3.1.

THz-Absorption Feature of Lactose Powder

Figure 1 shows the THz-spectra in the THz-TDS system without a lactose-sample, and the inset shows the THz-pulse and Gaussian-window superimposed on the pulse before DFT. Periodic fluctuation was observed in the THz-spectra (plain line) but successfully removed by using the Gaussian-window (bold-line). If the THz-pulse was sufficiently intense, the fluctuation due to aliasing was negligible, but the pulse-edge in relatively weak signal passed through samples should be taken into account for the precise analysis.

Fig. 1

Fourier transformed THz-spectra from the THz-pulse without Gaussian window (plain-line) and superposed Gaussian window (bold-line). The inset shows the THz-pulse and Gaussian window.

A typical prelimary absorption spectrum of the ${\mathrm{L}}_{\alpha }·{\mathrm{H}}_2\mathrm{O}$ powder consists of several narrow-bands and a broad-band as shown in Fig. 2, where the experimentally obtained data were shown by filled-circles with a fit (dash-line), by the deconvoluted spectra (solid-lines), and broad-band (dot-line). The spectral deconvolution was successfully achieved by Lorentzian as previously shown for the lowest lying spectrum⁸ after removal of a broad-band by a polynomial cubic function. The narrow-bands with peaks at $17.1{\mathrm{cm}}^{-1}$ (0.53 THz) and $45.6{\mathrm{cm}}^{-1}$ (1.37 THz) can be recognized as the fingerprint of ${\mathrm{L}}_{\alpha }·{\mathrm{H}}_2\mathrm{O}$,^9,10 which were denoted as ${\alpha }_1$ and ${\alpha }_2$, respectively. The absorptions derived from ${\mathrm{L}}_{\alpha }·{\mathrm{H}}_2\mathrm{O}$ are recognized to be associated to lactose molecular-rotations in the crystal as indicated by first principle calculations.¹⁰ A weak absorption with a peak at $39.7{\mathrm{cm}}^{-1}$ (1.19 THz) denoted as ${\beta }_1$ can be suggested to be derived from ${\mathrm{L}}_{\beta }$ because the absorption was dominant in ${\mathrm{L}}_{\beta }$ powder.⁴

Fig. 2

Absorption spectrum of preliminary used $\alpha$-lactose powder, where experimentally obtained data, broad band background, deconvoluted spectra and the fit are shown by filled-circle, bold dash-line, solid-line, and plain dash-line, respectively. Absorptions due to $\alpha$-lactose monohydrate and anhydrous $\beta$-lactose are denoted as “${\alpha }_1$,” “${\alpha }_2$,” and “${\beta }_1$,” respectively.

3.2.

Crystallization Behavior of Lactose in Supersaturated Solution

Figure 3 shows a photograph of crystallized lactose-particles observed by a Nomarski differential interference microscope, where the lactose was crystallized for (a) 24, (b) 72, and (c) 120 h and then dispersed in ethanol by ultra-sonic vibration for 20 s after being dried in an incubator. It has been recognized that lactose in the supersaturated solution around room-temperature can be mainly crystallized into ${\mathrm{L}}_{\alpha }·{\mathrm{H}}_2\mathrm{O}$ by seeding of the ${\mathrm{L}}_{\alpha }·{\mathrm{H}}_2\mathrm{O}$ powder. The crystallization behavior is also dependent on this condition because the $\beta$-lactose present in the aqueous solution selectively blocks the growth of the (020) face, which results in growth along the $b$ direction (not the $-b$ direction) and the Tomahawk shape as shown in Fig. 4.^11,12 Further, it was demonstrated by a dimethyl sulfoxide-lactose system with controlled $\beta$-lactose content in the solution that the Tomahawk shape is extended along the $-b$ direction, reducing the growth along the $c$ direction with increasing $\beta$-lactose content in the lactose solution.¹² Since $\beta$-lactose is present above 60% in aqueous lactose solutions around room-temperature by the mutarotation in equilibrium,¹³ the crystal is enlarged to the $-b$ direction as shown in Fig. 4. In this article, the crystal size was determined along the $b$ axis in the anisotropic shape, and the average crystal size was uniquely increased with the crystallized period as shown in Fig. 5.

Fig. 3

Nomarski photographs of extracted lactose from the supersaturated solution for (a) 24, (b) 72, and (c) 120 h.

Fig. 4

Miller indicates of Tomahawk shaped $\alpha$-lactose monohydrate crystal.¹²

Fig. 5

Dependence of average crystallized particle size of $\alpha$-lactose monohydrate on the crystallized period, where the crystal size was estimated along the $b$-axis.

3.3.

Dependence of THz-Absorption Feature on Crystallized Lactose Particle Size

Figure 6 shows the absorption spectra (solid-line) of lactose consisting of crystallized lactose particles with an average size of 4.3, 14.7, and 27.6 μm, where the lactose crystals were extracted for 24, 72, and 120 h from the lactose solution, respectively. The inset shows deconvoluted spectra of the absorptions due to ${\mathrm{L}}_{\alpha }·{\mathrm{H}}_2\mathrm{O}$ crystal, in which the absorption of anhydrous ${\mathrm{L}}_{\alpha }$ was removed. It was mentioned that the broad-band was numerically removed by a polynomial cubic function, and the absorption coefficient is normalized by the weight of the lactose sample because the density of lactose was different in aperture for each sample. As expected from the particle shape, lactose was mainly crystallized into ${\mathrm{L}}_{\alpha }·{\mathrm{H}}_2\mathrm{O}$ because the spectra were dominated by the absorptions due to ${\mathrm{L}}_{\alpha }·{\mathrm{H}}_2\mathrm{O}$ (${\alpha }_1$ and ${\alpha }_2$). Anhydrous ${\mathrm{L}}_{\beta }$ was also crystallized. It was probably formed on the ${\mathrm{L}}_{\alpha }·{\mathrm{H}}_2\mathrm{O}$ crystal in the drying process, but the content in the extracted lactose was within 4%. The absorption features of ${\alpha }_1$ and ${\alpha }_2$ were dependent on the particle size as shown in the inset of Fig. 6. Details on the integrated absorption intensity and the full-width at half-maximum (FWHM) for the average particle size are shown in Fig. 7, in which the results on the average particle size of 3 μm is for the preliminarily used ${\mathrm{L}}_{\alpha }·{\mathrm{H}}_2\mathrm{O}$ powder. The ${\alpha }_1$ line width (filled-square) was independent of the particle size. A significantly narrow absorption spectrum of ${\alpha }_1$ with a FWHM of about $1.3{\mathrm{cm}}^{-1}$ has been reported by using a photomixer and continuous-wave, however, the obtained THz-TDS was broader than that,⁸ which is because of the resolution of the spectroscopy methods. Since the FWHM of $3.7{\mathrm{cm}}^{-1}$ obtained in this work was smaller than that of $4.91{\mathrm{cm}}^{-1}$ as demonstrated by THz-TDS,⁸ but much broader compared to the native feature with an FWHM less than $1.3{\mathrm{cm}}^{-1}$, it is considered that the spectrum width was not apparently changed in the results under the resolution limit of the THz-TDS system. Previously, the significantly sharp feature of ${\alpha }_1$ was discussed by the solid-state density functional theory and assigned to externally hindered rotational modes in the crystal $b$-axis, not to the internal modes.¹⁴ In such modes, the absorption intensity can be expected to increase with the crystal size much less than the wavelength of the incident THz-electromagnetic wave as shown in Fig. 7 (closed circles). On the other hand, the absorption of ${\alpha }_2$ was broader than that of ${\alpha }_1$ and the line width increased with the particle size (open-squares). However, the integrated intensity of ${\alpha }_2$ (filled-squares) was scarcely increased with the particle size, but the dependence was very small compared to ${\alpha }_1$. The vibration mode of ${\alpha }_2$ was identified as molecular-rotation in a lactose active mode by the first principles calculation.¹⁰ The significant difference of ${\alpha }_2$ feature is possibly due to the absorption is due to the internal vibrations associated with intermolecular hydrogen-bonding. The significant difference of ${\alpha }_1$ and ${\alpha }_2$ intensities resulted in assignment of the particle size. Figure 8 shows the intensity ratio of ${\alpha }_2/{\alpha }_1$ for the average particle size. A ratio as high as 3.98 was linearly decreased with the particles’ size and to 3.45 for the size of 27.6 μm, where the correlative square-factor was 99.2% on the least squares method. As a result, if the particles are contained inside samples, the average particle size can be nondestructively evaluated by the ratio of ${\alpha }_2/{\alpha }_1$ obtained by THz-TDS.

Fig. 6

Absorption spectra of extracted lactose from the supersaturated solution with the average size of (a) 4.3, (b) 14.7, and (c) 27.6 μm. The inset shows the deconvoluted $\alpha$-lactose monohydrate spectra.

Fig. 7

Variation of relative integrated absorption intensity of ${\alpha }_1$ and ${\alpha }_2$ (filled circles and open circles) and full-width at half-maximum of ${\alpha }_1$ and ${\alpha }_2$ (filled squares and open squares) for average crystallized particle size of $\alpha$-lactose monohydrate.

Fig. 8

Dependence of integrated absorption ratio of ${\alpha }_2/{\alpha }_1$ on average crystallized particle size of $\alpha$-lactose monohydrate.