Journal of Nanoparticle Research

, Volume 10, Issue 7, pp 1109–1114

Application of SAXS to the study of particle-size-dependent thermal conductivity in silica nanofluids


    • Department of Physics and AstronomyOhio University
  • Wenhua Yu
    • Energy Systems DivisionArgonne National Laboratory
  • Dileep Singh
    • Nuclear Engineering DivisionArgonne National Laboratory
  • David Cookson
    • Australian Synchrotron Research ProgramAustralian Nuclear Science and Technology Organization
  • Jules Routbort
    • Energy Systems DivisionArgonne National Laboratory

DOI: 10.1007/s11051-007-9347-y

Cite this article as:
Chen, G., Yu, W., Singh, D. et al. J Nanopart Res (2008) 10: 1109. doi:10.1007/s11051-007-9347-y


Knowledge of the size and distribution of nanoparticles in solution is critical to understanding the observed enhancements in thermal conductivity and heat transfer of nanofluids. We have applied small-angle X-ray scattering (SAXS) to the characterization of SiO2 nanoparticles (10–30 nm) uniformly dispersed in a water-based fluid using the Advanced Photon Source at Argonne National Laboratory. Size distributions for the suspended nanoparticles were derived by fitting experimental data to an established model. Thermal conductivity of the SiO2 nanofluids was also measured, and the relation between the average particle size and the thermal conductivity enhancement was established. The experimental data contradict models based on fluid interfacial layers or Brownian motion but support the concept of thermal resistance at the liquid–particle interface.


NanofluidThermal conductivitySize effectInterfaceSAXSSilica colloidsNanoparticlesDispersion


A recent review of the properties of nanofluids highlights several inconsistencies in the experimental data of the effect of particle size on the thermal conductivity of nanofluids (Yu et al. 2007a). While the rough trend derived from the review is that the thermal conductivity increases with increasing particle size, there are several exceptions. This is a significant problem as the particle size is a critical parameter in all of the theoretical treatments of the enhancement of thermal conductivity (Yu and Choi 2003; Xuan et al. 2003; Wang et al. 2003). Therefore, it is very important that the nanofluids for which the conductivity is measured should be very well characterized with respect to their overall particle size distribution, including any agglomeration. Furthermore, when comparing the effects of particle size on thermal conductivity, it is important to use nanofluids with the same particle volume fraction and base fluid.

In order to obtain a definitive result on the effect of particle size/distribution on thermal conductivity, we have chosen to use commercially available nanofluids, “Ludox” (W.R. Grace & Co., Columbia, MD), primarily used for coatings, metal casting, refractory products, and catalysts. It is a colloidal silica solution using a water-based fluid (buffered to pH = 10) containing amorphous SiO2 particles. Ludox is available in several SiO2 sizes. Previous small-angle X-ray scattering (SAXS) studies of one of the Ludox sample indicated that SAXS had successfully measured nanoparticle size and distribution (Xu et al. 1996). Therefore, Ludox offers the possibility of a careful investigation of the size and size distribution using SAXS and the correlation of size to thermal conductivity, keeping volume fraction fixed and equal for all particle sizes. The results can then be used to confidently compare to theoretical predictions.


Samples used for this study are silica nanofluids that are commercially available (W.R. Grace & Co., Columbia, MD). The SiO2 particles were suspended in an alkaline solution (pH = 10), which was adjusted by the supplier to prevent particle aggregation. Three nanofluids with different particle sizes (Ludox SM, HS, and TM) were used for this study. The original particle concentrations were between 16 and 23 vol.%. The particle sizes and the suspension viscosities (at 25 °C) provided by the manufacturer were 8.4, 12.9, 23 nm, and 5.5, 7.1, 22.9 cp, respectively. It is interesting to see that at this high particle volume concentration, the viscosities of the colloidal suspensions are only a factor of 5–20 higher than that of water. The as-fabricated nanofluids show excellent clarity with no indication of particle settlement. The solutions were then diluted by a factor of up to 1000 in a potassium carbonate based buffer solution with pH = 10 (Fisher Scientific Inc., Fairlawn, NJ) for particle size measurements.

SAXS on nanofluids was performed on beamline 15-ID-D (ChemMatCARS) at the Advanced Photon Source, Argonne National Laboratory. General description of the beamline setup can be found elsewhere (Cookson et al. 2006). The nanofluids were drawn in with a syringe pump to an open-ended 1 mm glass capillary and irradiated with a 0.5 × 0.3 mm monochromatic X-ray beam (λ = 1.5 Å). X-ray scattering was measured with a charge-coupled device X-ray detector, with intensity calibrated from pure water measured in the identical capillary. All nanofluid SAXS profiles were background-subtracted using profiles obtained from pure buffer solution. For comparison purpose, we also measured the particle size with dynamic light scattering (DLS) using a lab-based instrument (Brookhaven Instruments Corp., Holtsville, NY).

The thermal conductivity was measured by the transient hot-wire technique that is described in detail elsewhere (Yu et al. 2007b).


Analysis of X-ray scattering from particles in a liquid can be complicated by interference between the X-rays elastically scattered from individual particles. This particle-particle interference becomes detectable at volume fractions larger than about 0.5%. Figure 1 shows the 1-D SAXS patterns of a silica nanofluid (i.e., Ludox SM) with three different particle volume fractions. The plot of X-ray scattering intensity versus scattering momentum change (q = 4πsin θ/λ), where θ (is the scattering angle, and λ is the wavelength) on a log–log scale provides information about the nanoparticles. The X-ray scattering intensity shows a maximum in the region 0.01 < q < 0.05 Å−1 for the 1 and 16 vol.% samples due to the interparticle interference effect (Xu et al. 1996). The oscillations observed above 0.1 Å−1 arise from the inherent form-factor scattering from the particles. These oscillations are often ‘washed-out’ by poly-dispersity in particles size. The fact that they are still intact for these fluids is due to the narrow size distribution of the nanoparticles. That no change in this oscillatory feature was observed in these three samples indicates that dilution does not affect the particle size distribution. To simplify the data analysis, we use data taken from the most diluted samples, where the effect of interparticle interference can be neglected.
Fig. 1

SAXS patterns of Ludox SM nanofluid with three different particle volume fractions

Quantitative data analyses of the SAXS patterns were performed using solid-sphere form factors fitted with a variety of least-squares methods implemented in the program suite IRENA (Ilavsky et al. 2005). Figure 2 shows the 1-D SAXS pattern of a 0.02 vol.% silica nanofluid fitted with a maximum entropy algorithm (Potton et al. 1988). This method assumes no particle-particle interference and apart from a non-negative criteria, imposes no further restriction on the resulting size distribution profile. Figure 3 shows the normalized particle size distribution of three diluted silica nanofluids. The concentrations of the samples SM, HS, and TM are 0.08, 0.02, and 0.02 vol.%, respectively. Only one major peak is observed in each of the size distribution profiles, confirming the mono-dispersity of the nanoparticles. The presence of small satellite peaks in the distributions may be due to a small amount of aggregation – but are just as likely to be artifacts of the maximum entropy technique. Further analysis of the dominant peaks in these profiles shows that the peak centers (average particle sizes) are located at 107, 167, and 286 Å, and the corresponding full widths at half maximum are 49, 43, and 68 Å. In comparison, the average particle sizes measured by the DLS were 104, 174, and 303 Å which correlate well to the SAXS results. We also performed data analysis on the concentrated samples using a more complex model that includes the particle-particle interaction (Beaucage et al. 2004). Results obtained from both diluted and concentrated samples are consistent, which suggests that the dilution does not affect the particle size distribution.
Fig. 2

SAXS data of a 0.02 vol.% SiO2 nanofluid and a fit using the maximum entropy method assuming spherical particles with an average diameter of 17 nm
Fig. 3

Particle size distribution of three silica nanofluid samples

Figure 4 shows a plot of the average particle size versus relative thermal conductivity of the nanofluids. These nanofluids have the same volume fraction of 16% and the base buffer solution was used as a standard for the thermal conductivity measurement. It is clear that the thermal conductivity of the nanofluids increases almost linearly with increasing particle size in the range of 10–30 nm.
Fig. 4

A plot of average particle size versus relative thermal conductivity showing a linear relationship for 16 vol.% SiO2 loading


While there are many experimental studies on the effective thermal conductivity enhancement of nanofluids, the particle size effect is still in doubt. In a recent review, Yu et al. compared published experimental data for nanofluids with the same particle species but different particle sizes (Yu et al. 2007a). The authors found that the effective thermal conductivity roughly increases with the diameter of the dispersed spherical nanoparticles with a few exceptions. It should be emphasized that the nanofluids compared in the review are from different research groups (Lee et al. 1999; Wang et al. 1999; Xie et al. 2002; Das et al. 2003), and the particle sizes are often not measured by the experiments but rather taken from the manufacturers’ powder data sheet. It is not known if the particles used for these studies were well dispersed or agglomerated. Moreover, the particle volume fraction of the nanofluids used for that comparison was no more than 5%. In our study, the size distributions of the dispersed nanoparticles were well characterized, and the effective thermal conductivity of the silica nanofluids with the same high particle volume fraction (16%) but different particle size was measured. As seen in Fig. 4, the increase of the effective thermal conductivity enhancement depends almost linearly (within experimental uncertainty) on the particle size, at least in the particle size range of 10–30 nm at 16 vol.% particle loading. Note that the linear relationship was derived from a narrow particle size range (10–30 nm), and, therefore, more data of nanofluids with larger particle sizes beyond 30 nm are necessary to verify the authenticity of the linear relationship.

Various investigators have proposed physical mechanisms and mathematical models to describe and predict the effective thermal conductivity enhancement phenomena of nanofluids. Among them, the theories of nanoparticle-base fluid interfacial layer effect (Yu and Choi 2003, 2004; Ren at al. 2005; Xie et al. 2005) and nanoparticle Brownian motion effect (Xuan et al. 2003; Jang and Choi 2004; Koo and Kleinstreuer 2004; Prasher et al. 2005, 2006a) predict that the thermal conductivity enhancement of nanofluids decreases with the increase of particle size for a fixed particle volume fraction. Therefore, the theories of Brownian motion or interfacial layer effect are contrary to our results. The theory of nanoparticle clustering/agglomeration effect (Wang et al. 2003; Prasher et al. 2006b) predicts that the nanoparticle cluster/agglomerate structures are partially responsible for the thermal conductivity enhancement of nanofluids. Our SAXS results show that agglomeration in the silica nanofluids is negligible. Therefore, the theory of nanoparticle agglomeration cannot be used to explain the observed particle-size dependent thermal conductivity.

Classic Maxwell theory predicts effective thermal conductivity of liquid–solid suspension (Maxwell 1881), which can be expressed as:
$$ \frac{{k_{eff} }} {{k_f }} = 1 + \frac{{3(k_p /k_f - 1)\phi }} {{(k_p /k_f + 2) - (k_p /k_f - 1)\phi }} $$
where keff is effective thermal conductivity of suspension; kf is thermal conductivity of liquid; kp is thermal conductivity of solid particles; and ϕ is volume fraction of particles. In our case, the measured thermal conductivity of the base buffer solution was 0.605 W/mK, and the thermal conductivity of silica (1.4 W/mK) was taken from a reference (Lide, 1997). Plugging these numbers and the value of volume fraction (ϕ = 0.16) into Eq. 1, we obtain keff/kf = 1.15, which agrees reasonably well with the measured thermal conductivity of Ludox TM. However, the Maxwell model cannot explain the particle-size-dependent thermal conductivity, which was observed in our experiment.

A nanofluid with a smaller particle size and a fixed particle loading means a larger area of particle-liquid interface. The fact that the thermal conductivity decreases with an increased particle-liquid interface area sheds light on the interfacial thermal resistance, which has been proved experimentally in carbon nanotube suspensions (Huxtable et al. 2003). A model that combines the Maxwell theory with interfacial thermal resistance has been developed to explain the thermal conductivity enhancement in carbon nanotube suspensions (Nan et al. 2004). In our case, we have a nanofluid system where the naoparticles have much lower thermal conductivity than carbon nanotube (by a factor of 2000), and we still observe the effect of interfacial thermal resistance. However, this interfacial effect in silica nanofluids is not prominent unless the average particle size is less than 30 nm. Further study is necessary to understand the physics behind this observation. Nonetheless, our experimental data support the concept of interfacial thermal residence.


We have used SAXS to characterize particle size distribution in silica nanofluids. It is found that the particles in these fluids are mono-dispersed with average sizes between 10 and 30 nm. Thermal conductivity measurements of 16 vol.% nanofluids with different sizes show a linear increase with increasing the average particle size. This result contradicts theoretical models based on fluid interfacial layer or Brownian motion. Our study suggests that thermal resistance at the solid-liquid interface may be critical to the thermal conductivity of nanofluids with small particle sizes.


This work was sponsored by Michelin American Research and Development Corporation and by the U.S. Department of Energy, under Contract No. DE-AC02-06CH11357 at Argonne National Laboratory, managed by University of Chicago Argonne LLC (USA). Use of the Advanced Photon Source was supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. ChemMatCARS Sector 15 is principally supported by the National Science Foundation/Department of Energy under grant number CHE-0535644.

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© Springer Science+Business Media B.V. 2008