level characterization of such a phase.
3.3.4. Bottlebrushes with Poly(Acrylic Acid) Side Chains