Methanol Mixtures for PNIPAM and PS-b

Article pubs.acs.org/Macromolecules

Cononsolvency of Water/Methanol Mixtures for PNIPAM and PS‑b‑PNIPAM: Pathway of Aggregate Formation Investigated Using Time-Resolved SANS Konstantinos Kyriakos,† Martine Philipp,† Joseph Adelsberger,† Sebastian Jaksch,† Anatoly V. Berezkin,† Dersy M. Lugo,‡ Walter Richtering,‡ Isabelle Grillo,§ Anna Miasnikova,∥ André Laschewsky,∥,⊥ Peter Müller-Buschbaum,† and Christine M. Papadakis*,† †

Physik-Department, Fachgebiet Physik weicher Materie/Lehrstuhl für Funktionelle Materialien, Technische Universität München, James-Franck-Str. 1, 85748 Garching, Germany ‡ Lehrstuhl für Physikalische Chemie II, Institut für Physikalische Chemie, RWTH Aachen University, Landoltweg 2, D-52056 Aachen, Germany § Large Scale Structures Group, Institut Laue-Langevin, 6, rue Jules Horowitz, 38042 Grenoble, France ∥ Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Str. 24-25, 14476 Potsdam-Golm, Germany ⊥ Fraunhofer Institut für Angewandte Polymerforschung, Geiselbergstr. 69, 14476 Potsdam-Golm, Germany ABSTRACT: We investigate the cononsolvency effect of poly(Nisopropylacrylamide) (PNIPAM) in mixtures of water and methanol. Two systems are studied: micellar solutions of polystyrene-b-poly(Nisopropylacrylamide) (PS-b-PNIPAM) diblock copolymers and, as a reference, solutions of PNIPAM homopolymers, both at a concentration of 20 mg/mL in D2O. Using a stopped-flow instrument, fully deuterated methanol was rapidly added to these solutions at volume fractions between 10 and 20%. Time-resolved turbidimetry revealed aggregate formation within 10−100 s. The structural changes on mesoscopic length scales were followed by time-resolved small-angle neutron scattering (TR-SANS) with a time resolution of 0.1 s. In both systems, the pathway of the aggregation depends on the content of deuterated methanol; however, it is fundamentally different for homopolymer and diblock copolymer solutions: In the former, very large aggregates (>150 nm) are formed within the dead time of the setup, and a concentration gradient appears at their surface in the late stages. In contrast, the growth of the aggregates in the latter system features different regimes, and the final aggregate size is ∼50 nm, thus much smaller than for the homopolymer. For the diblock copolymer, the time dependence of the aggregate radius can be described by two models: In the initial stage, the diffusion-limited coalescence model describes the data well; however, the resulting coalescence time is unreasonably high. In the late stage, a logarithmic coalescence model based on an energy barrier which is proportional to the aggregate radius is successfully applied.

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INTRODUCTION

cloud point is constant in a wide range of molar masses and concentrations (up to 20 wt %).5 Only for rather short chains (degree of polymerization N < 106) and low polymer concentrations (below 5 wt %), a concentration dependence of the cloud point curve has been reported.6 The stability of the thermoresponsive behavior of PNIPAM over molar mass and concentration makes it a very good candidate for many applications, ranging from switchable microfilters7,8 to drug delivery systems and bioscaffolds.9−11 Another advantage of PNIPAM is the possibility for cross-linking; so far, macroscopic gels,13 microgels,14 core−shell particles with a hydrophobic

Responsive or “smart” polymers have been in the scientific focus due to their strong response to various stimuli, e.g., temperature, pH, or light.1,2 Among them, poly(N-isopropylacrylamide) (PNIPAM) has a prominent place since the seminal work of Heskins and Guillet,3 who reported its thermoresponsive, lower critical solution temperature (LCST) behavior. When heated above the cloud point (Tcp), PNIPAM in aqueous solution undergoes a phase transition: Below the cloud point, the PNIPAM chains are hydrated by water molecules, while above the cloud point, the water molecules are partially released; the chains become more hydrophobic and collapse, thereby forming intra- and interchain H-bonds. Since this process is reversible, it is referred to as the coil-to-globule-tocoil transition.4 The LCST of PNIPAM is ∼32 °C, and the © XXXX American Chemical Society

Received: July 11, 2014 Revised: September 11, 2014

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dx.doi.org/10.1021/ma501434e | Macromolecules XXXX, XXX, XXX−XXX

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core and a cross-linked responsive shell,15 and nanogels16 have been studied. Of great importance for the understanding of the behavior of the different PNIPAM systems under various conditions is the mechanism of hydration and dehydration below and above the cloud point, respectively. Although the hydration of PNIPAM has been investigated on the level of the hydrogen bonding of the amide group,17 the overall picture about the hydration mechanism is still not entirely clear. It has been postulated that water forms sequences along the chain which are released in a collective way at the cloud point.18 This model can explain the sharp LCST behavior of PNIPAM. The organization of the water on and around the hydrated chain plays a very important role for the collapse transition.19,20 Above the cloud point, PNIPAM forms aggregates which typically have a size in the range between 50 nm and a few 100 nm; thus, they have been termed mesoglobules.21,22 Moreover, they are stable with time, even over several weeks.22,23 The origin of their colloidal stability has been under discussion: It was, for instance, suggested that hydrophilic groups present at the surface of the mesoglobule are at the origin of their longterm stability.22 An alternative model proposes that the initial spinodal decomposition is stopped by the accumulation of charges at the surface of the mesoglobule and that the mesoglobules subsequently grow by coalescence.23 In other works, the stability of the mesoglobules has been attributed to the viscoelastic effect: The characteristic time between the collisions of two mesoglobules is long compared to the reptation time of the chains at their surface.22,24 An entanglement force was put forward to explain why effective entanglement of the polymersand thus growth of the mesoglobulesoccurs only after numerous collisions of the globules.25 Another interesting finding is that the radius and inner structure of the mesoglobules depend on the heating rate: After fast heating, they are smaller (∼60 nm) and more compact than after slow heating where they achieve larger radii (∼100 nm) and feature a water-rich domain in the center surrounded by a dense shell formed by collapsed polymers.22,24,26,27 Recent spectroscopic and time-resolved structural studies on aqueous solutions of PNIPAM homopolymers28,29 and PNIPAM amphiphilic di- and triblock copolymers with short and hydrophobic polystyrene blocks30,31 have shown that the collapse transition is a complex process, which consists of distinctive regimes. This confirms earlier observations on telechelic PNIPAM.32 Thus, despite the widely accepted importance of PNIPAM as a versatile and useful material, the nature of its switching behavior is still under discussion. In many experimental approaches, temperature jump experiments have been applied to address the collapse transition of thermoresponsive systems.33−35 In particular, time-resolved small-angle neutron scattering (TR-SANS) has been successfully used to elucidate the collapse transition of aqueous solutions of various thermoresponsive polymers upon a temperature jump through the cloud point.31,36,37 This way, it was found that the collapse in a concentrated PNIPAM solution in D2O proceeds very rapidly and that the aggregation comprises two processes.38 A wealth of processes was observed in micellar solutions of PS-b-PNIPAM-b-PS triblock copolymers with fully deuterated polystyrene (PS) blocks in D2O:31,36 The collapse of the micellar PNIPAM shell is very rapid, and small, fractal aggregates form. These densify and grow by attachment of micelles from the solution and later by

coagulation with other aggregates. The time constants as well as the structure of the aggregate surface depend on the polymer concentration and on the target temperature. Recently, the behavior of PNIPAM in mixtures of water and a second, water-miscible solvent (e.g., methanol, ethanol, isopropanol, etc.) has attracted strong interest.39−49 Although the second solvent is a good solvent for PNIPAM, the polymer chain collapses in certain compositions of the solvent mixture, followed by the eventual reswelling when the second solvent is the majority.40,41 This behavior of the PNIPAM chains has been termed cononsolvency.42−44 The phenomenon manifests itself through an enhanced tendency for phase separation, resulting in a strong decrease of the LCST. For instance, the cloud point drops from 31.5 to −7 °C when methanol is added at a molar fraction of xmeth = 0.35 to an aqueous solution of PNIPAM.43−45 A recent study has mapped out the phase diagram of PNIPAM in water/ethanol mixtures over the entire composition range.49 Curves from temperature-resolved static SANS measurements were analyzed using a ternary random phase approximation model, and the three Flory−Huggins parameters were found to be inversely proportional to temperature. The chains were found to swell with increasing temperature. However, the kinetics of the transition was not investigated. Cononsolvency has also been observed to have an effect on the polymer dynamics of chemically cross-linked PNIPAM gels.39,46,47 Various models have been proposed in order to explain the phenomenon,40,50−54 each focusing on a different aspect of the ternary mixture water/methanol/polymer. Zhang and Wu address the formation of water/methanol clusters via Hbonds:40 The pentagon structure of free water (postulated by the authors) creates five hydration sites which are occupied by methanol molecules, and together, they behave as a poor solvent for PNIPAM. Since the methanol−water interaction is more favorable than the polymer−solvent interaction with both methanol and water, the PNIPAM chain dehydrates. Pang et al. confirmed the formation of complex structures between solvent molecules, reducing the interaction between NIPAM monomer and solvent of both species.50 They found that the addition of methanol does not alter the tetrahedral structure of the free water molecules, but rather the number of these structures decreases, implicating a very strong interaction between the two species via H-bonding. The model by Tanaka et al. puts forward the importance of the cooperative character of the PNIPAM hydration.51,52 It implies that both solvent species contribute to the hydration of the PNIPAM chain in a cooperative manner by the so-called competitive hydration: both water and methanol molecules hydrate the chain by forming polymer−water and polymer−methanol bonds, respectively. Since both types of bonds tend to occupy the same hydration sites on the PNIPAM chain, an increasing fraction of methanol molecules leads to an abrupt decrease of the solvent binding to the polymer. Consequently, the PNIPAM chains collapse and aggregate. This model successfully explains phenomena like the sharp collapse of PNIPAM at the cloud point and the sensitivity of the cloud point depression to the PNIPAM molar mass. Using molecular dynamics, Walter et al. found that methanol is predominantly found in the outer region of the solvation shell of PNIPAM and that the methyl groups are mostly oriented toward the bulk solvent, which makes the entire complex nonsoluble in the water/methanol mixture.53 Hao et al. propose that concentration fluctuations in the close vicinity of the critical regime play an important role.54 B


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Time-Resolved Turbidimetry. TR-turbidimetry was performed using a Bio-Logic SFM-20/S stopped-flow instrument coupled with a fluorescence spectrometer FP 6500 from Jasco (Langerwehe, Germany, Figure 1a). The light source was a Xe lamp with a shielded

As a result, the attractive interaction, similar to the screened Coulomb interaction, between the chain segments is increased significantly, leading to the collapse of the PNIPAM chain. Several experimental approaches have attempted to verify the validity of the above-mentioned models. Results from dynamic light scattering and FTIR have shown that it is necessary to take the formation of water−methanol complexes into account.55,56 However, neglecting the cooperative hydration makes it difficult to explain phenomena like the sharp LCST behavior and the sensitivity to the molecular weight of the polymers. Thus, the origin(s) of the cononsolvency phenomenon is far from being clear. In the present work, we focus on the effect of the chain architecture on the cononsolvency effect. At this, we use solutions of PNIPAM homopolymer or PS-b-PNIPAM diblock copolymer in D2O and rapidly add fully deuterated methanol, d-MeOD. The latter diblock copolymer has a short PS block, it is thus expected to form spherical micelles having a PS core and a thermoresponsive PNIPAM shell.38,57 Fully deuterated methanol was added in three different volume fractions (90:10 v/v, 85:15 v/v, and 80:20 v/v) to the polymer solutions in D2O, which had an initial polymer concentration of 20 mg/ mL. The aggregation process on the mesoscopic scale was followed using time-resolved turbidimetry (TR-turbidimetry) and TR-SANS, both with subsecond time resolution. On the basis of two theoretical models, we propose a mechanism for the growth process in the PS-b-PNIPAM system. The soft micelles coalesce to form sphere-like mesoglobules. This is different from rigid colloidal particles which aggregate to fractal structures. The later growth is slowed down by an energy barrier. The paper is structured as follows: After the Experimental Section, the phase diagram of the two polymers in D2O/d-MeOD mixtures is presented. The pathway of the transition is addressed by TR-turbidimetry. The detailed structural information found in TR-SANS experiments is discussed next. Finally, the findings are summarized.

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Figure 1. Scheme of the stopped-flow setups used for TR-turbidimetry (a) and TR-SANS (b). In both cases, the polymer solution in D2O (blue) was mixed with d-MeOD (purple) at the desired mixing ratios. For TR-turbidimetry the dead time was 7.6 or 6.7 ms. For TR-SANS, protonated methanol, MeOH (yellow), was used for cleaning after each run (see text). The dead time was ∼13 ms, where the residence times indicated were calculated from the flow rates selected for the syringes and from the volumes of the mixing chamber and the delay line. The system was operated through a PC.

EXPERIMENTAL SECTION

Materials. Two different polymers were investigated. The homopolymer PNIPAM (22 500 g/mol) was purchased from PSS (Mainz, Germany). The diblock copolymer PS14-b-PNIPAM310 was synthesized using reversible addition−fragmentation chain transfer (RAFT) polymerization;30,58 Number-average molar masses of the PS and the PNIPAM blocks are 1700 and 35 000 g/mol, respectively, with an overall polydispersity index of 1.2. The deuterated solvents D2O and d-MeOD (both 99.98%) were purchased from Deutero GmbH (Germany). For all measurements, the same sample preparation steps were followed: 2 weeks prior to experiments, the polymers were dissolved in D2O at 20 mg/mL. The mixtures were stirred at room temperature and subsequently cooled down to ∼5 °C several times until they became optically clear. Afterward, the solutions were kept at ∼5 °C to avoid demixing. Methods. Cloud Point Determination. For the determination of the cloud points, a Varian 50 UV−vis spectrometer from Varian Inc., Palo Alto, CA, with quartz cells was used, coupled with a single cell Peltier thermostat which regulated the temperature. All turbidity measurements were performed at a wavelength of 500 nm. The solutions were prepared in D2O or in D2O/d-MeOD at a concentration of 20 mg/mL. The transmittance of the solution in the one-phase state, i.e., below the cloud point, Tcp, was set to one. The solutions were heated from 18 to 40 °C with a rate of 1.0 K/min and in steps of 0.5 K. Transmittance measurements were acquired at each temperature after 20 min of equilibration. The cloud point was taken as the temperature value that corresponds to a transmittance of 90% of the initial value.

lamp housing driven at 150 W. The incident wavelength was 500 nm with a bandwidth of 5 nm. The transmitted beam was detected by a fluorescence spectrometer with a photomultiplier tube R3788. It was connected to the observation head of the stopped-flow instrument at 180° with respect to the incident beam using an optical fiber. A TC100/T cuvette made from black and transparent quartz (Suprasil 2 grade B) with a wall thickness of 300 μm and a light path of 10 mm with an aperture of 1.0 mm was connected to the stopped-flow instrument which enabled the rapid mixing of the polymer solution (20 mg/mL in D2O) with the desired volume fraction of d-MeOD. The total flow rates (TFR) used for the mixing ratios 85:15 v/v and 80:20 v/v D2O/d-MeOD were 4.00 and 4.50 mL s−1, respectively. Under these conditions, the time needed to transfer the sample from the mixer to TC-100/10T cuvette; i.e., the dead time, tdead, was 7.60 and 6.70 ms, respectively. The data acquisition was set to start 10 ms before the stop of the flow. The temperature in the reservoir and the observation head was maintained at the desired temperature by circulating water which was set to a temperature 3 K above Tcp of the respective mixed solution. A waiting time of 1 h was applied before the measurement. For both mixing ratios, the time resolution was 1 s. For the mixing ratio 80:20 v/v D2O/d-MeOD, additional measurements were carried out with a time resolution of 0.1 s to elucidate the initial stages and to get a time resolution similar to the one in TR-SANS (see below). For all measurements, the times were corrected for tdead and C


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where P(q) denotes the form factor of the aggregates and Iinc is the incoherent background which was set to 0.031 cm−1. This value was determined from fits to the curves in the later stages of the runs and is in good agreement with the calculated value. For the initial and the later stages, two different models were used for P(q). In the initial state, the scattered intensity features a smooth decay which was well described by the Guinier−Porod model.62 It consists of two contributions: a Guinier-like term at low q values describing the size and shape of the aggregate and a Porod-like term at high q-values describing the surface structure of the aggregates:

the pretrigger time. Reproducibility was ensured by applying 5−10 runs. They were averaged to improve the statistics. The turbidity τ is defined as59

⎛I ⎞ τ = l −1 ln⎜ 0 ⎟ ⎝ It ⎠

(1)

where I0 is the intensity of the incident light, It the transmitted intensity, and l the length of the optical path. Time-Resolved Small-Angle Neutron Scattering. TR-SANS experiments were performed at the high-flux small-angle neutron scattering instrument D22 at the Institut Laue-Langevin (ILL) in Grenoble, France. Addition of d-MeOD to the PNIPAM or PS-b-PNIPAM solutions in D2O was achieved using a stopped-flow instrument Biologic SFM-300 (Figure 1b). A three-syringe system was used; the initial polymer solution (20 mg/mL in D2O) was kept in the first syringe, d-MeOD for mixing with the polymer solution in the second one, and MeOH for cleaning the sample cell in the third one. All syringes and the sample cell were kept at a temperature 3 K above the respective cloud point of the final mixture. Mixing of the polymer solution and d-MeOD was accomplished by means of the mixing chamber, and the solution passed the delay line before reaching the sample cell. The sample cell was a quartz glass cell with a nominal thickness (neutron light path) of 1 mm. The mixing ratio of the polymer solution with d-MeOD was controlled by choosing the appropriate flow rates for the two syringes. Before each measurement, an aliquot of 1 mL fresh polymer solution was left to equilibrate thermally for 10 min in the syringe. The sample cell was homogeneously filled by rapidly injecting an overall amount of ∼1 mL of the mixed solution. At the end of the injection, a transistor− transistor logic (TTL) signal started the detector data acquisition, which resulted in a good reproducibility of the measurements. For all measurements, visual inspection after the run revealed that the solution had become turbid in the sample cell. After each measurement, the sample holder was cleaned thoroughly with MeOH and subsequently with d-MeOD until the count rate on the neutron detector dropped to a sufficiently low value (∼150 cts/s). The neutron wavelength was λ = 0.8 nm with a spread Δλ/λ = 10%, the sample−detector distances were chosen at 4.0 and 14.4 m and the collimation lengths at 5.6 and 14.4 m, respectively. Together with an asymmetrically positioned detector, these settings resulted in a q-range of 0.025−2.0 nm−1. q is the momentum transfer: q = 4π sin(θ/2)/λ where θ is the scattering angle. The aperture size was 6 mm × 9 mm. A 3 He detector consisting of 128 modules was used. The measuring times of the SANS images were increased by a factor of 1.1 starting at 0.1 s for the first 60 images (overall time ∼5 min). For the subsequent 30 min, the measuring time was 30 s. Thus, each run lasted ∼35 min. To improve the statistics, each run was repeated twice for the SDD of 4.0 m and thrice for the SDD of 14.4 m. In all cases, the azimuthally averaged intensity curves did not show systematic differences and were averaged. The transmission of each sample was measured at the end of each run. Corrections were made regarding the background scattering from the solvent-filled cell and parasitic scattering. The detector sensitivity was measured using H2O, which was also used for the conversion of the scattered intensity to absolute units. Boron carbide was used for measurement of the dark current. All operations were carried out using the LAMP software provided by ILL.60 The scattering length density (SLD) values of the four components of our system are ρPS = 1.31 × 10−4 nm−2, ρPNIPAM = 0.83 × 10−4 nm−2, ρD2O = 6.36 × 10−4 nm−2, and ρd‑MeOD = 5.81 × 10−4 nm−2. The SLDs of the different D2O/d-MeOD mixtures were calculated based on the respective volume fractions. Modeling of the SANS Curves. The SANS curves were modeled using the NIST SANS package 7.04 in the Igor Pro environment.61 Different functions were fitted to the curves, depending on the system and on the time regime. For the analysis of the curves of the PS-b-PNIPAM solutions, the following model was used

I(q) = P(q) + Iinc

IGuinier(q) =

IPorod(q) =

⎛ − q 2R 2 ⎞ IG0 g ⎜ ⎟ exp ⎜ 3 − s ⎟, qs ⎝ ⎠

IP0 , qa

q ≤ q1

(3)

q ≥ q1

where Rg is the radius of gyration, α is the Porod exponent, 3 − s is the so-called dimensionality parameter, and I0G and I0P are the scaling factors of the Guinier and the Porod contributions, respectively. The continuity between the two parts is ensured by the requirement that both the values of the Guinier and Porod terms and their slopes coincide at a value q = q1. The value of the s parameter indicates nonspherical objects: For spheres, s = 0, while for rods, s = 1, and for platelets, s = 2. At the later stages, i.e., from the point on when the fringe of the sphere form factor appears and dominates the intermediate q-range, a model describing spheres with a Gaussian size distribution was used:

P(q) =

⎛ 4π ⎞2 2 ⎜ ⎟ N (Δρ) ⎝ 3 ⎠ 0

∫0

∞

f (R )R6F 2(qR ) dR

(4)

where f (R sph) =

⎤ ⎡ 1 1 exp⎢− 2 (R − R sph)2 ⎥ ⎦ ⎣ 2σ σ 2π

(5)

is the normalized Gaussian distribution around the average radius Rsph, and

F(x) =

sin(x) − x cos(x) x3

(6)

is the scattering amplitude of a homogeneous sphere. N0 is the total number of spheres per unit volume, and Δρ is the difference in the scattering length densities of the (mixed) solvent and the spheres. Smearing with the resolution function was not possible for the curves from the diblock copolymer, most probably because the numerical approximation using the Gaussian quadrature yields too small intensity values at low q values where the most prominent features of the curves are present. This may lead to an overestimation of the polydispersity σ of the Gaussian size distribution. For the PNIPAM solutions, the following expression was used: I(q) =

IOZ IP0 + + Iinc qα 1 + (qξ)2

(7)

In eq 7, the first term is a generalized Porod law describing the strong forward scattering from large aggregates. The exponent α was left as a free parameter to describe the aggregate surfaces, i.e., diffuse boundaries.64 The value α = 4 is expected for smooth surfaces, while lower and higher values are due to surface roughness or a surface gradient, respectively.65 I0P is a scaling factor, which for α = 4 is related to the contrast and the specific surface of the aggregates. The second term is the Ornstein−Zernike (OZ) structure factor describing concentration fluctuations in the aggregates which give rise to scattering at high q-values. This term has been used for describing the concentration fluctuations in chemically cross-linked gels66 or thermal fluctuations of polymer chains.67,68 IOZ and ξ are the scaling factor and the correlation length of the fluctuations, respectively. Because of the relatively poor statistics in the first curves of the runs, 63

(2) D


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the values obtained for both ξ and IOZ in this time regime could not be determined reliably and will therefore not be discussed. The last term, Iinc, is the incoherent background and was treated as described above. Fitting to the curves from the two SDDs was carried out separately because, due to their difference in q-resolution, they did not fully overlap. When modeling the low and high q ranges, the focus was on the first and on the second term of eq 7, respectively. The agreement of the resulting parameters was within the experimental error. The resolution functions for the two SDDs were taken into account, following ref 12. The wavelength spread Δλ/λ as well as the divergence Δθ due to the finite collimation were combined to give 2 ⎡⎛ 4π ⎞2 ⎤ ⎛ Δλ ⎞ 1 2 2 ⎟ + ⎢⎜ ⎟ − q2 ⎥(Δθ)2 (Δq ) = q ⎜ ⎝ ⎠ ⎝ 2 2 ln 2 λ ⎠ ⎣ λ ⎦

PNIPAM solution is well above the critical micelle concentration in D2O,38 and therefore, the majority of the chains is expected to form core−shell micelles with a PS core and a PNIPAM shell. For consistency, the same polymer concentration was chosen for the PNIPAM homopolymer solutions. In the case of PNIPAM, the molecularly dissolved chains become hydrophobic, collapse, and form large aggregates, whereas in the case of PS-b-PNIPAM, the micellar shell collapses and the collapsed micelles form large aggregates. Already in pure D2O, the Tcp values of PNIPAM (32.3 ± 0.5 °C) and PS-b-PNIPAM (29.5 ± 0.5 °C) are significantly different which may be attributed to steric hindrances originating from the presence of the hydrophobic PS blocks; thus, a decrease of the water solubility and of Tcp is observed. Tcp decreases for both systems upon the addition of d-MeOD, as expected. The absolute values of Tcp are in good agreement with results from previous works.42,56,69 Pathway of the Phase Transition of PS-b-PNIPAM As Probed with TR-Turbidimetry. Figure 3 shows the TR-

(8)

For the collimation lengths of 5.6 and 14.4 m, the values for Δθ are 1.78 × 10−3 and 1.21 × 10−3 rad, respectively.12 The model function was convoluted with the resolution function

R(q , q′, Δq) =

⎡ (q′ − q)2 ⎤ ⎥ exp⎢ − Δq 2π ⎣ 2(Δq)2 ⎦ 1

(9)

as follows: ∞

Iexp(q) =

■

∫−∞ R(q , q′, Δq)I(q′) dq

(10)

RESULTS This section is structured as follows. First, the phase behavior of PS-b-PNIPAM in the mixed solvent D2O/d-MeOD as determined using turbidimetry and results from TR-turbidimetry during addition of d-MeOD to solutions of PS-b-PNIPAM in D2O are presented. Then, the results from TR-SANS during addition of d-MeOD to solutions of PS-b-PNIPAM in D2O are discussed. Theoretical models for the growth of the aggregates used to describe the aggregation mechanism observed for the PS-b-PNIPAM/D2O/d-MeOD system are addressed. TRSANS data during addition of d-MeOD to solutions of PNIPAM in D2O allow us to describe the influence of the chain architecture on the aggregation process. Finally, the results are summarized. Phase Behavior. In Figure 2, the cloud points (Tcp) of all samples as determined by turbidimetry are presented, together with representative light transmission curves (inset). The concentration chosen (20 mg/mL) ensures that the PS-b-

Figure 3. TR-turbidity curves after the addition of d-MeOD to a PS-bPNIPAM solution at 20 mg/mL in D2O for the mixing ratios 80:20 v/ v at 23 °C (red circles) and 85:15 v/v at 26 °C (black squares). The open symbols at short times were measured with higher time resolution (see text).

turbidity curves of PS-b-PNIPAM for two different methanol contents. After mixing, an increase in the turbidity is observed which reflects the aggregate formation due to phase separation. The larger the aggregates, the stronger they scatter the incident light, resulting in a reduction of the intensity of the transmitted beam. In both systems, three regimes are distinguished: (i) a very slow increase during the first ∼10 or ∼100 s for 80:20 v/v and 85:15 v/v, respectively, (ii) a fast increase from ∼10 to 300 s and from ∼100 to 700 s for 80:20 v/v and 85:15 v/v, respectively, and (iii) a plateau at later times. This observation can be explained as follows. Small aggregates are initially formed which later coalesce to form larger aggregates. At some point, the further coalescence is hindered, probably due to their slow diffusion or due to the existence of an energy barrier, as detailed in the Introduction. The higher the content of dMeOD, the earlier the aggregation process starts and the earlier the plateau is reached, but the final states are similar. The measurement with high time resolution (0.01 s) for the 80:20 v/v D2O/d-MeOD sample reveals that the collapse transition and the subsequent aggregation start at subsecond time scale; thus, techniques with a high time resolution are necessary to address the very first steps of these processes. To conclude, TRturbidimetry reveals the time scales of the aggregation process

Figure 2. Cloud points (Tcp) of PNIPAM and PS-b-PNIPAM at 20 mg/mL as a function of the d-MeOD content. Red circles: PNIPAM; blue squares: PS-b-PNIPAM. The lines are guides to the eye. Inset: temperature-dependent light transmittance of solutions of PNIPAM in 90:10 v/v (orange triangles), 85:15 v/v (green squares), and 80:20 v/v (black diamonds) D2O/d-MeOD. E


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of PS-b-PNIPAM which collapse upon the addition of dMeOD. The time scales of the aggregation path depend on the content of d-MeOD. To gain a more detailed picture of the collapse and aggregation processes, we now discuss the TRSANS results. Pathway of the Phase Transition of PS-b-PNIPAM as probed by TR-SANS. Figure 4 displays the SANS curves

subsecond time scale but only leads to a low turbidity (Figure 3). At the end of each run, the minimum in the SANS curves is still present and has moved to q ∼ 0.1 nm−1 (Figure 5). Thus,

Figure 5. Representative TR-SANS curves from the PS-b-PNIPAM solution with a mixing ratio of 80:20 v/v (symbols) together with fitting curves (lines). The curve measured 2103 s after the injection has been shifted by a factor of 20 for clarity. The dotted and the full lines correspond to the Guinier−Porod model (eq 3) and to the one describing spheres with a Gaussian size distribution (eq 4), respectively. The fine oscillations appearing at ∼0.4 nm−1 in the model curve at 2103 s are an artifact of the fitting procedure.

the aggregate radii are of the order of R = 45−50 nm. This is in contrast to our previous static SANS measurements in D2O, where we have observed Porod-like scattering from very large aggregates above the Tcp.38 Very large aggregates were also formed in solutions of PS-b-PNIPAM-b-PS in D2O above Tcp after a temperature jump.31,36,37 In the present case, the aggregate growth seems to be limited, i.e., the addition of dMeOD alters the aggregation path significantly compared to a temperature increase above Tcp. To extract more detailed information, we fitted structural models to the TR-SANS curves. In Figure 5, representative fits of the two models used are presented for three selected time frames (e.g., 0.7 and 2103 s after the injection) for the 80:20 v/v mixing ratio. In Figure 6, the parameters obtained from fitting eqs 3 and 4 to the SANS curves of the three runs are compiled. The fitting process was carried out in two steps. The first curves (until 30 s after the injection) were fitted with the Guinier−Porod model (eq 3), whereas the later curves were fitted with the model for spheres with a Gaussian size distribution (eq 4). For the intermediate region (15−30 s after mixing), both models were used and gave similar values for Rg and Rsph (Figure 6a). The radii of the aggregates (Figure 6a) have initial values of Rg ∼15.0 ± 3.5 nm for all three runs. As discussed above, the value for the radius obtained from the first curve (0.1 s after the injection) is too large to be assigned to single, collapsed micelles (5−7 nm),38,57 which confirms that, already very soon after mixing, aggregates are present. An effect that may contribute to this fast aggregation is the excess heat that is created upon mixing D2O and d-MeOD.70 By comparing the value of the initial aggregate radius with the radius of collapsed micelles of systems from the literature, the initial aggregation number, i.e., the number of micelles per aggregate, than can be resolved is estimated at ∼15. The question arises whether the PS-b-PNIPAM diblock copolymers form core−shell micelles in pure D2O, i.e., before mixing with d-MeOD, and whether these are affected by the

Figure 4. TR-SANS curves of the PS-b-PNIPAM diblock copolymer for all d-MeOD contents in dependence on time after the injection: (a) 90:10 v/v at 29 °C, (b) 85:15 v/v at 27 °C, and (c) 80:20 v/v at 23 °C.

taken during the measurements of the PS-b-PNIPAM diblock copolymer. For all three mixing ratios, the same general picture emerges: First, the curves decay smoothly, whereas after ∼15 s, a minimum appears at q ≅ 0.15 nm−1 which moves with time to lower q values. Using the relation known for the radius of monodisperse homogeneous spheres, R ≅ 4.5/qmin, where qmin is the position of the first minimum of the sphere form factor, we obtain R ≅ 25 nm. This value is much higher than the micellar radius known from similar PS-b-PNIPAM diblock copolymers in the collapsed state (∼5−7 nm).38,57 We therefore attribute the spheres to aggregates formed by a large number of polymers. The presence of aggregates of this size is consistent with the above-described observations from TR-turbidimetry which show that aggregation may happen on F


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than the one of H2O (δH2O = 23.5 cal1/2 cm−3/2), but PS is not soluble in MeOH.72 Thus, we expect that the core−shell micelles stay intact upon addition of d-MeOD but that dMeOD promotes the micellar exchange dynamics. With time, the aggregate radii increase in all three runs, reaching final values of 44.4 ± 1.4, 44.7 ± 1.2, and 49.2 ± 1.5 nm for mixing ratios of 90:10 v/v, 85:15 v/v, and 80:20 v/v, respectively; i.e., the final aggregate radii increase with d-MeOD content. Moreover, the higher the content of d-MeOD, the earlier starts the aggregate growth: after ∼1 s for 80:20 v/v and after ∼5 s for the two other mixing ratios. The radii obtained from the two models (eqs 3 and 4) coincide very well in the intermediate region, despite the fact that the Guinier−Porod model gives the radius of gyration, Rg, whereas the model for spheres with a Gaussian size distribution gives the average geometric radius, Rsph. We will discuss this in detail below. The inset in Figure 6a shows clearly that the increase of the radius slows down and that after ∼1500 s the growth has stopped. This confirms that mesoglobules have formed which reach a final size and do not grow or aggregate further. The dimensional parameter s reflects the anisotropy of the aggregates (Figure 6b). Initially, s = 1.1 for a mixing ratio of 80:20 v/v and s = 1.3 for 85:15 v/v and 90:10 v/v; i.e., the aggregates are elongated (for straight rods, s = 1). This is presumably a consequence of the low number of micelles per aggregate and of the very fast process of collapse and aggregation. For all d-MeOD contents, s decreases with time to a value of ∼0.2; i.e., the aggregates become more spherical (for spheres, s = 0), and therefore, the SANS curves could be fitted with the second model equally well. This transition explains the good agreement between Rg and Rsph: Comparing the three mixing ratios, we observe that this shape change begins the earlier, the higher the d-MeOD content. The polydispersity of the sphere radius decreases with time (Figure 6b); i.e., the distribution becomes narrower. As mentioned in the modeling section, σ may be slightly overestimated in the absence of the resolution function. The observed increase of the prefactor N0(Δρ)2 at later times is assigned mainly to the increase of the contrast between the polymer-rich aggregates and the solvent-rich surrounding, since the number of the aggregates is not expected to increase in this regime (see eq A2 in the Appendix). We note that the prefactor of the Guinier− Porod model has no obvious physical meaning and therefore is not plotted. It is striking that, in the time range where both fitting models could successfully be used, the values for the radius of gyration, Rg, and the geometric radius, Rsph, coincide (Figure 6a). For homogeneous spheres, this would not be the case; instead, they would differ by a factor of (3/5)1/2. On the other hand, for a spherical hollow shell with outer and inner radii R1 and R2, respectively, the relation is

Figure 6. TR-SANS on PS-b-PNIPAM solutions. Fitting results as a function of time after injection for the mixing ratios of 90:10 v/v at 29 °C (green diamonds), 85:15 v/v at 26 °C (blue squares), and 80:20 v/ v at 23 °C (red circles). Open symbols: results from the Guinier− Porod model; filled symbols: results from the model for spheres with a Gaussian size distribution. The gray box indicates the time range in which both models were used. We present (a) the radii Rg and Rsph from both models, (b) the dimensional parameter s from the Guinier− Porod model and the polydispersity σ of the sphere radius from the Gaussian distribution, and (c) the prefactor N0(Δρ)2 of the Gaussian size distribution as a function of time after the injection. The inset in (a) shows the radii as a function of time after the injection on a linear time scale.

addition of d-MeOD. The SANS curves do not show any scattering from core−shell micelles. Since neither the PS nor the PNIPAM block is deuterated, their scattering length densities are similar and, possibly, the core and the shell cannot easily be distinguished in the SANS experiment. The SANS curves of a similar diblock copolymer with a fully deuterated PS block, P(S-d8)11-b-PNIPAM431, at 20 mg/mL in D2O below Tcp (not shown) cannot be fitted with a homogeneous sphere model but only with a model for spherical core−shell particles. The core radius amounts to 2.5 nm, whereas the micellar radius is 9.7 nm. The same diblock copolymer in D2O/d-MeOD (14.5% v/v of d-MeOD) forms also core−shell micelles with a core radius of 2.5 nm and a micellar radius of 9.3 nm. By using the core radius and the mass density of bulk PS (1.05 g/cm3) together with the polymerization number of the PS blocks (NPS = 11), we obtain an aggregation number Nagg = 35, which is in the usual range. Therefore, we are convinced that the present P(S14-bNIPAM310) diblock copolymer forms core−shell micelles in D2O before mixing with d-MeOD. The addition of d-MeOD, however, may result in a softening of the PS core.71 The Hildebrand solubility parameter of MeOH (δMeOH = 14.5 cal1/2 cm−3/2) is closer to the one of PS (δPS = 9.13 cal1/2 cm−3/2)

Rg =

5 5 3 R1 − R 2 5 R13 − R 2 3

(11)

Thus, the more of the polymer is located in the outer part of the aggregates, the closer is the Rg value to Rsph. We conclude that the polymer concentration in the aggregates is inhomogeneous: the polymer concentration close to the aggregate surface is higher than in the center. An inhomogeneous radial density distribution has been observed previously in aqueous PNIPAM solutions22,24,26,27 and microgels.73 G


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Aggregation Pathway. We observe that the complex aggregation pathway observed differs from the ones known from simple colloidal systems which are commonly described by the diffusion-limited colloidal aggregation (DLCA) model74 or the reaction-limited colloidal aggregation (RLCA) model.75 In the DLCA model, the interaction between particles is shortranged and strongly attractive; therefore, each collision leads to aggregation, and the growth follows R ∝ t0.57.75 In the RLCA model, the particles must overcome a repulsive barrier before binding, which results in R ∝ exp(Ct) where C depends on the experimental conditions.75 The RLCA model was successfully used to describe the aggregation of PS particles in water.76 However, there is a fundamental discrepancy: Both the DLCA and the RLCA predict that the resulting aggregates are fractals. In our data, there is no evidence for fractal aggregates, but rather for compact ones; thus, the DLCA and RLCA models do not apply to the present system. The reason for this discrepancy may be that the aggregates are not glassy, as in the case of PS, but soft, possibly because they contain still solvent, at least in the initial stage of the growth.20,29,77−79 Furthermore, studies of the aggregation of soft particles have revealed kinetics which are fundamentally different from the DLCA and RLCA models.79−81 In such systems, the colloidal aggregation can be governed by the change of viscosity within the aggregates with the values depending strongly on the experimental conditions. Stepanyan et al. described the growth of aggregates upon the rapid addition of a poor solvent to a polymer solution in a good solvent by diffusion-limited coalescence (DLC).82 According to this model, the polymers coalesce and form compact aggregates. The following conservation law is assumed: 3

cp(t )R p (t ) = cp0R p0

3

Figure 7. TR-SANS on PS-b-PNIPAM solutions. Aggregate radii as a function of time after injection. Same symbols as in Figure 6a. The lines represent the fits of the respective models on the experimental data. Black full lines: DLC model (eq 13); White dashed lines: hindered aggregation model (eq 17).

Table 1. Kinetic Constantsa

3 η 8 cp0kBT

τlog (ms)

u

7.1 ± 0.5 6.5 ± 0.6 2.5 ± 0.4

5.1 ± 0.2 5.7 ± 0.2 10.1 ± 0.05

3.5 ± 0.2 3.3 ± 0.1 2.7 ± 0.2

τD from the DLC model (eq 13); τlog and u from the logarithmic coalescence model (eq 17).

values of cp0, we use them, on the one hand, together with the polymer concentrations in the mixed solutions (19, 18.5, and 18 mg/mL for the three mixing ratios, respectively) and the molar mass of PS-b-PNIPAM. This way, we estimate initial aggregation numbers of 25 × 106, 26 × 106, and 29 × 106 polymers/aggregate for the three mixing ratios, respectively. Estimating, on the other hand, the initial aggregate volumes from their initial radii (Figure 6a) and dividing these by the molar volume of the PS-b-PNIPAM chain, we obtain that each aggregate consists on average only of a few hundred polymers. This value is orders of magnitude lower than the ones calculated from the fitted τD. Hence, the model describes the initial growth qualitatively, but a quantitative discrepancy is present. Thus, the pathway of aggregation seems to be more complex than described by the DLC model. A reason for this discrepancy may be that the very first stages of the aggregation occur already in the mixing chamber and the delay line of the stopped-flow instrument: A fraction of the polymers may have remained there, possibly by adhesion to the large inner surface, resulting in a lower cp0 in the probed volume. This is corroborated by the fact that the initial aggregate radii are larger than the ones expected for single collapsed micelles. After this first regime, the growth of the aggregates slows down and follows logarithmic behavior, Rp(t) ∼ log(t), for all three runs (after 10−20 s). Such kinetics takes place in systems where structural transformations involve an activation energy that grows with time and have been observed in glasses, granular materials, proteins, etc.84 In colloidal systems of spherical particles, the activation energy of coagulation (i.e., the height of the energy barrier) is assumed to depend on Rp(t). In case of short-range repulsion, this dependence is linear according to the “chord theorem”, which says that the area of short-range contact between two identical spheres (and

(12)

(13)

where τD is the average aggregate lifetime during DLC (introduced as the coalescence time τcls by Stepanyan et al.82) τD =

τD (s)

90:10 85:15 80:20 a

where Rp(t) is the time-dependent particle radius and cp(t) the time-dependent number concentration of aggregates; Rp0 and cp0 are the values immediately after mixing. The following growth law is derived ⎛ t ⎞ R p3(t ) = R p0 3⎜1 + ⎟ τD ⎠ ⎝

mixing ratio (v/v)

(14)

with η being the solvent viscosity, kB Boltzmann’s constant, and T the temperature. Fitting eq 13 to our results of the timedependent aggregate radius (Figure 6a) reproduces the shape of the data points for all three d-MeOD contents during the first 30−40 s (Figure 7). The model captures the constant value of the aggregate radius in the beginning and the initial stage of the growth. One might thus attribute the initial growth process to the DLC of soft mesoglobules. For the coalescence time, τD, however, we obtain values between 2.5 and 7.1 s (Table 1) which seem to be orders of magnitude too high. This is reflected in the value of cp0 as calculated from τD (eq 14): Using the respective values of the viscosity of the D2O/d-MeOD mixtures83 and the temperature for each mixing ratio, we obtain values of cp0 = 1.37 × 1010, 1.26 × 1010, and 1.13 × 1010 cm−3 for the initial concentration of aggregates for 90:10, 85:15, and 80:20 v/v D2O/d-MeOD, respectively. To cross-check these H


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potential energy as well) is proportional to Rp(t).85 Thus, the dimensionless activation energy reads EA (t ) ∝ R p(t ) = u

R p(t ) R p0

(15)

In the present case, u = ε/kBT is the reduced activation energy of aggregation for two aggregates of radius Rp0. Equation 15 reflects the collective interaction between aggregates, which requires that the aggregates are soft enough to attain nearly spherical shape between the collisions. One can assume that the transition from diffusion-limited to logarithmic coalescence takes place when the activation energy of aggregation exceeds the energy of thermal fluctuations, kBT, and the aggregation probability pA ∼ exp(−EA) significantly drops below unity. To derive the time dependence of the aggregate radius, we assume that the rate of aggregation is given by ∂cp ∂t

∝ −pA cp 2

(16)

where the probability of aggregation decays exponentially with the aggregate radius, Rp(t). The aggregation rate, being integrated and simplified for the case of large aggregates, gives the expected logarithmic time dependence of the aggregate radius: R p(t ) R p0

≈

1 ⎛⎜ u t ⎞⎟ ln u ⎜⎝ 3 τlog ⎟⎠

(17)

where τlog is the average time between collisions of aggregates of radius Rp0 at the concentration cp0 in the absence of coagulation, and τlog ≪ τD. The derivation of eq 17 is given in the Appendix. Equation 17 was fitted to the radii given in Figure 6a for times longer than 15−20 s. Fitting parameters are u and τlog; the values of Rp0 were taken as 14.5, 14.8, and 16.0 nm for 90:10 v/v, 85:15 v/v, and 80:20 v/v D2O/d-MeOD, respectively. The resulting parameters are presented in Table 1. In all the cases, we see that the energy barrier ε = ukBT is notably higher than the thermal energy. By comparing the values obtained for the three mixing ratios, we observe that the content of d-MeOD has an influence on the aggregation. Especially in the case of the logarithmic coalescence regime at later times, the characteristic time τlog decreases with increasing content of d-MeOD which, in addition to the lower energy barrier, results in larger final aggregate radii. Effect of the Chain Architecture on the Aggregation Pathway. Additional TR-SANS measurements were carried out on PNIPAM in the same way as for PS-b-PNIPAM. The three sets of curves (Figure 8) exhibit strong forward scattering throughout the whole time range. In the beginning, due to short measurement times, the statistics are low, but later on, the curves are smooth and reveal slight changes with time. The forward scattering is an evidence of large aggregates (>∼150 nm) in the solution. It is present even in the very first curves, i.e., the collapse transition and the aggregation are faster than the dead time of the setup (0.1 s); thus, large aggregates have formed already during this time. The behavior is thus qualitatively different from the one of the PS-b-PNIPAM system, which may be due to the latter’s micellar structure involving the tethering of the PNIPAM blocks to the PS core, thus reducing the chain dynamics.

Figure 8. TR-SANS curves of the PNIPAM homopolymer for all dMeOD contents in dependence on time after the injection: (a) 90:10 v/v D2O/d-MeOD at 31 °C, (b) 85:15 v/v at 28 °C, and (c) 80:20 v/v at 23 °C.

In Figure 9, representative model fits are presented for two selected time frames (0.7 and 2103 s after the injection). The deviations of the fitting curves in the intermediate region are due to the different resolutions for two data sets (SDD 4.0 and 14.4 m). In addition to the strong forward scattering described by the generalized Porod law, a weak contribution in the high qregion described by the OZ term is present (eq 7). Figure 10 summarizes the fitting parameters from the Porod contribution. The Porod amplitude, I0P (Figure 10a), decreases with time for all d-MeOD contents, starting at the same initial value of 8 × 10−11. (Because of the varying value of α, see below, we cannot assign a dimension to I0P.) The amplitude stays constant during the first second for all d-MeOD contents. It decreases during the first 6 s with the rate being the same for all d-MeOD contents, but later it decreases the faster, the higher the d-MeOD content. Ca. 200−500 s after the injection, it reaches a final value which is the lower, the higher the dMeOD content. I


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IP0 = 2π (Δρ)2 (S /V )

(18)

where S/V is the specific surface of the aggregates and Δρ the scattering length density (SLD) difference between the PNIPAM-rich aggregates and the solvent. S/V, in turn, is related to the size of the aggregates. However, in the present case, α > 4, and eq 18 may not be used. To overcome this obstacle, we attempted to use the approach by Koberstein et al.,64 who assigned deviations of the Porod exponent from the nominal value α = 4 to the presence of diffusion-boundary layers. More precisely, a modified Porod expression was used, where the unperturbed Porod law was multiplied by a factor accounting for the layer width. Unfortunately, this attempt did not lead to physically acceptable values, even for qualitatively good fits; therefore, it was not pursued further. Thus, the behavior of I0P can only be discussed qualitatively. The decrease of I0P reflects the decrease of the specific surface of the aggregates with time, i.e., their increase in size. Thus, the different regimes of the behavior of I0P with time can be assigned to different phases of the aggregation process: In the first stage, all three solutions are in a similar state, as expected, which remains stable for the first second, whereas during the subsequent 6 s, the aggregation proceeds at the same rate for all three mixing ratios. Afterward, the path followed depends strongly on the content of d-MeOD. The aggregates in the solution with 80:20 v/v d-MeOD continue to grow at the same rate until 100 s after the injection and then stop growing. (In the latter regime, the exponent α is constant.) The samples with 85:15 v/v and 90:10 v/v grow at a lower rate. Thus, we conclude that the higher the d-MeOD content, the faster is the growth process. The observation of constant I0P values at the later stages is not necessarily due to an arrest of the aggregation but may be a result of the resolution limit of the TR-SANS setup. There have been reports of PNIPAM aggregates being a few hundred nanometers large87 or even larger28 that continue growing over longer times (∼5000 s) than probed in our work. In Figure 11, results of the fits of the OZ term, namely the correlation length, ξ, and the scaling factor, IOZ, are shown as a function of time. For the first ∼20 s, the curves suffer from poor statistics due to the low measurement times; therefore, we do not give any values in this time regime. At later times, the statistics are good enough to allow the fitting of the small shoulder in the high q region reliably. ξ decreases from 12 to 1−2 nm for all three mixing ratios and remains at this value after ∼100 s (Figure 11a), which is in consistency with the expected collapse in semidilute solution. From the fact that IOZ is finite even above Tcp, we conclude that even the aggregates formed by collapsed PNIPAM chains contain solvent and thus inhomogeneities on the length scale of ξ. The decrease of IOZ with time means that the osmotic modulus increases; i.e., the aggregates become more compact. This is in agreement with the behavior of the Porod exponent (Figure 10b) which points to an increasingly smooth aggregate surface. We observe that the large, polymer-rich aggregates not only increase in size by coagulation but also, at the same time, expel the entrapped solvent molecules, mainly from their outer part.

Figure 9. TR-SANS on the PNIPAM solution with a mixing ratio of 80:20 v/v. Symbols: experimental curves at the times given. For clarity, the curve at 2103 s after the injection is shifted by a factor of 100. Full lines: representative model fits for the two resolutions (eqs 7−10).

Figure 10. TR-SANS on PNIPAM solutions. Fitting results from the generalized Porod term: the Porod intensity I0P (a) and the Porod exponent α (b) as a function of time after injection for the mixing ratios of 90:10 v/v at 31 °C (green diamonds), 85:15 v/v at 28 °C (blue squares), and 80:20 v/v at 23 °C (red circles).

The Porod exponent, α, increases with time for all three mixing ratios (Figure 10b). Starting from a value of ∼4.8, it increases until 30 s after the injection and reaches a final value of 5.8 for all d-MeOD contents. These values are larger than expected for spheres with a smooth surface, α = 4 (ref 63), which may be assigned to a gradient of the SLD along the surface normal of the aggregates.63,86 Hence, the observed increase of α means that the interfaces become smoother. Thus, in the beginning, the aggregates still contain entrapped solvent which is expelled with time. In the beginning, solvent is expelled mainly from the outer part of the aggregate. This would imply the formation of a dense polymer skin at the outer surface and a concentration gradient of solvent. The fact that the exponent α is higher than 4 makes it difficult to interpret the behavior of I0P. For smooth interfaces, α = 4, and I0P is related to the specific interface by the relation:63

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CONCLUSIONS We have studied the collapse transition and the subsequent aggregation process induced by the rapid addition of d-MeOD to solutions of a diblock copolymer PS-b-PNIPAM and of a homopolymer PNIPAM in D2O, on a mesoscopic scale. By means of TR-turbidimetry and TR-SANS, we have elucidated J


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surface charges or from the increasing rigidity of the aggregates. Increasing the d-MeOD content results in a lower aggregate lifetime in the diffusion-limited coalescence regime as well as in an increased time between collisions and in a decreased barrier in the hindered growth regime. As a result, the final aggregate size increases with the content of d-MeOD. The comparison between PS-b-PNIPAM and PNIPAM reveals significant differences. We note that the PNIPAM blocks in the two polymers have slightly different molar masses, which makes a direct quantitative comparison difficult; however, the behavior seems to be generic and not primarily due to a difference in molar mass. The homopolymer forms much larger aggregates than the diblock copolymer. A reason for this may be the steric hindrances of the PNIPAM chains that are tethered to the micellar PS core in the case of PS-bPNIPAM. The absence of such limitations in PNIPAM results in increased chain dynamics which allows the formation of much larger aggregates (>150 nm). Interestingly, even within these large aggregates, there is evidence for density inhomogeneities; i.e., solvent molecules are still trapped in the aggregates consisting of collapsed chains. For both systems, the surface of the aggregates becomes more polymer-rich with time; a dense skin of highly collapsed polymer chains is created in the outer part of the aggregate, while solvent molecules are trapped in the center of the aggregate. An explanation may be that the solvent molecules closer to the surface diffuse rapidly into the surrounding pure solvent region, leaving behind a dense “skin” which is not easily permeable for the remaining solvent molecules. The difference between the aggregation processes observed in the present investigation, namely upon the addition of a cononsolvent and upon temperature jumps in previous works, is marked as highly interesting; it reveals the sensitivity of the collapse transition and the aggregation to the manner that the phase separation is induced. In parallel, the phenomena that are followed in the present investigation on the mesoscopic scale lead to the conclusion that even though the origin of cononsolvency lies in the molecular interactions between the polymer and the two types of solvent molecules, it has drastic implications even on the mesoscopic length scale and on a time scale as long as 30 min.

Figure 11. TR-SANS on PNIPAM solutions. Fitting results from the OZ term: (a) OZ intensity IOZ and (b) correlation length ξ as a function of time for the mixing ratios of 90:10 v/v (green diamonds), 85:15 v/v (blue squares), and 80:20 v/v (red circles).

the influence of the d-MeOD content on the phase separation process. The addition of d-MeOD results in a very fast collapse of the micellar PNIPAM shell and of the PNIPAM chains, respectively. In both cases, the hydrophobic collapsed entities form large aggregates which result in increased turbidity. TR-SANS gave structural information which is summarized in Figure 12. For PS-b-PNIPAM, small aggregates (∼15 nm)

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APPENDIX. LATE-STAGE KINETICS OF THE MICELLAR AGGREGATION The rate of aggregation follows the equation of a bimolecular reaction: ⎛ Rp ⎞ 2 ⎟⎟cp = −kpA cp 2 = −k exp( −EA )cp 2 = −k exp⎜⎜ −u dt ⎝ R p0 ⎠

dcp Figure 12. Schematics of the structural changes upon addition of dMeOD to solutions of PS-b-PNIPAM and PNIPAM in D2O.

(A1)

where k is the collision rate constant and pA the probability of aggregation upon collision. The latter is assumed to depend on the activation energy in the late stage of aggregation pA = exp(−EA) = exp(−uRp/Rp0). For small aggregates, one can expect that the potential energy barrier is low (EA ≪ 1). Thus, the value pA ≈ 1; aggregation is very fast and diffusion-limited. Under these conditions and at pA = 1, eq A1 transforms into a second-order reaction equation with the well-known solution

exist already in the beginning, i.e., as early as 0.1 s after injection, which subsequently grow with time. Different growth regimes are distinguished. Initially, the size of the aggregates remains constant, but after a certain time, which depends on the d-MeOD content, it starts to increase following the diffusion limited coalescence model, however, with an aggregate lifetime which is orders of magnitude too high. The later stage is described by the logarithmic coalescence model, describing the growth in the presence of an energy barrier which increases with the aggregate radius. This barrier may originate from

cp0 cp K

= 1 + kcp0t = 1 +

t τ

(A2)


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This result coincides with eq 13 if one takes into account relation 12. In this equation, τ = 1/kcp0 is the average lifetime of the aggregate, which can be approximated by eq 14 in the diffusion-limited regime. The larger the aggregates, the stronger is the repulsion between them. As a result, in the late stages, the decay of the aggregation probability (pA) cannot be neglected, and one has to solve eq A1. To do so, the aggregate size in eq A1 is replaced by concentration according to eq 12: ⎡ ⎛ ⎞1/3⎤ cp0 = −k exp⎢⎢ −u⎜⎜ ⎟⎟ ⎥⎥cp 2 dt c ⎣ ⎝ p⎠ ⎦

(A3)

This result is integrated from cp0 to cp and from 0 to t after variable separation, yielding ⎛ ⎡ ⎛ cp0 ⎞1/3 c u3kt ⎤ 1 − ⎥ ⎜⎜ ⎟⎟ = 1 + u ⎜ln⎢1 − u + u 2 /2 + p0 ⎜⎜ ⎢ 6 exp(u) ⎥⎦ ⎝ cp ⎠ ⎣ ⎝

(A4)

Since cp ≪ cp0, and the time of observation is much higher than the lifetime of the aggregates (cp0kt ≫1), eq A4 can be simplified to read ⎛ ⎡⎛ ⎞1/3⎤⎞ ⎛ cp0 ⎞1/3 c ⎤ ⎡ ⎜⎜ ⎟⎟ ≈ 1 ⎜ln⎢ u cp0kt ⎥ − 2 ln⎢⎜⎜ p0 ⎟⎟ ⎥⎟ ⎜ ⎢ c ⎥⎟⎟ ⎦ u⎜ ⎣3 ⎝ cp ⎠ ⎣ ⎝ p ⎠ ⎦⎠ ⎝

(A5)

Replacing the concentrations by particle radii and neglecting the second slowly changing term of the right-hand side, this solution takes the experimentally observed logarithmic form

Rp R p0

≈

1 ⎛⎜ u t ⎞⎟ ln u ⎜⎝ 3 τlog ⎟⎠

(A6)

The parameter τlog = (cp0k)−1 has the meaning of an average time interval between collisions of hypothetical noncoagulating aggregates of radius Rp0 at the concentration cp0.

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REFERENCES

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dcp

⎡ ⎤⎞ ⎛ cp0 ⎞1/3 ⎛ cp0 ⎞2/3 ⎟ − ln⎢⎢1 − ⎜⎜ ⎟⎟ u + ⎜⎜ ⎟⎟ u 2 /2⎥⎥⎟ ⎟ c c ⎝ p⎠ ⎝ p⎠ ⎣ ⎦⎠

Article

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected], phone +49 89 289 12 447, Fax +49 89 289 12 73 (C.M.P.). Present Address

S.J.: Jülich Centre for Neutron Science JCNS, Forschungszentrum Jülich GmbH, Outstation at MLZ, Lichtenbergstr. 1, 85748 Garching, Germany. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank R. Tuinier and M. A. Cohen-Stuart for stimulating discussions. This work was supported by the DFG priority program SPP1259 “Intelligente Hydrogele” (Pa771/4, Mu1487/8, La611/7). D.M.L. and W.R. acknowledge support by the DFG within SFB 985. We thank ILL for allocating beamtime and providing excellent equipment. L


Macromolecules

Article

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M


Methanol Mixtures for PNIPAM and PS-b

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