Directory UMM :Data Elmu:jurnal:A:Advances In Water Resources:Vol21.Issue6.1998:
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Advances in Water Resources 21 (1998) 523–531
q 1998 Elsevier Science Ltd
All rights reserved. Printed in Great Britain
0309-1708/98/$19.00 + 0.00
Time-dependent adsorption in near coastal
marine sediments: a two-step model
Anne M. Hansen a & James O. Leckie b
a
Instituto Mexicano de Tecnologı´a del Agua, Paseo Cuauhna´huac 8532, 62550 Jiutepec, Mor., Mexico
Environmental Engineering and Science, Department of Civil Engineering, Stanford University, Stanford, CA 94305, USA
b
(Accepted 23 September 1996)
Many important physical and chemical processes occur at phase boundaries. The role
of surface phenomena is frequently underestimated or overlooked although surfaces
play a significant role in many natural science disciplines. Experimental data from the
literature indicate that in adsorption from solution, most of the adsorbates move to the
adsorbent surface in a relatively short time period. Actual adsorption equilibrium,
however, may take longer to establish. In this study time variable parametric
experiments were performed with Co and a suspended marine sediment sample. Two
different time dependencies were observed: a rapid step that reached equilibrium in
5–10 days, while a slower step continued for more than 100 days. Observed behavior
was simulated with a time-dependent model that differentiates the slow and fast steps.
The fast step was considered to be due to diffusion of the adsorbate to the external and
macropore surface of the adsorbent and exchange at surface sites, while the slow step
was considered as diffusion of adsorbate into the adsorbent micropore capillaries where
adsorptive binding occurs. q 1998 Elsevier Science Limited. All rights reserved.
Key words: time dependent adsorption, two-step model, cobalt, marine sediments.
r ads
r des
r2
km
ki
K 01
NOMENCLATURE
r
radius of the dissolved species
rp
radius of the pore
D
diffusion coefficient of dissolved species in
small pores
diffusion coefficient in bulk solution
D0
A
specific surface area of the solid (m 2/g)
W
suspended solid concentration (g/l)
[Me]
bulk dissolved metal ion concentration (mol/l)
interfacial metal ion concentration (mol/l)
[Me] s
equilibrium metal ion concentration (mol/l)
[Me] eq
total metal ion concentration (mol/l)
[Me] tot
[SOH]
concentration of free surface adsorption sites
(mol/l)
[SOMe]
concentration of occupied surface adsorption
sites (mol/l)
total concentration of surface sites (mol/l)
S tot
[H]
proton concentration (mol/l)
ka
adsorption velocity constant (l/mol-day)
desorption velocity constant (l/mol-day)
kd
adsorption equilibrium constant (unitless)
KA
r1
transfer velocity of metal ion to the external and
macroporous surface (mol/g-day)
K 02
Ae
Ai
D1
D2
adsorption velocity (mol/l-day)
desorption velocity (mol/l-day)
net adsorption velocity (mol/l-day)
external mass transfer coefficient (mm/day)
internal mass transfer coefficient (mm/day)
mass transfer adsorption coefficient for the fast
step (per day)
mass transfer adsorption coefficient for the slow
step (per day)
specific external surface area (m 2/g)
specific internal surface area (m 2/g)
pre-exponential factor corresponding to fast
adsorption step (mol/l)
pre-exponential factor corresponding to slow
adsorption step (mol/l)
1 INTRODUCTION
Major components of oxidized sediments include hydrous
oxides of Fe, Al and Mn, aluminosilicate minerals,
carbonate minerals, and detrital organic matter. Sediment
particles occur most commonly as complex aggregates
523
524
A. M. Hansen, J. O. Leckie
with organic and inorganic coatings that strongly influence
the availability of mineral components to metal ions.11,15
The rate of adsorption of dissolved trace metal ions on
sediment particles depends on many factors. Of primary
importance are: size and structure of the adsorbates, composition of the solution, stoichiometry of the surface reactions, and characteristics of the adsorbent porosity. Every
adsorption process has at least two successive steps: (1)
diffusion transport of the adsorbate from the bulk phase to
the adsorbent surface, and (2) attachment or bond formation
on the adsorbent surface.
The first step depends on the characteristics of the
solution and adsorbate and is controlled by the laws of
diffusion. Pouchly and Erdo¨s,17 when considering the
kinetics of adsorption from solution, concluded that two
mass transport processes were involved: (a) diffusion of
the adsorbate to the external surface of the adsorbent
(external diffusion), and (b) diffusion of the adsorbate into
the adsorbent pores and capillaries (internal diffusion).
Chemical bond formation is itself, when attachment sites
are unobstructed, typically so rapid that it is difficult to
determine its characteristics.9
Intraparticle pores are usually classified according to size
in the manner originally proposed by Dubinin.6 Pores
having diameters less than 2 nm are termed micropores,
those between 2 and 50 nm, mesopores, and those greater
than 50 nm, macropores. Meso- and micropores can be
estimated by gas adsorption methods, while macropores
cannot be differentiated from the external surface by gas
adsorption.6
The linear dimensions of ions and simple organic
molecules in water are measurable in nanometers to tenths
of nanometers (10 ¹10 –10 ¹9 m). Linear dimensions of
interstices between particles in sediments, may be thought
of as being of the same order of magnitude as the particle
dimensions: micrometers (10 ¹6 –10 ¹5 m) for fine-grained
clayey sediments while internal pores may typically be in
the range from 10 ¹9 to 10 ¹8 m. Compared to these
distances, the dimensions of dissolved species are about
10 ¹4 of the interstices and 10 ¹1 of the intraparticle pores.
For intraparticle pores however, as pores become smaller,
diffusion of dissolved species is retarded by a combination
of geometric and hydrodynamic effects (hindrance by pore
walls through an increased drag force). An additional
limitation on transport is the electroneutrality constraint.
Because adsorption on oxide surfaces either produces
protons (cation adsorption) or consumes protons (anion
adsorption) the result is a coupled diffusion process with
ions moving in opposite directions.
Several models have been presented in the literature to
describe the kinetics of organic pollutant sorption to sediments or soil. Some researchers have assumed one fraction
of the sorbent has equilibrium sites and the other fraction of
sites are rate-limited and sorption kinetics may be described
by mass transfer.2,5,18 These models, however, are based on
the Freundlich isotherm representation of the actual sorption
phenomenon. Other studies have used a diffusion coefficient
and a tortuosity factor based on particle size,19,20 being the
description of sorption based on empirical weight to weight
based partitioning coefficients. More recently, Connaughton
et al.3 have described the release of naphthalene from
contaminated soils by assuming a continuum of mass
transfer coefficients that follow a gamma distribution.
None of these studies intended to describe variations in
the sorption behavior of inorganic ionic species as a
function of solution chemistry variations as would be
expected in a near-coastal marine environment being
influenced by tide and seasonally varying river inputs.
The objective of the present work was to develop a
methodology to describe the sorption of ionic species on a
natural sediment suspended in different electrolytes. This
method should be able to describe the effect of variations
in major electrolyte anion and cation concentrations, on the
sorption of trace ionic species. Equilibrium as well as timedependent situations should be accounted for to describe the
sorption phenomenon at different times of contact between
solute and adsorbent.
2 THE TIME-DEPENDENT MODEL
Most studies of adsorption at solid/solution interfaces
reported in the literature consider equilibrium conditions.
Often, the adsorption processes show two-step time dependencies, an initial fast step followed by a slower long-term
process. The long-term process may take from a few days to
several months to reach equilibrium, depending on the
nature of the solid phase. Lo and Leckie13 suggested that
the slow process may be due to solid state diffusion and/or
diffusion in micropores. This last mechanism can be
dominant for porous adsorbents. Given the typically fast
bond formation step,9 external mass transport (surfacefilm diffusion) and internal mass transport (pore diffusion)
combined with coupled diffusion may be the processes
limiting overall adsorption velocities.
Lo et al.14 developed a two-step model to describe the
incorporation of heavy metals in waste activated sludge,
based on a model of mass transfer and adsorption. This
two-step phenomenon was similar to the behavior found
for the adsorption of metals at porous oxide/solution interfaces.13 In this study, a two-step model was used to describe
the mass transfer process and obtain the mass transfer
coefficients corresponding to the fast and slow step of
Co(II) adsorption on complex coastal marine sediments.
Stoichiometric reactions describe the formation of surface
complexes.
In a perfectly well mixed system, the mass transfer due to
film diffusion can be expressed in the following way:
r1 ¼ ¹
1 d[Me]
¼ km Ae ([Me] ¹ [Me]s )
W dt
(1)
where r 1 is the transfer velocity of metal ion to the surface
plane and macropore volume (mol/g-day); k m, the external
mass transfer coefficient (mm/day); A e, the external surface
Time-dependent adsorption in near coastal marine sediments: a two-step model
area of the solid (m 2/g); W, the amount of suspended solid
(g/l); and [Me] and [Me] s are the dissolved and interfacial
metal ion concentrations (mol/l), respectively. Charges on
the ions have been omitted to maintain simplicity. Here we
will develop the mass transfer equations for the two-step
reaction using the surface complexation model (SCM)
format for the adsorption reaction.
The reaction stoichiometry for adsorption of the metal ion
at the sediment/solution interface can be represented as:
SOH þ Me ¼ SOMe þ H
(2)
and the mass action expression is:
KA ¼
ka [SOMe][H]
¼
kd [SOH][Me]
(3)
where SOH represents the adsorption sites at the surface;
Me the aqueous metal ion; SOMe the adsorbed metal ion; H
the proton; k a the adsorption velocity constant (l/mol-day);
k d the desorption velocity constant (l/mol-day); and K A is
the adsorption equilibrium constant. The site mass balance
requirement is
Stot ¼ [SOH] þ [SOMe]
(4)
where S tot is the total concentration of sites available for
adsorption (mol/l), and the adsorption and desorption
velocities (mol/l-day) can be expressed as:
rads ¼ ka [Me]s (Stot ¹ [SOMe])
(5)
rdes ¼ kd [SOMe][H]
(6)
respectively.
The net velocity at the film boundary (including
macropores), r 2 (mol/l-day), can be expressed in the
following way:
r2 ¼ ka [Me]s (Stot ¹ [SOMe]) ¹ kd [SOMe][H]
1
[SOMe][H]
¼ ka [Me]s (Stot ¹ [SOMe]) ¹
KA
ð7Þ
When film and macropore diffusion, and mass transfer are
both controlling processes, and no net accumulation in the
film boundary occurs (steady-state conditions at the film
boundary) then
(8)
r2 ,0
Since
[SOMe] ¼ [Me]tot ¹ [Me]
(9)
where [Me] tot is the total metal ion concentration, the
interfacial metal ion concentration can be calculated as
ÿ
!
[H] [Me]tot ¹ [Me]
1
ÿ
[Me]s ¼
KA Stot ¹ [Me]tot þ [Me]
¼
KA
[H]
Stot = [Me]tot ¹ [Me] ¹ 1
ÿ
ð10Þ
By substituting eqn (10) into eqn (1), the rate of change in
525
the bulk solution metal ion concentration is
d[Me]
¼
dt
[H]
ÿ
km Ae W [Me] ¹
KA Stot = [Me]tot ¹ [Me] ¹ 1
!
ð11Þ
At equilibrium
d[Me]
¼0
dt
(12)
and
[Me] ¼ [Me]s ¼ [Me]eq
(13)
where [Me] eq is the equilibrium metal ion concentration.
Now S tot can be calculated from eqn (10) under equilibrium
conditions:
ÿ
[H] [Me]tot ¹ [Me]
¹ [Me]eq þ [Me]tot
Stot ¼
[Me]KA
ÿ
[Me]tot ¹ [Me]eq
¼ [H] þ [Me]eq KA
ð14Þ
[Me]eq KA
By substitution of eqn (14) into eqn (11)
d[Me]
¼ ¹ k m Ae W 3
dt
ÿ
ÿ
[Me] ¹ [Me]eq [Me]tot [H] þ [Me][Me]eq KA
ÿ
ÿ
[H] [Me]tot ¹ [Me]eq þ [Me]eq KA [Me] ¹ [Me]eq
ð15Þ
The numerical value of log K A for the equilibrium Co sediment reactions with a proton stoichiometry of ¹ 2 has been
estimated by Hansen et al.8 to be ¹ 10.2 6 0.3. Therefore
it is reasonable to assume that
KA [Me][Me]eq p [Me]tot [H]
(16)
and
ÿ
ÿ
KA [Me]eq [Me] ¹ [Me]eq p [Me]tot ¹ [Me]eq [H]
(17)
Now eqn (15) can be simplified as follows:
ÿ
d[Me]
[Me]tot
¼ ¹ k m Ae W
[Me] ¹ [Me]eq
[Me]tot ¹ [Me]eq
dt
ÿ
ð18Þ
¼ ¹ K0 [Me] ¹ [Me]eq
where
K0 ¼
km Ae W[Me]tot
[Me]tot ¹ [Me]eq
(19)
Integrating eqn (18) from [Me] tot to [Me], yields
[Me] ¼ D exp( ¹ K0 t) þ [Me]eq
(20)
where D is a pre-exponential factor (mol/l) of the overall process. Since eqn (20) cannot describe the whole
526
A. M. Hansen, J. O. Leckie
time-dependent results, the data can be separated into two
parts using a separation technique, and integrated the result
is shown as eqn (21).
During the fast step both the external and the internal
mass transport processes occur. For that reason, k m as well
as k i (the internal mass transfer coefficient) must be
included in the K 0) value. The slow step is exclusively
due to internal mass transport,14 and under these conditions
K 0 includes the k i value. Now, the solution metal
concentration can be expressed as follows:
[Me] ¼ D1 exp( ¹ K01 t) þ D2 exp( ¹ K02 t) þ [Me]eq
(21)
where
K01 ¼
(km þ ki )Ae W[Me]tot
[Me]tot ¹ [Me]eq
(22)
ki Ai W[Me]tot
[Me]tot ¹ [Me]eq
(23)
and
K02 ¼
where K 01 and K 02 (per day) are the mass transfer
adsorption coefficients of the rapid and slow stages; A e
and A i represent the specific external and internal surface
areas (m 2/g), respectively, where
A ¼ Ae þ Ai
(24)
and D 1 and D 2 (mol/l) are the pre-exponential factors
corresponding to the fast and the slow adsorption steps,
respectively. Physically, these parameters were calculated
from the y-axis intercept of the time-dependent adsorption
curves for the fast and slow steps, respectively. [Me] eq was
calculated from the equilibrium surface reaction constant
found by Hansen et al.8 for the adsorption of Co(II) on a
Laguna Verde sediment sample.
3 EXPERIMENTAL
A marine sediment sample was collected in the near-shore
region of the Laguna Verde Nuclear Power Plant, Veracruz,
Mexico. The sediment was characterized to determine the
physical, chemical and mineralogical properties (Table 1).
In a split sample, calcite was eliminated by adding dilute
hydrochloric acid and the acidity of the solution was constantly monitored to avoid fluctuations below pH 5.5. The
calcite content was estimated as the weight difference
before and after the acid digestion.
Bulk mineralogy was analysed by X-ray diffraction and
by optical microscopy. Organic carbon content was
determined on five replicate sub-samples of each sediment,
following persulfate oxidation in an autoclave at 1308C for
4 h. Inorganic carbon was removed prior to autoclaving by
purging the persulfate-treated solution with a carbonate-free
inert gas. The organic carbon content was determined on a
Dohrman carbon analyser.
Nitrogen gas adsorption and the BET isotherm1 were
Table 1. Physical and chemical characteristics of Laguna
Verde sediment
Texture (%)
gravel
sand
silt
clay
Surface area (m 2/g)
BET method (N 2)
Organic carbon (mg/g)
Bulk mineralogy (%)
quartz
calcite
feldspars
hematite
zircon
goethite
muscovite
% w/w CaCO 3
Pore size distribution
micropores (d , 6 nm)
pore volume, % v/v
pore area, % a/a
meso and macropores (d . 6 nm)
pore volume, % v/v
pore area, % a/a
0.05
76.7
16.1
7.15
5.80
1.9 6 0.2
60
14
5
7
7
3
3
14
20
60
80
40
used to characterize the porous nature and the specific
surface area of the sediment sample. A BET surface area
and pore size distribution analyser model Digisorb 2500
(Micromeritics) was employed on samples previously
degassed at 1408C for 24 h. The isotherms were obtained
until the N 2 (g) pressure reached 590 mmHg (the saturation
pressure of N 2 (g) at the experimental temperature was
595.6 mmHg). The volume versus pressure data were
analysed using the equation described by Gregg and
Sing,7 and the computational procedure of Mackay.16 The
pore size distribution was analysed, using the desorption
isotherm obtained by reduction of the pressure to less than
50 mmHg. The adsorption and desorption isotherms joined
at N 2 (g) pressure of 195 mmHg.
The partitioning of Co between sediment and water was
determined using a radiochemical tracer (Co-57) and an
isotopic dilution technique.4 Weighted sediment subsamples were suspended in 6.3 ml aliquots of electrolyte
in polypropylene reaction vessels at 25 6 18C until the
suspension pH reached a constant value. A previous
experiment indicated that equilibration was complete
within a week. Aliquots (0.02 ml) of 3.15 3 10 ¹4 M
cobalt (II) with traces of cobalt-57 were added. At different
time intervals, pH was measured and phases were separated
by centrifugation at 4000 rpm for 15 min. The effectiveness
of this separation was verified by comparison with filtration
using 0.45 mm membrane filters.
Supernatant aliquots were transferred to counting vials
and liquid as well as mixed fractions were analysed for
cobalt-57 gamma activity on a Packard A5530 scintillation
counter with a 3 inch NaI(Tl) well crystal. Each sample was
measured to 10 000 decays to obtain counting errors of less
Time-dependent adsorption in near coastal marine sediments: a two-step model
Fig. 1. Pore size distribution of Laguna Verde sediment sample.
BET analysis of nitrogen gas adsorption and desorption isotherms.
than 1%. Exceptionally, when activities were low, the
counting was stopped after 10 min, and the counting error
was incorporated into measurement error calculations.
The fractions of cobalt removed from solution were
calculated by comparing supernatant (liquid) activities
with total activities. The fractions of adsorbed metal f,
were calculated from:
527
Fig. 3. Incorporation of Co(II) by Laguna Verde sediment sample
in seawater, pCo ¼ 6, pH ¼ 8.3. The data points represent the
experimental data and the solid lines represent the modelling
results.
4 RESULTS AND DISCUSSION
where N is the gamma activity. Subscripts l, tot and b
denote supernatant, total, and background activities,
respectively. Mass balances were performed on each
experiment to assure that no loss in radioactivity occurred
by adsorption on reaction vessels or by otherwise
uncontrolled experimental errors.
All chemicals used were analytical grade and the
solutions were prepared with double distilled deionized
water. The glassware was cleaned by immersion in dilute
nitric acid for at least three days and subsequent repeated
washing with deionized water. Reagent blanks were run to
assure adequate cleansing procedures.
The Laguna Verde sediment sample characteristics are
presented in Table 1. The sample was composed of the
following minerals: quartz, calcite, hematite, zircon,
K-feldspar, goethite, and muscovite.8 This sediment had a
low specific surface area and was mainly composed of badly
classified, fine sand, very asymmetrical towards course sizes
and extremely leptocurtical. The hysteresis of the gas
adsorption/desorption isotherm (BET analysis) indicated
that the pores behaved as though cylindrical with exterior
connections. The pores showed a bimodal distribution with
diameters around 2–3 and 10–40 nm (Fig. 1). The specific
external and internal surface areas were calculated using the
pore size distribution data, taking as a limit the pores of
6 nm, where a valley in the pore size bimodal distribution
was found (Fig. 1). The micropores (d , 6 nm) represented
about 20% of the pore volume and 60% of the surface area
(Fig. 2). The meso- and macropores (d . 6 nm) accounted
for 80% of pore volume and 40% of pore surface area.
Fig. 2. Cumulative pore area and volume as a function of pore size
of Laguna Verde sediment sample.
Fig. 4. Incorporation of Co(II) by Laguna Verde sediment without
calcite in seawater, pCo ¼ 6, pH ¼ 8.25. The data points represent
the experimental data and the solid lines represent the modelling
results.
f ¼ 1 ¹ (Nl ¹ Nb )=(Ntot ¹ 2Nb )
(25)
528
A. M. Hansen, J. O. Leckie
Fig. 5. Adsorption of Co(II) by Laguna Verde sediment without
calcite in different electrolytes, pSOH ¼ 3.4, pCo ¼ 6, pH ¼ 8.
The data points represent the experimental data and the solid lines
represent the modelling results.
Adsorption experiments were performed with sediment
samples suspended in different background electrolytes.
Experimental results of the Co interactions with various
amounts of marine sediment suspended in seawater are
illustrated as data points in Fig. 3. The solid lines represent
the modelling results. Uptake of Co continued throughout
the experiment. Sediment without calcite also showed an
increasing removal of Co with time (Fig. 4), eliminating
the hypothesis that time dependency could be due to the
formation of Co–calcite solid solution only. Both solids
with and without calcite showed a two-step adsorption
behavior: a fast step that lasted between 5 and 11 days
and a slow step that continued throughout the experiment
( . 100 days). The first step is too slow to be accounted for
by simple diffusion to particle external surface and therefore
must also include mass transport into the macro- and
mesopores of the particles. This is consistent with the
bimodal distribution of pore volume and pore surface
shown in Figs 1 and 2.
The effects of electrolyte type and concentration were
studied with calcite-free sediment suspended in different
electrolytes. The results indicate that Co sorption is reduced
at higher ionic strength (0.001 versus 0.7 M NaCl in Fig. 5).
This phenomenon may be explained by the reduction in free
aqueous Co 2þ since as much as 15% of Co is complexed as
chloro-complexes in seawater. Furthermore, Co formed
outer sphere complexes with the functional groups at the
sediment surface.8 As investigated by Hayes and Leckie,9
ionic strength strongly affects the position of pH-dependent
adsorption edges of trace cations forming outer sphere complexes. This is due to the rather weak character of this type
of bond and the competition with major electrolyte cations
for the same binding sites. However, dissolved ions in seawater affected the adsorption of Co to a much greater extent,
decreasing further the adsorption in this medium as
compared to the solution of NaCl at the same ionic strength
(i.e. seawater versus 0.7 M NaCl). SCM modelling of Co
sorption in the presence of Mg8 indicated that this major
cation reduced the sorption of Co by several tenths of a
percent, due to competition for the same adsorption sites
at the sediment surface.
The steepest line of the modelling results corresponds
to the fast reaction where the Co is adsorbing to the
external surface and inside macro- and mesopores. In
this step, a combination of external and internal mass
transport is believed to be controlling the time dependency (the first term of eqn (21)). The second step of
the adsorption curve represents the mass transport in
intraparticle micropores only. This step corresponds to the
second term of eqn (21), and is exclusively internal mass
transport limited.
Mass transport limitations in the internal pore structure,
specially the micropores, can arise from several simultaneous or sequential processes: (1) coupled counter diffusion
within small pores (rate limited by slowest diffusing
species); (2) surface diffusion in the smallest pores where
fluid properties and electrical double layer properties are
highly altered; (3) lability of adsorbed metal, limited by
the slowness of the desorption step; and (4) the possible
formation of outer sphere complex intermediates which
react to form inner sphere complexes at a slower rate.
An additional time-dependent process is possible and
cannot be distinguished from strict mass transport
limitations. The possibility exists, in principle, for mineral
assemblages, that adsorption kinetics are faster for thermodynamically weaker binding surfaces and slower for
thermodynamically more favorable binding surface sites.
In such a case the initial reactions would form essentially
thermodynamically metastable surface complexes and the
system would slowly relax (readjust) to a more stable
thermodynamic configuration with time. The resultant
macroscopic observation would be likely to appear similar
to the fast step observed in these experiments.
The mass transfer coefficients for the fast step, K 01, and
for the slow step, K 02, for the Co interactions with Laguna
Verde sediment and calcite-free sediment, are shown in
Tables 2 and 3. In sodium chloride solutions, the fast step
mass transfer coefficients, K 01, exceeded those of the slow
step, K 02, by two to three orders of magnitude. This relative
difference in magnitude between K 01 and K 02 was reduced to
one to two orders of magnitude in seawater. Under identical
experimental conditions, the ratio k m/k i was lower in
sediment without calcite as compared to whole sediment
when suspended in NaCl and dilute seawater. In seawater,
however, k m/k i was higher by a factor of two for sediment
without calcite.
Values of k m values in seawater were generally lower
than in 0.7 M NaCl for both Laguna Verde sediment and
calcite-free sub-samples. An exception was found at low
solid/solution ratio where k m values were higher for whole
sediment and identical for calcite-free sub-samples. k i, on
the other hand, showed larger values in seawater than in
0.7 M NaCl solutions. By applying triple layer modelling,8
a reduction was found of adsorbed Co from 95 to 65% in
a system of similar composition at pH 8 due to the
Time-dependent adsorption in near coastal marine sediments: a two-step model
529
Table 2. Mass transfer adsorption coefficients, external and internal mass transfer coefficients for Laguna Verde sediment
pCo tot
[sed] (g/l)
K 01 (per day)
(r 2)
K 02 (per day)
(r 2)
k m 3 10 2
(mm/day)
k i 3 10 4
(mm/day)
k m/k i
0.001 M NaCl
5
5
1.72
350
5
5
2.58
1.72
150
0.7 M NaCl
5
15
2.58
0.58
445
0.7 M NaCl
5
45
1.15
0.19
605
0.7 M NaCl
6
5
5.17
0.58
891
0.7 M NaCl
6
15
2.58
0.19
1358
0.7 M NaCl
6
45
1.05
0.06
1750
Seawater
6
5
8.51
11.5
74
Seawater
6
15
1.40
3.83
37
Seawater
6
45
0.47
1.28
37
Seawater
14.3%
Seawater
28.6%
Seawater
71.4%
6
15
2.58
0.58
445
6
15
2.15
0.58
371
6
15
0.003
(0.90)
0.003
(0.88)
0.003
(0.87)
0.003
(0.74)
0.001
(0.94)
0.001
(0.72)
0.001
(0.70)
0.02
(0.94)
0.02
(0.98)
0.02
(0.97)
0.003
(0.91)
0.003
(0.92)
0.003
(0.89)
6.02
0.7 M NaCl
0.70
(0.99)
0.30
(0.99)
0.90
(0.99)
1.2
(0.99)
0.60
(0.98)
0.90
(0.96)
1.1
(0.97)
1.0
(0.78)
0.50
(0.92)
0.50
(0.99)
0.90
(0.91)
0.75
(0.94)
0.70
(0.93)
2.01
0.58
347
Electrolyte
competition with Mg at concentrations found in seawater.
The experimental results of this work agrees with the
results of the equilibrium modelling,8 although sorption
increased with time. This result suggests that an appropriate modelling of the Co sorption in Laguna Verde sediment should include both time-dependent and equilibrium
considerations.
Lo and Leckie13 suggested that, under equal physical and
chemical conditions, the mass transfer coefficients should
be identical for different solid/solution ratios. Our results
suggest that the internal as well as the external mass transfer
coefficients decrease as the sediment/solution ratio
increases (Tables 2 and 3). A possible explanation for the
change in external mass transfer coefficients with increasing
solid/solution ratios, is an increasing tendency for
particle–particle interaction at higher solid concentration.
It is currently not understood why the internal mass transfer
coefficients decrease with an increase in the solid/solution
ratio.
Honeyman10 studied the effect of solid phase concentration on the adsorption in mono-mineral systems. He
found that adsorption at high adsorbate concentrations
differed from that at lower sediment contents, and attributed
this observation to an increase in particle interactions at high
solid/solution ratios. Kent et al.12 explained this phenomenon by the physical interactions between the electrical
double layers of adjacent particles, coagulation phenomena,
partial dissolution, adsorption and/or precipitation of one
adsorbent on the other.
5 CONCLUSIONS
The time-dependent adsorption of Co in a Laguna Verde
near-coastal marine sediment sample followed a two-step
process. A two-step kinetic model which related adsorption
reactions to mass transfer processes was developed and
applied to model the experimentally observed behavior.
The fast step is much slower than that found both for
non-porous adsorbents and for single phase porous
adsorbents.13 The extended duration of the fast step is
likely to be due to a combination of several sequential
steps with the slowest process being limiting. Possible
limiting processes include both diffusion in macro- and
mesopores and reaction limitation in adsorption/desorption
within the pore structure. The second slow step extends over
several months and is likely to be the result of the limited
internal mass transport into micro- and mesopores and
adsorption sites with otherwise difficult access.
The internal mass transport extends the adsorption
process in time as well as in magnitude, because the
amount of accessible internal surface area increases
with reaction time. The degree of competition of ions in
the background electrolyte for available surface sites
depends upon the strength of the chemical bonds formed
during adsorption.
A two-step time-dependent model was developed and
adapted to describe the time-dependent adsorption behavior
of the Co species on a porous and mineralogically complex
natural marine sediment sample. Internal and external mass
530
A. M. Hansen, J. O. Leckie
Table 3. Mass transfer adsorption coefficients, external and internal mass transfer coefficients for Laguna Verde sediment without
calcite
pCo tot
[sed] (g/l)
K 01 (per day)
(r 2)
K 02 (per day)
(r 2)
k m 3 10 2
(mm/day)
k i 3 10 4
(mm/day)
k m/k i
0.001 M NaCl
6
4.4
4.57
142
6
4.4
6.49
4.57
142
0.7 M NaCl
6
13.2
3.25
1.09
298
0.7 M NaCl
6
39.5
1.23
0.29
424
Seawater
6
4.4
6.49
4.57
142
Seawater
6
13.2
1.07
1.52
70
Seawater
6
39.5
0.36
0.51
71
Seawater
14.3%
Seawater
28.6%
Seawater
71.4%
Seawater
1.0%
Seawater
5.0%
Seawater
10.0%
Seawater
59.0%
6
13.2
1.08
0.44
245
6
13.2
1.30
0.65
200
6
13.2
1.29
1.31
98
6
15
2.87
0.04
100
6
15
2.24
0.38
250
6
15
1.71
0.96
148
6
15
0.007
(0.86)
0.007
(0.87)
0.005
(0.86)
0.004
(0.85)
0.007
(0.93)
0.007
(0.82)
0.007
(0.85)
0.002
(0.78)
0.003
(0.83)
0.006
(0.83)
0.0002
(0.60)
0.002
(0.75)
0.005
(0.69)
0.0055
(0.82)
6.49
0.7 M NaCl
1.0
(0.94)
1.0
(0.98)
1.5
(0.97)
1.7
(0.90)
1.0
(0.96)
0.50
(0.99)
0.50
(0.99)
0.50
(0.92)
0.60
(0.90)
0.60
(0.91)
1.0
(0.91)
0.78
(0.92)
0.60
(0.92)
0.50
(0.93)
1.43
1.05
136
Electrolyte
transfer coefficients were calculated and variations in these
were discussed leading to the following conclusions:
1. Ionic strength reduced the extent of initial adsorption
of Co in Laguna Verde sediment. In calcite-free
sediment, k m values were identical at high and low
ionic strength of the background electrolyte, suggesting that the presence of calcite partially influenced the
sorption behavior.
2. The external mass transfer coefficients for Co
adsorption were of the same order of magnitude for
whole sediment and calcite-free sub-sample at equal
solid/solution ratios when suspended both in 0.7 M
NaCl and in seawater. Values of k i, on the other
hand, were approximately 20 times lower for whole
sediment suspended in seawater as compared to 0.7 M
NaCl, while k i for the calcite-free sediment was of the
same order of magnitude for both types of electrolyte.
The slow adsorption behavior is probably due to a
combination of internal mass transport limitations in
addition to solid solution formation with calcite for
whole sediment samples.
3. In sodium chloride solutions, the fast step mass
transfer coefficients, k m, exceeded those of the slow
step, k i, by two to three orders of magnitude. This
ratio decreased to one to two orders of magnitude in
seawater. This difference indicates competition of
major cations in seawater for adsorption sites at the
sediment surface, and major anions for the solution
complexes of Co. Both types of competition may
have a retarding effect on the overall Co sorption
behavior.
4. k m/k i values in seawater were very similar for whole
sediment and calcite-free samples. By dilution of seawater, the difference in k m/k i values increased. This
effect was attributed to the competition of dissolved
salt constituents in the seawater.
5. The decrease in external mass transfer coefficients
with increasing sediment/solution ratio was possibly
due to increasing particle–particle interactions at
higher solid/solution ratios.
6. Values for k m/k i were higher by a factor of 4–6 for
whole sediment as compared to calcite-free sediment
when suspended in 0.7 M NaCl. In seawater as background electrolyte, this relationship was in the same
order of magnitude for both sediment types. This
result suggests that the presence of calcite appears
to have a stronger influence in relatively simple
systems. At higher complexity of the background
electrolyte, the composition of the liquid phase is
the controlling factor.
By combining triple layer surface complexation theory
with adsorption time dependencies the overall sorption
Time-dependent adsorption in near coastal marine sediments: a two-step model
behavior can be explained as a function of solution
chemistry and solid phase characteristics.
ACKNOWLEDGEMENTS
The authors gratefully acknowledge the financial support
given by the International Atomic Energy Agency (Contract
No. 301-K4-Mex-3491) for the research carried out at the
Instituto de Ciencias Nucleares at the UNAM; to the
Instituto de Investigaciones Ele´ctricas for additional support
given to A.M.H. and to the Comisio´n Federal de Electricidad for the help during the sampling. The authors also thank
the following: G. Hopkins for the TOC determinations;
G. Izquierdo for the XRD analysis; B. Balaguer and
K. Gruebel for the surface area determination; R. Oliver
for preparation and analysis of the thin sections; L. Conroy
and C. Arzate for the pore size distribution determinations;
J. L. Reza and A. Galva´n for the experimental assistance in
the laboratory.
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3. Connaughton, D. F., Stedinger, J. R., Lion, L. W. and Shuler,
M. L. Description of time-varying desorption kinetics:
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7. Gregg, S. J. & Sing K. S. W., Adsorption, Surface Area and
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8. Hansen, A. M., Leckie, J. O. and Mee, L. D. Cobalt(II)
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9. Hayes, K. F. & Leckie, J. O., Mechanism of lead ion
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11. Jenne, E. A., Trace element sorption by sediments and
soils—sites and processes. In Symposium on Molybdenium
in the Environment, ed. W. Chappel & K. M. Petersen.
M. Dekker Inc., New York, 1977, pp. 425–553.
12. Kent, D. B., Tripathi, V. J., Ball, N. B. and Leckie, J. O.,
Surface-complexation modeling of radionuclide adsorption
in sub-surface environments, NUREG/CR-4807, (SAND867175), U.S. Nuclear Regulatory Commission, 1988.
13. Lo, K. S.-L. and Leckie, J. O., Physical-chemical characterization of porous amorphous aluminium oxide. Proc. 2nd
IAWPRC Asian Conf. on Water Pollution Control, 1992,
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14. Lo, K. S.-L., Lin, C.-Y. and Leckie, J. O. The mass
transfer—adsorption model of metal ions uptake by waste
activated sludge. Proc. Nat. Sci. Counc. ROC(A), 1989,
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15. Luoma, S. M. and Davis, J. A. Requirements for modelling
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solid wastes for activated carbon production. PhD dissertation, Stanford University, Stanford, CA, 1981.
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19. Wu, S. C. and Gschwend, P. M. Sorption kinetics of
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20. Wu, S. C. and Gschwend, P. M. Numerical modeling of
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PII: S 0 3 0 9 - 1 7 0 8 ( 9 7 ) 0 0 0 3 9 - 0
Advances in Water Resources 21 (1998) 523–531
q 1998 Elsevier Science Ltd
All rights reserved. Printed in Great Britain
0309-1708/98/$19.00 + 0.00
Time-dependent adsorption in near coastal
marine sediments: a two-step model
Anne M. Hansen a & James O. Leckie b
a
Instituto Mexicano de Tecnologı´a del Agua, Paseo Cuauhna´huac 8532, 62550 Jiutepec, Mor., Mexico
Environmental Engineering and Science, Department of Civil Engineering, Stanford University, Stanford, CA 94305, USA
b
(Accepted 23 September 1996)
Many important physical and chemical processes occur at phase boundaries. The role
of surface phenomena is frequently underestimated or overlooked although surfaces
play a significant role in many natural science disciplines. Experimental data from the
literature indicate that in adsorption from solution, most of the adsorbates move to the
adsorbent surface in a relatively short time period. Actual adsorption equilibrium,
however, may take longer to establish. In this study time variable parametric
experiments were performed with Co and a suspended marine sediment sample. Two
different time dependencies were observed: a rapid step that reached equilibrium in
5–10 days, while a slower step continued for more than 100 days. Observed behavior
was simulated with a time-dependent model that differentiates the slow and fast steps.
The fast step was considered to be due to diffusion of the adsorbate to the external and
macropore surface of the adsorbent and exchange at surface sites, while the slow step
was considered as diffusion of adsorbate into the adsorbent micropore capillaries where
adsorptive binding occurs. q 1998 Elsevier Science Limited. All rights reserved.
Key words: time dependent adsorption, two-step model, cobalt, marine sediments.
r ads
r des
r2
km
ki
K 01
NOMENCLATURE
r
radius of the dissolved species
rp
radius of the pore
D
diffusion coefficient of dissolved species in
small pores
diffusion coefficient in bulk solution
D0
A
specific surface area of the solid (m 2/g)
W
suspended solid concentration (g/l)
[Me]
bulk dissolved metal ion concentration (mol/l)
interfacial metal ion concentration (mol/l)
[Me] s
equilibrium metal ion concentration (mol/l)
[Me] eq
total metal ion concentration (mol/l)
[Me] tot
[SOH]
concentration of free surface adsorption sites
(mol/l)
[SOMe]
concentration of occupied surface adsorption
sites (mol/l)
total concentration of surface sites (mol/l)
S tot
[H]
proton concentration (mol/l)
ka
adsorption velocity constant (l/mol-day)
desorption velocity constant (l/mol-day)
kd
adsorption equilibrium constant (unitless)
KA
r1
transfer velocity of metal ion to the external and
macroporous surface (mol/g-day)
K 02
Ae
Ai
D1
D2
adsorption velocity (mol/l-day)
desorption velocity (mol/l-day)
net adsorption velocity (mol/l-day)
external mass transfer coefficient (mm/day)
internal mass transfer coefficient (mm/day)
mass transfer adsorption coefficient for the fast
step (per day)
mass transfer adsorption coefficient for the slow
step (per day)
specific external surface area (m 2/g)
specific internal surface area (m 2/g)
pre-exponential factor corresponding to fast
adsorption step (mol/l)
pre-exponential factor corresponding to slow
adsorption step (mol/l)
1 INTRODUCTION
Major components of oxidized sediments include hydrous
oxides of Fe, Al and Mn, aluminosilicate minerals,
carbonate minerals, and detrital organic matter. Sediment
particles occur most commonly as complex aggregates
523
524
A. M. Hansen, J. O. Leckie
with organic and inorganic coatings that strongly influence
the availability of mineral components to metal ions.11,15
The rate of adsorption of dissolved trace metal ions on
sediment particles depends on many factors. Of primary
importance are: size and structure of the adsorbates, composition of the solution, stoichiometry of the surface reactions, and characteristics of the adsorbent porosity. Every
adsorption process has at least two successive steps: (1)
diffusion transport of the adsorbate from the bulk phase to
the adsorbent surface, and (2) attachment or bond formation
on the adsorbent surface.
The first step depends on the characteristics of the
solution and adsorbate and is controlled by the laws of
diffusion. Pouchly and Erdo¨s,17 when considering the
kinetics of adsorption from solution, concluded that two
mass transport processes were involved: (a) diffusion of
the adsorbate to the external surface of the adsorbent
(external diffusion), and (b) diffusion of the adsorbate into
the adsorbent pores and capillaries (internal diffusion).
Chemical bond formation is itself, when attachment sites
are unobstructed, typically so rapid that it is difficult to
determine its characteristics.9
Intraparticle pores are usually classified according to size
in the manner originally proposed by Dubinin.6 Pores
having diameters less than 2 nm are termed micropores,
those between 2 and 50 nm, mesopores, and those greater
than 50 nm, macropores. Meso- and micropores can be
estimated by gas adsorption methods, while macropores
cannot be differentiated from the external surface by gas
adsorption.6
The linear dimensions of ions and simple organic
molecules in water are measurable in nanometers to tenths
of nanometers (10 ¹10 –10 ¹9 m). Linear dimensions of
interstices between particles in sediments, may be thought
of as being of the same order of magnitude as the particle
dimensions: micrometers (10 ¹6 –10 ¹5 m) for fine-grained
clayey sediments while internal pores may typically be in
the range from 10 ¹9 to 10 ¹8 m. Compared to these
distances, the dimensions of dissolved species are about
10 ¹4 of the interstices and 10 ¹1 of the intraparticle pores.
For intraparticle pores however, as pores become smaller,
diffusion of dissolved species is retarded by a combination
of geometric and hydrodynamic effects (hindrance by pore
walls through an increased drag force). An additional
limitation on transport is the electroneutrality constraint.
Because adsorption on oxide surfaces either produces
protons (cation adsorption) or consumes protons (anion
adsorption) the result is a coupled diffusion process with
ions moving in opposite directions.
Several models have been presented in the literature to
describe the kinetics of organic pollutant sorption to sediments or soil. Some researchers have assumed one fraction
of the sorbent has equilibrium sites and the other fraction of
sites are rate-limited and sorption kinetics may be described
by mass transfer.2,5,18 These models, however, are based on
the Freundlich isotherm representation of the actual sorption
phenomenon. Other studies have used a diffusion coefficient
and a tortuosity factor based on particle size,19,20 being the
description of sorption based on empirical weight to weight
based partitioning coefficients. More recently, Connaughton
et al.3 have described the release of naphthalene from
contaminated soils by assuming a continuum of mass
transfer coefficients that follow a gamma distribution.
None of these studies intended to describe variations in
the sorption behavior of inorganic ionic species as a
function of solution chemistry variations as would be
expected in a near-coastal marine environment being
influenced by tide and seasonally varying river inputs.
The objective of the present work was to develop a
methodology to describe the sorption of ionic species on a
natural sediment suspended in different electrolytes. This
method should be able to describe the effect of variations
in major electrolyte anion and cation concentrations, on the
sorption of trace ionic species. Equilibrium as well as timedependent situations should be accounted for to describe the
sorption phenomenon at different times of contact between
solute and adsorbent.
2 THE TIME-DEPENDENT MODEL
Most studies of adsorption at solid/solution interfaces
reported in the literature consider equilibrium conditions.
Often, the adsorption processes show two-step time dependencies, an initial fast step followed by a slower long-term
process. The long-term process may take from a few days to
several months to reach equilibrium, depending on the
nature of the solid phase. Lo and Leckie13 suggested that
the slow process may be due to solid state diffusion and/or
diffusion in micropores. This last mechanism can be
dominant for porous adsorbents. Given the typically fast
bond formation step,9 external mass transport (surfacefilm diffusion) and internal mass transport (pore diffusion)
combined with coupled diffusion may be the processes
limiting overall adsorption velocities.
Lo et al.14 developed a two-step model to describe the
incorporation of heavy metals in waste activated sludge,
based on a model of mass transfer and adsorption. This
two-step phenomenon was similar to the behavior found
for the adsorption of metals at porous oxide/solution interfaces.13 In this study, a two-step model was used to describe
the mass transfer process and obtain the mass transfer
coefficients corresponding to the fast and slow step of
Co(II) adsorption on complex coastal marine sediments.
Stoichiometric reactions describe the formation of surface
complexes.
In a perfectly well mixed system, the mass transfer due to
film diffusion can be expressed in the following way:
r1 ¼ ¹
1 d[Me]
¼ km Ae ([Me] ¹ [Me]s )
W dt
(1)
where r 1 is the transfer velocity of metal ion to the surface
plane and macropore volume (mol/g-day); k m, the external
mass transfer coefficient (mm/day); A e, the external surface
Time-dependent adsorption in near coastal marine sediments: a two-step model
area of the solid (m 2/g); W, the amount of suspended solid
(g/l); and [Me] and [Me] s are the dissolved and interfacial
metal ion concentrations (mol/l), respectively. Charges on
the ions have been omitted to maintain simplicity. Here we
will develop the mass transfer equations for the two-step
reaction using the surface complexation model (SCM)
format for the adsorption reaction.
The reaction stoichiometry for adsorption of the metal ion
at the sediment/solution interface can be represented as:
SOH þ Me ¼ SOMe þ H
(2)
and the mass action expression is:
KA ¼
ka [SOMe][H]
¼
kd [SOH][Me]
(3)
where SOH represents the adsorption sites at the surface;
Me the aqueous metal ion; SOMe the adsorbed metal ion; H
the proton; k a the adsorption velocity constant (l/mol-day);
k d the desorption velocity constant (l/mol-day); and K A is
the adsorption equilibrium constant. The site mass balance
requirement is
Stot ¼ [SOH] þ [SOMe]
(4)
where S tot is the total concentration of sites available for
adsorption (mol/l), and the adsorption and desorption
velocities (mol/l-day) can be expressed as:
rads ¼ ka [Me]s (Stot ¹ [SOMe])
(5)
rdes ¼ kd [SOMe][H]
(6)
respectively.
The net velocity at the film boundary (including
macropores), r 2 (mol/l-day), can be expressed in the
following way:
r2 ¼ ka [Me]s (Stot ¹ [SOMe]) ¹ kd [SOMe][H]
1
[SOMe][H]
¼ ka [Me]s (Stot ¹ [SOMe]) ¹
KA
ð7Þ
When film and macropore diffusion, and mass transfer are
both controlling processes, and no net accumulation in the
film boundary occurs (steady-state conditions at the film
boundary) then
(8)
r2 ,0
Since
[SOMe] ¼ [Me]tot ¹ [Me]
(9)
where [Me] tot is the total metal ion concentration, the
interfacial metal ion concentration can be calculated as
ÿ
!
[H] [Me]tot ¹ [Me]
1
ÿ
[Me]s ¼
KA Stot ¹ [Me]tot þ [Me]
¼
KA
[H]
Stot = [Me]tot ¹ [Me] ¹ 1
ÿ
ð10Þ
By substituting eqn (10) into eqn (1), the rate of change in
525
the bulk solution metal ion concentration is
d[Me]
¼
dt
[H]
ÿ
km Ae W [Me] ¹
KA Stot = [Me]tot ¹ [Me] ¹ 1
!
ð11Þ
At equilibrium
d[Me]
¼0
dt
(12)
and
[Me] ¼ [Me]s ¼ [Me]eq
(13)
where [Me] eq is the equilibrium metal ion concentration.
Now S tot can be calculated from eqn (10) under equilibrium
conditions:
ÿ
[H] [Me]tot ¹ [Me]
¹ [Me]eq þ [Me]tot
Stot ¼
[Me]KA
ÿ
[Me]tot ¹ [Me]eq
¼ [H] þ [Me]eq KA
ð14Þ
[Me]eq KA
By substitution of eqn (14) into eqn (11)
d[Me]
¼ ¹ k m Ae W 3
dt
ÿ
ÿ
[Me] ¹ [Me]eq [Me]tot [H] þ [Me][Me]eq KA
ÿ
ÿ
[H] [Me]tot ¹ [Me]eq þ [Me]eq KA [Me] ¹ [Me]eq
ð15Þ
The numerical value of log K A for the equilibrium Co sediment reactions with a proton stoichiometry of ¹ 2 has been
estimated by Hansen et al.8 to be ¹ 10.2 6 0.3. Therefore
it is reasonable to assume that
KA [Me][Me]eq p [Me]tot [H]
(16)
and
ÿ
ÿ
KA [Me]eq [Me] ¹ [Me]eq p [Me]tot ¹ [Me]eq [H]
(17)
Now eqn (15) can be simplified as follows:
ÿ
d[Me]
[Me]tot
¼ ¹ k m Ae W
[Me] ¹ [Me]eq
[Me]tot ¹ [Me]eq
dt
ÿ
ð18Þ
¼ ¹ K0 [Me] ¹ [Me]eq
where
K0 ¼
km Ae W[Me]tot
[Me]tot ¹ [Me]eq
(19)
Integrating eqn (18) from [Me] tot to [Me], yields
[Me] ¼ D exp( ¹ K0 t) þ [Me]eq
(20)
where D is a pre-exponential factor (mol/l) of the overall process. Since eqn (20) cannot describe the whole
526
A. M. Hansen, J. O. Leckie
time-dependent results, the data can be separated into two
parts using a separation technique, and integrated the result
is shown as eqn (21).
During the fast step both the external and the internal
mass transport processes occur. For that reason, k m as well
as k i (the internal mass transfer coefficient) must be
included in the K 0) value. The slow step is exclusively
due to internal mass transport,14 and under these conditions
K 0 includes the k i value. Now, the solution metal
concentration can be expressed as follows:
[Me] ¼ D1 exp( ¹ K01 t) þ D2 exp( ¹ K02 t) þ [Me]eq
(21)
where
K01 ¼
(km þ ki )Ae W[Me]tot
[Me]tot ¹ [Me]eq
(22)
ki Ai W[Me]tot
[Me]tot ¹ [Me]eq
(23)
and
K02 ¼
where K 01 and K 02 (per day) are the mass transfer
adsorption coefficients of the rapid and slow stages; A e
and A i represent the specific external and internal surface
areas (m 2/g), respectively, where
A ¼ Ae þ Ai
(24)
and D 1 and D 2 (mol/l) are the pre-exponential factors
corresponding to the fast and the slow adsorption steps,
respectively. Physically, these parameters were calculated
from the y-axis intercept of the time-dependent adsorption
curves for the fast and slow steps, respectively. [Me] eq was
calculated from the equilibrium surface reaction constant
found by Hansen et al.8 for the adsorption of Co(II) on a
Laguna Verde sediment sample.
3 EXPERIMENTAL
A marine sediment sample was collected in the near-shore
region of the Laguna Verde Nuclear Power Plant, Veracruz,
Mexico. The sediment was characterized to determine the
physical, chemical and mineralogical properties (Table 1).
In a split sample, calcite was eliminated by adding dilute
hydrochloric acid and the acidity of the solution was constantly monitored to avoid fluctuations below pH 5.5. The
calcite content was estimated as the weight difference
before and after the acid digestion.
Bulk mineralogy was analysed by X-ray diffraction and
by optical microscopy. Organic carbon content was
determined on five replicate sub-samples of each sediment,
following persulfate oxidation in an autoclave at 1308C for
4 h. Inorganic carbon was removed prior to autoclaving by
purging the persulfate-treated solution with a carbonate-free
inert gas. The organic carbon content was determined on a
Dohrman carbon analyser.
Nitrogen gas adsorption and the BET isotherm1 were
Table 1. Physical and chemical characteristics of Laguna
Verde sediment
Texture (%)
gravel
sand
silt
clay
Surface area (m 2/g)
BET method (N 2)
Organic carbon (mg/g)
Bulk mineralogy (%)
quartz
calcite
feldspars
hematite
zircon
goethite
muscovite
% w/w CaCO 3
Pore size distribution
micropores (d , 6 nm)
pore volume, % v/v
pore area, % a/a
meso and macropores (d . 6 nm)
pore volume, % v/v
pore area, % a/a
0.05
76.7
16.1
7.15
5.80
1.9 6 0.2
60
14
5
7
7
3
3
14
20
60
80
40
used to characterize the porous nature and the specific
surface area of the sediment sample. A BET surface area
and pore size distribution analyser model Digisorb 2500
(Micromeritics) was employed on samples previously
degassed at 1408C for 24 h. The isotherms were obtained
until the N 2 (g) pressure reached 590 mmHg (the saturation
pressure of N 2 (g) at the experimental temperature was
595.6 mmHg). The volume versus pressure data were
analysed using the equation described by Gregg and
Sing,7 and the computational procedure of Mackay.16 The
pore size distribution was analysed, using the desorption
isotherm obtained by reduction of the pressure to less than
50 mmHg. The adsorption and desorption isotherms joined
at N 2 (g) pressure of 195 mmHg.
The partitioning of Co between sediment and water was
determined using a radiochemical tracer (Co-57) and an
isotopic dilution technique.4 Weighted sediment subsamples were suspended in 6.3 ml aliquots of electrolyte
in polypropylene reaction vessels at 25 6 18C until the
suspension pH reached a constant value. A previous
experiment indicated that equilibration was complete
within a week. Aliquots (0.02 ml) of 3.15 3 10 ¹4 M
cobalt (II) with traces of cobalt-57 were added. At different
time intervals, pH was measured and phases were separated
by centrifugation at 4000 rpm for 15 min. The effectiveness
of this separation was verified by comparison with filtration
using 0.45 mm membrane filters.
Supernatant aliquots were transferred to counting vials
and liquid as well as mixed fractions were analysed for
cobalt-57 gamma activity on a Packard A5530 scintillation
counter with a 3 inch NaI(Tl) well crystal. Each sample was
measured to 10 000 decays to obtain counting errors of less
Time-dependent adsorption in near coastal marine sediments: a two-step model
Fig. 1. Pore size distribution of Laguna Verde sediment sample.
BET analysis of nitrogen gas adsorption and desorption isotherms.
than 1%. Exceptionally, when activities were low, the
counting was stopped after 10 min, and the counting error
was incorporated into measurement error calculations.
The fractions of cobalt removed from solution were
calculated by comparing supernatant (liquid) activities
with total activities. The fractions of adsorbed metal f,
were calculated from:
527
Fig. 3. Incorporation of Co(II) by Laguna Verde sediment sample
in seawater, pCo ¼ 6, pH ¼ 8.3. The data points represent the
experimental data and the solid lines represent the modelling
results.
4 RESULTS AND DISCUSSION
where N is the gamma activity. Subscripts l, tot and b
denote supernatant, total, and background activities,
respectively. Mass balances were performed on each
experiment to assure that no loss in radioactivity occurred
by adsorption on reaction vessels or by otherwise
uncontrolled experimental errors.
All chemicals used were analytical grade and the
solutions were prepared with double distilled deionized
water. The glassware was cleaned by immersion in dilute
nitric acid for at least three days and subsequent repeated
washing with deionized water. Reagent blanks were run to
assure adequate cleansing procedures.
The Laguna Verde sediment sample characteristics are
presented in Table 1. The sample was composed of the
following minerals: quartz, calcite, hematite, zircon,
K-feldspar, goethite, and muscovite.8 This sediment had a
low specific surface area and was mainly composed of badly
classified, fine sand, very asymmetrical towards course sizes
and extremely leptocurtical. The hysteresis of the gas
adsorption/desorption isotherm (BET analysis) indicated
that the pores behaved as though cylindrical with exterior
connections. The pores showed a bimodal distribution with
diameters around 2–3 and 10–40 nm (Fig. 1). The specific
external and internal surface areas were calculated using the
pore size distribution data, taking as a limit the pores of
6 nm, where a valley in the pore size bimodal distribution
was found (Fig. 1). The micropores (d , 6 nm) represented
about 20% of the pore volume and 60% of the surface area
(Fig. 2). The meso- and macropores (d . 6 nm) accounted
for 80% of pore volume and 40% of pore surface area.
Fig. 2. Cumulative pore area and volume as a function of pore size
of Laguna Verde sediment sample.
Fig. 4. Incorporation of Co(II) by Laguna Verde sediment without
calcite in seawater, pCo ¼ 6, pH ¼ 8.25. The data points represent
the experimental data and the solid lines represent the modelling
results.
f ¼ 1 ¹ (Nl ¹ Nb )=(Ntot ¹ 2Nb )
(25)
528
A. M. Hansen, J. O. Leckie
Fig. 5. Adsorption of Co(II) by Laguna Verde sediment without
calcite in different electrolytes, pSOH ¼ 3.4, pCo ¼ 6, pH ¼ 8.
The data points represent the experimental data and the solid lines
represent the modelling results.
Adsorption experiments were performed with sediment
samples suspended in different background electrolytes.
Experimental results of the Co interactions with various
amounts of marine sediment suspended in seawater are
illustrated as data points in Fig. 3. The solid lines represent
the modelling results. Uptake of Co continued throughout
the experiment. Sediment without calcite also showed an
increasing removal of Co with time (Fig. 4), eliminating
the hypothesis that time dependency could be due to the
formation of Co–calcite solid solution only. Both solids
with and without calcite showed a two-step adsorption
behavior: a fast step that lasted between 5 and 11 days
and a slow step that continued throughout the experiment
( . 100 days). The first step is too slow to be accounted for
by simple diffusion to particle external surface and therefore
must also include mass transport into the macro- and
mesopores of the particles. This is consistent with the
bimodal distribution of pore volume and pore surface
shown in Figs 1 and 2.
The effects of electrolyte type and concentration were
studied with calcite-free sediment suspended in different
electrolytes. The results indicate that Co sorption is reduced
at higher ionic strength (0.001 versus 0.7 M NaCl in Fig. 5).
This phenomenon may be explained by the reduction in free
aqueous Co 2þ since as much as 15% of Co is complexed as
chloro-complexes in seawater. Furthermore, Co formed
outer sphere complexes with the functional groups at the
sediment surface.8 As investigated by Hayes and Leckie,9
ionic strength strongly affects the position of pH-dependent
adsorption edges of trace cations forming outer sphere complexes. This is due to the rather weak character of this type
of bond and the competition with major electrolyte cations
for the same binding sites. However, dissolved ions in seawater affected the adsorption of Co to a much greater extent,
decreasing further the adsorption in this medium as
compared to the solution of NaCl at the same ionic strength
(i.e. seawater versus 0.7 M NaCl). SCM modelling of Co
sorption in the presence of Mg8 indicated that this major
cation reduced the sorption of Co by several tenths of a
percent, due to competition for the same adsorption sites
at the sediment surface.
The steepest line of the modelling results corresponds
to the fast reaction where the Co is adsorbing to the
external surface and inside macro- and mesopores. In
this step, a combination of external and internal mass
transport is believed to be controlling the time dependency (the first term of eqn (21)). The second step of
the adsorption curve represents the mass transport in
intraparticle micropores only. This step corresponds to the
second term of eqn (21), and is exclusively internal mass
transport limited.
Mass transport limitations in the internal pore structure,
specially the micropores, can arise from several simultaneous or sequential processes: (1) coupled counter diffusion
within small pores (rate limited by slowest diffusing
species); (2) surface diffusion in the smallest pores where
fluid properties and electrical double layer properties are
highly altered; (3) lability of adsorbed metal, limited by
the slowness of the desorption step; and (4) the possible
formation of outer sphere complex intermediates which
react to form inner sphere complexes at a slower rate.
An additional time-dependent process is possible and
cannot be distinguished from strict mass transport
limitations. The possibility exists, in principle, for mineral
assemblages, that adsorption kinetics are faster for thermodynamically weaker binding surfaces and slower for
thermodynamically more favorable binding surface sites.
In such a case the initial reactions would form essentially
thermodynamically metastable surface complexes and the
system would slowly relax (readjust) to a more stable
thermodynamic configuration with time. The resultant
macroscopic observation would be likely to appear similar
to the fast step observed in these experiments.
The mass transfer coefficients for the fast step, K 01, and
for the slow step, K 02, for the Co interactions with Laguna
Verde sediment and calcite-free sediment, are shown in
Tables 2 and 3. In sodium chloride solutions, the fast step
mass transfer coefficients, K 01, exceeded those of the slow
step, K 02, by two to three orders of magnitude. This relative
difference in magnitude between K 01 and K 02 was reduced to
one to two orders of magnitude in seawater. Under identical
experimental conditions, the ratio k m/k i was lower in
sediment without calcite as compared to whole sediment
when suspended in NaCl and dilute seawater. In seawater,
however, k m/k i was higher by a factor of two for sediment
without calcite.
Values of k m values in seawater were generally lower
than in 0.7 M NaCl for both Laguna Verde sediment and
calcite-free sub-samples. An exception was found at low
solid/solution ratio where k m values were higher for whole
sediment and identical for calcite-free sub-samples. k i, on
the other hand, showed larger values in seawater than in
0.7 M NaCl solutions. By applying triple layer modelling,8
a reduction was found of adsorbed Co from 95 to 65% in
a system of similar composition at pH 8 due to the
Time-dependent adsorption in near coastal marine sediments: a two-step model
529
Table 2. Mass transfer adsorption coefficients, external and internal mass transfer coefficients for Laguna Verde sediment
pCo tot
[sed] (g/l)
K 01 (per day)
(r 2)
K 02 (per day)
(r 2)
k m 3 10 2
(mm/day)
k i 3 10 4
(mm/day)
k m/k i
0.001 M NaCl
5
5
1.72
350
5
5
2.58
1.72
150
0.7 M NaCl
5
15
2.58
0.58
445
0.7 M NaCl
5
45
1.15
0.19
605
0.7 M NaCl
6
5
5.17
0.58
891
0.7 M NaCl
6
15
2.58
0.19
1358
0.7 M NaCl
6
45
1.05
0.06
1750
Seawater
6
5
8.51
11.5
74
Seawater
6
15
1.40
3.83
37
Seawater
6
45
0.47
1.28
37
Seawater
14.3%
Seawater
28.6%
Seawater
71.4%
6
15
2.58
0.58
445
6
15
2.15
0.58
371
6
15
0.003
(0.90)
0.003
(0.88)
0.003
(0.87)
0.003
(0.74)
0.001
(0.94)
0.001
(0.72)
0.001
(0.70)
0.02
(0.94)
0.02
(0.98)
0.02
(0.97)
0.003
(0.91)
0.003
(0.92)
0.003
(0.89)
6.02
0.7 M NaCl
0.70
(0.99)
0.30
(0.99)
0.90
(0.99)
1.2
(0.99)
0.60
(0.98)
0.90
(0.96)
1.1
(0.97)
1.0
(0.78)
0.50
(0.92)
0.50
(0.99)
0.90
(0.91)
0.75
(0.94)
0.70
(0.93)
2.01
0.58
347
Electrolyte
competition with Mg at concentrations found in seawater.
The experimental results of this work agrees with the
results of the equilibrium modelling,8 although sorption
increased with time. This result suggests that an appropriate modelling of the Co sorption in Laguna Verde sediment should include both time-dependent and equilibrium
considerations.
Lo and Leckie13 suggested that, under equal physical and
chemical conditions, the mass transfer coefficients should
be identical for different solid/solution ratios. Our results
suggest that the internal as well as the external mass transfer
coefficients decrease as the sediment/solution ratio
increases (Tables 2 and 3). A possible explanation for the
change in external mass transfer coefficients with increasing
solid/solution ratios, is an increasing tendency for
particle–particle interaction at higher solid concentration.
It is currently not understood why the internal mass transfer
coefficients decrease with an increase in the solid/solution
ratio.
Honeyman10 studied the effect of solid phase concentration on the adsorption in mono-mineral systems. He
found that adsorption at high adsorbate concentrations
differed from that at lower sediment contents, and attributed
this observation to an increase in particle interactions at high
solid/solution ratios. Kent et al.12 explained this phenomenon by the physical interactions between the electrical
double layers of adjacent particles, coagulation phenomena,
partial dissolution, adsorption and/or precipitation of one
adsorbent on the other.
5 CONCLUSIONS
The time-dependent adsorption of Co in a Laguna Verde
near-coastal marine sediment sample followed a two-step
process. A two-step kinetic model which related adsorption
reactions to mass transfer processes was developed and
applied to model the experimentally observed behavior.
The fast step is much slower than that found both for
non-porous adsorbents and for single phase porous
adsorbents.13 The extended duration of the fast step is
likely to be due to a combination of several sequential
steps with the slowest process being limiting. Possible
limiting processes include both diffusion in macro- and
mesopores and reaction limitation in adsorption/desorption
within the pore structure. The second slow step extends over
several months and is likely to be the result of the limited
internal mass transport into micro- and mesopores and
adsorption sites with otherwise difficult access.
The internal mass transport extends the adsorption
process in time as well as in magnitude, because the
amount of accessible internal surface area increases
with reaction time. The degree of competition of ions in
the background electrolyte for available surface sites
depends upon the strength of the chemical bonds formed
during adsorption.
A two-step time-dependent model was developed and
adapted to describe the time-dependent adsorption behavior
of the Co species on a porous and mineralogically complex
natural marine sediment sample. Internal and external mass
530
A. M. Hansen, J. O. Leckie
Table 3. Mass transfer adsorption coefficients, external and internal mass transfer coefficients for Laguna Verde sediment without
calcite
pCo tot
[sed] (g/l)
K 01 (per day)
(r 2)
K 02 (per day)
(r 2)
k m 3 10 2
(mm/day)
k i 3 10 4
(mm/day)
k m/k i
0.001 M NaCl
6
4.4
4.57
142
6
4.4
6.49
4.57
142
0.7 M NaCl
6
13.2
3.25
1.09
298
0.7 M NaCl
6
39.5
1.23
0.29
424
Seawater
6
4.4
6.49
4.57
142
Seawater
6
13.2
1.07
1.52
70
Seawater
6
39.5
0.36
0.51
71
Seawater
14.3%
Seawater
28.6%
Seawater
71.4%
Seawater
1.0%
Seawater
5.0%
Seawater
10.0%
Seawater
59.0%
6
13.2
1.08
0.44
245
6
13.2
1.30
0.65
200
6
13.2
1.29
1.31
98
6
15
2.87
0.04
100
6
15
2.24
0.38
250
6
15
1.71
0.96
148
6
15
0.007
(0.86)
0.007
(0.87)
0.005
(0.86)
0.004
(0.85)
0.007
(0.93)
0.007
(0.82)
0.007
(0.85)
0.002
(0.78)
0.003
(0.83)
0.006
(0.83)
0.0002
(0.60)
0.002
(0.75)
0.005
(0.69)
0.0055
(0.82)
6.49
0.7 M NaCl
1.0
(0.94)
1.0
(0.98)
1.5
(0.97)
1.7
(0.90)
1.0
(0.96)
0.50
(0.99)
0.50
(0.99)
0.50
(0.92)
0.60
(0.90)
0.60
(0.91)
1.0
(0.91)
0.78
(0.92)
0.60
(0.92)
0.50
(0.93)
1.43
1.05
136
Electrolyte
transfer coefficients were calculated and variations in these
were discussed leading to the following conclusions:
1. Ionic strength reduced the extent of initial adsorption
of Co in Laguna Verde sediment. In calcite-free
sediment, k m values were identical at high and low
ionic strength of the background electrolyte, suggesting that the presence of calcite partially influenced the
sorption behavior.
2. The external mass transfer coefficients for Co
adsorption were of the same order of magnitude for
whole sediment and calcite-free sub-sample at equal
solid/solution ratios when suspended both in 0.7 M
NaCl and in seawater. Values of k i, on the other
hand, were approximately 20 times lower for whole
sediment suspended in seawater as compared to 0.7 M
NaCl, while k i for the calcite-free sediment was of the
same order of magnitude for both types of electrolyte.
The slow adsorption behavior is probably due to a
combination of internal mass transport limitations in
addition to solid solution formation with calcite for
whole sediment samples.
3. In sodium chloride solutions, the fast step mass
transfer coefficients, k m, exceeded those of the slow
step, k i, by two to three orders of magnitude. This
ratio decreased to one to two orders of magnitude in
seawater. This difference indicates competition of
major cations in seawater for adsorption sites at the
sediment surface, and major anions for the solution
complexes of Co. Both types of competition may
have a retarding effect on the overall Co sorption
behavior.
4. k m/k i values in seawater were very similar for whole
sediment and calcite-free samples. By dilution of seawater, the difference in k m/k i values increased. This
effect was attributed to the competition of dissolved
salt constituents in the seawater.
5. The decrease in external mass transfer coefficients
with increasing sediment/solution ratio was possibly
due to increasing particle–particle interactions at
higher solid/solution ratios.
6. Values for k m/k i were higher by a factor of 4–6 for
whole sediment as compared to calcite-free sediment
when suspended in 0.7 M NaCl. In seawater as background electrolyte, this relationship was in the same
order of magnitude for both sediment types. This
result suggests that the presence of calcite appears
to have a stronger influence in relatively simple
systems. At higher complexity of the background
electrolyte, the composition of the liquid phase is
the controlling factor.
By combining triple layer surface complexation theory
with adsorption time dependencies the overall sorption
Time-dependent adsorption in near coastal marine sediments: a two-step model
behavior can be explained as a function of solution
chemistry and solid phase characteristics.
ACKNOWLEDGEMENTS
The authors gratefully acknowledge the financial support
given by the International Atomic Energy Agency (Contract
No. 301-K4-Mex-3491) for the research carried out at the
Instituto de Ciencias Nucleares at the UNAM; to the
Instituto de Investigaciones Ele´ctricas for additional support
given to A.M.H. and to the Comisio´n Federal de Electricidad for the help during the sampling. The authors also thank
the following: G. Hopkins for the TOC determinations;
G. Izquierdo for the XRD analysis; B. Balaguer and
K. Gruebel for the surface area determination; R. Oliver
for preparation and analysis of the thin sections; L. Conroy
and C. Arzate for the pore size distribution determinations;
J. L. Reza and A. Galva´n for the experimental assistance in
the laboratory.
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