Introduction
Microgel particle systems have attracted increasing interest in the field of Soft Condensed Matter as their ability to swell or expand upon change of variables such as temperature, pH or ionic strength allows studying a broad phase behavior in within a single sample [1-4]. Furthermore, due to their intra-particle structure and uneven or discontinuous mass distribution, microgel particles can deform, interpenetrate or enhance their polydispersity which ultimately results in a strikingly different phase behavior than typical hard sphere systems [5-7]. In this project we study a recent class of thermally responsive microgel system where PEG is employed as cross-linker of linear PNiPAM. PEG is a hydrophilic non-degradable polymer extensively used in bio-related materials as it is biocompatible, non-toxic, non-immunogenic and soluble in water. Moreover, research on colloidal particles which are surface modified with PEG has drawn attention as PEG facilitates control of protein adsorption and minimizes non-specific cell adhesion [8,9]. Thus PNiPAM-PEG microgels lay a promising system that can be employed not only in fundamental research but also in bio- and nano-technological applications such as drug delivery in biological systems [10].

Cross-linked PNiPAM-particles are soluble in water at temperatures below the Lower Critical Solution Temperature (LCST) of PNiPAM at T ~ 33°C. In the fully swollen state at low temperatures their behavior varies from more polymer-like to more colloid-like behavior depending on the cross-linking density [11]. As the temperature increases, the size of the PNiPAM-microgels decreases continuously up to the LCST. Beyond the LCST the microgels collapse forming now more colloidal-type systems, which aggregate unless they are stabilized in some way [12]. To PNiPAM-PEG particles, the hydrophilic properties of PEG at low temperatures differentiate this system from other microgels. When the temperature is low enough, PEG chains protrude from the microgel network which results in an uneven mass distribution dissimilar to typical microgel systems [13,14]. We employ Static and Dynamic Light Scattering (SLS and DLS) to investigate the structure and dynamics of aqueous suspensions of these microgels at different volume fractions and at different temperatures. Furthermore, we also employ Rheology to explore the mechanical properties of this particular class of microgel system.

SLS and DLS of PNiPAM-PEG microgel suspensions in the low-concentration regime.
We have characterized our PNiPAM-PEG microgel particles using SLS and DLS for temperatures, T, within the range 20C ≤ T ≤ 46C. In all SLS experiments and at large enough q-vectors, the scattered intensity depends linearly with q ² when displayed in a logarithmic-linear scale; this indicates that in the available q-range of our experiments we access the Guinier region of the microgel form factor, as shown in Figure 1(a) [15]. Furthermore, the slope of the scattered intensity increases when the temperature is increased, indicating the decrease in the particle size. Since our suspensions are dilute, there are no spatial correlations between the particles and beside prefactors, the scattered intensity I(q) corresponds to the microgel form factor, P(q). In the Guinier region, P(q) ~ exp(-R_g² q²/3) and therefore it is straightforward to obtain the radius of gyration, R_g, for every temperature, which is shown in Figure 1(c) with open circles. We also quantify the de-swelling behavior using DLS. We measure the intensity correlation functions, g₂(τ) - 1, and find they exhibit a linear dependence with the lag time, τ, when displayed in a logarithmic-linear scale. This indicates the exponential character of these functions, as shown in Figure 1(b). Since the scattered intensity fluctuations are Gaussian, the Siegert relation must be fulfilled: g₂(τ) - 1 = g₁(τ)², where g₁(τ) is the field correlation function. Then, g₂(τ) - 1 ~ exp(-2τ/&tau₀), where τ₀ = 1/(q²D), with D the diffusion coefficient [16]. The exponential character of g₁(τ) is suggestive of diffusion, which we further confirm by verifying that τ₀ depends linearly on q². The diffusion coefficient at each temperature is further related to the hydrodynamic radius of the particles, R_h, invoking Stokes-Einstein: D = kBT/6πηR_h, with k_B the Boltzmann constant, T the temperature and η the solvent viscosity. Consistent with the findings for the radius of gyration, we find that R_h decreases with temperature down to a minimal size at the LCST, as shown in Figure 1(c) with closed circles.

Despite the behavior of R_h and R_g with temperature is remarkably similar, they have very different magnitudes; the hydrodynamic radius is larger than the radius of gyration at all temperatures. This difference can be attributed to an uneven distribution of cross-linker, which decreases from the center of the particle towards its periphery [17]. Because of the higher density of PNIPAM within the core, the core scatters significantly more than the low-density shell, and thus in SLS the radius of the cross-linked core is portrayed in contrast to DLS which portrays the effective hydrodynamic radius. Note that above the LCST, the interaction between the particles contains an attractive contribution. However, we do not observe aggregation, indicating there must also be a repulsive contribution to the particle-particle interactions, which in our case results from the presence of charge at the surface of the particles from the ionic initiator used in the microgel synthesis [11,17]. This charge remains unscreened and provides suspension stability for T > LCST.