Block copolymer synthesis in ionic liquid via polymerisation-induced self-assembly: a convenient route to gel electrolytes

We report for the first time a reversible addition–fragmentation chain transfer polymerisation-induced self-assembly (RAFT-PISA) formulation in ionic liquid (IL) that yields worm gels. A series of poly(2-hydroxyethyl methacrylate)-b-poly(benzyl methacrylate) (PHEMA-b-PBzMA) block copolymer nanoparticles were synthesised via RAFT dispersion polymerisation of benzyl methacrylate in the hydrophilic IL 1-ethyl-3-methyl imidazolium dicyanamide, [EMIM][DCA]. This RAFT-PISA formulation can be controlled to afford spherical, worm-like and vesicular nano-objects, with free-standing gels being obtained over a broad range of PBzMA core-forming degrees of polymerisation (DPs). High monomer conversions (≥96%) were obtained within 2 hours for all PISA syntheses as determined by 1H NMR spectroscopy, and good control over molar mass was confirmed by gel permeation chromatography (GPC). Nanoparticle morphologies were identified using small-angle X-ray scattering (SAXS) and transmission electron microscopy (TEM), and further detailed characterisation was conducted to monitor rheological, electrochemical and thermal characteristics of the nanoparticle dispersions to assess their potential in future electronic applications. Most importantly, this new PISA formulation in IL facilitates the in situ formation of worm ionogel electrolyte materials at copolymer concentrations >4% w/w via efficient and convenient synthesis routes without the need for organic co-solvents or post-polymerisation processing/purification. Moreover, we demonstrate that the worm ionogels developed in this work exhibit comparable electrochemical properties and thermal stability to that of the IL alone, showcasing their potential as gel electrolytes.


Additional dynamic light scattering data
Figure S4.DLS traces obtained of selected 0.15% w/w dispersions block copolymer series.

Additional transmission electron microscopy images
Figure S5.TEM images obtained for a 15% w/w dispersion of PHEMA30-b-PBzMA146.

Small-angle X-ray scattering
Programming tools within the Irena SAS Igor Pro macros 1 were used to implement the scattering models.
In general, the intensity of X-rays scattered by a dispersion of nano-objects [as represented by the scattering cross-section per unit sample volume, Σ Ω (q)] can be expressed as: where (,  1 , … ,   ) is the form factor,  1, … ,   is a set of k parameters describing the structural morphology, Ψ( 1, … ,   ) is the distribution function, S(q) is the structure factor and N is the number density of nano-objects per unit volume expressed as: where ( 1 , … ,   ) is the volume of the nano-object and  is its volume fraction within the dispersion.
It is assumed that S(q) = 1 at the sufficiently low copolymer concentrations used in this study (1.0%w/w).

Spherical micelle model
The spherical micelle form factor for Equation S1 is given by 2 where   is the volume-average sphere core radius and   is the radius of gyration of the coronal steric stabilizer block (in this case, PHEMA30).The X-ray scattering length contrasts for the core and corona blocks are given by   =   (  −   ) and   =   (  −   ) respectively.Here,   ,   and   are the X-ray scattering length densities of the core block (  = 10.41 x 10 10 cm -2 ), corona block (  = 11.50 x 10 10 cm -2 ) and [EMIM][DCA] solvent (  = 9.90 x 10 10 cm -2 ), respectively.  and   are the volumes of the core block (  ) and the corona block (  ), respectively.The sphere form factor amplitude is used for the amplitude of the core self-term: where Φ(  ) = 3[sin(  )−  cos (  )] (  ) 3 .A sigmoidal interface between the two blocks was assumed for the spherical micelle form factor (Equation S3).This is described by the exponent term with a width  accounting for a decaying scattering length density at the micellar interface.This  value was fixed at 2.5 during fitting.
The form factor amplitude of the spherical micelle corona is: The radial profile,   (), can be expressed by a linear combination of two cubic b splines, with two fitting parameters  and  corresponding to the width of the profile and the weight coefficient respectively.This information can be found elsewhere, 3,4 as can the approximate integrated form of Equation S5.The self-correlation term for the coronal block is given by the Debye function: where   is the radius of gyration of the PHEMA coronal block.In all cases   was fixed to be 1.4 nm, which is estimated by assuming the total contour length of PHMEA30 is 7.66 nm (30 × 0.255 nm, where 0.225 nm is the contour length of one HEMA monomer unit with two C-C bonds in all-trans conformation).Given a mean Kuhn length of 1.53 nm, based on the known literature value for poly(methyl methacrylate) 5 , an estimated unperturbed   of 1.4 nm is determined using   = (7.66× 1.53/6) 0.5 .
The aggregation number,  s , of the spherical micelle is given by: where   is the standard deviation for   .In accordance with Equation S2, the number density per unit volume for the micelle model is expressed as: where  is the total volume fraction of copolymer in the spherical micelles and ( 1 ) is the total volume of copolymer within a spherical micelle [( 1 ) = (  +   )  ( 1 )].

Worm-like micelle model
The worm-like micelle form factor for Equation S1 is given by: where all the parameters are the same as those described in the spherical micelle model (Equation S3), unless stated otherwise.
The self-correlation term for the worm core cross-sectional volume-average radius   is: where and  1 is the first-order Bessel function of the first kind, and a form factor   (,   ,   ) for selfavoiding semi-flexible chains represents the worm-like micelles, where   is the Kuhn length and   is the mean contour length.A complete expression for the chain form factor can be found elsewhere. 6e mean aggregation number of the worm-like micelle,  w , is given by: where   is the volume fraction of solvent within the worm-like micelle cores, which was found to be zero in all cases.The possible presence of semi-spherical caps at both ends of each worm is neglected in this form factor.
A polydispersity for one parameter ( w ) is assumed for the micelle model, which is described by a Gaussian distribution.Thus, the polydispersity function in Equation S1 can be represented as: where   w is the standard deviation for  w .In accordance with Equation S2, the number density per unit volume for the worm-like micelle model is expressed as: where  is the total volume fraction of copolymer in the worm-like micelles and ( 1 ) is the total volume of copolymer in a worm-like micelle [( 1 ) = ( s +  c ) w ( 1 )].

Vesicle model
The vesicle form factor in Equation S1 is expressed as:  where all the parameters are the same as in the spherical micelle model (see Equation S3) unless stated otherwise.
The amplitude of the membrane self-term is: where   =   − 1 2   is the inner radius of the membrane,   =   + 1 2   is the outer radius of the membrane ( m is the radius from the centre of the vesicle to the centre of the membrane),   = 4 3   3 and   = 4 3   3 .It should be noted that Equation S16 differs subtly from the original work in which it was first described. 7The exponent term in Equation S17 represents a sigmoidal interface between the blocks, with a width   accounting for a decaying scattering length density at the membrane surface.The value of   was fixed at 2.5 during fitting.The mean vesicle aggregation number,   , is given by: where   is the volume fraction of solvent within the vesicle membrane, which was found to be zero in all cases.Assuming that there is no penetration of the solvophilic coronal blocks into the solvophobic membrane, the amplitude of the vesicle corona self-term is expressed as: where the term outside the square brackets is the factor amplitude of the corona block polymer chain such that: For the vesicle model, it was assumed that two parameters are polydisperse: the radius from the centre of the vesicles to the centre of the membrane and the membrane thickness (denoted   and   , respectively).Each parameter is considered to have a Gaussian distribution of values, so the polydispersity function in Equation S1 can be expressed in each case as: where   and   are the standard deviations for   and   , respectively.Following Equation S2, the number density per unit volume for the vesicle model is expressed as: where  is the total volume fraction of copolymer in the vesicles and ( 1 ,  2 ) is the total volume of copolymers in a vesicle [( 1 ,  2 ) = (  +   )  ( 1 ,  2 )].

Gaussian chain model
Data for the 1% w/w solution of PHEMA30-b-PBzMA49 were fitted to a Gaussian chain model. 8enerally, the scattering cross-section per unit sample volume for an individual Gaussian polymer chain can be expressed as: where [] = 9.90 x 10 -10 cm -2 .The generalized form factor for a Gaussian polymer chain is given by: where the lower incomplete gamma function is (, ) = ∫  −1 exp(−)   0 and  is the modified variable: Here,  is the extended volume parameter and  g cop is the radius of gyration of the copolymer chain.
Table S3.Summary of parameters obtained when fitting SAXS data to appropriate models. sphere ,  worm and  vesicle are the volume fraction of spheres, worms and vesicles, respectively. sphere is the spherical nanoparticle diameter ( sphere = 2 s + 4 g , where  g is the radius of gyration of the stabiliser block and  s is the core radius). worm is the worm thickness ( worm = 2 w + 4 g , where  w is the worm core cross-sectional radius). worm is the worm length. vesicle is the overall vesicle diameter ( vesicle =  m +  m + 4 g , where  m is the centre of the vesicle to the centre of the membrane and  m is the membrane thickness). g cop is the radius of gyration of dissolved copolymer chains. is the extended volume parameter.PHEMA30-b-PBzMAy is denoted as H30-By for brevity.

Figure S7 .
Figure S7.Background-subtracted SAXS data obtained for 1.0% w/w PHEMA30-PBzMA98 in [EMIM][DCA] at 25 °C.Dashed lines represent the model fit obtained using the spherical micelle model with an additional power law to account for the upturn in scattering at low q.

Figure S9 .
Figure S9.Background-subtracted SAXS data obtained for 1.0% w/w PHEMA30-PBzMA196 in [EMIM][DCA] at 25 °C.Dashed lines represent the model fit obtained using a combination of the spherical micelle model and worm-like micelle model.

Figure S10 .
Figure S10.Background-subtracted SAXS data obtained for 1.0% w/w PHEMA30-PBzMA201 in [EMIM][DCA] at 25 °C.Dashed lines represent the model fit obtained using a combination of the spherical micelle model and worm-like micelle model.

Figure S11 .
Figure S11.Background-subtracted SAXS data obtained for 1.0% w/w PHEMA30-PBzMA216 in [EMIM][DCA] at 25 °C.Dashed lines represent the model fit obtained using a combination of the spherical micelle model and worm-like micelle model.

Figure S12 .
Figure S12.Background-subtracted SAXS data obtained for 1.0% w/w PHEMA30-PBzMA228 in [EMIM][DCA] at 25 °C.Dashed lines represent the model fit obtained using a combination of the spherical micelle model and worm-like micelle model.

Figure S13 .
Figure S13.Background-subtracted SAXS data obtained for 1.0% w/w PHEMA30-PBzMA233 in [EMIM][DCA] at 25 °C.Dashed lines represent the model fit obtained using a combination of the spherical micelle model and worm-like micelle model.

Figure S14 .
Figure S14.Background-subtracted SAXS data obtained for 1.0% w/w PHEMA30-PBzMA240 in [EMIM][DCA] at 25 °C.Dashed lines represent the model fit obtained using a combination of the spherical micelle model and worm-like micelle model.

Figure S16 .
Figure S16.Background-subtracted SAXS data obtained for 1.0% w/w PHEMA30-PBzMA265 in [EMIM][DCA] at 25 °C.Dashed lines represent the model fit obtained using a combination of the spherical micelle model and worm-like micelle model.

Figure S17 .
Figure S17.Background-subtracted SAXS data obtained for 1.0% w/w PHEMA30-PBzMA269 in [EMIM][DCA] at 25 °C.Dashed lines represent the model fit obtained a combination of the spherical micelle model and worm-like micelle model.

Figure S18 .
Figure S18.Background-subtracted SAXS data obtained for 1.0% w/w PHEMA30-PBzMA279 in [EMIM][DCA] at 25 °C.Dashed lines represent the model fit obtained using a combination of the spherical micelle model and worm-like micelle model.

Figure S19 .
Figure S19.Background-subtracted SAXS data obtained for 1.0% w/w PHEMA30-PBzMA291 in [EMIM][DCA] at 25 °C.Dashed lines represent the model fit obtained using a combination of the spherical micelle model and worm-like micelle model.

Figure S20 .
Figure S20.Background-subtracted SAXS data obtained for 1.0% w/w PHEMA30-PBzMA301 in [EMIM][DCA] at 25 °C.Dashed lines represent the model fit obtained using a combination of the spherical micelle model and worm-like micelle model.

Figure S21 .
Figure S21.Background-subtracted SAXS data obtained for 1.0% w/w PHEMA30-PBzMA314 in [EMIM][DCA] at 25 °C.Dashed lines represent the model fit obtained using a combination of the wormlike micelle and vesicle models.

Figure S22 .
Figure S22.Background-subtracted SAXS data obtained for 1.0% w/w PHEMA30-PBzMA317 in [EMIM][DCA] at 25 °C.Dashed lines represent the model fit obtained using a combination of the wormlike micelle and vesicle models.

Figure S23 .
Figure S23.Background-subtracted SAXS data obtained for 1.0% w/w PHEMA30-PBzMA330 in [EMIM][DCA] at 25 °C.Dashed lines represent the model fit obtained using a combination of the wormlike micelle and vesicle models.

Figure S24 .
Figure S24.Background-subtracted SAXS data obtained for 1.0% w/w PHEMA30-PBzMA340 in [EMIM][DCA] at 25 °C.Dashed lines represent the model fit obtained using a combination of the wormlike micelle and vesicle models.