Spatial distribution of core monomers in acrylamide-based core-shell microgels with linear swelling behaviour

The peculiar linear temperature-dependent swelling of core-shell microgels has been conjectured to be linked to the core-shell architecture combining materials of different transition temperatures. Here the structure of pNIPMAM-core and pNNPAM-shell microgels in water is studied as a function of temperature using small-angle neutron scattering with selective deuteration. Photon correlation spectroscopy is used to scrutinize the swelling behaviour of the colloidal particles and reveals linear swelling. Moreover, these experiments are also employed to check the influence of deuteration on swelling. Using a form-free multi-shell reverse Monte Carlo approach, the small-angle scattering data are converted into radial monomer density profiles. The comparison of ‘core-only’ particles consisting of identical cores to fully hydrogenated core-shell microgels, and finally to H-core/D-shell architectures unambiguously shows that core and shell monomers display gradient profiles with strong interpenetration, leading to cores embedded in shells which are bigger than their isolated ‘core-only’ precursor particles. This surprising result is further generalized to different core cross-linker contents, for temperature ranges encompassing both transitions. Our analysis demonstrates that the internal structure of pNIPMAM-core and pNNPAM-shell microgels is heterogeneous and strongly interpenetrated, presumably allowing only progressive core swelling at temperatures intermediate to both transition temperatures, thus promoting linear swelling behaviour.


Contrast variation
Two pNNPAM microgel systems (CCC = 1.9 mol%, same as for the shell) have been purpose-synthesized for contrast variation using H2O/D2O. The scattering length density (SLD) of the effective partially deuterated D7-pNNPAM microgel including the cross-linker was determined to be 5.54·10 10 cm -2 (see Figure S1), resulting in a density of 1.24 g cm -1 based on the theoretical value of 4.47·10 10 cm -2 at a density of 1.00 g cm -1 . The contrast variation of H-pNNPAM revealed a SLD of 1.05·10 10 cm -2 and is displayed in Figure S2.
The q-values of the contrast variation of D7-pNNPAM in Figure S1a are from black squares to brown right facing triangles: (0.005, 0.00625, 0.00816, 0.01005, 0.01192, 0.0138, 0.0157) Å -1 and the q-values of H-pNNPAM in Figure S2a are (0.00436, 0.00624, 0.00814, 0.01002, 0.01189, 0.01377, 0.01567) Å -1 . They are chosen to be all in the low-q range. The identical match-point in Figure S1a and S2a for different qvalues can be seen as an extrapolation (of a constant) to q → 0 as done in classical contrast variation. The superposition in Figure S1c and S2c indicates that the polymer chains are the only source of contrast in these experiments, and the contrast variation gives identical results on all measurable scales. Figure S1: Contrast variation of D7-pNNPAM microgels with a CCC of 10 mol%. (a) Plotted is the sign corrected square root of the coherent intensities vs. the SLD of the solvent varied from pure H2O to pure D2O (-0.561, 1.173, 2.907, 4.641, 6.375) · 10 10 cm -2 for seven q-values ((0.005, 0.00625, 0.00816, 0.01005, 0.01192, 0.0138, 0.0157) · Å -1 ). The dashed line indicates the match point of 5.54 · 10 10 cm -2 . (b) Scattering functions from the contrast variation. (c) Contrast scaled scattering functions.

Effect of the CCC on pNIPMAM-pNNPAM microgels
The effect of the CCC on the density profiles of H-pNIPMAM-H-pNNPAM microgels at 55 °C is discussed in the main article. Here, we present the experimental SANS data ( Figure S3a and S4a) and the density profiles ( Figure S3b and S4b), respectively.

Particle mass determination by analysing the structure factor peak
Calculating the number of monomers in one microgel by analysing I(q→0) reveals a Nmono of 160 000 monomers, if monodispersity is assumed.
As a second method, the number of monomers was calculated from the position of the first structure factor peak. It is found that this leads to a number of pNIPMAM-core monomers Nmono which is of the same order of magnitude as the one determined from I(q→0) (factor 1.2). Average 0.002954 197 000 Table S1: Calculated numbers of monomers of a pNIPMAM microgel from the first structure factor oscillation at different temperatures. Figure S5 shows the monomer density profiles of H-pNIPMAM cores without shell and with a contrast matched D7-pNNPAM Shell with 5, 10 and 15 mol% CCC at 55 °C.  Figure S6 shows the dependence of the temperature (15°C, 35°C, and 55°C) of a H-pNIPMAM core without shell and with a contrast matched D7-pNNPAM Shell with a CCC of 10 mol%. Figure S6: Density profiles of H-pNIPMAM core without shell (black squares) and with a contrast matched D7-pNNPAM Shell (red circles) with a CCC of 10 mol%.

Effect of the B-Spline
In a first approach, we have investigated the necessity of smoothing the density profiles using B-splines (Origin). As shown in the Figure below, this was not needed. Figure S7 shows the smoothening effect of the B-spline used in Figure 7. The black dashed lines show the not smoothened density profiles, respectively.

RMC Fit without low q data
We applied our RMC algorithm on the same SANS data set with and without the data at very low q where the structure factor S(q) is relevant. Figure S11 shows that the revealed density profile is the same in both cases for 15 and 55 °C. Thus the structure factor does not affect the density profiles.

Comparison of the RMC fit with a fuzzy sphere fit
The fuzzy sphere model has been shown by us to be fully compatible with the core data from Cors et al. 1,2 The model, however, is less general than our form-free multi-shell model. Unexpected density profiles like the ones reported here, with a strong presence of shell polymer in the core, cannot be described with a fuzzy sphere model without adaptation, whereas this result is directly provided by our RMC analysis. Figure S12: SANS intensity curve of a pNIPMAM-pNNPAM core-shell microgel with a matched shell at 55 °C and a CCC of 10 mol% with a RMC fit and a Fuzzy Sphere fit.
We performed PCS measurements of a pNIPMAM core and of the same core under the same conditions as the shell synthesis (core, shell monomer, cross linker, surfactant concentration but without the cross linker).
The swelling curves are shown in Figure S13. Figure S13: PCS measurement of a pNIPMAM core and the same core under shell synthesis conditions (core, shell monomer, cross linker, surfactant concentration but without the cross linker).

χ 2 -values of RMC Fits
The χ 2 -values of RMC Fits are listed in the Table below. These χ 2 -values are not absolute as they are weighted with the errors in intensity for each q-value and are different for each experiment due to merging procedures of different SANS configurations. Altogether, however, they are comparable within one series of experiments, and can be used to compare the quality of the fits.    Figure S1: Contrast variation of D7-pNNPAM microgels with a CCC of 10 mol%. Figure S2: Contrast variation of H-pNNPAM microgels with a CCC of 10 mol%.      Figure S10: Hydrodynamic radius as a function of the temperature for a heating-cooling-heating-cooling cycle of a pNIPMAM-pNNPAM core-shell microgel with a CCC of 10 mol%.
Figure S11: RMC simulations with and without the SANS data at low q where the structure factor is relevant. Figure S12: SANS intensity curve of a pNIPMAM-pNNPAM core-shell microgel with a matched shell at 55 °C and a CCC of 10 mol% with a RMC fit and a Fuzzy Sphere fit. Figure S13: PCS measurement of a pNIPMAM core and the same core under shell synthesis conditions.