3D Micromachined Polyimide Mixing Devices for in ... - ACS Publications

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Interface Components: Nanoparticles, Colloids, Emulsions, Surfactants, Proteins, Polymers

3D-Micromachined Polyimide Mixing Devices for in situ X-ray Imaging of Solution-based Block Copolymer Phase Transitions Mohammad Vakili, Stefan Merkens, Yunyun Gao, Paul V. Gwozdz, Ramakrishna Vasireddi, Lewis Sharpnack, Andreas Meyer, Robert H. Blick, and Martin Trebbin Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.9b00728 • Publication Date (Web): 18 Jul 2019 Downloaded from pubs.acs.org on July 19, 2019

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3D-Micromachined Polyimide Mixing Devices for in situ X-ray Imaging of Solution-based Block Copolymer Phase Transitions Mohammad Vakili,a Stefan Merkens,a Yunyun Gao,a,b Paul V. Gwozdz,c Ramakrishna Vasireddi,a Lewis Sharpnack,d Andreas Meyer,e Robert H. Blick,c,f Martin Trebbina,g,* a Centre for Ultrafast Imaging (CUI), University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany b Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany c Center for Hybrid Nanostructures (CHyN), University of Hamburg, Luruper Chaussee, 22761 Hamburg, Germany d Beamline ID02, European Synchrotron Radiation Facility (ESRF), 71 Avenue des Martyrs, 38043 Grenoble, France e Institute for Physical Chemistry, University of Hamburg, Martin-Luther-King Platz 6, 20146 Hamburg, Germany

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f Department of Materials Sciences and Engineering, University of Wisconsin- Madison, 1500 University Ave., Madison, Wisconsin 53706, USA g Department of Chemistry, BioXFEL, RENEW and Hauptman-Woodward Medical Research Institute (HWI), State University of New York at Buffalo, 760 Natural Sciences Complex, Buffalo, New York 14260-3000, USA *Corresponding author KEYWORDS. Microfluidics, Polyimide, 3D Flow-Focusing, Block Copolymers, Micelles, Xray Scattering, Self-Assembly, Time-Resolved ABSTRACT. Advances in modern interface- and material sciences often rely on the understanding of a system’s structure-function relationship. Designing reproducible experiments that yield in situ time-resolved structural information at fast time scales are therefore of great interest, e.g. for better understanding the early stages of self-assembly or other phase transitions. However, it can be challenging to accurately control experimental conditions, especially when samples are only available in small amounts, prone to agglomeration or if X-ray compatibility is required. We address these challenges by presenting a microfluidic chip for triggering dynamics via

rapid

diffusive-mixing

for

in

situ

time-resolved

X-ray

investigations.

This

polyimide/Kapton®-only-based device can be used to study the structural dynamics and phase transitions of a wide range of colloidal and soft matter samples down to ms-time scales. The novel multi-angle laser ablation 3D-microstructuring approach combines, for the first time, the highly desirable characteristics of Kapton (high X-ray stability with low background, organic solvent compatibility) with a 3D flow-focusing geometry that minimizes mixing dispersion and wall agglomeration. As a model system, to demonstrate the performance of these 3D-Kapton


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microfluidic devices, we selected the non-solvent-induced self-assembly of biocompatible and amphiphilic diblock copolymers. We then followed their structural evolution in situ at ms-time scales using on-the-chip time-resolved small-angle X-ray scattering (TR-SAXS) under continuous flow conditions. Combined with complementary results from 3D finite-element method computational fluid dynamics (FEM-CFD) simulations, we find that the non-solvent mixing is mostly complete within a few tens of milliseconds, which triggers initial spherical micelle formation, while structural transitions into micelle lattices and their deswelling only occurs on the hundreds of milliseconds to second time scale. These results could have important implication for the design and formulation of amphiphilic polymer nanoparticles for industrial applications and their use as drug delivery systems in medicine.


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INTRODUCTION Small-angle X-ray scattering (SAXS) is a powerful method to investigate the structure, interactions and structure-formation mechanisms of nanoscaled systems such as block copolymer nanoparticles.1 With the increasing availability of X-ray sources with high peak brilliance and high photon flux (e.g. at synchrotrons), an ongoing sample renewal becomes increasingly important to avoid radiation-induced damage to the sample. One way to minimize the absorbed X-ray dose and radiation damage is through the continuous sample replenishment provided by microfluidic devices. Furthermore, microfluidic sample environments enable precise control over fluids on the nanoliter scale which ensures low sample consumption and promotes fast diffusive mixing.2–6 Fast and controlled diffusion is essential when it comes to the systematic analysis of mixing-induced reaction kinetics and structural dynamics.7 Since the continuous flow (maintained by a constant flow velocity) ensures steady-state-like conditions, each position along the flow direction corresponds to a specific time in the channel orthogonal to the flow direction.8 Therefore, microfluidics in combination with micro-focused X-rays allows for time-resolved studies that can unravel fast structural transitions of fluid samples.9,10 In contrast to stopped flowor static diffusion measurements,11 where time resolution is dictated by the minimal exposure times and data collection rate, continuous flow microfluidics typically allows for much higher time resolutions down to the sub-ms regime since they are only limited by the beam size of the probe (usually several micrometers) and flow velocity of the fluid (typically several tens of mm s-1).12,13 However, the fabrication of microfluidic devices is usually time- and material consuming and such devices often lack important features such as low and non-degrading X-ray scattering background, solvent resistance or 3D flow-focusing.14 So far there are only a few materials


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known which meet these requirements. The thermoplastic TOPAS®

COC (cyclic olefin

copolymer) is one of these materials, however, it is not very stable at high temperatures (depending on the grade it degrades between 78-134 °C15) and is not compatible with THF. Kapton® polyimide is an excellent candidate which has been applied in a number of X-ray experiments.2,12,13,16–19 By using this extremely inert polyimide, its vacuum-compatibility and thermal stability (Kapton® HN degrades at ca. 230 °C) can be exploited to fabricate highly robust microfluidic devices. Moreover, Kapton has a steady X-ray background signal20 and is resistant towards organic solvents.21 Furthermore, Kapton allows for surface modifications.18 Linking functional groups to the surface not only changes the wettability, but can also be used to promote adhesion to other materials.22 In order to seal microstructured Kapton with plain Kapton windows, the silane-coupling approach can be applied.23 Although Kapton is not malleable like common microfluidic device materials such as PDMS (poly(dimethylsiloxane))24 or COC,25 it can be rapidly microstructured using pulsed laser ablation.26,27 This reproducible top-down method follows the ‘rapid prototyping’ scheme known from soft lithography28 as it allows one to design a structure, fabricate it, test it and rapidly create the next refined iteration to obtain incrementally improved devices on the path towards highly optimized device geometries.29 While there have been examples for rapid mixing continuous flow devices for time-resolved Xray studies, most of these devices only use lateral (or 2D) flow-focusing from the side channels which can easily lead to agglomerations of the sample at the channel walls.19 Additionally, pressure-driven flows in microchannels are usually laminar and a parabolic flow profile can be observed due to the no-slip condition.30 As a result, species flowing near the wall have a higher residence time (promoting agglomeration) compared to those flowing in the center which leads to an inhomogeneous mixing known as Taylor dispersion. However, 3D hydrodynamic flow-


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focusing minimizes this dispersion effect as it positions the species in the center of the 3D parabolic flow profile where the velocity mismatch between fluid layers is minimal. Such a 3D flow-focusing can, for instance, be realized via sheath flow geometries where the flows from side channels completely surround the stream incoming from a centrally-positioned sample inlet. While such geometries have already been realized via multi-layered soft lithography, e.g. based on poly(dimethylsiloxane) (PDMS) or Nordland Optical Adhesive 81 (NOA81),12,31 their use with organic solvents or exposure to X-rays is very limited.19 These shortcomings could be overcome by a Kapton-only-based microfabrication approach, but so far there are no examples of such devices with 3D flow-focusing in literature. Herein, we report a novel laser micromachining procedure that is cost-efficient, semi-automated and reproducible. It involves laser ablation from multiple angles on a flexible Kapton foil which results in the convenient incorporation of a small, centered 3D flow-focusing inlet pore that connects the main channel with the T-shaped mixing region as shown in Figure 1. Hereby, the incoming focused sample stream has initially no wall contact, efficiently preventing (radiationinduced) wall agglomeration and a more uniform mixing is enabled as described above.32 As a case study, we used our 3D flow-focusing microfluidic platform for a time-resolved SAXS study to investigate the amphiphilic diblock copolymer phase transitions from relaxed dissolved polymer chains to spherical micellar assemblies. Such block polymer nanostructures belong to most widely studied systems in soft matter sciences33 and offer great possibilities in pharmaceutical applications due to their drug encapsulation properties among others.34–36 Therefore, knowledge on their phase transitions is essential for tailoring efficient drug encapsulation vehicles. Here, as a self-assembly model system, biocompatible poly(N,Ndimethylacrylamide)-poly(2-methoxyethyl acrylate) (PDMAm-PMEA) diblock copolymers were


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investigated, which were synthesized via RAFT (reversible addition-fragmentation chain transfer) aqueous dispersion polymerization.37 This synthetic route relies on the use of a hydrophilic polymer (here: PDMAm) that allows for chain-extension with a second charge of monomer (here: MEA). Hence, the resulting diblock copolymers self-assemble into selfstabilized nano-objects such as spherical micelles, and, most importantly do so in the absence of additional surfactants used in classical emulsion polymerization. The polymerization proceeds from a monomer-in-water dispersion, where the monomer (MEA) is initially water-soluble, but becomes water-insoluble upon chain-growth. The block length (degree of polymerization) of the hydrophilic block (PDMAm) and the hydrophobic block (PMEA) were targeted to be in the same magnitude in order to facilitate spherical micelles in water. Besides spheres, other morphologies such as cylindrical micelles (‘worms’) and vesicles can be obtained by pursuing larger solvophobic block lengths.38 For the SAXS-based study under flow, the finished and purified diblock copolymers were dissolved in THF and flow-focused with water (a non-solvent for poly(MEA)) to trigger the formation of micelles. While With et al.17 and Fürst et al.39 performed analogous experiments, the first one used a conventional 2D flow-focusing Kapton device while the latter one used a soft lithographic 3D-SIFEL pre-mixer connected to a quartz capillary at which the sample was probed with X-rays. To our knowledge, the results presented here provide the first description of a solvent and X-ray resistant microfluidic device with full 3D flow-focusing allowing for on-chip in situ X-ray probing of the entire mixing process.


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EXPERIMENTAL Chemicals and Materials Acetone, isopropanol, methanol, tetrahydrofuran (THF) and ethanol were purchased from Roth. (3-aminopropyl)trimethoxysilane (97%, APTMS), (3-glycidyloxypropyl)trimethoxysilane (98%, GPTMS) were purchased from Sigma-Aldrich. Kapton® HN foils of 125 µm thickness were purchased from Detakta. Kapton® HN foils of 25 µm thickness were purchased from Müller Ahlhorn. PEEK NanoPort connectors, tubings and fittings, ferrules (product code N-333) as well as Perlast® perfluoroelastomer (FFKM) gaskets were purchased from IDEX. The synthesis of the poly(N,N-dimethylacrylamide) macro-RAFT agent is described elsewhere.40

Characterization Methods 1H-NMR

spectra were recorded on a 400 MHz Bruker Avance-400 spectrometer using

deuterated solvents (chloroform-D, acetone-D6, deuterium oxide) and tetramethylsilane (TMS) as the internal standard. Molecular weight distributions were determined by gel permeation chromatography (GPC) using N,N-dimethylformamide (DMF) as eluent. The measurements were performed on a custom-made chromatograph consisting of a SpectraSystem AS100 autosampler, a SpectraSystem P1000 pump injection module, a combination of two MZ gel SDplus pre-columns (50 Å, 100 Å) and a MZ gel 5 µm SDplus column (MZ-Analysentechnik) equipped with a Merck LaChrom L-7490 refractive index detector. DMF was used as eluent at 60 °C and a series of near-monodisperse poly(methyl methacrylate) standards were used for calibration. The flow rate was 1 mL min-1. For the mobile phase, polymer solutions (1% w/v) were prepared in DMF (containing 10 mmol L-1 LiBr). Differential scanning calorimetry (DSC) of solid state polymers (ca. 5 mg) was performed on a DSC1 device by Mettler Toledo. Glass


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transition temperatures (Tg) were determined at a heating rate of 10 K min-1 over three heating/cooling cycles. Data were evaluated using the STARe 15.0 thermal analysis software. Mass density of solid state polymers (ca. 4 mg) was determined using an AccuPyc 1330 helium pycnometer (Micrometrics) and averaged over 10 runs. The intensity-average hydrodynamic diameters (Dh) of the block copolymers were determined using a Malvern Zetasizer NanoZS dynamic light scattering (DLS) instrument at 25 °C. Aqueous dispersions of 0.2 wt% were analyzed using disposable polystyrene cuvettes while quartz cuvettes were used for THF solutions and data were averaged over three consecutive runs each consisting of ten measurements of ten seconds. The denoted standard deviation is the square root of the dispersity index times the mean diameter. Scanning electron microscopy (SEM) images were taken with a ZEISS Crossbeam 550 with Gemini II optics. To increase contrast, the polymeric samples were sputtered with gold atoms to yield a ca. 40 nm-thick conductive layer. Optical microscopy images were taken with a Nikon D5300 camera on an IX73 optical microscope by Olympus.

Microfluidic Device Fabrication Laser micromachining. Kapton® HN polyimide foils of 125 µm thickness were first rinsed with isopropanol, then with water and afterwards dried in an oven at 75 °C before use. Using Scotch®tape, the foils were fixed to a small metal plate and mounted on the x-y stage of the laser micromachining system (Optec MM200-FLEX). This system was equipped with an ArF excimer laser (ATLEX300i) by ATL Laser Technologies which provides 6 ns pulses with a wavelength of  = 193 nm. The best laser ablation results for smooth microchannel surfaces have been observed at a pulse energy of 11 mJ/pulse with a repetition rate of 200 Hz. Similarly to the approach described by Barrett et al.,26 the depth of the microchannel was controlled by the


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number of pulses where, in our case, 1000 pulses per spot were sufficient to completely write through a 125 µm-thick Kapton foil. The control software Optec Process Power (ver. 1.0) translated a DWG file (designed with AutoCAD 2016) into the laser beam trajectory to write the microchannel geometry where the 120 µm-wide laser spot determined its width. The 3D-microstructuring process was achieved by splitting the writing process into two steps as illustrated in Figure 1A. First, the main channel (MC), side channels (SC) and mixing channel (MxC) were written as a sequence of polylines onto the flat substrate. Here, a circular-shaped beam was chosen to write the microchannels with a width of 120 µm, therefore, yielded an almost quadratic cross-sectional area. Then, the polyimide foil was bent to form an arc in order to access the 125 µm-thick Kapton edge face-on as indicated in Figure 1A (right). This orientation towards the laser beam was achieved by using Scotch®-tape and a small metal block as a temporary support structure. Through the in-line microscope camera view of the laser ablation instrument, the position for the MC inlet channel circular pore (50 µm diameter, theoretically tunable down to 3 µm, Figures 1B,D) was chosen to conform a T-shaped flowfocusing region where pore was centered in the 125 µm deep mixing channel (Figure 1E). After laser writing, the micromachined foil was sonicated in acetone for 10 min to remove any Kapton debris from the surface.


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Figure 1. (A) Schematic representation of the 3D laser ablation route for a Kapton mixing channel with indicated laser pulses (red cone) writing direction and flow direction (black arrow) as well as channel allocation (SC = side channel, MC = main channel, MxC = mixing channel). (B-E) optical microscopy/SEM images featuring different views of the laser structured device with a 50 µm pore: (B) face-on-view of the pore, (C) top-view of the mixing region with indicated flow direction (black arrows), (D) perspective view of the pore connecting the MxC with the MC and (E) perspective view of the T-shaped mixing cross looking downstream (flow direction is indicated with white arrows).

Silane-coupling for device bonding. The microstructured foil containing the channel was sealed with 25 µm-thick Kapton® HN foils through strong amine-epoxy bonds.23 Figure 2 shows a schematic representation of this procedure. To access the inlets of the mixing channel, 2 mm-


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wide holes were cut in one foil using a hollow metal puncher. Afterwards, all layers were rinsed with isopropanol and dried with pressurized air. Then, they were treated in a low-pressure plasma chamber (ATTO by Diener Electronic). Plasma activation occurred at 50 W using air as a process gas at a pressure of 0.38 mbar for 10 min in order to generate reactive hydroxyl groups on the surfaces. The Kapton® HN foils as window material and the microstructured device were then immediately immersed in aqueous solutions (8 wt% in a 1:1(v/v)-mixture of water:methanol)

of

APTMS

((3-aminopropyl)trimethoxysilane)

or

GPTMS

((3-

glycidyloxypropyl)trimethoxysilane), respectively. The surface functionalization occurred at room temperature under stirring for 1 h. Afterwards, the functionalized foils were dried under a stream of nitrogen and then pressed together mechanically. Excess solvent was removed by doctor blading the assembly between a cleanroom cloth envelope. The compressed Kapton sandwich, embedded in two cloth-covered glass slides compressed by a weight, was cured in an oven at 90 °C overnight to ensure a tight bonding between the Kapton foils yielding closed microchannels.

Figure 2. Schematic representation of the silane-coupling bonding route for microfluidic devices, here exemplarily shown for polyimide-based devices: Surface activation and hydroxylation of the foils by air plasma treatment is followed by anchoring of aminosilane and epoxysilane on the plasma-treated Kapton, respectively. The bonding is finalized by conformal contact of the foils at 90 °C overnight.


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Polymer Sample Preparation The poly(N,N-dimethylacrylamide)-poly(2-methoxyethyl acrylate) diblock copolymer was synthesized via reversible addition fragmentation chain transfer (RAFT) aqueous dispersion polymerization of the water-soluble 2-methoxyethyl acrylate (MEA) in the presence of a poly(N,N-dimethylacrylamide) macro-RAFT agent.40 As radical initiator, the redox couple of tert-butyl hydroperoxide (TBH) and sodium sulfite (Na2SO3) was used.41 The synthesis was pursued with a macro-CTA/initiator molar ratio of 3:1 and a monomer/macro-CTA molar ratio of 100:1. In the laboratory scale, 0.28 g (5.66×10-5 mol, 1 eqv.) of the PDMAm48 macro-CTA were dissolved in 6.63 g of deionized water. Then, 1.40 g of a 13.5 mmol L-1 stock solution of TBH in water (1.89×10-5 mol, 0.33 eqv.) and MEA (0.74 g, 5.6×10-3 mol, 100 eqv.) were added to the solution to receive a final concentration of 10% (w/w). After degassing by bubbling with nitrogen for 30 min, 1.19 g of a 15.8 mmol L-1 sodium sulfite in water stock solution (equimolar to TBH) were injected under nitrogen and the reaction mixture was stirred at room temperature for 24 h before the polymerization mixture was quenched by exposure to oxygen and cooling in an ice bath. 1H-NMR determined PDMAm and PMEA repeating units of 48 and 61, respectively. GPC determined a molecular weight of Mn = 17 kg mol-1, and a dispersity of Mw/Mn = 1.4. DSC revealed two glass transitions temperatures with Tg = 99.4 °C and Tg = -34.1 °C, arising from the two distinct blocks. DLS measurement of the diluted reaction mixture (0.2% w/w) revealed a hydrodynamic diameter of Dh = 106±14 nm. A static SAXS measurement of the sample (Figure S4) indicated spherical micelles with a core radius of R = 38±7 nm. For the in-flow SAXS experiment, the polymerization mixture with the finished product was freeze-dried from its native aqueous medium and subsequently dissolved in THF (a good solvent for both blocks) to give a 10% (w/w) solution.


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Small-angle X-ray Scattering (SAXS) SAXS patterns were collected at beamline ID02 at ESRF42 (Grenoble, France) using monochromatic X-ray radiation with a wavelength of  = 0.10 nm (12.46 keV) and q ranging from 0.01 to 0.75 nm-1, where q = 4π/ sin() is the length of the scattering vector and  is the half scattering angle. The beam diameter was adjusted to 72.4 µm in the horizontal (x) direction and 42.3 µm in the vertical (y) direction (FWHM at the sample). Assuming a Gaussian distribution, the portion of the beam that is hitting outside the channel can be estimated. When the channel is centered, this is ~0.3% but closer to the edge, more beam overlaps the edge. The beamstop diameter was 2 mm. As a detector, a 2D Rayonix MX-170HS with a pixel size of 44 µm × 44 µm was used which was housed in an evacuated flight tube at a sample-to-detector distance of 10 m. The exposure times for the background- and sample measurements were 1 s. Additional static measurements of polymers in THF (shown in the SI) were performed at the same instrument with 0.5 s exposure times using 1 mm quartz capillaries (Hilgenberg). The samples were measured at 2-10 wt% solids. All SAXS data were reduced (normalized by incident flux and transmission, background-corrected, azimuthally integrated) using a custom pyFAI code and analyzed using Scatter43,44 (ver. 2.5) and Irena45 (ver. 2.65) for Igor Pro. The fitted values for all curves can be found in Table S1. The cumulative first-ranked singular-values correlation map was used to trace the similarity between SAXS profiles for different time points as previously described in detail elsewhere.46 The color assignment of each metric in the map was done by utilizing the ‘gist_stern‘ color map in matplotlib package. The white color maps the lowest similarity (0.78) while the black color maps identity (m = 1.00). The color gradient is in a linear progression.


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RESULTS AND DISCUSSION Microfluidic Mixing and Time Scales In order to control fast diffusive mixing, which triggers diblock copolymer phase transitions, we developed a microfluidic polyimide sample environment with 3D-hydrodynamic flow-focusing capabilities. 3D diffusive mixing of water and the THF stream along the y and z direction initiated the hydrophobic PMEA blocks to assemble to spherical micelles. The mixing-induced phase transitions were simultaneously investigated via in situ SAXS. For the flow experiment, the polymer solution (10% w/w in THF) was pumped through the main channel (MC) at a flow rate of QMC = 100 µL h-1 and flow-focused with water, coming in at QSC = 500 µL h-1 from each of the side channels (SC). Due to the laminar flow in the microchannels (Reynolds number Re~3), diffusion is the predominant factor of mixing between the fluids while the time axis of the mixing process can be correlated to different downstream (x) positions. To relate the investigated channel position to a mixing time, the middle of the mixing cross (x = 0, y = 0) is defined as the starting point of mixing between THF and water. The mean retention time is therefore

𝑉 𝑡mean = , 𝑄

(1)

with the volume V being the product of channel width wc (120 µm), the channel height hc (125 µm) and x, the distance to the mixing starting point. Moreover, Q is the total volumetric flow rate (1100 µL h-1). Further, the width of the focused central stream, wf, can be predicted with the flow rate ratio 𝑤f =

𝑄MC 𝑤. 𝑄SC1 + 𝑄MC + 𝑄SC2 c

(2)


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With the aforementioned flow rates, wf amounts to 10.9 µm. In order to estimate the diffusion time tD, i.e. the time of a solvent to diffuse from both edges of the focused central stream to its center, the mean square displacement in y direction is first considered to be

Δ𝑦 =

𝑤f = 2 𝐷 𝑡D. 2

(3)

Using a solvent interdiffusion coefficient of D = 10-9 m2 s-1, which is in between the values for water and THF, and following the estimations of Fürst and co-workers,39 an expression for the diffusion time is obtained with

𝑤2f 𝑡D = = 14.9 ms. 8𝐷

(4)

Water has a known X-ray scattering reflection at ca. q = 20 nm-1 which corresponds to an interparticle distance in the order of a particle size of approximately d ~ 2π/q = 0.3 nm. Assuming a hypothetical particle radius of R = 0.15 nm and using the Stokes-Einstein equation as a crude estimation, a diffusion coefficient of DWater = 1.6×10-9 m2 s-1 is obtained. THF, as a bigger molecule, has a diffusion coefficient in the range of DTHF = 0.9×10-9 m2 s-1.47 In this experiment, with the flow velocity being v = 20.4 mm s-1, a diffusion time of 14.9 ms corresponds to a distance of x = vt = 0.30 mm. The solvent diffusion in the y direction across half of the microfluidic channel, i.e. over a distance of x = wc/2 = 60 µm, will have occurred after a time tD = wc2/(8D) = 1.8 s. This mean time corresponds to a downstream distance of Δx = ν×t = 36.7 mm and shows where complete diffusional mixing resulting in a homogeneous


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solvent mixture across the total channel width will have occurred. This is still accessible in our microchannel. However, this position is not necessarily the point where the water concentration threshold, which drives in situ self-assembly, is reached. Figure 3 shows an exemplary microfluidic device in action with indication of wc and wf.

Figure 3. A black ink dispersion in water was pumped through the main channel (MC) and 3D flow-focused with water from the sheathing side channels (SC) in the Kapton mixing device (wc×h = 120 µm × 125 µm, pore diameter: 30 µm) demonstrating the agreement of the theoretical width of the focused stream wf (Eq. (2)) and experimental values from microscopy images. The applied ratios of the flow rates in µL h-1 are SC:MC:SC = 100:50:100 (A), 200:200:200 (B), 400:400:400 (C) and 5000:1000:5000 (D), respectively. With the variation of the flow rate ratios, different wf were tuned as follows. A (theoretical value: 24 µm); experimental value: 27 µm. B (theoretical value: 40 µm); experimental value: 42 µm. C (theoretical value: 40 µm); experimental value: 44 µm. D (theoretical value: 11 µm); experimental value: 12 µm. Further, D shows a 5:1:5 flow rate ratio as used in the in situ SAXS experiment.

To achieve a better understanding of the mixing process, the microfluidic mixing between the miscible phases was simulated in a three-dimensional model using the finite-element method in COMSOL Multiphysics.48,49 The system was approximated using the steady-state incompressible Navier-Stokes equation in combination with convection and diffusion application modes in order to compute the concentration of liquid species. The simulation was carried out with the same flow rate ratios as used in the X-ray experiment. The THF concentration was extracted and plotted as a function of the channel width (across y) and the channel height (across z) (Figure 4). The position, which according to Eq. (4) corresponds to a mixing time of 14.9 ms, is denoted as x1.5 in Figure 4 as it is located between x1 and x2. At x1.5, a THF concentration of 17% (w/w) is


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obtained. However, the CFD simulation predicts further dilution as the THF concentration decreases with increasing position number until x3. From x3 (after 0.21 s of mixing) onwards no further change of THF concentration across y and z direction is observed and a homogeneous THF concentration of 9.1% (w/w) across the channel is reached. This final concentration is also reflected in the flow rate ratios as cTHF,final = cTHF,initial × QMC/(QMC+QSC1+QSC2) = 9%. The theoretical values are in very good agreement with the SAXS curves because at x3 the first structure-related feature emerges due to the onset of the diblock copolymer micellization (Figure 7).

Figure 4. Simulated concentration distribution of THF in the mixing channel. The concentrations are shown as a function of the channel width (left) and channel height (right) at the X-ray scan positions x0 (violet) to x3 (turquoise) along the downstream (x) flow direction. The black curve (x=0, y=0) represents the middle of the mixing cross. It is evident that at x3 (4.3 mm after the mixing cross) complete mixing has occurred with no change of concentration at further positions.

Experimental Time Scales and SAXS Analysis The microfluidic channel geometry and the beamsize of the micro-focused X-rays determine the limiting time scales of the flow experiment which are the time resolution tres and the maximum


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residence time tmax. The time resolution tres is given by the X-ray beamsize in horizontal direction, xbeamsize = 72.4 µm, and the average flow velocity of the fluid stream v by tres = xbeamsize/v. With a measured channel width of wc = 120 µm, a channel height of hc = 125 µm and the sum of the flow rates of Q = 1100 µL h-1, one obtains an average flow velocity of v = Q/(wc×hc) = 20.4 mm s-1 and therefore a tres of 3.5 ms. The maximum residence time tmax is given by the channel length lc (47.6 mm) divided by the flow velocity, hence tmax = lc/v = 2.3 s. The downstream flow direction is referred to as x, while the channel width ranges over y (perpendicular to the flow direction). The channel height ranges over z, in which the X-rays also propagate. SAXS patterns of the sample and background (i.e. pure THF focused with water) have been collected in the microchannel under continuous flow conditions with an exposure time of 1 s. They were normalized by incident flux and transmission, before the sample image was subtracted with its corresponding background pattern. Figure 5 shows the background-corrected SAXS patterns recorded at 15 downstream positions x0 to x14. The distance of the detection points (x1-x14) from the start point x0 is given in Table S1. The patterns suffer from a symmetrical streak (resulting from grazing-incidence reflection at the channel walls in combination with beamstop scattering) which has been masked out for further data processing by only integrating a custom region of interest, as indicated by the red area in the top left detector image (x0) of Figure 5.


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Figure 5. Overview over the scan positions along the microchannel depicted inside a true-to-scale drawing of the Kapton polyimide channel with indication of the corresponding 2D SAXS patterns (normalized and backgroundcorrected). The patterns show the structural evolution along the x direction (flow direction) in the center of the channel. Position x0 is located before the main channel inlet pore and the image shows the 10% (w/w) polymer in THF solution. The subsequent images with increasing position number show with increasing distance from the mixing cross the transition from disorder to order. The distance of the detection points (x1-x14) from the start point x0 is given in Table S1. The dimensions of the X-ray beam are indicated by the small green rectangle in the enlarged depiction of the mixing cross.

From fluid dynamic formulations and the CFD simulations, we expect a homogeneous solvent composition at x3 with a THF concentration of 9% (w/w) across the channel. The 2D scattering pattern at position x9 in particular shows alignment and lattice orientation of the formed micelles: pronounced Bragg reflections with a six-fold rotational symmetry can be observed, indicating orientation of an fcc (face-centered cubic) lattice as shown in Figure 6. This is in agreement with the known shear orientation of fcc lattices that orient in a way that the [110] direction, i.e. the line of highest micellar density, is parallel to the flow direction.50 The experimental scattering pattern is therefore in good agreement with a calculated 2D pattern showing the characteristic six-fold symmetry expected when the X-ray beam is parallel to the [111] direction, thus placing the (111) plane perpendicularly. The fact that scattering from the (220) plane does not show


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distinctive reflections at the detector but rather an isotropic ring, is a strong evidence that the shear-induced ordering of (220) plane is experiencing continuous relaxation due to the insufficient shear stress at the center of the channel.51

Figure 6. (Top left) Unit cell of an fcc lattice (yellow cube) with indicated (111) planes (red) and indication of stacking order. (Bottom left) Orientation of an fcc lattice in a microfluidic channel. The (111) planes of hexagonally close-packed spheres expand in the [110] direction, parallel to the flow direction x. The X-ray beam is perpendicular to the flow direction and parallel to the [111] direction. (Right) Calculated six-fold-symmetric scattering pattern for the relevant projection of the fcc lattice using fit parameters from position x9’s SAXS curve (a = 100 nm, Dradial = 250 nm, Dazim = 100 nm, a = 10 nm, R = 34 nm, R = 10%) merged diagonally with its experimental pattern. There is good agreement between calculated and experimental pattern which indicates that micelles densely pack in an fcc lattice along the flow direction.

To facilitate further discussion, the SAXS patterns were azimuthally integrated over a valid region of interest without the influence of the streak (indicated by the red sector in the pattern x0 in Figure 5). For a quantitative analysis, the 1D SAXS curves (Figure 7) were fitted to an analytical expression describing the total scattered intensity of the micelles given by Eq. (5).52 A complete list of the obtained fit parameters for the scattering curves is provided in Table S1.

𝐼(𝑞) = 𝑁 𝛥𝜌2 𝑉2 𝑃(𝑞) 𝑆(𝑞)

(5)


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with the number of particles N, the particle volume V and the excess scattering length density  = 1-2, where 1 is the scattering length density of the particles which are embedded into a matrix of scattering length density 2. P(q) and S(q) are the form factor and structure factor for the particles, respectively. For P(q), the sphere form factor (Eq. (6)) can be used as the particles are assumed to be micelles of spherical shape described by their radius R.53

[

]

sin (𝑞𝑅) ― 𝑞𝑅 cos(𝑞𝑅) 𝑃(𝑞) = 3 (𝑞𝑅)3

2

(6)

For the structure factor, S(q), which describes the particle positions relative to each other, Eq. (8) was used39

(2π)3 𝑆(𝑞) = 𝑛 𝑉d

∑𝐹

2 ℎ𝑘𝑙𝐿ℎ𝑘𝑙(𝑞,𝑔ℎ𝑘𝑙).

(7)

Here, h, k, and l are the Miller indices which describe the crystallographic directions and distances. Moreover, n is the number of particles per unit cell (n=4 for fcc), Fhkl is the unit cell structure factor that takes into account symmetry-related extinction rules, Vd is the volume of the d-dimensional unit cell, hence d = 3, and Lhkl(q,ghkl) is a normalized peak shape function that depends on the reciprocal lattice vectors ghkl. Fits to Eq. (8) yielded the fcc space group with unit cell size a, mean ordered domain size D and average deviation of the particles from lattice position a (displacement). The relation between a and R in an fcc lattice is given by R = a 2 /4. Figure 7 shows the scattering curves and the first shape-related curve can be seen at the critical point x3 with a weak peak at q = 0.18 nm-1 which corresponds to an interparticle distance of d ~


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2π/q = 35 nm and at a point where the mixing is just completed (see Figure 4). However, this weak peak becomes less pronounced in the following scan positions (x5-x8) which might indicate the simultaneous presence of smaller and larger structures, e.g. phase separation and the emergence of micelles. This interpretation is supported by the increasing scattering intensity at these time points (see Porod invariant versus time in Figure S5). Once the concentration of spherical micelles is high enough (x9 onwards), pronounced Bragg reflections (q = 0.11 nm-1) and a Debye-Scherrer ring (q = 0.18 nm-1) appear (see Figure 5 & 7) which indicates particle interactions. Further downstream, a sharpening of the peaks with increased scattering intensity occurs, indicating shear-induced alignment and the formation of a lyotropic liquid-crystalline micellar phase. Further, the sizes of the micelles become gradually smaller along the flow indicating a deswelling of the micelles. This structural evolution based on the scattering curve analysis is further visualized with a cumulative first-ranked singular-value correlation map (Figure 7, right) where sudden drops of the scattering profile similarity suggest fast structural transitions.46,51 The indicated green region is dominated by the colors in the upper range of the color scale (black to dark red), which indicates the early onset of phase separation while no significant number of micelles has formed yet. The fast transition from single polymer chains to micellar assemblies can be clearly observed at x8/x9 (between green and pink triangles) with the least similarity among all scattering profiles (indicated by the black arrow). In general, the correlation map suggests three separate mixing regions which are 1: solvent dilution (green); 2: assembly (pink) and 3: deswelling (orange).


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Figure 7. (Left) SAXS curves taken at the downstream positions xn along the microchannel showing the mixinginduced disorder-order transition upon solvent exchange. The intensity profiles are scaled proportionally for easier comparison. Each curve depicts the same range in intensity. For a better comparison, the curves have been offset vertically. The fits (grey curves) refer to Eq. (5) with the sphere form factor and the structure factor from Eq. (7). Observed diffraction peaks from an fcc lattice are indicated with horizontal lines which are from left to right: (111) (at q = 0.11 nm-1), (220) (0.18 nm-1) and (531) (0.38 nm-1). The fit with the red curve for x0 refers to Eq. (8). All values of the fitted parameters are given in Table S1. (Right) Cumulative first-ranked singular-value correlation map for the scattering curves demonstrating structure-related transitions during and after mixing. The onset due to ordered micelles is indicated by the significant change of metrics between x8 and x9 (black arrow). The map suggests three mixing regions which can be assigned to 1: solvent dilution (green); 2: assembly (pink); 3: deswelling (orange).

For the diblock copolymer in pure THF at position x0 (before it enters the mixing region) as well as the static (capillary) measurement, the scattering curve was modeled using

𝐼chain(𝑞) = 𝑁 2chain 𝐹chain.

(8)

Here, the total excess scattering length of a polymer chain, is defined as chain = Vchain(chain-solv). Vchain is the volume of the polymer chain and can be obtained by Vchain = Mn,poly/(NA m,poly) where the mass density m of 1.25 g cm-3 based on the value for PMEA block54 is used as it has a higher scattering length density. Further, the number average molecular weight of the diblock


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copolymer, as determined by 1H-NMR, is Mn = 48×99.13 g mol-1 + 61×130.14 g mol-1 = 12.7 kg mol-1. With Avogadro’s constant NA, this leads to a volume of Vchain = 16.9 nm3. Moreover, chain and solv are the X-ray scattering length densities of the diblock polymer (PMEAPDMAm

~11.5×1010 cm-2) and the surrounding solvent (THF = 8.4×1010 cm-2), respectively. The

self-correlation Fchain is based on the Debye function55 and describes flexible polymer chains which obey Gaussian statistics in their conformation.56

exp ( ― 𝑞2𝑅2g) ― 1 + 𝑞2𝑅g2 𝐹chain(𝑞,𝑅g) = 2 . (𝑞2𝑅2g)2

(9)

Eq. (8) hence fits Rg, the radius of gyration of the coiled polymer chains, while assuming that the chain is thermally relaxed in a ‘theta’ solvent which can be characterized by a Flory exponent (excluded volume parameter) of  = 0.5.57,58 A theoretical value for the radius of gyration is obtained by Rg2 = Lb/6, where L is the total contour length and b is the statistical segment (Kuhn) length of the polymer chain.59 Assuming a C-C bond length of a 0.154 nm,60 the contour length of a monomer (two C-C bonds in all-trans conformation) amounts to 0.252 nm. Hence, the total contour length of the PDMAm48 stabilizer block is L = n×l = 48×0.252 nm = 12.1 nm while the core-forming block has a total contour length of LPMEA61 = 61×0.252 nm = 15.4 nm. Using a mean Kuhn length of 1.69 nm (based on the value for PMMA61), the radii of gyration amount to Rg,PDMAm48 = 12.1 × 1.69 nm2/6 = 1.85 nm (fitted: 2.61 nm) and Rg,PMEA61 = 2.08 nm. As the polymer blocks are weakly segregated in THF, the theoretical radius of gyration of the diblock copolymer is assumed to be the sum of the radii of gyration of the two respective homopolymers,39 therefore Rg = Rg,PDMAm48 + Rg,PMEA61 = 3.9 nm. This theoretical number is in


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relative agreement with the fitted value of the unperturbed radius of gyration Rg = 4.95 nm obtained from the static measurement in THF (Figure S4). Moreover, the Flory exponent was determined as  = 0.6 which indicates swollen polymer chains in a good solvent. The Rg of the flowing diblock copolymer in the microchannel at x0 was determined to be 18±4 nm. In comparison to the curve from the static measurement, the curve for x0 (in situ measurement) is less steep (I ∝ q-1) and shows a smaller Flory exponent of  = 0.4, therefore indicating a flowinduced anisotropy of the chain conformation.62 Due to the loose packing of micelles (inherent to soft matter samples), considerable dispersity of the single polymer chains and rather low electron density contrast between polymer and water, it is insufficient to describe the scattering curves solely with a model-based quantitative method (i.e. curve fitting). Also, due to the uniaxial orientation in flow, all the reflections from an ideal fcc lattice cannot be fulfilled. Qualitative studies should therefore be conducted to evaluate structure-related transitions. The comparison between difference scattering curves, which result from subtracting x0 from each scattering curve xn, singular values decomposition63 or the investigation of the Porod invariant64 of the curves as function of space/time are common approaches to monitor the change in a system. A discussion regarding the Porod invariant is offered in the Supporting Information.

CONCLUSIONS A fully polyimide-based microfluidic mixing device has been fabricated via ns-pulsed laser ablation. The computer-aided channel design enabled a convenient and reproducible microstructuring approach for innovative 3D flow-focusing of laminar microflows within inert polyimide foils. With this sample environment, effective diffusive mixing between solutions can


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be controlled, which is of broad appeal to various sample systems. The usefulness of our 3D polyimide microchannels for time-resolved studies in the hard X-ray regime was, in this example, successfully demonstrated by a solvent-induced macromolecular self-assembly experiment: THF, containing dissolved amphiphilic PDMAm48-PMEA61 diblock copolymers, was pumped through the main channel and mixed with water from the sheathing side channels. The temporal structural evolution of the dispersed nanoparticles during mixing could be mapped onto different positions along the microchannel to realize millisecond time resolution. Upon fast solvent exchange (within 200 ms), the assembly of dissolved diblock copolymer chains to spherical micelles was triggered and the structural transitions as well as orientational transitions of the amphiphilic particles were monitored in situ via microfocus SAXS. In addition to conventional scattering curve modeling, a cumulative first-ranked singular-values correlation map was created to trace the similarity between these SAXS profiles for different time points. These approaches were combined to unravel the structure-related transitions during and after mixing which suggests three dynamic states: solvent dilution, assembly and deswelling. During the first second of mixing, the formation of spherical micelles and a shear-induced arrangement into an ordered lattice was observed. Upon further and more complete mixing, a decrease in the spheres’ size due to continuous deswelling was monitored. The 2D and 1D analysis of SAXS data further indicated an fcc liquid-crystalline phase with a unit cell size of 100 nm which is consistent with the expected micellar core radius determined by the static SAXS measurement. A numerical CFD simulation aided the understanding of the mixing behavior inside the microchannel between THF and water, and the extracted mixing times were in good agreement with the experimental data as shown by the appearance of pronounced peaks due to micellar structures in the SAXS patterns.


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The presented experimental data, which combines in situ SAXS with high time resolution with CFD simulations, sheds light on the solvent-induced self-assembly processes of low Tg-block copolymers in general. These results point out the importance of considering not only the polymers themselves, but also the mixing time scales and rate of solvent concentration change during their self-assembly process when designing targeted polymeric nanoparticles, e.g. for medical application or drug encapsulation.

ASSOCIATED CONTENT Supporting Information. The Supporting Information is available. SI-movie (‘InkTest_5000_1000_5000.mov’, MOV) CAD file (‘MV_Kapton_2_8.dwg’, DWG) Rapid prototyping via laser micromachining; Microfluidic sample environment; Mixing and convection; Continuous flow SAXS measurements; Static SAXS measurements; The Porod invariant; DLS analysis; Solvent-compatibility study (PDF) AUTHOR INFORMATION Corresponding Author *Dr. Martin Trebbin, Empire Innovation Assistant Professor, Department of Chemistry, BioXFEL, RENEW and Hauptman-Woodward Medical Research Institute (HWI), State University of New York at Buffalo, 760 Natural Sciences Complex, Buffalo, New York 142603000, USA, email: [email protected], phone: (+1) 716 645 4274.


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Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding Sources DFG-EXC 1074 - project ID 194651731 ACKNOWLEDGMENTS We are grateful to the ESRF for providing synchrotron beam time and thank Theyencheri Narayanan and his team at the ID02 beamline for technical assistance. Furthermore, we thank Stephan Fleig and Bernd Krambeer from the mechanical workshop of the University of Hamburg for technical support in the fabrication of the sample holder. Tobias Gerling and Robert Seher (University of Hamburg) are thanked for fruitful discussions on microfluidic device and sample holder designs. Diana Monteiro and Florian Kopf (University of Hamburg) are thanked for fruitful discussions on fluid dynamic simulations. Further, we thank Matthew Derry (University of Sheffield) for very helpful discussions on SAXS data modelling. Moreover, we express our gratitude to Claudia Leopold (University of Hamburg) for enabling pycnometry measurements, the NMR team of the Institute for Organic Chemistry (University of Hamburg), Felix Scheliga, Stefen Bleck, and Katrin Rehmke for GPC and DSC measurements as well as Sven Bettermann for access to the DLS Zetasizer. We also thank Yannig Gicquel (University of Hamburg) and Michael Heymann (Max-Planck-Institute of Biochemistry, Martinsried) for fruitful discussions about surface functionalization. This work has been supported by the Cluster of Excellence 'The Hamburg Centre for Ultrafast Imaging' of the Deutsche Forschungsgemeinschaft (DFG) - EXC 1074 - project ID 194651731.


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SYNOPSIS Novel 3D flow-focusing X-ray compatible microfluidic devices are used to study rapid mixinginduced self-assembly of diblock copolymers using microfocus SAXS.


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3D Micromachined Polyimide Mixing Devices for in ... - ACS Publications

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