Correlated Morphological Changes in the Volume Temperature

Article pubs.acs.org/Macromolecules

Correlated Morphological Changes in the Volume Temperature Transition of Core−Shell Microgels Andreea Balaceanu, Yaroslav Verkh, Dan E. Demco,* Martin Möller, and Andrij Pich* Functional and Interactive Polymers, Institute of Technical and Macromolecular Chemistry, DWI RWTH Aachen University, Forckenbeckstraße 50, 52056 Aachen, Germany S Supporting Information *

ABSTRACT: PVCL and PNIPMAAm core−shell components in microgel particles are shown to have different volume phase temperature transition behavior than the respective homopolymer microgel particles due to confinement effects. A combination of dynamic light scattering (DLS) data that gives access to the temperature dependence of hydrodynamic radius and modified Flory−Rehner theory in the presence of networks confinement allowed obtaining information about correlated morphological changes of components inside of core−shell microgels. The core−shell components individual temperature behavior is analyzed by modifying the Flory−Rehner transition theory in order to account for core−shell morphology and the existence of an interaction force between core and shell. Describing the dependence on temperature of the radial scale parameter, the ratio between the radius of the core and the hydrodynamic radius, we gain access to the swelling behavior of the core and shell components irrespective of the swelling behavior of the total hydrodynamic radius. Furthermore, the theoretical description of volume phase temperature transition permits the development of scenarios for the correlated changes in the core and shell radial dimensions for the two microgels with reversed morphologies. The fact that the theoretical model is appropriate for the treatment of core−shell microgels is proved a posteriori by obtaining a temperature dependence of the components that is in accordance with the expected physical behavior. Novel core−shell microgel systems of PVCL (poly(N-vinylcaprolactam))-core/PNIPMAAm (poly(N-isopropylmethacrylamide))-shell and PNIPMAAmcore/PVCL-shell, with a double volume phase temperature transition due to the thermoresponsive components, were used for this study.

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techniques, such as light scattering,17 neutron scattering,18−21 nuclear magnetic resonance,22−24 and other analytical methods in order to analyze their morphology, composition, and volume transition. Theoretical models, like the Flory−Rehner swelling theory25,26 was used to study microgels, in order to obtain information about the specific polymer swelling parameters, or to investigate the structure of the particle. It was determined that the polymer−solvent interaction parameter depends not only on the temperature but also on the concentration of polymer.27 The modified Flory−Rehner theory26 for elastic contribution was combined with an extended Flory−Huggins model25,28 for mixing solvent and network and used to fit experimental data obtained for submicrometer gel particles and bulk gels.29 By modifying the Flory interaction parameter, the model for homopolymer gel particles was generalized to the copolymer gel/solvent systems.30 By comparing the pressure and temperature induced deswelling, the pressure dependence of the Flory solvency parameter was obtained.31 Flory swelling theory was also used to describe the behavior of microgel

INTRODUCTION Microgels are intramolecularly cross-linked polymeric chains with colloidal dimensions that can be built from a large variety of different monomers allowing precise control of their responsive properties. Stimuli sensitive microgels, which change their swelling behavior as response to external stimuli such as temperature, pressure, pH, and ionic strength, attract attention because of their versatility to many fields, such as drug delivery,1 catalysts,2 chemical separation, design of biomaterials,3 and development of sensors.4 The most studied responsive polymer is cross-linked poly(Nisopropylacrylamide) (PNIPAAm).5−7 Another frequently used temperature-sensitive polymer for microgel design is poly(Nvinylcaprolactam) (PVCL).8−13 Poly(N-vinylcaprolactam) is not only thermosensitive but also a biocompatible polymer. The hydrophilic amide group connected to the hydrophobic polymer backbone chain will not produce small amide compounds which act against biomedical applications via hydrolysis.14,15 In addition, it has been reported that the monomer N-vinylcaprolactam (VCL) is less cytotoxic than Nisopropylacrylamide (NIPAAm).16 Because of these important applications, microgels were studied widely in the recent years by various experimental © XXXX American Chemical Society

Received: March 8, 2013 Revised: May 25, 2013

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dx.doi.org/10.1021/ma400495y | Macromolecules XXXX, XXX, XXX−XXX

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Table 1. Components Quantities Used for Microgel Synthesis microgel PVCL-core/PNIPMAAm-shell PNIPMAAm-core/PVCL-shell

core shell core shell

monomer [g]

CTAB [g]

BIS [g]

AMPA [g]

H2O [g]

T [°C]

2.215 2.023 2.023 2.215

0.0221 − 0.02 −

0.06 0.06 0.06 0.06

0.05 0.05 0.05 0.05

150 − 150 −

80 80 80 80

described in previous papers for homopolymer microgels prepared by precipitation polymerization,32,33 was synthesized. The appropriate amount of monomer, CTAB, BIS and deionized water (Table 1) were placed in a double-wall glass reactor equipped with mechanical stirrer. After 1 h of the incubation at the appropriate temperature and nitrogen purging, initiator AMPA dissolved in 5 g water was added under continuous stirring to start the polymerization reaction. This reaction was carried out for 8 h. During second step the appropriate amount of the second monomer and cross-linker BIS were added to the seeded dispersion of the core, followed by nitrogen purging. Finally, AMPA solution in water was added to start the polymerization of the shell (Table 1). Although the reaction time is 8 h, we have previously showed40 on a similar microgel system that the polymerization and crosslinking are completed much faster. The monomer conversion reaches 85% in the first 20 min of reaction time and 90% in the first 2 h. Therefore, the formation of a thick interface between core and shell is not expected. The reaction was continued for another 8 h to ensure maximal monomer conversion and decomposition of the initiator. Colloidally stable microgel dispersions were obtained and were purified by dialysis (Millipore Labscale TFF System). The synthesized core−shell microgels will be referred to in the text as PVCL-core/ PNIPMAAm-shell and PNIPMAAm-core/PVCL-shell. The theoretical molar ratio is 1:1 core:shell for both microgel systems. We have measured the composition of each component in the microgel using 13C NMR spectroscopy. The 13C nuclear magnetic resonance lines determined for the PVCL microgel are: 22.4 ppm (a in Figure 1), 29 ppm (b), 36.7 pmm (c), 42.4 ppm (d), 47 ppm (e), and 178.3 ppm (f). For the PNIPMAAm microgel the 13C NMR spectrum is characterized by: 16.7 ppm (x in Figure 1), 20 ppm (y), 42.1 ppm (z), 45 ppm (t), and 177.9 ppm (v). For the composition analysis, we have used the resonance lines that do not overlap,

particles with different cross-link density in core and corona, by including a concentration dependent Flory interaction parameter.18 In previous publications we have investigated different microgel morphologies, from homopolymer microgel32 to statistical copolymers33 and amphoteric microgels24 using mainly dynamic light scattering, nuclear magnetic resonance and adapted Flory transition theory to analyze the structure, heterogeneous morphology and proprieties of the microgel particles. Nevertheless, it was demonstrated that the versatility of the microgels’ stimuli responsiveness can be enhanced when core−shell microgels with different properties of core and shell are prepared.34−36 PNIPAAm core−shell microgels were synthesized where either core or shell consisted of a copolymer of PNIPAAm with acrylic acid (AAc). Incorporation of AAc shifts the low critical solution temperature (LCST) to higher temperatures and furthermore, introduces pH sensitivity. These core−shell microgels are multiresponsive. PNIPAAm and PNIPMAAm were also used to create doubly temperaturesensitive core−shell microgels,37,38 and by using a mechanical model to interpret the DSC experimental data, the shift in temperature transitions was investigated.39 In these publications double temperature transitions of the microgels measured with DSC were presented. The aims of this work are to develop a novel core−shell microgel system and to analyze the correlated changes in the morphology during the volume transition temperature by dynamic light scattering (DLS) and Flory−Rehner transition theory. The experimental results are fitted by an extended Flory volume transition theory for core−shell microgels, which is able to analyze the individual swelling behavior of the core and shell regions, and the total effect on the microgel particle. For this purpose we have designed core−shell microgels, which are a new combination of thermoresponsive polymer components, with different lower critical solution temperatures (LCST), 32 °C for PVCL and 45 °C for PNIPMAAm, and synthesized reverse microgel systems, PVCL-core/PNIPMAAm-shell and PNIPMAAm-core/PVCL-shell.

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EXPERIMENTAL SECTION Microgel Synthesis. N-Vinylcaprolactam (VCL) and Nisopropylmethacrylamide (NIPMAAm) were purified by distillation under high vacuum (between 2 × 10−2 and 9 × 10−2 mbar) at 80 °C. Cationic surfactant N-cetyl-N,N,Ntrimethylammonium bromide (CTAB), initiator 2,2′-azobis(2methylpropionamidine) dihydrochloride (AMPA), cross-linker N,N′-methylenebis(acrylamide) (BIS) (Aldrich), were used as received. The microgel synthesis method used for the core− shell microgels is documented in the literature (see refs 37 and 38) for thermosensitive microgel components, and the influence of the amount of monomer and cross-linker added in the synthesis was thoroughly investigated by DSL, SLS, optical transmission, and small angle neutron scattering. The core−shell cross-linked microgels were prepared using a two steps synthesis method. First, the core, following the recipe

Figure 1. 13C NMR spectra for homopolymer and core−shell microgels used for determining the molar ratio of the components in core−shell systems. B


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THEORY Flory−Rehner Theory for Homopolymer Microgels. In previous publications, we have discussed the temperature swelling behavior of homopolymer and copolymer microgels, treated as a polymer network with heterogeneous cross-link morphology.32,33 In the case of core−shell microgel systems we are considering for the components a homogeneous cross-link morphology, and we are using the previously calculated swelling parameters characteristic for the polymeric microgels of pure PVCL or PNIPMAAm systems. Hence, we shall briefly discuss the Flory−Rehner theory for homopolymer microgels with homogeneous morphology, which was detailed in other publications.26,31,32 The Flory−Rehner gel swelling theory26 is based on the assumption that the free energy change on swelling consists of two contributions, which are assumed to be separable and additive. There is some controversy in literature concerning the separability of the mixing and elastic contribution to the osmotic pressure assumed in writing eq 4. Some authors find that a mixing-elastic cross term is necessary to fit the experimental data. 42,43 However, in ref 44, computer simulations show that the violation of separability does not play a significant role in the description of salt-free hydrogels. The equilibrium is achieved when the chemical potential of the solvent inside and outside the microgel become equal. This is equivalent to considering the net osmotic pressure (Π) equal to zero, i.e., Π = 0, where

respectively b and c for PVCL and x for PNIPMAAm. The experimental molar ratios of the components, determined by comparing the integral lines in the 13C spectra (Figure 1) are 0.9:1 for the PVCL-core/PNIPMAAm-shell microgel and 1:0.8 for the PNIPMAAm-core/PVCL-shell microgel. Dynamic and Static Light Scattering. The volume phase transition of the microgels was monitored using an ALV/LSE5004 light scattering multiple τ digital correlator and electronics with the scattering angle set at 90°, by following the decrease of the hydrodynamic radius of microgels with temperature. The temperature interval was 10−58 °C, and the temperature was controlled to a precision of ±0.1 °C. At each step the temperature was maintained constant for 5 min for equilibration of the sample and to avoid kinetic effects. We investigated diluted microgel samples, in order to avoid microgel clustering and multiple scattering effects. Static light scattering (SLS) measurements at different angles were performed keeping the temperature constant at 20 °C, to show that the size of the particle does not depend significantly on the measurement angle. Dynamic light scattering theory states that the time autocorrelation function is related to the normalized firstorder electric field time correlation function. This function provides a direct means to determine the diffusion coefficient D in dilute monodisperse solutions,41 ⟨I(q , 0)I(q , t )⟩ = ⟨I(q , 0)⟩2 + [⟨[I(q , 0)]2 ⟩ − ⟨I(q , 0)⟩2 ] exp( − 2q2Dt )

(1)

Π = Π mix + Πelastic

2

⟨I(q , 0)I(q , t )⟩ = [A exp( −q Dt )] + B

Π mix = −

kBT 6πηSD

NAkBT [ϕ + ln(1 − ϕ) + χϕ2] νS

(5)

and

(2)

Πelastic

The software of the dynamic light scattering device derives the mean diffusion coefficient from the intensity autocorrelation function using cumulant analysis and converts it into mean particle size via the Stokes−Einstein equation for spherical particles, RH =

(4)

The mixing and elastic contribution to the total osmotic pressure is given by

where q is the magnitude of the wavevector, I(q,t) is the instantaneous scattering intensity, and D is the translational diffusion coefficient. For simplification, the autocorrelation function is fit to a simple expression with three fitting parameters in practicethe diffusion coefficient D, the amplitude A, and the baseline B: 2

Article

1/3⎤ ⎡ NkBT ⎢⎛ ϕ ⎞ ⎛ ϕ ⎞ ⎥ ⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ = V0 ⎢⎣⎝ 2ϕ0 ⎠ ⎝ ϕ0 ⎠ ⎥⎦

(6)

In the above equations, kB is the Boltzmann constant, NA is the Avogadro number, and S = 1.80 × 10−5 m3 is the molar volume of H2O, which is our solvent. The Flory parameter, χ, accounts for the solubility of the polymer in the solvent, ϕ is the polymer volume fraction in the particle and N is the number of subchains in a microgel particle. The hydrodynamic radius in the deswollen state is denoted by RH0 and V0 = 4πRH03/3. In order to account for the steep or discrete volume transition, the polymer−solvent interaction parameter χ is assumed to be concentration dependent and has the approximate form30

(3)

where kB is the Boltzmann constant, RH is the hydrodynamic radius, and ηS is the solvent viscosity. Data Processing. Mathcad14, developed by the Parametric Technology Corporation, was used to fit the extended core− shell Flory−Rehner state equation to the experimental data obtained by DLS measurements. Genfit is a generalized leastsquares fitting procedure built into Mathcad to find the optimal fit parameters for an arbitrary (nonlinear) model function. The genfit function was used with the gradient operator supplement, and has the following form: genfit (X, Y, guess, F), where X and Y are vectors containing the x-values and the y-values respectively, of the data; guess is a vector of initial guess values for the free parameters, and F is a vector function that contains the model function that should fit the data and the partial derivative of this function with respect to the unknown parameters.

χ ≈ χ0 + ϕχ1

(7)

with χ0 =

⎛ 1 ΔH − T ΔS Θ⎞ = − A ⎜1 − ⎟ ⎝ kBT 2 T⎠

(8)

where ΔS and ΔH are the corresponding entropic and enthalpic changes. The quantity A is given by A=(2ΔS + kB)/2kB, Θ is the temperature of the polymer−solvent system described by Θ = 2ΔH/(2ΔS + kB), and for T = Θ and χ = 0.5 the second virial coefficient of the mixture becomes zero. C


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Rcore(T ) = ρi RH(T )

Furthermore, for a microgel with a homogeneous morphology that swells isotropically, we can write45

⎛ R H ⎞3 ϕ =⎜ ⎟ ϕ0 ⎝ RH 0 ⎠

where i∈[1,n] and n is the number of intervals dividing the temperature range. We can write now the Flory equation of state for core−shell microgel particles using the ratio between the radius of the core and shell, i.e.

(9)

where we choose RH (RH0) and ϕ(ϕ0) as the particle size and volume fraction in the swollen (deswollen) state. The temperature dependence of the microgel size is accounted for through the temperature dependence of χ. By introducing eqs 7 and 9 into eq 4, we obtain an explicit equation of state relating the temperature with the hydrodynamic radius RH, i.e.31 TΠ= 0

Π total = ρi 3 Πcore + (1 − ρi 3 )Πshell

⎛ RH 0 ⎞6 ⎡ νSN ⎡ 1 ⎛ RH 0 ⎞3 ⎛ RH 0 ⎞⎤ ⎢ ⎜ = A Θϕ0 ⎜ ⎟⎥ ⎟ /⎢ ⎟ −⎜ ⎝ RH ⎠⎥⎦ ⎝ RH ⎠ ⎢⎣ NAV0 ⎢⎣ 2 ⎝ RH ⎠

⎛ ⎛ R ⎞3 ⎞ ⎛ ⎛ R ⎞3 1⎞ − ϕ0⎜ H 0 ⎟ − ln⎜⎜1 − ϕ0⎜ H 0 ⎟ ⎟⎟ + ⎜A − ⎟ϕ0 2 ⎝ R 2⎠ ⎠ ⎝ ⎝ RH ⎠ H ⎠ ⎝

(10)

The above equation of state is valid for a uniform distribution of cross-link density throughout the microgel particle. Flory Theory for Core−Shell Microgel Systems. The microgel systems under investigation having a bimodal morphology present a complex swelling−deswelling behavior, which comes from constraining interactions between core and shell due to different volume transition temperatures of the two components. In order to describe the behavior of the bimodal morphology microgel system in the Flory−Rehner formalism, we considered that the contributions of the core and shell are volume weighted: Π total =

V core core V shell Π + total Πshell total V V

(16)

F = kT

The elastic osmotic pressure of both the core and shell has to account for this elastic force, that influences the swelling/ deswelling behavior of the microgel, and because the total osmotic pressure is volume weighted, the effect of the force will still be present in the equation of state. The total osmotic pressures in core or shell have similar expressions, i.e. / shell / shell Πcore / shell = Π core + Πcore + mix elastic

(11)

where core Πcore = Π core mix + Π elastic

kT S core

(17)

where Score is the surface of the core in contact with the shell. We shall note that at the interface the same force is acting on the core and shell but in opposite directions. Taking into account that the ratio of the core is considered proportional to the radius of the particle on certain temperature intervals, the volume ratios can be written

(12)

and shell shell Πshell = Π mix + Πelastic

(15)

and Πtotal = 0. In order to account for the shift in transition temperature of the components of the core−shell microgel compared to the homopolymer microgels of the same chemical components, we assume that the core and shell are connected by an interpenetrating network layer. The temperature shift may be understood as being caused by an elastic force developed in the shell and acting on the core that for the PVCL-core/ PNIPMAAm-shell system decreases the shrinking force in the core, while for the PNIPMAAm-core/PVCL-shell system increases the shrinking force in the core. Using DSC measurements it was shown39 that the total interaction elastic force acting at the interface between core and shell is temperature dependent, where k is an interfacial parameter, which proved to be temperature independent,39

2

⎞⎤ 9 ⎛ ⎛ R H 0 ⎞6 3 RH 0 ⎟⎥ ⎟ − χ1 ϕ0 ⎜ ⎜ ⎝ R H ⎠⎦ ⎝ RH ⎠

(14)

(13)

At thermodynamic equilibrium of the system, we have Πtotal = 0. The radius of the core is expected not to have the same temperature dependence as the total particle radius, since the swelling/deswelling of the core and shell have different behaviors. In general we can write: Rcore(T) = ρ(T)RH(T), where Rcore(T) is the radius of the core, RH(T) is the total hydrodynamic radius of the particle and ρ(T) is the temperature dependent radial scale factor. An exact definition of the radius of the core and the hydrodynamic radius is not possible because of the fuzziness of the interface between core and shell and at the exterior of the particle, especially considering the dangling chains. Nevertheless, in order to simplify the Flory transition state equation, we introduce a coarse-grained assumption that the radius of the core has a constant proportionality to the radius of the microgel particle on different temperature intervals along the volume temperature transition curve, i.e.,

⎛ ρ ⎞3 ⎛ R ⎞3 ϕcore = ⎜⎜ 0 ⎟⎟ ⎜ H 0 ⎟ ϕ0core ⎝ ρi ⎠ ⎝ RH ⎠

(18)

and, ϕshell ϕ0shell

⎛ 1 − ρ 3 ⎞⎛ R ⎞ 3 0 ⎟ H0 = ⎜⎜ ⎟ 3 ⎟⎜ R 1 − ρ ⎝ i ⎠⎝ H ⎠

(19)

where ρ0 is the ratio between the radius of the core and the hydrodynamic radius of the microgel particle in the deswollen state, in the last temperature interval, while ρi corresponds to each chosen temperature interval. Considering the above assumptions the equation of state for a core−shell microgel system can be written D


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T = [Acore Θcore(φcore)2 ρi 3 + Ashell Θ shell(φshell)2 (1 − ρi 3 )]/ ⎡ ν ⎡ core ⎢ − [M coreρ 3 + M shell(1 − ρ 3 )] + S ⎢ N E coreρ 3 i i i NA ⎢⎣ V 0core ⎢⎣ +

⎤ νSk ⎤ N shell shell 3 ⎥ ⎥ E − ρ + (1 ) i ⎥ NAkBS core ⎥⎦ V0shell ⎦

(20)

where M core / shell = ϕcore / shell + ln(1 − ϕcore / shell ) + (ϕcore / shell )2 ⎛1 ⎞ ⎜ − Acore / shell ⎟ + χ1core / shell (ϕcore / shell )3 ⎝2 ⎠ (21)

and E

core / shell

=

ϕcore / shell 2ϕ0core / shell

⎛ ϕcore / shell ⎞1/3 − ⎜⎜ core / shell ⎟⎟ ⎝ ϕ0 ⎠

(22)

are mixing and elastic terms that have the same form for core and shell, and were used to simplify the expression of the equation of state. The connection between the temperature and the measured hydrodynamic radius is made through eqs 18 and 19. Finally, we can note that the equation of state for core shell microgel given by eq 20, in the limit of ρcore → 1, Nshell → 0, and k → 0, when the microgel consists only of the core region, agrees with the equation of state derived for the homopolymer microgel eq 10.

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RESULTS AND DISCUSSION Volume Phase Transition Temperature by DLS for Homopolymer and Core−Shell Microgels. Dynamic and static light scattering measurements were performed for homopolymer and core−shell microgel systems to determine the monodispersity, the angular dependence of particle size and the change of the hydrodynamic radius with increasing temperature. In Supporting Information, Figures S1a and b show that the size distribution of the core−shell microgel particle is monotonic and narrow, excluding the formation of secondary seeds in the second synthesis step. Parts a and b of Figure S2, Supporting Information show the static light scattering angular dependent measurement, demonstrating no significant change in the size of the particles with changing angle. In Figure 2 the volume temperature transitions for homopolymer PVCL (Figure 2a) and PNIPMAAm (Figure 2b) microgels in H2O are presented, as well as the first derivatives for the transition curves. The derivative was made on the interpolated data, and a smoothing function was subsequently applied in order to minimize the measurement errors. The first derivative provides the possibility of identifying more accurately the volume temperature transition point. From DLS measurements in water, PVCL microgel has a volume transition temperature of 29 °C, while PNIPMAAm microgel has a volume transition temperature of 46 °C. Figures 3a and 4a show the temperature transition curves determined with DLS measurements in water for PVCL-core/ PNIPMAAm-shell and PNIPMAAm-core/PVCL-shell microgels, respectively. These figures show the measured data and also the interpolation used later for selecting the temperature intervals. From the first derivatives of the transition curves

Figure 2. Dynamic light scattering measurement of hydrodynamic radius for (a) PVCL and (b) PNIPMAAm homopolymer microgels in H2O. The dashed lines represent the interpolations used to obtain the derivatives of the transition curves. The inserts show the first derivatives of the temperature transition curves.

(Figure 3b and 4b) we can detect a two steps volume transition, with two temperature transition points, one corresponding to the PVCL component, and the other one to the PNIPMAAm component. We cannot detect significant differences between the PVCL-core/PNIPMAAm-shell and PNIPMAAm-core/ PVCL-shell microgel systems. Furthermore, the temperature transition of the PNIPMAAm component is much influenced by the presence of the PVCL component, decreasing its transition point with about 4 °C compared to the homopolymer microgel. The volume transition temperatures are given in Table 2. Temperature Dependence of the Radial Scale Factor. Our aim is to investigate correlated morphological changes into the process of volume phase transition of the structural components of the core−shell microgel particle by applying the Flory−Rehner swelling theory modified for core−shell morphology as presented above, in the theory section. Using the state equation (eq 20) to fit the experimental data obtained by dynamic light scattering of the hydrodynamic radius evolution with temperature we can determine information related to the individual transition of the structural components, through the ρ parameter, which is the radial E


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Figure 3. (a) Dynamic light scattering measurement of PVCL-core/ PNIPMAAm-shell microgel and the temperature intervals for the evaluation of the radius scaling factors ρi. The dashed line is the interpolation used to fit the Flory state equation (eq 20). (b) First derivative of the volume temperature transition curve shown in part a, revealing different transition temperatures of the microgel components.

Figure 4. (a) Dynamic light scattering measurement of PNIPMAAmcore/PVCL-shell microgel and the temperature intervals for the evaluation of the radius scaling factors ρi. The dashed line is the interpolation used to fit the Flory state equation (eq 20). (b) First derivative of the volume temperature transition curve revealing different transition temperatures of the microgel components.

Table 2. Transition Temperatures of Homopolymer and Core-Shell Microgels Determined from DLS Measurements

scale factor, the ratio between the radius of the core and the hydrodynamic radius (eq 14). In order to have all information needed for the core−shell microgels, we first have to find the characteristic swelling parameters of the homopolymer microgels. For this purpose we fit the dynamic light scattering data with the Flory−Rehner state equation for homopolymer microgel, described by eq 10, and also presented in ref 32. In this way we can determine the parameters A, Θ, χ1, and ϕ0, which are characteristic for each homopolymeric microgel, and assume that they do not change in the core−shell morphology. In the framework of this approach we also determine the number of subchains, N, for the core component. For the shell component we estimate the value of N considering that the same amount of subchains will be formed for the same polymeric microgel on the same volume, in this case a hollow sphere. The values of these parameters are shown in Table 3 for PVCL and PNIPMAAm microgels. The number of subchains for the PVCL-core/ PNIPMAAm-shell microgel shell was thus calculated Nshell(PNIPMAAm) = 3.67 × 105 and for the PNIPMAAmcore/PVCL-shell microgel shell, Nshell(PVCL) = 1.473 × 107. The radial scale factor, ρ, has an unknown dependence on temperature that can be obtained from the DLS data fitted with the extended Flory−Rehner theory for core−shell microgels. One possible approach to solve this complex problem is to use

microgel

Tc1 [°C]

PVCL homopolymer PNIPMAAm homopolymer PVCL-core/PNIPMAAm shell PNIPMAAm-core/PVCL-shell

29

Tc2 [°C] 46 42 42

29 27

Table 3. Microgel Network Swelling Parameters for Homopolymer Microgels microgel

A

Θ [K]

χ1

ϕ0

N

PVCL homopolymer PNIPMAAm homopolymer

−7.84 −1.689

309.58 356.43

0.56 0.93

0.85 0.7

7.4 × 105 2.07 × 106

a coarse-grained approximation by dividing the total temperature interval for RH(T) in n intervals. For each temperature interval the radial scale factor is considered constant and is denoted by ρi for i = 1 − n. The next step is to find the interfacial elastic force parameter k and the radial scale factor in the deswollen state, ρ0, where ρ0 ≡ ρn corresponds to the last temperature interval, ΔTn. For this purpose we estimate from dynamic light scattering measurements of the core and core−shell microgels an average ρ̅ for the F


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entire temperature range, without taking into consideration the correlations of the core and shell swelling behavior. The values of ρ̅ = 0.8 and ρ̅ = 0.7 were used for PVCL-core/PNIPMAAmshell and PNIPMAAm-core/PVCL-shell microgels, respectively. By fitting eq 20 using the core and shell parameters (Table 3) determined from homopolymer fits and considering a constant ρ̅ for the whole temperature range, instead of ρi in eq 20, we determine ρ0 and k. The quality of the fits (Figure S3a and b in Supporting Information) in the double transition area is influenced by the disregard of the different swelling behavior of the components in this approximation. Nevertheless, the fits are good in the deswollen state, which means we can determine the radial scale factor in the deswollen state, ρ0, which is our goal. The fitting results for PVCL-core/ PNIPMAAm-shell were ρ0 = 0.75 and k = 5.33x10−11N/K, and for PNIPMAAm-core/PVCL-shell ρ0 = 0.75 and k = 3.28x10−9N/K. Using the coarse grained approach in order to find the radial scale parameter dependence on temperature, we have first divided the temperature range into five nonequidistant intervals ΔTi where i = 1−5. Figures 3a and 4a show the temperature intervals on the interpolated data points defined by arrows where we consider the radius of the core proportional to the hydrodynamic radius for PVCL-core/PNIPMAAm-shell and PNIPMAAm-core/PVCL-shell microgels, respectively. We have selected these intervals by considering regions where the profile of the transition curve does not change significantly, so that the approximation does not introduce significant errors. Furthermore, in order to demonstrate that the final result does not depend essentially on the choice of n = 5 intervals, we have also divided the temperature range into n = 10 intervals. We then use eq 20, and ρ0 and k as previously determined, to find ρi corresponding to each temperature interval. The quality of the fits (Figure 5, parts a and b) on n = 5 separate intervals improves considerably from the one considering an average ρ̅, allowing the radius of the core to vary with respect to the hydrodynamic radius, therefore taking into account the differences in the swelling behavior of the components. Nevertheless, there are still problems in the transition area (for ρ4). This can be explained by the limitations imposed by the Flory swelling theory itself, and by the modifications we have introduced in order to account for core−shell morphology. Scenarios for the Correlated Morphological Changes of Core−Shell Microgels. Figures 6 and 7 show the morphological changes of the core−shell microgel systems, i.e., the individual behavior of the core−shell components reflected in the change of the radial scale factor with temperature for n = 5 (Figure 6a and 7a) and n = 10 (Figure 6b and 7b) temperature intervals considered in the coarse grained approach. For the PVCL-core/PNIPMAAm-shell microgel the core component PVCL, shrinks in the first temperature intervals because the volume transition temperature for PVCL begins first. Results show this by a decrease in the ratio of the radius of the core and the hydrodynamic radius (Figure 6, parts a and b). Afterward, the shell component, PNIPMAAm, undergoes a collapse, and the radial scale factor increases. In the last intervals the shell component, already collapsed makes the radial scale factor continue to increase slowly. Figure 6c shows the pictorial diagram of the morphological changes with temperature in the PVCL-core/ PNIPMAAm-shell microgel.

Figure 5. Hydrodynamic radius by dynamic light scattering fitted with Flory−Rehner volume transition theory (continuous lines) for core− shell microgels divided into temperature intervals ΔTi (i = 1−5) (see text): (a) PVCL-core/PNIPMAAm-shell and (b) PNIPMAAm-core/ PVCL-shell microgels.

In the case of PNIPMAAm-core/PVCL-shell microgel the first changes in the morphology take place in the shell. Hence, the results show that only the shell shrinks in the first temperature intervals, which can be seen from an increase in the ratio of the radius of the core to the hydrodynamic radius in Figure 7, parts a and b. Afterward, the PNIPMAAm core collapses decreasing its radius, and so the ratio between the radius of the core and the hydrodynamic radius decreases. In the last temperature intervals the dramatic decrease in the core stops since the PNIPMAAm component is also collapsed, so the radial scale factor increases again. Figure 7c shows the pictorial diagram of the morphological changes with temperature in the PNIPMAAm-core/PVCL-shell microgel. It is clear from comparing the profile of the radial scale parameter dependence on temperature for n = 5 and n = 10 intervals, for both microgel systems, that the trend is very similar. This proves that the choice of the intervals does not affect the radial scale factor dependence on temperature. Moreover, the accuracy of the method increases with more intervals considered. Under the assumption that some of the parameters characteristic for homopolymer microgels (Table 3) have different values in the core−shell morphology, we made several attempts to improve the quality of the fits: (i) the volume fraction in the deswollen state (ϕ0) for both components of core−shell was considered a free parameter, but because these G


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Figure 6. (a) Variation of the radius scaling parameter Rcore/RH with temperature for n = 5 intervals and (b) for n = 10 intervals obtained by dividing in two the n = 5 intervals for PVCL-core/PNIPMAAm-shell microgel. (c) Pictorial representation of the evolution of the core and hydrodynamic radius. The arrows in the pictorial diagram of the morphological changes symbolize the collapse processes of the components due to deswelling in different temperature intervals.

°C (Figure 5a, 5b, and Figure S3b in Supporting Information). Such results were reported previously in literature for weakly ionized gels, (see ref 46 and references therein).

parameters appear in eq 20 at different powers, it is impossible for the function to fit the experimental data; (ii) we have manually changed the values of ϕ0 for both components, but the fits did not improve, and the values obtained did not have physical meaning; (iii) we have considered the interaction parameters χ1 for core and shell as free fitting parameters, the fits improved, but the physical meaning of the evolution of the radial scale factor with temperature (see Figures 6 and 7) disappeared. Therefor, we have concluded that to our knowledge the method described above gives the best fits possible, keeping the physical meaning of the resulting parameters, and providing a believable scenario for the evolution of the components of the microgel particle with temperature. It is obvious from eq 20 that RH(T) is an equation of the ninth degree, a multivalued function, with nine solutions. The value of RH at equilibrium corresponds to the lowest minimum of free energy. Nevertheless, there are RH for which there are two or more minima with the same value of free energy, and a discrete volume-transition takes place, which explains the behavior of the fitting function in the transition area of 40−50

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CONCLUSION We report the synthesis of new core−shell temperature responsive microgel systems, composed of poly(N-vinylcaprolactam) and poly(N-isopropylmethacrylamide) in 0.9:1 and 1:0.8, respectively, experimental molar ratio, constructing two reversed morphological systems, PVCL-core/PNIPMAAmshell and PNIPMAAm-shell/PVCL-core. Investigating these morphologically inverse systems we gain knowledge regarding the confinement effects on the swelling/deswelling of individual components in the microgel particle. The Flory−Rehner volume temperature transition theory was extended for the core−shell morphology microgels, taking into account the dependence on temperature of the radial scale factor, the ratio between the radius of the core and the hydrodynamic radius. This was done using the coarse-grained approximation, dividing the temperature range of the temperature transition curve into intervals. The newly developed H


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Figure 7. (a) Variation of the radius scaling parameter Rcore/RH with temperature for n = 5 intervals and (b) for n = 10 intervals in the case of PNIPMAAm-core/PVCL-shell microgel. (c) Pictorial representation of the evolution of the core and hydrodynamic radius. The arrows in the pictorial diagram of the morphological changes symbolize the collapse processes of the components due to deswelling in different temperature intervals.

core−shell Flory state equation was used to fit experimental dynamic light scattering data showing the hydrodynamic radius dependence on temperature. Using this simple method we gain access to quantitative information about the swelling behavior of the confined core compared to the swelling behavior of the entire particle. Furthermore, the theory developed allows an estimation of the force of confinement that influences the transition of the core due to the transition of the shell. The swelling/deswelling behavior of the individual components of core−shell microgels with temperature can be investigated directly by performing small-angle neutron scattering (SANS) measurements at different temperatures. Such investigations were performed on core−shell microgels38 and on homopolymer microgels with heterogeneous core− corona cross-linking.18 In the first reference the core−shell particles are investigated at three different temperatures, but a profile of the swelling behavior of the components is not reported. The second reference reports the differences between the swelling behaviors of the differently cross-linked morpho-

logical components, and even if the microgel is a homopoylmer the authors find significant profile swelling differences between components. The major drawback of SANS is the necessity to use predeuterated polymers that is not the case for the DLS, NMR, or DSC techniques. We introduced in this work an indirect method of analyzing the swelling profile of the differently thermosensitive components of core−shell microgel particles, by means of dynamic light scattering data fitted with the generalized core− shell Flory−Rehner transition theory. The results of the radial scale parameter dependence on temperature show a predictable temperature behavior, which proves a posteriori the model that we used and the theoretical treatment. The novelty and the value of developing the core−shell Flory swelling theory is that it gives semiquantitative information about the individual temperature behavior of the components. We can estimate the temperature interval when the components undergo temperature transition that is influenced by the restrains and interactions imposed by the core−shell morphology. The I


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theoretical treatment also allows determination of the size of the core relative to the total hydrodynamic radius at different temperatures. We can determine also the interaction force between the two morphological components. Nevertheless, from Figure 5 it is evident that the modified Flory−Rehner theory is not able to describe accurately the dependence of hydrodynamic ratio on temperature in the temperature range of 40−50 °C, which is dominated by the volume transition of PNIPMAAm. The theoretical method has limitations because it is based on several assumptions, such as from the Flory− Rehner theory itself, and the coarse-grained approach used for the dependence of the radial scale factor on temperature. Nevertheless, the availability of the method and the relevant semiquantitative morphological information that can be obtained recommend it for stimuli responsive core−shell microgel systems.

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ASSOCIATED CONTENT

S Supporting Information *

Size distribution of microgel particles, angular dependence of the size of microgel particles, and DLS data fitted with the Flory state equation considering an average ρ̅. This information is avialable free of charge via the Internet at http://pubs.acs.org/ .

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AUTHOR INFORMATION

Corresponding Author

*Fax: +49-241-233-01. E-mail: (A.P.) [email protected]. de; (D.E.D.) [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS A.B. and A.P. thank the Volkswagen Foundation for financial support of their research. REFERENCES

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Correlated Morphological Changes in the Volume Temperature

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