Visualisation and characterisation of heterogeneous bimodal PDMS networks

The existence of short-chain domains in heterogeneous bimodal PDMS networks has been con ﬁ rmed visually, for the ﬁ rst time, through confocal ﬂ uorescence microscopy. The networks were prepared using a controlled reaction scheme where short PDMS chains were reacted below the gelation point into hyperbranched structures using a ﬂ uorescent silicone compatible cross-linker. The formation of the hyperbranched structures was con ﬁ rmed by FTIR, 1 H-NMR and size exclusion chromatography (SEC). The short-chain hyperbranched structures were thereafter mixed with long-chain hyperbranched structures to form bimodal networks with short-chain domains within a long-chain network. The average sizes of the short-chain domains were found to vary from 2.1 to 5.7 m m depending on the short-chain content. The visualised network structure could be correlated thereafter to the elastic properties, which were determined by rheology. All heterogeneous bimodal networks displayed signi ﬁ cantly lower moduli than mono-modal PDMS elastomers prepared from the long polymer chains. Low-loss moduli as well as low-sol fractions indicate that low-elastic moduli can be obtained without compromising the network's structure.


Introduction
Polydimethylsiloxane (PDMS) elastomers are known for their unique properties, such as high extensibility, high thermal stability, low surface tension and chemical and biochemical inertness. 1 PDMS elastomers consist of a PDMS network, usually resulting from hydrosilylation, radical or condensation reactions, silica particles and other llers. 2 PDMS networks without llers suffer from low tear strength and are therefore not easily handled as thin lms. The reinforcing silica particles in the elastomer formulations result in a very weak but still not negligible optical distortion, which constitutes a problem in many commercial applications such as adaptable lenses and optical biochips. 3,4 The mechanical properties of PDMS elastomers, as an alternative, can be improved by creating bimodal networks which are prepared by applying advanced mixing schemes. Bimodal networks consist of very short and relatively long chemically identical polymer chains cross-linked into a network, and their mechanical properties are superior to traditional elastomers. 5,6 Several studies have investigated the unexpected high tear resistance and ultimate strength of bimodal networks. [7][8][9] The elastic modulus of bimodal networks increases signicantly at high elongations, so the ultimate strength of the networks is very high. Improvements in ultimate strength stem from the limited extensibility of the short chains, which gives the networks toughness. 10,11 Furthermore, the relatively long chains retard the rupture process and provide extensibility to the network. 9 Therefore, bimodal networks exhibit both a substantial ultimate stress and ultimate strain. 6 Bimodal networks can be created by the random distribution of short polymer chains within the long chains, 6,12-14 or as heavily cross-linked short-chain domains joined to the long-chain network. [15][16][17] Bimodal networks with homogenous (random) distributions of short and long chains are prepared in one-step procedures where the chains are mixed and cross-linked simultaneously to form random networks. In contrast, heterogeneous bimodal networks are prepared in two-step procedures. The short-chain domains are prepared in a reaction that happens prior to the cross-linking, where the short chains are reacted below the gelation threshold into hyperbranched structures which are subsequently mixed and cross-linked together with the long chains. Consequently, short-chain domains are created within the long-chain network. Furthermore, the long chains can also be reacted with cross-linker molecules below the gelation thresholdprior to the network formationin order to obtain even higher control over the network and the distribution of longand short-chain domains. 17 We have previously demonstrated that the advantage of forming heterogeneous bimodal networks with a controlled distribution of short-chains is that the elastic modulus becomes lower compared to both homogenous bimodal networks with similar short chain concentrations and mono-modal PDMS networks. 17 In so doing, soer and more stretchable PDMS elastomers are obtained. The lms are at the same time easily handled as thin lms, which for the homologues mono-modal PDMS network is difficult without the addition of silica particles. Furthermore, heterogeneous bimodal networks have been shown to exhibit very low viscous losses in combination with low elastic moduli. 17 So they are therefore excellent alternatives to both mono-modal PDMS elastomers, which require llers to have sufficiently high tear strength to make them manageable as thin lms, and to homogenous bimodal networks, which have higher elastic moduli due to the random distribution of short chains.
We herein present a novel method for analysing the size of short-chain domains in heterogeneous bimodal PDMS networks. A recently developed silicone compatible cross-linker allowing for orthogonal chemistry 18 is used to tag the shortchain hyperbranched structures at their cross-linking points with uorescent molecules. The size of the short-chain domains will furthermore be correlated to the nal mechanical properties of the networks. The design scheme offers an unprecedented way of tuning the properties of heterogeneous bimodal networks and thereby paves the way for the implementation of such networks in advanced applications where strong, unlled and largely extensible networks are needed. The properties of the resulting networks will full the demands of many commercial PDMS elastomer applications, including so lithography applications where higher fracture energy is needed, 19 optical applications where strong elastomers without optically distorting llers are desired 3,4 and dielectric elastomers where so networks with high extensibilities and low viscous losses are essential. [20][21][22][23][24][25] Experimental General methods FTIR analyses were conducted on a Perkin-Elmer Spectrum One model 2000 Fourier Transform Infrared apparatus equipped with a universal attenuated total reection accessory on a ZnSediamond composite. The spectra were recorded in the range of 4000-650 cm À1 with 16 scans using 4 cm À1 resolution. 1 H-NMR spectra were recorded on a Bruker 300 MHz spectrometer. Sizeexclusion chromatography (SEC) was performed on a Viscotek GPCmax VE-2001 instrument, equipped with a Viscotek TriSEC Model 302 triple detector using two PLgel mixed-D columns, provided by Polymer Laboratories. Samples were run in THF at a rate of 1 ml min À1 , and molar mass characteristics were calculated using polystyrene standards. Optical characterisations were performed on a Leica TCS SPE high-resolution confocal microscope with a 10Â lens at 400 nm in the z-direction, equipped with a Leica CTR4000 electronic box. Image analysis was performed with ImageJ, and the domain diameter was taken as an average over 100 domains. Differential scanning calorimetry (DSC) measurements were performed on a DSC Q1000, provided by TA Instruments. The thermal analyses were performed with a heating and cooling rate of 10 C min À1 , from À90 to 150 C. Thermogravimetric analysis (TGA) was performed on a Q500 (TA Instruments) in a nitrogen atmosphere with a heating rate of 10 C min À1 , from RT to 950 C. All degradation temperatures were taken as the peak temperature of the rst derivative of the temperature with time. Linear rheology of the bimodal lms was performed with a TA Instruments TA 2000 Rheometer set to a controlled strain mode of 1%, which was ensured to be within the linear viscoelastic regime. The measurements were performed in the frequency range 100-0.01 Hz with a parallel plate geometry of 25 mm. The lms were approximately 1 mm thick and were measured with a small normal force from the upper plate, which ensured that there were no-slip conditions.
General procedure for preparing heterogeneous bimodal networks (amounts given for 10 wt% short chains) The uorescent tri-functional cross-linker (3, 0.027 g, 0.0054 mmol) was dissolved in THF (0.6 ml) and mixed with short PDMS chains (DMS-H11, 1050 g mol À1 , 0.212 g, 0.020 mmol). The platinum cyclovinylmethyl siloxane complex catalyst (511) (10 ppm) in dry THF was thereaer added to give a stoichiometry of r ¼ 0.4 and the mixture was mixed in a FlackTek Inc. DAC 150.1 FVZ-K SpeedMixer™ and allowed to react for 1 hour at 60 C. Next, a 16-functional vinyl cross-linker (VDT-431, 28 000 g mol À1 , 0.014 g, 5 Â 10 À5 mmol) and the long PDMS chains (DMS-H31, 28 000 g mol À1 , 1.91 g, 0.0068 mmol) were mixed with platinum cyclovinylmethyl siloxane complex catalyst (511) (10 ppm) in dry THF to give a stoichiometry of r ¼ 0.06. The mixture was combined in the SpeedMixer and thereaer allowed to react for 1 hour at 60 C. Aer the initial reactions, the short-and long-chain mixtures were combined and additional cross-linker (VDT-431, 28 000 g mol À1 , 0.838 g, 0.0030 mmol) and catalyst (10 ppm) were added to give an overall stoichiometry of r ¼ 1.2 (20% excess of vinyl groups). The mixture was blended in the SpeedMixer and poured into 1 mm thick steel moulds on an FEP uorocarbon substrate, degassed in vacuo for 1 hour, cured for 24 hours at RT and then post-cured at 60 C for 1 hour. Short and long chain amounts were varied to create bimodal networks with mass ratios of short : long chains

Swelling experiments
Swelling experiments were performed by placing a pre-weighed sample in a ask containing toluene until the equilibrium swelling state was reached (typically one week). At the end of the swelling period, the samples were removed from the solvent, dried quickly and carefully with lint-free tissue paper and then weighed. The volume degree of equilibrium swelling (Q v ) was then calculated according to: where n toluene is the specic volume of toluene and n PDMS is the specic volume of PDMS. Q w is calculated as: Q w ¼ m 0 /m, where m 0 is the initial weight of the (dry) sample before swelling and m is the weight of the wet (swollen) sample. Aer the swelling experiment, the samples were washed several times with toluene and dried for 24 hours. The sol fractions (W sol ) were thereaer calculated as: W sol (%) ¼ (1 À (m e /m 0 )) Â 100, where m e is the weight of the dry sample aer the swelling/extraction.

Results and discussion
The heterogeneous bimodal PDMS networks were prepared in a two-step procedure combining short-and long-chain hyperbranched PDMS structures, as illustrated in Fig. 1. First, uorescent short-chain hyperbranched structures were prepared in a reaction prior to the network formation using a previously prepared uorescent tri-functional cross-linker. 18 The crosslinker was used in concentrations below the gelation point, as determined by the Flory-Stockmayer expression: where r c is the stoichiometry between the reactive groups on the cross-linker and the reactive groups on the polymer required for critical gelation, and f is the functionality of the cross-linker. By using a stoichiometry where r < r c no innite short-chain network will be created, and the formed hyperbranched structures still have reactive end groups. 26,27 The short-chain hyperbranched structures were characterised by FTIR, 1 H-NMR and size-exclusion chromatography (SEC). The reaction between the uorescent cross-linker and the short PDMS chains was followed by FTIR and the decreasing intensity of the cross-linker C]C band at 1610 cm À1 . Furthermore, FTIR spectra conrmed the presence of the remaining Si-H end groups (at 2125 cm À1 ) on the short-chain polymers aer the reaction. The reaction employed to form the short-chain hyperbranched structures was also followed with 1  aer the reaction. This number is consistent with the stoichiometric ratio of r ¼ 0.4 used in this instance. 1 H-NMR spectra can be found as ESI. † SEC was used to conrm the postreaction increase in molecular weight of the hyperbranched structures, which appear in the higher molecular weight region compared to the low molecular weight short-chain PDMS (as seen in the SEC traces in the ESI †). In addition, the SEC trace clearly shows that the reaction results in a distribution of hyperbranched structures and not in a mono-modal structure, which is as expected for a hyperbranched structure.
In a similar manner, the long-chain hyperbranched structures were prepared by using a commercial cross-linker (28 000 g mol À1 , bearing, on average, 16 vinyl groups per chain) and a higher molecular weight PDMS (28 000 g mol À1 ). The hyperbranched structures, based on the short and long chains, were mixed and cross-linked by using the commercial crosslinker in excess. The uorescent and reinforcing short-chain hyperbranched structures thereby became covalently bound to the long-chain hyperbranched structures, ensuring sufficient separation of the short-chain structures to maximise the reinforcing effect.
The heterogeneous bimodal networks were prepared with varying contents of short-chain hyperbranched structures, in order to illustrate the effect of the ratio between long-and shortchain hyperbranched structures. The concentration of shortchain structures varied from 0 to 30 wt%, corresponding to 0 to 92 mol% (of the total number of hydride functional polymers). Films based entirely on the short-chain polymer could not be prepared, as the polymer was of a too low molecular weight to form a mechanically stable lm.
The prepared heterogeneous bimodal networks were characterised by confocal microscopy, which uses single-point illumination and rejects out-of-focus light. Thus, images with better vertical optical resolution than traditional uorescence microscopy are obtained. The acquired images had reduced background haze and represent a thin cross-section of the sample, as shown in Fig. 2 (original uorescence confocal microscopy images of all samples can be found as ESI †).
The uorescent domains are evenly distributed within all networks. Furthermore, it can be seen from Fig. 2 that the uorescent domains vary in size and abundance, depending on the ratio between the short-and long-chain hyperbranched structures in the network. The mean diameters of the uorescent domains were determined as an average of 100 domains, the results for which are summarised in Table 1. As seen in Table 1, the sizes of the uorescent domains vary only moderately for the concentrations of short-chain hyperbranched structures, from 3 wt% to 20 wt%, whereas substantially larger domains are observed at 30 wt%. Furthermore, it is clear from Fig. 2 that the domains are very well distributed, and the number of domains is high for both samples. When the concentration of the short-chain hyperbranched structures is increased to 30 wt%, a substantial increase in the domain's size is evident (Fig. 2), due to the short-chain hyperbranched structures becoming so tightly packed that even upon ideal distribution they will interconnect covalently and turn into larger agglomerates. This is also substantiated by the large increase in the standard deviation of the measured average short-chain domain diameter.
The inuence on the distribution and size of the observed domains on the elastic and mechanical properties of the bimodal networks was determined by employing small amplitude rheology. The resulting shear storage moduli (G 0 ) and loss moduli (G 00 ) are summarised in Table 1. The mono-modal PDMS reference network, with 0% of short chains, has a storage modulus of 93.4 kPa. Upon the addition of the short-chain hyperbranched structures, the modulus decreases signicantly to 11.8 kPa. From fundamental theories on rubber elasticity the elastic moduli are expected to scale linearly with the inverse average molecular weight of the polymer chains in the network. 28 As such, the addition of very short polymer chains to the system would be expected to decrease the average molecular weight of the system and thus increase the elastic modulus signicantly. This decrease in the elastic modulus in heterogeneous bimodal networks has been shown previously but not explained with supporting data. 16,17 Based on the unprecedented correlation between the network composition, size and distribution of the uorescent domains, and the elastic properties of heterogeneous bimodal networks, we believe that the decrease in the elastic modulus can be explained by a multidomain theory. When short-chain hyperbranched structures are added, they naturally contain a large concentration of unreacted hydride groups on the surface. These groups react with crosslinker molecules, which upon initial reaction are hindered from diffusion by reptation. 29 Consequently, there is a large concentration of cross-linker molecules on the surface of the hyperbranched structures. Small cross-linker molecules, such as those used in our previous study, 17 are packed tightly around the surface, whereas the long-chain cross-linker molecules used in this study tend to fold around the short-chain hyperbranched structures. In both cases, this creates areas around the crosslinker molecules where the effective cross-linking density is lower than in the bulk long-chain network, as a large number of the cross-linking sites are present around the short-chain domains, as illustrated in Fig. 3. In this study, with a high molecular weight cross-linker, folding back to the short-chain domains also leads to the formation of loops, which do not contribute to elasticity to the same extent as the true crosslinking sites. 30 Domains with surrounding cross-linker molecules therefore create a local soening effect in the PDMS networks. The heterogeneous bimodal elastomers will consequently be soer and have a lower elastic modulus than the homologous mono-modal networks despite higher average cross-linking density. The reduction in the modulus, from mono-modal to a small amount of short-chain domains, is conrmed experimentally. The elastic modulus is then increased with increasing short-chain concentration. At high concentrations of short chains the elastic modulus drops again. This can be explained by a drop in the number average concentration of short-chain domains C N ¼ ((6 Â wt%)/ (pD 3 ))(1/r PDMS ), with the additional increase of short chains (see Table 1). From the calculations it can be seen that for the bimodal networks, the elastic modulus increases with increasing C N , although, not in a trivial way.
Interfaces with a lower cross-linking density are still perfectly cross-linked due to the high number of functional groups on each hyperbranched structure, and as such they cannot be regarded as network imperfections, since their mechanical properties are not destroyed.
Very so silicone elastomer behaviour can also be observed for imperfect networks, which occurs as a result of unreacted groups. This lack of reactivity can be introduced either from stoichiometrically imbalanced reactions 27,31 or from incomplete catalyst inhibition reactions. 32 It can also arise naturally from steric hindrance or heterogeneity, thus leading to local crosslinker and polymer excesses, respectively. Therefore it is important to ensure that heterogeneous bimodal networks do not contain a large fraction of solubles, so-called sol fractions. The sol fractions of heterogeneous bimodal PDMS networks were determined by conducting swelling experiments with toluene, the results for which can be found in Table S1 in the ESI. † The sol fractions were found to lie in the range of 5-10% and were apparently independent of short chain concentration. The addition of the short chains as domains therefore does not create additional imperfections in the innite networks, which  means that there is complete compatibility between the shortchain domains and the long-chain matrix. Swelling experiments were performed in order to determine the relationship between the volume degree of equilibrium swelling (Q v ) and the mechanical properties. The results can be found in the ESI. † Q v is found to decrease with increasing shortchain concentration, due to the strong increase in cross-link density. Furthermore, as expected, there is not a linear relationship between the elastic moduli (3G 0 ) and the equilibrium swelling degree (see Fig. S3 in the ESI †), which is observed for traditional mono-modal PDMS elastomers. Heterogeneous bimodal networks therefore behave quite different to monomodal PDMS networks, since the modulus decreases following the addition of short-chain domains, i.e. with increasing crosslink density. This means that swelling capacity is determined from the continuous long-chain part of the network, whereas elasticity is governed by a combination of short-and longchains properties.
In general, it is difficult to obtain PDMS elastomers with low elastic moduli without deteriorating other network properties. So PDMS elastomers therefore usually suffer from high viscous losses. The frequency-dependent viscous loss can be determined from the shear loss modulus G 00 . All the prepared bimodal elastomers are seen to have lower viscous loss than the mono-modal PDMS network. Furthermore, the heterogeneous bimodal networks are well cross-linked, as the storage moduli (G 0 ) is 10 to 100 times larger than the loss moduli (G 00 ) for the investigated frequency range, with differences being smallest at high frequencies. A plot of the storage and loss moduli as functions of frequency can be found as ESI. † Viscous loss at the low strain low frequency limit is measured as a few percentage points only. This is comparable to our previously reported results for heterogeneous bimodal networks. 17 Viscous loss in a polymer network is due to dangling chains and sol molecules, i.e. incomplete network formation. 27 It is therefore evident from the low viscous losses of the heterogeneous bimodal networks that the obtained low moduli are not a result of incomplete reactions but rather of network artefacts, as shown in Fig. 3. The loops do not contribute signicantly to the elastic modulus, but at the same time they do not contribute a loss, since they cannot relax. Heterogeneous bimodal networks are therefore an effective and simple method of creating so elastomers with very low viscous losses.
The thermal transition behaviour of the heterogeneous bimodal networks was determined using differential scanning calorimetry (DSC). The resulting thermograms can be found as ESI, † while the crystallisation and melting temperatures are summarised in Table S1 in the ESI, † too. A large decrease in the area under the crystallization peaks can be seen in the thermograms, along with an increasing concentration of shortchains. This means that there is a smaller degree of crystallinity in the material in line with increasing short-chain content. Consequently, the PDMS elastomers become inherently amorphous at large concentrations of short chains, as almost no crystalline behaviour is observed. This is most likely due to an increased cross-linking density as the short chain domains are highly dense structures in elastomers. This high cross-link density means that the polymer chains are no longer able to arrange into the positions necessary for crystalline regions to form. Melting temperatures are also observed to decrease with higher concentrations of short chains because of the dilution of the crystalline segments. Furthermore, areas under the melting peaks are reduced at higher concentrations, which mean that the energy required for melting is reduced at larger concentrations of short chains.
Moreover, the effect of short-chain domains on the thermal stability of the PDMS networks was investigated by thermal gravimetric analysis (TGA). The determined degradation temperatures for the bimodal PDMS networks with different short-chain concentrations are summarised in Fig. S5 and Table  S1 in the ESI. † The rst degradation step occurs due to the cleavage of Si-CH 3 bonds. This degradation temperature increases signicantly with increasing amounts of short chains (from $430 C to $530 C), which demonstrates that heterogeneous bimodal networks also have a benecial inuence on the thermal stability of PDMS elastomers.

Conclusions
In summary, a novel method of visualising the size of shortchain domains in heterogeneous bimodal PDMS networks was developed. The method allows for the determination of the size of short-chain domains by confocal uorescence microscopy. The size of the domains was furthermore correlated to the nal elastic properties of the bimodal networks for the rst time, which makes it possible to explain the surprisingly low elastic moduli obtained for heterogeneous bimodal networks. The results thereby make it possible to tune the properties of PDMS networks in line with the size and concentrations of short-chain hyperbranched structures. This opens up the possibility of heterogeneous bimodal network implementation in advanced applications where strong, unlled and largely extensible networks are needed, such as in the eld of optics and in the emerging eld of dielectric elastomers.