Swelling Behaviors of Doubly Thermosensitive Core–Shell

Article pubs.acs.org/Macromolecules

Swelling Behaviors of Doubly Thermosensitive Core−Shell Nanoparticle Gels Sang Min Lee and Young Chan Bae* Department of Chemical Engineering and Molecular Thermodynamics Laboratory, Hanyang University, Seoul 133-791, Korea S Supporting Information *

ABSTRACT: Novel UCST (upper critical solution temperature) type doubly thermosensitive core−shell nanoparticle gels were prepared in order to investigate swelling behaviors. The core−shell nanoparticle gels are synthesized via precipitation polymerization and are composed of a chemically cross-linked poly(methyl methacrylate) (PMMA) core and a poly(2-hydroxyethyl methacrylate) (PHEMA) shell. Both polymers exhibit a UCST phase transition in 1-propanol solution; the transition temperatures are 25 °C for PHEMA and 68 °C for PMMA. Photon correlation spectroscopy (PCS) measurements indicate that the large UCST gap between the shell- and core-forming polymers gives rise to a clear two-step swelling process upon heating. For theoretical analysis, a corrected modified-double-lattice (MDL) model with a new type of interaction parameter (ε̃ij), called the MDL-T model, is introduced to represent the optimized thermal behavior of the interchange energy and is combined with the Flory−Rehner (F− R) chain model to express the net free energy of mixing. Required model parameters are obtained from the experimental swelling data of homopolymer nanoparticle gel solutions and are directly applied to core−shell swelling calculations. The model is applied to two LCST (lower critical solution temperature) type doubly thermosensitive core−shell nanoparticle gels such as poly(Nisopropylacrylamide) (PNIPAM) core/poly(N-isopropylmethacrylamide) (PNIPMAM) shell in water and PNIPMAM core/ poly(N-n-propylacrylamide) (PNNPAM) shell in water. A comparative analysis of the MDL-T and other lattice based models is carried out, and a noticeable improvement is observed.

1. INTRODUCTION Polymer gels are chemically cross-linked networks swollen with solvents that are highly impact resistant, elastically soft, and highly solvent absorptive. In particular, environmentally sensitive polymer gels undergo abrupt volume changes in response to surrounding conditions such as temperature,1 ionic strength,2 radiation,3 pH,4 and solvent composition.5 These features are employed in a wide variety of applications such as drug delivery,6−9 sensors,10 chemical separations,11 and catalysis.12 They have received considerable attention for more than four decades from both theoretical and technological viewpoints. The phase behavior of linear polymer solutions directly influences the swelling behavior of cross-linked polymer networks. A polymer with LCST-type thermal behavior in a certain solvent exhibits a swelling-to-collapsing volume transition upon heating when the polymer is cross-linked. For example, chemically cross-linked PNIPAM nanoparticle gels reveal a drastic particle size decrease upon heating in aqueous solution.13−15 A reverse transition is observed in UCST-type polymer networks such as PMMA and PHEMA in aliphatic alcohols, exhibiting a collapsing-to-swelling volume transition upon heating.5,16 In recent years, a novel architecture of polymer nanoparticle gels consisting of at least two different polymersone forming © XXXX American Chemical Society

the core and another forming the shell of the particleshas been designed in order to obtain enhanced versatility in nanoparticle gels. These core−shell structures have attracted much attention due to their superior properties, which are not present in the individual components. Lyon and co-workers17−19 introduced multiresponsive core−shell nanoparticle gels composed of a PNIPAM core/PNIPAM-co-acrylic acid (AAc) shell with simultaneous temperature and pH sensitivities. Babu et al.20 combined hydrophilic (acrylamide) and hydrophobic (methyl methacrylate) monomers in order to produce responsive core− shell nanoparticle gels for controlled release applications. Richtering and co-workers21−24 recently presented core−shell nanoparticle gels consisting of two different temperatureresponsive polymers, PNIPAM and PNIPMAM, with LCSTs of 34 and 44 °C, respectively. Similarly, Zeiser et al.25 substituted PNIPAM with PNNPAM (LCST = 21 °C) to increase the LCST gap (ΔT = 23 °C) between the core and shell polymer and confirmed a linear swelling behavior within the temperature range. Although LCST-type (NIPAM based) core−shell nanoparticle gels have been widely studied, experimental and Received: October 13, 2014 Revised: November 10, 2014

A

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polymers: ca. 25 °C for PHEMA and 68 °C for PMMA. For the theoretical approach, we introduce a corrected modified-doublelattice42 (MDL) model, referred to as an MDL-T model, optimizing a temperature-dependent interaction parameter (ε̃) for thermosensitive gels. Combining the MDL-T model with the F−R chain model,43 we correlated the experimental swelling data of homopolymer nanoparticle gels and obtained interaction parameters. The parameters were directly applied to calculate the swelling behavior of the core−shell nanoparticle gels using Lian’s simple geometrical approach.44 The procedure was applied to one UCST-type core−shell network presented here (PMMAcore/PHEMA-shell) and two LCST-type core−shell networks (PNIPAM-core/PNIPMAM-shell21 and PNIPMAM-core/ PNNPAM-shell25).

theoretical studies for UCST-type core−shell nanoparticle gels are scarce, and the UCST-type doubly temperature-sensitive core−shell nanoparticle gels have not yet been reported. Theoretical analysis and quantitative descriptions of swelling behaviors in polymer gel networks are essential research areas for industrial applications. Based on the pioneering work of Flory,26 thermodynamic models have been reported for swelling calculation. Coleman et al.27 incorporated the influence of hydrogen bonding into an association model and combined it with the Flory−Rehner (F−R) chain model. Freitas et al.28 suggested an oriented, quasi-chemical thermodynamic model considering a competition between hydrogen bonding and dispersion forces. Zhi et al.29 developed a molecular thermodynamic model for multisensitive hydrogels. Quesada-Pérez et al. analyzed properties of gel networks through a simulation approach within a coarse-grained model.30,31 Recently, Bae et al.16,32−35 proposed a systematic approach predicting various types of swelling behavior using the same interaction parameters obtained from non-cross-linked polymer solutions. These models are for homogeneous gel networks, and core− shell networks have a fundamentally different internal structure. The core and shell are physically constrained by each other, and neither can swell to the homogeneous and isotropic state; thus, the deformation of a core−shell particle is inhomogeneous and anisotropic. Sekimoto and Kawasaki36,37 first used a general but complicated field theory to describe the phase coexistence of gels in an inhomogeneous state. Suo and co-workers38,39 developed a thermodynamic model to analyze the swelling behavior of hydrogels under the constraints of hard materials that cause inhomogeneous swelling. Gernandt et al.40 combined Suo’s approach with a classical Flory−Huggins26,41 theory to analyze the properties of core−shell nanoparticle gels made out of two different stimuli-responsive polymers. Although these works are in agreement with the swelling behavior characteristics of polymeric gels with inhomogeneity, the modeling results deviate somewhat from experimental data and are too complex for practical applications. Herein we report novel, UCST-type doubly thermosensitive, core−shell nanoparticle gels and suggest a simple and systematic approach to quantitatively represent the abnormal volume transition of the core−shell networks. The core−shell nanoparticle gels are composed of PMMA as core materials, with PHEMA forming the shell (see Figure 1), and exhibit a two-step swelling transition corresponding to the UCSTs of core and shell

2. EXPERIMENTAL SECTION 2.1. Chemicals. 2-Hydroxyethyl methacrylate (HEMA) and methyl methacrylate (MMA) monomers, 1-propanol, acetone, N,N′methylenebis(acrylamide) (BIS, cross-linker), and ammonium persulfate (APS, initiator) are commercially available from Aldrich and were used as received. Distilled deionized water was used for synthesizing gel particles. 2.2. PMMA Core Synthesis. PMMA core particles were prepared via precipitation polymerization, as reported previously.5 The MMA monomer (1 g), the BIS cross-linker (1 mol % of monomer), and an acetone−water mixture (50 mL, 35 vol % acetone) were added to a Pyrex glass polymerization reactor equipped with a reflux condenser, mechanical stirrer, gas inlet, and thermometer.45 After 30 min of premixing at 70 °C, the APS initiator was added (0.01 g, 1 mL of 1 wt % aqueous solution), and the polymerization was performed for 4 h under a nitrogen stream. After polymerization, the acetone was evaporated at 55 °C for 3 h, and the product was filtered through a 0.45 μm syringe filter. 2.3. PHEMA Shell Synthesis. PHEMA shell synthesis was performed using PMMA core particles as nuclei for subsequent precipitation polymerization, resulting in the growth of the PHEMA shell on the existing particles. The core solution was mixed with a separately prepared shell mixture containing the HEMA monomer (0.65 g), the BIS cross-linker (2 mol % of monomer), and distilled deionized water (50 mL) as the solvent. The core particles initiated by APS contain a small number of charged groups on the surface. These charges stabilize the particles in the next step in which a shell of PHEMA is polymerized on the core particles.46,47 After heating to 80 °C, shell polymerization was initiated via the APS initiator (0.005 g, 1 mL of 0.5 wt % aqueous solution) and proceeded for 4 h. Since the shell polymerization was performed in aqueous media at a high temperature, the PMMA core particles were fully collapsed during the synthesis, hindering the interpenetration of shell materials into the core.48 The product was filtered using the method applied to the core solution. 2.4. Swelling Measurement via the PCS Technique. The diameters of the gel particles were measured via the PCS technique, using a Malvern’s Zetasizer Nano ZS equipped with a He−Ne laser (λ = 633 nm) at a 173° angle and analyzed using Malvern Zetasizer Software (ver. 5.10). Whether the shell polymerization on the core surface was well performed or not can be confirmed by the results of PCS measurement. If the separated PHEMA particles were synthesized, the PCS result of the core−shell may show double or multiple peaks and high polydispersity index (PDI) value. However, as shown in Figure 2, the polydispersity index (PDI) values obtained from the software were less than 0.08 for each set of conditions, indicating uniform size of the core−shell particles.49 The sample results of the PCS measurements for the PMMA core and the PMMA/PHEMA core−shell particles are depicted in Figure 2.

3. MODEL DEVELOPMENT 3.1. Swelling Equilibrium of Polymer Gel Solutions. The swelling behaviors of cross-linked polymer gel networks are

Figure 1. Schematic drawing of a core−shell structure consisting of PMMA core/PHEMA shell. The cross-linker content of the core network is 1 mol %, and that of the shell is 2 mol %. B

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Figure 2. Results of intensity-based particle-size distributions of PMMA core and PMMA/PHEMA core−shell nanoparticles in 1-propanol at (a) 5 °C for the reference state and (b) 40 °C for the shell swelling state.

Figure 3. Typical types of the reduced interchange energy parameter (ε̃ij) for (a) LCST-type polymer gels and (b) UCST-type polymer gels. The symbols are calculated from experimental swelling data, and the solid lines are the fitting results of ε̃ij of the MDL-T model.

constants (Cγ = 1.7986 and Cβ = 0.1415) determined from fitting the Monte Carlo simulation data,42 and ε̃ij is the reduced interchange energy parameter (defined in section 3.2). The elastic contribution, ΔGel, proposed by Flory and Rehner43 and revised by Moerkerke and co-workers,50 is given by

determined via two separate and additive contributions. One is the free energy of mixing (ΔGmix), describing interactions between polymer chains and solvents, and the other is the free energy of elasticity (ΔGel), considering the cross-linking degree and other constraints of the gel network. Thus, the total change in Gibbs energy (ΔGnet) of nonionized polymer gel solutions is given by ΔGnet = ΔGmix + ΔGel

⎛ 3Aϕ 2/3 ⎞ ⎛ ⎞ ΔGel g0 ⎟(ϕ 1/3 − ϕ ) + ⎜ B ⎟ϕ ln ϕ =⎜ g g g ⎜ 2m ⎟ NRT ⎝ mc ⎠ g c ⎝ ⎠

(1)

The mixing contribution, ΔGmix, is expressed by the MDL theory proposed by Oh and Bae42 as follows: Δmix G = NrkT K

K

K

∑∑ i=1 j=1

⎛ϕ ⎞⎞ ϕ⎞ ⎛ εij̃ ⎛ ⎜2 − ⎜ i + j ⎟ + ⎜ 1 + 1 ⎟⎟ϕϕ ⎜ ⎟ ⎜ 2 ⎜⎝ rj ⎠ ⎝ ri rj ⎟⎠⎟⎠ i j ⎝ ri K

K

− (∑ ∑ εij̃ ϕϕ Cγ /4 )2 − i j ⎛1 ⎞2 1 + ∑ ∑ ϕϕ⎜ − ⎟⎟ 2 i = 1 j = 1 i j⎜⎝ ri rj ⎠ K

∑ i=1

i=1 j=1

Cβ

A=

ϕi ri

2ϕg f−2 , + f f

B=

(3)

2ϕg f

(4)

where mc is the average number of lattice sites between two crosslinking sites, ϕg is the volume fraction of the cross-linked polymer in a gel network, and ϕg0 is the fraction at the reference state. When the gel network is fully collapsed in a perfectly dried state, ϕg0 = 1. We assume that the gel network is a perfect tetrafunctional network; thus, the functionality of the crosslinker f = 4. To calculate the swelling equilibrium condition, the chemical potentials for each component are required. They can be determined via the formula

ln ϕi

K

(2)

where k is the Boltzmann constant, ϕi is the volume fraction, ri is the size parameter of component i, Cγ and Cβ are the universal C

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Figure 4. (a) Swelling behaviors of PMMA (◇), PHEMA16 (▼), and PMMA/PHEMA core−shell (●) gels in 1-propanol as a function of temperature. (b) Schematic diagram of the PMMA/PHEMA core−shell nanoparticle, which undergoes two-step transitions upon heating.

⎡ ∂(ΔGnet /kT ) ⎤ =⎢ ⎥ ∂Ni kT ⎦T , V , N ⎣

4. RESULTS AND DISCUSSION 4.1. Experimental Results. The average diameters of the nanoparticle gels presented in this work were measured in a wide temperature range between 5 and 85 °C using the PCS technique. The swelling ratio of a nanoparticle gel is generally determined via the volume ratio of the gel. This is done with the assumption of negligible surface effect, which has been supported by recent simulation studies performed by Quesada-Pérez et al.55,56 The swelling ratio is determined as follows:

Δμi

j≠i

(5)

When a polymer gel solution is in the equilibrium condition, the chemical potentials of the solvents inside (Δμini ) and outside (Δμout i ) the gel network are equal. In the case of core−shell gels, ) the chemical potentials of solvents both inside the core (Δμin,core i ) should be equal to those outside the network and shell (Δμin,shell i (Δμout i ). Since the solvent in our discussion is a pure solvent for each system, Δμout i is considered to be zero. 3.2. Temperature-Dependent Interchange Energy Parameter (ε̃ij). The swelling behaviors of thermosensitive polymer gels strongly depend on the interactions between polymers and solvents. Generally, LCST-type polymer gels abruptly pull the solvent into the network below the LCST of the polymer, while UCST-type polymer gels rapidly absorb the solvent above the UCST of the polymer. This indicates that the change of interaction between the polymer gels and solvents occurs near the critical solution temperature. Figure 3 shows the behavior of the temperature-dependent interchange energy parameter (ε̃ij) calculated from experimental swelling data: (a) PNIPAM/water and (b) PHEMA/1-propanol system. The behavior of ε̃ij depending on temperature can be divided into the swollen, transition, and collapsed regions. Though the ε̃ij has a converged value before and after the transition region, an abrupt change is observed in the transition portion. The ε̃ij in the MDL model, however, does not represent this type of interaction energy behavior; thus, we give a new expression of ε̃ij as follows: εij̃ = εij̃ ,weak +

swelling ratio =

ϕg

=

⎛ d ⎞3 V =⎜ ⎟ V0 ⎝ d0 ⎠

(7)

where d0 is the diameter (d) of a particle in a reference condition, and V and V0 are the gel volumes in equilibrium at the state of interest and the reference state, respectively. In the case of core− shell gel systems, the swelling ratio was determined via Lian’s simple geometrical approach for core−shell gels,44 given by swelling ratio =

×

ϕg0,shell ϕg,shell

⎛ d0,core ⎞3⎞ ⎛d ⎞3 ⎛ V ⎟⎟ ⎟ = ⎜⎜ total ⎟⎟ = ⎜1 − ⎜⎜ ⎜ V0 d d ⎝ 0,total ⎠ ⎟⎠ ⎝ 0,total ⎠ ⎝

⎛ d0,core ⎞3 ϕg0,core ⎟⎟ + ⎜⎜ ⎝ d0,total ⎠ ϕg,core

(8)

where dcore is the diameter of the core (the inner diameter), dtotal is the total diameter of the core−shell particle, and the subscript 0 is the reference state. The reference state can be regarded as the most collapsed state at low temperature (5 °C), which is well below the UCST of PMMA and PHEMA. Figure 4a displays the influence of temperature on the swelling behaviors of the PMMA/PHEMA core−shell nanoparticle gels and, for comparison, of the PMMA and the PHEMA16 homopolymer nanoparticle gels. Each homopolymer gel exhibits an abrupt volume transition when the temperature is increased above the UCSTs of each polymer (PMMA: 68 °C and PHEMA: 25 °C in 1-propanol). This thermosensitivity appears directly in the PMMA/PHEMA core−shell system, representing a two-step swelling process upon heating. Figure 4b is a schematic diagram of the doubly thermosensitive volume transition occurring in the core−shell nanoparticle gels. Below the UCST of the PHEMA shell (T < 25 °C), the core−shell gel is fully collapsed due to a lack of affinity between the gel materials and 1-propanol. Above

δεij̃ 1 + κ(δεij̃ )2

ϕg0

(6)

where ε̃ij,weak (= ε/kT) and δε̃ij = (δε/kT) are the reduced interaction parameters of the ordinary and oriented interactions, respectively, and κ is a degeneracy parameter. The interaction parameters ε and δε are replaced by ε = εH − εS × T and δε = δεH − δεS × T to consider the enthalpic and entropic energy contributions.54 The function form of eq 6 is a mathematically optimized semiempirical form for this type of interaction energy behavior without a specific physical meaning. D

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T = 25 °C, 1-propanol becomes a good solvent for the PHEMA shell network, initiating the first swelling process, though the solvent still cannot penetrate the PMMA core network. At temperatures higher than the UCST of the PMMA core (T > 68 °C), the core materials pull the solvent into the network, resulting in a second volume transition. Figure 5 shows a comparison of the PMMA/PHEMA coreshell swelling results in 1-propanol between the experimental

of doubly thermosensitive core−shell nanoparticle gels with model parameters obtained from homopolymer networks. First, we correlated the MDL-T model to the experimental swelling data of homopolymer gel networks in order to obtain the interchange energy parameters between the polymer segments and the solvents. We then calculated the swelling behavior of the newly synthesized UCST-type doubly thermosensitive core− shell system using the same interaction parameters obtained from the homopolymer gel systems. As mentioned previously, two separate and additive contributions are needed to calculate the swelling behavior of gel networks: the free energy of mixing and the free energy of elasticity. In the mixing term, the lattice size (ri) and the temperature-dependent interchange energy parameters (ε̃ij) are dominant factors. The size parameter is a relative segment size of component i; thus, the smallest molecule (rwater) is set to 1, and the other solvent (r1‑propanol) is set to 3.68, based on the Bondi van der Waals volume.58 For polymer nanoparticle gels, rgel is considered infinite. The energy parameters are determined from fitting the experimental swelling data. For the elasticity term, both the volume fraction of polymer in the reference state (ϕg0) and the cross-linking density (mc) parameters should be determined. The reference state is regarded as the most collapsed state, and we assumed the network in the reference condition is perfectly collapsed (ϕg0 = 1). The determination of the cross-linking density parameter (mc), which is the number of lattice sites occupied by an average network chain, is not an easy task because the exact amount of cross-linker participating in the gel formation process is unclear.51 However, several studies14,50 have reported that reasonable results of mc could be obtained from experimental conditions, as follows:

Figure 5. Comparison of the experimental (●) and the calculated (○) swelling data of the PMMA/PHEMA core−shell nanoparticle gels in 1propanol.

data and the simply calculated data from eq 8. The decreased swelling ability of the core-shell gel is clearly observed. This is an interesting result, because the cross-linking density of the core and shell network is the same as that of each homo-polymer network (1 mol % BIS for PMMA core and 2 mol % BIS for PHEMA shell); thus, the swelling ability appears to be maintained at least in a similar degree. However, the comparison result demonstrates that the properties of core-shell networks are not a simple sum of the individual core and shell components. This can be explained by the structural characteristic of the coreshell network. First, mechanical constraints near the core/shell interface impact on the swelling behavior of the shell network. Based on SANS and SAXS results, Ballauf and co-workers46 have shown that the swelling process of shell is restricted due to the fixation of the network on the core surface. Another structural factor is the shell restriction on core network.57 At high temperature above 80 °C, the core-shell exhibits an upturn swelling behavior which shows a decreased swelling ability of the PMMA core network. This is because the loosely cross-linked network near the core periphery is restricted by the presence of the shell, prohibiting the core from expanding to the volume it possessed prior to shell addition. Although the swelling ability of the core−shell nanoparticles is limited by the structural constraints, research has revealed that the degree of swelling can be controlled via the cross-linker type, concentration, and the amount of synthesized monomer.21,25 4.2. Thermodynamic Modeling. A relationship between the homopolymer nanoparticle gels and the core−shell nanoparticle gels was verified experimentally in the previous section. However, quantitative descriptions of swelling behaviors are often required in many fine chemical processes; thus, we carried out a direct calculation using a thermodynamic model. In this work, we focus primarily on representing the swelling properties

1 number of moles of monomer × × rmonomer 2 number of moles of cross‐linker v 1 = × m 2ϕj v1

mc =

(9)

where vm and v1 are respectively the molar volume of the monomer and the smallest molecule (water in this work), ϕj is the mole fraction of the cross-linker to total monomer, and rmonomer is the relative segment size of monomer. The calculated mc values for each polymer network are listed in Table 1. Table 1. Cross-Linking Density Parameters for the Determination of mc Values system 21

PNIPAM PNIPMAM21 PNNPAM52 PHEMA53 PMMA a

ϕj (exp value)

vm (cm3/mol)

v1a (cm3/mol)

mc

0.014 0.03 0.024 0.02 0.01

123.7 143.5 128.6 121.3 109.4

18 18 18 18 18

248.9 132.9 148.8 168.5 303.9

The smallest molecule for determining relative segment size.

The interchange energy parameter (ε̃ij) between polymer and solvent segments is the only temperature-dependent term in this model; thus, the accuracy of model calculation for thermosensitive gels is strongly dependent on whether the energy parameter could represent a proper temperature-dependent function for gel network systems. Figure 6 shows the experimental swelling data and the reduced interaction parameter (ε̃ij) of the PMMA and the PHEMA homopolymer gel system. The ε̃ij values for each swelling datum can be calculated when other model parameters E

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Figure 6. Experimental swelling data and reduced interaction parameter values of (a) PMMA/1-propanol and (b) PHEMA/1-propanol16 gel solutions as a function of temperature. The solid lines are calculation results using the MDL-T model.

Table 2. Model Parameters of the MDL-T Model for Swelling Calculationa homopolymer gels PMMA (1)/1-propanol (2) PHEMA (1)/1-propanol (2) PNIPAM (1)/water (2) PNIPMAM (1)/water (2) PNNPAM (1)/water (2) core−shell gels PMMA-core/PHEMA-shell PNIPAM-core/PNIPMAM-shell PNIPMAM-core/PNNPAM-shell

εH12/k (K)

εS12/k (K)

126.55 113.73 −1.18 × 103 −1.26 × 103 −1.98 × 103 kcoreb

δεH12/k (K)

0.26 0.25 −4.27 −4.50 −6.88

1.83 1.15 1.55

kshellb

467.36 833.65 −7.01 × 103 −8.41 × 103 −1.23 × 104 d0,core/d0,total

4.27 0.29 4.25

δεS12/k (K)

κ

ϕg0

1.38 2.85 −22.65 −26.27 −41.38

677.7 99.8 8.42 4.49 20.39

1 1 1 1 1

ϕg0,core

ϕg0,shell

1 1 1

1 1 1

0.83 0.815 0.555

a

The interaction parameters for core−shell gel solutions are obtained from each homopolymer gel solution. Cross-linking density parameters (mc) for homopolymer gels are listed in Table 1. bAdjustable parameters.

(ri, mc, and ϕg0) are fixed. The ε̃ij values for each system (open symbols) exhibit a similar tendency toward temperature because both materials are the UCST-type polymer in 1-propanol; however, they show a significantly different shape of ε̃ij due to their own thermal energy behavior characteristics. The ε̃ij values are objective function values for the temperature-dependent functional form of ε̃ij(T), proposed in section 3.2. We correlated the ε̃ij(T) with the objective values and obtained interaction parameters for each binary system (blue lines). We present reasonably accurate calculated results (red lines) and confirm the validity of the functional form of ε̃ij(T). The obtained model parameters are listed in Table 2. A model comparison among the original MDL,42 the MDL with a new ε̃ij (MDL-T), and Yang’s model59,60 was carried out in Figure 7. The elastic free energy was calculated via the F-R chain theory in all three cases, and the consistency of calculation is maintained. The major difference between the three models is in the temperature-dependent energy parameter. Figures 6a,b are the experimental swelling data and the calculated results of (a) PMMA and (b) PHEMA homopolymer nanoparticle gels. The original MDL model shows accurate results in the low temperature region and near the volume transition temperature but does not converge in the high temperature region. On the other hand, Yang’s model shows a converging trend in the high swelling region but underestimates the volume transition temperature. Figures 7c,d show the experimental data and model calculations for the swelling behavior of the PMMA/ PHEMA core−shell nanoparticles. The required interaction parameters are obtained from each homopolymer gel system,

and a thickness parameter (d0,core/d0,total) is calculated from PCS data at the reference state (Figure 2a). Since the constraint effect of core−shell was confirmed in Figure 5, we applied the constraint parameters (kcore and kshell) to the free energy of elasticity for the core−shell network as follows: ΔGel,core NRT

2/3 ⎞ ⎛ 3Aϕ g0,core ⎟(ϕ 1/3 − ϕ ) = kcore⎜ g,core ⎜ 2m ⎟ g,core c,core ⎝ ⎠

⎛ B ⎞ ⎟⎟ϕg,core ln ϕg,core + kcore⎜⎜ ⎝ mc,core ⎠ ΔGel,shell NRT

(10)

2/3 ⎞ ⎛ 3Aϕ g0,shell ⎜ ⎟(ϕ 1/3 − ϕ ) = kshell g,shell ⎜ 2m ⎟ g,shell c,shell ⎝ ⎠

⎛ B ⎞ ⎟⎟ϕg,shell ln ϕg,shell + kshell ⎜⎜ ⎝ mc,shell ⎠

(11)

where kcore and kshell ≥ 1. This is theoretically reasonable because when k ≥ 1, the free energy of elasticity of the core and shell networks is larger than that of each homopolymer network, resulting in increased stiffness of the core and shell networks. As shown in Figure 7c, the calculated result of the MDL-T model with the constraint parameters successfully represents the twostep volume transition and the degree of swelling of the core− shell particles with great accuracy. In Figure 7d, the other two models show some deviations both in the volume transition F

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Figure 7. Experimental swelling data and modeling calculation of (a) PMMA, (b) PHEMA, and (c, d) PMMA-core/PHEMA-shell nanoparticle gels in 1-propanol. Three lattice models are compared: MDL-T (solid line), MDL (dashed line), and Yang’s model (dotted line).

PNIPAM/PNIPMAM core−shell is less than 1, indicating bigger swelling ability of the shell network than that of homopolymer network. This is an opposite trend from several works,25,46 and Berndt and Richtering21 explain that the restriction of shell can differ depending on core material. When the shell is attached to a swellable core network, the forces which would restrain the shell are weak, and the shell swelling will mechanically expand the collapsed core. In the first collapsing transition range (310−320 K), the MDL and Yang’s model underestimate the experimental data. The MDL-T model exhibits superior agreement in describing the two-step volume transitions and the degree of swelling when compared to the other two models. Figure 9 shows another doubly thermosensitive core−shell nanoparticle gel system composed of PNIPMAM core and PNNPAM shell.25 Interaction parameters between PNNPAM and water are obtained from fitting the experimental swelling data of PNNPAM homopolymer gel52 (Figure 9a). The PNIPMAM core material is the same as the shell polymer in Figure 8; thus, the same interaction parameters were used. However, the cross-linking density (ϕj) is different from the PNIPMAM network in Figure 8 (0.03 → 0.02); the mc was recalculated, and the value is 199.3. Figure 9b is the modeling result of the core−shell swelling behavior using these parameters (Table 2). The first swelling transition (ca. 315 K), corresponding to the PNIPMAM core transition, occurs at a

temperatures and the degree of swelling due to the inaccurate modeling results in the homopolymer systems. We applied the MDL-T model to two other doubly thermosensitive core−shell nanoparticle gels to verify the applicability of the model and the validity of the calculation procedure proposed in this work. Figure 8 shows experimental swelling results and modeling calculations of PNIPAM and PNIPMAM homopolymer nanoparticle gels and PNIPAM-core/ PNIPMAM-shell nanoparticles gels in aqueous solutions.21 These systems exhibit LCST-type volume transitions, which have a completely different transition mechanism from the UCST-type gel network.34 The LCST transition is driven by specific interactions; thus a more drastic interaction change between dissimilar components occurs in the transition. The MDL model and Yang’s model cannot clearly represent the rapid solvent absorption; thus they deviate somewhat from the experimental results, as shown in Figures 7a,b. On the other hand, the MDL-T model corresponds well with the volume transition temperature as well as to the overall degree of swelling. Figure 8c presents the experimental swelling data and a model calculation of the LCST-type doubly thermosensitive core−shell nanoparticle gels consisting of PNIPAM core and PNIPMAM shell. The energy parameters and cross-linking density parameters obtained from each homopolymer gel system are directly applied (Table 2). It is interesting that the kshell of the G

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Figure 8. Experimental swelling data21 and modeling calculation of (a) PNIPAM, (b) PNIPMAM, and (c) PNIPAM-core/PNIPMAM-shell nanoparticle gels aqueous solutions. Three lattice models are compared: MDL-T (solid line), MDL (dashed line), and Yang’s model (dotted line).

Figure 9. Experimental swelling data and modeling calculations of (a) PNNPAM homopolymer52 and (b) PNIPMAM core/PNNPAM shell25 nanoparticle gels in water. Three lattice models are compared: MDL-T (solid line), MDL (dashed line), and Yang’s model (dotted line).

4.3. Significances and Limitations. Different temperaturesensitive polymers can be combined in core−shell structures with both similar and varied swelling properties associated with each homopolymer gel network. A newly synthesized core−shell nanoparticle gel presented herein exhibits a two-step uptake property upon heating, and its volume transition is investigated

slightly lower temperature than the PNIPMAM homopolymer gel transition temperature (ca. 318 K) due to a “corset effect”,25 meaning a shell restriction on core swelling. Because all three models are unable to display this effect, they overestimate the first transition temperature, though the overall tendency corresponds well with experimental observations. H

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Notes

both experimentally and theoretically within the framework of the molecular thermodynamics. A notable improvement in the swelling calculation was achieved using a new temperaturedependent function form of the interchange energy parameter (section 3.2) within the MDL model. The corrected MDL model (MDL-T) successfully describes the abrupt volume transition as well as the convergence of swelling in the high swelling region, which could not be represented by other models. All of the required interaction parameters were obtained from the homopolymer gel systems and directly applied to the core− shell gel system. It is difficult for the proposed model to consider all factors that influence the swelling behavior of polymer gel networks, including the heterogeneity of cross-linking density and the solvent density difference between the inside and outside of the gel network. In particular, the model calculation of the core− shell networks cannot be achieved without additional parameters (kcore and kshell) because it cannot consider the structural characteristics of core−shell structure such as the shell restriction57 and the mechanical constraints near the core/shell interface.46 Although some adjustable parameters are needed, the proposed modeling procedure enables us to describe the swelling behavior of doubly thermosensitive core−shell nanoparticles with great accuracy, indicating a possibility to predict the swelling properties of multicomponent polymer networks using information from homopolymer networks.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean Government (MSIP) for the Center for Next Generation Dye-sensitized Solar Cells (No. 2008-0061903).

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5. CONCLUSION A UCST-type thermosensitive core−shell nanoparticle gel consisting of a PMMA core and a PHEMA shell has been prepared and investigated via photon correlation spectroscopy. When the two different thermoresponsive polymers are arranged as the core and shell of the particle, two distinct volume transitions are displayed in 1-propanol at 25 and 68 °C, corresponding to the volume transition temperatures of each homopolymer gel. For a quantitative description, the corrected MDL model (MDL-T model), optimizing the thermal behavior of polymer gel solutions, and the F−R chain model were combined to express the net free energy of mixing. With the newly introduced interchange energy parameter (ε̃ij(T), section 3.2), the thermodynamic model successfully describes an abrupt volume transition and the overall degree of swelling in the PMMA and PHEMA gel solutions. The model parameters obtained from the homopolymer gel solutions were directly applied to the swelling calculation of the PMMA/PHEMA core− shell particle gel solution, and two adjustable parameters (kcore and kshell) were introduced to consider structural characteristics of the core−shell structure. The model represents the two-step volume transition of the core−shell nanoparticles with great accuracy, and its applicability was verified via application to two other LCST-type doubly thermosensitive core−shell systems.

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ASSOCIATED CONTENT

* Supporting Information S

Derivation process for ε̃ = f(Q). This material is available free of charge via the Internet at http://pubs.acs.org.

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