(3-glycidyloxypropyl)trimethoxysilane (GTMS) is the typical organotrialkoxysilane used as a coupling agent. The structure evolution during hydrolytic polycondensation of GTMS is determined mainly by catalytic conditions, as is usual for the sol-gel process. The acid (TSA)-catalyzed polymerization is very slow, and the system finally gels in 15 days at 80°C, with the stoichiometric amount of water, rH = 1.5 . Under catalysis with DBTDL and BDMA, the polymerization is faster compared to TSA; however, mainly relatively stable low-molecular-weight products are formed in the early stage (see SEC record in Fig. 1.10). The dominant oligomer prevailing in the reaction mixture corresponds to the compact cubic octamer cage produced by intramolecular condensation of GTMS (Scheme 1.3a). Due to the preferential intramolecular reaction to form polyhedral cyclics, the trifunctional monomer does not gel under DBTDL catalysis. In addition to the fully condensed octamer cage, mass spectrom-etry also reveals distribution of products involving incompletely closed cages or nonamer and decamer cages present in the oligomer fraction. The most prominent structures proved by electrospray ionization mass spectrometry are illustrated in Scheme 1.3b. The fraction of the cages increases with dilution of the reaction mixture and with excess of water. A high yield of the cage (~90%) was obtained using BDMA catalyst and a water content of rH> 5. On the contrary, only a small amount of low-molecular-weight polyhedral products arise in the reaction mixture catalyzed with TSA. In this case, the intermolecular condensation is preferred, high-molecular-weight polymers are formed slowly (see Fig. 1.10c), and GTMS gels. The structure is less branched and linear polysiloxane chains prevail.
In addition to the effect of catalysis, the size of the organic substituent R in organotrialkoxysilanes plays a crucial role in the reaction mechanism and final structure. The polymerization of small trialkoxysilanes, such as methyltrimethoxysi-lane or vinyltriethoxysilane, is relatively fast, and the systems quickly gel under both acid and basic conditions. An increasing length of R in octyltriethoxysilane and alkoxysilyl-endcapped oligomers leads to a reduction of the reaction rate. Moreover, in this case only stable low-molecular weight products are formed, and no gelation occurs independent of catalysis . The long organic substituents R in the trialkoxysilanes cause steric hindrance around the functional alkoxysilane groups, resulting in restriction to the intermolecular polycondensation. The SiOH groups mostly react intramolecularly to form polyhedral cyclics yielding a narrow distribution of almost fully condensed polyhedral frameworks that are very stable. No high-molecular-weight polymer is produced by polymerization of the long tri-alkoxysilanes, in contrast to polymerization of the GTMS/DBTDL system where
the octamer cage appears; however, a broad molecular weight distribution of polymers is formed as well (see Fig. 1.10a). In the case of alkoxysilyl-capped poly(oxyethylene) of the molecular weight M = 350, SPOE350, a gradual consumption of the long "macromonomer" takes place, and evolution of the molecular weight during polymerization leads to the bimodal distribution (see Fig. 1.11) . The oligomer fraction corresponding to the "macrooctamer" is preferentially built-up from the beginning of the reaction. The distribution of the T units, determined by NMR analysis of the octamer isolated from the reaction mixture of the polymerized oligomer SPOE350/DBTDL, is as follows: T0 = T1 = 0, T2 = 0.21, T3 = 0.79. The absence of T1 units characterizing chain ends of the Si-O-Si sequences, and a high fraction of branched T3 units in such a low-molecular-weight product, imply
highly cyclic structures. A high yield of polyhedral oligoSSQO, mainly octahedrons and decahedrons, in the polymerization of the trialkoxysilanes with sterically demanding substituents, was observed also by Feher et al.  and Fasce et al. . Evidently, the size of the substituent affects the tendency of the trialkoxysilane to cyclization and formation of polyhedral structures. Consequently, this is a procedure to prepare stable, low-molecular-weight SSQO clusters with emanating organic chains.
Fig. 1.11 Evolution of the molecular weight distribution during polymerization of SPOE350 catalyzed with DBTDL; T = 80°C. Curves (reaction times): (1) t = 0, (2) t = 24 h, (3) t = 120 h, (4) t = 288 h
The SSQO structure evolution in polymerization of organotrialkoxysilanes is determined by a competition between the intermolecular polycondensation and intramolecular reactions to form cyclics, ladders, and cages. Moreover, because an O-I block copolymer is formed, the microphase separation occurring during the reaction is often accompanied by a spontaneous self-organization, typical of block copolymers.
The self-organization of GTMS during polymerization under DBTDL catalysis is revealed by SAXS analysis (Fig. 1.12a). The gradual structure ordering during the reaction manifests itself by a growth of the intensity maximum in SAXS curves at q ~ 0.4 A-1. The peak becomes apparent at a high condensation conversion, when the system is filled up predominantly with the compact microphase-separated cagelike structures and corresponds to the intermolecular interference coming from scattering on regularly arranged cages. The structure is organized into micelles, with the compact SSQO polyhedral core and protruding glycidyloxypropyl groups. The length of the organic group of these octopus-like molecules determines the separation distance of the cages, as shown in Scheme 1.4a. The correlation distance d is characterized by the position of the maximum qmax according to the expression, d = 2p/qmax. The experimentally determined value d1 = 15.7 A is in good agreement with the theoretical estimate 15.0 A.
Fig. 1.12 Evolution of the SAXS profiles during polymerization of GTMS catalyzed with (a) DBTDL and (b) TSA; T = 80°C. Curves (reaction times): (1) t = 5 min, (2) t = 90 min, (3) t = 3 h, (4) t = 8 h, (5) t = 48 h, (6) t = 168 h, (7) t = 336 h. Curves are mutually vertically shifted
The incompletely condensed cages also present in the system (see Scheme 1.3b) can interconnect to form a higher-molecular-weight branched polyhedral or ladderlike SSQO structures (Scheme 1.4b). Also Eisenberg et al.  found that most species are incompletely condensed, and the SSQO structure is built by combining
""w* glycidyloxypropyl groups Scheme 1.4 Ordering of cage-like structures in the polymerized GTMS
fundamental octamer building blocks. In the case of higher-molecular-weight, ladder-like SSQO structures, the interpenetration of the organic dangling substitu-ents, glycidyloxypropyl groups, is less likely due to increasing steric hindrance. As a result, the structures with a larger separation distance d2 are also formed, as displayed in the Scheme 1.4b. These structures are characterized by the second broad maximum at q = 0.15 Á-1 in Fig. 1.12a.
No self-assembly of the regularly arranged domains occurs under acid (TSA) catalysis of GTMS polymerization. A broad distribution of high-molecular-weight polySSQOs with dangling organic substituents formed in the acid polymerization (see Fig. 1.10c) does not allow for any regular arrangement. In this case, no interference maxima at q < 0.50 Á-1 are observed in Fig. 1.12b . The initial maximum at q ~ 0.6 Á-1 characterizes the intramolecular distances in GTMS and products. It does not suggest any intermolecular regular arrangement.
The significant ordering, more pronounced than in GTMS, takes place mainly during the polymerization of the trialkoxysilanes with long organic substituents. The structure evolution in the polymerization of SM600, i.e., the trialkoxysilane-capped poly(oxypropylene) of molecular weight M = 600, is characterized by the SAXS profiles in Fig. 1.13. The sharp maximum growing at q = 0.18 Á-1 reveals a microphase separation and a high degree of ordering of the polyhedral domains. The self-organization of the long organotrialkoxysilanes happens both under DBTDL (Fig. 1.13a) and TSA (Fig. 1.13b) catalysis, unlike the GTMS polymerization. The
position of the SAXS maximum correlates with the molecular weight of the organic chain, (refer to qmax = 2p/d) (see Fig. 1.14, curves 4-6 for the substituents R = octyl and POP chains of M = 600 and 2000, respectively) proving that its length controls the space separation of the cage frameworks in the micelle-like arrangement. The small trialkoxysilanes - methyltrimethoxysilane, vinyltriethoxysilane, and triethox-ysilane - do not form ordered structures (Fig. 1.14, curves 1-3).
A perfect supramolecular ordering of the SSQO cages is directed by crystallization of a long poly(oxyethylene) chain in sol-gel polymerization of SP0E2000 and SP0E5000. During hydrolytic polycondensation at 135°C, the self-organization into micellar SSQO domains sets in, with a correlation distance corresponding to the POE coil size in the melt (Scheme 1.5). The melts of both polymerized SPOE oligomers exhibit SAXS interference maxima: qmax ( SPOE2000) = 0.16 A" 1 (see Fig. 1.15a, curve 1) and qmax(SPOE5000) = 0.10 A-1, corresponding to correlation lengths 39 and 63 A, respectively, given by the POE chain length. The theoretical end-to-end distance r for SPOE2000 and SPOE5000 is 40 and 63 A, respectively. During cooling, crystallization of fully extended POE chains in SPOE2000 or folded chains in SPOE5000 takes place. The crystallization of SPOE2000 chains on cooling manifested itself by a gradual appearance of the crystalline reflection in WAXS (Fig. 1.15b). Simultaneously, the micelle arrangement of the SSQO cages, characterized by a SAXS peak at 0.16 A" 1 is gradually disappearing, and a new
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