Effect of Salt on the Formation and Stability of Water-in-Oil Pickering Nanoemulsions Stabilized by Diblock Copolymer Nanoparticles

Sterically stabilized diblock copolymer nanoparticles are prepared in n-dodecane using polymerization-induced self-assembly. Precursor Pickering macroemulsions are then prepared by the addition of water followed by high-shear homogenization. In the absence of any salt, high-pressure microfluidization of such precursor emulsions leads to the formation of relatively large aqueous droplets with DLS measurements indicating a mean diameter of more than 600 nm. However, systemically increasing the salt concentration produces significantly finer droplets after microfluidization, until a limiting diameter of around 250 nm is obtained at 0.11 M NaCl. The mean size of these aqueous droplets can also be tuned by systematically varying the nanoparticle concentration, applied pressure, and the number of passes through the microfluidizer. The mean number of nanoparticles adsorbed onto each aqueous droplet and their packing efficiency are calculated. SAXS studies conducted on a Pickering nanoemulsion prepared using 0.11 M NaCl confirms that the aqueous droplets are coated with a loosely packed monolayer of nanoparticles. The effect of varying the NaCl concentration within the droplets on their initial rate of Ostwald ripening is investigated using DLS. Finally, the long-term stability of these water-in-oil Pickering nanoemulsions is assessed using analytical centrifugation. The rate of droplet ripening can be substantially reduced by using 0.11 M NaCl instead of pure water. However, increasing the salt concentration up to 0.43 M provided no further improvement in the long-term stability of such nanoemulsions.

. 19 F NMR spectrum recorded for PSMA32-PTFEMA53 diblock copolymer dissolved in CDCl3. From the residual monomer signal observed at -73.8 ppm, a final TFEMA conversion of 97% can be calculated. S2 Figure S2. Effect of varying the applied pressure and number of passes during microfluidization on the initial z-average aqueous droplet diameter of w/o Pickering nanoemulsions prepared using 5.0% w/w PSMA32-PTFEMA53 nanoparticles at a fixed water volume fraction of 0.10, as determined by DLS. S3 Figure S3. Intensity-average droplet size distributions recorded by DLS for Pickering nanoemulsions prepared using either a neutral (pH 7) or acidic (pH 2) aqueous solution containing 0.11 M NaCl.   Figure S5. Representative TEM image recorded for dried water-in-n-dodecane Pickering nanoemulsions prepared using 5.0% w/w PSMA32-PTFEMA53 nanoparticles with 0.11 M NaCl dissolved in the aqueous phase. Conditions: microfluidization pressure = 10 000 psi; 5 passes. Figure S6. Effect of varying the aqueous droplet concentration on the apparent droplet diameter of a water-in-n-dodecane Pickering nanoemulsion as determined by analytical centrifugation (LUMiSizer instrument). This so-called 'hindrance' function indicates that the optimum droplet concentration for such analyses is approximately 1.0% v/v, with higher concentrations leading to hindered creaming and hence undersizing. Figure S7. Volume-weighted cumulative distributions determined by analytical centrifugation (LUMiSizer instrument) for n-dodecane-in-water Pickering nanoemulsions prepared using various amounts of NaCl dissolved in the aqueous phase) after ageing for 4 weeks at 20 °C.

Structural models for SAXS analysis
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: 1

S1
where is the form factor, is the distribution function, Nl is the number density per unit volume and is the structure factor of the l th population in the system. Here, rl1,...,rlk is a set of k parameters describing the structural morphology of the l th population.

Spherical Micelle SAXS Model
In terms of Equation S1, a dispersion of spherical micelles formed by an amphiphilic diblock copolymer can be described as a single population system (n = 1). Assuming that only the micelle core radius is polydisperse, Equation S1 for this system can be rewritten as:

S2
The spherical micelle form factor for Equation S2 is given by:

S3
where r11 is the spherical micelle core radius, Rg is the radius of gyration of the PSMA coronal block, and the X-ray scattering length contrast for the core and corona blocks is given by s = s ( s − sol ) and c = c ( c − sol ), respectively. Here ξs, ξc and ξsol are the X-ray scattering length densities of the core block (ξPTFEMA = 12.76 x 10 10 cm -2 ), the corona block (ξPSMA = 9.24 x 10 10 cm -2 ) and the solvent where it is assumed that the solvent is absent in the micelle core. The sphere form factor amplitude is used for the amplitude of the core self-term:

S5
A sigmoidal interface between the two blocks was assumed for the spherical micelle form factor (Equation S4). This is described by the exponent term with a width σ accounting for a decaying scattering length density at the membrane surface. This σ value was fixed at 0.25 nm during fitting.
The form factor amplitude of the spherical micelle corona in Equation S3 is given by: The radial profile, μc(r), can be expressed by a linear combination of two cubic b splines, with two fitting parameters s and a corresponding to the width of the profile and the weight coefficient, respectively. This information can be found elsewhere, 4

S8
Herein the form factor of the average radial scattering length density distribution of micelles is expressed as 1 av ( , 1 ) = s [ s s ( , 11 ) + c c ( )] and PY ( , PY , PY ) is a hard-sphere interaction structure factor solved using the Percus-Yevick closure relation, 1,7 where RPY is the interaction radius and fPY is the hard-sphere volume fraction. For dilute dispersions of micelles it is assumed that PY ( , PY , PY ) = 1.
A polydispersity of the micelle radius in Equation S2 can be described by a Gaussian distribution: where Rs is the mean of the micelle core radius and σRs is its standard deviation. The number density per unit volume for the micelle model is expressed as: where φ1 is the total volume fraction of copolymer in the spherical micelles and is the total volume of copolymer in a spherical micelle [ ( 11 ) = ( s + c ) s ].
Assuming that the projected contour length of a PSMA monomer is 0.255 nm (two C-C bonds in alltrans conformation), the total contour length of a PSMA32 block, LPSMA32 = 32 x 0.255 nm = 8.16 nm.

Two-population SAXS Model
In order to construct a structural model for the SAXS analysis of water-in-oil emulsion droplets stabilised by PSMA32-PTFEMA53 spherical micelles, a previously used formalism for core-particulate shell spherical particles was employed. 9 It was assumed that the differential cross-section per unit sample volume for the studied system patterns can be represented as a sum of two terms corresponding to scattering signals generated by two populations (n = 2 in Equation S1): spherical micelles forming the particulate shell (the first population, l = 1 in Equation S1) and core-shell particles (the second population, l = 2 in Equation S1). The contribution to the scattering signal from the first population can be described by the same term used for the spherical micelle dispersion (Equation S2). By expressing the scattering signal from the second population in a similar manner to that of the first population, the differential scattering cross-section per unit sample volume of the whole system could be written as: where it is assumed that only the particle core radius is polydisperse. The form factor for the second population, corresponding to the core-shell particles, is given by: total shell sol 21 shell core core shell 21 where r21 is the core radius and Tshell is the shell thickness.
the solvent (n-dodecane = 7.63  10 10 cm -2 ), respectively. As for population 1, a Gaussian distribution is assumed for the particle core radius (with a mean radius Rc and its standard deviation Rc): where 2 is the volume fraction of core-shell particles (i.e., nanoparticle-stabilized aqueous droplets) within the w/o nanoemulsion. Since the 2 used for the SAXS measurements is relatively low (0.01) and the q range resolved in the SAXS experiment ( Figure 7) is virtually unaffected by the interdroplet interactions, it was assumed that the structure factor was equal to unity [ 2 ( ) 1 Sq ]. However, since the nanoparticles (a.k.a. spherical micelles) are expected to form reasonably close-packed layer at the surface of the aqueous droplets (Figure 6b), a structure factor for the first population [ ) ( 1 q S ], as represented by Equation S8, had to be used in the analysis.