Ultrasonic attenuation by nanoporous particles : Part II: Experimental

Ultrasonic attenuation by nanoporous particles

Part II: Experimentalw

William N. Rowlands,aJames K. Beattie,*

aAlex M. Djerdjev

aand

Richard W. O’Brienb

Received 19th April 2006, Accepted 17th August 2006

First published as an Advance Article on the web 5th September 2006

DOI: 10.1039/b605617m

In Part I of this paper O’Brien presented a new theory that describes the dissipation of ultrasonic

energy by porous colloidal particles in suspension. In this paper we present experimental

measurements on several such suspensions and compare the resulting ultrasonic attenuation

spectra with O’Brien’s theory. We find that microporous colloids (e.g. zeolites) and mesoporous

colloids (e.g. porous silicas) both show greater attenuation of ultrasound than would solid

particles of the same size and effective density, as predicted by O’Brien. Fitting theoretical spectra

to the experimental data provides information about the porosity and pore diameters in the

particles. This makes the technique potentially suitable as a convenient method of characterizing

nanoporous materials, especially those already in suspension.

1. Introduction

The use of ultrasound to characterize colloidal suspensions of

particles has recently been reviewed.2 The formulae developed

by Allegra and Hawley3 to describe the attenuation of ultra-

sound by solid particles in suspension have been extensively

experimentally tested. The phenomena are sufficiently under-

stood to provide the basis for a number of commercial instru-

ments that use ultrasonic attenuation to measure particle size in

concentrated colloidal suspensions. In Part I of this paper1

O’Brien presented a new theory for the additional attenuation

expected for porous particles due to the flow of the fluid in and

out of open connected pores. In the present paper we present

experimental data that are compared with O’Brien’s theory,

with the aim of obtaining quantitative information about the

pore structure inside the colloidal particles.

While some investigators have reported ultrasonic attenuation

spectra for flocculated emulsions,2 there appear to be no reports

of the attenuation spectra of micro- or mesoporous colloidal

particles with rigid lattice structures. Some earlier experimental

results on a poorly defined commercial porous colloid measured

in this laboratory have been presented by O’Brien.4

Colloidal materials suitable for testing the theory should

ideally have the following characteristics:

(i) They should exhibit significant porous attenuation in the

frequency range that can be measured experimentally, i.e. 1 to

18 MHz in this case.

(ii) The particles should be (preferably) monodisperse

spheres with the particle diameter much less than the sound

wavelength in the above frequency range.

(iii) Suspensions of the particles in water should be stable

and not flocculated, so that the measurement is characteristic

of the primary particles.

(iv) The particles should have well-defined connected (open)

pore structures, with the pore diameter much less than the

particle diameter.

(v) The lattice material should be rigid.

(vi) The pores should be readily wetted when the particles

are exposed to saturated water vapour or are suspended in

water, and the closed porosity should be small.

Particles satisfying most or all of these criteria include

zeolites, especially those with larger pore sizes, and mesopor-

ous particles of silica and other materials. Criterion (ii) is

particularly difficult to satisfy since many colloidal materials

are appreciably polydisperse. Therefore when calculating the

theoretical viscous and porous components of the total at-

tenuation we have assumed a log-normal volume-based dis-

tribution of particle sizes characterized by a median diameter

d50 and an 85th percentile diameter d85.

2. Materials and methods

Materials studied are: a faujasite-type zeolite Linde type Y;

two commercial silica chromatography supports, Platinumt

Silica (Alltech) and LiChrosphers Si 100 (5 mm) (Merck); and

TUD-1, a synthetic mesoporous silica. Important properties of

the particles and suspensions determined or inferred by meth-

ods other than our ultrasonic attenuation analysis are given

in Table 1. Throughout our analysis we have assumed that the

particles consist of a solid lattice containing connected pores

that are fully hydrated before measurement. The samples are

all hydrophilic in nature and previous observations of sedi-

mentation velocities and suspension densities for the mesopor-

ous silica-based samples lead us to believe that all samples

are fully saturated (hydrated) under the conditions used.5

The materials were suspended at least three days before

a School of Chemistry, University of Sydney, NSW 2006, Australia.E-mail: [email protected]

bColloidal Dynamics Inc., 11 Knight Street, Building E18, Warwick,RI 02886, USA.

w For Part I, see ref. 1.

5124 | Phys. Chem. Chem. Phys., 2006, 8, 5124–5130 This journal is �c the Owner Societies 2006

PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics

measurement, and repeated ultrasonic attenuation measure-

ments at later times were reproducible. We did not observe any

changes due to increasing hydration of the samples with time.

A mesoporous silica known as Platinumt Silica was ob-

tained from Alltech Associates Inc., IL USA. Information

from the manufacturer suggested that the material had a high

porosity, of around 52%. Nitrogen adsorption measurements

on the sample in our laboratory indicated a much lower

porosity of 29%. The sample was originally obtained a decade

ago, and had been suspended in distilled water for a prolonged

period during that time, prior to being dried and recovered.

The internal surface area of the particles may have been

reduced during that period due to dissolution and re-precipi-

tation of silica. A sample was suspended in 5 mM sodium

chloride solution at pH 9, at a hydrated particle weight

fraction of 0.2117. For ultrasonic attenuation and electroa-

coustic measurements this suspension was further diluted with

water to a hydrated particle weight fraction of 0.103. The

suspension was sonicated in an ultrasonic cleaning bath for

5 min prior to measurement. The hydrated weight fraction was

determined from the more concentrated suspension by mea-

suring the weight loss of the sample when heated overnight to

350 1C in vacuum, after first allowing the free water to

evaporate from the sample at room temperature in air. The

effective hydrated particle density calculated from using the

effective weight fraction and pyknometer measurements of the

density of the aqueous suspension was consistent with that

calculated assuming the framework density to be the same as

that of amorphous silica, 2.2 g cm�3, and a porosity of 29%, at

1.85 g cm�3. SEM and TEM investigations in our laboratory5

have shown the Platinumt silica particles to be approximately

spherical with a narrow size distribution. The porosity is not

well defined but is apparently three-dimensional (3-D) in

nature and the surface layer of the particles appears to be

porous, without any significant areas of impermeable shell.

TUD-1 is the name given to a mesoporous silica family with

3-D pore structures, the pore sizes being determined by the

template molecules used in their synthesis.6 A sample of

TUD-1 with an average pore diameter of 11.7 nm and a

porosity of 69% based on nitrogen adsorption/desorption

measurements was prepared by Dr L. van de Water of the

University of Sydney. The sample was very polydisperse, with

only a small proportion of the material in the colloidal size

range. The sample was suspended in water adjusted to pH 9

with NaOH and sonicated with an ultrasonic horn (dr.hiesch-

ler GmbH UP 200S) for 4 min at 50% output, 50% duty cycle

while being cooled with ice water. The suspension was then

fractionated by sedimentation in order to obtain the material

with diameters in the range 2–5 mm. Because of the limited

amount of colloidal material available, the resulting suspen-

sion was very dilute, around the lower limit of particle con-

centration suitable for measurement on the AcoustoSizer II

instrument. The hydrated weight fraction was determined by

evaporating the free water from the sample at room tempera-

ture in an oven at 40 1C, and this value was found to be in

good agreement to the value inferred from heating the sample

to constant weight at 210 1C (cooling in a desiccator) and then

calculating the effective weight fraction from the weight frac-

tion of solid lattice material, assumed to be amorphous silica

with a density of 2.2 g cm�3, and a porosity of 69%.

A sample of Zeolite Y was provided by Dr S. Carr. For

ultrasonic attenuation and electroacoustic measurements the

sample was suspended in 15 mMNaCl solution adjusted to pH

9 with NaOH at a hydrated particle weight fraction of 0.050.

Before measurement the suspension was sonicated with the

ultrasonic horn for 4 min at 50% output, 50% duty cycle. The

Table 1 Properties of microporous and mesoporous colloidal particles

MaterialPlatinumt Silica TUD-1 Silica Zeolite Y LiChrospher s Si 100 5 mm Silica

PropertyThisstudy

Previousstudies

Thisstudy

Previousstudies

Thisstudy

Previousstudies

Thisstudy

Previousstudies

Porosity data(N2 adsorption)Total pore volume/cm3 g�1 0.19 0.5b 1.03 — — — 1.29 1.25b

Pore volume fraction 0.29a 0.52a 0.69a — — 0.34–0.48c 0.74a 0.73a

BET surface area/m2 g�1 57.8 210b 335 — — — 277 400b

Pore diameter/nm 10.5 10b 11.7 — — 0.74c 16 10b

Suspension dataHydrated particledensity/g cm�3

1.85ad 1.6a 1.37ad — 1.86d 1.92 1.31ad 1.32a

Hydrated particleweight fraction

0.103d — 0.0041d — 0.050d — 0.10d —

SuspensionDensity/g cm�3 — — — — 1.020 — 1.020 —Particle size dataTEM d50/mm 2.0 — — — — — 5.0b

TEM, d85/mm 2.4 1.5b — — — — —DLS Zave/mm 1.86 — — 0.72e — —DLS PDI 0.054 — — 0.203e — —Sedimentation d50/mm — 2.02 — 0.85 — 5.28Sedimentation d85/mm — 3.20 — 1.40 — 6.5

a Calculated from total pore volume assuming solid lattice density of 2.2 g cm�3. b Manufacturers’ data, methodology unknown. c See main body

of text for details and references. d These data are used in calculation of experimental attenuation spectra. See Experimental section for

details. e Conversion to volume distribution gives d50 = 1.03 mm, d85 = 1.45 mm.

This journal is �c the Owner Societies 2006 Phys. Chem. Chem. Phys., 2006, 8, 5124–5130 | 5125

powder sample was assumed to be fully saturated with atmo-

spheric water vapour at the time it was suspended, and this

was later confirmed by evaporating the free water from the

sample at room temperature in air. The density of the hy-

drated particles was calculated as 1.86 g cm�3 based on the

measured suspension density and the hydrated particle weight

fraction. This is close to the hydrated density of 1.92 g cm�3

given by Breck for zeolite Y.7

LiChrosphers Si 100 (5 mm) was obtained from Merck. For

ultrasonic attenuation and electroacoustic measurements the

sample was suspended in 1 mM NaCl solution at pH 7.5, at a

hydrated particle weight fraction of 0.10. The suspension was

sonicated in an ultrasonic cleaning bath for 5 min prior to

measurement. The hydrated weight fraction was determined by

evaporating the free water from the sample in an oven at 40 1C

until the sample was apparently dry. This procedure was

repeated several times by adding back just sufficient water to

form a gel of the sample and then re-drying. This method was

deemed to be sufficiently accurate for the purposes of the present

study, given the low relative external surface area of the particles

and the high porosity. The value obtained was found to be

consistent with pyknometer measurements of the density of the

aqueous suspension assuming a framework density the same as

that of amorphous silica, 2.2 g cm�3, and a porosity of 74%.

Ultrasonic attenuation and electroacoustic measurements

were made using a Colloidal Dynamics AcoustoSizer II in-

strument. All measurements were carried out at 25 � 1 1C.

Approximately 40 mL of each suspension is required as a

minimum measurement volume in the present configuration of

the instrument. The instrument was calibrated prior to mea-

surement with a dilute potassium tungstosilicate solution as

recommended by the manufacturer. The solution is dilute and

is taken to have the same attenuation characteristics as water.

Electroacoustic measurements were made automatically at the

same time as ultrasonic attenuation measurements. Electro-

acoustics is a complementary technique to ultrasonic attenua-

tion, and the dynamic mobility frequency spectrum derived

from electroacoustic measurements provides information

about the electrostatic charge, particle size distribution, and

the nature of micropores and mesopores in colloidal materials.

The electroacoustic properties of suspensions of some of the

microporous and mesoporous materials measured here have

been reported previously.5,8

Particle size distribution measurements by TEM were made by

measuring diameters of approximately 150 particles and convert-

ing these observations to a log-normal volume based distribution.5

Particle size measurements by dynamic light scattering

(DLS) were made using a Malvern HPPS 3.3 instrument.

The results are expressed as the mean (Zave) and polydispersity

index (PDI) of the intensity distribution. To convert this to a

volume-based distribution, using the Rayleigh–Debye equa-

tion incorporated in the instrument software, requires the

refractive index and absorption coefficient of the particles.

For Zeolite Y the refractive index of faujasite (n = 1.48) and

an adsorption coefficient of 0.01 were used. Data for the

Platinumt silica was not converted in this way because the

refractive index for this material is unknown and the distribu-

tion is narrow anyway, so that the intensity mean diameter

should be similar to the volume median diameter.

Particle size measurements by sedimentation were made using

a Horiba Capa 700 disk photocentrifuge in gravitational and/or

centrifugal sedimentation modes. The same value for the effec-

tive hydrated density was used for the sedimentation analysis as

for the ultrasonic attenuation analysis. The instrument firmware

allows an optional correction for the absorption coefficient of

the particles as a function of particle diameter. Following the

recommendation of Allen and Davies9 the correction parameters

were entered as numerically equivalent to the particle radius in

microns. The correction is significant for polydisperse samples

such as Zeolite Y and TUD-1.

Nitrogen adsorption and desorption isotherms were mea-

sured using a Micromeritics ASAP 2020 Surface Area and

Porosity Analyser. Average pore sizes and total pore volumes

were obtained from desorption isotherms by the BJH method

and from adsorption isotherms using the single point method,

respectively, using the instrument software.

Suspension densities were measured with a Parr DMA 35N

density meter.

Treatment of results

In Part I of this paper1 it is shown (eqn (23)) that the pressure

amplitude of a plane wave in a suspension is given by

P ¼ P0 expðkIxÞ

where x is the distance travelled by the wave into the suspen-

sion. The quantity kI is always negative, so the wave decays

exponentially with distance.

The AcoustoSizer II attenuation measurements are reported

in terms of a non-dimensional attenuation coefficient Catt

Catt ¼ �lfkI

Here, l is the sound wavelength and f is the particle volume

fraction. For a solid particle f is the volume fraction of

particles in suspension. In the porous case f is replaced by

feff, the effective volume fraction. This is the volume fraction

of the solid particles plus the pore liquid. In practice, the

software requires the weight fraction, w, as an input para-

meter, and f is then calculated from w and the particle density.

Therefore, the required parameters are weff and reff, the

effective weight fraction and density of the hydrated particles,

as recorded in Table 1.

In order to compare the theory presented in Part I1 with the

experimental data a computer program was used to calculate the

theoretical non-dimensional attenuation coefficient given by eqn

(51) of Part I as a function of frequency. To calculate the viscous

attenuation component F(Y) given by eqn (53) of Part I, reff is

used for rp. To calculate the porous attenuation component

H(g) given by equation (52) of Part I, two adjustable parameters

were entered, the pressure diffusivity Dp and the porosity, given

by (1 � fp), where fp is the volume fraction of solid material in

the suspension, i.e. excluding the volume of the pores.

3. Experimental results and comparisons with theory

Platinumt silica

Fig. 1 shows the experimental attenuation spectrum for this

sample together with the theoretical viscous, porous, and total


attenuation spectra for a log-normal particle size distribution

with the parameters shown in Table 1 (TEM data). Clearly in

this case the experimental attenuation has a different magnitude

and shape than viscous attenuation alone would predict. In this

case we are able to adjust the pressure diffusivity and porosity in

the theoretical fit for the porous attenuation independently;

essentially the pressure diffusivity determines the frequency of

the maximum in the total attenuation and the porosity deter-

mines the overall magnitude of the attenuation. Fig. 1 shows the

fitted total attenuation curve with parameters Dp = 0.025 cm2

s�1 and porosity of 29%. The agreement is excellent.

From eqn (13) in Part I, the fitted pressure diffusivity

corresponds to a pore diameter of around 6 nm, which is

smaller than that given by nitrogen adsorption–desorption.

The probable reason for this is that the simple cylindrical pore

model used will tend to give a result more like the average

limiting pore diameter in the main channels, while the BJH

method will tend to give a diameter based more on the average

available surface area of pores that are assumed to be spheres.

The fitted porosity agrees very well with the value obtained by

nitrogen adsorption–desorption method.

TUD-1

Fig. 2 shows the measured attenuation spectrum of the TUD-l

sample. The data below 3.3 MHz was flagged as unreliable by

the AcoustoSizer II software because of the low absolute

attenuation in the dilute sample. It has therefore been omitted

from the figure. From eqn (15) of Part I we would expect a

maximum in the porous attenuation at a frequency of about 3

MHz for 2 mm diameter particles with 12 nm diameter pores

(R/aE 200). We do not observe a peak in the total attenuation

in our frequency range, and it seems likely that the maximum

lies at higher frequencies in this case. This may be due to the

effective pore diameter being greater than measured by nitro-

gen adsorption–desorption or the presence of substantial

numbers of particles with diameters smaller than 2 mm.

The fractionation of the suspension could reasonably

be expected to give a broader distribution than described

by assumed log-normal distribution, and the centrifugal

sedimentation results indicate that this is the case. The dis-

tribution has more sub-median particles than would be present

if the distribution were log-normal. The theoretical curves

shown correspond to the viscous porous and total (viscous

plus porous) attenuations calculated using d50 = 2.02 mm and

d85 = 3.2 mm, with Dp = 0.45 cm2 s�1 and porosity 69% It is

clear that the sample shows a substantial porous component to

the total attenuation. The fitted pressure diffusivity corre-

sponds to a pore diameter of around 24 nm, rather greater

than the value calculated from the nitrogen desorption iso-

therm using the BJH model. The difference may be due to the

assumption of a log-normal particle size distribution for the

separated fraction. However, given the constraints imposed by

the small amount of material available for study the agreement

is satisfactory.

Zeolite Y

The structural and physical characteristics of Zeolite Y are well

known.7 Another faujasite-type zeolite, X, has a similar struc-

ture to Y, the main differences being in the nature and location

of cations. Where noted, literature data for Zeolite X have been

used as representative of Y, if data for Y are unavailable.

In zeolite Y, the void spaces accessible to water molecules

comprise b-cages of 0.66 nm in diameter and larger supercages

of 1.2 nm in diameter. The cages are linked by a 3-D network

of channels. The channels interconnecting the b-cages are

hexagonal prisms with a diameter of 0.22 nm. Those connect-

ing the supercages are formed by 12-oxygen rings and have a

diameter of 0.74 nm. These are the main channels and thus this

Fig. 1 Experimental and theoretical ultrasonic attenuation spectra

for Platinumt silica. The non-dimensional attenuation coefficient Catt

is defined at the end of section 2. Experimental data are shown as solid

points. Theoretical data: (- - -) viscous attenuation; (� � �) porous

attenuation; solid line total attenuation (viscous + porous). Para-

meters used: hydrated particle weight fraction 0.103; hydrated particle

density 1.85 g cm�3; porosity 0.29; pressure diffusivity 0.025 cm2 s�1;

d50 2.0 mm, d85 2.4 mm.


for TUD-1 silica. Experimental data are shown as solid points.

Theoretical data: (- - -) viscous attenuation; (� � �) porous attenuation;solid line total attenuation (viscous + porous). Parameters used:

hydrated particle weight fraction 0.0041; hydrated particle density

1.37 g cm�3; porosity 0.69; pressure diffusivity 0.45 cm2 s�1;

d50 2.02 mm, d85 3.2 mm.


pore diameter is the effective diameter most likely to be

suitable for comparison with our model.

When fully hydrated, Zeolite X is understood to contain

about 265 water molecules per unit cell in both the b-cages andthe supercages.7,10 The total volume available to water mole-

cules is theoretically around 7.332 nm3 of a total unit cell

volume of 14.428 nm3, or 54%. This is close to the experi-

mentally measured value of 50–51%. The equivalent value for

Zeolite Y is around 48%.7 It is doubtful that the water

molecules in the b-cages can be regarded as accessible pore

water from the point of view of our ultrasonic measurements.

Dielectric measurements on Zeolite A, which has similar-sized

b-cage windows and cavities as Y, suggest that at low water

loadings it may take of the order of tens of days for water

molecules to penetrate into the b-cages.11 Exclusion of the b-cage volume would reduce the ‘available’ pore volume to

around 46%. This is in line with experimental adsorbed

amounts of gases other than water or nitrogen, but still larger

than the ‘‘accessible volume’’ of 34%, calculated from a hard-

sphere geometric model for the volume accessible in faujasite

to the centre of a water molecule.12 We might then expect the

available porosity into which the ultrasonic pressure waves can

diffuse to lie between 34 and 46%.




with the parameters shown in Table 1 (sedimentation data). In

this sample the extra attenuation due to the porosity of the

particles does not dominate the viscous attenuation, however the

additional attenuation due to the porosity of the zeolite is still

evident, particularly at the lower measurement frequencies.

It is possible to obtain reasonable and virtually identical fits

to the experimental data by assuming either a porosity of 34%

and a pressure diffusivity of 4 � 10�5 cm2 s�1 or with a

porosity of 48% and a pressure diffusivity of 2 � 10�5 cm2 s�1.

Thus, the porosity and Dp cannot be determined uniquely in

this case. The curves are so nearly identical that only the 34%

porosity data is shown in Fig. 3 for clarity. The porosities

fitted represent approximately the lower and upper limits of

the values found from geometric considerations and from

experiment by other investigators, as discussed previously.

However, in either case the pressure diffusivity is very small.

From eqn (13) of Part I, pressure diffusivities of 4 � 10�5 cm2

s�1 and 2 � 10�5 cm2 s�1 correspond to pore diameters of 0.22

and 0.16 nm, respectively. These are much smaller than the

window diameters between the supercages in Zeolite Y (0.74

nm) and this indicates that the physical properties of the pore

water are different from those of the bulk solvent. This is

discussed further later in this section.

The small apparent pressure diffusivity explains why the

porous component of the attenuation is relatively small in this

case and occurs mainly at the lower frequencies in the mea-

surement range. For a particle with radius R = 0.4 mm at

1 MHz (corresponding to an angular frequency o of 2p �106 Hz) the quantity (eqn (9) of Part I)

oR2

Dp¼ 2p� 106 � ð4� 10�7Þ2

4� 10�9¼ 240

The maximum in the porous attenuation occurs when this

quantity is O(1). So the porous attenuation in this micropor-

ous material occurs mainly at lower frequencies than measur-

able with the AcoustoSizer II (i.e. o1 MHz), and the part that

can be measured is in the high frequency tail of the effect. The

pressure variations diffuse into the particle to a depth of order

ffiffiffiffiffiffiDp

o

r

which at 1 MHz is only 25 nm. The pressure diffusivity factor

is so small for these particles that the pressure variations are

confined to a thin layer on the outer surface of the particle.

The maximum porous attenuation occurs when the penetra-

tion depth is of the order of the particle radius. Therefore we

can obtain more information for mesoporous particles in our

current frequency range, and lower frequency measurements

will be required to obtain more information about micropores.

Physical properties of confined water in nanopores

In a recent review Bellissent-Funel13 concluded that water in

the vicinity of a hydrophilic surface may be regarded as being

in a state equivalent to bulk water at a lower temperature. The

degree of the effect may depend on the proximity of the water

molecules to the pore walls. For example Takahara et al.14,15

modelled the pore water of MCM-41 materials with pore

diameters of 2.14 and 2.84 nm as comprising monolayer water

and capillary-condensed water. MCM-41, like TUD-1, is a

mesoporous silica with narrow pore size distributions con-

trolled by template molecules during synthesis. The pores in

MCM-41 are largely 1-D straight through channels with

limited interconnection, unlike the 3-D networks in TUD-1.

In the MCM-41 samples, the more mobile ‘capillary-con-

densed’ water molecules had translational diffusion coeffi-

cients approximately half those of bulk water, and the

mobility decreased with decreasing pore size. The effect is

even more pronounced in the narrower pores of zeolites, and

Fig. 3 Experimental and theoretical ultrasonic attenuation spectra for

Zeolite Y. Experimental data are shown as solid points. Theoretical

data: (- - -) viscous attenuation; (� � �) porous attenuation; solid line total

attenuation (viscous + porous). Parameters used: hydrated particle

weight fraction 0.05; hydrated particle density 1.86 g cm�3; porosity

0.34; pressure diffusivity 0.000 04 cm2 s�1; d50 0.85 mm, d85 1.4 mm.


here the picture is complicated by the presence of exchange-

able cations that also modify the properties of the water

around them. Paoli et al.16 studied the dependence of the

self-diffusion coefficient of pore water in Na-A and NaCa-A

zeolites. Zeolite NaA has a smaller limiting pore diameter than

ZeoliteY—the window diameter into the largest (a) cage is

0.42 nm. They found that the pressure diffusivity increased

with increasing water loading and decreased with increasing

Ca substitution, but was in all cases substantially less than the

bulk value. The diffusivities varied with the measurement

method, with quasi-elastic neutron scattering (QENS) giving

higher diffusivities than pulsed field gradient nuclear magnetic

resonance (PFG NMR).

For micropores and smaller mesopores (of a few nano-

meters diameter), therefore, the altered mechanical properties

of the pore water compared to bulk water should be taken into

account in any more detailed modelling of the porous attenua-

tion. Eqn (54) of Part I models the decreased compressibility

and increased effective viscosity of the pore water compared to

that of the bulk by means of the (c/cbulk)2 parameter. In effect,

these particles behave as if they have lower porosity and

smaller pores than if the pore water had the same properties

as bulk water.

LiChrosphers Si 100 (5 lm)




with the parameters shown in Table 1 (sedimentation data).

Again, the experimental attenuation is greater than the viscous

attenuation expected for particles of this size and density.

From eqn (15) of Part I we would expect a maximum in the

porous attenuation at a frequency of about 0.4 MHz for 5 mmdiameter particles with 10 nm diameter pores (R/a E 500).

This is below the lower limit of 1 MHz for the AcoustoSizer II,

so, as for Zeolite Y, we are measuring only the tail of the

porous attenuation, yet even so it dominates the viscous

attenuation for these particles.

In this case, the porous attenuation can be modelled with

Dp = 0.0004 cm2 s�1 and 74% porosity. This pressure

diffusivity corresponds to a pore diameter of around 0.7 nm,

which is substantially smaller than an estimate based on the

manufacturer’s data and on nitrogen adsorption experiments

(10–16 nm). One possible explanation for this is that LiChro-

sphers silica particles have been observed by electron micro-

scopy to have substantial areas of the particle surface

composed of apparently non-porous shell, and in some cases

to have apparently solid internal boundaries5,17,18 These may

not significantly affect the nitrogen adsorption characteristics

of the particles, but might affect the diffusion of pressure

waves into the particle interior. The nature of the pore

structure in these particles is not clearly defined, but the

SEM investigations of the pores in similar LiChrosphers

silicas with larger nominal pore diameters have shown that

there is a wide distribution of pore sizes. An effective pore

diameter of 1 nm would shift the expected maximum in the


for LiChrosphers Si 100 silica. Experimental data are shown as solid

points. Theoretical data: (- - -) viscous attenuation; (� � �) porous

attenuation; solid line total attenuation (viscous + porous). Para-

meters used: hydrated particle weight fraction 0.10; hydrated particle

density 1.31 g cm�3; porosity 0.74; pressure diffusivity 0.0004 cm2 s�1;

d50 5.28 mm, d85 6.5 mm.

Table 2 Summary of parameters fitted to ultrasonic attenuation spectra using porous particle theory. Quantities in parentheses have beencalculated from either the fitted Dp or from the nominal pore diameter using eqn (13) of Part I1

Material How obtained Porosity

PressurediffusivityDp/cm

2 s�1

Correspondingaverage porediameter/nm Comments

PlatinumtSilica

Fitted to attenuation data 0.29 0.025 (6) The only sample to show a maximum in the totalattenuation in the measured frequency range.

Based on properties in Table 1 0.29 (0.07) 10.5TUD-1 Silica Fitted to attenuation data 0.69 0.45 (24) Polydisperse sample of very low concentration.

Maximum in attenuation probably lies to higherfrequency.

Based on properties in Table 1 0.69 (0.1) 11.7Zeolite Y Fitted to attenuation data 0.34 0.00004 (0.22) Maximum in attenuation probably lies to lower

frequency.Based on properties in Table 1 0.34–0.48 (0.0004) 0.74

LiChrosphers

SilicaFitted to attenuation data 0.74 0.0004 (0.7) Wide pore size distribution and some non-porous

boundaries. Maximum in attenuation probablylies to lower frequency

Based on properties in Table 1 0.74 (0.18) 16


porous attenuation into the KHz range, well below the current

measurement range. It seems probable that the narrowest

pores in this sample are limiting the extent to which the

pressure disturbances can diffuse into the particles.

4. Summary of results

Table 2 summarises the results obtained from the ultrasonic

attenuation spectra using the theory presented in Part I.1

Conclusion

The experimental measurements presented here clearly de-

monstrate the presence of an additional component that adds

to the viscous attenuation in the overall attenuation spectrum

of these nanoporous colloids. The additional porous attenua-

tion can be modelled simply as described in Part I,1

by assuming that it arises from a network of connected

cylindrical pores. Within the limitations of the model and

the uncertainty in the particle size and pore size distributions

in some of the samples, the derived pressure diffusivity

and porosity parameters are in good agreement with those

obtained by other methods.

In principle, the ultrasonic method has many features

to recommend it as a method of studying microporous

and mesoporous colloids. The measurements are rapid com-

pared to adsorption methods and the choice of continuous

phase is not limited to water. Therefore it should be possible

to obtain additional information by selecting solvents with

different molecular sizes, polarities and bulk properties than

those of water.

Acknowledgements

We thank Dr Peter Southon for the nitrogen adsorption

measurements on the one of chromatography support silicas,

and Dr Leon van de Water and Ms. Cindy Aquino for the

provision and characterisation of the TUD-1 sample. This

work was supported in part by the University of Sydney

Research & Development Scheme.

References

1 Richard W. O’Brien, Phys. Chem. Chem. Phys., 2006, 8, DOI:10.1039/b605597d.

2 R. E. Challis, M. J. W. Povey, M. L. Mather and A. K. Holmes,Rep. Prog. Phys., 2005, 68, 1541.

3 J. R. Allegra and S. A. Hawley, J. Acoust. Soc. Am., 1972, 51, 1545.4 R. O’Brien, Strong Ultrasonic Attenuation by Nano-porous Parti-cles, presented at Particulate Systems Analysis 2005, 21–23 Sep-tember 2005, Stratford-upon-Avon, United Kingdom. Conferencepresentations published on DVD.

5 S. E. Gibb, The Electroacoustics of Porous Particles, PhD thesis,University of Sydney, 2001.

6 J. C. Jansen, Z. Shan, T. Maschmeyer, L. Marchese, W. Zhou andN. v. d. Puil, Chem. Commun., 2001, 713.

7 D. W. Breck, Zeolite Molecular Sieves, John Wiley and Sons, NewYork, 1974.

8 J. K. Beattie, A. M. Djerdjev and S. E. Gibb, New J. Chem., 2003,27, 1433.

9 T. Allen and R. Davies, Evaluation of Instruments for Particle SizeAnalysis, DuPont Engineering Services, Wilmington, Delaware,1989.

10 D. W. Breck and E. M. Flanigen, Molecular Sieves, Society ofChemical Industry, London, 1968.

11 B. A. Glazun, M. M. Dubinin, I. V. Zhilenkov and M. F.Rakityanskaya, Izv. Akad. Nauk SSSR, Ser. Khim., 1967, 1193.

12 C. Baerlocher and L. B. McCusker, Database of Zeolite Structures,Laboratory of Crystallography, ETH-Zentrum, Zurich, Switzer-land, http://www.iza-structure.org/databases/, 2006.

13 M. Bellissent-Funel, Eur. Phys. J. E, 2003, 12, 83–92.14 S. Takahara, N. Sumiyama, S. Kittaka, T. Yamaguchi and

M. Bellissent-Funel, J. Phys. Chem. B, 2005, 109, 11231.15 S. Takahara, M. Nakano, S. Kittaka, Y. Kuroda, T. Mori,

H. Hamano and T. Yamaguchi, J. Phys. Chem. B, 1999, 103, 5814.16 H. Paoli, A. Methivier, H. Jobic, C. Krause, H. Pfeifer,

F. Stallmach and J. Karger, Microporous Mesoporous Mater.,2002, 55, 147.

17 K. K. Unger, Porous Silica: its properties and uses as supportin column liquid chromatography, Elsevier Scientific PublishingCo., Amsterdam, 1979.

18 N. Tanaka, K. Kimata, K. Hosoya, T. Araki and K. Hashizume,J. High Resolut. Chromatogr., 1991, 14, 40.


https://www.researchgate.net/publication/284932707_Zeolite_Molecular_Sieves?el=1_x_8&enrichId=rgreq-879a14d68e497c7eb0991d2219f51155-XXX&enrichSource=Y292ZXJQYWdlOzY3MDY0MzM7QVM6MTgyMjI3NTQ3NzI5OTIxQDE0MjA0NTc4NDEyOTE=

https://www.researchgate.net/publication/284932707_Zeolite_Molecular_Sieves?el=1_x_8&enrichId=rgreq-879a14d68e497c7eb0991d2219f51155-XXX&enrichSource=Y292ZXJQYWdlOzY3MDY0MzM7QVM6MTgyMjI3NTQ3NzI5OTIxQDE0MjA0NTc4NDEyOTE=

Ultrasonic attenuation by nanoporous particles : Part II: Experimental

Documents

Transcript of Ultrasonic attenuation by nanoporous particles : Part II: Experimental