Vermicious thermo-responsive Pickering emulsifiers† †Electronic supplementary information (ESI) available: The theoretical background to the SAXS analysis, gel permeation chromatography analysis of the worms, optical microscopy images and laser diffraction analysis of water droplets. See DOI: 10.1039/c5sc00598a

Thermo-responsive vermicious (or worm-like) diblock copolymer nanoparticles prepared directly in n-dodecane are used to stabilise water-in-oil Pickering emulsions.


Theoretical background for SAXS analysis
In view of our TEM observations ( Figure 2) and previously reported SAXS data obtained for a PLMA 16 -PBzMA 37 solution in n-dodecane 1 , it was assumed that the SAXS patterns corresponded to (i) a pure worm phase (Figure 4a) for the dilute PLMA 16 -PBzMA 37 dispersion and (ii) spherical aqueous droplets stabilised by a layer of adsorbed worms for the concentrated water-in-n-dodecane emulsion ( Figure 4b).
Thus data analysis utilized two models: a worm-like micelle model 2, 3 (model 1) and a core-shell model comprising a particulate shell formed by the adsorbed worms (model 2).
In general, the X-ray intensity scattered by a system composed of n different (non-interacting) populations of polydisperse objects [usually described by the differential scattering cross-section per unit sample volume, dΣ(q)/dΩ] can be expressed as S1    per unit volume and is the structure factor of the l th population in the system. r l1 ,...,r lk is a set of k ) (q S l parameters describing the structural morphology of the l th population. In terms of Eq. S1, a dispersion of block copolymer worms can be described as a single population system (n = 1). The form factor for such anisotropic nano-objects can be expressed in terms of semiflexible chains with a circular cross-section 2 densities of the core block [ PBzMA = 10.38  10 10 cm -2 ], the corona block ( PLMA = 11.37  10 10 cm -2 ) and the solvent ( n-dodecane = 7.63  10 10 cm -2 ), respectively. V s and V c are the volumes of the core block (V PBzMA37 = 9.4 nm 3 ) and the corona block (V PLMA16 = 5.6 nm 3 ), respectively. The volumes were obtained from using solid-state homopolymer densities determined by helium pycnometry  A w N M V  ( PBzMA = 1.15 g cm -3 and  PLMA = 1.20 g cm -3 ). The self-correlation term for the worm micelle core with radius R sw , , is a product of a core cross-section term where J 1 is the first-order Bessel function of the first kind, and the form factor for self-avoiding semi-flexible chains representing the worm is given by cross-term between the worm-like micelle core and the coronal stabiliser chains is expressed as: , where is the form factor amplitude of the corona chain, R g is the radius of gyration of the corona block (PLMA), and J 0 is the zero-order Bessel function of the first kind. The interference term between the worm corona chains is expressed as: . The mean aggregation number of the , where x sol is the solvent volume fraction within the worm cores.
A Gaussian distribution for the worm core radius (with a mean radius R sw and a standard deviation  11 ) is assumed for model 1 such that: . Thus, the number density in Eq. S1 is ]. Thus, Eq. S1 for model 1 can be rewritten as where R sw used in Eq. S2 for the expression of the form factor is replaced by r 11 to account for the size distribution of the worm core radius.
In order to construct a structural model for the SAXS analysis of aqueous emulsion droplets (stabilised by PLMA 16 -PBzMA 37 worms) in n-dodecane, a previously used formalism for core-particulate shell spherical particles has been employed in this work. The emulsion droplets composed of aqueous cores and a particulate shell comprising adsorbed worms is reminiscent of the core-particulate shell particles previously reported 4 , where it was demonstrated that SAXS patterns can be successfully fitted using a two-population model represented by the superposition of two scattering patterns, corresponding to core-shell spherical particles and particles forming a particulate shell respectively.
Considering these previous results 4 , it was assumed that the SAXS patterns can be represented as a sum of scattering signals generated by two populations (n = 2 in Eq. S1): worms forming the particulate shell (the first population, l = 1 in Eq. S1) and core-shell particles (the second population, l = 2 in Eq. S1).
The terms for the two-population model used in this work can be expressed as follows. The form factor for the first population is identical to that used for model 1 (Eq. S2). The form factor for the second population, corresponding to the core-shell particles, is given by 5 : where R cs is the distance from the centre of the particle to the middle of the shell and T cs is the shell thickness. and are volumetric parameters for the core-shell  10 10 cm -2 ), respectively. Function is a normalized form factor for a homogeneous sphere: As for model 1, a Gaussian distribution for the worm core radius (with a mean radius R sw and an associated standard deviation  11 ) is used for the first population of model 2. For the second population, a Gaussian distribution is also assumed for both the core-shell particle radius (with a mean radius R cs and a standard deviation  21 ) and the shell thickness (with a mean thickness T cs and a standard deviation . Thus, Eq. S1 for model 2 can be rewritten as: where R cs and T cs used in Eq. S4 for the expression of the core-shell form factor are substituted by r 21 and r 22 in order to account for the size distributions of both the core-shell radius and the shell thickness. Since the worms forming the particulate shell are expected to be quite densely packed (see Figure 2c), a structure factor for the first population, , is incorporated into the model. In principle, a structure ) ( 1 q S factor based on the polymer reference interaction site model (PRISM) proposed for interacting worms could be used in this case. 6 However, there was no opportunity in the present SAXS study to obtain the S5 appropriate PRISM parameters to describe the effect of copolymer concentration on the scattering profile. Instead, a simplified approach based on a virial expansion 7 was used to account for the effect of worm packing within the shell. Thus, the structure factor for the first population in model 2 (Eq. S5) is expressed as: where A 2 is an effective virial coefficient.
The experimental SAXS pattern obtained for the 1.0 % w/w diblock copolymer worms prepared in ndodecane can be satisfactorily fitted using the worm model (model 1), see Eq. S3 and Figure 4a. The resulting structural parameters (Table S3) are consistent with SAXS data recently reported for a worm dispersion with an identical target copolymer composition. 1 In particular, the worm contour length obtained in the present work (L w = 591 ± 9 nm) is close to the lower limit estimated earlier (L w ~ 600 nm), based on SAXS patterns that were truncated below q ~ 0.023 nm -1 . Moreover, the R sw , b w and L w values are consistent with TEM observations (Figure 1 and Figure 2c). The copolymer volume fraction of 0.0069 obtained from SAXS analysis (Table S3) corresponds to a mass fraction of 0.01, which is in excellent agreement with the copolymer concentration of 1.0 % w/w used to prepare these emulsion droplets.
Model 2 (Eq. S5) produces a good fit to the SAXS data for the water droplets stabilised by the PLMA 16 -PBzMA 37 worms in n-dodecane (Figure 4b). Unfortunately, there was no opportunity to collect SAXS data for this emulsion at lower q values (Figure 4b, q < 0.08 nm -1 ). In order to obtain satisfactory data fits, several structural parameters, which are mainly associated with the high q region, were taken either from SAXS analysis of the worms alone (e.g., L w and b w ) or from the volume-average droplet size distribution given by laser diffraction (e.g., the mean radius, R cs , and associated standard deviation,  21 , for the aqueous droplets, see supporting information) (Table S1).

Estimate of the specific surface area of a worm
Assume a worm of mean length L and mean width 2R, where R is the worm radius.
If L >> R, then the contribution from the spherical caps becomes negligible and hence = 2 Thus this As value for worms is only ~ 33 % less than that for the corresponding spheres of mean radius R and identical copolymer density ρ, for which As = 3/ρ.R L 2R R Determined using the following characterization techniques: (a) visible absorption spectroscopy, (b) optical microscopy and (c) laser diffraction. The standard deviation for the latter two techniques is also reported. This is calculated by taking the square root of the average of the squared differences of the values from their mean value.  Figure S1. Gel permeation chromatography curves obtained for the precursor PLMA 16 macro-CTA and the resulting PLMA 16 -PBzMA 32 diblock copolymer worms.   Figure S4. Linear Beer-Lambert plot constructed using visible absorption spectroscopy at an arbitrary wavelength of 450 nm. This calibration plot was used to estimate the supernatant concentration of nonadsorbed PLMA 16 -PBzMA 37 worms remaining in the n-dodecane phase. S14 Figure S5. TEM images of ~ 0.1 % w/w PLMA 16 -PBzMA 37 worms before (left) and after (right) heating to 150 °C for 90 minutes. S15 Figure S6. Optical microscopy and laser diffraction sizing data for Pickering emulsions formed using 0.50 % w/w PLMA 16 -PBzMA 37 copolymer worms or spheres. Note the significant flocculation indicated by laser diffraction for the sphere-stabilised emulsion. S16 Figure S7. Digital photographs obtained for 0.06 % w/w PLMA 16 -PBzMA 37 worms in n-dodecane plus an equal volume of water prior to homogenisation (left), the Pickering emulsion obtained after high shear homogenisation (center) and the phase separation caused by heating this emulsion up to 95°C for 5 min.