Investigation of Melts of Polybutylcarbosilane Dendrimers by 1H NMR Spectroscopy

Melts of polybutylcarbosilane (PBC) dendrimers from third (G3) up to sixth (G6) generations are investigated by 1H NMR spectroscopy in a wide temperature range up to 493 K. At room temperature, NMR spectra of G3-G5 dendrimers exhibit resolved, solution-like spectra (“liquid” phase). In contrast, the spectrum of the G6 dendrimer is characterized by a single unresolved broad line at whole temperature range, which supports the presence of an anomalous phase state of G6 at temperatures higher than glass transition temperature. For the first time, an unexpected transition of G5 dendrimer from a molecular liquid state to an anomalous state/phase upon temperature increase has been detected using NMR data. Specifically, an additional wide background line appears in the G5 spectrum above 473 K, and this line corresponds to a G5 state characterized by restricted molecular mobility, i.e., a state similar to the “anomalous” phase of G6 melt. The fraction of the G5 dendrimers in “anomalous” phase at 493 K is approximately 40%. Analysis of the spectral shapes suggests that changes in the G5 dendrimers are reversible with temperature.

However, the mechanism of the physical entanglements in the PBC dendrimer melts is still unclear. At this point, two hypotheses about the nature of the entanglements have been published. According to one hypothesis 31 low and high density regions are formed in the peripheral layer. The formation of these regions is associated with steric constraints arising from the growth of dendrimer generations. Authors of work 31 suppose that high density regions lead to entanglements between dendrimers. An alternative hypothesis 30 is that intermolecular cavities grow with increasing G due to the increase of the dendrimer size and the decrease in the penetration of macromolecules into each other. These factors may lead to the formation of a compact structure that minimizes free space in such systems 32 .
Additionally, we would like to underline that the presence of entanglements in the melt of hyperbranched polymers is experimentally established in ref. 33 .
To the best of our knowledge, this effect has not been investigated by NMR spectroscopy, which is one of the most efficient tools to study structure, conformations and dynamics of macromolecules [34][35][36][37] . Also note that NMR spectroscopy has been successfully applied to studies of dendrimers in solutions in our works [38][39][40] . In this paper we apply 1 H NMR spectroscopy to reach new insights on the molecular dynamics and phase transitions of PBC dendrimers.  Table 1. Structural parameters of the PBC dendrimers. N i is a portion of hydrogen atoms contributing to the signal of the peak #i to the total number of hydrogen atoms in the dendrimer at room temperature; T g is glass transition temperature (data from ref. 15 ).   Fig. 1 and Table 1.

Experimental
The structure of the PBC dendrimers is shown in Fig. 1 and some parameters of the dendrimers are presented in Table 1. In the studied PBC dendrimer, the core functionality was 4 and the functionality of the branching points was 3. The synthesis of PBC dendrimers was described earlier 16 . The structure and composition of the PBC dendrimers was confirmed by the 1 H NMR spectra (see Table 1). The measurements were carried out at 500 MHz using a BRUKER AVANCE 500 spectrometer. The chemical shifts, δ, were referenced by setting the position of peak 1 to −0.05 ppm according to data for carbosilane dendrimers in chloroform 38 . The PBC dendrimer melts were studied in the range of 298-493 K, which was significantly higher than T g . For each temperature point, the equilibration time was at least 20 minutes. The number of scans varied between 8 and 32 depending on the initial signal-to-noise ratio in the NMR spectrum. The integral of each spectrum was normalized by the number of protons in accordance with the theoretical formula of the dendrimer (see Table 1). ACD/Labs software was applied in the deconvolution of G5 experimental spectrum into a number of lorentzian components, using the Levenberg-Marquardt algorithm. For diffusion measurements, the pulsed-field-gradient stimulated echo method was used with maximum gradient strength 1280 G/cm. The gradient pulse length and the diffusion time were set to 4 ms and 400 ms, respectively. The proton spin-lattice relaxation times, T 1H , were measured using conventional inversion-recovery π-τ-π/2 pulse sequence with 6 μs duration of π/2 pulse, 16 tau delays, 2 scans for each delay, and a 3 to 8 s recycle time between scans. In the paper we use relaxation rate function R 1H = 1/T 1H . The proton spin-spin relaxation was measured by a spin-echo sequence π/2-τ-π/2, 16 tau delays, 8 scans for each delay, and a 3 to 8 s recycle time between scans.

Results
Room temperature NMR spectra of PBC dendrimers of G3-G6 generations are displayed in Fig. 2. Spectra of G3-G5 exhibit resolved peaks that were assigned to different structural groups. The spectra can be divided into four main groups of peaks in accordance with Table 1. Peak with chemical shift (δ) near zero ppm corresponds to the signal of the СН 3 -Si group with a chemical environment similar to that found in the reference compound Si(CH 3 ) 4 . The following peaks, in ascending order of δ, are СН 2 -Si, terminal СН 3 -groups neighboring with СН 2 -groups, and finally the СН 2 -groups, which are neighbors of СН 2 -or СН 3 -.
In contrast, a spectrum of G6 melt consists of a single, unresolved broad line covering the entire area of expected chemical shifts. Such a shape of the spectrum can be explained as a consequence of much higher viscosity of the G6 melt compared to that of G3-G5 dendrimers. This high viscosity reduces the T 2 * relaxation time of each spectral line, leads to a significant increase of the line width, Δν = 1/(πT 2 * ) 41 , and results in the unresolved total G6 spectrum.
In order to obtain a temperature dependence of the G6 linewidth it is necessary to keep in mind that the unresolved chemical shift range contributed to the observable linewidth of total spectrum. G3 and G4 samples display relatively narrow lines, whose widths continuously decrease with increasing temperature. In contrast, the G5 sample exhibits complex behavior of the spectrum in different temperature ranges (see Fig. 3). A conventional narrowing of peak width and an increase of spectral resolution with increasing temperature are observed between 298 and 423 K. However, an additional broad background peak appears in the spectra at 473 K and higher temperatures (see Fig. 3 and SI for more details). We would like to emphasize that no broadening is observed for narrow spectral lines, and, hence, it is not possible to fit the shape of whole G5 spectrum at 473 K without adding an additional background line. We have verified that no similar effect is present in G3 and G4 dendrimers (Fig. 4).
The diffusion coefficients D for G = 3-5 dendrimers were measured at different temperatures and, as expected, decrease with both an increase in molecular mass and a decrease in temperature (Fig. 5). Unfortunately, we could  Fig. 1 and Table 1. not measure D for G6 even at elevated temperatures, due to the limitation imposed by a very short spin-spin relaxation time T 2 . The difference in spin-spin relaxation rate R 2H = 1/T 2H between G6 and other dendrimers can be seen in Fig. 6b.
In contrast to large differences in the shapes and widths of the NMR spectra, differences in NMR spin-lattice relaxation rates R 1H of the G3-G6 dendrimers are not so significant (Fig. 6a). First of all, numerical values of measured R 1H are of the same order of magnitude and this means that the local orientational mobility exists in all dendrimers, including in G6. Moreover, in the investigated temperature range, broad R 1H maxima were found for all investigated dendrimers with R 1H maximum positions which are not far from one another, see Fig. 6a. According to the theory of orientation mobility in dendrimers [42][43][44] these results suggest that local orientational mobility in G6 is similar to the mobility of low generation dendrimers.
In addition, in Fig. 7 we show the full width at half maximum (FWHM) of lines of PBC dendrimers for unresolved spectra and line #1 (at −0.05 ppm) for other spectra.

Discussion
As mentioned above, sample G6 is characterized by one wide spectral line. This fact may be associated with the anomalous phase, which has been observed in previous studies by other methods 15,18,19,28 . Since no anomalous phase is present in low generation dendrimers (<G5), highly resolved spectra are observed (Fig. 2). We will refer to such a low generations phase as an ordinary "liquid" phase. Now we would like to discuss the anomalous temperature behavior of the spectra of G5 dendrimer melt (Fig. 3). In order to fit G5-melt spectrum at 493 K correctly, we have to introduce an additional broad component (line #5). We assume that the shape of the broad line is similar to that of the unresolved G6 spectrum. Thus, to fit this line we used the same parameter of Lorentz/Gauss ratio which gave the best fit for G6 PBC dendrimer spectrum (see Fig. S5 in SI). Deconvoluted G5-melt spectrum at 493 K is shown in Fig. 8.  The relative integral intensities of the spectral components are summarized in Table 2. As seen in Tables 1 and 2, the relative integral intensities of the narrow peaks 1-4 (i.e., excluding the additional broad peak which is marked #5 in Table 2) correspond to the ratios calculated using a structural formula of the dendrimer. This correspondence indicates that the appearance of the broad component (peak 5) is associated with changes in the dynamics of the dendrimer as a whole but not with changes in the mobility of some fragments of the   . The 1 Н NMR spectrum of G5 dendrimer melt at 493 K (solid black peak) and the decomposition of the spectrum into components: red dotted peaks show the fitting of standard narrow peaks; blue dashed peak marks the wide peak, which is similar to the G6 spectrum. macromolecule. The shape and position of peak 5 are indeed similar to the spectrum of G6 melt (see Fig. S5 in SI). This suggests that a part of the G5 dendrimer is in an anomalous phase similar to the melt of G6. A fraction of this part of the G5 can be estimated by comparing integral intensities of the broad peak 5 and of the remaining narrow peaks 1-4 in the spectrum. As shown in Table 2, a fraction of the second phase at 493 K is ca. 42% ± 4%. We note that the peak 5 disappears when returning the sample to a temperature of 423 K, i.e. the formation of the second phase is reversible.
It is important to note that the physical processes, leading to the temperature dependent changes in the spectral shapes of the G5 sample at low temperature and in the vicinity of 470-490 K, are not the same. The conventional broadening of the spectral peaks of macromolecules at lowering temperature is caused by a decrease in molecular mobility and a related decrease of spin-spin relaxation times T 2 41 . This broadening is observed for dendrimers of low generations (see Figs 2 and 4). On the contrary, the additional broad peak in the spectrum of G5 dendrimer, emerging at high temperatures, is associated with a part of the sample undergoing phase transition to an anomalous state, while the rest of the sample exhibits narrow peaks typical for conventional liquids. As an illustration, the temperature dependences of the full widths at half maximum (FWHM) of line #1 are included in Fig. 7.
We would like to stress the coincidence between the region of the nonmonotonic behavior in C p (370 K-460 K, see Fig. S1 in SI) and the appearance of the broad line of spectra for G5 PBC dendrimers. The spectra at 473 K and 493 K where we can reliably determine the broad line are immediately above the maximal temperature of this region. This suggests that the nonmonotonic behavior in the C p reflects the formation of a new state in the G5 melt. Given the similarity of the NMR spectral shapes, it is reasonable to assume that the new phase in G5 is analogous to the G6 anomalous phase. Thus, besides unexpected temperature changes in NMR spectral shapes, our results demonstrate a rather unusual effect -a transition of a part of the G5 dendrimers from the "liquid" state to the anomalous state upon temperature increase. The simultaneous presence in the NMR spectrum of a broad unresolved peak, corresponding to an anomalous phase, and a set of relatively narrow peaks, corresponding to the "liquid" state of dendrimer, indicates the coexistence of the two states.
Thus, the results of this work indicate a similarity in the behavior of G5 and G6 dendrimers, which manifests in the formation of aggregates of dendrimer molecules in an anomalous state. In the G6 melt such clusters cover all or at least an overwhelming part of the melt, while in the G5 melt the clusters appear only at 473 K and above and coexist with the molecular state of the dendrimer.   Table 2. Spectrum deconvolution of G5 dendrimer melt at 493 K. The peak numbering corresponds to an increase in their chemical shift.