J. Phys. Chem. B 2009, 113, 12655–12662
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Mixing Behavior and Interphase Formation in the Diethylene Triamine-Water System Studied by Optical Imaging and Spatially Resolved Brillouin Scattering Martine Philipp,*,† Florimond Collette,† Michael Veith,‡ Pierre Seck,§ Roland Sanctuary,† Ulrich Mu¨ller,† John Kieffer,|,⊥ and Jan K. Kru¨ger† Laboratoire de Physique des Mate´riaux, Laboratoire de Chimie, UniVersity of Luxembourg, Luxembourg, Luxembourg, Institut fu¨r Neue Materialien, UniVersita¨t des Saarlandes, Saarbru¨cken, Germany, and Department of Materials Science and Engineering, UniVersity of Michigan, Ann Arbor, United States ReceiVed: May 20, 2009; ReVised Manuscript ReceiVed: August 5, 2009
The injection of water beneath liquid diethylene triamine in a glass cuvette leads to an unexpected phase evolution behavior of the two liquids. The space and time dependent developments of the molecular structure and the underlying transport associated with mixing of the two liquids are monitored by optical imaging and scanning Brillouin microscopy. Apparently, results obtained by either experimental technique lead to disparate interpretations. Whereas optical imaging suggests the existence of a two phase structure, which disappears within a few hours, acoustic microscopy indicates the evolution of a more gradually evolving and longerlived three phase structure. According to molecular acoustics, the transport of diethylene triamine into water and vice versa behaves strongly asymmetric in time. An attempt is made to reconcile the observed optical and acoustic manifestations of the mixing process on the basis of molecular complex formation. I. Introduction Static and dynamic acoustic properties are known to respond sensitively to molecular level structural developments in condensed matter.1-3 Molecular acoustics can be expected to yield valuable insights into the structural evolution resulting from molecular association phenomena.1-3 Because of their tendency to exhibit hydrogen bonding, polar liquids such as water and diethylene triamine (DETA) already tend to form molecular associates by themselves.4-9 Hence, the question as to how both kinds of molecules interact if they are brought into contact with one another is of fundamental interest. Given that DETA is a three-dent ligand the molecular structures that form could either be dominated by hydrogen bonds or by chelate complexes.4,6-12 From a chemical point of view, these associations are not stable but in constant transition between different states! A hydrogen atom of a water molecule can be coordinated just by one nitrogen atom (normal hydrogen bridge) or by two nitrogen atoms of the same molecule. The latter type of binding leads to a chelate complex. In this bonding configuration, the hydrogen atom has one bond to oxygen and two coordinative bonds to the nitrogen atoms; as these latter are connected by two CH2-groups, a ring is formed of the type · · H · · N1-C-CN2 · · , H and N2 being connected. The present work describes a remarkable phase evolution that ensues from carefully injecting water into DETA and is initially subject to rapid but incomplete convective mixing, followed by gradual diffusive homogenization. Water, which is denser than DETA, is injected at the bottom of a column of DETA so as to minimize turbulent motion of the liquids. The subsequent * To whom correspondence should be addressed. Tel: +352 466 644 6784. Fax: +352 466 644 6331.
[email protected]. † Laboratoire de Physique des Mate´riaux, University of Luxembourg. ‡ Universita¨t des Saarlandes. § Laboratoire de Chimie, University of Luxembourg. | University of Michigan. ⊥ Sabbatical at the Laboratoire de Physique des Mate´riaux, University of Luxembourg.
mixing process and structural evolution is monitored by means of optical imaging and scanning Brillouin microscopy,13,14 which allows one to record a temporal and spatial evolution of phase boundaries that depends on the method of observation. To better understand this temporal and spatial evolution, we compare the results to those obtained for homogeneously mixed samples of a variety of DETA/water concentrations. Originally, optical imaging was not expected to deliver useful information about the mixing process of these two transparent polar liquids like water and DETA. However, our interest in optical imaging intensified after observing an optically visible phase boundary that persisted for several hours. The optical and acoustic investigations of the mixing process between DETA and water turned out to yield completely different perspectives on the molecular association process. We illustrate this by first presenting the optical results followed by those obtained from scanning Brillouin microscopy. II. Experimental Section A. Samples and Sample Preparation. Fresh singly distilled water and diethylene triamine (DETA, Fluka) were the basic constituents. To prevent any water contamination of the dry DETA, it was stored above a molecular sieve. Two types of samples were prepared; in one convective mixing upon bringing the two liquids in contact with each other was minimized and in the other one it was maximized. For the first kind of samples, denoted as S1, 2 cm3 of DETA were filled into a glass cuvette having a base of 1 × 1 cm2 and a height of 4 cm. A volume of 1 cm3 of water was added beneath the DETA column at the bottom of the cuvette using a pipet (see Figure 2a,b). Afterward the cuvette was sealed with a lid. Of the different ways we tried to layer the two liquids, gently injecting water, which is the denser of the two liquids, at the bottom of a DETA column was the only approach in which a distinct interface between the two liquids could be preserved. However, despite careful manipulation, some degree of convective mixing, predominantly pulling
10.1021/jp904714g CCC: $40.75 2009 American Chemical Society Published on Web 08/28/2009
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DETA into the water-rich bottom layer, could not be prevented. Two samples of type S1 were prepared, one for the optical imaging and another one for the scanning Brillouin microscopy (SBM). The second preparation scenario, designated as S2, consisted in thoroughly mixing 30 g batches of different DETA/water concentrations through mechanical stirring. Hence, the mass of a sample S2 is about 15 times larger than that of a sample S1. It should be stressed that during the mixing for all concentrations, except those close to pure DETA or pure water, significant heat production was observed, albeit not measured. After sitting for several hours, those homogenized samples S2 revealed a significantly increased viscosity in combination with thixotropy. To ascertain homogeneity in S2 samples and assess whether overall structural developments in S2 samples are comparable to those in S1 samples, the acoustic properties and refractive indices of the former were measured several hours after preparation. The whole sample preparation and investigations took place at ambient temperature (T ) 295 ( 0.5 K). B. Optical Imaging. The macroscopic appearance of the samples was monitored through optical imaging. The photographs were taken using a Nikon D200 digital camera with a macroobjective (AF Micro Nikkor 60 mm 1:2.8D). The camera was mounted on a tripod facing the samples. During the entire process the camera and its optics were held in a fixed position. C. Brillouin Spectroscopy and Scanning Brillouin Microscopy. Brillouin spectroscopy is an optical measurement technique giving access to the acoustic properties of optically transparent or translucent samples at hypersonic frequencies.15,16 It should be stressed that it is especially suited for our purpose as it provides access to the bulk properties of the samples while being entirely nondestructive. The present investigation was performed with a modified six-pass tandem Brillouin spectrometer of the Sandercock type.13,15,16 Internally the six-pass tandem Brillouin spectrometer is optimized for a maximum optical throughput. Using a second photon counting device, an additional beamsplitter and shutter system, the interferometer can be stabilized independently of the scattered light intensity and the duration of the measurement. A Gaussian telescope is used to focus the spectral components of the scattered light onto the recording avalanche diode. The scattered light is coupled to the entrance pinhole of the tandem spectrometer by an intermediate imaging system. By means of a periscope this entrance pinhole in combination with the primary imaging optics can be adjusted perfectly to the scattering volume of interest. The primary imaging optics consists of a two lenses system with a lens L (see Figure 1a, f ) 80 mm) being the entrance lens. The exit lens of this imaging system has a focal length of 250 mm. By using lens L to focus the incident laser light and to collect the scattered light and by advancing this focal volume along the length coordinate of the sample, we can determine the hypersonic velocities and attenuations in the material with micrometer spatial resolution.13,14 Photon counting was performed using a multichannel analyzer. A typical spectrum is shown in Figure 1b. The technical challenge with the mixing of DETA and water in sample S1, which is governed by convection, diffusion, and chemical association rate phenomena, was to simultaneously achieve adequate spatial and temporal resolution, especially at the beginning of the mixing process. As a compromise that provides sufficient spatial coverage while keeping the time for each scan short compared to the characteristic relaxation time of the overall mixing process, we chose to perform SBM measurements at spatial increments of 100 µm. A simple description of the theoretical background of this technique, which is based on the inelastic scattering of laser light
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Figure 1. (a) Experimental setup for the backscattering geometry and the sample holder. b ki and b ks, wave vector of the incident and scattered laser light; L, imaging lens; A, aperture; C1, liquid column 1; C2, liquid column 2; d, vertical axis fixed to the cuvette coordinate system with origin at the bottom of the cuvette. Cuvette dimensions: 10 × 10 × 40 mm3. (b) Typical Brillouin spectrum, recorded after 1.5 h at the position d )19.5 mm (see Figure 5). The Rayleigh line is omitted for technical reasons.
by thermal acoustic phonons, can be derived by a kinematic approach.17 For a given scattering geometry the phonon frequency f and phonon wave vector b q are deduced from the laws of energy and momentum conservation:
pωs ) pωi ( 2π · pf
(1)
bi ) pk bi ( pq pk b
(2)
where b ki,s and ωi,s designate the wave vector and angular frequency of the incident (i) and the scattered (s) light. The so-called backscattering geometry consists of choosing the wave vector of the incident and scattered light b ki,s to be antiparallel (see Figure 1a). Consequently the phonon wave vector b q is collinear to b ki and b ks. This leads to the largest possible magnitude of the phonon wave vector b q for a given direction of phonon propagation. In principle, only one longitudinally polarized phonon doublet can be measured in the backscattering geometry for a homogeneous, isotropic sample. Transverse phonons are forbidden by symmetry.15 Under these conditions the Brillouin spectrum is composed of the socalled Rayleigh line (centered at the frequency ωi/2π) and one Brillouin doublet. The Rayleigh line results from elastically scattered light. Inelastically scattered light leads to the Brillouin doublet centered at the frequencies ωi/2π ( f. The physically relevant hypersonic frequency f(q b) and the temporal acoustic attenuation Γ(q b) of the underlying longitudinally polarized acoustic phonon can be obtained by deconvoluting the measured Brillouin doublet, taking into account the instrumental broadening along the optical path. Here, f and Γ designate the position and half width at half-maximum of the Brillouin lines. The statistical error of the
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Figure 2. (a) Filling the water beneath DETA, (b) withdrawal of the pipet, (c) 0 min, (d) 0.33 min, (e) 1 min, (f) 6 min, (g) 0.25 h, (h) 0.5 h, (i) 2.7 h, (j) 4.9 h, (k) 8 h, (l) 26 h. Cuvette dimensions: 10 × 10 × 40 mm3.
hypersonic frequency data typically lies in the one-tenth of a percent regime. The error in determining the hypersonic attenuation Γ is larger than that for the hypersonic frequency by roughly a factor of 10. The vertical scanning of the cuvette in 100 to 500 µm intervals was realized by means of an electronically controlled scanning stage (Owis). Using this scanning technique we probed the acoustic properties along a vertical line d, advancing from the initially DETA-rich column C2 to the water-rich C1. As shown in Figure 1a, the origin of the d-axis was chosen at the bottom of the cuvette. Recording spectra in the immediate vicinity of the C1/C2 phase boundary was possible because the meniscus at this interface is almost flat (see Figure 2). The scattering volume corresponded to the laser beam’s volume within the cuvette and had a length of 10 mm. Because the incident beam was focused near the center of the cuvette, the lateral dimension of the laser beam was not constant but varied between an estimated 10 to 50 µm. The Brillouin signal contains acoustic information that is spatially averaged over this scattering volume. In order to obtain reliable phonon spectra, the accumulation time was at least of 20 s for each spectrum. If the refractive index n of the investigated material in the scattering volume is known, the longitudinal hypersonic velocity V can be determined according to
λLaser 2π · f V(q) ) ) f·Λ ) f· q 2n
TABLE 1: Refractive Index nD, Mass Density G, Hypersonic Frequency f, Hypersonic Velocity W, Longitudinal Modulus c11, and Hypersonic Attenuation Γ for the Constituents DETA and Water at T ) 295 K nD F (g/cm3) f (GHz) V (m/s) c11 (GPa) Γ (GHz)
DETA
water
1.482 0.946 10.44 1870 3.3 1.0
1.333 0.997 7.90 1580 2.5 0.3
For further details about the acoustic/mechanical properties see Section II.C.
access to the time and space dependent refractive index n of the scattering volume was given. As a first approximation, the space and time dependent sound velocities were estimated on the basis of the measured sound frequencies f(t,d) and a constant refractive index of nD ) 1.431, which corresponds to the refractive index interpolated between those of pure water and DETA at a molar ratio of xmol DETA ) 25 mol % DETA. According to Table 1 and
Xmol
DETA
)
(3)
Fwater Mwater
FDETA · Xvol DETA MDETA Fwater FDETA + · Xvol MDETA Mwater
(
)
DETA
where M describes the molar mass, or in our case where Λ is the wavelength of the probed phonon and λLaser is the vacuum wavelength of the laser.15 A frequency doubling diode laser from Coherent with a vacuum wavelength of λLaser ) 532 nm was used. The laser power was kept below 5 mW to avoid heating of the scattering volume. The acoustic wavelengths and the sound velocities could only be roughly estimated for sample S1, as no
Xmol
DETA
)
0.009 · Xvol DETA 0.055 - 0.046 · Xvol DETA
the ratio 25 mol % DETA equals to a volume ratio of 1/2 water/ DETA. In the frame of this approximation, the acoustic wavelength is Λ ) 186 nm. The relative error of the sound
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velocity data so obtained is estimated in the percent regime. Such an approximation was not necessary for samples S2, since their refractive indices were measured. III. Results and Discussion A. Optical Investigations. The optical investigations concerning the DETA-water mixing process of sample S1 are presented in the photo sequence Figure 2a-l. Figure 2a-d shows the instants when water is added beneath the DETA column. In Figure 2a the pipet is still partly filled with water, and in Figure 2b the pipet is already empty and on the way to be retracted from the cuvette. The photograph Figure 2c is taken immediately after removing the pipet and corresponds to the start time of the whole experiment. Despite the precautions we took to prevent turbulent flow upon adding the water, some convective mixing occurred at least during the first hours in the lower column C1. This mixing process was visible due to optical heterogeneities caused by differences in the refractive indices between water, DETA and possibly DETA-water complexes. After 0.25 h, optical streaks are still observable in the lower column C1. An optical two phase structure develops from the beginning of the filling process, which suggests that water and DETA only partly mix in the lower column C1 in the cuvette during the first instants. Any remaining DETA, which cannot be dissolved quickly in the injected water seems to be lifted upward (top column C2). Once the initial turbulences have settled, and the columns C1 and C2 are clearly delineated by the interface between them, molecular transport processes must occur between both columns. Because of at least two observations, this transport cannot be purely diffusive since (i) convection channels connect both columns (white streaks indicated by arrows in Figure 2h) and (ii) if the significant volume exchange between C1 and C2 were purely due to molecular diffusion the sharp interface shown in Figure 2 would blur sooner than after 4.9 h (see also below). The temporal evolution of the mixing between the columns C1 and C2 is described by the optical meniscus’ position dmen versus time t. Whereas the relative position of the meniscus can be evaluated within 0.2 mm, the absolute error corresponds to 0.5 mm. During the first hours of the experiment the height of C1 increases slowly at the expense of that of C2, indicating that DETA is further dissolved in C1. Therefore at least during the first 5 h the composition of the water-DETA mixture in C1 must change continuously. The optical interface between C1 and C2 is slightly corrugated just after injecting the water. With time the interface corrugation disappears, leaving the impression of a sharply defined flat phase boundary until 4.9 h. The flat, white shining surface in Figure 2i,j is attributed to an optical parallax error at a totally reflecting interface, but is not an indication for the genesis of an interphase. That the same mirror plane is not observed in pictures taken earlier is due to the surface corrugation of the meniscus. At 26 h, any optical phase boundary has disappeared. Figure 3 shows the temporal evolution of the meniscus position dmen, which is equivalent to the height of C1. The fact that the initial height of C1 is ca. 10.6 mm instead of 10.0 mm supports the argument that DETA is incorporated in water during the initial turbulent flow. For as long as the meniscus is detectable its position can be used to monitor the progress of the molecular transport process. The advancement of the interface with time can satisfactorily be fitted by a stretched exponential
dmen ) d∞ - (d∞ - ds) · e- t/τ β (
)
(4)
Figure 3. Position of the optical meniscus dmen versus time t.
allowing us to determine the characteristic relaxation time τ of the transport process, that is, τ ) 0.62 h. In this expression, 0 < β ) 0.55 e 1 is a measure for the distribution of the “relaxation times” τ, ds is the initial height of C1 (at t , τ) and d∞ is the height C1 asymptotically approaches for t . τ. It should be stressed that after 4.9 h eq 4 becomes meaningless since the meniscus blurs and soon disappears. It is astonishing that during the first 4.9 h a sharp optical boundary is visible between C1 and C2. In other words, once DETA molecules cross the boundary from C2 to C1 they do not contribute to a visible concentration gradient at this interface. Apparently they dissolve and migrate rapidly in C1 and only grow the volume of the water-rich zone C1 at the expense of C2. At a first glance, eq 4 in conjunction with Figure 2 seems to suggest simple explanations for the optical observations; after the initial demixing of the less dense pure DETA (C2) from a denser water-DETA mixture (C1), a slow but continuous dissolution of DETA in C1 and water in C2 takes place, while an optical phase contrast at the interface between C1 and C2 is maintained for more than 8 h. Optically the interface disappears when the discontinuity between the refractive indices of liquids in C1 and C2 vanishes. A continuously varying refractive index across the interfacial region is still compatible with the experimental observations. B. Acoustic Microscopic Investigations. In the following, we present sound velocity data as a function of space and time, revealing a long-lived spatial inhomogeneity that results from the complex interplay between transport and chemical reaction processes. To facilitate an approximate quantitative interpretation of the sound velocity data of sample S1, as it undergoes local compositional (and structural) changes with time we provide in Figure 4 the acoustic properties of homogeneously mixed DETA-water compositions, as obtained for S2 samples. The refractive indices, needed for the calculation of the sound velocities according to eq 3, were measured by an Abbe refractometer. The sound velocity and refractive index curves will be discussed in a subsequent publication, when the related density data have been obtained. The clear deviation of the sound velocity curve from a linear mixing rule is attributed to networks formed by complexation and hydrogen bonding of DETA and water molecules. The maximum sound velocity reaches a value of 2530 m/s at about 25 mol % of DETA, corresponding to a water/DETA volume ratio of 1/2, being 40% higher than that obtained by a simple mixing rule (1780 m/s). This maximum sound velocity (∼square root of the longitudinal elastic modulus) reflects a maximum in cohesive molecular interactions. The composition of this DETA-water mixture suggests that each of the three amine teeth of a DETA molecule forms a complex interaction with one water molecule. Hence,
DETA-water System by Optical Imaging and Brillouin Scattering
Figure 4. Hypersonic frequency f and velocity V versus DETA molar concentration xmol DETA for the homogeneous DETA/water samples S2 at 295 K.
Figure 5. (a) (b) Overview of the spatial and temporal evolution of the hypersonic velocity V and frequency f until 166 h near the phase boundary. d0 is the position of the steepest descent for the first spatial scan at 0.23 h. (a) DETA’s and the water’s values are indicated by horizontal lines.
the overall composition of the S1 sample was chosen as that corresponding to this maximum sound velocity. In comparison to the optical imaging given in Section III.A, a drastically different physical picture about the temporal and spatial mixing process of the sample S1 is obtained from the SBM measurements. A summary overview of this evolution, covering 166 h, is given in Figure 5. All data points correspond to measured frequency values, the velocity axis must be considered in the context of the aforementioned refractive index approximation (see Section II.C). Although optical investigations indicate that a homogeneous sample is achieved after 26 h, the spatial variation of the sound velocity reveals that complete homogenization needs a much longer time. Note that due to 15 times smaller masses of the S1 samples compared to those of
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Figure 6. Spatial evolution of the hypersonic frequency f/velocity V (filled squares) and attenuation Γ (open squares) after 0.23 h. The horizontal lines indicate DETA’s values for f/V and Γ. For this scan d0 ≈ dmen.
the S2 samples, and the slow mixing of DETA and water in S1, the heat production in the latter is assumed to be negligible and the evolution of the hypersonic properties is not due to temperature changes. This argument was confirmed by the absence of thermal lensing during the Brillouin measurements. Because of the finite amount of time it takes to complete each SBM scan, the time since the beginning of the experiment attributed to each sound velocity vs distance curve bears some imprecision. The optical meniscus disappears much earlier than the atypical acoustic behaviors including the interphase. For the sake of consistency, we label the data of each SBM scan with a time that is defined as the duration between the injection of water in the cuvette and the moment the scattering volume passes through a particular position d0 along the sample length axis. The position d0 was chosen to coincide with the steepest descent in the sound velocity versus distance curve during the first scan. Four minutes after the injection of the water the first scan was started with the scattering volume positioned at d ) 16.5 mm, that is, safely inside the column C2. Subsequently the scattering volume was lowered toward and across the interface between C1 and C2 by lifting the scanning stage. Nine minutes later, that is, at t ) 0.23 h, the scattering volume passed the position d0 ) 14.1 mm for the first time, later identified as the location where the sound velocity changes most sharply. For this scan, the position d0 also coincides roughly with the optical meniscus (see Figure 3). As can be seen in Figure 6, both the hypersonic velocities V(d) and the corresponding hypersonic attenuations Γ(d) exhibit irregular behavior near d0. When approaching the interface between C1 and C2 from the initially DETA-rich side both the sound velocity and attenuation increase. Note that the sound velocity and attenuation of pure DETA are higher than those of pure water. Above 15.1 mm the sound frequency is roughly 10.1 GHz. According to Figure 4 a DETA/water composition with 7 mol % DETA would exhibit this value. It is very unlikely that well above d0 the DETA concentration would be this low. Instead, we believe that the drop of the sound velocity below that of pure DETA is a transient phenomenon. As small amounts of water penetrate the DETA-rich compartment, a complex or hydrogen bond network is not established immediately, but initially water molecules interfere with the dipolar interactions between DETA molecules and act as plasticizers. A linear interpolation between the sound frequencies of DETA and water (using volume fractions), which neglects for sure the nonequilibrium nature of the structures that form upon mixing, yields a DETA concentration of about 55 mol % above 15.1 mm.
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Closer to the interface, for d values descending from 15.1 to 14.1 mm, the hypersonic frequency/velocity increases steeply by about 10% instead of diminishing, as would be expected considering that the sound velocity and attenuation for water are indeed smaller than for DETA. These results are striking since in the initially water-rich bottom column (d < d0) the sound velocity and attenuation values significantly exceed those of both water and DETA! Such behavior possibly results from the formation of DETA-water complexes and the development of H-bonds that are long-lived compared to the characteristic probe time (∼1 ns). Close cohesion between these DETA-water complexes and the formation of extensive H-bond networks can be responsible for the relatively high sound velocities. Note that for d < d0, the gradual increase in velocities with decreasing d-values most likely originates from the fact that the recording time of ∼20 min for the scan is comparably long within the time frame of the sample’s structural evolution. In other words, at this early state structures with higher sound velocities/ attenuation continue to form while the scattering volume is moved through the initially water-rich column toward lower d-values. The mean sound frequency in segment C1 during the course of the first scan is 11.4 GHz. According to Figure 4, we determine a DETA concentration of close to 11 mol % at this time in C1. This rough estimation agrees with the value obtained by estimating the relative heights of C1 and C2. Thus, the sound velocity and attenuation data shown in Figure 6 can be interpreted to vary respectively between two relatively constant values, one corresponding to the water-rich and the other to the DETA rich regions of the specimen. This changeover occurs between d ) 14.1 and 15.1 mm. We refer to this region, which is situated in the vicinity of the optically visible phase boundary as the acoustic interphase. Accordingly, the observed acoustic interphase is likely chemically and structurally diffuse and represents the transition region between two differently associated molecular liquids. The d-dependence of the hypersonic attenuation shows qualitatively the same behavior as the velocity. The higher sound attenuation in the water-rich region compared to the DETA-rich region is due to the increased dynamical viscosity of the liquids with the stronger DETA-water complexation, as is already confirmed for samples S2 (see Section II.A). As seen in Figure 7a, the gradient in the acoustic profile changes accentuates with time. At 0.58 h we can distinguish four different acoustic regimes. In sequence of increasing d-coordinate, these are (i) a region C1 of constant V- and Γ-values within the initially water-rich phase, that is, for roughly d < 14.1 mm; (ii) a region C1a in which V- and for the first hour of the experiment also Γ-values increase with d; (iii) a region C1b in which V- and Γ-values decrease; and (iv) a region C2 in which V- and Γ-values remain constant at levels corresponding to those for pure DETA. The regions C1a and C1b constitute the acoustic interphase. With time this interphase grows into the finally remaining mixed phase at the expense of zones C1 and C2. The peak in sound velocity, which marks the boundary between regions C1a and C1b increases with time to reach its highest value at around 20.7 h (see Figure 7b). Beyond that time the peak broadens significantly and slightly drops in magnitude, so that eventually the sound velocity characterizing the entire sample is only a little lower than the highest peak value (see Figure 7c). A detailed discussion of the evolution in zones C1, C1a, and C1b follows. During the first two hours, the sound frequency in C1 increases considerably, while it remains homogeneous across this compartment. This is attributed to a fast increase of
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Figure 7. Spatial evolution of the hypersonic frequency f/velocity V (filled symbols) and attenuation Γ (open symbols) between 0.58 and 166 h. The solid vertical lines indicate the positions dmen of the optical meniscus for the given times (see Figure 3).
the DETA concentration in C1 due to predominantly convective fluxes. According to Figure 4, the frequency level of 12.5 GHz after 2.3 h corresponds to a DETA concentration of roughly 14 mol %. With time, the convection becomes hindered due to the increased viscosity of the liquid in C1 associated with the formation of DETA-water complexes. After roughly 2 h, convective transport of DETA is so reduced that it is likely surpassed by diffusion. The fast increase of the sound velocity in C1 is accompanied by a significant change in shape of the adjacent interphase C1a/C1b. Whereas during the first scan, the sound velocity across the interphase changes rather steplike, during subsequent scans it shows a peak. The sound velocity profiles shown in Figure 7a exhibit sharp onsets at the boundary between C1 and C1a. With time, the onset shifts only slightly upward, indicating that the convection of DETA in C1 is increasingly reduced. Concomitantly, the peak in the profile grows in height and width and shifts to higher d-values. Considering the shape of the sound velocity profiles in zones
DETA-water System by Optical Imaging and Brillouin Scattering C1b and C2, there is no evidence for an upward transport of water via convection. The astonishing evolution of the sound velocity profile can be elucidated by discussing the two peaks observed after 1 and 2.3 h. The increase in peak height and its shift toward the DETA-rich zone is understandable only if a sufficient amount of water diffuses in positive d-direction. According to Figure 4 the peak sound velocity at 15.5 mm after 2.3 h corresponds to about 20 mol % DETA. The loss of DETA from C1a and above is attributed to a predominant convective transport of DETA to C1. It surprises that the sound velocity, which peaks at 15 mm after 1 h, still has the same magnitude at this location after 2.3 h, while the peak shifts toward higher d-values. This suggests that at 15 mm the DETA/water composition remains rather constant (∼18 mol %) during this period. Taking into account the permanent water diffusion upward the latter observation is understandable only if the obvious DETA transport to C1 does not affect the DETA concentration within the already developed interphase (e.g., at 15 mm), but rather short-circuits through the layer. Apparently, the formation of yet denser DETA-water complex networks is limited to the DETA-rich side of the sound velocity peak, as is indicated by the growing peak height. Accordingly, it is difficult for DETA molecules to permeate already formed interphase layers, while water can diffuse through more readily. To conclude, the growth of the acoustic interphase’s sound velocity in thickness and in height is caused by diffusion of water molecules upward and by a combination of convection and diffusion of DETA molecules downward. The interphase region develops because of the chemical affinity between the two constituents and grows with time as governed by the reaction kinetics. As the interphase expands along the sample axis, it increasingly acts as a transport barrier hampering the permeation of DETA into water and vice versa. Figure 7a suggests that at least during the first hours the diffusion coefficient for water is higher than the one for DETA. This transport barrier explains the slowing rise of the meniscus as shown in Figure 2 and also the large time scales of the overall phase equilibration. Between 0.58 and 1.0 h a pronounced hypersonic loss maximum arises in the interphase, but completely disappears by 2.3 h. The origin of this high hypersonic attenuation is not clear yet. It can as well be due to acoustic Mie scattering as to hypersonic relaxations.17 The sound velocity maximum in the interphase is obviously not caused by the hypersonic losses since this peak still grows after the loss peak disappeared. While the optically visible phase boundary considerably blurs after 4.9 h and vanishes by 6.1 h, the acoustic interphase remains well defined for a much longer period of time (see Figure 7b). At later times the definition of an acoustic interphase becomes also somewhat arbitrary as the V(d)-gradients become more and more gentle. The sound velocity peak reaches its maximum value of Vmax ≈ 2600 m/s at 20.7 h. This value exceeds that of water by about 77% and that of DETA by 35%. By this time the hypersonic attenuation is already rather constant throughout the acoustically studied region. Especially the initially DETArich column C2 undergoes significant changes for at least another 140 h. The sound velocity noticed in the equilibrated sample S1 is quite consistent with the ones observed for similar concentrations of the homogeneous samples S2. This result implies that the transient transport barriers in S1 are sufficiently permeable that a state similar to the equilibrium state of S2 is achieved after more than 160 h.
J. Phys. Chem. B, Vol. 113, No. 38, 2009 12661 Combined, the optical and acoustic probes clearly delineate the interphase, which separates the initially water- and DETArich phases and which continuously grows to eventually occupy the entire sample volume. On the water-rich side, the boundary of the interphase is indicated by a sharp change of slope in the sound velocity versus distance curve that persists for nearly 5 h; on the DETA-rich side the boundary of the interphase is marked by the discontinuity in the refractive index. It is remarkable that this index jump occurs consistently at the location at which the sound velocity drops to approximately 2020 m/s. Eventually, as the structural formation progresses into the initial columns C1 and C2, the delineation of the interphase becomes less and less defined. One remaining problem concerns the discrepancy between the optical observation of a sharp meniscus, which would indicate a discontinuous change in refractive index at the interface between C1b and C2, and the continuous change of chemical composition and structure based on the acoustic measurements. Given that the optical interface resides at a location of constant sound velocity, we surmise that a particular structural characteristic, such as a percolation threshold for dipolar interactions within a liquid partially constrained by a network of DETA-water complexes may cause a small jump in optical polarizability.18,19 Even such a small jump could be responsible for a sufficiently large change in refractive index to render the interface optically visible, and would be consistent with the observed sound velocity profile. IV. Conclusion Complementary information about molecular structural formation processes is obtained by optical imaging and acoustic microscopy. Taking into account the polar nature of water and DETA and their good initial miscibility a rather quick homogenization was expected, leading possibly to DETA-water associates. The complex structural developments are attributed to the interplay between convection, diffusion, and hindered diffusion caused by transport barriers. Convection dominates at the initial state of mixing during the absence of complex formation. However, only after 6 h an optically visible meniscus between two different phases starts to blur considerably. In contrast to the optical evidence the acoustic microscopy indicates right from the start the development of an extended interphase (over several millimeters), that is, a three phase system. The complexation by DETA is directed to the protonic hydrogen atoms of the water. As DETA has three nitrogen atoms, each of these atoms can interact with a proton independently or simultaneously. In the latter case, the bonding is called chelatelike. The complexes are made responsible for the genesis of unexpected high sound velocities. At the moment, we can only speculate about the nature of a sharp optical meniscus, which is not reflected in the smoothly varying sound velocity profile. However, the meniscus is consistently observed at a location within the interface characterized by a constant sound velocity, and inferably, a specific complexes network structure. Accordingly, a discontinuous polarizability change can be attributed to this structure, in which dipolar interactions in DETA transition from bulk behavior to that dominated by DETA-water association. Acknowledgment. This work was financially supported by the National Research Fund of Luxembourg. References and Notes (1) Hamilton, M. F. J. Acoust. Soc. Am. 1994, 96, 3225. (2) Matheson, A. J. Molecular Acoustics; John Wiley: New York, 1971.
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Philipp et al. interphases in epoxies as seen by non-destructive high-performance Brillouin microscopy. In Adhesion - Current research and applications; Possart, W., Ed.; Wiley-VCH: Weinheim, 2005; p 125. (14) Sanctuary, R.; Bactavatchalou, R.; Mu¨ller, U.; Possart, W.; Alnot, P.; Kru¨ger, J. K. J. Phys. D: Appl. Phys. 2003, 36, 2738. (15) Kru¨ger, J. K. Brillouin spectroscopy and its application to polymers. In Optical Techniques to Characterize Polymer Systems; Ba¨ssler, H., Ed.; Elsevier: Amsterdam, 1989. (16) Kru¨ger, J. K.; Alnot, P.; Baller, J.; Bactavatchalou, R.; Dorosz, S.; Henkel, M.; Kolle, M.; Kru¨ger, S. P.; Mu¨ller, U.; Philipp, M.; Possart, W.; Sanctuary, R.; Vergnat, C. About the nature of the structural glass transition: An experimental approach. In Ageing and the Glass Transition; Henkel, M., Pleimling, M., Sanctuary, R., Eds.; Springer: Berlin, 2007. (17) Berne, J. B.; Pecora, R. Dynamic light scattering with applications to chemistry, biology, and physics; Wiley: New York, 1976. (18) Lorentz, H. A. Ann. Phys. Chem. 1880, 9, 641. (19) Lorenz, L. V. Ann. Phys. Chem. 1880, 11, 70.
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