Bottom-up device fabrication via the seeded growth of polymer-based nanowires† †Electronic supplementary information (ESI) available: Experimental details of the polymer preparation, growth of micelles, characterisation and data analysis (cyclic voltammetry, AFM and electrical measurements). See DOI: 10.1039/d0sc02011g

Living crystallisation-driven self-assembly facilitates the bottom-up assembly of electronic devices.


Introduction
The bottom-up fabrication of nanoelectronic devices was conceptualised decades ago 1,2 but remains as an important challenge of intense interest. Overwhelmingly, in examples to date, preformed components, ranging from small single molecules to anisotropic nanostructures e.g. carbon nanotubes, are directed towards the inter-electrode region to complete an electrical circuit. Simple circuits have thus been assembled using a variety of approaches for component organisation such as ow, 3-5 electrophoresis, 6 dipping, 7 hydrogen bonding/molecular recognition (DNA), 2 chemisorption in a nanogap, 8 and dip-pen lithography. 9 An alternative, much less explored, approach is to extend the self-assembly stages to the components themselves and for these to be grown in situ. [10][11][12][13] This could, in principle, allow components to adapt to changes in device conguration, such as electrode spacing, number etc. and enable more complex architectures to be constructed from simple molecular building blocks. However, previous efforts have relied on simple electropolymerisation with the resulting lack of precise control in the morphology of the resulting interconnects leading to poor denition of morphology and size. [10][11][12] Living crystallisation-driven self-assembly (CDSA) is a wellestablished seeded growth approach to uniform 1D [14][15][16][17][18][19][20] and 2D 21-28 nanostructures using amphiphilic polymeric or molecular building blocks. The living CDSA process resembles a living covalent polymerisation except that it occurs on a longer lengthscale and involves an epitaxial growth mechanism. 14,29 Ultrasonication of bre-like micelles with a crystalline core leads to fracture by Gaussian scission to give shorter micelles which function as seed initiators for bre-like micelle growth by living CDSA. 29 The addition of further block terpolymer in a molecularly dispersed form (unimers) leads to epitaxial growth at the seed termini to yield uniform bre-like micelles with length dependent on the mass ratio of the added unimer to the pre-existing seeds. Epitaxial growth of bre-like block terpolymer micelles has been achieved from the edges of platelet micelles, from the surface of thin lms of homopolymer 30 and from seed micelles localised on silica, colloidosome, and silicon surfaces. [31][32][33][34] In a previous study, CDSA has been used to assemble well-dened templates for the preparation of polyaniline nanowires with controlled lengths in solution-phase. 35 Here we exploit this CDSA behaviour to demonstrate an in situ approach to construct a simple electrical circuit using redox-active brelike block terpolymer micelles as building blocks. Specically, we demonstrate that block terpolymer seeds from Gaussian scission of micelles can be designed to chemisorb onto electrode surfaces and initiate the controlled interfacial growth of micelles of well-dened length. Further, these bre-like micelles are capable of spanning an interelectrode gap and Fig. 1 outlines the scheme for device assembly based on this three-step seeded-growth approach. Here, in this proof of concept work, we use a triblock terpolymer poly (ferrocenyldimethylsilane)-block-poly(dimethylsiloxane)-blockpoly(3-octylthiophene) (PFDMS 44 -b-PDMS 250 -b-P3OT 17 ). The design criteria for this material were to use the wellcharacterised, crystallisable PFDMS 36 core-forming block for living CDSA and an electroactive, p-conjugated polymer, poly(3octylthiophene) ($17-mer), the peripheral coronal segment with a central PDMS corona-forming block inbetween. The P3OT block was incorporated into the polymer to play two roles in the bre-like micelle structure. First, the conjugated thiophene block can be switched to an electronically conducting form aer doping. 37,38 Second, thiophene residues should facilitate attachment of the seeds to the gold surface by spontaneous chemisorption. 39,40 In the initial stage towards device assembly we sought to conrm chemisorption of seeds at metal surfaces. As a simple proof, Au-on-Si substrates were immersed in a solution of PFS-b-PDMS-b-P3OT seeds in decane. Cyclic voltammetry of these substrates exhibited, aer extensive washing, the expected redox behaviour for the ferrocenyl/thiophene-containing polymer (ESI Fig. S4 †). The chemisorption was further conrmed by AFM which also allowed the stability of the attachment to be monitored. Scanning the same area of the modied substrate (Fig. 1F, G and S5A-E †) showed that no seeds were removed from the gold surface aer immersion in decane for 2, 4, 6, and 24 hours (see details in the ESI †).
AFM imaging (Fig. 1H) shows a single adsorbed seed on a gold surface that is about 120 nm in length. Such modied surfaces act to seed the growth of bre-like micelles and conrm that the ends of the seeds remain active even aer the chemisorption on the gold surface. Fig. 1I shows a bre-like micelle self-assembled on the gold surface from an adsorbed seed by immersion in a solution of unimers. The bre-like micelle is well dened with uniform diameter of 7.7 nm (as expected from simple models) and extends 2.4 mm in length. Such a well-dened size and morphology of the bre-like micelle is in marked contrast to the (electro)chemically grown polymer systems. [10][11][12] The AFM data reveal the living nature of the CDSA process 29 by showing clear evidence for the increase in the seed length. In contrast, a control sample (Fig. S5F †) of a pre-cleaned gold substrate immersed for 18 h in a decane solution of unimers showed no micelles, conrming that the living CDSA process by self-initiation is inefficient over this timeframe. Seeding the surface is much more efficient than selfnucleation of bre-like micelles in a similar manner to the growth of the bre-like micelles in homogeneous solution. 30 Control of seed density and bre-like micelle length on gold surfaces Next, we set out to establish details of the experimental conditions required for optimising the seed density on the electrode surface and for control of micelle length in an effort to provide parameters for device construction. In these experiments, seeds at different concentrations (0.02, 0.1, 0.2, 0.4 and 1 mg ml À1 ) were diluted in 1 ml of decane and allowed to interact with the gold surfaces (Au-on-Si; 8 Â 8 mm). Immobilisation was judged to occur in appreciable numbers aer around 7 min. However, all the samples have been immersed for 2 h in order to increase the loading of adsorbed seeds. Fig. 2A-C shows AFM images of PFDMS-b-PDMS-b-P3OT seeds immobilised on gold substrates. The number of the adsorbed seeds on the surface increased in proportion to the concentration of seeds in solution, as expected (Fig. 2D). Importantly, this makes it possible to grow a desired number of micelles per micrometer by adjusting the concentration of the seed solution. From this analysis, solutions of 0.02 mg ml À1 or less were considered to produce the most suitable density of seeds on the surface for bre-like micelle growth. This concentration range allows sufficient space for the micelles to grow on the surface with minimum crossing.
Growth of bres with well-controlled length from the adsorbed seeds is an important factor for fabrication of nanowire devices. Controlling the length of the bre-like micelles by variation of the unimer-to-seed ratio in a solution was previously demonstrated; 29,41 here we investigate the kinetics of the process on solid surfaces. Seeds were adsorbed onto gold-  in Fig. 2H shows the variation in bre-like micelle length as a function of unimer solution concentration. The average contour lengths of the micelles were determined by tracing the length of 50 bre-like micelles from at least 6 AFM images on randomly selected areas of each sample. It is clear from these data that the micelles grow to greater lengths as the unimer concentration is increased. However, it was found that micelles assembled from unimer solutions of 4 mg ml À1 and higher, start to aggregate and form networks on the surface, (Fig. S6 †). It can also be judged from AFM images (e.g. Fig. 2G) and the error bars in Fig. 2H that bre-like micelles grow with more variability of length at higher concentrations of unimer solution.

Kinetic analysis of bre-like micelle length distributions on gold surfaces
Owing to the limitations on control of the bre-like micelle length using the concentration of the unimer solutions, the effect of immersion time was studied in order to identify conditions for controlled growth of long monodisperse micelles at surfaces. Our experimental results indicate that living CDSA to form PFDMS 44 -b-PDMS 250 -b-P3OT 17 bre-like micelles can continue for weeks. The AFM images in Fig. S7 † were obtained by adsorption of seeds from 0.02 mg ml À1 seed solutions and growth of the bre-like micelles by immersion in 2 mg ml À1 unimer solutions in decane for one day and 20 days, respectively. In the sample immersed for one day (Fig. S7A †) the micelles have grown to less than 1 mm. By comparison aer 20 days the micelles have grown over 10 microns in length and formed a dense network (Fig. S7B †).
In Fig. 2I-K, the bre-like micelles were self-assembled from surfaces with low numbers of seeds (adsorbed from a 0.005 mg ml À1 seeds solution) in order to form a less dense network of long bres which are amenable to quantitative analysis. The bre-like micelles were le to grow in 0.5 mg ml À1 unimer solution in decane for different immersion times (2, 4, 6, 8 and 10 days). The relationship (Fig. 2L) between the immersion time and the bre-like micelle length shows a high degree of control over the self-assembly process. In this relationship, the small error bars indicate a more uniform rate of the bre-like micelle growth compared to Fig. 2H. The AFM images and the data analysis of this slow growth of the bre-like micelles show that these may be grown precisely to a desired length by controlling the immersion time of adsorbed seeds in the unimer solution at an appropriate concentration.
The kinetic data in Fig. 2I-K can be analysed further by considering the growth process as an example of chain growth polymerisation. Such a mechanism, in which growth occurs solely by addition of the unimers to the end of the bre-like micelle and for which there is no termination, yields a probability mass distribution of Poisson form as in eqn (1).
The parameter l is the mean rate of growth of micelles and is a pseudo-rst order rate constant proportional to the unimer concentration (mg ml À1 ) as shown in Fig. 2E-H. We estimate a value of al ¼ 8.0 AE 0.20 Â 10 À1 mm day À1 from the data of Fig. 2L by linear regression.
In order to compare the experimental data on length distributions to eqn (1), we need to estimate the value of the parameter a in order to convert the measured lengths to integer numbers of fundamental units. The correct value of a is not necessarily the size of a single unimer, because growth may occur in spurts if a particular repeat unit is more stable than average. However, a may be estimated from the data by linear regression of the variance of the lengths on the mean lengths as a function of time (details in the ESI Fig. S8 †). We obtain a value of a ¼ 11.6 AE 0.3 nm. This is very close to the value of 11.6 AE 1.0 nm for PI 550 -b-PFS 50 bre-like micelles which was derived by applying the analysis based on eqn (1) to the solution phase data of previous work 29 and of a similar order to the value of 16.1 AE 3.9 nm for PFS-b-(PEO-g-TEG). 41 Once the values of a and l are determined, there are no other free parameters and Fig. 3 compares the Poisson distribution to the experimental data. The agreement of eqn (1) with the data supports a living chain growth mechanism which explains the origin of the narrow length distributions in these structures. In comparison with a step growth process, in which bre-like micelles may add to each other, the length distribution in chain growth is much narrower. In this example it is worth noting that the seeds and bre-like micelles are anchored on a surface and are immobile on the experiment timescale.
To test the generality of this method we also conrmed that surface-grown bre-like micelles could be selectively functionalised, as is known for solution-based assembly. 14,42 It was demonstrated that bre-like micelles could be grown from surface-bound seeds from different unimer solutions (see details in the ESI Fig. S9 †). In this way parts of the bre-like Fig. 3 Fibre-like micelle length distributions against reaction time. Probability mass functions for the length of micelles grown on goldcoated silicon slides in Fig. 2L. The solid black line shows the Poisson distribution at each time point and the x-axis is given in terms of a normalised length described in the text. The micelles were grown from 0.005 mg ml À1 seeds on gold surfaces and immersion in 0.5 mg ml À1 of unimers solution for the times stated on the legend. The probabilities were estimated using AFM to measure the length of 50 separate micelles (30 in the case of the 10 day time point); standard deviations on each data point were obtained by applying counting statistics. micelles could be selectively functionalised with different functional groups.

Fibre-like micelle growth across a gap
Having established appropriate conditions for the chemisorption of seeds and subsequent bre-like micelle growth at gold surfaces, we next performed similar experiments at gold lms which contain a 600 nm gap. The terpolymer seeds were adsorbed on the clean gold surface by immersion in a solution (0.005 mg ml À1 ) in decane for 1 h to provide small numbers of seeds on the surfaces, as shown by AFM in Fig. 4A and B. Next, bre-like micelles were self-assembled on the gold surface by immersion in a solution of unimer (1 mg ml À1 ) in decane for 5 days. The micelles grow to about 4 mm in length and readily span the gap of 600 nm (Fig. 4C). The three-dimensional AFM image in Fig. 4D shows detail of the bre-like micelle structure crossing the 600 nm gap. These data show the remarkable tolerance of the micelle formation by the living CDSA process as it navigates height changes of over 100 nm between the underlying silicon substrate and the deposited gold. This demonstration of conformal tracking of a thin (7 nm) bremicelle across the device is a useful feature of the selfassembly process and highlights excellent tolerance of changes in both substrate height and material composition.

Device fabrication and electrical measurements
For electrical measurements, and to further test the length-scale of the assembly process, bundles of bre-like block terpolymer micelles were grown on patterned platinum microband electrodes (MBE) with a 10 mm inter-electrode gap ( Fig. 5A and S10 †). Current-voltage curves collected for the as-prepared bre-like micelles showed negligible current was passed when a voltage in the AE2 V range was applied to the device. However, a readily measurable current could be passed aer doping the bundles of bre-like micelles with the oxidising agent nitrosonium tetrauoroborate (NOBF 4 ). I-V curves collected aer this treatment (Fig. 5B) show an expected increase in conduction consistent with oxidative doping of the polythiophene. 43 Control experiments where NOBF 4 was applied to MBEs in the absence of bre-like micelles showed negligible background currents (Fig. S11 †).

Conclusions
In this study, we have established a detailed protocol for the growth of well-dened polymer-based nanowires based on PFDMS-b-PDMS-b-P3OT bre-like micelles across electrode gaps to fabricate simple electrical circuits. This was demonstrated over two quite different length scales and shows that the growth process is conformal over considerable changes in  Schematic representation of a simple electrical circuit constructed from bundlesv of fibre-like terpolymer micelles grown on platinum microband electrodes. (B) I-V measurements of the fibre-like micelles before (red) and after (green) doping with NOBF 4 . Inset, an optical image of bundles of fibre-like micelles grown from adsorbed seeds on a platinum microband electrode (MBE). Bundles of fibre-like micelles were grown from a high concentration of seeds (0.1 mg ml À1 , 10 min) and unimer (10 ml ml À1 , 7 days); they appear as red spots on the platinum MBE in the optical micrograph.
substrate height and compatible with commercially available microelectrodes.
The bre-like micelles were grown from chemisorbed seeds on the gold surfaces via living CDSA using PFDMS triblock terpolymer. AFM, supported by cyclic voltammetry, demonstrates the spontaneous adsorption of the seeds onto metal electrodes and their suitability for growing bre-like micelle structures with a range of functionality at electrode devices. The seed ends can be kept active for device construction and growth by storage in THF at room temperature for up to 6 months. A comprehensive study of the self-assembly process for the PFDMS 44 -b-PDMS 250 -b-P3OT 17 block terpolymer to form brelike micelles from the adsorbed seeds on gold substrates demonstrates that it is possible to grow near monodisperse bre-like micelles by setting up an appropriate ratio between the number of adsorbed seeds and the concentration of unimer solution, and controlling the subsequent immersion time in the unimer solution. The length distributions of the bre-like micelles can then be measured by AFM and understood on the basis of a chain-growth type of mechanism that is welldescribed by a Poisson process. This ability to control the length and chemical architecture of these structures from surface-adsorbed seeds represents an important feature of our approach, which complements the currently available bottomup methods for assembling functional devices. Finally, a mesoscopic electrical device was demonstrated in which bre-like micelles were grown across parallel microband electrodes and the current-voltage characteristics were switched between insulating and ohmic conduction by oxidative doping.

Conflicts of interest
There are no conicts to declare.