Abstract
We present a model for quasielastic neutron scattering (QENS) by an aqueous solution of compact and inflexible molecules. This model accounts for time-dependent spatial pair correlations between the atoms of the same as well as of distinct molecules and includes all coherent and incoherent neutron scattering contributions. The extension of the static theory of the excluded volume effect [A. K. Soper, J. Phys.: Condens. Matter 9, 2399 (1997)] to the time-dependent (dynamic) case allows us to obtain simplified model expressions for QENS spectra in the low Q region in the uniform fluid approximation. The resulting expressions describe the quasielastic small-angle neutron scattering (QESANS) spectra of DO solutions of native and methylated cyclodextrins well, yielding in particular translational and rotational diffusion coefficients of these compounds in aqueous solution. Finally, we discuss the full potential of the QESANS analysis (that is, beyond the uniform fluid approximation), in particular, the information on solute–solvent interactions (e.g., hydration shell properties) that such an analysis can provide, in principle.
R.E.L. thanks G. Steiner and B. Urban for very valuable technical assistance during the NEAT experiment. Two of us (A.K. and R.E.L.) thank the Hahn-Meitner-Institut for its hospitality. Financial support for A.K. by the Institute of Chemistry and Biochemistry of the Freie Universität Berlin is gratefully acknowledged.
I. INTRODUCTION
II. THEORY
A. The scattering function for an aqueous solution
B. Uniform fluid approximation
C. Low Q limit and scattering contrast
III. EXPERIMENT
A. Experimental details
B. Data analysis
IV. RESULTS
V. DISCUSSION
Key Topics
- Molecule scattering
- 32.0
- Neutron scattering
- 25.0
- Diffusion
- 24.0
- X-ray scattering
- 21.0
- Solution processes
- 17.0
Figures
Chemical structure of β-cyclodextrin.
Chemical structure of β-cyclodextrin.
Examples of fitting of the model to the QENS spectra of cyclodextrins dissolved in DO, for the experiment with Å. “EXP” and “FIT” stand for experimental data and the fitted curve, respectively; the “FIT”-curve is the same in both columns. and are the solute and DO scattering, respectively (both coherent plus incoherent); is the coherent scattering due to DO-solute time-dependent spatial correlations. The energy resolution function, R(ϕ, ω), is plotted for the comparison of instrumental broadening with the broadening of the separate scattering contributions. For the theoretical origin of the scattering functions , , and , see the beginning of this section.
Examples of fitting of the model to the QENS spectra of cyclodextrins dissolved in DO, for the experiment with Å. “EXP” and “FIT” stand for experimental data and the fitted curve, respectively; the “FIT”-curve is the same in both columns. and are the solute and DO scattering, respectively (both coherent plus incoherent); is the coherent scattering due to DO-solute time-dependent spatial correlations. The energy resolution function, R(ϕ, ω), is plotted for the comparison of instrumental broadening with the broadening of the separate scattering contributions. For the theoretical origin of the scattering functions , , and , see the beginning of this section.
Examples of fitting of the model to the QENS spectra of cyclodextrins dissolved in DO, for the experiment with Å. The notations are the same as in Fig. 2. As compared to Fig. 2, (i) the broadening of the and -terms is clearly observable; (ii) the intensity of the -term is negligible. The scattering is due to and due to the scattering from DO that is practically the same as the pure DO scattering.
Examples of fitting of the model to the QENS spectra of cyclodextrins dissolved in DO, for the experiment with Å. The notations are the same as in Fig. 2. As compared to Fig. 2, (i) the broadening of the and -terms is clearly observable; (ii) the intensity of the -term is negligible. The scattering is due to and due to the scattering from DO that is practically the same as the pure DO scattering.
Fit of the same model to the same spectrum as shown in Fig. 2 for DIMEB, the only difference is that the intermolecular DO scattering due to a finite size of water molecules was not approximated by the corresponding term for pure DO [i.e., Eq. (4b) was used instead of Eq. (24)]. The notations are the same as in Fig. 2. For reasons why the fit quality is somewhat better, see text.
Fit of the same model to the same spectrum as shown in Fig. 2 for DIMEB, the only difference is that the intermolecular DO scattering due to a finite size of water molecules was not approximated by the corresponding term for pure DO [i.e., Eq. (4b) was used instead of Eq. (24)]. The notations are the same as in Fig. 2. For reasons why the fit quality is somewhat better, see text.
Curves of the experimental scaling factor obtained in fitting of QENS spectra from the experiment carried out with Å. The approximately correct -curve (which should ideally be a horizontal straight line) is given by of DO. The filled and empty symbols give the values obtained with and without detailed consideration of intermolecular DO–DO and DO–solute coherent scattering, respectively. This corresponds to using Eq. (3) and Eq. (25), respectively.
Curves of the experimental scaling factor obtained in fitting of QENS spectra from the experiment carried out with Å. The approximately correct -curve (which should ideally be a horizontal straight line) is given by of DO. The filled and empty symbols give the values obtained with and without detailed consideration of intermolecular DO–DO and DO–solute coherent scattering, respectively. This corresponds to using Eq. (3) and Eq. (25), respectively.
Tables
Parameter values for the DO scattering model: = translational diffusion coefficient of water molecules; = translational diffusion correlation time in this model; = mean-square displacement; = rotational diffusion coefficient of water molecules; these parameter values were taken from the literature, see Sec. III B for details.
Parameter values for the DO scattering model: = translational diffusion coefficient of water molecules; = translational diffusion correlation time in this model; = mean-square displacement; = rotational diffusion coefficient of water molecules; these parameter values were taken from the literature, see Sec. III B for details.
Solute translational [ ( cm/s)] and rotational [ (μeV)] diffusion coefficients in DO solutions. The values with uncertainties were obtained by fitting the model to the QENS spectra.
Solute translational [ ( cm/s)] and rotational [ (μeV)] diffusion coefficients in DO solutions. The values with uncertainties were obtained by fitting the model to the QENS spectra.
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