Interplaying Role of Particle Size and Polymer Layer Thickness on the Large Tunable Optical Response of Polymer-coated Silver Nanostructures


The interplaying role of particle size and polymer layer thickness on the tunable optical response of polymer-coated Ag nanoparticles (NPs) has been studied experimentally and theoretically. A large redshift (\(\sim\) 38 nm) of surface plasmon resonance (SPR) peak position has been observed experimentally for Ag NPs of sizes in the range of 8−18 nm synthesized by polyol process with the varying concentration of metal precursor (AgNO\(_{3}\)) and using a surfactant (PVP) as a stabilizer. The observed large redshift of the SPR peak position of Ag NPs coated with PVP has been argued due to mainly change of NP size as well as change of local dielectric environment in the vicinity of the Ag NPs. The experimentally observed SPR peak shift has been explained by considering the system as a metal-core polymer-shell nanostructure. The change of local dielectric environment of the surrounding of the NPs is due to the change in the PVP layer on the NPs. Such observation has been confirmed through the theoretical studies considering the changes of NP size as well as the effective thickness of the PVP layers on the NPs. The SPR peak of the system with core-shell nanostructure has been found to vary linearly with the increase in radius of core and thickness of shell together. However, it changes exponentially with particle size alone. It has been found from a detailed study that the change in the ratio of radius of core and thickness of the shell is responsible for the observed redshift. Thus, the redshift of SPR peak position of Ag NPs cannot be justified by only considering the increase in particle size. Rather shell thickness has been found to play a prominent role in the SPR peak shift. This study can be used to understand the optical response of noble metal NPs coated with organic polymers.


Metal nanoparticles (NPs), specifically plasmonic NPs (like Au, Ag ), have significant roles in electronic, optoelectronic, thermal and biomedical applications and that is why they have attracted the attention of the scientific community for a long time [1,2,3,4,5]. Due to these functional properties of plasmonic NPs, nanoplasmonics becomes an interesting research area that has inspired the researchers to carry out intense investigations for future practical applications. One of the important aspects of it is the optical absorption (OA) in an external electromagnetic field [6, 7], and the tunable optical response which is very useful for optical applications [8,9,10,11]. OA of plasmonic NPs related to the surface plasmon resonance (SPR) which is a collective oscillation of the conduction electrons subjected to an electromagnetic excitation [12,13,14]. Reducing the size of the metal NPs (up to few nm) enables to enhance light-matter interaction on a subwavelength scale, and it would be scientifically interesting to study the extreme confinement of electromagnetic radiation at this length scale which can lead us to develop a wide range of interesting future materials for different applications[15, 16]. Earlier studies reveal that SPR has a strong dependence on the particle size as well as the dielectric medium surrounding the nanoparticles [17, 18]. Most of the earlier reports pointed out the enhancement of electric filed on metal NPs and increase in scattering coefficient with particle volume is the cause behind the SPR peak shift for increasing Metal NPs [17]. But along with the particle size and the dielectric medium, another important factor for SPR peak shift and broadening is the surfactant used for stabilizing the metal NPs [19, 20]. These surfactants can effectively change the dielectric behavior of the medium in close vicinity of the NPs. So, it can be a very important aspect to investigate how the interplay of particle size with the surfactant layer thickness effectively tune the OA spectra of metal NPs. We consider Ag NPs for the investigation of the aforementioned aspect as the SPR peak of Ag NPs can be tuned over a wide range of wavelengths [21].

Fig. 1

The color variation of different Ag NP solutions prepared with varying the molar concentrations of AgNO\(_3\)

Here, we have presented a combined experimental and theoretical study on the tunable optical absorption of PVP stabilized Ag NPs, where we have emphasized on a joint effect of the nanoparticle core size and the size of polymer shell(PVP) around it for the observed redshift (\(\sim\) 38 nm).

To explain such a large redshift of the SPR peak, we performed theoretical calculations using the effective medium theory to obtain optical absorption curves for the NPs. From the theoretical calculations, we have shown that the increase in the uncoated Ag NP particle size (as estimated from the experimental data) can produce a redshift of the SPR peak, but this shift is not comparable with the redshift observed in the experimental OA data. So, we considered a core-shell structure of the particles with various thicknesses of PVP shell around the Ag NP core and showed that the ratio of the core to shell radius causes the large redshift for the larger Ag NPs. We also found that the SPR peak shift is actually linear with respect to the combined radius of the core and shell. Thus, we have provided both experimental and theoretical understanding of how the size of the NP core and the polymer shell can simultaneously change the plasmon resonance spectra of Ag NPs which may help to understand the optical response of other plasmonic NPs coated with polymer layers.


Ag NPs were prepared by Polyol process [22, 23]. Different weight percentages of AgNO\(_3\) were used to dissolve in fixed volume (20 mL) of Ethylene Glycol (EG) for making various molar concentrations of AgNO\(_3\) solution. Polyvinylpyrrolidone (PVP) solution (2 mM) was added as a stabilizer into the prepared solution of AgNO\(_3\). The prepared mixture was stirred for 30 minutes at room temperature to get a homogeneous solution. Finally, it was heated up to 70\(^{0}\)C and observed a significant color change with the variation of AgNO\(_3\) concentration (shown in Fig. 1). UV-Visible (UV-Vis.) absorption spectra of the synthesized samples were measured by Dual Beam Spectro-Photometer (Jasco V-630) varying the wavelength from 340 nm to 700 nm. All the samples were spin-coated on a glass substrate which was properly cleaned using a standard RCA cleaning method. We performed X-Ray Diffraction (XRD) on each sample to find out the nano-crystallite size. All the chemicals were analytically grade and used as purchased.

Fig. 2

(a) XRD of different Ag-NP solutions with the precursor concentration of 1mM, 10mM and 50 mM. (b) Estimated change \(\large \Delta\)D in particle size (from Debye–Scherrer’s equation) vs. AgNO\(_3\) concentration

Experimental Results

The Dependence of Particle Size on the Precursor Concentration

The size variation of Ag NPs is estimated for the samples using different precursor concentrations from the XRD analysis (shown in Fig. 2a, b). Different crystal planes of Ag (shown in Fig. 2a) were confirmed by matching the data with ICDD database. It is found that the preferred orientation of the crystal planes of Ag NPs is [1 1 1] direction for all the precursor concentration and the other orientations like [2 0 0], [2 2 0] and [3 1 1] appeared only for the higher precursor concentration. The particle size was estimated using Debye–Scherrer’s equation

$$\begin{aligned} D=\frac{K\lambda }{\beta cos\theta } \end{aligned},$$

where K=0.9, \(\lambda\)=1.54 Å, \(\beta\) is FWHM of the XRD peak and \(\theta\) is the XRD peak position. The instrumental broadening (\(\beta _0\) =0.103) has been taken in consideration to estimate the correct \(\beta\) value using \(\beta = \sqrt{(\beta _m)^2-(\beta _0)^2}\) where \(\beta _m\) is the measured value of \(\beta\). The size (D) of the Ag NPs with different concentrations (c) of the precursor was estimated between 8 nm to 18 nm for the lowest to highest precursor concentration (1 mM and 50 mM). The change in particle size (\(\Delta\) D) with the precursor concentration ”c” is shown in Fig. 2b (1 mM precursor concentration is considered as reference). The variation of \(\Delta\) D with ’c’ can be expressed as

$$\begin{aligned} \Delta D= \Delta D_m[1-exp(-\frac{c}{c_0})] \end{aligned}$$

and from the fitting we found that the value of \(\Delta D_m\) \(\sim\) 10 nm which is the maximum change in particle size and ”\(c_0\)” =17.3 mM is the critical precursor concentration for which the change in particle size becomes 63\(\%\) of the maximum change of 10 nm.

The Size Distribution of the Ag NPs

Along with the particle size, the morphology of the particles also has an effect on the OA spectra of metal NPs. Transmission electron microscopy (TEM) was done in two samples (having precursor concentrations of 1 mM and 50 mM) to determine the microscopic structure as well as the morphology of the NPs in the prepared solution. TEM image and selected area electron diffraction (SAED) pattern of the NPs for 1 mM precursor concentration are shown in Fig. 3a, b, respectively. Figure 3a shows that the NPs are spherical with a nominal size distribution. We estimated the average size as \(\sim\) 8 nm (form the histogram shown in the left inset of Fig. 3a). From the right inset of Fig. 3a, the lattice spacing (d) came out as 2.41 nm. The estimated ”d” value from the HRTEM analysis is the same as the ”d” value of the Ag NP crystallites from XRD data. The prominent crystal planes [111], [200], [220] and [311] are present in the SAED pattern (shown in Fig. 3b) of the NP. We found the similar crystal planes from their XRD data (Fig. 2a). Figure 3c is the TEM image of the NPs for 50 mM precursor concentration. Figure 3d shows the SAED pattern of NPs for 50 mM precursor concentration. The NPs for 50 mM precursor concentration also have a spherical shape (shown in Fig. 3c). The NPs have size distribution mostly around 20 nm (from the histogram shown in the left inset of Fig. 3c). The estimated size of the NPs (for 50 mM precursor concentration) from TEM and XRD analysis is nearly equal. The ”d” value of the NPs (prepared with 50 mM precursor concentration) is 2.37 nm (shown in the right inset Fig. 3c).

Fig. 3

(a) TEM images (in 20 nm scale) of the Ag NPs synthesized using 1 mM of AgNO\(_3\) (right inset shows the HRTEM image, and left inset shows the particle size distribution) (b) SAED pattern of the Ag NP synthesized using 1 mM of AgNO\(_3\) (right inset shows the HRTEM image, and left inset shows the particle size distribution). (c) TEM images (in 20 nm scale) of the Ag NPs synthesized using 50 mM of AgNO\(_3\) (right inset shows the HRTEM image, and left inset shows the particle size distribution). (d) SAED pattern of the Ag NP synthesized using 50 mM of AgNO\(_3\)

The Shift of Surface Plasmon Resonance Peak for Different Precursor Concentration

From the discussions in the previous sections, it is evident that precursor concentration plays a pivotal role in determining the size of the NPs. Here, we will discuss the effect of precursor concentration on the OA spectra of Ag NPs. From the OA measurements, we observed a noticeable change in SPR peak position of the prepared Ag NP samples having different molar concentrations (1 mM to 50 mM) of AgNO\(_3\) (shown in Fig. 4a). We increased the precursor concentration as 1 mM, 2 mM, 5 mM, 10 mM,15 mM, 25 mM and 50 mM to get the remarkable SPR shift.

Fig. 4

(a) The change in SPR peak position of Ag-NP solutions prepared with different molar concentrations of AgNO\(_3\). (b) The shift of SPR peak position (\(\Delta \lambda\)) with AgNO\(_3\) concentration. \(\Delta \lambda\) shows an exponential growth with AgNO\(_3\) concentration

From Fig. 4a, it is evident that the SPR peak position gradually shifted toward a higher wavelength with the increase in molar concentration of the precursor (AgNO\(_3\)). The SPR peak appears at 440 nm for the highest concentration (50 mM) of the precursor, and there is a significant redshift (\(\Delta \lambda\)) of \(\approx\) 38 nm in SPR peak position with respect to the lowest SPR peak position (403 nm) for 1 mM precursor concentration, which is the reference value. Here, we used a constant amount (2 mM) of surfactant (PVP) for all the Ag NP solutions. Figure 4b shows the observed variation of \(\Delta \lambda\) with the different molar concentrations of the precursor. We found that \(\Delta \lambda\) grows exponentially with the amount of precursor used for making various Ag NP solutions , and the dependence of \(\Delta \lambda\) on the precursor concentration is

$$\begin{aligned} \Delta \lambda = \Delta \lambda _m[1-exp(- \frac{c}{c_0} )] \end{aligned},$$

where \(\Delta \lambda _m\)= 38 nm is the maximum shift, \(''c''\) is the precursor concentration and ”\(c_0\)”(=17.5 mM) is attributed as a critical concentration for which \(\Delta \lambda\) is nearly 63\(\%\) of \(\Delta \lambda _m\). Interestingly, both \(\Delta \lambda\) and \(\Delta D\) have a similar dependence on precursor concentration. From equation 1 and 3, we get \(\frac{\Delta \lambda }{\Delta \lambda _m} \propto \frac{\Delta D}{\Delta D_m}\), i.e., the shift in SPR peak position depends on the change in the particle size \(\Delta\)D which is actually controlled by the precursor concentration ”c”. So, equation 1 and 3 show that the increasing precursor concentration controls the nanoparticle’s growth, which affects the SPR. The SPR has a direct relationship with nanoparticle diameter [24, 25]. The critical concentration ”\(c_0\)” is correlated with the change in critical particle size \(\Delta D_0\) when c=c\(_0\) (\(\Delta D_0\) = 6.3 nm form equation. 1) above which there would not be any appreciable change in the SPR peak. Although the particle size and SPR peak have a relation, the observed change in the SPR peak position cannot be explained only due to the particle size variation. We should not ignore the other crucial parameters like the dielectric interface between the particle and the surrounding medium [26] and the role of surfactant, which also controls the NP size (the presence of PVP surrounding the Ag NPs) [27]. The surfactant covers the nanoparticle (core) as a shell, which prevents the particles from further agglomeration [28]. The core-shell ratio (in terms of radius or volume) plays a crucial role in the SPR, which we have discussed in detail in the next section.

Theoretical Model and Discussions

UV-Vis. absorption measurements of different Ag NP solutions with varying precursor concentration (”c”) show a noticeable SPR peak shift (\(\Delta \lambda\)) of \(\sim\) 38 nm (shown in Fig. 4b), which found to be proportional to the variation of particle size (D). But the particle size is not only controlled by precursor concentration but also depends on the surrounding dielectric medium [29] as well as the surfactant layer, which implies that the SPR peak shift is not solely for the change in precursor concentration. In this section, we will show that \(\Delta\)D is not sufficient enough to produce such a large \(\Delta \lambda\). Here, we will discuss that the SPR peak shift is also a result of the changing ratio between the radius of the nanoparticle (core) and the surfactant layer (shell). We have considered the Ag NP as the spherical core of radius \(R_C\) (as TEM analysis confirms the spherical structure), and the surfactant (PVP) layer surrounds the core as a spherical shell. The core plus shell radius is \(R_S\) [30] which is schematically shown in Fig. 5.

Fig. 5

Schematic diagram of Ag NP and PVP Core-Shell Model

Here, we will consider the effective medium theory [31, 32] for the electromagnetic response of the composite nano-particle system. The equivalent dielectric constant of the core-shell nanoparticle [33] system can be expressed as

$$\begin{aligned} \epsilon _E= f\epsilon _C+(1-f)\epsilon _S \end{aligned},$$

where \(\epsilon _E\) is the effective dielectric constant of the composite system, \(\epsilon _C\) is the dielectric constant of the core, \(\epsilon _S\) is the dielectric constant of the shell and f is the volume fraction of the core and \(f= \frac{R^3_c}{R^3_S}\). The effective dielectric constant \(\epsilon _E\) becomes \(\epsilon _C\) when f=1 and when there is no NP, i.e., \(R_C\) equals to Zero or f=0, \(\epsilon _E\) becomes \(\epsilon _S\). In the later section, we will show that this f plays a vital role to control the SPR peak shift (\(\Delta \lambda\)). To study the effects of PVP shell thickness on the shift of optical absorption (OA) of Ag NPs, we have theoretically calculated the OA spectra of Ag NPs considering uncoated and PVP-coated (Ag-PVP core-shell) systems. For the calculations, we have followed the model of García et al.. [34]. This is a modified form of Maxwell–Garnett theory [35] and is basically an effective medium theory for the calculation of the OA spectra of metal NPs when embedded in a dielectric medium. The details of the theoretical model can be found elsewhere [36, 37]. This theory was very successful in calculating the OA data for Ag [38] and Au [34, 39] NPs. Recently, the model of García et al. was successfully employed for the calculation of OA data for Al [40] NPs, and alloys of noble metals NPs [41] as well as for Ag-Al NPs [42]. For calculation of the OA spectra of Ag NPs coated with PVP (as the case in the present study), we have extended this model for Ag-PVP core-shell structure using equation (4). It is to mention that the parameters used for the present theoretical study were kept fixed as in the case of [37] except the size (radius) of Ag NPs and the medium dielectric constant. The sizes of the Ag NPs were considered as estimated using XRD data, and the medium dielectric constant for uncoated Ag NPs was kept fixed to a value of 2.04. For PVP-coated Ag NPs, the dielectric constant of PVP was taken from the work of Ref. [43]. Also, the optical constants of Ag were taken from the work of Johnson and Christy [44]. To obtain the OA peak positions as per the present experimental data, we have also varied the PVP shell thickness (\(R_S\)-\(R_C\)) through the parameter, f, via equation (4). Figure 6a shows the calculated normalized OA spectra of uncoated Ag NPs in EG for different sizes. The OA spectra corresponding to the Ag NP radius of 4.10 nm shows an absorption band with a peak at around 391 nm and for the NP radius of 9 nm, the OA peak appears nearly at 395 nm (shown in the inset of Fig. 6b). This absorption band corresponds to the surface plasmon resonance (SPR) of Ag NPs. With the increasing NP size, a systematic shift of the absorption peak toward higher wavelength (redshift) with the corresponding reduction in its FWHM is observed. Such a peak shift with reduced FWHM is due to the growth of the Ag NPs [37]. Figure 6b shows the variation of the OA peak position as a function of Ag NP radius and can be expressed as

$$\begin{aligned} \lambda _{Peak}= \lambda _m[1-A exp(- \frac{R_c}{R_0} )] \end{aligned}$$

where, \(\lambda _m\)=395 nm,A=0.08 and \(R_0\)=1.9 nm. The OA peak position changes exponentially toward a higher wavelength side with an increasing radius. One can notice that there is a peak shift of about 4 nm for the lowest sized to highest sized Ag NPs. Such an SPR peak shift in OA spectra is due to the metal NP size effect [37]. This shift is much smaller than that we have observed experimentally (\(\sim\)38 nm) in the present study. Thus, the size of the Ag NPs alone is insufficient to accommodate the experimentally observed peak shift in the OA band.

Fig. 6

(a) Theoretically calculated normalized OA spectra of uncoated Ag NPs in EG for different NP sizes. (b) Variation of OA peak position as a function of the Ag NP radius (from theoretical model). Magnified portion of the peak area of figure (a) is shown in the inset which shows a redshift in SPR peak position for different \(R_c\)

To accommodate such a large peak shift (\(\sim\)38 nm) of the OA spectra, we have considered core-shell nanostructure of Ag-PVP (i.e., Ag NPs-coated with PVP). This is due to the process of preparation of Ag NPs which can lead to the coating of Ag NPs by PVP. Figure 7a shows the OA spectra of Ag-PVP core-shell NPs for different core-shell radius (\(R_S\) =\(R_C\) + PVP shell thickness). It is to mention that for each case the core radius (R\(_C\)) was considered as it was for the uncoated Ag NPs (Fig. 6a). The PVP shell thickness was chosen in such a way so that the calculated OA spectra for each case would produce the OA band with SPR peak positions as observed experimentally. Hence, this process of choice will accommodate the required shift of OA peak position as seen experimentally (Fig. 2). One can see from Fig. 7a a clear redshift of OA peak positions with an increase in shell thickness. The variation of peak position as a function of \(R_S\). is shown in Fig. 7b. The peak position increases nearly linearly with an increase in \(R_S\).

Fig. 7

(a) Theoretically calculated normalized OA spectra of PVP-coated Ag NPs in EG for different NP sizes. (b) Variation of OA peak position as a function of the radius of core-shell of Ag-PVP NPs from theoretical model


In conclusion, the tunable optical response of PVP-coated Ag NPs has been studied considering the varying particle size as well as the shell thickness. UV-Vis. absorption of the as-prepared nanoparticle solutions having different precursor concentrations shows a large redshift(\(\sim\)38 nm). The maximum change in particle size was found to be \(\sim 10\) nm (from 8 nm to 18 nm) from the XRD analysis of the samples. But from the theoretical model considering uncoated Ag NPs, it has been found that this change in nanoparticle size cannot produce the observed shift with changing core radius \(R_C\) up to 9 nm. The SPR peak (\(\lambda _{Peak}\)) of Ag NPs has been found to have a profound dependence on shell thickness (\(R_S\)-\(R_C\)) along with the particle size \(R_C\). But the variation of \(\lambda _{Peak}\) on \(R_C\) and \(R_S\) is different. We found that the \(\lambda _{Peak}\) has a linear dependence on \(R_S\), while it has an exponential dependence on \(R_C\). The finding of this work can also be applied to understand and analyze the optical response of other polymer-coated plasmonic NPs.

Data Availability

The authors declare that all the data supporting the findings of this study are available within the article. The data that support the findings of this study are available on request from the corresponding author.


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Dilip Sao acknowledges Sumit Mukherjee and Aveek Banerjee for fruitful suggestions and discussions. Sandip Das acknowledges the financial support from CSIR, India. The authors would like to thank IIT, Kharagpur for extending their help for the TEM facility.


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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Dilip Sao, Sandip Das and Subhamay Pramanik. The first draft of the manuscript was written by Rajib Nath and Probodh K Kuiri, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Rajib Nath.

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Sao, D., Das, S., Pramanik, S. et al. Interplaying Role of Particle Size and Polymer Layer Thickness on the Large Tunable Optical Response of Polymer-coated Silver Nanostructures. Plasmonics (2021).

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  • Surface plasmon resonance
  • Core-shell
  • Silver nanoparticles
  • Optical absorption