Study on transport of molecules in gel by surface-enhanced Raman spectroscopy

Surface-enhanced Raman spectroscopy (SERS)-based biosensors have recently been extensively developed because of their high sensitivity and nondestructive nature. Conventional SERS substrates are unsuitable for detecting biomolecules directly from human skin. As a result, considerable effort is being devoted on developing a gel-based SERS sensor capable of segregating and detecting biomolecules because of differences in molecular transport phenomena within the gel. However, no comprehensive studies on the transport processes of molecules in gels have been published for gel-type SERS sensors. This paper reports the differences in the transport phenomena of different molecules based on the time change of SERS spectrum intensity. The Au nanorod array substrate was coated with HEC gel to prepare a sample cell to study diffusion. The SERS spectra of aqueous solutions of 9 types of molecules were measured using the prepared sample cells. The rate at which each molecule diffuses into the gel differs depending on the molecule. The time variation of the characteristic SERS peak of each molecule was investigated on the basis of a one-dimensional diffusion model, and the diffusion coefficient D was calculated for each molecule. The diffusion coefficient was compared with the molecular weight and size, and it was discovered that the larger the molecular weight and size, the slower the diffusion, which is consistent with molecular motion theory and the inhibitory effect of the gel substance.


Introduction
Surface-enhanced Raman spectroscopy (SERS) is a vibrational spectroscopic technique that has emerged as a promising method for the nondestructive study of materials down to the single-molecule level (Schlucker 2013). SERS has proven to be a powerful analytical tool for molecular structure analysis, cell imaging, and biomolecule detection, among other things (Kumar et al. 2015;El-Zahry and Lendl 2018;Yu et al. 2020;Hickey and He 2021). SERS has found its application not only in the fields of physics, chemistry, and biology, but also in engineering, pharmacy, and medicine (McNay et al. 2011;Sharma et al. 2012;Bochenkov et al. 2015;Singh et al. 2019;Segawa et al. 2019a;Kumar et al. 2020c, d). Surfaceenhanced Raman scattering is the phenomenon of enormous enhancement in the Raman scattering crosssection of molecules adsorbed in the vicinity of plasmonic nanoparticles (Le Ru and Etchegoin 2009). Recently, SERS-based biosensors have been proposed for detecting trace levels of biomolecules and diagnostics (Kumar et al. 2015;Premasiri et al. 2018;Joseph et al. 2018). A SERS substrate is any nanostructure that supports SERS enhancement. Conventional SERS substrates are metal nanoparticles in either a colloidal solution or a solid substrate (Suzuki et al. 2006;Rajput et al. 2017;Segawa et al. 2019b;Gahlaut et al. 2020;Yadav et al. 2021). As the colloidal solution is liquid and the structure of the solid substrate is rigid and brittle, it drastically limits the applicability of the SERS sensor and makes it unsuitable for detecting biomolecules directly from the human skin. As a result, a new gel-type porous SERS sensor that can collect biomarkers directly from the surface should be developed.
Yu and White have reported paper-based SERS devices for chromatographic separation and detection of target analytes in complex samples (Yu and White 2013). Similarly, because of differences in the transport processes of biomolecules permeating the gel, gel-based SERS sensors may differentiate and detect biomolecules. If this technology is developed, it may serve as a biosensor and a new means of analyzing biomolecules. Recently, we reported a gel-based SERS sensor for the direct collection of biomarkers from the skin (Kumar et al. , 2020b. We found that the probe molecule solution permeated the gel quickly and could be detected by SERS within 1 min. However, no studies have been reported on the timedependent SERS spectrum for the transport phenomena of various molecules and differences in transport phenomena in gels, depending on the type of molecule. A few other reports on the gel-based SERS sensor and the diffusion studies of molecules in a gel (Lauffer 1961;Muhr and Blanshard 1982;Amsden 1998;Samprovalaki et al. 2012;Tokita 2016;Sandrin et al. 2016;Chen et al. 2019aChen et al. , b, 2021Innocenzi and Malfatti 2019;Ogundare and Zyl 2019;Wu et al. 2020;Kim et al. 2020;Hu et al. 2021). However, the focus of these studies was on the SERS enhancement and practical application of this sensor and theoretical studies on the diffusion of micro-solutes in a homogeneous gel. To our knowledge, the transport phenomena of molecules with varying molecular weights in the gel have not been elucidated using SERS.
The interactions between a solute in a polymer network can be described as frictional or chemical (Johansson et al. 1991b). The chemical interaction is the electrostatic interaction between the solute and the polymer chains. In contrast, the frictional effects include the physical size and proximity of neighboring parts of the molecule in a solvent, e.g., steric hindrance, hydrodynamics. Furthermore, the thickness and stiffness of the polymer chains that make up the network also influence solute diffusion (Johansson et al. 1991a). The diffusion of molecules is essential not only from a fundamental physics standpoint but also for adequately evaluating the diffusion of drugs and particles (Lock et al. 2018), transport of molecules in tumors (Jain 1987), and the release of small bioactive molecules from physical gels for encapsulation and controlled release of small therapeutic molecules (Mayr et al. 2018). This study elucidates the difference in transport phenomena of different molecules based on SERS spectral intensity time change. The time change of the SERS spectra of an aqueous solution of nine different molecules was studied using a Hydroxyethylcellulose (HEC) gel-based cell. A method for calculating the SERS spectral intensity from collected data and characterizing the transport of molecules in the gel was also developed. Finally, the temporal change in SERS spectral intensity was fitted using the model. The diffusion phenomena were quantified for nine types of molecules, and the relationship between molecular weight and molecular size and the diffusion phenomena was investigated.

Materials and methods
Gel and Raman probe molecules HEC gel, which is nontoxic to humans and is used as a thickening agent in cosmetics and external medicines, was used to prepare the gel-based cell for the experiment. HEC polymer is a cellulose hydroxyethyl ether produced by processing cellulose with sodium hydroxide and reacting it with ethylene oxide and when mixed with water, it behaves as a transparent gel (Di Giuseppe 2018). The feasibility of a gel-based SERS sensor using HEC gel has been reported by Kumar et al. (Kumar et al. 2020b). HEC powder (SE400, Daicel FineChem Ltd.) was mixed with ultrapure water to a mass ratio of 10%, then well mixed and allowed to stand for at least 15 h to form an HEC gel from which bubbles were removed. The molecular weight, molecular formula, van der Waals volume (vdW volume), and solvent-exposed surface area (SEA) of the nine types of Raman probes used in this study are shown in Table 1, and the molecular structure is shown in Figure S1 (Supplementary Information). The vdW volume of a molecule is defined as the space occupied by the molecule inaccessible to other molecules at room temperature (Askadskiǐ 2003), and SEA is defined as the surface area of a molecule in which the molecule can come into contact with the solvent (Hamelryck 2005).

SERS chip and preparation of diffusion cells
The SERS chip was purchased from Nidek Co., Ltd, Japan. The SERS chip with elongated Au nanorod arrays (AuNRAs) was developed by Suzuki et al. and is now commercially available as the Wavelet (Supplementary information). The SERS chip was fabricated using a dynamic OAD technique (Suzuki et al. 2005;Kumar et al. 2014Kumar et al. , 2020a. The detailed fabrication process of AuNRAs can be found elsewhere (Suzuki et al. 2007;Kumar et al. 2020e).
The prepared sample cell is shown in Fig. 1. A 1-mm-thick silicone rubber was sliced into 20 mm 9 25 mm pieces, with a 12 mm 9 12 mm hole in the center. The prepared rubber was placed on a cover glass measuring 22 mm 9 26 mm. A small amount of HEC gel was applied to the cover glass to prevent bubbles from forming between the SERS substrate and the cover glass, and then the SERS substrate was placed in the center and squeezed from above with tweezers. On the SERS substrate, HEC gel greater than the volume of the rubber hole was applied. The excessively applied HEC gel was horizontally scraped off from the surface of the rubber in the same manner as the doctor's blade technique to prepare an HEC gel layer with a constant film thickness.
On top of that, another piece of rubber was applied in an overlapping pattern. To account for the surface drying of the HEC gel over time, the sample cell was created immediately before each molecule measurement. The SERS spectrum was monitored after 100 lL of an aqueous solution of each Raman probe molecule was dropped from the top of the gel and covered with a cover glass.
Time-dependent SERS measurement SERS spectra were acquired using a Raman spectrometer (RAM200S; LambdaVision Inc). A 785-nm laser with a 50 9 objective and approximately 30 mW power on the sample was used for excitation. 100 lL droplets of 1 mM aqueous solution of Raman probe molecules were deposited on the cell, and its SERS spectra were recorded as a function of time. Data were  (Rh6G), and Rose Bengal (RB) have 1 s exposure duration and four accumulations. Since the SERS spectrum of (S)-Equol (SE), Acid Orange 7 (AO7), and Acid Orange 12 (AO12) is weaker than that of other molecules, the exposure time was kept at 5 s. OriginPro 2018 (OriginLab Corporation, Northampton, MA, USA) was used to process the SERS spectra and analyze the data. Before analysis, all data were baseline adjusted.
A fourth-order polynomial were fitted to the raw SERS spectra and subtracted for baseline correction. For the diffusion analysis, the most intense peak area was selected.

Model for diffusion in gel
In this section, we will examine the method to evaluate the intensity of the measured SERS spectrum. We will determine a function that indicates the time change of the SERS spectral intensity. We will consider the diffusion of solutes in homogeneous solvents on a macro-scale using the diffusion equation for simplicity. According to Fick's first law, a solute's diffusion flux is proportional to its concentration gradient. At this time, if the concentration is C (z, t) as a function of the coordinates z in the vertical direction and the time t, and the amount of solute transported through the unit area in the unit time is J, then where D is the diffusion coefficient of the solute molecule. Simultaneously, the mass flowing into the region of height z and z ? Dz during time Dt is expressed as Since this is equal to the increase in solute concentration DC (z, t) during the time Dt, the following equation satisfies the continuity equation.
Equation 4 is called the diffusion equation. From kinetic theory, the diffusion coefficient is proportional to the inverse square root of the molecular weight. The higher the diffusion coefficient, the faster the diffusion. The transport processes of solutes can be described by providing the diffusion equation initial and boundary conditions, and the diffusion coefficient D can be used to quantify the diffusion of solutes. The diffusion equation of Eq. (4) is modeled in one dimension for the sample cell as shown in Fig. 1c, with the initial condition.
and boundary condition As the molecules of interest are confined to a limited region and must satisfy the above boundary conditions in this region, the diagram in Fig. 1c was replaced with Fig. 1d using the mirror image method. The solution of Eq. 4 using the boundary conditions is given by where a is the thickness of the gel layer. The detailed calculation can be found in the supplementary information.
By putting z = a in the above equation, we get Since the SERS spectral intensity of a molecule is proportional to its concentration (Salemmilani et al. 2019;Wang et al. 2019), the SERS spectral intensity S(t) can be written as Equation 7 will be used for fitting the SERS intensity curve in the linear region. When the solute diffuses into the gel, it is considered to have three main diffusion inhibitory effects (Lauffer 1961). The first is the interference of the gel with the diffusion of solutes due to the obstruction effect and increased hydrodynamic drag. The second is that the gel network may be thinner than the solute particles, and the third way the gel substance may affect the diffusion is by binding the solute (Muhr and Blanshard 1982). These effects are accounted for in the diffusion coefficient D reported from the experiments in this study.

SERS measurement
First, let us consider the SERS spectrum of BPY. BPY was chosen as the probe molecule because of its wellestablished vibrational bands and lack of fluorescence (Joo 2004). Figure 2a shows the background and SERS spectrum after 1800s when the Raman peak was well stabilized. The four prominent characteristic Raman bands of BPY at 1000, 1200, 1265, and 1600 cm -1 were observed, attributed to the pyridine ring breathing, ring deformation, C = C in-plane ring mode, and C = C stretching mode, respectively (Lu et al. 1989). Figure 2b shows the difference spectrum obtained by subtracting the background spectrum from the SERS spectrum shown in Fig. 2a. Similar timedependent difference spectra were also obtained for all molecules by subtracting the background spectra from the SERS spectrum. Figure 3 shows the difference spectra for the other eight types of molecules. All the molecules diffused through the gel rapidly and reached Au nanoparticles in less than 60 s, giving SERS peaks. For all molecules, the SERS peak was observed at the wavenumber unique to the molecule. Additionally, Raman signal intensity increased continuously with time, indicating the process of an increase in the concentration of the molecular solute arriving at the AuNPs was driven by diffusion. BPE has the strongest peak intensity among the measured molecules, and SE, AO7, and AO12 exhibited the weakest peak intensity even after increasing the exposure period by five times. Furthermore, their SERS spectra were identical because Acid Orange 7 and Acid Orange 12 are structural isomers. Figure 4 shows the highest peak area as a function of time. It is preferable to use the peak area because the peak widths of SERS and ordinary Raman are different (Pérez-Jiménez et al. 2020). In the SERS spectrum of every molecule, the highest intensity peak was selected. The rise in the peak area can be considered directly proportional to the molecule concentration arriving at the AuNP hotspot and was used to estimate the diffusion coefficient. This curve can be divided into three regions. In region I (red), probe molecules diffuse quickly within the gel and reach the AuNPs giving the first SERS signal. The time interval corresponds to when the probe molecule covers a distance equal to the gel thickness. In region II (green), the peak intensity increases linearly and tends to saturate.

Diffusion-dependent SERS intensity
The rise in peak intensity was found to depend upon the probe molecule. In other words, the transport phenomenon of molecules in the gel differs depending on the molecular weight. Additionally, the region I and region II's width corresponds to the arrival time and saturation time, respectively-was also found to depend on the probe molecule. In region III (blue), the SERS intensity attained a plateau and was almost constant. This implies that the molecules have reached an equilibrium state with a uniform concentration throughout the gel, or the number of available SERS hotspots has been occupied.
The diffusion coefficient can be calculated by slicing the gel after the experiment and measuring the solute concentration as a function of time or by measuring the total amount of solute that penetrates the gel at a given time (Lauffer 1961). We fitted the intensity-time curve using S(t) examined as a model function previously for the gel film thickness of 0.8 mm to obtain the diffusion coefficient. The linear portion of the curve was chosen for the fitting as it corresponds to the diffusion-limited transport regime where our boundary conditions are valid (Eqs. 5 and 6), see Fig. 5.
The graph shows a strong agreement between the experimental data and the fit. Since Acid Orange 7 and Acid Orange 12 always showed a gradual increasing tendency across the measurement time (3 h), the fitting was done throughout the complete data set. Table 2 shows the diffusion coefficient D of each molecule obtained by fitting.
We examined the diffusion coefficient as a function of molecular weight. Figure 5a shows the logarithmic plot of D as a function of molecular weight. The diffusion coefficient decreased with the increase in the molecular weight for all probe molecules. Light molecules PY, BPY, and BPY were found to have the maximum, and heavier molecules like RB had a lower diffusion coefficient in decreasing order of their molecular weight. This observation is consistent with a tendency based on the kinetic theory that molecules with smaller and lighter molecular weights diffuse faster in the solvent. However, when examined closely, Rh6G has a higher value of D than AO7, AO12, or CV; all three are lighter than Rh6G. Also, AO7 and AO12 have the value of D, which is similar to RB, which has approximately three times their molecular weight. Figures 5b and c show the diffusion coefficient plotted as a function of vdW volume and SEA to understand this strange behavior better. The diffusion coefficient D was found to have a similar tendency when plotted against vdW volume and SEA. This behavior is based on the inhibitory effect of the gel substance that tends to inhibit movement as the molecular size increases, and the pathway length is extended. The trend was similar to the molecular weight for the lightest three molecules with the highest D value. Comparing CV and Rh6G, Rh6G has a higher molecular weight, while Crystal Violet has a higher vdW volume and SEA than Rh6G, explaining its lower D value. Therefore, it can be considered that the vdW Comparing the molecular size of RB with CV, the vdW volume is about the same, and the solvent exposure area is smaller than CV. However, CV has a higher D. As a result, when compared to CV, the molecular weight has a more significant effect on D in the case of RB. The two molecules, AO7 and AO12, have a small diffusion coefficient D, even smaller than CV and Rh6G, even though they have smaller molecular weight values, vdW volume, and SEA. This is assumed to be because of chemical factors such as the activity of functional groups increasing due to the intricate molecular structure as the molecular weight and size grow, affecting the molecule's diffusion. AO7 and AO12 have a hydroxyl group that may have an inhibitory effect on the gel and delay molecules' diffusion by binding the gel substance to curve is the fitted curve using Eq. 7, and the black cross points are the experimental data. The blue line is the boundary condition for the fitted curve. Regions I, II, and III are colored red, green, and blue, respectively Logarithmic plot of diffusion co-efficient as a function of (a) molecular weight, (b) solvent exposed area, (c) van der Waals volume the solvent. The three types of molecules with a large diffusion coefficient D do not have functional groups, and their molecular structures are relatively simple and like each other. Therefore, it is considered that a few chemical factors contribute to the difference in molecular transport phenomena (Johansson et al. 1991b(Johansson et al. , 2007.
We did not observe the phenomenon of small molecules slowing down as in size exclusion chromatography, implying an interaction between the gel network and molecules. The coulomb interaction with molecules is negligible because HEC is a neutral polymer. Then, the molecules may interact with the network via the steric hindrance provided by the gel mesh or through another interaction such as hydrogen bonding. However, all the probe molecules and HEC are hydrated, and it is impossible to say whether the interaction with the gel is caused by direct hydrogen bonding. Moreover, we observed a monotonic decrease in diffusion rate as molecular weight increased. This result indicates the strength of the solute's interaction with the gel network. Even with these results, the presence of hydrogen bonding is uncertain. Additional experiments involving changes in ionic strength are necessary to confirm the presence of hydrogen bonding. The difference in molecular diffusion was found to be based on the kinetic theory of molecules and the inhibitory effect of gel substances, which means that the larger the molecular weight and size of the molecule, the slower the diffusion.

Conclusions
In conclusion, we investigated the differences in transport processes of molecules of varying molecular weight as a function of SERS intensity when dispersed across HEC gel. We investigated a model function that can characterize this temporal change and derived the diffusion coefficient D for each molecule that matches the experimental observations. The diffusion coefficient D was examined in connection with the molecular weight, vdW volume, and solvent exposure area. This investigation agrees with prior observations based on the molecular motion concept that diffusion slows as molecular weight and size increase and the inhibitory effect of the gel substance.
Funding This work was supported by JST COI under Grant Number JPMJCE1307.

Declarations
Conflict of interest The authors have no conflicts of interest to declare.
Human and animal rights This article does not contain any studies with human participants or animals conducted by any author.