Fast Diffusion-Limited Lyotropic Phase Transitions Studied in Situ

Article pubs.acs.org/Langmuir

Fast Diffusion-Limited Lyotropic Phase Transitions Studied in Situ Using Continuous Flow Microfluidics/Microfocus-SAXS Sebastian With,† Martin Trebbin,† Christian B. A. Bartz,‡ Christian Neuber,‡ Martin Dulle,† Shun Yu,§ Stephan V. Roth,§ Hans-Werner Schmidt,‡ and Stephan Förster*,† †

Physical Chemistry I and ‡Macromolecular Chemistry I, University of Bayreuth, Universitätsstr. 30, 95447 Bayreuth, Germany HASYLAB/DESY, Notkesstr. 85, 22607 Hamburg, Germany

§

S Supporting Information *

ABSTRACT: Fast concentration-induced diffusion-limited lyotropic phase transitions can be studied in situ with millisecond time resolution using continuous flow microfluidics in combination with microfocus small-angle X-ray scattering. The method was applied to follow a classical selfassembly sequence where amphiphiles assemble into micelles, which subsequently assemble into an ordered lattice via a disorder/order transition. As a model system we selected the self-assembly of an amphiphilic block copolymer induced by the addition of a nonsolvent. Using microchannel hydrodynamic flow-focusing, large concentration gradients can be generated, leading to a deep quench from the miscible to the microphase-separated state. Within milliseconds the block copolymers assembly via a spinodal microphase separation into micelles, followed by a disorder/order transition into an FCC liquid-crystalline phase with late-stage domain growth and shear-induced domain orientation into a mesocrystal. A comparison with a slow macroscopic near-equilibrium kinetic experiment shows that the fast structural transitions follow a direct pathway to the equilibrium structure without the trapping of metastable states.

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INTRODUCTION There has been increasing interest in studying fast structural changes in complex fluids triggered by changes in concentration, temperature, or pH as they often occur under industrial processing and formulation conditions.1−4 Understanding the underlying structure-formation mechanisms can lead to better control of formulations and the prediction of structure-related properties. Microfluidics as an experimental technique that allows us to investigate fast kinetic processes has been considerably improved in recent years.5,6 An example is stopped-flow mixing techniques that are widely used to induce rapid changes in concentration to trigger chemical reactions, structural changes in proteins, surfactant self-assembly, and particle nucleation and growth processes.7−10 Recent progress in microfluidic device engineering has also made fast continuous-flow mixing schemes possible, which allow for the first time to investigate fast mixing processes also in complex fluids.11,12 These methods involve a center stream of slowly diffusing macromolecules hydrodynamically focused by two orthogonal flows from side channels with quickly diffusing small molecules, mostly solvents. The diffusion into the resulting central stream initiates assembly or a chemical reaction process. The method benefits from several advantages. Fluids in microchannels exhibit laminar flow even at very high flow rates. Under laminar flow conditions, interdiffusion is the only mixing processes, and thus well-defined stationary © 2014 American Chemical Society

concentration gradients can be established very fast. Furthermore, under laminar flow different times, concentrations, and structures formed after mixing can be mapped onto different locations in the microchannel. The temporal resolution of such experiments is thus not limited by the temporal resolution of the detection technique but rather by the spatial resolution of the detection technique and the flow rate in the experiment. Similar to microfluidics, X-ray optics has considerably advanced in recent years. It has become possible to focus Xray beams to very small spot sizes, at dedicated synchrotron beamlines even reaching submicrometer dimensions.13,14 This enables high-resolution microbeam X-ray diffraction experiments to follow local structural evolutions in microfluidic channels. The combination of both methods then allows one to follow fast structural changes with spatial and temporal resolutions that have not been possible so far and enables us for the first time to study complex and viscous fluids. A further technical advantage is that the local structure at a given channel position, corresponding to a certain time after mixing, can be measured for any time necessary to reach good signal-to-noise ratios and without beam damage to the sample, a particular Received: July 28, 2014 Revised: September 12, 2014 Published: September 12, 2014 12494

dx.doi.org/10.1021/la502971m | Langmuir 2014, 30, 12494−12502

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Each position in the channel corresponds to a certain solvent/ polymer composition and time after mixing. A measurement of the scattering curve at this position can then relate the local structural changes to the time after mixing. We used a 31 × 22 μm2 (x × y) spot size very intense X-ray beam at microfocus beamline P03 at third-generation synchrotron PETRA III at DESY (Hamburg, Germany).18 The beam is scanned over the stationary concentration gradient that develops in the microchannel upon diffusive mixing. The measured small-angle scattering patterns allow one to follow the local structural evolution. Depending on the time scale of the experiment, the structures can be studied in their relaxed equilibrium state or followed in their temporal evolution toward the equilibrium state. For the measurements we used fully polyimide-based microfluidic devices to meet the requirements of our experiments involving the use of organic solvent (dioxane) and the need for high X-ray transmission, which rule out the use of the commonly used PDMS- or NOA-based microfluidic chips.

advantage compared to real-time techniques when using highly brilliant focused synchrotron X-ray beams. This was recently applied to study the flow reorientation of anisotropic colloids in narrow microchannels.15 Fast, even submillisecond proteinfolding kinetics could be followed using this technique.16 Very fast Mg2+-induced RNA-folding events were followed by this method on time scales of 2−150 ms.17 A particular challenging and interesting class of structural transformations that can be investigated using this combination of microfluidics with microfocus SAXS involves lyotropic phase transitions. In the present study we chose to study the fast structural transition of an amphiphilic copolymer into micellar and lyotropic phases upon fast solvent exchange. We used an amphiphilic poly(isoprene-b-ethylene glycol) (PI-PEG) block copolymer as a model system because the hydrophobic PIblock has a low glass-transition temperature and thus a high chain backbone mobility. The hydrophilic PEG block is very water-soluble and also possesses a high chain segment mobility. The PI/PEG and PI/water interfaces have high interfacial energies, and thus the system will be in the strongly segregated state in water-rich solutions. This system thus combines extreme cases for the two most relevant factors for structure equilibration during self-assembly, i.e., the high local chain mobility that would favor fast structural transitions and the high interfacial energy that may prohibit fast structural changes. In our study we follow the self-assembly behavior of the block copolymer starting from single block-copolymer chains that assemble into micelles and then form a disordered micellar phase that undergoes a phase transition into an ordered FCC liquid-crystalline micellar phase. For the experiments a synchrotron X-ray-compatible microfluidic chip has been designed, which allows for the hydrodynamic focusing of a stream of the block polymer at high concentration in common solvent A for both polymer blocks (dioxane) using two streams of selective solvent B (water), which is miscible with solvent A. Upon mixing, a stable concentration profile of solvents A and B and polymer is established downstream from the central channel (Figure 1).

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MATERIALS AND METHODS

Preparation of Microfluidic Devices. Polyimide films were used to fabricate X-ray-transparent microfluidic devices enabling experiments with organic solvents and at elevated temperatures. Only a few microfluidic devices based on laser-cut polyimide films are described in the literature.14,19−21 The experiments described in this publication were performed in a dioxane/water system. No changes in the dimension of the microfluidic channel were observed during the experiments. The devices were prepared in a multilayer lamination process, as described in detail in the Supporting Information. Three different types of commercial polyimide films and laser cutting were utilized to fabricate all-polyimide devices with integrated metal tube connectors. The microchannel downstream of the channel cross has a width of 110 μm, a height of h = 115 μm, and a length of l = 31 mm. Sample Preparation. The poly(isoprene-b-ethylene glycol) copolymer was synthesized by sequential living anionic polymerization in THF.22 Therefore, isoprene was polymerized after initiation with sBuLi in the presence of phosphazene base t-Bu-P4, which allows the subsequential addition and block copolymerization of ethylene oxide to obtain the PI-PEG block copolymer. The polymer was precipitated in methanol and dried to constant weight. The PI120-PEG394 copolymer shows block lengths of 120 and 394 monomer units respectively, a molecular weight of Mw = 25 500 g/mol, and a polydispersity of Mw/Mn < 1.10. The PI-PEG copolymer was dissolved in 1,4-dioxane to obtain a 20 wt %/wt solution. There was no further sample treatment necessary. Small-Angle X-ray Scattering. The experiments were performed at MiNaXs beamline P03 of the PETRA III synchrotron at DESY/ HASYLAB (Hamburg, Germany).18 The beam diameter was adjusted to 31 μm in the x direction and 22 μm in the y direction with a wavelength of λ = 0.1088 nm. As a detector, a Pilatus 300 K (DECTRIS) with a pixel size of 172 μm × 172 μm and a sample− detector distance of 4.97 m was used. Between the sample and the detector, an evacuated tube was positioned. The adjustment of the device within the sample environment of the X-ray facility was carried out via motors. The in-house glass capillary measurements were performed on a GANESHA (SAXSLAB) small-angle X-ray scattering setup equipped with a microfocus rotating anode (Rigaku Micromax 007 HF) and a Pilatus 300 K detector (DECTRIS). The X-ray beam (λ = 0.154 nm) was focused to 100 μm for the scanning experiment. Microfluidic/SAXS Experiment. The gastight syringes (Hamilton) were set up in a high-precision syringe pump (NEMESYS, Cetoni GmbH) and connected via PE tubing (Scientific Commodities Inc.) with the microfluidic chip. The background measurements were performed prior to the experiments with pure water in the microfluidic channel under quiescent conditions. The background was measured

Figure 1. (A, B) Schemes of the microfluidic channel and indicated positions of the SAXS scans (x positions along and y positions across the channel) with distances from the channel cross section. The inlets and flow direction are indicated by arrows. (C) Optical microscopy image of the crossing of microfluidic channels. The scale bar is 200 μm, and the color bar denotes a relative linear scale. 12495


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for 30 s. All presented scattering curves in this report are backgroundsubtracted. To align the microfluidic device in the sample environment of the beamline, the pin-diode intensity in front of the detector was monitored while moving the device through the beam path. The motor positions corresponding to positioning the X-ray beam in the center of the microchannel could be followed by an increasing beam intensity measured at the diode due to decreasing chip material in the beam path. With this procedure the motor position corresponding to the beam penetrating the channel walls could be identified along with the positions for the channel cross. Afterward the flow rates were set to 100 μL/h for the main channel (PI-PEG/dioxane-solution) and 400 μL/h for both side channels (water). Figure 1 shows the positions of the X-ray measurements along the microfluidic channel. The first position (x1) was within the main channel with only the polymer dissolved in dioxane. The other measurements were performed in the microfluidic outlet channel (x2− x6). For all scans the distances from the beginning of the channel cross to the position of the scan and are determined on the basis of the motor positions. The structural evolution is followed by scanning different positions (y1, y2,..., y20) across the channel at different downstream positions (x1, x2,..., x6) along the main channel with a 31 × 22 μm2 spot size X-ray beam as shown in Figure 1. Positions y1 and y20 were chosen such that the X-ray beam transects the device between 20 and 40 μm above the upper and between 20 and 40 μm below the lower channel wall. The distance between both positions was always 190 μm. For the scan, a step length of 10 μm (y direction) was chosen that sums up to 20 measurements for each scan, and each adjacent position overlaps by approximately 12 μm. The integration time was 1 s. Static SAXS Experiment. A glass capillary (Ø 2 mm, Müller & Müller OHG Glasbläserei, Germany) was filled with ca. 0.5 mL of PIPEG dissolved in dioxane (20 wt %) and then carefully topped with the same amount of water to achieve a visible interface between both solutions. The capillary was stored for 3 days for equilibration and interdiffusion until it was measured via SAXS. Here, a detector distance of 900 mm was chosen. The scan was performed with 500 μm steps over an overall range of ca. 55 mm. The beam spot size was set to approximately 100 μm. The integration time for each sample measurement as well as for the background measurement, which was carried out with solely water in a separate capillary, was 20 min.

Figure 2. Scheme of experimental and molecular length and time scales of the microfluidic experiment. The red rectangle indicates the window of temporal and spatial resolution. The time/distance values for downstream channel positions x1−x6 and cross-sectional positions y1−y20 are shown.

process for the interdiffusion of the binary solvent system water/dioxane. The corresponding diffusion coefficient depends on the solvent ratio and the solvent concentration. For further calculations, we assume a value of D11 = 4 × 10−9 m2/ s.23 We further assume the polymer or micellar diffusion to be at least 2 orders of magnitude smaller, taking a value of D22 = 1 × 10−11 m2/s. This is based on the estimation that a solvent (water) molecule has a diameter of ∼0.3 nm, whereas the PIPEO micelles have a diameter of ∼50 nm using the measured micellar distance values a from Table 1. Table 1. Overview over Scan Positions x1−x6 (Lateral Position y10 Always) with the Distance d from the Beginning of the T Junction to the Position of the Measurement and with Δt, the Corresponding Averaged Flow Time of the Solutionsa

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RESULTS AND DISCUSSION Experimental Time Scales. The microfluidic/SAXS setup determines the two limiting time scales of the experiment, i.e., its time resolution tmin and the maximum residence time tmax. The time resolution of the experiment is given by the spot size Δxspot of the X-ray beam, and the flow rate of the stream, ν, is given as tmin = ((Δxspot)/v). From the volumetric flow rate of Q = 900 μL/h, the channel width w = 110 μm, and the channel height h = 115 μm, we calculate an average flow velocity of v = (Q/wh) = 19.8 mm/s. For a spot size of Δxspot 31 μm, this results in a time resolution of tmin = 1.6 ms. The maximum residence time in the channel is given by the channel length l = 31 mm and the flow velocity as tmax = l/v = 1.6 s. Only processes that occur in the tmin = 1.6 ms ≤ t ≤ tmax = 1.6 s time window can be followed in the experiment. These time limits are indicated in Figure 2. Interdiffusion. Because flow in microfluidic channels is laminar, diffusion is the only mixing process. For a ternary system such as water/dioxane/polymer, thermodynamically one has to consider four independent diffusion coefficients Di,j (i, j = 1, 2) that determine diffusional transport. The description can be simplified in our case because the solvent molecules have much faster mobilities compared to the block copolymers or the block copolymer micelles. For the estimation of the relevant time scales, we consider it to be the fastest

D (mm) Δt (ms) N f χ Rg (nm) a (nm) Δ (nm) σa (nm) Rc (nm)

x1

x2

x3

x4

x5

x6

0 0 502 0.0474 0.555 8.70

0.5 25 515 0.049 0.514 9.80

1.0 50 515 0.049 0.514 10.8 45.2 113 3.94 8.94

3.1 156

13 656

22.8 1150

43.3 160 2.04 8.8

43.7 180 2 8.6

49.9 219 3.89 7.8

a Also given are the results of the fits to eq 3 and an FCC structure, i.e., degree of polymerization N, molar fraction f, Flory−Huggins interaction parameter χ, radius of gyration Rg, unit cell size a, ordered domain size Δ, average deviation from lattice position σa, and micellar core radius Rc. For position x3, both fits were performed (Figure 3C).

Diffusion vs Convective Transport in the x Direction. In the microfluidic channel, we have convective transport by pressure-driven flow with a flow velocity v and the diffusional transport of solvent molecules and polymer assemblies characterized by diffusion coefficients Dij. A measure of the relative magnitude of convective and diffusional transport is given by the Péclet number Pe = ((Δxv)/D). For a flow 12496


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Figure 3. (A) Sets of SAXS measurements recorded at six downstream positions x1−x6. Each set consists of 20 scattering curves obtained upon scanning across the microchannel from position y1−y20 at each downstream position with a step length of Δy = 10 μm. The arrows indicate the set of scattering curves measured within the central polymer stream. (B) Two-dimensional scattering patterns measured at six downstream positions x1−x6 in the middle of the measurement range (y10), indicated in red in panel A. (C) The same data as azimuthally averaged curves (squares) together with fitted curves. Dotted curves are fits to eq 3, and solid curves are fits to an FCC lattice.

velocity of ν = 19.8 mm/s, a spatial resolution of Δx = 31 μm, and the solvent interdiffusion coefficient of D11 = 4 × 10−9 m2/ s, Pe = 153. The Péclet number is even larger when considering micellar diffusion. Thus, within experimental resolution the transport in the x direction downstream from the channel is completely determined by the flow velocity. Diffusion vs Convective Transport in the y Direction. Because there is no velocity component in the y direction perpendicular to the flow direction, transport in this direction is completely determined by diffusion. With the mean square displacement in the y direction given by Δy = (2Dt)1/2, solvent diffusion in the y direction across half of the microfluidic channel, i.e., a distance of Δy = w/2 = 55 μm, will have occurred after a time t = 0.38 s, which at a flow velocity of ν = 19.8 mm/s corresponds to a downstream distance of Δx = νt = 7.5 mm. This means that complete diffusional mixing in the flow-focusing experiment resulting in a homogeneous solvent mixture across the channel will have occurred after this distance, i.e., between downstream positions x4 and x5 (Figure 1). Polymer or micelle diffusion across the channel will be only

a few micrometers over the whole experimental time scale. Thus, we would expect the solvents to reach homogeneous composition by interdiffusion ca. 9 mm downstream from the channel with respect to the T junction, whereas the polymer chains and their assemblies would be expected to be localized in the center stream. These are favorable and simple conditions for the kinetic mixing experiment. Mean Times after Mixing. Because of the laminar flow in a microfluidic channel, the time axis of any given reaction or mixing process can be mapped on different downstream positions x. With the average velocity v, each downstream position can be transformed to a certain time t after mixing. Table 1 and Figure 2 show the data for the distance between the channel cross and the position of the measurements, and the corresponding time of the kinetic process. Figure 2 gives an overview over experimental and molecular time and length scales. The experimental window is determined by the beam spot size and the channel length, which together with the flow velocity determine the time resolution and the maximum residence time. The channel width together with the 12497


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diagram in Figure 3A. For each given downstream position x1− x6, it shows a set of μSAXS curves for all cross-sectional positions y. For peripheral positions y1, y2,..., y20 we observe featureless scattering curves corresponding to positions where the X-ray beam transects the microfluidic chip without passing the microchannel. Measurements transecting the microchannel walls often exhibit excess low-angle scattering intensity due to reflections. For all inner-channel positions y, we observe either broad peaks as in position x1 or sharp Bragg peaks as in positions x2−x6. For the first downstream positions x2−x4, the intensity of the Bragg peaks is weaker in the middle of the channel because water has not yet diffused to this position to induce pronounced ordering, which already has occurred at the periphery of the polymer stream, where there is direct contact between dioxane and water. Already at position x2 at the polymer stream periphery, higher-order peaks can be clearly observed, gaining in intensity further downstream from the channel. At position x4, only slight differences in the SAXS curves over the channel cross section are visible. At subsequent positions x5 and x6, there are no differences between the scattering curves across the microchannel, indicating a homogeneous mixed solvent composition across the channel. This is in agreement with our estimate based on the diffusion coefficients of the solvents and the average flow rate that complete mixing would be expected at a position 8 mm after the T junction, which is between positions x4 (3.1 mm) and x5 (12.9 mm). After that position, the structural changes of the lyotropic phase are mainly driven by domain growth and shear alignment. At position x6, a well-defined oriented FCC phase has been formed across the whole channel. Figure 3C shows the scattering curves obtained by azimuthally averaging the scattering patterns shown in Figure 3B. From bottom (x1y10) to top (x6y10), we observe a shift of the main peak from a q value of 0.31 nm−1 to 0.22 nm−1. There is a development of higher-order peaks at positions further downstream from the channel, indicating the formation of a well-defined FCC phase. The broad peak observed at position x1 before mixing at the T junction can be nearly quantitatively described by a Leibler-type structure factor, indicating weak segregation of the block copolymer chains in the solvent.24 The scattering intensity for this case is given by

interdiffusion time of the solvents determines the mixing time. Within the experimental window (red rectangle), convective transport, which is determined by the straight line (“flow”), is always much larger than the diffusive transport of either solvent, polymer, or micelles. Thus, for any downstream transport in the x direction the Péclet numbers are Pe ≫ 1. In Figure 2 also, downstream scanning positions x2−x6 and cross-stream scanning positions y1−y20, for which their x range corresponds to the time resolution, are indicated. Experimental Time Scales and Molecular Processes. Mixing experiments in microfluidic channels occur on very fast time scales because the concentration gradients can be regulated to be very high. When hydrodynamic flow-focusing is used, nearly step-function-like concentration profiles can be generated. This leads to very fast concentration changes following Fick’s second law:

∂c ∂ 2c =D 2 ∂t ∂y

(1)

Assuming that the concentration profile c(y) can be approximated by an error function, the first derivative ∂c/∂y is a Gaussian and the second derivative is given by ∂ 2c(y , t ) ∂y 2

=−

⎡ y2 ⎤ ⎢− 2 ⎥ exp 2π σ 3 ⎣ 2σ ⎦ y

(2)

It follows that in a given volume element the concentration changes with time proportionally to σ−3. Thus, decreasing the width by a factor of 10 increases the concentration gradient within a given time interval by a factor of 1000. In our case, this is used to generate a concentration-induced rapid deep quench from a homogeneous equilibrium state to an unstable or metastable postquench state, which evolves along a topological path through a sequence of structures, finally reaching the microphase-separated equilibrium state. Relevant molecular dynamic processes involve, in order of increasing relaxation times, (1) solvent interdiffusion, (2) local motions of polymer segments (β relaxation), (3) the diffusion of single polymer chains in pure dioxane, (4) the diffusion of micelles in dioxane/water mixtures, (5) the mobility of micelles in the lyotropic phase (α relaxation), and (6) large-scale liquidcrystalline domain reorientations induced by shear. If topological rearrangements or transitions toward the equilibrium structure during the fast microfluidic experiment involve some of the slower, more cooperative processes, then metastable states could be trapped. Measured SAXS Patterns and Scattering Curves. Figure 3 shows sets of measured SAXS patterns and scattering curves at the six downstream positions x1−x6 in the microfluidic channel. Each set represents a y scan across the microchannel consisting of 20 individual measurements with a step length of Δy = 10 μm. In Figure 3B, the scattering patterns measured in the middle of the channel (y10) for each of the six scans are shown as an example. The first measurement (x1y10) corresponds to the pure polymer−dioxane solution before the T junction. It already shows a weak Debye−Scherrer ring indicating weak microphase separation. After mixing in the T junction, a pronounced sharpening of the Debye−Scherrer ring is observable. Further downstream, more highly ordered peaks develop, indicating the formation of a lyotropic liquidcrystalline micellar phase. To facilitate further discussion, we consider the azimuthally averaged scattering curves, which are displayed in a waterfall

S(q) =

N F(x) − 2χN

(3)

with χ being the Flory−Huggins interaction parameter characterizing the effective interaction between both monomer groups and N being the degree of polymerization. For function F(x) =

g (1, x) 1

g (f , x) g (1 − f , x) − 4 [g (1, x) − g (f , x) − g (1 − f , x)]2 (4)

x = qRg, with Rg being the radius of gyration, f being the fraction of monomer A in the chain, and g( f, x) being the Debye function given by g( f, x) = ((2( f x + e−fx − 1))/x2). Fits of eq 3 to the measured scattering curves yielded values, nearly independent of the downstream position, of N ≈ 500, f ≈ 0.05, and χ ≈ 0.5 with a systematically increasing value of the radius of gyration from Rg = 8.7 nm at position x1, to Rg = 9.8 nm at position x2 to Rg = 10.8 nm at position x3, corresponding to the systematic shift of the peak position to 12498


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Figure 4. (A) Orientation of the FCC lattice in the microfluidic channel. Indicated in gray are the {111} layers of hexagonally close-packed micelles, which orient with their ⟨110⟩ direction, which is the direction of highest line density, parallel to the flow direction v. The X-ray beam is parallel to the ⟨110⟩ direction. (B) Calculated scattering patterns for the three relevant orthogonal projections of the FCC lattice. There is very good agreement between the calculated 6-fold-symmetric [111] scattering pattern and the observed scattering patterns in Figure 3B.

proportional to the viscosity ratio, η, and the volumetric flow ratio, Q:

lower q values. The fitted parameters are summarized in Table 1. The values obtained from the fits are not expected to be quantitatively correct but to be in a reasonable range with correct systematic changes. For example, the obtained N values are in quite good agreement with the actual degree of polymerization. The fitted f values are in a reasonable range, with the degrees of polymerization of NPI = 120 and NPEO = 394 and a fitted value of f PI = 0.049 that we would calculate for the number of solvent molecules per polymer chain NS = 1900, which corresponds to a 5-fold swelling of the PEO-micellar volume upon mixing with water. From the literature,25 we find that the Rg value for polyisoprene in dioxane with NPI = 514 is 5.9 nm, which is also in a reasonable range compared to the fitted values in Table 1 considering that PEO has a longer persistence length. Beginning at position x3, the peak develops higher-order features indicating the formation of ordered micellar assemblies. These additional features can be accounted for by assuming the micelles to be arranged on an FCC lattice (space group Fm3n). Beginning at position x4, sharp higher-order reflections can be observed. The measured scattering curves can be quantitatively fitted to the structure factor of an FCC lattice. The assumed models and fitting functions are derived and discussed in detail in refs 26−28. Peak sharpening proceeds further at positions x5 and x6. The fit parameters are summarized in Table 1. We observe the unit cell dimension to increase from a = 43 nm at position x4 to a = 50 nm at position x6, corresponding to a shift of the first-order reflection to lower q. The average ordered domain size increases from D = 100 to 220 nm corresponding to the sharpening of the reflections. The Debye−Waller factor describing the relative average deviation of the micellar positions from the lattice points is in the range of 5% of the unit cell dimension, indicating very good ordering of the micelles within the FCC lattice. The micellar core radius is in the range of the radius of gyration, determined at positions x1 and x2, and is systematically decreasing from values of Rc = 8.9 to 7.8 nm as a result of the deswelling and segregation of the micellar core for more water-rich solvent mixtures. Central Stream Dimension. From the intensity of the measured scattering curves across a y scan (Figure 3A), we estimate a center polymer stream width of ∼90 μm, which is quite broad considering the total width w of 110 μm of the channel. The relatively large diameter results from the higher viscosity of the center stream. It follows from the hydrodynamic relation that the diameter ratio of two merging streams, where 1 is the central stream and 2 is the focusing side stream, is

η Q d1 = 1 1 d2 η2 Q 2

(5)

Thus, a quite viscous central stream, as in our case, can have large diameters even if the side stream has a higher velocity, as is the case in our experiment.29,30 Shear Orientation of the FCC Phase. Beginning at position x4, there is a homogeneous solvent composition across the channel. All subsequent structural changes are then shearinduced. The observed scattering patterns at positions x4 and x5 clearly show alignment and lattice orientation. We observe sharp Bragg reflections with 6-fold rotational symmetry. The innermost hexagon comprising the 111 reflections has its vertices on the meridian, indicating a shear orientation of the FCC crystal as shown in Figure 4. This is in line with the known shear orientation of FCC lattices that orient such that the ⟨110⟩- direction, i.e., the line of highest micellar density, is parallel to the flow direction.31 The observed scattering pattern is in good agreement with a calculation shown in Figure 4B, showing the characteristic 6-fold symmetry of the scattering pattern expected if the X-ray beam is parallel to the ⟨111⟩ direction. The calculation of the scattering patterns in Figure 4 has been outlined in detail in refs 28 and 31 Comparison of Ultrafast and Slow Interdiffusion Experiments. A rapid, deep quench is expected to lead to an unstable state that structurally evolves via spinodal decomposition. Indeed, we observe a characteristic broad peak in the initial scattering curves, which gains in intensity and shifts to lower q values as known for spinodal phase separation. There the system develops composition fluctuations on a certain length scale that grow in amplitude, finally developing sharp interfaces separating adjacent microphases. If the system had been quenched to a metastable state, then further structural evolution would have proceeded via nucleation and growth with the initial development of segregated domains with sharp interfaces. In the initial scattering curves, we observe no structural features other than the broad main peak and therefore there no indications for the formation of strongly segregated domains. Only at a later stage during the disorder/ order transition are such domains formed, as signaled by clearly observable domain form factor oscillations in the scattering curve. At subsequent times, the observed peak sharpens and develops higher-order reflections indicating the disorder/order transition. At still later time scales >100 ms, we observe ordered domain growth and shear-induced orientation of the domains. 12499


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The scattering curves from the slow capillary experiment can be directly compared to the results from the fast microfluidic experiment. As shown in Figure 6, for all scattering curves

With our microfluidic experiment, we could clearly show that the self-assembly occurred synchronously with solvent interdiffusion, and thus is diffusion-limited. To investigate whether the observed fast diffusion-driven structural evolution follows a topological path corresponding to a set of equilibrium structures at the same solvent composition, without the formation of metastable states, we performed an interdiffusion experiment on much slower time scales, i.e., after 3 days of equilibration. In this experiment, a 20 wt % polymer/dioxane solution was brought into contact with water within a 2-mm-thick glass capillary and equilibrated over 3 days. The capillary setup and the measured scattering curves are shown in Figure 5. By

Figure 6. Comparison of the scattering curves measured during fast mixing in the center of the microfluidic channel (positions x1−x6, red) and the scattering curves measured over a concentration gradient obtained by slow mixing in a capillary over 3 days (blue). We observe that the scattering curves are very similar for the two experiments in terms of peak positions and releative peak intensities, indicating that during the fast microfluidic experiment the structural evolution proceeds through a topological path that corresponds to a set of near-equilibrium states developed in the slow experiment. The broader Gaussian-shaped peaks observed for the capillary experiments are due to larger peak smearing of the lab-based X-ray-beam compared to the focused synchrotron beam.

Figure 5. (A) Photograph of the capillary, where a PI-PEG/dioxane solution was covered with water to establish a concentration gradient slowly over 3 days. (B) Scattering curves measured over the concentration gradient by scanning with a step width of 500 μm and a spot size of 100 μm over a distance of 55 mm. The scattering curves represent a complete overview of the solution structure from pure water to pure dioxane. We observe the peak positions of the sharp first- and higher-order peaks to be almost constant over a broad range of compositions. The relative intensities of the higher-order peaks change considerably as a result of a decreasing micellar core radius that gives rise to a shift in the first form factor minimum indicated by the dashed line.

measured at positions x1−x6 in the fast microfluidic experiment it is possible to pick a well-matched scattering curve from the slow capillary mixing experiment along the dioxane/water gradient. The pairs of scattering curves show reflections at the same q values. The second- and third-order peak positions, their relative intensities, and the positions of the form factor oscillations are in good agreement. There are differences in the first-order peak shapes because the microfluidic experiments had been performed at a highly collimated microfocus synchrotron beamline, whereas the capillary experiments were performed on our in-house rotating anode source with a larger beam diameter and therefore larger peak smearing at low q values, leading to broader Gaussian-type peaks. From this comparison we conclude that the structural evolution in both sets of experiments, which run along the same composition trajectory in a ternary phase diagram, proceeds along the same topological path. From our observations we conclude that the rapid selfassembly is diffusion-limited, with the assembly step into micelles finished after 100 ms in our experiment. This is considerably faster than recently reported for stopped-flow experiments on the formation kinetics of Pluronic micelles that occurred on time scales of seconds31 but is in good agreement with earlier reports using T-jump experiments on Pluronic micelles.32 The slower kinetics observed in the stopped-flow experiment may be caused by weaker concentration gradients involved during the mixing of the solutions. We further observe that the fast assembly process proceeds via a sequence of structures along a topological path equal to the series of structures that are observed in the much slower close-toequilibrium capillary mixing experiments. This means that all

scanning with the X-ray beam across the concentration gradient that had developed in the capillary after 3 days, we determined the sequence of structures corresponding to the varying solvent composition across the gradient. Concentration gradients in the capillary are established over millimeters, i.e., 3 orders of magnitude larger compared to the microfluidic experiment, where this is established over micrometers. Thus, in the slow experiment even a very slow molecular process can synchronously follow solvent interdiffusion and compositional changes to develop toward its equilibrium structure. Similar to the observation in the microfluidic experiment, we observe a broad peak for the dioxane-rich mixtures indicating weak segregation. This is followed by a disorder−order transition to form an FCC-lyotropic phase indicated by peak sharpening and the development of higher-order reflections. With further increases in the water fraction, the peak position and thus the unit cell size do not change. The intensity changes of the higher-order reflections reflect the decreasing size and segregation (deswelling) of the micellar core. The form factor of the micellar core has a sharp minimum that shifts to higher q (indicated by the dotted line in Figure 5) with decreasing size, and thus extiguishes reflections at this q value. 12500


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In Supramolecular Chemistry from Molecules to Nanomaterials; Gale, P. A., Steed, J. W., Eds.; John Wiley & Sons: Chichester, U.K., 2012; Vol. 2, pp 437−450. (3) Ihee, H. Visualizing Solution-Phase Reaction Dynamics with Time-Resolved X-ray Liquidography. Acc. Chem. Res. 2009, 42, 356− 366. (4) Liu, Y.; Li, M.; Bansil, R.; Steinhardt, M. Kinetics of phase transision from lamellar to hexagonally packed cylinders for a triblock copolymer in a selective solvent. Macromolecules 2007, 40, 9482−9490. (5) Squires, T. M.; Quake, S. R. Microfluidics: Fluid physics at the nanoliter scale. Rev. Mod. Phys. 2005, 77, 977−1026. (6) Stone, H. A.; Stroock, A. D.; Ajdari, A. Engineering Flows in Small Devices: Microfluidics toward a Lab-on-a-chip. Annu. Rev. Fluid Mech. 2004, 36, 381−411. (7) Weiss, T. M.; Narayanan, T.; Gradzielski, M. Dynamics of Spontaneous Vesicle Formation in Fluorocarbon and Hydrocarbon Surfactant Mixtures. Langmuir 2008, 24, 3759−3766. (8) Gummel, J.; Sztucki, M.; Narayanan, T.; Gradzielski, M. Concentration dependent pathways in spontaneous self-assembly of unilamellar vesicles. Soft Matter 2011, 7, 5731−5738. (9) Pappenberger, G.; Saudan, C.; Becker, M.; Merbach, A. E.; Kiefhaber, T. Danaturant-induced movement of the transition state of protein folding revealed by high-pressure stopped-flow measurements. Proc. Natl. Acad. Sci. U.S.A. 1999, 97, 17−22. (10) Abécassis, B.; Testard, F.; Spalla, O.; Barboux, P. Probing in situ the Nucleation and Growth of Gold Nanoparticles by Small-Angle Xray Scattering. Nano Lett. 2007, 7, 1723−1727. (11) Li, W.; Simms, R.; Greener, J.; Jagadeesan, D.; Pinto, S.; Günther, A.; Kumacheva, E. Microfluidic Study of Fast Gas−Liquid Reactions. J. Am. Chem. Soc. 2012, 134, 3127−3132. (12) Brennich, M. E.; Nolting, J.-F.; Dammann, C.; Nöding, B.; Bauch, S.; Herrmann, H.; Pfohl, T.; Kö ster, S. Dynamics of intermediate filament assembly followed in micro-flow by small angle X-ray scattering. Lab Chip 2011, 11, 708−716. (13) Daubersies, L.; Leng, J.; Salmon, J.-B. Steady and out-ofequilibrium phase diagram of a complex fluid at the nanolitre scale: combining microevaporation, confocal Raman imaging and small angle X-ray scattering. Lab Chip 2012, 13, 910−919. (14) Barrett, R.; Faucon, M.; Lopez, J.; Cristobal, G.; Destremaut, F.; Dodge, A.; Guillot, P.; Laval, P.; Masselon, C.; Salmon, J.-B. X-ray microfocussing combined with microfluidics for on-chip X-ray scattering measurements. Lab Chip 2006, 6, 494−499. (15) Trebbin, M.; Steinhauser, D.; Perlich, J.; Buffet, A.; Roth, S. V.; Zimmermann, W.; Thiele, J.; Förster, S. Anisotropic particles align perpendicular to the flow direction in narrow microchannels. Proc. Natl. Acad. Sci. U.S.A. 2013, 110, 6706−6711. (16) Pollack, L.; Tate, M. W.; Darnton, N. C.; Knight, J. B.; Gruner, S. M.; Eaton, W. E.; Austin, R. H. Compactness of the denatured state of a fast-folding protein measured by submillisecond small-angle x-ray scattering. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 10115−10117. (17) Rhiju, D.; Kwok, L. W.; Millett, I. S.; Bai, Y.; Mills, T. T.; Jacob, J.; Maskel, G. S.; Seifert, S.; Mochrie, S. G. J.; Thiyagarajan, P.; Doniach, S.; Pollack, L.; Herschlag, D. The Fastest Global Events in RNA Folding: Electrostatic Relaxation and Tertiary Collapse of the Tetrahymena Ribozyme. J. Mol. Biol. 2003, 332, 311−319. (18) Buffet, A.; Rothkirch, A.; Döhrmann, R.; Körstgens, V.; Abul Kashem, M. M.; Perlich, J.; Herzog, G.; Schwarzkopf, M.; Gehrke, R.; Müller-Buschbaum, P.; Roth, S. V. P03, the microfocus and nanofocus X-ray scattering (MiNaXS) beamline of the PETRA III storage ring: The microfocus endstation. J. Synchrotron Radiat. 2012, 19, 647−653. (19) Min, K.-I.; Lee, T.-H.; Park, C. P.; Wu, Z.-Y.; Girault, H. H.; Ryu, I.; Fukuyama, T.; Mukai, Y.; Kim, D.-P. Monolithic and Flexible Polyimide Film Microreactors for Organic Microchemical Applications Fabricated by Laser Ablation. Angew. Chem., Int. Ed. 2010, 49, 7063− 7067. (20) Cordovez, B.; Chung, A. J.; Mak, M.; Erickson, D. A novel polymer microneedle fabrication process for active fluidic delivery. Microfluid. Nanofluid. 2011, 10, 785−791.

structural rearrangements of the polymer chains necessary to microphase separate into micelles and subsequently to localize the micelles in an FCC lattice are sufficiently fast either to occur synchronously with or immediately after solvent interdiffusion. For highly mobile polymer chains having a low glass-transition temperature, such as polyisoprene, this could have been expected. The situation may be different for high-Tg polymers with much more restricted chain mobility or if largescale cooperative motions of polymer chains localized in strongly segregated interfaces would have been required, such as in structural transitions from spheres to cylinders or lamellae. As we observe, structural rearrangements over longer distances, such as for the shear orienation of domains, indeed require longer time scales as we observe for positions x4 (>100 ms) and later.

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CONCLUSIONS AND OUTLOOK We find that the combination of microfocus small-angle X-ray scattering and microfluidics is a very promising technique for investigating fast self-assembly processes. In microfluidic laminar flows, the temporal structural evolution during the process can be mapped onto different positions in the downstream microchannel to realize millisecond time resolution. When investigating the micelle formation of an amphiphilic block copolymer induced by the addition of a nonsolvent, we observe a self-assembly sequence where within milliseconds structures evolve via spinodal microphase separation into micelles followed by a disorder/order transition into an FCC liquid-crystalline phase with late-stage domain growth and shear-induced domain orientation into a mesocrystal. A comparison with a slow macroscopic near-equilibrium kinetic experiment shows that the fast structural transitions follow a direct pathway to the equilibrium structure without the trapping of metastable states. Thus, the combination of microfluidics and micro-X-ray scattering represents a new and powerful experimental tool for studying very fast structural rearrangements on the nanoscale and mesoscale.

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ASSOCIATED CONTENT

S Supporting Information *

Preparation of microfluidic devices and an X-ray-transparent, all-polyimide microfluidic device. SEM image of the channel cross section. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was supported by an ERC Advanced Grant STREAM (no. 291211). We thank UBE Industries for the Upilex VT film samples and Dr.-Ing. Jaroslaw Kita (Functional Materials, Prof. Dr.-Ing. Moos, University of Bayreuth) for the UV laser cutting. S.Y. acknowledges the Knut and Alice Wallenberg Foundation for its kind financial support.

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REFERENCES

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