Spatiotemporal Reaction Dynamics Control in Two‐Photon Polymerization for Enhancing Writing Characteristics

Since 2001, 3D microfabrication based on two‐photon polymerization (TPP) has drawn extensive attention and interest in biology, optics, photonics, material science, and high‐energy physics. The in‐volume fabrication capability due to the threshold behavior of two‐photon absorption enables TPP higher flexibility compared with other nanofabrication techniques. However, as determined by the in‐volume fabrication feature as well as various reaction dynamics, the writing characteristics of TPP, such as throughput, accuracy, surface quality, and fabrication capability, are still limited. Herein, a comprehensive study is performed on the spatiotemporal behavior of reaction dynamics during TPP fabrication, mainly focusing on spatiotemporal characteristics of radical diffusion, photothermal effect, microscale mechanics, and voxel stacking process. Based on the study, a nonsequential fabrication method is established to simultaneously improve key writing characteristics of TPP and realize sharp features, high speeds, large overhang structure, and smooth surfaces. The method established in this work can be applied to improve the performance of functional devices for various fields.


Introduction
Due to the capability of creating arbitrary 3D structures with fine resolutions at the micro/nanoscale, direct laser writing by TPP has demonstrated its revolutionary impact in various industrial and research fields, such as photonics, optics, biomedicine, can reduce the writing resolution, the reaction time of the polymerization process limits throughput, thermal accumulation induces residual stresses and distorts microstructures, and surface finishes of microstructures are textured due to the voxel stacking process. [14]17][18][19][20] Therefore, further understanding and manipulating the spatiotemporal behavior of reaction dynamics during TPP fabrication is a potential and easy-to-apply method to enhance the key characteristics of TPP, and therefore laying the foundation to achieve better device performance fabricated using TPP.Herein, to address this knowledge gap, we systematically investigated the reaction dynamics during TPP fabrication.Specifically, the spatiotemporal diffusion behavior of free radicals was experimentally investigated at the microscale.Then, a detailed experimental investigation was conducted to explore the thermal effect during the TPP process.Our results show that the diffusion of free radicals is confined within ≈3 μm and the cooling time during TPP is in the range of ∼ms, providing valuable guidance to manipulate the reaction dynamics via scanning method.Based on the study, challenges in the fabrication of thin, porous structures were addressed via a nonsequential printing methodology, where the thermal effect and radical diffusion are well-tuned to realize higher precision and throughput in nanofabrication.Surprisingly, for certain structures, the throughput of using nonsequential scanning is ten times faster than conventional scanning.Moreover, to realize higher shape accuracy and smoother surfaces, the mechanics during TPP printing, the voxel stacking process, and error generation in TPP were systematically investigated.As a result, the software programming, motion control, and the physical-chemical process are combined to achieve nanoscale smoothness (Rq < 300 nm) and faster throughput in TPP fabrication.Finally, various microstructures with extreme surface smoothness were achieved without sacrificing the fabrication throughput.As our method requires no alterations to hardware or materials, it can be widely applied in various applications that utilize TPP.As demonstrations, we showcased functional biomimicry surfaces with a broader tunability in wettability, targets for laser nuclear fusion with higher shape accuracy, and optical gratings with better performances, which reveals the broader impacts of our technology.

TPP Basics and Reaction Dynamics
Briefly, in TPP, photo-initiators absorb two photons simultaneously in response to femtosecond laser exposures and decompose into free radicals.The sp 2 carbons from monomers react with surrounding free radicals to form polymer networks until termination occurs.Via scanning the laser spot in a 3D trajectory, 3D structures are formed after washing the unreacted resin.However, as shown in Figure 1a-e, at the time domain, different reactions occur upon laser exposure and finally determine the writing characteristics of TPP.First, at the ultrafast time scale, due to the threshold behavior of two-photon absorption, the initial reaction volume is confined at the laser focal spot.Over the following 1-100 ps after two-photon absorption, nuclei move in response to their altered photoexcited electronic structure, priming the photoexcited molecule for either intermolecular transfer of photoexcited states or covalent bond breakage/formation, which occurs at the ns-to-μs time scale.
Once photogenerated free radicals are released.which finally determines the writing resolution of TPP, as shown in Figure 1b.Consequently, as shown in Figure 1c, buoyancy starts to be applied on the microstructures with the network formation (ms ∼ s) as the solidified material is denser than the liquid resin. [22]To realize high-precision fabrication and avoid stitching errors, the buoyancy during printing needs to be well managed.Moreover, during the layer-by-layer stacking process, thermal accumulation at the solidified material becomes nonneglectable and stirs the polymerization kinetics locally, making TPP fabrication unique and varies case by case.Finally, the 3D structures are formed by scanning the focus in a 3D space (> s).Therefore, the surface morphology of the printed structures is textured (Figure 1d).
In summary, the writing characteristics of TPP, which are critical for application-oriented research, are directly determined by the spatiotemporal behavior of reaction dynamics during the fabrication process.Therefore, understanding and manipulating the reaction dynamics can enhance the writing characteristics of TPP directly and can be employed in different hardware setups.Following the fabrication logic of TPP, which is stacking voxel lines to form a layer and then stacking layers to form a 3D structure, various reaction dynamics during the stacking process are investigated.Based on the investigation, we established a nonsequential fabrication method that could simultaneously enhance the writing characteristics of TPP.

Radical Diffusion and Writing Resolution
As mentioned above, diffusion starts after the photodecomposition of initiators, which has two effects on the writing resolution of TPP.One effect is that the solidification area is larger than the two-photon absorption area due to the diffusive transportation.Another effect is the "add-on" effect.Specifically, due to free radical diffusion, the voxel's vicinity is not a clear-cut division of solid and liquid.In fact, the surroundings of the solidification area are still crosslinked but below the gelation threshold, which affects the writing resolution at the microscale.
In fabrication, depending on the design of structures, further crosslinking can occur due to the diffused radicals and turn the surrounding area into solid phases.A systematic study of the diffusion process can be found in ref. [23].We conducted a similar experiment using a 63× objective lens (NA = 1.4) and the IP-Dip resin, as summarized in Figure 2a and the inset.Specifically, two lines were printed, and we measured the line width as an indicator for radical diffusion.As we can see from the results, the effect of radical diffusion is obvious within the range of 3 μm.The detailed experiment can be found in Figures S1 and S2 (Supporting Information).In summary, depending on the viscosity of the liquid resin, the diffusion of radicals occurs in the range of several micrometers, and typically, the radicals are quenched in a few seconds.
[26] Specifically, as shown in Figure 2, we demonstrate the enhancement of writing resolution and printing speed by considering the spatiotemporal behavior of radical diffusion.Specifically, different parameters were selected to fabricate similar gratings with pitch distance and grating unit thickness ≈1 μm, which is within the diffusion range.As shown in Figure 2a, following the traditional fabrication sequence, due to the diffusion of free radicals, the polymerization reaction also occurs among the grating units and finally induces nanoscale polymer fibers, which generate undesired scattering.To achieve clear-cut features, a general strategy is to decrease the scan speed so that the time delay between each grating unit is extended.Therefore, free radicals are diffused away or quenched.In Figure 2b, when the scan speed is decreased from 10 mm s −1 to 50 μm s −1 , the nanoscale polymer fibers were not observed in the SEM image.However, this strategy inevitably increases the printing time to 14 min/grating.The introduction of radical quenchers is a direct method to suppress the diffusion of free radicals.Still, this method inevitably deteriorates the mechanical strength of printed structures, which is unfavorable if the grating is later used as a template.In Figure 2c, the grating was printed non-sequentially with designed priorities, as highlighted using a bar code with different colors.Using this strategy, the time delay and spatial separation between each grating unit is extended even using a high scan speed.As seen in the SEM, no nanoscale polymer fibers are observed due to the extended time delay and spatial separation, and the printing time is reduced to 82 s.For more information, Videos S1 and S2 (Supporting Information) provide a detailed comparison of the sequence of each scanning method.

Buoyancy, Thermal Accumulation, and In Situ Deformation
With the formation of networks after the line-by-line stacking, thermal accumulation, and buoyancy become the main factors that affect the writing characteristics, mainly the shape accuracy and structure limit.For the thermal accumulation, it originates from two aspects, as shown in Figure 3a.The first aspect is that heat accumulation occurs within each layer. [27]In our case, the material cooling time under the irradiation of high repetition laser can be estimated as t c = (2 0 ) 2 /D, where  0 is the beam radius, which is 0.595 μm for the given objective lens, D is the temperature diffusion constant of the resin, which is between 20-100 μm 2 s −1 based on the studies in ref. [27].We infer that the cooling time for IP-L is between 14-100 ms, which means that during the line-by-line stacking process, the localized heat can accumulate.The second aspect is the proximity effect, which occurs during the layer-by-layer stacking process [28,29] Specifically, the proximity effect is caused by the fact that after polymerization, the near IR single-photon absorptivity (SPA) of the crosslinked network becomes non-negligible in microfabrication.In the fabrication of solid 3D geometries, the SPA also generates localized heat and augments the polymerization reaction.
During fabrication, the thermal accumulation affects the shape accuracy via the size effect.To explain, we printed a series of cubes with different dimensions using the same process parameters, as shown in Figure 3b.The printing process was recorded using a live-view camera, as seen in the screenshot in Figure 3c.With the increase in dimension, the damage threshold of the cube is reduced accordingly.This can be explained by the fact that with the increase in structure dimension, the printing time increases dramatically (as calculated in Figure 3b, red line), which augments the polymerization via more thermal accumulation.In the meantime, the time delay between each voxel line is also extended after increasing the structure geometry, which explains why the damage threshold in Figure 3b tends to become flat at the late stage as the thermal accumulation and heat dissipation start to balance with each other.
Due to the size effect, the polymerization kinetics varies locally depending on the geometry of the designs.For structures with cross-scale features, the processing parameters need to be dynamically tuned according to the size of the structures to realize high shape accuracy.For example, Figures 3d-f show the fabrication of a classical model with cross-scale features: the Eiffel Tower with submillimeter size at the bottom and nanoscale feature at the top.With the changing of structure dimension, the size effect described above becomes dominant.Therefore, to maintain a high shape accuracy, the laser dose for the top part must be higher than the one for the bottom to ensure that the submillimeter features are not overexposed and nanoscale features are crosslinked sufficiently to survive the development process.In some cases, heat accumulation and radical diffusion both need to be considered to realize high shape accuracy and writing resolution.For example, the micro/nano hybrid structure in Figure 3g has a wide application in meta optics. [24,30] d,e) Due to the size effect, the Eiffel Tower is divided into subblocks to make sure each part is crosslinked sufficiently to maintain the designed geometry.g) A micro/nano hybrid structure based on the study in ref. [24] h) Using the printing strategy illustrated in Figure S3, the hybrid design is fabricated with sharp features.Scale bars are 10 μm for (c), 100 μm for (f), 20, and 2 μm for (h).
However, the fabrication of such a structure is challenging as the microscale feature is solid and heat-affected, and the nanoscale feature is porous and diffusion-affected.Based on our investigation, both the solid layer and porous layer of the design in Figure 3g are printed with the nonsequential method, similar to the method in Figure 2c, so that both the thermal accumulation and radical diffusion are suppressed without sacrificing the fabrication speed.As can be seen in Figure 3h, the structure obtained shows sharp features.A detailed scanning strategy can be found in Figure S3 (Supporting Information).
In a macroscopic view, another reaction dynamic occurring with network formation is the in situ deformation due to gravity, as summarized in Figure 4. Generally, the average atomic distance is reduced after polymerization, making the solidified networks denser than the liquid resin, as sketched in Figure 4a.Therefore, the net force of gravity and buoyancy is not zero.After network formation, which typically occurs in the range between ms and s, the effect of gravity and buoyance on the shape of the printed structure becomes evident and deforms the structures printed, as sketched in Figure 4b.
Generally, to fabricate long overhang structures, stitching of printing areas is required due to the limited field of view of the objective lens, as shown in Figure 4c,d.Following the printing sequence (using a 300 μm block size) in Figure 4e, the deflection after solidification becomes not neglectable which finally induces the stitching errors.Via reducing the block size to 5 μm, the printing sequence was changed so that the rigidness of each block is increased, and therefore stitching errors are reduced, as shown in Figure 4e-g.Considering the size effect mentioned above, the laser dose should be increased with the decrease in block size, or the fabricated structure can deform due to insufficient crosslinks, as shown in the overview SEM of Figure 4g.In conclusion, by considering the size effect and gravity, the structure limit as well as the shape accuracy of TPP can be simultaneously enhanced.

Radical Diffusion, Aliasing, and Surface Morphology
After the layer-by-layer stacking, 3D structures are formed with defined surface morphologies.To enhance the surface morphology via control of the reaction dynamics, we start by analyzing the formation of surface morphology.In a sentence, the formation of the surface profile is aliased, as summarized in Figure 5. Specifically, for 3D structures with curved geometries, the stacking process directly determines the surface roughness, which is named the aliasing effect.In computer science, the aliasing effect is the appearance of jagged edges in an image rendered using pixels, which typically occurs when the sampling frequency is below the Nyquist sampling frequency. [31,32]Similarly in TPP, the 3D structures are formed via stacking the voxels.Therefore, the printed structures also exhibit jagged edges, which is the surface roughness of microstructures.In reality, the stacking process is realized using a galvo scanner or motorized stage.A detailed discussion of the motion control is provided in Figure S4 (Supporting Information).In summary, the to-be-printed structures are quantized by hatching and slicing distances using the galvo scanner or motorized stage, which determines the voxel overlap.Specifically, a higher overlap rate will lead to a smoother and more precise surface at the cost of the fabrication throughput.As shown in Figure 5a, during the layer-by-layer manufacturing process, the structures to be printed are quantized with a step of SD, leading to surface roughness and fabrication errors, including stepping terraces and missing layers, as highlighted in the green area in Figure 5a.Similarly, for each layer, which is quantized with a step of HD, the line-by-line stacking process also generates stepping terraces and missing hatching lines, as highlighted in the green area in Figure 5b.Figures 5c,d show the fabrication of a dome structure with different hatching and slicing distances.As can be seen in the SEM images, the missing layer and stepping terrace are observed from the top view.Noteworthy, the accumulation of stepping terrace at each layer induces fringes at the outer surface of the dome structures, as highlighted in Figure 5d.
Besides the aliasing, further crosslinks shown in Figure 2a also occur within the fabrication of each layer.That's the reason why all the top layers in Figures 5c,d are smooth.However, as the radical diffusion is only limited to ≈3 μm and the lifetime for polymer radicals is typically in the order of seconds, further crosslinks among each printing layer are very limited due to the extended fabrication time and large size. [23]However, considering the spatiotemporal behavior of radical diffusion, we can utilize the diffusion to realize a smooth surface via nonsequential scanning at the structural level, which is named core-contour nonsequential scanning in this work.As shown in Figure 6a, for any structures to be printed, the laser scanning path can be divided into two parts: the core part and the contour layer.The core part utilizes a traditional filling strategy to print the structures.After that, a contour layer is scanned separately.As shown in Figure 6a, as the contour layer is scanned separately, further crosslinks still occur, which smoothens the laser tracks and therefore improves the surface smoothness.
The core-contour nonsequential scanning can avoid the tradeoff between surface smoothness and throughput.Figures 6b-d show an example that could be applied to other structures.Traditionally, denser slicing and hatching distances reduce both errors and surface roughness significantly, as calculated in Figure S5 (Supporting Information) of the support material.However, this strategy decreases the fabrication throughout quadratically and makes TPP extremely time-consuming for meso and millimeterscale fabrication, such as the example provided in Figure S7 (Supporting Information).As shown in Figure 6b, in the case of large slicing and hatching distances (2 and 1.5 μm respectively), fabrication errors can be clearly observed in the SEM image while the printing time is very short.Following the straightforward strategy, decreasing the hatching and slicing distance to 100 nm eliminates fabrication errors while increasing the printing time quadratically to ≈2 h.However, using the nonsequential scanning strategy, similar surface quality is realized in 4 min, demonstrating enhancement of surface smoothness and fabrication speed simultaneously.

Applications and Outlook
Based on the research in the previous part, we successfully demonstrate the simultaneous enhancement of writing characteristics of TPP via considering and manipulating different reaction dynamics both spatially and temporally.The achievements of this research work can be applied to address general challenges in the TPP application in micro-optics, photonics, and biology.Figures 7a-f show a comparison fabrication of concave structures, microlens arrays, and aspherical microlenses using traditional and nonsequential scanning.As we can see, the surface roughness as well as the stepping error was reduced, which is very important for the application of TPP in nanoimprint, fiber optics, and X-ray optics. [33,34]As an example, detailed scanning method for Figure 7e can be seen in the support Video S3 (Supporting Information).To further illustrate the significance and generality of this work, we show the enhancements of device performance that benefitted from this work.First, as known to all, the microstructures could tune surfaces' wettability.Based on the Cassie-Baxter equation, various microstructures with superhydrophobic/hydrophilic wettability have been developed.TPP is a very effective and straightforward method to bring the design into reality. [16,35]As shown in Figures 7g-l, the mushroom-like structure could be directly printed by TPP to realize extreme wettability.However, based on the work in Section 2.4, the surface morphologies of the mushroom structures could be further modified based on the nonsequential method we developed, which finally enables more tunability in wettability.As we can see, after smoothening the mushroom-like structures with a contour layer, the contact angle decreased to 132.2°.
Last but not least, it is worth mentioning that to realize such nonsequential scanning, the programming complexity was in-creased significantly.For example, to apply the nonsequential scanning in the capsule fabrication for fusion research, the printing sequence needed to be tailored to avoid scattering due to the change of refractive index after solidification, as can be seen in Figure S8 and Videos S4 and S5 (Supporting Information).For the future perspective, incorporating our findings in the control software of commercial TPP systems will be promising, as it will reduce the labor workforce and increase the performance of current systems without hardware modifications.

Conclusion
This research systematically investigated the spatiotemporal reaction dynamics during TPP fabrication, including spatiotemporal characteristics of radical diffusion, which occurs in the scale of ms and μm; buoyancy force and gravity, which occurs in the scale of ms and submillimeter; thermal accumulation, which occurs in the scale of sub-second and submillimeter; formation of surface morphology, which occurs in the structural scale.Based on understanding the spatiotemporal behavior of reaction dynamics, a nonsequential scanning method is developed to enhance/suppress reactions.As a result, different writing characteristics of TPP are simultaneously improved.Specifically, considering the diffusion of free radicals, the nonsequential method simultaneously enhances the writing resolution and speed; considering buoyancy and thermal accumulation, shape accuracy, writing resolution, and structure limit of TPP are enhanced; considering the voxel stacking process, the surface morphology and fabrication speed are enhanced.The enhancement of writing characteristics of TPP can be widely applied in different fields.As a proof-of-concept, various functional structures for other fields are demonstrated using the research described above, such as diffractive optical elements, micro lenses, wettability surfaces, and fuel capsules.During the experiments, a femtosecond (fs) laser was focused into the resin pool to induce two-photon absorption.The focused laser beam decomposed initiators into free radicals by two-photon photolysis.Formed radicals consumed the C═C bonds of methacrylatecontaining monomers to create carbon-carbon single bonds, leading to highly crosslinked solidified polymer networks.

Experimental Section
Two-Photon Polymerization: All samples used in this study were fabricated using a commercial 2PP system (Photonic Professional GT from Nanoscribe GmbH).The fs laser was focused by a Carl Zeiss objective lens (63×NA1.4,or 25×NA0.8)and scanned by a computer-controlled galvo in the resins using the dip-in laser lithography configuration (DiLL).After printing, all samples were immersed in 50 mL of propylene glycol monomethyl ether acetate (PGMEA) (3 m) for 1 h to thoroughly dissolve the unreacted resin, followed by a rinse in 2-propanol (Sigma-Aldrich) for 20 min to remove residual PGMEA.
Scanning Electron Microscopy: A Hitachi S4700 field-emission scanning electron microscope (FE-SEM) was used to observe the shapes and morphologies of the 3D structures after pyrolysis.The dimensions of printed samples were estimated using ImageJ.

Figure 1 .
Figure 1.Simultaneous enhancement of writing characteristics of TPP.a) Key writing characteristics of TPP, include writing resolution, shape accuracy, surface roughness, structure limit, and speed.b-e) Reaction dynamics at different time scales determine the writing characteristics of TPP.b) Radical diffusion determines writing resolution and occurs in μs-ms scale and in a range of μm.c) Network formation occurs in the ms scale.Upon solidification, buoyancy and thermal effect start to affect the printing process and finally determine the shape accuracy of TPP.d) At a longer time scale, the voxel stacking process determines the surface roughness of TPP structures.

Figure 2 .
Figure 2. Simultaneous improvement of writing resolution and speed.a) Examination of diffusion length of free radicals via tuning the pitch distance of two lines and measuring the change of line width.In this experiment, all line pairs were printed from the left to the right side with a scan speed of 2000 μm s −1 , a laser power of 40 mW, and a length of 12.5 μm.Due to the diffusion, further crosslinks occur between the grating unit.b) To avoid further crosslinks, sequential scan requires slow scanning to let the radical to be quenched, which decreases the throughput.c) Using the nonsequential scanning method where the pitch distance of scanning is larger than the diffusion length, the same grating can be fabricated with sharp features and high throughput.Scale bars are 5 μm.

Figure 3 .
Figure 3. Simultaneous improvement of shape accuracy and writing resolution.a) Origins of thermal accumulation during TPP.b,c) Size effect in TPP due to thermal accumulation.Except for the laser power.other parameters were kept constant (scan speed = 10 mm −1 s, hatch distance = 0.5 μm, and slice distance = 1 μm) to test the damage threshold for cubes with different edge length.d,e)Due to the size effect, the Eiffel Tower is divided into subblocks to make sure each part is crosslinked sufficiently to maintain the designed geometry.g) A micro/nano hybrid structure based on the study in ref.[24] h) Using the printing strategy illustrated in FigureS3, the hybrid design is fabricated with sharp features.Scale bars are 10 μm for (c), 100 μm for (f), 20, and 2 μm for (h).

Figure 4 .
Figure 4. Simultaneous enhancement of structure limit and shape accuracy.a,b) With solidification, gravity and buoyancy force can distort the structure at the microscale.c,d) printing of long overhang structures via stitching print areas.e-g) Printing of a cantilever with an overall dimension of 1 mm.The block sizes are 300, 50, and 5 μm, respectively.Black lines with arrows refer to the laser scanning path within each block.By reducing the block size, the rigidness is increased due to the increased second moment of inertia.Scale bars are 100 μm for overview and 20 μm for zoomed view.

Figure 5 .
Figure 5. Aliasing in TPP fabrication.a,b) stepping and hatching errors in TPP determine c,d) surface morphology of TPP structures after layer-by-layer printing.Scale bars are 10 μm.

Figure 6 .
Figure 6.Simultaneous enhancement of surface smoothness and throughput via nonsequential scanning at the structural level.a) The structure to be printed is divided into the main body and contour part.b,c) The trade-off of throughput and surface smoothness using traditional filling.d) Nonsequential scanning realizes a smooth surface (Rq < 300 nm) with a high throughput.The surface profile is measured using a Zygo interferometer with detailed results provided in Figure S6 (Supporting Information).Scale bars are: 50 μm for overview images and 20 μm for zoomed images.

Figure 7 .
Figure 7. Comparisons of functional microstructures fabricated using TPP with/out enhanced writing characteristics.a-c) Microlens array, aspherical microlens array, and imprint templates fabricated via traditional slicing show stepping errors.d-f) Same structures fabricated with smoother surfaces using nonsequential scanning.g-l) Wettability surfaces fabricated through different strategies.Surface smoothening enhances hydrophilicity as measured by a contact angle analyzer.Scale bar: 25 μm for (a-f), 100 μm for (g,j), 50 μm for (h,k), 5 μm for (i,l).