**1. Introduction**

The anionic polymerization of organocyclosiloxanes, especially in the nonequilibrium variant, makes it possible not only to obtain silicone rubbers, whose production is currently estimated in the hundreds of thousands of tons, but also different macromolecular systems of various designs [1–10]. We dedicate this work to Chojnowski, whose large contribution to this area, including in terms of the synthesis of various multiarm systems, cannot be overestimated [11–13].

Star-shaped polydimethylsiloxane polymers have a long history; the first works on obtaining three- and four-armed systems were carried out in the 1960s in Kraus' [14] and Andrianov's [7] laboratories. At that time, researchers regarded them primarily as tools for the formation of defect-free polymer networks, but this approach was postponed for a long time due to the imperfection of the synthetic methods for such structures. The modern approach to the synthesis and research of star-shaped polydimethylsiloxanes was much more widespread and prepared. In this case, the real transition to precise multiarm stars occurred because of the appearance of dendrimers, with their practically unlimited and, at the same time, definite number of functional groups [15,16]. The work on synthesizing such structures was carried out by Roovers [17], Muzafarov [4], and Gnanou [18] and was largely initiated by the theoretical studies by Daoud and Cotton [19]. This time, the researchers were interested in the unusual rheology of stars, i.e., a decrease of their solution and melt viscosities upon an increase in the number of arms. Roovers and Hadjichristidis

**Citation:** Tikhonov, P.A.; Vasilenko, N.G.; Gallyamov, M.O.; Cherkaev, G.V.; Vasil'ev, V.G.; Demchenko, N.V.; Buzin, M.I.; Vasil'ev, S.G.; Muzafarov, A.M. Multiarm Star-Shaped Polydimethylsiloxanes with a Dendritic Branching Center. *Molecules* **2021**, *26*, 3280. https://doi.org/ 10.3390/molecules26113280

Academic Editors: Sławomir Rubinsztajn, Marek Cypryk and Wlodzimierz Stanczyk

Received: 5 May 2021 Accepted: 26 May 2021 Published: 29 May 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

synthesized the first star-shaped structures using carbosilane dendrimers as branching centers, and they found that the high functionality of the initial branching center is a necessary but insufficient condition as the problem of the complete substitution of the center active groups by oligomeric arms in the case of their large number is not easy. Various strategies for multiarm star synthesis have been developed: convergen<sup>t</sup> (arm-first) and divergent (core-first), as well as a combination of these two approaches [20]. The structures obtained with their help had properties so different from classical polymers that it was proposed to refer to them as macromolecular nanoobjects, or macromolecular particles, along with dendrimers, dense molecular brushes, and nanogels [21,22]. The boundary between low-arm stars that belong to branched polymers and multiarm stars can be determined using the α coefficient of the Mark–Kuhn–Houwink equation [η]=KηM<sup>α</sup>. Its magnitude and, more importantly, the absence of the dependence of its magnitude on the molecular weight of the arm within the experimentally obtained values make it possible to unambiguously refer to the new objects as one or another classification group [23–26]. If a star-shaped polymer has a number of arms f > 30, the value of the α coefficient decreases with the number of arms to very low values for such systems (at f > 100, α = 0.06) [24], which characterizes the object as a rigid and compact globule. The nature of these specific polymeric macromolecules determines the peculiarities of their behavior. A number of papers [27,28] have distinguish two limiting cases in star-shaped systems: the first type is stars with a small number of long arms and a low-volume core that remains permeable to elements of the neighboring stars and do not become arranged, and their terminal dynamics are mainly controlled by the relaxation of the arms. The second type is stars with a large number of short arms and a core that is impermeable to the elements of the neighboring stars, which show a clear arrangemen<sup>t</sup> and where the slowest dynamics are controlled by structural rearrangements. The first group can be regarded as a typical polymer system, but the second one demonstrates analogies with colloids. The studies were carried out on examples of polyisoprene and polybutadiene stars.

This work is an extension of the studies on star-shaped polydimethylsiloxanes (PDMSs) with a different number of arms [5,29–31]. It was previously shown that PDMS stars with a number of arms f > 30, based on an examination of their diluted solutions, refer to dense globular objects with α = 0.06–0.15. A study on PDMS star rheology showed the Newtonian nature of the flow in systems with f = 8 and 32, and a pseudoplastic flow at f = 128 [31]. In this case, the viscous flow activation energy value Eact of all the synthesized samples, regardless of the number of arms, insignificantly differed from the Eact of linear PDMS [32], which indicated the polymeric nature of the objects—even a 128-arm star with an arm length of ~60 links did not show signs of colloidal behavior. To further study the properties of multiarm PDMS systems, a series of model 128-arm objects based on a sixth-generation carbosilane dendrimer with different arm lengths were synthesized and studied, and an attempt was made to synthesize a 512-arm PDMS star based on dendrimer G8.

#### **2. Results and Discussion**

The possibility of obtaining multiarm stars with a known number of arms and their adjustable and known length was determined by the use of the nonequilibrium anionic polymerization of hexamethylcyclotrisiloxane with a regularly structured polylithium dendritic initiator (Scheme 1). The polyfunctional initiator was a derivative of a carbosilane dendrimer with a protective hydrocarbon layer to prevent the intermolecular aggregation of lithium atoms [31].

The shielding outer layer consisting of methyldidodecylsilyl groups was created by the hydrosilylation of didodecylmethylsilane (DDMS) and dendrimer **1**, leaving half of the outer allyl groups unreacted (Figures S1–S4). Based on the synthesized DDMS derivative **2**, we obtained a polylithium anionic polymerization macroinitiator **3** via reaction with nbutyllithium and TMEDA in a hexane solution. The lithiation reaction was monitored by the appearance of lithium carbanion signals on the 1H NMR spectra, along with disappearance signals from allyl groups, using diffusion filtration to suppress hexane signals. Based on

the absence of signals from allyl groups in the 1H NMR spectra (Figure S5), it is fair to say that the conversion of the carbanion formation reaction in the case of DDMS derivatives of fourth- and sixth-generation dendrimers was close to 100%, which allows, within the NMR technique error, one to assert with a high degree of certainty the presence of active lithium centers in the structure of the macroinitiator, in an amount similar to the number of allyl groups in the dendrimer-derived DDMS. Earlier, the GPC technique showed [29] that the organolithium product of lithiation terminated by trimethylchlorosilane is monomodal and has a narrow polydispersity, which proves the complete absence of intermolecular crosslinking reactions.

**Scheme 1.** Synthesis of star-shaped PDMS based on carbosilane dendrimer, where k = 32, 128, and 512.

The polymerization of hexamethylcyclotrisiloxane using a synthesized polyfunctional initiator with different monomer/initiator ratios (Table S1) yielded a series of 128-arm star-shaped PDMSs, with monomodal narrow-dispersed molecular weight distributions according to GPC data (Figure 1). The presence of a certain number of didodecylsilyl group protons on the branching center in the structure of the synthesized compounds made it possible to calculate the number average molecular weight of the macromolecule and the arm length using the 1H NMR spectra data (Figures S6–S9, Formula S1). The results of calculations are presented in Table 1.

**Figure 1.** GPC curves of star-shaped PDMSs with number of arms f = 128 and different arm lengths.

In the text, samples of star-shaped polydimethylsiloxanes (PDMS) are designated as St-arms number-arm length, for example, St-128-114.

The light scattering method confirmed the monomodality and narrow dispersion of the obtained objects according to the GPC data; as an example, the obtained curves for a specimen St-128-33 are shown in Figure 2.


