J. Phys. Chem. B 2006, 110, 25729-25733
25729
Swelling Kinetics of Poly(N-isopropylacrylamide) Minigels Iva´ n J. Sua´ rez,*,† Alberto Ferna´ ndez-Nieves,† and Manuel Ma´ rquez‡,§,| Group of Complex Fluids Physics, Department of Applied Physics, UniVersity of Almeria, Almerı´a 04120, Spain, Arizona State UniVersity Ira A. Fulton School of Engineering, Department of Bioengineering, Tempe, Arizona 85287-9709, Research Center, Philip Morris USA, Richmond, Virginia 23234, and NCTCN Center, Physical and Chemical Properties DiVision, NIST, Gaithersburg, Maryland 20899 ReceiVed: July 11, 2006; In Final Form: October 2, 2006
We synthesize poly(N-isopropylacrylamide) (PNIPAM) gels with different sizes in the micrometer scale by a slight variation of a recent emulsion polymerization method (ref 1). The procedure is different than that typically used for obtaining macroscopic PNIPAM hydrogels. The resultant minigel suspension is polydisperse thus allowing the swelling kinetics for different gel sizes to be studied; we do so at temperatures below the volume-transition temperature by wetting with water previously dried particles. The resultant swelling is followed by optical video microscopy. We find that the characteristic swelling time scales with the inverse of the particle dimension squared, in agreement with theoretical predictions (ref 2). The proportionality constant is the network diffusion coefficient D, which for the minigels under consideration appears to be in between that of PNIPAM macrogels and the self-diffusion coefficient of water.
1. Introduction Polymer gels are cross-linked polymer networks immersed in a liquid that can change their volume in response to external stimuli. In particular, poly(N-isopropylacrylamide) (PNIPAM) gels can undergo a first-order volume phase transition as a function of temperature or solvent composition.3-6 Typically, PNIPAM gels are swollen and de-swollen at temperatures (T) below and above 32 °C, respectively, due to the hydrophobic interaction between polymer chains. The colloidal PNIPAM counterparts, however, do not exhibit such discontinuous size change despite identical chemical composition and qualitatively similar swelling behavior.3,7,8 The fabrication procedures are different though and while macrogels are made at room temperature, microgels are typically synthesized at 70 °C, under bad solVent conditions. In addition, microgels typically have charge on their periphery as a result of the ionic character of the initiator that ends up located in this region.7-13 Perhaps these facts affect the continuous or discontinuous character of the phase transition. In this paper, we explore whether these differences also reflect in the swelling kinetics. We make PNIPAM gels with sizes ranging between 8 and 60 µm, with a recent chemical synthesis procedure;1 these are smaller than typical macrogels and are made at high temperature, as are most microgel suspensions. Our results bridge an existing gap for swelling kinetic studies, which, in addition to being scarce, have essentially focused either on large or small gels. The works of Loxley et al.,14 Bradley et al.,15 and Dupin et al.16 deal with the swelling kinetics of microgels. Essentially, these are stopped-flow measurements where the change in particle size with time is monitored by following the sample turbidity after a pH or a temperature jump. * Address correspondence to this author. E-mail:
[email protected]. Phone: +34 950015910. Fax: +34 950015434. † University of Almeria. ‡ Arizona State University. § Philip Morris USA. | NIST.
The results show that microgels respond fast, but no detailed analysis of the results is given. As for macroscopic gels, the works of Matsuo et al.,3 Andersson et al.,17 Tanaka,18 and Makino et al.19 quantify the swelling response to temperature pulses and the swelling kinetics from dried gels after solvent addition. Andersson et al. studied the swelling kinetics of PNIPAM gels through temperature pulses below the volume phase transition temperature.18 They found that the network diffusion coefficient D was in between 3.6 × 10-11 and 5.1 × 10-11 m2 s-1. Tanaka et al. found an inverse correlation between D and temperature, with diffusion coefficients equal to 5 × 10-12 and 2 × 10-11 m2‚s-1 for de-swollen (T > 32 °C) and swollen (T < 32 °C) PNIPAM gels, respectively.20 The study by Makino et al. focused on the gel-water interaction mechanisms above, near and below the transition temperature and did not reported any values of D.20 In all cases, the results were in agreement with Tanaka’s predictions for the swelling kinetics, with reported diffusion coefficients typically several orders of magnitude below the water self-diffusion coefficient2,18,20,21 and in general agreement with equilibrium estimates of D reported by Shibayama et al.,22 Hellweg et al.,23 and Sierra-Martı´n et al.24 Here, we show that the swelling kinetics of our minigels can also be described with Tanaka’s ideas; in particular, we show that the characteristic swelling time scales with the inverse of the particle dimension squared. However, the diffusion coefficient obtained for our minigels is about 50 times larger than that of PNIPAM macrogels and about 10 times smaller than that of water. The rest of the paper is organized as follows. In Section 2 we briefly describe the swelling kinetic model that correctly describes the temporal size evolution of PNIPAM macrogels. We then describe in Sections 3A and 3B the synthesis of the minigel suspension and the experimental methods adopted for acquiring kinetic data. The results are presented and discussed in Section 4 and the main conclusions are summarized in Section 5.
10.1021/jp0643754 CCC: $33.50 © 2006 American Chemical Society Published on Web 12/05/2006
25730 J. Phys. Chem. B, Vol. 110, No. 51, 2006
Sua´rez et al.
2. Theoretical Background: Swelling Kinetics Tanaka et al. derived a model to understand the swelling kinetics of a polymer gel network.2 The displacement of a point in the network from its final equilibrium location is represented by u. With this definition, u ) 0 at time t f ∞. It is the time dependence of u that determines the swelling kinetics. The equation of motion is given by Newton’s second law for a continuum medium, assuming the network does not accelerate: 22
f
= ∂ub ) 3‚σ ∂t
(1)
where f is the solvent-network friction coefficient and σ is the stress tensor:
(
σik ) K3‚uδik + 2µ uik -
)
3‚uδik 3
(2)
with K and µ the bulk and shear modulus of the polymer network, respectively, and uik ≡ 1/2[(∂uk/∂xi) + (∂ui/∂xk)]. Equation 1 simply establishes that the forces due to internal stresses, produced by volume changes and shear deformations, are balanced by the friction exerted by the liquid on the network. For a spherically symmetric swelling process, eq 1 becomes:2
{[
∂u ∂ 1 ∂ 2 ) D‚ (r u) ∂t ∂r r2 ∂r
]}
(3)
Figure 1. Histogram of the size distribution of the polydisperse PNIPAM minigel suspension in the swollen state (room temperature). The inset shows a bright field optical microscopy image of the suspension. The scale bar corresponds to 60 µm.
and thus the magnitude of the displacement vector obeys a Ficklike diffusion equation, with D ) (K + 4µ/3)/f, the gel diffusion coefficient. The solution to this equation can be solved in the form of Fourier series to yield:2
a(t) ) a -
() 6
π2
∞
∆ao
∑
n)1
( )
t exp -n2 τ n2
(4)
where
τ)
a2 π2D
(5)
is the characteristic swelling time, a the final equilibrium gel radius, and ∆ao the total radius increase in the entire swelling process; a - ∆ao then corresponds to the initial gel radius. In solving eq 3, it is assumed (i) that for t ) 0 the magnitude of the displacement vector equals u(r,t)0) ) ∆ao(r/a), (ii) that the normal stress σ⊥ is zero at the gel surface, and (iii) that u ) 0 for r ) 0. 3. Experimental Section A. Synthesis. Minigels are synthesized by inverse polymerization techniques following a modification of the procedure established by Dowding et al.1 The main monomer, cross-linker, and initiator are N-isopropylacrylamide (Aldrich, 5.0046 g), N,N′-methylenbisacrylamide (Fluka, 0.1548 g), and potassium persulfate (Fluka, 0.3523 g), respectively. The cross-linker concentration ends up being ∼3 wt %. All these components are dissolved in 40 mL of deionized water (conductivity
