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Phase Behavior of PNiPAM-PEG Microgel Suspensions

Joaquim Clara-Rahola, L. Andrew Lyon
and Alberto Fernandez-Nieves

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 ~ 33C. 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(-Rg² q²/3) and therefore it is straightforward to obtain the radius of gyration, Rg, 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, Rh, invoking Stokes-Einstein: D = kBT/6πηRh, with kB the Boltzmann constant, T the temperature and η the solvent viscosity. Consistent with the findings for the radius of gyration, we find that Rh decreases with temperature down to a minimal size at the LCST, as shown in Figure 1(c) with closed circles.

Despite the behavior of Rh and Rg 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.

Figure 1. SLS intensity variation with the wave vector q (a) and DLS intensity correlation functions (b) for PNiPAM-PEG microgel particles at different temperatures. Both, the DLS hydrodynamic radius and the SLS radius of gyration gradually decrease with increasing temperature up to a constant size above the LCST (c).

Statics, dynamics and mechanical properties of PNiPAM-PEG microgel suspensions in the high-concentration regime.
At high enough concentration of PNiPAM-PEG particles, the system eventually jams and a solid-like structure is formed as shown in figure 2. We quantify the particle concentration by using a generalized volume fraction ξ=c(R(T)/R(T=46C))³ where c is the microgel weight concentration, R(T) is the particle hydrodynamic radius at temperature T and R(T=46C) is the one corresponding to T=46C. Note that the magnitude of ξ can be above unity, which suggests that at such volume fractions the particles either shrink, interpenetrate or vary their shape, or all of them. Indeed, for &xi < 1 the system is at a liquid state while at ξ > 1 the system is at a solid phase. Here our focus is to explore the structural, dynamic and static properties of our samples in the solid state as this state is approached. Therefore we study the phase behavior of PNiPAM-PEG microgel systems at extreme high concentrations. As an example we draw our attention on suspensions at a volume fraction at &xi =1.5 and introduce the behavior corresponding to the temperature range 20C ≤ T ≤ 32C. At these temperatures the effective structure factor, Seff(q), displays a peak at a position where qpeakRh ~ π as illustrated in figure 3. Despite this hallmark indicates that the spatial configuration of our microgels is governed by their hydrodynamic radii, Seff(q) is also characterized by a gradual decrease of the ratio Seff (q = qpeak)/Seff (q ~ 0) by decreasing the temperature. This feature indicates a gradual loss of in the probability of two particles found at distance ~ π/ qpeak which suggests a gradual structuring(unstructuring) of the system by raising(decreasing) the temperature. Note that the effective structure factor is determined by the ratio Seff(q)=(cconc/cdiluted)x(I(q)conc/I(q)diluted) where cconc and cdiluted respectively are the mass concentrations of the system at ξ=1.5 and the one corresponding to the diluted sample. The magnitudes I(q)conc and I(q)diluted also respectively are the single static scattered intensity of the system at ξ=1.5 and the one corresponding to the diluted sample. This protocol enables to display the effective structure factor, Seff(q), where prefactors due, for example, to the microgel index of refraction in the diluted, concentrated or different temperature states are omitted. Moreover, we consider that the single particle form factor does not vary at the considered volume fraction ξ=1.5. Note that we take full advantage of the scattering set-up and standard protocols are applied to obtain the single static intensity, I(q)conc, in fairly turbid systems [18].

Figure 2. PNiPAM-PEG microgel particles at a 40wt% concentration. At room temperature the particles are swollen and the system exhibits the properties of a solid (a). When the temperature is raised up to T=40C, the particle size is low enough so that a liquid state is reached (b). Note the different contrast of the suspension in between (a) and (b) not only due to the different particle sizes but also due to different indexes of refraction as the amount of solvent in the particles at swollen and de-swollen states is different.

At these conditions of temperature and volume fraction, DLS measurements are performed simultaneously than SLS experiments yielding the intensity correlation function g2(τ) 1 shown in figure 3. These correlation functions exhibit a single decay regardless of the q-vector position and are stretched exponentials in character, i.e. g2(τ) 1 ~ βexp(-2(τ/&tau0)p) where β is the experimental intercept, p is the stretched exponent and τ0 is the relaxation time. The normalized relaxation time τ0D, where &tauD is the relaxation time that corresponds to diffusive dynamics, varies with the q-vector in a similar fashion than the effective structure factor Seff(q). Moreover, at all temperatures the stretched exponent p ~ 0.7. These features are reminiscent of hard sphere systems [19], however, the ratio τ0D gradually decreases by decreasing temperature as shown in figure 3 and therefore dynamics becomes faster and closer to diffusion for low temperature systems.

To gain further knowledge on PNiPAM-PEG microgel phase behavior, we perfom rheological experiments on suspensions at different temperatures at ξ = 1.5 and focus on the frequency response of these systems. As shown in figure 4, at high temperature elasticity clearly dominates over the viscous modulus and exhibits an onset to a frequency independent plateau, hallmark to viscoelastic solids. However, the magnitude of the elastic modulus gradually decreases by gradually decreasing the temperature down to a profile where the viscous modulus gains authority over the elastic one. Additionally, the crossover time in between elastic and viscous moduli gradually shifts to shorter frequencies and denotes that the system relaxes faster at low temperatures which is as well pointed out by the different ratios τ0D at high and low temperatures.

Figure 3. Effective structure factors, Seff(q) (right y-axis) and normalized relaxation times τ0D (left y-axis) of PNiPAM-PEG microgel suspensions at ξ = 1.5 and temperature T = 32C (a), T =28c (b), T = 22C(c), T = 17.5C (d).

Figure 4. Frequency response of PNiPAM-PEG microgels at ξ = 1.5 and at T = 32C (a), T = 28C (b), T =22C (c) and T =17.5C (d). Elastic and viscous moduli are respectively represented by green and blue circles.

We study highly concentrated suspensions of PNiPAM-PEG microgel systems through different invasive (Rheology) and non-invasive (SLS and DLS) techniques at different temperatures. Despite at each temperature the response of the system exhibits common features, there are remarkable differences that suggest a more structured system at high than low temperatures. Moreover, DLS and frequency response experiments suggest that particle dynamics is faster at low than high temperature where the system displays longer relaxations. Such behavior is striking as we focus on volume fractions ξ > 1, where an arrested glass-like state should be expected. To better understand the nature of our suspensions we are currently expanding our studies to a larger spectrum of temperatures and volume fractions. Howverer, the behavior of the system just at ξ = 1.5, suggests that the configuration of the particle plays a key role as microgels reconfigure their intra-structure at each temperature, evidenced by DLS and SLS measurements in dilute PNiPAM-PEG suspensions.


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Contact Information:
Joaquim Clara-Rahola
Office: Boggs Building, Room B-55A
Email address: joaquim.clara-rahola [at] mail.gatech.edu
Phone: 404-385-3682

Soft Condensed Matter Laboratory, School of Physics, Georgia Institute of Technology
770 State Street NW, Atlanta, GA, 30332-0430, USA
Phone: 404-385-3667 Fax: 404-894-9958
alberto.fernandez [at] physics.gatech.edu