Facile Molecular Weight Determination of Polymer Brushes Grafted from One-Dimensional Diffraction Grating by SI-ATRP Using Reflective Laser System

Gelatin was immobilized selectively on the amide groups-modified bottom of a trench array of a photoresist template with 2 μm resolution by the ethyl(dimethylaminopropyl) carbodiimide/N-hydroxysuccinimide reaction. The gelatin-immobilized line array was brominated to generate a macroinitiator for atom transfer radical polymerization. Poly(methacrylic acid) (PMAA) brushes were grafted from the macroinitiator layer as line arrays of one-dimensional diffraction gratings (DGs) for various grafting polymerization times. A laser beam system was employed to analyze the optical feature with a characteristic diffraction effect of the PMAA DGs at a 45° incident angle along the transverse magnetic and transverse electric polarization. The growth of the PMAA brush lines increased both their heights and widths, leading to a change in the reflective diffraction intensity. The PMAA brushes under various grafting polymerization times were cleaved from the substrate by digestion of gelatin with trypsin, and their molecular weights were obtained by gel permeation chromatography. The change degree of the diffraction intensity varied linearly with the molecular weight of the PMAA brushes over a wide range, from 135 to 1475 kDa, with high correlation coefficients. Molecular weight determination of polymer brushes using the reflective diffraction intensity provides a simple method to monitor their growth in real time without polymer brush cleavage.


Introduction
Polymer brushes are formed by the tethering of the ends of polymer chains to a surface, leading to various structures [1]. The functional groups of polymer brushes can be manipulated arbitrarily by the monomer species during polymerization for tailoring the physicochemical properties or functionalization of biomolecules [2]. For example, many types of functional groups, such as carboxyl acid, primary amino, epoxy, and hydroxyl groups, can be anchored on the chains of polymer brushes to immobilize biomacromolecules. The flexibility of polymer brushes facilitates their surface modification for several applications, such as biological detection [3], cell affinity substrate [4], and bacterial resistance [5]. Immobilization of biomacromolecules on surfaces using polymer brushes for wide applications [25]. The line arrays of the DGs can provide transverse magnetic (TM) and transverse electric (TE) polarization optical modes to vary the diffraction effect. Characterization of the optical properties of the PMAA DGs, including electromagnetic wave propagation and scattering through STP media [26,27], is an interesting topic to correlate with the molecular weights of the brushes. Growth of the PMAA DGs on the surfaces varies the heights and widths of the lines, resulting in a change in the reflective diffraction intensity, which is measured by an in-house-constructed laser system. The change in the diffraction intensity of the PMAA DGs with the grafting polymerization time is used as an indicator to establish the correlation with the molecular weight of the PMAA, obtained by digesting the gelatin backbone with trypsin. Polymer chains stretch and coil in the bulk solution and dry state on the substrates respectively, which may result the difference in measurement of polymer molecular weight. In general, polymers grafted on the surface are stripped from the substrate to measure the exact molecular weight. This strategy offers a convenient approach for monitoring the growth of polymer brushes in real time without destructed cleavage. Although the exact molecular weight of the polymer grafted on the surface is not well-known, the molecular weight measured by our method is expected to be proportional to that molecular weight measured in the bulk solution.

Strategy of Molecular Weight Determination with PMAA DGs by Laser Beam System
Scheme 1 illustrates the strategy of the molecular weight determination of the PMAA brushes with reflective diffraction intensity using a laser system [28]. (A) A photoresist was coated on Si wafers to pattern as trench arrays of 2 µm resolution by I-line lithography. (B) Oxygen plasma was induced to generate a hydrophilic region in the trench bottom, and subsequently, the photoresist was removed from the surface. (C) The samples were immersed in a 0.5 wt.% 3A aqueous solution for 1 h at 25 • C to assemble selectively on the hydrophilic regions of the wafer substrates. (D) The as-prepared samples were incubated with ethyl(dimethylaminopropyl) carbodiimide (EDC) and N-hydroxysuccinimide (NHS) solutions, leading to activation of the amide groups of 3A. Subsequently, a gelatin backbone was immobilized on the 3A-modified samples in phosphate-buffered saline (PBS) solution at 2 mg mL −1 for 3 h at 10 • C, denoted as DG-gel. (E) The as-prepared samples were sequentially reacted with 2B for 6 h at room temperature to generate halogen groups on the surface of DG-gel as macroinitiators, denoted as DG-gel-Br. (F) PMAA brushes were grafted from the DG-gel-Br via ATRP using MAA, Cu(I)Br, CuBr 2 , and pentamethyldiethylenetriamine in methanol for 1, 2, 4, 6, 8, and 16 h of grafting polymerization times at 30 • C. These are denoted as DG-g-PMAA1, DG-g-PMAA2, DG-g-PMAA4, DG-g-PMAA6, DG-g-PMAA8, and DG-g-PMAA16, respectively. After various grafting polymerization times, the samples were immersed in a mixture of water and ethanol (1:1, wt.%) for 5 min and then rinsed with double-distilled water at least five times. (G) The DG-g-PMAA samples were evaluated for their diffraction efficiency using an in-house laser beam system. (H) The samples were incubated with trypsin for 30 min to digest the gelatin and release the PMAA brushes from the surfaces for molecular weight analysis by gel permeation chromatography (GPC). Surface components of the samples were analyzed based on the presence and states of the elements by X-ray photoelectron spectroscopy (XPS; Scientific Theta Probe, Waltham, MA, USA). Morphologies of the various DGs were observed via atomic force microscopy (AFM; Veeco Dimension 5000 scanning probe microscope, Plainview, NY, USA). The molecular weights were analyzed via GPC using a VISCOTEK-DM400 instrument (Malvern, UK) and an LR 40 refractive index detector, as described in a previous study [29].
brushes were grafted from the DG-gel-Br via ATRP using MAA, Cu(I)Br, CuBr2, and pentamethyldiethylenetriamine in methanol for 1, 2, 4, 6, 8, and 16 h of grafting polymerization times at 30 °C. These are denoted as DG-g-PMAA1, DG-g-PMAA2, DG-g-PMAA4, DG-g-PMAA6, DG-g-PMAA8, and DG-g-PMAA16, respectively. After various grafting polymerization times, the samples were immersed in a mixture of water and ethanol (1:1, wt.%) for 5 min and then rinsed with double-distilled water at least five times. (G) The DG-g-PMAA samples were evaluated for their diffraction efficiency using an in-house laser beam system. (H) The samples were incubated with trypsin for 30 min to digest the gelatin and release the PMAA brushes from the surfaces for molecular weight analysis by gel permeation chromatography (GPC). Surface components of the samples were analyzed based on the presence and states of the elements by X-ray photoelectron spectroscopy (XPS; Scientific Theta Probe, Waltham, MA, USA). Morphologies of the various DGs were observed via atomic force microscopy (AFM; Veeco Dimension 5000 scanning probe microscope, Plainview, NY, USA). The molecular weights were analyzed via GPC using a VISCOTEK-DM400 instrument (Malvern, UK) and an LR 40 refractive index detector, as described in a previous study [29]. Scheme 1. Strategy of molecular weight determination of PMAA brush with DG structure using laser beam system.

Optical Analysis of Reflective STP Grating by a Laser Beam System
STP DG in the reflective mode was analyzed by a home-designed laser beam system. Our DG may be regarded as integration of DG of a PMAA brush and a polished silicon surface with a high reflection efficiency. One may achieve a fully reflective STP DG by Scheme 1. Strategy of molecular weight determination of PMAA brush with DG structure using laser beam system.

Optical Analysis of Reflective STP Grating by a Laser Beam System
STP DG in the reflective mode was analyzed by a home-designed laser beam system. Our DG may be regarded as integration of DG of a PMAA brush and a polished silicon surface with a high reflection efficiency. One may achieve a fully reflective STP DG by combining PMAA brush lines and polished silicon trenches. When electromagnetic waves pass through a line with low resolution at an incident angle, the waves reflecting near an impediment tend to curve around that impediment and reflect out, resulting in wave scattering.
When the impediment features regular repeating patterns, the wave scattering of the electromagnetic waves yields an orderly reflective diffraction phenomenon comprising a series of diffraction orders (m). The reflective diffraction phenomenon is predominately dependent on a comparable optical resolution of grating to the wavelength of the electromagnetic waves traveling through the grating. Two modes of transverse magnetic (TM) and transverse electric (TE) polarization modes occur along directions perpendicular and parallel to the incident laser, respectively. Scheme 2a depicts the reflective diffraction from line arrays of STP DGs for TE polarization. When parallel incident waves input the conventional line array of DG for TE polarization, a symmetric diffraction pattern with symmetry in both angles (θ m ) and amplitudes of the diffracted orders (P m ) appears. In addition, temporal frequency (ω 0 ) of the incident field does not change for a monochromatic input wave, indicating that the diffracted orders possess identical temporal frequency. However, line arrays of DGs possess symmetric profiles, resulting in a reciprocal diffraction reflection response because of restriction of the Lorentz reciprocity theorem [30]. Scheme 2b depicts the reflective diffraction from line arrays of STP DGs for TM polarization. When perpendicular incident waves input the STP DG for TM polarization, the nonreciprocity of reflective diffraction occurs. The output waves are asymmetric with the input of the incident wave, indicating no spatial inversion. For TM polarization, the reflective diffraction pattern shows obvious nonreciprocity of the reflective STP DGs. To investigate the angle asymmetry of the reflective STP DG, input incidence of waves under an incident angle (θ i ) can be employed to analyze the results of output incidence.
The obvious angle asymmetry, including angles and intensity of the reflective diffracted orders by the DGs, may be observed. The spatial frequency (K), spatial periodicity of the STP grating (Λ = 2π/K), and the temporal frequency (Ω) can be employed to determine these parameter properties of the diffracted orders according to the momentum conservation law and the energy conservation law [31]. The reflective diffraction angle of output incidence for the diffracted orders can be predicted by the following [27]: where c, n 1 , m, and n represent the velocity of the light in the vacuum, the refractive index in the air, the numbers of the space, and time harmonics, respectively. The reflective diffraction intensity was recorded as 2D and 3D patterns by a BeamMic system consisting of a laser beam analyzer (Ophir-Spiricon, LLC, North Logan, UT, USA) and BeamMic software.
olymers 2021, 13, x 5 of 17 combining PMAA brush lines and polished silicon trenches. When electromagnetic waves pass through a line with low resolution at an incident angle, the waves reflecting near an impediment tend to curve around that impediment and reflect out, resulting in wave scattering.
When the impediment features regular repeating patterns, the wave scattering of the electromagnetic waves yields an orderly reflective diffraction phenomenon comprising a series of diffraction orders (m). The reflective diffraction phenomenon is predominately dependent on a comparable optical resolution of grating to the wavelength of the electromagnetic waves traveling through the grating. Two modes of transverse magnetic (TM) and transverse electric (TE) polarization modes occur along directions perpendicular and parallel to the incident laser, respectively. Scheme 2a depicts the reflective diffraction from line arrays of STP DGs for TE polarization. When parallel incident waves input the conventional line array of DG for TE polarization, a symmetric diffraction pattern with symmetry in both angles (θm) and amplitudes of the diffracted orders (Pm) appears. In addition, temporal frequency (ω0) of the incident field does not change for a monochromatic input wave, indicating that the diffracted orders possess identical temporal frequency. However, line arrays of DGs possess symmetric profiles, resulting in a reciprocal diffraction reflection response because of restriction of the Lorentz reciprocity theorem [30]. Scheme 2b depicts the reflective diffraction from line arrays of STP DGs for TM polarization. When perpendicular incident waves input the STP DG for TM polarization, the nonreciprocity of reflective diffraction occurs. The output waves are asymmetric with the input of the incident wave, indicating no spatial inversion. For TM polarization, the reflective diffraction pattern shows obvious nonreciprocity of the reflective STP DGs. To investigate the angle asymmetry of the reflective STP DG, input incidence of waves under an incident angle (θi) can be employed to analyze the results of output incidence. The obvious angle asymmetry, including angles and intensity of the reflective diffracted orders by the DGs, may be observed. The spatial frequency (K), spatial periodicity of the STP grating (Λ = 2π/K), and the temporal frequency (Ω) can be employed to determine these parameter properties of the diffracted orders according to the momentum conservation law and the energy conservation law [31]. The reflective diffraction angle of output incidence for the diffracted orders can be predicted by the following [27]: where c, n1, m, and n represent the velocity of the light in the vacuum, the refractive index in the air, the numbers of the space, and time harmonics, respectively. The reflective diffraction intensity was recorded as 2D and 3D patterns by a BeamMic system consisting of a laser beam analyzer (Ophir-Spiricon, LLC, North Logan, UT, USA) and BeamMic software. Figure 1a displays the XPS survey spectra of DG-gel, DG-gel-Br, and DG-g-PMAA16.

Surface Characterization of DGs
The XPS spectrum of DG-gel exhibited Si 2p, C 1s, N 1s, and O 1s peaks in the ranges of 99-104, 285-293, 396-403, and 528-535 eV of the silicon wafers, respectively. The surfaces did not present a Br 3d5 peak of the halogen group in the range of 65-73 eV before the bromination reaction. This peak appeared in the XPS spectrum of DG-gel-Br, verifying the presence of the brominated gelatin layer [32]. The signals of the Si 2s, Si 2p, and Br 3d5 peaks disappeared in the DG-g-PMAA16 spectrum. A significant increase in both the carbon to oxygen intensity ratio and nitrogen elemental signal was observed in the DG-g-PMAA16 spectrum due to the coating of the PMAA brushes.  The XPS spectrum of DG-gel exhibited Si 2p, C 1s, N 1s, and O 1s peaks in the ranges of 99-104, 285-293, 396-403, and 528-535 eV of the silicon wafers, respectively. The surfaces did not present a Br 3d5 peak of the halogen group in the range of 65-73 eV before the bromination reaction. This peak appeared in the XPS spectrum of DG-gel-Br, verifying the presence of the brominated gelatin layer [32]. The signals of the Si 2s, Si 2p, and Br 3d5 peaks disappeared in the DG-g-PMAA16 spectrum. A significant increase in both the carbon to oxygen intensity ratio and nitrogen elemental signal was observed in the DG-g-PMAA16 spectrum due to the coating of the PMAA brushes. Figure 1b depicts the C 1s high-resolution spectrum of DG-g-PMAA16 with curve fitting to identify the surface bindings. Three characteristic peaks at binding energies of 284.9, 285.6, and 288.5 eV were observed corresponding to the C-C, C-N, and O=C-O bonds, respectively. The binding energies of these surface bindings represent the PMAA grafting on the gelatin, consistent with the values reported in [33]. The characteristic peak of DG-gel-Br at 67.5 eV in the Br 3d high-resolution spectrum disappeared after PMAA grafting (Figure 1c). The intensity of the N 1s high-resolution band of DG-gel-Br was weaker than that of DG-g-PMAA, verifying the PMAA-grafted gelatin (Figure 1d). Figure 2a shows the 2D/3D AFM topographies and cross-section profiles of the polymer templates for identifying the real topography. The photoresist templates exhibited a 2.4 µm line width and a 1.9 µm trench width with a smooth surface, indicating a slight difference from the designed textures. After the immobilization of gelatin on the bottom of the trenches by the EDC/NHS reaction, clear gelatin lines appeared in the 2D/3D AFM topographies and cross-section profiles. The widths of the gelatin lines matched the trench widths, verifying that the gelatin was grafted on the trench bottom. In the cross-section profiles of DG-gel, the lines had heights of 3.5 nm, suggesting a high regularity of the gelatin immobilization [34,35]. A double-edge structure appeared in each gelatin line, attributed to the edges of the lines readily attaching more biomacromolecules. Figure 1b depicts the C 1s high-resolution spectrum of DG-g-PMAA16 with curve fitting to identify the surface bindings. Three characteristic peaks at binding energies of 284.9, 285.6, and 288.5 eV were observed corresponding to the C-C, C-N, and O=C-O bonds, respectively. The binding energies of these surface bindings represent the PMAA grafting on the gelatin, consistent with the values reported in [33]. The characteristic peak of DG-gel-Br at 67.5 eV in the Br 3d high-resolution spectrum disappeared after PMAA grafting (Figure 1c). The intensity of the N 1s high-resolution band of DG-gel-Br was weaker than that of DG-g-PMAA, verifying the PMAA-grafted gelatin (Figure 1d). Figure 2a shows the 2D/3D AFM topographies and cross-section profiles of the polymer templates for identifying the real topography. The photoresist templates exhibited a 2.4 μm line width and a 1.9 μm trench width with a smooth surface, indicating a slight difference from the designed textures. After the immobilization of gelatin on the bottom of the trenches by the EDC/NHS reaction, clear gelatin lines appeared in the 2D/3D AFM topographies and cross-section profiles. The widths of the gelatin lines matched the trench widths, verifying that the gelatin was grafted on the trench bottom. In the cross-section profiles of DG-gel, the lines had heights of 3.5 nm, suggesting a high regularity of the gelatin immobilization [34,35]. A double-edge structure appeared in each gelatin line, attributed to the edges of the lines readily attaching more biomacromolecules.  As depicted in Figure 3, PMAA is grafted successfully from DG-gel-Br as line arrays of DGs for various grafting polymerization times. All DGs exhibited irregular line surfaces, attributed to the collapse of the PMAA brushes because of the flexibility. The average height of the line patterns of the DG-g-PMAA1 brushes was 145 ± 9 nm, with a distinct interval between the lines. Note that the intervals between the lines suggested a polished Si surface that predominantly reflects the input waves generating the diffraction effect. The irregular textures of the line surfaces were not significantly affected by the diffraction effect. For DG-g-PMAA1, the widths of the bottom regions of the polished silicon wafers remained at 1.9 μm, indicating that the polymer brushes did not extend to the trench bottom regions (Figure 3a). The height of DG-g-PMAA2 increased from 145 ± 9 to 194 ± 13 nm (Figure 3b). The trench bottom regions of the polished silicon wafers were slightly As depicted in Figure 3, PMAA is grafted successfully from DG-gel-Br as line arrays of DGs for various grafting polymerization times. All DGs exhibited irregular line surfaces, attributed to the collapse of the PMAA brushes because of the flexibility. The average height of the line patterns of the DG-g-PMAA1 brushes was 145 ± 9 nm, with a distinct interval between the lines. Note that the intervals between the lines suggested a polished Si surface that predominantly reflects the input waves generating the diffraction effect. The irregular textures of the line surfaces were not significantly affected by the diffraction effect. For DG-g-PMAA1, the widths of the bottom regions of the polished silicon wafers remained at 1.9 µm, indicating that the polymer brushes did not extend to the trench bottom regions (Figure 3a). The height of DG-g-PMAA2 increased from 145 ± 9 to 194 ± 13 nm (Figure 3b). The trench bottom regions of the polished silicon wafers were slightly occupied owing to the collapse of the PMAA brushes. As the grafting polymerization time was increased to 4 h, the heights of the PMAA lines continuously increased to 237 ± 18 nm (Figure 3c). Extension of the PMAA brushes to the bottom regions was clearly observed, suggesting that their growth affected the diffraction effect. After PMAA grafting for 6 and 8 h, the heights were 262 ± 18 and 284 ± 20 nm respectively, which did not exhibit any significant changes. In comparison, the occupation degrees of the trench bottom regions by PMAA were remarkably enhanced for DG-g-PMAA6 and DG-g-PMAA8, indicating that the growth of the polymer chains predominantly extended to the trench bottom regions, instead of the heights (Figure 3d,e). The height of DG-g-PMAA16 reached 377 ± 30 nm without clear trench bottom regions (Figure 3f). Note that the trench region of the polished silicon surface predominantly affected the diffraction effect. The change in the widths of the trench bottom regions with PMAA growth was expected to correlate with the reflective diffraction intensity. As depicted in Figure 3, PMAA is grafted successfully from DG-gel-Br as line arrays of DGs for various grafting polymerization times. All DGs exhibited irregular line surfaces, attributed to the collapse of the PMAA brushes because of the flexibility. The average height of the line patterns of the DG-g-PMAA1 brushes was 145 ± 9 nm, with a distinct interval between the lines. Note that the intervals between the lines suggested a polished Si surface that predominantly reflects the input waves generating the diffraction effect. The irregular textures of the line surfaces were not significantly affected by the diffraction effect. For DG-g-PMAA1, the widths of the bottom regions of the polished silicon wafers remained at 1.9 μm, indicating that the polymer brushes did not extend to the trench bottom regions (Figure 3a). The height of DG-g-PMAA2 increased from 145 ± 9 to 194 ± 13 nm (Figure 3b). The trench bottom regions of the polished silicon wafers were slightly occupied owing to the collapse of the PMAA brushes. As the grafting polymerization time was increased to 4 h, the heights of the PMAA lines continuously increased to 237 ± 18 nm (Figure 3c). Extension of the PMAA brushes to the bottom regions was clearly observed, suggesting that their growth affected the diffraction effect. After PMAA grafting for 6 and 8 h, the heights were 262 ± 18 and 284 ± 20 nm respectively, which did not exhibit any significant changes. In comparison, the occupation degrees of the trench bottom regions by PMAA were remarkably enhanced for DG-g-PMAA6 and DG-g-PMAA8, indicating that the growth of the polymer chains predominantly extended to the trench bottom regions, instead of the heights (Figure 3d Figure 4b,c display the reflective diffraction patterns of the laser beam from DG-g-PMAA16 for the TM and TE polarization, respectively. The green spots represent the diffracted orders reflected by the laser beam from the DGs for the TM and TE polarization. For the TE polarization, the laser beam travels parallel through the grating as well as through multi-slits, resulting in a diffraction phenomenon that is perpendicular to the incident laser beam (Figure 4b). Equation (1) can be used to calculate the angles of the diffracted orders at a particular incident angle, where the diffraction orders satisfying |sin (θm)| < 1 are called "propagating" orders. These evanescent orders play important roles in several surface-enhanced grating properties and are considered in the equation, suggesting that the intensities reduce exponentially with the distance from the DGs. Diffracted orders at a distance less than a few wavelengths from the DGs were selected to analyze the diffraction properties. For the TM polarization, the reflective diffraction spots were ordered with various diffraction angles along the input laser beam owing to nonreciprocity (Figure 4c). Incidence of the laser beam at 45° was considered to investigate the angle asymmetry of the reflective DGs. (Table 1) A full angle asymmetry, including the angles and intensities of the reflective diffracted orders, of the DGs was clearly observed for the TM polarization. Note that the fuzzy diffractive multi-spots of PMAA DG suggest that the direction of the input laser beam was not well-aligned along the TM polarization. For the TE polarization, the diffraction spots were ordered along a horizontal direction  Figure 4b,c display the reflective diffraction patterns of the laser beam from DG-g-PMAA16 for the TM and TE polarization, respectively. The green spots represent the diffracted orders reflected by the laser beam from the DGs for the TM and TE polarization. For the TE polarization, the laser beam travels parallel through the grating as well as through multi-slits, resulting in a diffraction phenomenon that is perpendicular to the incident laser beam (Figure 4b). Equation (1) can be used to calculate the angles of the diffracted orders at a particular incident angle, where the diffraction orders satisfying |sin (θm)| < 1 are called "propagating" orders. These evanescent orders play important roles in several surface-enhanced grating properties and are considered in the equation, suggesting that the intensities reduce exponentially with the distance from the DGs. Diffracted orders at a distance less than a few wavelengths from the DGs were selected to analyze the diffraction properties. For the TM polarization, the reflective diffraction spots were ordered with various diffraction angles along the input laser beam owing to nonreciprocity (Figure 4c). Incidence of the laser beam at 45 • was considered to investigate the angle asymmetry of the reflective DGs. (Table 1) A full angle asymmetry, including the angles and intensities of the reflective diffracted orders, of the DGs was clearly observed for the TM polarization. Note that the fuzzy diffractive multi-spots of PMAA DG suggest that the direction of the input laser beam was not well-aligned along the TM polarization. For the TE polarization, the diffraction spots were ordered along a horizontal direction perpendicular to the direction of the input wave (Scheme 2a). Thus, the diffraction angles at diffracted orders (m) from −3 to +3 were almost identical to those from −3 to +3, indicating the reciprocity of the diffraction. Table 1. Diffraction angles, θ m ( • ), of reflective STP DGs at a 45 • incident angle using a 532 nm laser beam. Evanescent spatiotemporal orders are represented by "Ev". Each measurement was repeated independently three times.

Sample Type
Diffraction Orders For the TM polarization, the diffraction angles at m from −3 to −1 were significantly different from those from +1 to +3, indicating the angle asymmetry of the diffraction due to the nonreciprocity (Scheme 2b).
Note that the m ranging from −1 to +3 waves was presented as propagating diffracted orders, whereas m ≤ −2 and m ≥ +4 were diffracted as evanescent orders. Compared to the diffraction angles for the TM polarization, those for the TE polarization exhibited better angle symmetry. Therefore, it was more convenient to analyze the diffraction due to the larger interval among the diffractive spots for the TM polarization. Figure 5a,b display the 2D and 3D patterns of DG-gel and DG-gel-Br collected from the reflection at a 45 • incident angle for the TM polarization.
The reflective intensity of the laser beam from the polished silicon wafer without any patterns was 62.3 Mcnts. The reflective diffraction intensity of DG-gel at m = 0 was ca. 47.2 Mcnts, indicating that the diffraction effect was significant through the line array. Since the trench bottom regions of DG-gel did not change significantly after the bromination reaction, the diffraction intensity reduced slightly from 47. to the nonreciprocity (Scheme 2b).
Note that the m ranging from −1 to +3 waves was presented as propagating diffracted orders, whereas m ≤ −2 and m ≥ +4 were diffracted as evanescent orders. Compared to the diffraction angles for the TM polarization, those for the TE polarization exhibited better angle symmetry. Therefore, it was more convenient to analyze the diffraction due to the larger interval among the diffractive spots for the TM polarization. Figure 5a,b display the 2D and 3D patterns of DG-gel and DG-gel-Br collected from the reflection at a 45° incident angle for the TM polarization.   The trench bottom regions of the PMAA DGs became gradually occupied with the growth of the polymer chains, modifying the diffraction intensity. We observed an approximately linear increase in Ed as the grafting polymerization time increased from 1 to 16 h. To correlate the dependence of the reflective diffraction intensity on the PMAA molecular weight, 300 μL of trypsin was dropped on 1 cm 2 PMAA DGs at room temperature to cover the surfaces for 30 min to digest the gelatin layer. Subsequently, these chips were rinsed for 10 min using the PBS solution. The cleaved PMAA chains were collected from the rinsed solution by dialysis to measure the molecular weight by GPC. Figure 7b shows the dependence of the molecular weight of a PMAA brush for various grafting polymerization times on the Ed value. Linear relationships of Mn and Mw corresponding to the Ed values were observed. The linear regression equations were Mn (kDa) = 23.8 (Ed (%)) + 5.07 and Mn (kDa) = 33.6 (Ed (%)) + 5.8, with correlation coefficients of 0.9984 and 0.9988 respectively, with the PDI values ranging from 1.32 to 1.61. The high correlation coefficients indicate that the Ed values can be used to rapidly monitor the growth of polymer brushes in real time without polymer cleavage. The intensity of the reflected laser beam from the polished silicon wafer with a pattern-free PMAA layer did not change significantly, suggesting that the molecular weight was predominated by the diffraction effect, The trench bottom regions of the PMAA DGs became gradually occupied with the growth of the polymer chains, modifying the diffraction intensity. We observed an approximately linear increase in E d as the grafting polymerization time increased from 1 to 16 h. To correlate the dependence of the reflective diffraction intensity on the PMAA molecular weight, 300 µL of trypsin was dropped on 1 cm 2 PMAA DGs at room temperature to cover the surfaces for 30 min to digest the gelatin layer. Subsequently, these chips were rinsed for 10 min using the PBS solution. The cleaved PMAA chains were collected from the rinsed solution by dialysis to measure the molecular weight by GPC. Figure 7b shows the dependence of the molecular weight of a PMAA brush for various grafting polymerization times on the E d value. Linear relationships of Mn and Mw corresponding to the E d values were observed. The linear regression equations were Mn (kDa) = 23.8 (E d (%)) + 5.07 and Mn (kDa) = 33.6 (E d (%)) + 5.8, with correlation coefficients of 0.9984 and 0.9988 respectively, with the PDI values ranging from 1.32 to 1.61. The high correlation coefficients indicate that the E d values can be used to rapidly monitor the growth of polymer brushes in real time without polymer cleavage. The intensity of the reflected laser beam from the polished silicon wafer with a pattern-free PMAA layer did not change significantly, suggesting that the molecular weight was predominated by the diffraction effect, instead of reflection. Our proposed approach could rapidly determine the molecular weights of polymer brushes with high accuracy and reliability, which can provide a rapid real-time indicator for monitoring their growth.

Conclusions
PMAA brushes were grafted from a brominated gelatin line array under various grafting polymerization times as DGs via ATRP. The growth of the PMAA brushes not only contributed to the height of the lines but also their widths. Concurrently, side extension of the polymer brushes with their growth reduced the widths of the trench bottom regions, which predominantly determined the reflective diffraction intensity. A laser beam system was designed to analyze the reflective diffraction intensity of the line arrays of the DGs for TM and TE polarization with 2D and 3D diffraction patterns. The diffracted spots were ordered along directions perpendicular and parallel to the input wave for the TE and TM polarization, respectively. A line array with a 2 µm designed resolution for the TM polarization was efficient for analyzing the diffraction intensity because of the ability of the trench width to extend the polymer brushes with their growth. The growth of the polymer brush DGs changed the geometrical structure corresponding to the diffraction intensity with grafting polymerization. The diffraction intensity change ratio (E d ) along the TM polarization at m = 0 can be regarded as an indicator for monitoring the growth of the polymer brushes. A correlation between the molecular weight and the E d values was established, which presented a wide linear range and high correlation coefficients. In comparison with free radical grafting polymerization, SI-ATRP could form the regular pattern of polymer brushes to exhibit good accuracy and reliability for real-time analysis for molecular weight determination by our proposed approach. Furthermore, heights of the grafted polymers below 50 nm made it difficult to establish the calibration curve. The height of the grafted polymers over 100 nm was better to achieve higher accuracy in the measurement of molecular weight. Since the crystalline structure of polymers may interfere with the laser travel through the polymer, molecular weight determination for polymer brushes with a crystalline structure by our proposed approach needs to be further investigated in the future work. This strategy offers a convenient approach for monitoring the growth of polymer brushes in real time without destructed cleavage for molecular weight determination.