Cluster Formation and Phase Transitions Induced by Vibrational Strong Coupling

Abstract

Vibrational strong coupling (VSC) has been shown to significantly modify the chemical and physical properties of molecules and materials. Here we report the non‐resonant Rayleigh scattering of various molecules in liquid phase, such as toluene and water, and find that it is enhanced by ca. two orders of magnitude in the visible upon VSC of vibrational bands of the solvent in the infrared (IR). The results show that the enhanced scattering is due to the formation of new phase possibly consisting of clusters. The VSC phase undergoes a well‐defined transition with temperature and solvent composition. This finding has significant consequences for understanding how VSC influences molecular processes such as chemical reactivity and self‐assembly.

Non ‐ resonant Rayleigh scattering reveals that vibrational strong coupling induces clustering and phase transitions in liquids that undergo well defined transitions with temperature and solvent composition.

In recent years, light‐matter strong coupling has attracted much attention as a means to modify a variety of molecular and material properties such as chemical and biochemical reactivity, self‐assembly, energy and charge transport.^{[ 1} , ² , ³ , ⁴ , ⁵ , ⁶ , ⁷ , ⁸ , ⁹ , ¹⁰ , ¹¹ , ¹² , ¹³ , ¹⁴ , ¹⁵ , ¹⁶ , ¹⁷ , ¹⁸ , ¹⁹ , ²⁰ , ²¹ , ²² , ²³ , ²⁴ , ²⁵ , ²⁶ , ²⁷ , ²⁸ , ²⁹ , ³⁰ , ³¹ , ³² , ³³ , ³⁴ , ³⁵ , ³⁶ , ³⁷ , ³⁸ , ³⁹ , ⁴⁰ , ⁴¹ , ⁴² , ⁴³ , ⁴⁴ , ⁴⁵ , ⁴⁶ , ⁴⁷ , ⁴⁸ , ⁴⁹ , ⁵⁰ , ⁵¹ , ⁵² , ⁵³ , ⁵⁴ , ⁵⁵ , ⁵⁶ , ^{57 ]} Of particular interest to molecular science is vibrational strong coupling (VSC) which has surprisingly large effects on the chemical and physical properties of molecules.^{[ 2} , ⁶ , ⁷ , ⁸ , ⁹ , ¹⁰ , ¹¹ , ¹² , ¹³ , ¹⁴ , ¹⁵ , ¹⁶ , ¹⁷ , ¹⁸ , ¹⁹ , ²⁰ , ²¹ , ²² , ²³ , ²⁴ , ²⁵ , ²⁶ , ²⁷ , ²⁸ , ²⁹ , ³⁰ , ³¹ , ³² , ³³ , ³⁴ , ³⁵ , ³⁶ , ³⁷ , ³⁸ , ³⁹ , ⁴⁰ , ⁴¹ , ⁴² , ⁴³ , ⁴⁴ , ⁴⁵ , ⁴⁶ , ⁴⁷ , ^{48 ]} For instance, the potential energy surfaces, and as a consequence the kinetics and yields of chemical reactions, are altered and symmetry has been shown to play a key role in the observed modifications.^{[ 14} , ¹⁵ , ^{47 ]} However, much of the underlying physical chemistry remains to be understood.

Under collective VSC, as in these studies, a large number N of molecules are coupled to a resonant optical cavity mode as illustrated in Figure 1a. This results in the formation of two bright vibro‐polaritonic states, P+ and P‐ and N‐1 dark states (DS). P+ and P‐ are separated by the Rabi splitting (ℏΩ _VR ) which increases as $\sqrt{\mathrm{N}}$.^{[ 6} , ^{7 ]} While DS is shown as centered in the middle between P+ and P‐, this is not necessarily the case when the entropy of the collective coupling is taken into account.^{[ 56 ]} VSC occurs even in the dark because the coupling involves the zero‐point fluctuations of both the optical mode and the vibrational transition. It is important to note that the Rabi frequency Ω _VR  must be faster than the decay rate of the vibration and the optical mode for the system to be in the strong coupling regime. P+, P‐, and DS are collective states that potentially extend over the volume of the optical mode, i.e., on the micrometer scale in the present IR cavities. Obviously, the molecular thermal motion breaks up these extended states, reducing the correlation length. In this study we show that VSC modifies the intermolecular interactions resulting in the formation of molecular domains or clusters that can undergo a phase transition by either increasing the temperature or adding another solvent.

Figure 1.

a) Schematic representation of the formation of polaritonic collective states by vibrational strong coupling of toluene molecules. b) Rayleigh scattering from off‐ and on‐ resonance cavities of pure liquids.

Inspired by the enhanced resonant scattering reported for molecules under electronic strong coupling, ^{[ 37} , ^{53 ]} we have studied non‐resonant Rayleigh scattering in the visible of molecular liquids under VSC (Figure 1b). This has the advantage that the IR modes of the Fabry–Perot cavity barely modulate the optical response around 400 nm (see Supporting Information), the wavelength of our scattering experiments, and in addition the signal to noise ratio is extremely high.

In the present study, the experiments were carried out using a microfluidic Fabry–Perot (FP) cavity. The cavity was assembled using two parallel Au mirrors separated with a 6 µm Mylar spacer. The mirrors were prepared by sputtering 10 nm Au onto the surface of CaF₂ windows. To prevent the direct interactions between the solvents and the Au mirrors, an insulating layer was deposited on the Au surface by spin‐coating 100 nm of polyvinyl alcohol (PVA) for the toluene studies and polymethylmethacrylate (PMMA) in the case of water. Details of the fabrication of FP cavities are given in the Supporting Information. FP cavities will produce many resonant modes separated by fixed intervals, the so‐called free spectral range (FSR) as shown in Figure 2a. For achieving VSC, the cavity mode is tuned at normal incidence ^{[ 7 ]} to the molecular vibration of choice by simply adjusting the spacing between the Au mirrors with a screw‐driver (see Supporting Information). Alternatively, suitable fixed pathlength cavities, fabricated by LioniX, with constant FSR throughout the cavity and where the mirrors are coated with SiOx, were used as an additional control.^{[ 23 ]} The Rayleigh scattering was measured using Horiba Jobin Yvon Fluorolog at 10° from normal incidence (for details see Supporting Information).

Figure 2.

Fourier Transform infra‐red (FTIR) spectra of a) empty cavity, b) off‐resonance cavity, c) the C═C stretching (1603 cm⁻¹) mode and the coupled cavity, and d) the aromatic C─H stretching mode (3027 cm⁻¹) and the coupled cavity. In all the cases, the cavity transmission is given in blue color and the red traces represent the FTIR spectrum of the toluene under non‐cavity conditions, scaled for visibility.

We have analyzed the scattering of several molecules in the liquid phase under VSC but for clarity we start by focusing on toluene as a representative example. The Rayleigh scattering of distilled toluene molecule was measured under VSC (on‐resonance) and compared with the uncoupled situation (off‐resonance). In the off‐resonance cavity, none of the vibrational transitions of toluene are in resonance with any of the cavity modes (as in Figure 2b). The toluene transitions of the aromatic C═C stretching vibration at 1603 cm⁻¹ and the aromatic C─H stretching at 3027 cm⁻¹ were brought under VSC separately in different cavities as shown in Figure 2c,d.

Interestingly, upon VSC, the Rayleigh scattering is enhanced by as much as two orders of magnitude (Figure 3a,b). The enhancement factor is calculated from the ratio of scattering intensities (integrated over the peaks) and corrected for the background scattering from a “half‐cavity” containing the same solution but lacking the mirror on the back substrate. More specifically, upon coupling the C═C stretching vibration at 1603 cm⁻¹, the scattering is enhanced by a factor ca. 84 (Figure 3a) while for the coupling of C─H stretching vibration (3027 cm⁻¹) it is ca. 93 (Figure 3b). We estimate that the error in the magnitude of the enhancement is ca. ± 10%. Furthermore, the scattering intensity is very sensitive to detuning at normal incidence^{[ 6} , ^{7 ]} as shown in Figure 3c for the VSC of C═C stretching vibration. The scattering intensity enhancement follows exactly the IR absorption peak (Figure 3c).

Figure 3.

Rayleigh scattering measured at 400 nm, upon VSC of a) the C═C stretching vibration at 1603 cm⁻¹ and b) the C─H stretching vibration at 3027 cm⁻¹ (red traces), and compared to the corresponding off‐resonance scattering (blue traces). c) The Rayleigh scattering intensity monitored by slight detuning of the cavity modes nearby the C═C stretching vibration centered at 1603 cm⁻¹. The black trace represents the corresponding FTIR peak of toluene measured under non‐cavity conditions. The red squares in c) represent the enhancement factor for the different detunings of the cavity mode.

In order to understand the origin of the enhanced scattering, we studied the angular dependency of Rayleigh scattering under on‐resonance and off‐resonance conditions using a home‐built laser set‐up with a charge coupled device (CCD) detector (see Figure S2). The results show that the angular distribution remains the same whether the solvent is under VSC or not. This angular distribution is typical of the situation when the scattering domain is very small compared to the scattered wavelength.

We have also measured the Rayleigh scattering of other liquids and it is clear that the scattering enhancement varies with the molecule and the coupled vibration. For instance, in the case of mesitylene (1,3,5‐tri‐methyl‐benzene), coupling the C═C stretching mode at 1608 cm⁻¹ resulted in the 25‐fold scattering enhancement while coupling the CH₃ deformation mode at 1375 cm⁻¹, it was found to be 20 (see Supporting Information). Of particular importance is H₂O where the enhancement is a factor of ∼150 under VSC and this case will be discussed in more detail further down.

Next, we analyze the Rayleigh scattering enhancement in terms of well‐known theory applied to pure liquids.^{[ 58} , ⁵⁹ , ^{60 ]} The Rayleigh scattering intensity is then dominated by fluctuations of the dielectric constant typically associated with density fluctuations of the liquid for which the scattering intensity is given in its simplest form by Equation (1):

$$I=I_0\frac{{\pi }^2{V}^{\ast }V{\sigma }_{\epsilon }^2}{2{\lambda }^4{R}^2}\left(1+co{s}^2\mathrm{\Theta }\right)$$ (1)

where I and I ₀ are respectively the intensity of scattering and the excitation light, V* is the volume of the scattering center/density fluctuations, V the probed volume of the sample, ${\sigma }_{\epsilon }^2$ the variance of the fluctuating dielectric constant, λ the wavelength used, R the distance from scatterer and Θ the scattering angle. In the present case, the experiments for the off‐ and on‐resonance conditions, I _0, λ, R, and Θ are all constant. Thus the enhancement ratio is simply given by Equation (2):

$$\frac{{\mathrm{I}}_{\mathrm{c}}}{{\mathrm{I}}_{\mathrm{u}}}=\frac{V_c^{\ast }.{\sigma }_{\epsilon }^2\left(c\right)}{V_u^{\ast }.{\sigma }_{\epsilon }^2\left(u\right)}$$ (2)

where I _c and I _u are the intensity of the scattering under VSC and uncoupled conditions, and $V_c^{\ast }$ and $V_u^{\ast }$ _, ${\sigma }_{\epsilon }^2(c)$ and ${\sigma }_{\epsilon }^2(u)$ are the corresponding scattering volumes and dielectric variances. Adding another solvent to the original one should enhance the inhomogeneity of the medium and increase scattering but as we show next, it is the opposite that happens under VSC and this gives us a clue to what has happened under strong coupling.

In Figure 4a, the scattering intensity is plotted as function of volume content of toluene when mixed with tetrahydrofuran (THF). THF does not have any vibrational peaks in the region of C═C stretching frequency (1603 cm⁻¹) of toluene, and thus we can selectively couple this peak. As can be seen, there is an abrupt collapse in the scattering intensity occurring at 75% under dilution with THF at room temperature. In the same figures are plotted the square of Rabi splitting (blue curves) which vary monotonically unlike the scattering (the IR spectra of the Rabi splitting are given in the Supporting Information). This confirms that the VSC scattering domains are broken up in binary solvents even when the main solvent remains strongly coupled. The sharp change in the Rayleigh intensity in binary mixtures has the signature of a phase transition. In addition, it indicates that the domains are well defined, most likely clusters, whose formation is induced by VSC and will be discussed below. To confirm the presence of a new phase, temperatures studies were carried out. As shown in Figure 4b, the transition point occurs at higher compositions of THF, i.e., the VSC phase of the binary mixture is stabilized at lower temperatures as one would expect. Plotting the % composition at the transition midpoint against the temperature yields the phase diagram of Figure 4c for toluene ‐THF binary mixture with C═C stretching mode of toluene under VSC. In other words, VSC of binary mixtures can result in two different phases, monomeric and probably clusters, depending on the temperature and composition. Similar behavior is observed for toluene upon dilution with benzene‐D6, when the C─H stretching vibration (3027 cm⁻¹) of toluene is selectively coupled. Benzene‐D6 has the advantage that it has no band at the C─H stretching vibration of toluene. In this case, the sudden collapse in scattering intensity occurring at 65% toluene dilution with benzene‐D6 at room temperature as shown in Figure 5a.

Figure 4.

Rayleigh scattering at 400 nm for binary toluene–THF solvent mixtures when the C═C stretching frequency of toluene at 1603 cm⁻¹ is under VSC. a) Normalized variation of the Rayleigh scattering intensity under on‐resonance (black trace) and off‐resonance (red trace) conditions, with the increase in the volume % of toluene in toluene: THF mixtures. The blue points represent the square of the Rabi splitting for different compositions and the solutions are always in the VSC regime for these conditions. b) Normalized temperature dependence of the scattering as a function of composition in toluene: THF mixtures. c) The variation of phase transition point with temperature for toluene‐THF mixtures under VSC. The lines are just guiding to the eye.

Figure 5.

a) Normalized Rayleigh scattering at 400 nm for toluene–benzene‐D6 binary solvent mixtures when the C─H stretching vibration of toluene at 3027 cm⁻¹ is under VSC. The variation of the Rayleigh scattering intensity under on‐resonance (black trace) and off‐resonance (red trace) conditions, with the increase in the volume % of toluene in toluene: benzene‐D6 and b) Normalized temperature dependence of scattering of toluene when its C─H vibrational band at 3027 cm⁻¹ is under VSC in a 10 µm cavity and without background correction. The error bars reflect the standard deviation of at least three measurements. The lines are just guiding to the eye.

From the variation of phase transition point with temperature (Figure 4c), we expect that at high enough temperature, even pure toluene under VSC should undergo a phase transition back to the normal conditions of the uncoupled solvent. As shown in Figure 5b, this is indeed the case, with a transition point at ca. 45 °C when the C─H vibrational band at 3027 cm⁻¹ is under VSC.

Water is obviously a very important solvent that has been coupled in VSC experiments, in particular to modify biochemical systems^{[ 9} , ¹⁰ , ¹¹ , ^{12 ]} such as enzyme activity. When coupling the broad stretching mode of H₂O around 3400 cm⁻¹, the scattering is strongly enhanced and undergoes a sharp phase transition at 92% volume of H₂O in H₂O‐D₂O mixtures as shown in Figure 6a. The scattering intensity increases by a factor of 150 relative to that diluted with 15% D₂O (Figure S5), implying the formation of VSC induced phase, as in the case with toluene. Additionally, we have confirmed that we get the similar results from fixed pathlength cavities, developed for NMR purposes,^{[ 23 ]} where the whole cavity has the same FSR (Figure S6) and the mirrors are coated with SiOx as opposed to PMMA in experiments of Figure 6.

Figure 6.

Water and VSC clusters. a) IR absorption curve of H₂O (red) and Rabi splitting (blue‐black) at the H₂O stretching mode absorption peak at ca. 3400 cm⁻¹ for different % H₂O in H₂O:D₂O mixtures. b) Normalized Rayleigh scattering intensity at 400 nm as function of % volume H₂O in H₂O: D₂O mixtures for samples under VSC (black points), out of resonance (red points) and the corresponding Rabi splitting (blue points). The lines are just guiding to the eye.

It should be noted Rayleigh scattering can be enhanced in cavities due to weak coupling effects under a very specific geometry and high cavity Q factor.^{[ 61 ]} This does not explain our results since not only is the cavity Q factor is typically ca. 100 but most importantly because the enhancement disappears with detuning and in binary solvent mixtures.

Our results show that VSC can induce a new phase in pure liquids that can be broken up with increasing temperature or by addition of another uncoupled solvent. Binary solvent mixtures can also undergo phase transitions. The temperature necessary to break up the phase is on the order of k _BT, the typical energies of the collective Rabi splitting, suggesting that is driven by the formation of the collective vibropolaritonic states. Second, the one to two orders magnitude increase in scattering intensity implies that the new phase under VSC is not a homogenous one. The simplest explanation is that the VSC induced phase is composed of domains or clusters. The actual size of the clusters cannot be determined from our static scattering measurements. Techniques such as dynamical light scattering should provide the answer.

In addition to the VSC induced extended collective states, the intermolecular interactions such as the London dispersion forces and polarizability of the molecules are most likely modified contributing to clustering and phase formation. Recent theoretical studies^{[ 38} , ³⁹ , ⁴⁰ , ^{41 ]} show that the polarizability of molecules are modified under VSC. One study indicates that, while the polarizability does not vary on average, there will be hot‐spots where the local polarizability is more strongly modified. Such process could contribute to cluster formation.^{[ 38 ]} Other studies find that while polarizability per molecule decreases, it increases upon the number of molecules that are coupled and the coupling strength. Simultaneously the dipole moment of the coupled molecules is reduced.^{[ 39} , ⁴⁰ , ^{41 ]} Experimentally, London dispersion forces have also been shown to be modified.^{[ 23 ]} Interestingly, a more recent theoretical study suggest that long range intermolecular electron correlations are modified under collective strong coupling also affecting the intermolecular forces and possibly contributing to a phase transition in the dispersion forces.^{[ 42 ]} So it is probably an interplay of changes in intermolecular forces and the formation of extended collective states that leads to the VSC induced phase. The energies involved are obviously comparable to k _BT considering the phase diagram in Figure 4d and the cluster size must be limited by thermal agitation. Water and other solvents are known to form clusters in both gas phase and in binary solvents^{[ 62} , ⁶³ , ⁶⁴ , ^{65 ]} such as in water‐ethanol mixtures. VSC could provide another tool to favor and study clusters. A totally different possibility to explain the new VSC phase is the formation of a macroscopic quantum phase as recently suggested by Huo and his colleagues.^{[ 66 ]} To check for such condensate formation, further studies are necessary and an associated spectroscopic signature needs to be identified.

The VSC phase should naturally affect self‐assembly and probably explains why supramolecular assemblies and polymorphism of metal‐organic frameworks are significantly modified under VSC.^{[ 17} , ¹⁸ , ¹⁹ , ²⁰ , ²¹ , ^{22 ]} Self–assembly should be further tested under VSC in conjunction with scattering to look for any correlation. Chemical reactivity under VSC has so far been explored in various conditions, including in cases where the reactants are liquid and form a significant fraction of the solutions. We have checked that mesitylene–I ₂ complexation studied under VSC reported earlier^{[ 14} , ^{47 ]} in binary solvents with heptane does not show any enhanced Rayleigh scattering and therefore did not involve clustering (Figure S3). Therefore, the phase transition like behavior on going from weak to strong coupling reported in one of the complexation studies^{[ 14 ]} is most likely due to the collective coupled vibrations involving cooperative effects.^{[ 13} , ^{48 ]} However when nearly pure solvent under VSC are used such as in the study of enzyme activity in water, clustering might have played a role in the outcome and in the thermodynamics.^{[ 9} , ¹⁰ , ¹¹ , ^{12 ]} Further studies will be necessary to understand such details. Finally, as shown here, Rayleigh scattering is clearly a sensitive probe of VSC phenomena and a useful tool to characterize the quality of the cavities that complements other spectroscopic techniques.

In summary, vibrational strong coupling of molecular liquids can lead to the formation a new phase, most likely consisting of clusters which can easily be detected by non‐resonant Rayleigh scattering. The appearance of the VSC induced phase depends on the vibration that is coupled and can be affected by the presence of other molecules. Such VSC induced phases have numerous consequences for chemical reactivity, physical chemistry and material science, opening up many new directions to explore.

Conflict of Interests

The authors declare no conflict of interest.

Supporting information

Supporting Information

Sandeep K., Swaminathan S., Jayachandran A., Nagarajan K., Gautier J., Kushida S., Chervy T., Vergauwe R. M. A., Thomas A., Ebbesen T. W., Angew. Chem. Int. Ed. 2026, 65, e16917. 10.1002/anie.202516917

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.