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Rules to Determine Thermal Conductivity and Density of Anodic Aluminum Oxide (AAO) Membranes Begoña Abad, Jon Maiz, and Marisol S. Martin-Gonzalez J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b00643 • Publication Date (Web): 12 Feb 2016 Downloaded from http://pubs.acs.org on February 19, 2016

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The Journal of Physical Chemistry

Rules to Determine Thermal Conductivity and Density of Anodic Aluminum Oxide (AAO) Membranes Begoña Abad, Jon Maiz, and Marisol Martin-Gonzalez* IMM-Instituto de Microelectrónica de Madrid (CNM-CSIC), Isaac Newton 8, PTM, E-28760 Tres Cantos, Madrid, Spain

ABSTRACT. Extracting the thermal conductivity of single nanowires is greatly important in investigating the phonon scattering phenomena that can occur due to the reduction of the dimensions of the material. In order to extract the thermal conductivity of a single nanowire from a measurement of the whole nanowire array, the effective medium theory (EMT) is employed. To appropriately use EMT, the template thermal conductivity must be known, but the values reported in the literature vary greatly. In this work, the Photoacoustic technique was used to determine thermal conductivity of different anodic aluminum oxide (AAO) membranes as a function of the pore diameter and the type electrolyte used. To accurately obtain the thermal conductivity, values for the porosity, skeletal density and specific heat of each AAO membrane were measured. These values are critically needed in the most mathematical models to obtain the thermal conductivity of nanowires/AAO composites and theoretical work. Values of 1.07 W·m1

·K-1 for the skeletal AAO prepared in sulfuric acid and 1.32 W·m-1·K-1 in oxalic and phosphoric acid membranes

are obtained. Also, general equations to determine the thermal conductivity and skeletal density by determining its percentage of porosity are obtained.

KEYWORDS. Anodic aluminum oxide (AAO) membranes, thermal conductivity, density, photoacoustic technique, specific heat, thermal diffusivity

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INTRODUCTION Thermal conductivity, κ, is an intrinsic material property which describes the capability of a material to transfer heat. The thermal diffusivity, α, is a measure of the thermal inertia of a material. Both properties are related by means of the specific heat, Cp, and the density, ρ, by the expression κ=ρ·Cp·α. In many research fields such as chemistry, optoelectronics, solid-state physics, and thermoelectrics, among others, it is necessary to know these thermal transport properties since thermal properties are inherently involved in these research fields. Particularly, characterization of thermal conductivity is one of most important aspects in development of novel thermoelectric materials for future energy applications 1. In this field, size effects are known to dramatically modify the properties by phonon scattering processes at the interfaces, thus reducing thermal conductivity

2-4

. Recently, this strategy

allowed for remarkable improvement in thermoelectric efficiency. Specifically, one-dimensional (1D) structures have been shown to be a promising approach to reduce the thermal conductivity, since the characteristic lengths can be comparable to the phonon mean free path and wavelength. The thermal conductivity of the nanowires (NWs) can be reduced compared with bulk values by boundary scattering, provided that the nanowire characteristic length is smaller than the phonon mean free path. In addition, this kind of structure can be integrated in thermoelectric modules allowing for either single-NW or packed NWs supported by matrix devices. Conversely, recent studies have shown that thermal conductivity can be controllably increased by infiltrating polymers inside a matrix, since it is possible to vary the thermal conductivity of the polymer nanowires by tuning the crystal orientation, reaching values up to an order of magnitude higher than the typical value of the bulk polymers (around 0.2 W·m-1·K-1)5. The fabrication of semiconductor NWs can be achieved by both bottom-up and top-down approaches 6. Templateassistant processes are considered one of the main bottom-up approaches. Among these templates, anodic aluminum oxide (AAO) membranes is one of the most commonly used membranes. AAO membranes form a hexagonally close packed (HCP) ordered structure.7-8 These structures, which are often fabricated by the two-step anodization process 9, can be obtained with a large range of pore diameters depending on the acid electrolyte used during the anodization steps, ranging from around 8 nm to 530 nm

10-13

. Afterward, AAO membranes can be filled by many

techniques, such as electrodeposition, pressure injection, vapor deposition or methods based on wetting phenomena, among others 14-15, thereby synthesizing nanowires within the membrane. The techniques used to measure thermal conductivity can be divided into two main groups: those which are able to measure a single nanowire and those that measure the whole nanowire array. Microchip suspended structures

16


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and Raman thermography

17

stand out among the techniques able to measure the thermal conductivity of a single

nanowire. Other techniques, such as time-domain thermoreflectance (TDTR) Microscopy (SThM)

20

or Photoacoustic technique (PA)

21

18

, laser flash

19

, Scanning Thermal

have been used to extract the effective thermal

conductivity of the whole nanowire array. In these cases, in order to obtain the thermal conductivity of the single nanowire, the effective medium theory (EMT) may be applied provided that the heat goes through the matrix in such a way that the temperature in the in-plane direction can be considered isothermal 18. Moreover, it is interesting to note that this model neglects the thermal resistances at the AAO/NW interfaces

22

, but it is the most frequently

employed model in literature. With appropriate simplifications coming from these assumptions, the EMT is given by equation 1: = + 1 −

(1)

Where κcom is the effective thermal conductivity of the composite, x is the areal packing density or porosity, κNW is the thermal conductivity of a single nanowire and κAAO is the AAO membrane thermal conductivity. Regarding this theory, it is necessary to characterize both the thermal conductivity of the AAO membrane and its porosity in order to obtain an accurate value of the nanowire thermal conductivity. Furthermore, many of the measurement techniques which are able to obtain κcom, such as TDTR, laser flash, or PA techniques require knowledge of the density and the specific heat of the composite. For that reason, it is also crucial to measure these values corresponding to the skeletal AAO membrane (i.e. the case where there is nothing filling the matrix) in order to obtain the composite values from these two expressions: = + 1 −

(2)

= + 1 −

(3)

where the subscripts com, NW, and AAO stand for composite, nanowire and AAO membrane, respectively. Previous studies of both effective, κcom and skeletal, κAAO, thermal conductivity of the AAO membranes at room temperature have been reported in literature, see in Table I. Stark et al. report the thermal conductivity of thin non-porous amorphous alumina film, which showed a value of 1.6 W·m-1·K-1 measured by the bolometer strip technique 23. Commercial alumina membranes have also been studied and the values of κAAO were reported to be of 1.9 W·m-1·K-1

24

and 1.31 W·m-1·K-1 21 for samples of 20 nm and 200 nm in pore

diameter, respectively. Lee et al. measured the effective thermal conductivity of AAO membranes, κcom, produced by employing different acid electrolytes and obtained values of 1.31-1.62 W·m-1·K-1 for oxalic


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acid, 0.53-1.01 W·m-1·K-1 for sulfuric acid and 0.82-1.12 W·m-1·K-1 for mixed acid depending on the anodization temperature given different porosities

25

. Chen et al. studied also κcom of 120 nm pore diameter

of unfilled AAO membranes by the laser flash technique, showing a value of 0.98 W·m-1·K-1 with a 25% porosity. AAO templates of 30 nm pore diameter prepared in a sulfuric acid electrolyte have reported values of κcom = 1.4 W·m-1·K-1 with 30 % of porosity

26

. Finally, AAO membranes anodized in phosphoric acid

with three different porosities were studied and a value of κAAO = 1.38 W·m-1·K-1 was found for all of them 5

. Thus, as can be observed in Table 1, the values of κAAO vary greatly, ranging from 1.9 to 0.8 W·m-1·K-1.

The discrepancy between these values may arise not only from the measurement of thermal conductivity, but also in the calculation of the AAO porosity, density and specific heat, as small changes could lead to a considerable error in the calculation of the skeletal thermal conductivity. In order to improve the metrology in the field and establish general rules to obtain these thermal conductivity and density values, a systematic study of the skeletal thermal conductivity of different AAO membranes as a function of the pore diameters is required.

Table 1. Reported values of thermal conductivity values at room temperature for different types of alumina. For porous samples, the skeletal thermal conductivity has been calculated by means of the effective medium theory when it was not calculated in the original reference.


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Type of sample

Remarks

Al α -Al2O3 corundum/sapphire

Purity dependent (80-99%) Sintered

amorphous -Al2O3 amorphous-Al2O3 amorphous -Al2O3 amorphous -Al2O3 amorphous -Al2O3 amorphous -Al2O3 Commercial AAO Commercial AAO AAO Sulfuric acid AAO Oxalic acid

AAO Oxalic acid

AAO Sulfuric acid

AAO Phosporic acid AAO Sulfuric acid

AAO phosphoric acid

Thin film: anodic oxidation Thin film: RF sputtering on AlN Thin film: RF sputtering on MgO Thin film: RF sputtering on Si Thin film: DC sputtering on Si Minimum thermal conductivity theory Pore diameter:20nm Porosity: 30% Pore diameter:200nm Porosity: 72% No data about pore diameter/ porosity No data about pore diameter/ porosity Pore diameter:35 nm Porosity: 13 % Pore diameter:26 nm Porosity: 4 % Pore diameter:16 nm Porosity: 34% Pore diameter:12nm Porosity: 1% Pore diameter:120nm Porosity: 25% Pore diameter: 30 nm Porosity: 30% Pore diameter: 120nm Porosity: 8 % Pore diameter: 220nm Porosity: 25% Pore diameter: 350 nm Porosity: 55%

Thermal conductivity (W·m-1·K-1) 237

Measurement Method

Reference

15-40

--

28

30 35 (273K) 26 (373 K)

--

29

--

27

1.6 ± 0.2

Bolometer strip

23

1.20

3ω

30

1.15

3ω

30

1

3ω

30

1.6

3ω

30

1.6

theory

30

κcom =1.33 κAAO =1.9±0.3

Photothermoelectric technique

κcom = 0.38±0.02 κAAO =1.31±0.10

Photoacoustic technique

21

κcom =0.65, 0.81, 0.85

Transient heat flow

31

κcom =0.63,0.79,0.86,1.30,1.33

Transient heat flow

31

Steady-State technique

25

Steady-State technique

25

κcom =0.98 κAAO =1.3

Laser flash

19

κcom =1.4±0.1 κAAO =1.9

Laser flash

26

3ω technique

5

27

24

κcom =1.31 κAAO =1.62 κcom =1.5 κAAO =1.6 κcom =0.53 κAAO =0.8 κcom =1.01 κAAO =1.1

κcom = 1.27 κAAO =1.38 κcom =1.04 κAAO =1.38 κcom = 0.64 κAAO =1.38

EXPERIMENTAL SECTION Fabrication of the anodic aluminum oxide membranes. The fabrication of highly ordered AAO templates is based on a two-step anodization method 9. The aluminum foil employed in our work is ultrapure (99.999%) aluminum foil supplied by Advent Research Materials (England), thickness of 0.5 mm and diameter of 1.6 cm. In


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order to fabricate AAO templates 9, the aluminum foils must be first cleaned and degreased by sonication with solvents of different polarity (acetone, isopropanol, water and ethanol) and then electropolished in a constant voltage of 20 V (to eliminate the oxide barrier layer formed by the air), in a mixture of HClO4:EtOH (25:75). The first anodization process is carried out by using different parameters according to the desired template characteristics. The main anodization parameters are: the constant output voltage, the anodization time, the temperature, and the nature and concentration of the electrolyte. As a consequence of the first anodization, a porous alumina layer is formed. The pores of the formed alumina layer are not ordered at the free surface, but are hexagonally distributed at the alumina-aluminum interface. During their growth, the pores sculpt hemispherical concaves on the aluminum, which tend to arrange together with the pores. Then, the first alumina layer is dissolved in an aqueous solution of CrO3 + H3PO4 and the second anodization is carried out. In the second anodization, the concave points act as nucleation points for the growth of new pores. Therefore, the hexagonal arrangement is transferred to the new pores. Thus, a hexagonal close-packed array of closed-end pores is obtained. A summary of the experimental conditions for both first and second anodization conditions to obtain alumina templates with 100 µm in length is given in Table 2. Table 2. Experimental conditions of the aluminum anodization in sulfuric, oxalic and phosphoric acid electrolytes. The time for the 1st anodization is the time use to get a well ordered structure and the time for the 2nd anodization is the time required to grow 100 µm for each template.

Electrolyte

Concentration

Voltage (V)

Temperature (°C)

1st anodization time (h)

H2SO4 (ethyleneglycol 50 wt%) H2SO4 H2C2O4 H3PO4 (0.01M Al2(C2O4)3)

10 wt%

19

0

24

2nd anodization time (h) l ~ 100 µm 100

0.3 M 0.3 M 1 wt%

25 40 205

1-2 3-5 5

24 24 6

24 30 20

In order to obtain a large range of pore diameter sizes, a controlled reduction of pore walls with a phosphoric acid solution, 5 wt.% at 35 ºC, is carried out. In general, the rate of oxide wet-etching depends considerably on the temperature of the process. Also, the time required for this pore widening depends on the template used. In order to employ the AAO templates as a membrane it is necessary to open the pores in contact with the aluminum surface. First, the aluminum substrate is removed with a mixture of CuCl2, HCl and H2O. The alumina of


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oxide barrier layer can be easily removed by dissolving it in a 10 wt.% phosphoric acid solution at 30 ºC. Then the oxide barrier layer face contacts the surface of the solution (note that due to surface tension, the sample is never submerged). After the sample remains in contact for the appropriate duration for the type of template used, the layer is completely removed, which is typically indicated by bubbles emerging from the alumina nanocavities. Morphology characterization. The pore diameter and thickness of the films has been studied by a Philips® XL305-FEG field emission scanning electron microscope (FE-SEM) and by a FE-SEM Hitachi one model SU8000 with TE detector operated at 0.5–3 kV. These microscopes have been calibrated with known patterns to obtain accurate values. The porosity measurements were performed by analysing five images from different areas of the samples with the same magnification of each sample. These analysis were performed with the software imageJ® by calculating the surface area represented by pores, and comparing to the total surface area in the image to obtain the porosity, P. Secondly, the porosity was also calculated with the formula which relates the mean pore radius, r, and the interpore distance, Dint, derived by Masuda et al.9 =

√

(4)

It is worth noting that both values agree since the AAO membranes are highly ordered. The uncertainty associated with the value of porosity obtained by image analysis was found to be lower than that obtained from Eq. 4; thus, the porosity obtained from image analysis was the value used in the calculations. In order to compare and verify the results obtained by SEM images, the specific surface area measurement and porosity analysis were performed using N2 adsorption isotherms (Micromeritic, ASAP 2020 MICROPORE DRY Analyzer). Therefore, BET technique for surface area calculation and the Barrett – Joyner – Halenda (BJH) method were employed for average pore size and pore volume calculations. Raman spectroscopy. The Raman spectra of the AAO membranes were measured by a LabRam HR Raman spectrometer (Horiba Jobin-Yvon) with a 532 nm wavelength Nd:YAG laser with an optical power of 8.5 mW in the range from 300 cm-1 to 1300 cm-1, in air at room temperature. Density measurements, ρ. Density measurements were performed by Archimedes’ principle with the aid of ethanol as the auxiliary liquid whose density (ρet) is well-known. A balance XS105DU from Mettler Toledo was used to weigh the samples both in air (Wair) and in ethanol (Wet) so that the skeletal density is finally calculated by means of the following equation:


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=

!"

!"#$

%& − '( + '(

Page 8 of 25

(5)

Several tests were performed on each sample, ensuring that the uncertainty was under 5%. Specific heat measurements, Cp. Specific heat measurements were carried out with a Discovery DSC from TA instruments in a temperature range from -10 ºC to 60 ºC so that the samples did not undergo any physical change. Several trials were performed in order to ensure the accuracy of the measurements, with experimental uncertainty lower than 5%. Thermal conductivity measurements. The photoacoustic technique was used to determine the thermal conductivity of the AAO along the direction parallel to the template channels. The technique is based on the photoacoustic effect in which the sample is periodically heated and cooled by incident modulated radiation. The air in contact with the surface of the sample expands and contracts due to this periodic heating, thereby generating acoustic waves, which are, in turn, detected by a microphone. The thermal properties of the sample can be derived by comparing the incident modulated signal with the acoustic signal. A multilayer model developed by Hu et al.

32

was used for the data reduction. As a verification of the reliability and accuracy of the system, several reference samples have been measured by both this system and other techniques, giving the same values 33-34. Moreover, both organic

35

and inorganic films

36

have been measured by this technique. The experimental setup is made up of a

PMMA photoacoustic cell designed so that acoustic resonances do not disturb the measurements. A fiber-couple laser diode LDF-10 series Alphalas GmbH of 980 nm with an optical power of 260 mW was used as the radiation source. The acoustic signal was detected by a G.R.A.S. 46 BL ¼” CCP Pressure Microphone Set. The recorded signal is then amplified and filtered by a power module type 12AQ G.R.A.S. Finally, a Signal Recovery Model 7270 DSP Lock-in Amplifier was used to obtain the required signal. An 80 nm titanium layer was evaporated via electron-beam evaporation onto the samples in order to ensure that the laser beam is absorbed within the sample. The Supporting information contains more detailed information regarding the experimental errors associated with this technique, the theoretical model applied to the AAOs membranes, the measurement conditions, and the sensitivity of the technique.

RESULTS AND DISCUSSION Morphology. Figure 1 shows FE-SEM images of the samples anodized in various acid electrolytes and conditions (see (a) to (i)) along with two commercial samples with pore dimeters of 200 nm and 40 nm (see (j) and (k), respectively). The anodization process yields a honeycomb-like arrangement of hexagonal cells with long-range


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order, and with a pore in the center of each cell, whose diameter depends on the preparation conditions. A histogram was obtained from these images in order to determine the pore diameter distributions. These plots are shown next to their respective image in Figure 1. The average pore diameter for each sample, Dp, was determined by analysing such images taken at various regions of each sample. In the lab-made AAOs, the obtained dimensions range from 17 nm to 396 nm. Pristine AAO, i.e., AAO membranes directly obtained from the anodization process, present pore diameters of 17 nm (see Figure 1a), 28 nm (1b), 39 nm (1c), and 149 nm (1e), from the electrolytes composed of sulfuric acid and ethylene glycol 50 wt.%, sulfuric acid, oxalic acid and phosphoric acid, respectively. The other AAO membranes were obtained by widening the pristine ones at different times, which yields a large range of pore diameters: 67 nm (see Figure 1d), 184 nm (1f), 223 nm (1g), 267 nm (1h) and 396 nm (1i).


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Figure 1. FE-SEM images of the top-surface of samples with different pore diameter along with the statistical distribution of the pore diameter for each sample. Two commercial samples (see Figure 1k and 1j) were also analysed. The study of these samples is important since many groups use them for numerous types of investigations. Figure 1k show an average pore diameter in the vicinity of 40 nm whereas the AAO commercial membrane with a pore diameter of 200 nm of Figure1k shows an


10

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irregular pore shape, whose diameter distribution varies greatly (with a large number of pores ranging between 100 nm-400 nm) when compared to lab-made AAOs (see Figure 1j). Figure 2 shows (a) the cross section of a commercial AAO membrane of 200 nm in pore diameter and (b) the cross section of a lab-made AAO where the channels are completely parallel with each other, which is representative of all the lab-made prepared samples, as well as the commercial samples of 40 nm.

Figure 2. Cross section of (a) a commercial AAO membrane with a pore diameter of 200 nm and (b) lab-made AAO membranes. Thermal conductivity. The thermal conductivity was determined by the photoacoustic technique by using a multilayered model depicted in Figure S2 in the Supporting information. The suitable frequency range used to perform the experiment was determined by performing simulations of the photoacoustic phase shift as a function of the modulation frequency shown in Figure S3 in the Supporting information. The samples were covered by 80 nm titanium layer. Figure S4 in the Supporting information shows this layer on samples with pore diameters of 27 nm (a) and 184 nm (b). Moreover, the accuracy of the measurements was studied by the sensitivity and the quality of the fittings. An example of both is given in Figure S5 in the Supporting information. Figure 3a shows the composite thermal conductivity, κcom, as a function of the porosity and (b) the skeletal thermal conductivity value, which is obtained by means of the effective medium theory as explained above in Eq. 1. The dispersion of data observed can be understood by analyzing the composite thermal conductivity values versus the porosity, which yields a straight line (see Figure 3a). The effective thermal conductivity reduces with increasing porosity, due to the contribution of air within the pores, which has a very low thermal conductivity (0.026 W·m-1·K1

) in comparison with the solid amorphous alumina thermal conductivity (around 1-1.5 W·m-1·K-1). This reduction

could be linked to phonon boundary scattering. However, this actually may be ruled out because: i) the heat conduction induced when measuring the thermal conductivity takes place along the direction of the nanochannels so


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that the reduction in the wall thickness of the AAO membrane only influences the heat transport due to the increase in percentage of air within the sample and ii) even if the heat conduction were to take place in the in plane direction, the phonon mean free path of the amorphous alumina is in the order of the interatomic distance 23, which means that this reduction in the wall thickness would not affect the heat conduction in the solid alumina unless the wall thickness were reduced to the order of inter-atomic spacing of amorphous alumina, which is not physically possible. Therefore, the reduction of composite thermal conductivity is better described by the effective medium theory, which predicts a linear relationship between the effective thermal conductivity and porosity as shown in Figure 3a, from which the skeletal thermal conductivity can be derived. The effective thermal conductivity of samples prepared in oxalic and phosphoric electrolytes in this work along with a lab-made alumina measured by Chen et al.19, by Muñoz-Rojo et al.5 and a commercial porous alumina of a pore diameter of 200 nm previously measured by Biwas et al.21, show the same trend. This suggests that the skeletal thermal conductivity, κAAO, is the same for all these membranes which can be extracted from the intercept of the line with porosity%=0. This value corresponds to κAAO =1.32±0.07 W·m-1·K-1, for all the phosphoric and oxalic acid membranes. The R2 results 0.96153 which is still close to 1. The linear trend is finally confirmed by the literature values which follow the same trend, showing an R2 of 0.99235 when fitting along with our values giving a value of κAAO =1.31 W·m-1·K-1. Values found by Muñoz-Rojo et al.5 and Chen et al.19 are expected to have the same trend since the AAO membranes used in these works are of high quality, i.e., highly ordered with parallel nanochannels, so that both porosity and thermal conductivity can be accurately extracted. Despite the fact of the highly irregularity of the commercial AAO template studied by Biwas et al., the thermal conductivity measured in this work also fit our linear trend, probably because exhaustive statistics of both porosity and thermal conductivity measurements of this sample were carried out. However, it is also worth noting that some data presented in Table 1 did not fit our trend. For the case of the oxalic acid solution, Lee et al. found values of κAAO around 1.6 W·m-1·K-1, which is far from our findings. This may be due to a low quality of the samples as seen in the SEM images showed in that work, where pores seem to be interconnected. This fact could yield inaccuracies in the study of the porosity and the subsequent extraction of thermal conductivity 25.


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Figure 3.(a) Effective thermal conductivity as a function of the porosity. Rule for calculating any alumina template thermal conductivity values by calculating the porosity % and the relation of the fitting values with the effective medium theory is presented (b) Skeletal thermal conductivity value for each sample by applying the EMT independently. In the case of sulfuric acid solution, we have two data points coming from the samples of 17 nm and 28 nm which are not enough to perform a fitting. The two data point fitting would give a value of 1.09 W·m-1·K-1. Lee et al. found values that approximately fit our linear trend as shown in Figure 3a. However, if a linear fitting is performed a value of R2 of 0.90418 is obtained. The value of the skeletal conductivity obtained from that fitting is 1.01 W·m-1·K-1 which is lower than that of obtained by fitting just the two points. Since the quality of the fitting is not good enough, the skeletal thermal conductivity of our two samples was calculated separately, using the EMT, and finally an average of both values was found, yielding a value of skeletal thermal conductivity of 1.07 ± 0.11 W·m-1·K-1. Other values of κAAO around 1.9 W·m-1·K-1, were found in the literature which differs strongly from the found value in this work, κAAO =1.07 W·m-1·K-1.24, 26 This can be due to the fact that the membranes were heated up above 150 ºC so that some crystallization may take place. In the case of the work performed by Cai et al., the value could be different from the one obtained in this work due to the necessity of knowing density and specific heat of both the AAO membrane and the aluminum foil for the two-layer model developed 26. The κAAO calculated for each sample is also shown in Figure 3b as a function of the pore diameter. For sulfuric acid solution, the thermal conductivity results 1.08 W·m-1·K-1 and 1.06 W·m-1·K-1 for 17 nm and 28 nm, respectively. In the case of the oxalic acid solution, values of 1.33 W·m-1·K-1 and 1.28 W·m-1·K-1 were found for 38


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nm and 69nm, very near to the value obtained for the commercial AAO of 40 nm, 1.35 W·m-1·K-1, prepared in similar conditions. In the case of the phosphoric acid, all the values were found to be in the vicinity of 1.3-1.5 W·m1

·K-1 which match the obtained value of the commercial AAO membrane of 200 nm, 1.31 W·m-1·K-1, also prepared

with phosphoric acid. As explained above, samples prepared under similar conditions, but in different labs, give rise to the same values of skeletal thermal conductivity of AAO. It is also worthy to note the strong reduction in the thermal conductivity of all the measured amorphous alumina in comparison with the crystalline alumina whose thermal conductivity is in the range of 15 W·m-1·K-1 at room temperature, as seen in Table 1

28, 37

. This is a common phenomenon when a crystalline material becomes

amorphous, such as SiO2. Crystalline SiO2 has a thermal conductivity value of 10 W·m-1·K-1 whereas its amorphous counterpart has 1 W·m-1·K-1at room temperature

29

. In amorphous materials, heat is carried through localized

vibrations or excitations, which are frequently denoted as tunnelling states. These localized vibrations give rise to the minimum thermal conductivity of the material

29

. It is also explained by the change in density between

crystalline and amorphous phases which will be explained below. In order to understand why alumina membranes prepared in sulfuric acid yields lower thermal conductivity, micro-Raman spectroscopy was performed. As can be observed in Figure 4 the Raman spectrum of the AAO prepared from the sulfuric acid solution shows a different spectrum than what is obtained for oxalic and phosphoric acid templates measured under the same conditions. In the sulfuric acid spectrum, two clear bands located at the wavelengths 980 cm-1 and 1053 cm-1 are identified. They correspond to the υ1 and υ3 vibrations, respectively, of the SO4 group in aluminum sulfate 11. This shows a clear bonding of the SO4 groups from the electrolyte with the Al from the template. Additionally, the band placed at 452 cm-1 has been previously attributed to alumina Eg (external) mode, and the band positioned at 627 cm-1 was assigned to the infrared (IR) active modes, according to literature 11. However, for oxalic and phosphoric acid solutions, there are not clear bands due to their higher luminescence. This suggests a strong structural difference between the three types of alumina membranes, which explains why that AAO membranes obtained from the sulfuric acid solution are less thermally conductive and with a slightly lower skeletal density.38-39


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Εg (external)

Raman Intensity (arb. units)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


IR

ν1SO4 ν3SO4

Sulfuric acid Oxalic acid Phosphoric acid

400 500 600 700 800 900 1000 1100 1200 -1

Wavenumber (cm )

Figure 4. Raman spectra of the AAO anodized in sulfuric, oxalic and phosphoric acid measured under the same conditions.

Porosity, density and specific heat of AAO membranes. The thermal conductivity values showed above were extracted from the photoacoustic measurements. The data reduction requires the knowledge of the density, and specific heat. Moreover, the composite density is in turns obtained from the porosity and the skeletal density values measured by Archimedes´method. Therefore, a deep study of these parameters has been performed. Figure 5a shows how the porosity increases when the pore diameter increases for samples prepared with the same electrolyte, as seen for the oxalic and phosphoric acid samples. This follows the expected trend since a reduction in the pore walls takes place during the widening step. In the case of the AAO prepared by anodizing in oxalic and phosphoric acid, the pristine samples, 39 nm and 149 nm, present a low porosity of 15.6 % and 9 %, respectively. However, it is well-known that anodizations carried out in sulfuric acid yield notable dissolving of the pore walls so that the porosity of the pristine AAO membrane from sulfuric acid is higher, 23.6%, for 28 nm.11 This value was verified by the BET technique from isotherm shown in Figure S1 in the Supporting information. In the case of 17 nm, also prepared from a sulfuric acid solution with 50 wt% ethylene glycol, a porosity of 13.1% was obtained. The lower porosity may be attributed to the ethylene glycol providing a protective effect on the alumina pore walls as proposed by Martín et al.10-11 The porosity commercial AAO membrane of 200 nm is difficult to determine accurately since the image analysis is only valid provided that the channels are parallel to each other. However, as


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seen in Figure 2, the commercial AAO membrane channels are not parallel and they are even interconnected so that the associated porosity presents higher error as calculated from a statistical analysis.

Figure 5. (a) Porosity, (b) skeletal density, (c) composite density (AAO and air) and (d) Specific heat at room temperature as a function of the pore diameter for both commercial and lab-made samples prepared with different acid electrolytes. The samples that are connected by lines correspond to membranes that have been widened from the initial.

The skeletal density of the samples was measured by Archimedes’ principle. However, in order to obtain the effective density needed for the thermal conductivity data reduction, the rule of mixtures was applied to the measurements by using the following equation: = '( + 1 − ,

(6)


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where ρAAO is the skeletal density of the AAO membrane, ρair is the air density with a value of 1.275 kg·m-3 at room temperature (300 K) and P is the porosity of the sample. As seen in Figure 5b the skeletal density of the AAO templates ranges from 2.770 g·cm-3 to 2.930 g·cm-3, which is in agreement with previous studies 39. These values are lower than the crystalline alumina whose density is approximately 3.6 g·cm-3. 30 The reduction in the density values may be explained by the contamination of the alumina with the anions of the electrolyte since anion-contaminated alumina presents lower density than the anion-free pure alumina 38. It is well-known that the density of the AAOs varies strongly with the anodization conditions.39 The density of the AAO obtained by anodization in sulfuric acid is 2.773 g·cm-3 for 28 nm, and 2.789 g·cm-3 for 17nm, which is in agreement with previously reported data from samples prepared with sulfuric acid solutions, whose density was found to be between 2.4 g·cm-3 and 3.2 g·cm-3.39 In the case of the AAOs prepared in the oxalic acid solution, values of 2.972 g·cm-3 and 2.928 g·cm-3 were measured for 39 nm and 67 nm, respectively, which agrees with the value obtained for the commercial AAO membrane of 40 nm, 2.930 g·cm-3. Finally, the density of the five samples prepared in-lab using phosphoric acid solutions and the commercial AAO sample all yielded values in very good agreement with each other: 2.928 g·cm-3, 2.996 g·cm-3, 2.848 g·cm-3, 2.868 g·cm-3 and 2.797 g·cm-3 for 149 nm, 184 nm, 223 nm, 268 nm, 39 6nm, respectively, for the samples prepared in-lab, and 2.840 g·cm-3 for the commercial AAO membrane of 200 nm. Figure 5c shows that the composite density as a function of the pore diameter which is lower than the skeletal density due to the air component (Eq. 6). If composite density is plotted versus the porosity of the samples, two linear trends can be found for the samples depending on the acid solution used to fabricate them. As seen in Figure 6, two different groups of samples can be distinguished: samples prepared in phosphoric and oxalic acid and those fabricated in sulfuric acid. If a linear fitting is performed, two different values of the skeletal density can be found depending on the electrolyte used. In the case of the phosphoric and oxalic acid this resulted in a value of ρAAO =2.945 ± 0.013 g·cm-3, which yields a linear fit with an R2 value 0.99591, indicating a good fitting. For samples prepared by sulfuric acid, only two had been fabricated for use as a membrane with well-established pore diameter, so to confirm the linear trend in density, another sample was prepared in sulfuric acid with a posterior chemical etching, in order to include another value for composite density with a higher porosity, 40%, whose skeletal density value is 2.770 ± 0.054 g·cm-3. Fitting this data yields an R2 value of 0.99923, which indicates a high-quality linear fitting. From the fitting parameter, the value of the skeletal density is found to be 2.788 ± 0.193 g·cm-3 where the


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uncertainty is about 6% of the value. This uncertainty is acceptable, considering that the composite density values are affected by the porosity because the small pore size increases the uncertainty of the pore diameter distribution. Moreover, this uncertainty was taken into account in the subsequent thermal conductivity derivation.

Figure 6. Composite density as a function of the porosity for both sets of samples. These results serve to unify all the different values found in the literature and can be used to calculate the composite density by knowing the porosity of the sample, depending on the electrolyte used to prepare the sample. Figure 5d shows the specific heat as a function of the pore diameter for all the samples. The values were obtained from these samples prepared from the same electrolyte and the following widening process, by weighted averages since all the values were very similar. The values range from 0.772 J·g-1·K-1 to 0.889 J·g-1·K-1. The Cp value of aluminum is approximately 0.897 J·g-1·K-1 27 and the non-porous aluminum oxide (Al2O3) is in the vicinity of 0.800 J·g-1·K-1 40. Although AAO membranes have been found to be amorphous 41, the specific heat as a function of the electrolyte does not vary greatly in comparison with that of the crystalline aluminum oxide specific heat. The AAO membranes prepared from sulfuric acid solution present a specific heat of 0.791 J·g-1·K-1, 0.782 J·g-1·K-1 for 17 nm and 28 nm, respectively. In the case of the oxalic acid solution, the specific heat results 0.889 J·g-1·K-1. For membranes grown from phosphoric acid solution the specific heat is 0.772 J·g-1·K-1. In the case of the commercial membranes, the specific heat is found to be 0.857 J·g-1·K-1 and 0.877 J·g-1·K-1 for the 40 nm and 200 nm,


18

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respectively. The characteristic curve of the specific heat as a function of the temperature is shown in Figure S6 in the Supporting Information. From all these data, we obtained two rules from where all AAO thermal conductivity and density can be calculated, just by knowing the electrolyte used to prepare the template and analysing the percentage of porosity of the sample. The general equations and the skeletal values are compiled in Table 3. Moreover, the thermal diffusivity is shown in Table S4 in the Supporting information.

Table 3. Skeletal thermal conductivity and density as function of the porosity along with the overall values for each acid solution.

Acid solution

AAO Density calculation rule

Value of Skeletal density ρAAO (g·cm-3)

AAO thermal conductivity rule

Value of AAO Skeletal thermal conductivity κAAO (W·m-1·K-1)

Oxalic and Phosphoric Acid

ρcom = 2.945 – 0.031P

2.945 ± 0.013

κcom=1.32-0.01P

1.32 ± 0.07

Sulfuric Acid

ρcom = 2.788 – 0.028P

2.788 ± 0.193

−

1.07 ± 0.11

CONCLUSIONS The thermal conductivity of AAO membranes as a function of the pore diameter and the electrolyte used for their preparation has been studied in depth. To this end, the photoacoustic technique was employed, which relies on the values of the porosity, specific heat and density of each membrane, as do many other commonly used techniques. These values were also measured for each template. Values of 1.07 W·m-1·K-1 and 1.32 W·m-1·K-1 have been obtained for the AAO prepared in sulfuric and oxalic and phosphoric acid electrolyte, respectively. There is no variation of the thermal conductivity as a function of the pore diameter but a reduction in the value is observed when using sulfuric acid, due to the incorporation of SO4-2 to the alumina structure.

ASSOCIATED CONTENT


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Supporting Information. Supplementary material consists of BET characterization, uncertainty analysis, thermal conductivity model, frequency range determination and sensitivity of the fitting of the photoacoustic technique, specific heat as a function of the temperature and thermal diffusivity. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Notes Authors declare no competing financial interest ACKNOWLEDGMENT The authors would like to acknowledge the financial support from ERC StG NanoTEC 240497 and national project PHOMENTA MAT2011-27911. The authors also thank to the group of Polycondensation and Polymer Membranes of the ICTP-CSIC, especially to Dr. Cristina Álvarez and Prof. Jose de la Campa for the aid with the density measurements. Authors acknowledge Adam A. Wilson for valuable comments on the manuscript.

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Insert Table of Contents Graphic and Synopsis Here

The composite thermal conductivity of any porous alumina sample can be extracted by determining the porosity percentage.


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Rules to Determine Thermal Conductivity and ... - ACS Publications

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