A new ultrasonic transducer sample cell for in situ small-angle scattering experiments

Irradiating biological and soft matter samples by ultrasound and high frequency acoustic instrumentation is gaining more and more importance.^1–8 On the one hand, ultrasound imaging is a very important non-invasive technology that can image materials at μm length-scale.^9,10 On the other hand, high intensity focused ultrasound has found application in tuning the shape of biodegradable polymers,¹¹ rupturing lipid coated micro-bubbles,¹² and crossing epidermis (skin)¹³ for drug delivery. Low intensity ultrasound at a frequency of 1–2 MHz is used in sonodynamic therapy for treating cancer.¹⁴ Despite the strong influence that ultrasound may have on the materials, its time dependent effect on the nm length-scale has not yet been explored.

Scattering experiments are well established in measuring the structure and dynamics of soft matter samples, such as polymers,^15–19 microgels,⁵⁹ polymer composites and nanocomposites,^{20–27,60,61} and polymer aggregates like micelles,^28–30 biopolymers,³¹ proteins,^32,33 and glasses on the nm length scale.^34–36 A variety of methods to manipulate samples and to record in parallel the morphology or dynamics are described in the literature.^37–39 For example, sample environments to accurately regulate the physical parameters, like temperature, magnetic field, pressure, or humidity belong to the standard equipment of small-angle neutron scattering (SANS) instruments. While these techniques have its primary focus on keeping a certain parameter fixed, other techniques such as in situ stretching or rheology experiments manipulate the mesostructure of the sample during measurement.^40–42 Recording SANS data during static deformation or low frequency oscillatory shear rheology enables us to measure the influence of an external force on the structure at the nm length scale and thereby to understand the molecular interactions in detail.^40,41 Such studies permit to derive material models that can themselves be used to understand the macroscopic properties.^43–47 

A high frequency perturbation of samples is possible by exposure to an ultrasonic field. We designed and built a new sample cell by incorporating an ultrasonic transducer that was used to successfully record scattering diagrams in situ, during and immediately after sonication. It has been well documented in the literature that small-angle neutron scattering (SANS) experiments on micelles show a clear response to external perturbations.^28,48–50 Therefore, for our first experiments, we have chosen to use sodium dodecyl sulfate (SDS) surfactant micelles in aqueous solution, whose unperturbed state is well-documented. Following Bergström and Pedersen,⁵¹ SDS forms ellipsoidal micelles at 40 °C and a concentration, ϕ_w = 0.5%. Form factor analysis yields a semi-major axis of 23 Å and semi-minor axis of 13 Å. The number of surfactant molecules per micelle is defined by their aggregation number, N_agg = 54. Following a detailed SANS investigation, the aggregation number of SDS micelles was found to decrease with increasing temperature and decreasing concentration.⁵² At 25 °C and, ϕ_w = 5%, a pronounced structure factor shows up in the scattering intensity, where N_agg = 89, and a micellar volume of 3.64 × 10⁴ ų was reported.⁵² We will use this particular concentration and temperature for our investigation to determine the time constant associated with micellar self-assembly followed by ultrasound induced disintegration at a fixed temperature. During both disintegration and self-assembly, we observe a time dependent change, showing the importance of our new in situ sonication tool.

In addition to SDS, we present the in situ SANS diffraction data for commercial (Brij100) alkyl-poly (ethylene oxide) (n-PEO) micelles in D₂O. We have chosen n-PEO surfactant since it is a well-established model system for frozen micelles.^53,54

In this section, some technical details about the novel ultrasonic sample cell are given. To make the cell user friendly, two important design criteria are satisfied. First, the setup fits inside the standard sample environments so that we have access to a wide range of well-established instrument controls like variation of temperature, humidity, or magnetic fields as if required by the user community. Second, we included the option to vary the sample thickness, which fit the needs of multiple experimentalists. Figure 1(a) illustrates the schematic representation of the ultrasonic transducer cell. The outer dimensions are about 25 × 25 × 50 mm³. Cylindrical passages for the neutron beam (Ø is equal to 18 mm) are drilled on each side and threaded to fit aluminum (Al) caps, which are used as exit- and entrance windows. The distance between the caps is variable and defines the sample thickness in the neutron beam. We used 2 mm path length for our SANS experiment. The transducer is glued with epoxy onto one of the aluminum hulls as indicated. This design allows us to use one or two transducers if needed. The bottom opening was sealed with a screw coated with Teflon ribbon and allows for future upgrades of the cell like a sensor to measure the amplitude of the sonic field. As shown in Fig. 1(b), the transducer is a piezoelectric ring, purchased from Steminc (Part No. SMR1585T07111R), with an outer diameter of 15 mm, a thickness of 0.7 mm, and inner diameter of 8.5 mm. The ring transducer is essentially a ceramic ring (piezo material SM111) with silver (Ag) electrodes on the same side. It resonates at thickness mode with a resonant frequency of 2.95 ± 0.09 MHz, with electromechanical coupling coefficient ≥49%, and it has a resonant impedance of ≤0.65 Ω and a static capacitance of 1840 ± 276 pF at 1 KHz frequency. The glued transducer is in direct contact with the sample in the sample chamber (Fig. 1). The neutron beam is guided through the central passage of the transducer and is limited in diameter using a standard ¼ in. (6.35 mm) SANS cadmium aperture. The only material in the neutron beam besides the sample is the aluminum end caps with a total wall thickness of less than 1 mm. If required, Al can be replaced by other materials like niobium, quartz, or sapphire. More than 95% empty cell transmission was measured for neutrons.

Figure 2(a) illustrates the block diagram of the circuit, Fig. 2(b) the photo of the transducer cell and Fig. 2(c) that of the circuit. The radio frequency (RF) circuit consists of a RF amplifier which is driven by a waveform generator producing a continuous sinusoidal waveform of fixed frequency and can feed a power up to 100 W. By connecting the RF circuit to a serial resonant circuit, we can easily vary the frequency up to 3 MHz by changing the inductance. For our tests, we used an air coil [N = 10, length 5 mm, Ø = 25 mm, see Fig. 2(c)]. We have also tested the option to generate ultrasonic signal at a fixed frequency by connecting the resonant circuit of the transducer to a separately purchased mist generation kit (SMUTK2500RS112) which is self-tuning to a frequency predefined by the transducer and an onboard inductance. As Fig. 2(a) indicates, the option to use the setup to trigger the SANS detector in pulsed mode for time-of-flight (ToF) experiments is available without any changes to the electronics. A transistor-transistor-logic (TTL) signal produced by the waveform generator can be used to trigger the reset of the timing mechanism for the detector at a fixed interval which synchronizes the neutron measurement with the ultrasonic setup.

A typical frequency range of 1–2 MHz is used for ultrasound in sonodynamic therapy.¹⁴ So in our tests we used the ultrasonic transducer at 1.5 MHz, feeding a power of 10–30 W to the resonant circuit yielding an estimated ultrasonic field intensity of I₀ ∼ 10 W cm⁻² at 100% pulse amplitude. In addition, such a cell can be used for ultrasonic imaging and diagnostic echocardiography using a large diameter transducer with higher frequency and a receiver. It will open up the possibilities to acquire ultrasonic images and scattering data of different soft matter samples simultaneously.

The SANS experiments were carried out using the NGB 30 m SANS instrument of the NIST Center for Neutron Research (NCNR) at National Institute of Standards and Technology (NIST).⁵⁵ The sample-to-detector distance was fixed to 2 m and the neutron wavelength was λ = 6 Å. This configuration covers a Q-range from ∼0.02 Å⁻¹ to ∼0.23 Å⁻¹, where Q = 4π sin(θ/2)/λ, with the scattering angle θ. A wavelength resolution of Δλ/λ = 10% was used. All data reduction into intensity I(Q) vs. momentum transfer $Q=|Q→|$ was carried out following the standard procedures that are implemented in the NCNR macros of the Igor software package.⁵⁶ The data are scaled into absolute units (cm⁻¹) using a direct beam, and a detector sensitivity correction was done with a plexiglass measurement. The solvents and empty cell are measured separately as backgrounds. The ultrasonic transducer cell was mounted inside a standard multi-position heating/cooling block for SANS designed to hold up to 9 standard demountable titanium cell holders. The block has the dimension of 53 × 35 × 38.1 mm³, with a beam aperture of 12.5 mm. The heating element in the block provides a temperature range from ambient to 300 °C, with an accuracy of ±0.5 °C. Quartz or silicon windows can be used to prevent heat loss by convection.

Figure 3 displays the SANS intensity, I, as a function of the momentum transfer, Q, for ϕ_w = 5%, SDS in D₂O. The data are presented over a Q-range centering around the structure factor peak in the presence and absence of ultrasonic pulses for several selected times, t. The measurements were performed at a constant temperature of 25 °C, following a three-step protocol. At first, we measured unperturbed sample to determine the initial state at time, t = 0 s. Second, the sample was sonicated for t_p = 65 s (pulse on), at a frequency of ν_s = 1.5 MHz and amplitude 100% that corresponds to an intensity of I₀ ∼ 10 W cm⁻². Third, we waited for t_off = 1305 s (pulse on). Hereafter, we use the notion “pulse” for the perturbation by ultrasound of a certain amplitude and duration t_on at a constant frequency ν_s. The scattering diagrams were recorded with a repetition rate of 30 s for a total period of 1400 s (off-on-off cycle). Figure 3(a) reports the SANS data acquired during ultrasonic irradiation time, pulse width, t_p. Here, t = 0 s represents the unperturbed sample. Figure 3(b) shows SANS data after the sonication was switched off. The legends in Fig. 3(b) indicate the SANS scattering pattern evolving with time once the ultrasonic pulse was turned off. As indicated by the arrow, there is a clear indication of a decrease (pulse on) and increase (pulse off) in the height of the scattering peak/intensity with time. It is accompanied by a systematic shift of the mean peak position (Q₀). The error bars represent the standard deviation.

To explore the changes more in detail, we have modeled the data in Fig. 3 by a log-normal distribution,

Here, A is the area under the scattering curve, Q₀ is the mean peak position of the scattering peak, σ characterizes the standard deviation of the distribution, and B is the background. It should be noted that A is directly related to the amplitude of the scattered intensity, which is proportional to the volume and aggregation number of the scattered micelles.^28,29,49

The symbols in Fig. 4(a) represent the normalized area, A(t)/A(t = 0 s). The sonication is indicated by the shaded area. Starting the sonication (pulse on), there is a rapid decrease in the area to 60% of the initial unperturbed value after a pulse duration of t_p = 65 s. After the sonication is switched off, the initial unperturbed value is reached by an exponential increase with time with a time constant, t_A = 156 ± 5 s. After sonication is switched off, the system reaches the initial unperturbed value for t ≥ 900 s within the statistical accuracy. The time constant t_c of our exponential growth process corresponds to the time, t, it takes to reach, $At=tc/A0=1−1/e$⁠, (∼63.2%) of its asymptotic value. This shows the plateau value is reached after t > 5t_c. In the case of Fig. 4(a), the initial unperturbed (plateau) is reached for t ≥ 900 s, within the statistical accuracy. The corresponding inter-particle distance, d₀ = 2π/Q₀, is plotted in Fig. 4(b). Here the system also shows an exponential recovery to the equilibrium distance of 67.30 ± 0.02 Å. We obtain a time constant, t_c(d₀) = 185 ± 5 s. At the end of the ultrasonic pulse, d₀ was reduced to 63.16 Å, about ∼6% of the equilibrium distance. The standard deviation, σ, is only slightly perturbed. The average value σ = 0.243 ± 0.002 is identical to that of the unperturbed micellar structure. It should be noted that a difference between the time constants, t_A, and, t_c(d₀), is expected. Here, t_A, represents the micellar reformation time associated with the area of the scattering intensity. For similar peak width (σ) and shape, it is proportional to the volume (V_micelle) and N_agg of the individual scattered micelles, $A∼VmicelleNagg$⁠.^28,29,49,50 Whereas t_c(d₀) is associated with the recovery time of the inter-micellar distance and is related to their interaction potential.^28,29 In fact, the dynamics associated with the individual micelle is faster than that of the collective micelles (t_A < t_A(d₀)).

To test the reproducibility of the experiments and/or a possible degradation of the sample, we performed multiple test experiments. In each, we sonicated the sample for t_p = 65 s (pulse on) followed by a waiting time of t_off = 1305 s (pulse off). Figure 5 represents the area obtained from Eq. (1) for five different on-off cycles. The first data point in each cycle marks the initial state (pulse off), followed by two data points in pulse on state that shows a rapid decay of the scattering intensity and area. It is followed by the off state waiting time that represents an exponential growth to the initial state. The error bars in the data represent the standard deviation obtained from the fitting.

In order to calculate the statistically averaged response over a time period of 110 min, the normalized area, A(t)/A(0), from Fig. 5 is plotted as a function of time within each cycle [Fig. 6(a)]. There is no indication for systematic changes as evident from Fig. 6(a). Such statistical nature of the exponential growth opens the opportunity to accumulate the intensity over several cycles to increase the signal-to-noise ratio or to reduce the acquisition time. We observe the same behavior as described earlier for Fig. 3. The mean response of micellar recovery following ultrasonic irradiation is obtained in Fig. 6(b) as the normalized mean area, ⟨A(t)/A(0)⟩, from five different on-off cycles. The data are modeled for an exponential growth, yielding a mean time constant, ⟨t_A⟩ = 169 ± 2 s. A similar analysis for the mean inter-particle distance yields a time constant, ⟨t_c(d₀)⟩ = 202 ± 2 s, and a mean standard deviation, ⟨σ⟩ = 0.243 ± 0.001.

To understand the micellar disintegration during sonication, we have performed similar analysis for three consecutive on-off cycles with an ultrasonic pulse duration, t_p = 112 s. The choice of t_p is a compromise between following the decay as long as possible and repeating the number of pulses to accomplish optimum statistics. The corresponding SANS diffraction pattern follows a similar trend like Fig. 3(a). It was analyzed using Eq. (1), and the mean value of the normalized area, ⟨A(t)/A(0)⟩, and the inter-particle distances, ⟨d₀⟩ = ⟨2π/Q₀⟩, are plotted in Figs. 7(a) and 7(b), respectively. They exhibit exponential decay with mean decay constants, ⟨t_A^decay⟩ = 49 ± 3 s and ⟨t_d0^decay⟩ = 37 ± 3 s, as indicated by the solid lines. The inset of Fig. 7(b) illustrates the corresponding mean standard deviation, ⟨σ^decay⟩ = 0.23 ± 0.002.

It should be noted that the set of parameters immediately after the ultrasonic pulse, ⟨t_A⟩, ⟨t_c(d₀)⟩, and ⟨σ⟩, reflects the statistical average micellar reformation time, recovery of the inter-particle distances, and the associated polydispersity, respectively. During the ultrasonic pulse, a similar set of parameters, ⟨t_A^decay⟩, ⟨t_d0^decay⟩, and ⟨σ^decay⟩, reflects statistical average perturbed decay time depicting micellar disintegration, decaying of the inter-particle distances from its equilibrium value and the associated polydispersity, respectively. A possible explanation for such a time constant can be associated with the formation of the micelles after an initial breakdown of the entire micelles during sonication.^57,58 It should be noted that such a process is associated with the change in both size and aggregation number of the micelles. A detailed further investigation of such phenomena is required.

Figure 8 illustrates the SANS diffraction data for commercially available 18-alkyl-poly(ethylene oxide) (C₁₈-PEO5) in D₂O at a volume fraction, ϕ = 0.5%. Here the 1D scattering data are obtained by summing 10 scattering curves with each measured for 12 s during the ultrasound pulse on state. During the pulse off state, we performed summation over 20 separate scattering curves with each measured for 21 s. The solid line represents the calculated scattering intensity using a frozen micelle form factor²⁸ using a micellar radius, R_m = 8.6 nm, taken from the literature.⁵⁴ We did not see a difference in the diffraction pattern.

In summary, we have designed and implemented a new ultrasonic transducer sample cell for neutron scattering, especially adapted for the standard SANS sample holder and temperature control. The cell enables us to perform a unique, first of its kind time resolved in situ SANS experiment by periodically switching on and off the high intensity ultrasonic pulse. Using our cell, we successfully demonstrated test measurements to determine the time constant associated with SDS micellar self-assembly followed by ultrasound induced disintegration at a fixed temperature. We have also presented a weak scattering case for frozen alkyl-PEO micelles where we do not see any ultrasound induced structural change. Additional advantage of the cell is a very low incoherent background that will allow us to gain structural information over a broader Q-range.

We acknowledge the support of Louisiana Consortium for Neutron Scattering (LaCNS). The neutron scattering work is supported by the U.S. Department of Energy (DoE) under EPSCoR Grant No. DE-SC0012432 with the additional support from the Louisiana Board of Regents. We would like to acknowledge Paul Butler and Cedric Gagnon from the National Institute of Standards and Technology Center for Neutron Research (NIST-NCNR) for offering SANS time, helpful discussions, and technical assistance. We acknowledge Christopher Van Leeuwen, department of Chemistry, Louisiana State University, for carefully proofreading the manuscript. The authors acknowledge the support of the National Institute of Standards and Technology (NIST), U.S. Department of Commerce, in providing the neutron research facilities used in this work. Access to NGB30SANS was provided by the Center for High Resolution Neutron Scattering, a partnership between the NIST and the National Science Foundation under Agreement No. DMR-1508249.