Supporting information
Alexander M. Puziy 1 , Olga I. Poddubnaya 1 , Anna Derylo-Marczewska
Magdalena Blachnio 2 , Mykola M. Tsyba 1 , Vitaliy I. Sapsay
2 , Adam W. Marczewski 2 ,
3 , Dmytro O. Klymchuk 3
1 Institute for Sorption and Problems of Endoecology, National Academy of Sciences of Ukraine,
General Naumov Street 13, 03164 Kyiv, Ukraine
2 Maria Curie-Skłodowska University, Faculty of Chemistry, Maria Curie-Skłodowska Sq. 2, 20-
031 Lublin, Poland
3 M.G. Kholodny Institute of Botany, National Academy of Sciences of Ukraine,
Tereshchenkivska St. 2, 01601 Kyiv, Ukraine
Table S1. Templates used for synthesis of nanoporous carbons
Template A
BET
V tot m 2 /g cm 3 /g
Shape, size Characteristics Precursor
NaY
SG60
KSKG
847 0.47 Irregular granules,
0.2-0.3 µm
Synthetic zeolite with the faujasite structure furfuryl alcohol
454 0.53 Irregular granules,
0.063-0.2 mm
Silica gel for the column chromatography, Fluka furfuryl alcohol
322 0.74 Near-spherical granules, 4-7 mm
Wide pore silica gel, Karpov
Chemical Plant, Russia sucrose
ZK 296 0.76 Near-spherical granules, 4-7 mm
Wide pore silica gel, POCh,
Poland
Ludox AS40 122 0.21 Colloidal silica, 24 nm (Li and
Jaroniec 2001)
Colloidal silica, Sigma-
Aldrich furfuryl alcohol sucrose

Supporting information
C(NaY)
C(SG60)
C(KSKG)

Supporting information
C(ZK)
C(AS40)
Fig. S1. SEM image of nanoporous carbons.

Supporting information
Table S2. Point of zero charge (PZC), total amount of acidic surface groups (Q a
), amount of particular surface group (Q i
) and pK i
.
Carbon
C(NaY) 2.60 1.24
C(SG60) 4.58 0.77
C(SG60)-T 7.59 0.84
C(KSKG) 2.61 0.83
C(ZK) 3.58 0.51
C(AS40) 3.58 3.55 average standard deviation
PZC Q a mmol/g
Q
1 mmol/g pK
1
Q
2 mmol/g pK
2
Q
3 mmol/g pK
3
Q
4 mmol/g pK
4
Q
5 mmol/ g
0.10
0.25
0.09
0.12
2.90 0.14
2.82
3.67
3.83
3.30
0.45
0.03
4.70 0.11
4.74 0.05
4.72
0.02
0.06
0.15
6.27 0.21
6.89 0.15
0.57
0.04
0.12
7.22 0.07
6.18 0.08
6.43 0.11
7.85 0.22
8.34
7.86
7.39 0.04
8.79
7.87 0.92
8.02
0.44 pK
5
Q g
6 mmol/
9.26 0.46
0.54 pK
6
0.80 10.24
8.62 0.42
0.27 10.07
9.33 2.24
9.07
0.32
10.59
10.21
9.83
10.74
10.28
0.31

Supporting information
Fig. S2. Adsorption kinetics of BSA (left) and OVA (right) on zeolite-templated carbon
C(NaY). Squeare root time scale. Symbols – experimental points, lines – fit with multiexponential equation.
Fig. S3. Dependence of indetermination coefficient (1-R 2 ) in fitting experimental adsorption of BSA (left) and OVA (right) by carbon C(SG60)-T on the number of exponential terms of multi-exponential equation.

Supporting information
Mixed 1,2-order rate equation assumes that the rate has 1 st and 2 nd order contributions: da dt
 k
1 a
( a eq
 a )
 k
2 a
( a eq
 a )
2
or equivalently  dc dt
 k
1 c
( c
 c eq
)
 k
2 c
( c
 c eq
)
2
gives dF

 k
1 a
 k
2 a a eq
  f
1
( 1

F )
 f
2
( 1

F ) 2


 k
1 a
 k
2 a a eq
 
( 1

F )( 1
 f
2
F )

where dt k ia
 k ic
( m / V ) i

1 , f i
 k
1 a k i ia a eq

1
 k
2 a a eq
and f
1
 f
2

1 . above f i
specifies contribution of i -th order kinetics and adsorption progress F is:
F
 c c eq

 c o c o


 eq



 o o
and c
 c o

F ( c eq
 c o
) or
   o

F (
 eq
  o
)
Alternatively dF dt

1
 k
1 f
2
( 1

F )( 1
 f
2
F ) where k
1
 k
1 c
 k
1 a
and f
2
<1.
Integrated form of MOE if f
2
≠1:
F




1
1

 f
2 exp(
 k
1 t exp(
)
 k
1 t ) if
1 k
'
2 t
 k
'
2 t if f
2 f
2

1

1
where k
1
 k
1 c
 k
1 a
, k
2
'  k
2 a a eq
and kinetic half-time is t
1 / 2


 ln( 2

1 / f k
2
'
2
) / k
1 if if f
2 f
2

1

1
The initial rate is dF dt
 ini
 t lim

0 dF dt
 k
1
 k
2
' 
1
 k
1 f
2

1 k
2

' f
1
If f
2
<1, then near the equilibrium MOE attains 1 st order behavior with t lim
  d ln( 1

F ) dt
  k
1
The rate for m-exp is: dF dt
 i n 

1 f i k i exp(
 k i t ) with the initial value t lim

0 dF dt
 i n 

1 f i k i
.
However, near the equilibrium we have t lim
  dF dt
 f m k m exp(
 k m t )
where k m
 min( k
1
, k
2
,  k n
) .

Supporting information
McKay’s pore diffusion model assuming unreacted shrinking core and including external film transfer resistance:
Capacity factor: C h
= u eq
= ( c o
c eq
)/ c o
, B=1-1/Bi, where Biot number Bi=K f r/D p
– (D p
– pore diffusion coefficient, r – particle radius, K f
- external mass transfer coefficient), dimensionless time in McKay’s pore diffusion model τ s
:
 s

1
6 C h
2 B

1 a ln


 x
3
1

 a a
3
3




3 ln a

 x
1

 a a




 a
1
3 C h arctan

 a a
3


 arctan


2 a x

3 a


 where x

( 1

F )
1 / 3
, a

( 1 / C h

1 )
1 / 3 , then x
3  a
3 
1 / C h

F and 1
 a
3 
1 / C h
and rate: dF d
 s

3 ( 1
1


C h
B
F
( 1
)( 1

F

F
)
1 / 3
)
1 / 3
The reduced experiment time, may be then calculated as
  t / t
1 / 2
  s
/
 s 1 / 2
, where ½ index denotes value at F =0.5 and t ( F )
  s
( F ) /
 s
( 0 .
5 ) t
1 / 2
.
Intraparticle diffusion model, assuming c =const F

1


6
2 n



1
1 n
2 exp(
 
2 n
2
D a t / r
2
) where r is adsorbent particle radius and D a
is the effective diffusion coefficient:
D a

 p
( 1

D

K
H
 p
) where D is the molecular diffusion coefficient, τ p
is the dimensionless pore tortuosity factor, ρ is particle density, ε p
is particle porosity and K
H
is Henry adsorption constant (linear adsorption isotherm is assumed).
However, when the concentration of adsorbate is varying, then:
F

1

6 ( 1
 u eq
) n



1
9 exp( u eq


( p n
2
1

Dt u eq
/ r
)
2
2
) p
2 n where p n
are non-zero roots of equation tan p n

3 p n
/[ 3

( 1 / u eq

1 ) p n
2
] .
This equation (in tables and calculations referred to as Crank (a)) corresponds to non-converging series and in practical applications some approximations must be used (Carman and Haul 1954;
Reichenberg 1953). However, the most accurate calculations may be performed by using

Supporting information approximation by (Haynes and Lucas 2007) and some series approximations (Marczewski et al.
2013).
However, the initial part of IDM (F<<1) is always linear function of square root of time (for u eq
=0 shown by (Boyd et al. 1947), widely known as Weber-Morris kinetics, WM, (Marczewski et al. 2013; Weber and Morris 1963):
F

( 6 /

1 / 2
)( 1
 u eq
)( D a t / r
2
)
1 / 2 or c o
 c

( 6 /

1 / 2
) c o u eq
( 1
 u eq
)( D a t / r
2
)
1 / 2

Supporting information
Table S3. Best-fit parameters of protein adsorption kinetics using multi-exponential equation and D a
values from IDM model.
System
BSA / C(NaY)
BSA / C(SG60)
A max
, mg/g t
1/2
Optimal number of exponents f
1
19.4 0.11
3.1 1240
BSA / C(SG60)-T 13.2 1480
BSA / C(KSKG)
BSA / C(ZK)
BSA / C(AS40)
OVA / C(NaY)
OVA / C(SG60)
62.8 64
18.2 143
70.3 292
18.2 0.82
7.0 3180
OVA / C(SG60)-T 12.5 1300
OVA / C(KSKG)
OVA / C(ZK)
OVA / C(AS40)
80.0 115
34.5 256
73.8 152
3
1
3
4
3
4
3
1
3
4
3
3 k
1
, min -1 f
2 k
2
, min -1 f
3 k
3
, min -1 f
4 k
4
, min -1
D a
, cm 2 /s
0.51 26.9
1.00 0.0006
0.46 0.5012 0.04 0.0141 1.4×10 -9
6.8×10 -15
0.02 0.1155 0.06 0.0102 0.91 0.0004 2.3×10 -13
0.14 1.1220 0.17 0.0871 0.46 0.0076 0.23 0.0011 4.3×10 -10
0.12 0.1514 0.32 0.0145 0.56 0.0015
0.05 22.9
9.6×10 -12
0.05 0.0813 0.17 0.0093 0.73 0.0013 5.1×10 -11
0.81 1.1482 0.11 0.0676 0.08 0.0047 1.5×10 -9
1.00 0.0002
0.12 1.1482 0.06 0.0195 0.81 0.0004
1.3×10 -14
2.3×10 -13
0.15 0.7244 0.21 0.0309 0.31 0.0044 0.32 0.0005 5.0×10 -10
0.10 0.1950
0.03 5.13
0.33 0.0182 0.58
0.17 0.0646 0.81
0.0006
0.0032
3.7×10 -11
1.1×10 -10
A max
=(c o
-c eq
)V/m – estimated (by using m-exp fitting) equilibrium adsorption value, t
1/2
– kinetic halftime, k i
, f i
– rate coefficient and relative contribution for the i-th equation term; D a
– estimated effective diffusion coefficient

Supporting information
Table S4. Relative standard deviations SD(c)/c o
for FOE, SOE, MOE, m-exp, McKay pore diffusion and IDM model (Crank).
Best of FOE/SOE/MOE fits are underlined, best overall for MOE and m-exp fits are bold/red, and best fits for diffusion models are blue.
System
BSA / C(NaY)
No. of parameters
Data points
101
3 4 3 5 7 9 11 Optimum m-exp 4 3 4
PSOE MOE FOE 2-exp 3-exp 4-exp 5-exp m-exp m-exp McKay Crank a Crank b
0.456% 0.458% 0.618% 0.491% 0.423% 0.421% 0.426% 0.423% 3-exp 0.927% 0.848% 0.574%
BSA / C(SG60)
BSA / C(SG60)-T
BSA / C(KSKG)
BSA / C(ZK)
BSA / C(AS40)
OVA / C(NaY)
OVA / C(SG60)
OVA / C(SG60)-T
OVA / C(KSKG)
OVA / C(ZK)
126
54
91
96
97
95
133
46
96
77
0.640% 0.626% 0.624% 0.629%
0.220% 0.222% 0.243% 0.086% 0.074% 0.076%
0.624% 1-exp 0.612% 0.363% 0.363%
0.074% 3-exp 0.222% 0.270% 0.267%
2.370% 2.384% 3.610% 1.409% 0.800% 0.585% 0.591% 0.585% 4-exp 1,756% 1.066% 0.861%
0.663% 0.666% 1.023% 0.280% 0.168% 0.168% 0.170% 0.168% 3-exp 0.423% 0.350% 0.318%
1.544% 1.553% 2.153% 0.859% 0.471% *0.398% 0.392% 0.398% 4-exp 2.048% 4.522% 0.701%
0.621% 0.625% 1.033% 0.392% 0.341% 0.345% 0.341% 3-exp 1.360% 1.274% 0.656%
0.365% 0.367% 0.365% 0.368% 0.365% 1-exp 0.412% 0.451% 0.451%
0.530% 0.536% 0.555% 0.150% *0.069% 0.046% 0.047% 0.069% 3-exp 0.389% 0.382% 0.371%
3.003% 3.019% 4.408% 1.729% 0.585% 0.485% 0.491% 0.485% 4-exp 1.620% 1.759% 0.830%
1.359% 1.368% 1.673% 0.661% 0.573% 0.578% 0.586% 0.573% 3-exp 1.242% 0.787% 0.646%
2.440% 1.914% 2.612% 0.502% *0.448% 0.438% 0.444% 0.448% 3-exp 2.359% 7.052% 1.524% OVA / C(AS40) 96 a Full IDM model including variable concentration (change of concentration) and fully correlated model parameters (u eq
=1-c eq
/c o
). b Full IDM model including variable concentration (change of concentration) but with disassociated solute uptake parameter u eq
and equilibrium concentration c eq
.
*Some kinetic half-times associated with additional terms of multi-exponential equation (with lower deviation) were much higher than the experiment duration and were rejected despite lower SD (see also the following table).
In several cases MOE fit resulted in model parameter f
2
→ 1, i.e. SOE or f
2
=0 i.e. FOE – both fits were in fact identical (same deviations and indetermination coefficient 1-R 2 ), however, MOE had higher number of adjustable parameters and thus SD had to be higher. With the exception of 1 system (BSA / C(SG60)) both m-exp or MOE fits were better than for diffusion models. Only in one case (BSA / C(SG60)) unconstrained IDM (Crank 1975) was the best overall and only in one case (OVA / C(SG60)) McKay’s pore diffusion model was better that Crank with 4 adjustable parameters. Both such atypical cases were adsorption on C(SG60), where maximum observed adsorption was very low and in consequence determination coefficients R 2 were also low)

Supporting information
Table S5. Experiment duration and estimated kinetic half-times (time where half of equilibrium adsorption is attained) for FOE,
SOE, MOE, m-exp, McKay pore diffusion and IDM model (Crank 1975).
System
BSA / C(NaY)
BSA / C(SG60)
BSA / C(SG60)-T
BSA / C(KSKG)
BSA / C(ZK)
BSA / C(AS40)
OVA / C(NaY)
OVA / C(SG60)
OVA / C(SG60)-T
OVA / C(KSKG)
OVA / C(ZK)
OVA / C(AS40)
No. of parameters
Experiment duration [min]
1391
5312
1594
1526
1403
1450
1417
1393
1496
1400
2777
1429
3 4 3 5 7
PSOE MOE FOE 2-exp 3-exp
9
4-exp
11 best 4 3 4
5-exp m-exp m-exp McKay Crank a Crank b
0.44 0.44 0.74 0.09
2383 1235 1235 311.3
0.11 1.25
∙ 10 6 136.5 0.11 3-exp
1235 1-exp
1339 1331 698.2 1199 1478
79.8 79.7 89.7 62.2 55.7
3774
63.8
0 1478 3-exp
136.5 63.8 4-exp
0.87
1442
3.4
∙ 10
49.5
4
0.82
1.8
∙ 10 5
69.4
0.31
5.8
∙ 10 4 1.1
∙ 10
6.9
∙ 10
55.3
4
4
174.4 173.2 175 110.4 136.2
434.6 432.9 305.2 306.1 282.2
143.3
291.6
204.2 143.3 3-exp
392.4 291.6 4-exp
131.9
346.0
138.3
218.1
167.0
386.5
0.91
8322
333.9
116.2
108.7
163.5
0.91
8090
332.8
116.0
108.6
186.4
1.12
3180
256.5
133.5
90.7
183.7
0.86
156.5
257.1
84.9
372.5
156.5
0.82
1304
67.3
255.8
152.1
0.04
8200
114.8
243.1
178.9
0.82 3-exp
1304 3-exp
114.8 4-exp
8800 255.8 3-exp
152.1 3-exp
0.68
277.6
64.9
145.1
155.0
0.76 0.33
3180 1-exp 3.0
∙ 10 4 2.8
∙ 10 6 1.5
∙ 10 6
345
95.1
171.4
59.0
674.4
126.2
384.3
139.0
Comparison of estimated half-times shows high differences between models – longer half-time means lower estimated (extrapolated) equilibrium concentration. The values of half-time higher than the duration of the experiment (marked red) are not reliable and such fits should be avoided. The same may be said for the half-times associated with various terms of multi-exponential equation, where a small improvement of fit is accompanied by a sudden change of trend for the half-time vs. parameters number.
MOE (mixed-order-equation) (Marczewski 2010b) is a generalization of FOE and SOE with parameter f
2
(0 to 1) defining the contribution of 2 nd order kinetics (FOE: f
2
=0, SOE, f
2
=1)).
Details of optimization for McKay pore diffusion model (McKay et al. 1996) as well as for classic IDM (Crank 1975) are described in
(Marczewski et al. 2013).
Adsorption half-time for FOE is t
1/2
=ln(2)/k
1
, for MOE t
1/2
=ln(2-f
2
)/k
1
for SOE t
1/2
=1/(k
2a a eq
). For m-exp, McKay and IDM this parameter must be calculated numerically. Adsorption half-time is essentially model-independent, however, estimation of the

Supporting information equilibrium concentration (especially if it is not very low) may require to assume some kind of equation in order to be able to estimate
(actually: extrapolate) this value.

Supporting information
0.020
0.015
0.010
0.005
0.000
-0.005
-0.010
0
BSA/C(NaY) (McKay)
BSA/C(NaY) (Crank (a))
BSA/C(NaY) (Crank (b))
0.005
0.004
0.003
0.002
0.001
0.000
-0.001
-0.002
-0.003
-0.004
-0.005
0
BSA/C(SG60) (McKay)
BSA/C(SG60) (Crank (a))
BSA/C(SG60) (Crank (b))
10 20 40 20 40 t
60
0.004
0.003
0.002
0.001
0.000
-0.001
-0.002
-0.003
-0.004
0
BSA/C(SG60)-T (McKay)
BSA/C(SG60)-T (Crank (a))
BSA/C(SG60)-T (Crank (b))
10 20
0.020
0.010
0.000
-0.010
-0.020
-0.030
-0.040
0
BSA/C(KSKG) (McKay)
BSA/C(KSKG) (Crank (a))
BSA/C(KSKG) (Crank (b))
40 10 20 40
0.008
0.006
0.004
0.002
0.000
-0.002
-0.004
BSA/C(ZK) (McKay)
BSA/C(ZK) (Crank (a))
BSA/C(ZK) (Crank (b))
0.040
0.030
0.020
0.010
0.000
-0.010
-0.020
-0.030
-0.040
-0.050
0
BSA/C(AS40) (McKay)
BSA/C(AS40) (Crank (a))
BSA/C(AS40) (Crank (b))
-0.006
0 10 20 40 10 20 40
Fig. S4. Comparison of optimization deviations for BSA adsorption and PDM (McKay et al.
1996), classic IDM (variable concentration, Crank a) and IDM with disassociated c eq
and u eq parameters (Crank b) in linear W-M coordinates
For most BSA systems differences between IDM (two variants) and PDM are not very pronounced
– there are systematic and random deviations (see also Tables S4-S5). The most obvious case is the
BSA on C(AS40) where systematic deviations are much higher than the random ones – in this case classic IDM model including dependence on actual changes of concentrations (Crank (a), 3 parameters) is the worst - much better agreement is obtained for McKay’s PDM model
(approximation of IDM with additional resistance of the external film, 4 parameters), but the best is the IDM (Crank (b), 4 parameters), where u eq
is disassociated from c eq
and c o
). This difference between IDM proper (Crank (a)) and Crank (b) shows that the actual change of concentration outside the granule affects rate in a different manner than it results from Fickian diffusion. It is probably the effect of difference between the assumed linear adsorption model and the actual highly non-linear adsorption isotherms characteristic for aqueous solutions of organics in contact with microporous carbon materials. To a lesser extent it is also visible for BSA on C(KSKG).
Very similar behavior may be observed for OVA adsorption (next Figure).

Supporting information
0.015
0.010
0.005
0.000
-0.005
-0.010
-0.015
0 10
OVA/C(NaY) (McKay)
OVA/C(NaY) (Crank (a))
OVA/C(NaY) (Crank (b))
20 30 t 1/2
40
0.006
0.004
0.002
0.000
-0.002
-0.004
-0.006
-0.008
0
OVA/C(SG60) (McKay)
OVA/C(SG60) (Crank (a))
OVA/C(SG60) (Crank (b))
10 20 30 t 1/2
40
0.005
0.003
0.001
-0.001
-0.003
-0.005
0
OVA/C(SG60)-T (McKay)
OVA/C(SG60)-T (Crank (a))
OVA/C(SG60)-T (Crank (b))
10 20 t 1/2
30
0.020
0.015
0.010
0.005
0.000
-0.005
-0.010
-0.015
-0.020
0 10
OVA/C(KSKG) (McKay)
OVA/C(KSKG) (Crank (a))
OVA/C(KSKG) (Crank (b))
20 30 t 1/2
40
0.020
0.015
0.010
0.005
0.000
-0.005
-0.010
-0.015
0 10
OVA/C(ZK) (McKay)
OVA/C(ZK) (Crank (a))
OVA/C(ZK) (Crank (b))
20 30 40 t 1/2
50
0.060
0.040
0.020
0.000
-0.020
-0.040
-0.060
-0.080
-0.100
0
OVA/C(AS40) (McKay)
OVA/C(AS40) (Crank (a))
OVA/C(AS40) (Crank (b))
10 20 30 t 1/2
40
Fig. S5. Comparison of optimization deviations for OVA adsorption and PDM (McKay), classic IDM (variable concentration, Crank a) and IDM with disassociated c eq
and u eq
parameters
(Crank b) in linear W-M coordinates

Supporting information
Experimental deviations are discussed by using OVA and BSA adsorption on C(SG60) and
C(SG60)-T. where adsorbed amounts are very low and data scatter is well visible.
The scatter for OVA and BSA on C(SG60) (expressed as SD(c)) is of the same order as for the other systems, however due to low total change of concentration (and appropriately adjusted scale) it is visually larger. If we compare SD(c)/co values for best-of-all fitted curves (due to large number of data points compared to the parameter number and relatively low flexibility of equations – monotonous behaviour of kinetic curves and their derivatives it is reliable estimation of data deviations) we obtain the range of SD(c)/co = 0.07-0.58% (see Table S4 and Figs. S4, S5 in
Supplementary Information). Most of the deviations are random in character, whereas in some cases we see larger, seemingly non-random discrepancies. It all results from the measurement method and system properties – we use UV/Vis spectrometer with peristaltic pump and thin teflon tubing (to minimise dead volumes) with glass wool filters and 1 cm quartz liquid cell (3 mm dia.) to measure protein concentration. We remove dust from carbon, however, it may reappear during long stirring what may result in filter clogging and solution foaming (there are breaks in some curves due to this phenomenon – when spotted, filters are replaced between subsequent measurements) – also small carbon dust particles and bubbles affect measurements. Moreover, for the protein concentration used, absorption peak height at 279 nm was ABS~0.260 and best-fit SD(c)’s mentioned above correspond to SD(ABS) ±0.00018 to ±0.0015 (average deviations from fitted curves), which are in fact quite small
Every data point for each curve corresponds to a single adsorbent sample and a single solution. The only variable is time, possible instrumental noise (typical for UV/Vis spectrometers and other related to cyclic measurements by using narrow-path flow-cell – e.g. UV/Vis beam wobble – and peristaltic pump with filter – air bubbles and particulate matter may block liquid sampling or obstruct UV/Vis beam), adsorbent/solution changes (e.g. buffer pH variation due to adsorption of buffer components etc. – pH deviated by no more than ±0.04) and adsorbate properties (proteins a prone to foaming spoiling measurements by using peristaltic pump and a flow-cell). There might be a systematic error related to such measurements due to: adsorbents sampling (carbon samples were
0.25 g, sieved) or preparation of solutions (controlled by absorbance checking). However, whereas there may be differences in curve-to-curve comparisons, the curve properties (curve character, type of best fit equation, rate coefficients) are always very similar.
Each kinetic data point is calculated by using concentration data obtained by fitting UV//Vis absorbance peaks (in this case 251-303 nm, 1 nm step, i.e. 53 spectrum points) of the kinetic system to the absorption peaks of the protein standard (of the same concentration and pH), thus reducing random spectrum noise.
Table S6. Experimental deviations for adsorption on C(SG60) and C(SG60)-T
Adsorbent
C(SG60)
C(SG60)
C(SG60)-T
Adsorbate
OVA
BSA
OVA
SD(C i
)/Co
(exp. data point) mean (min – max)
0.318% (0.190% - 0.402%)
0.515%
0.061%
(0.056% - 0.793%)
(0.031% - 0.081%)
SD(C)/Co
(fitting)
0.365%
0.363%
0.069%
(1-exp)
(IDM)
(3-exp)
C(SG60)-T BSA 0.178% (0.022% - 0.228%) 0.074% (3-exp)
SD(Ci)/Co (data point average, min, max)- average SD for all concentrations (concentrations determined by fitting entire absorbance peaks 251-303 nm (λ max
278-279 nm) to those of standard

Supporting information protein solution – more reliable than single λ max
calibration, reduces effect of absorbance noise and some background deviations (e.g. due to air bubbles and dust/microparticles in a flow-cell)
SD(C)/Co (fitting) – for the fitted kinetic curve
1.02
C/Co
1.01
1
0.99
0.98
0.97
0.96
0.95
0 200 400
OVA/C(SG60)
OVA/C(SG60)
600 800 1000 fit
1200 1400 time [min]
1600
1.01
C/Co
1
0.99
0.98
0.97
0.96
0.95
0 1000
BSA/C(SG60)
BSA/C(SG60)
2000 3000 fit
4000 5000 time [min]
6000
Fig. S6. OVA/C(SG60): Large absorbance noise (0.318%) visually exaggerated by low adsorbate uptake; weak fitting (0.365%) due to relatively short experiment and data scatter.
BSA/C(SG60): Large absorbance noise (0.515%) , but relatively smooth curve (0.624%) with scatter less obvious due to larger uptake and longer experiment (missing curve segment due to blocked filter).
1
0.99
C/Co 0.98
0.97
0.96
0.95
0.94
0.93
0.92
0.91
0.9
0 200
OVA/C(SG60)-T
OVA/C(SG60)-T
400 600 800 fit
1000 time [min]
1200
1
0.99
C/Co 0.98
0.97
0.96
0.95
0.94
0.93
0.92
0.91
0.9
0 200 400
BSA/C(SG60)-T
BSA/C(SG60)-T
600 800 1000 fit
1200 1400 time [min]
1600
Fig. S7. OVA/C(SG60)-T: Much lower absorbance/concentration deviations (0.061%) (error bars shorter than data point symbol diameter) and fitting deviations 0.069%.
BSA/C(SG60)-T: Slightly larger absorbance/concentration deviations (0.178%) (error bars comparable do data point symbol diameter), but fitting as for OVA (0.074%).
Boyd, G.E., Adamson, A.W., Myers, L.S.: The Exchange Adsorption of Ions from Aqueous
Solutions by Organic Zeolites. II. Kinetics. J. Am. Chem. Soc. 69, 2836–2848 (1947).
Carman, P.C., Haul, R.A.W.: Measurement of Diffusion Coefficients. Proc. R. Soc. A Math. Phys.
Eng. Sci. 222, 109–118 (1954).
Crank, J.: Mathematics of Diffusion. Clarendon Press, Oxford (1975).
Haynes, P.D., Lucas, S.K.: Extension of a short-time solution of the diffusion equation with application to micropore diffusion in a finite system. ANZIAM J. 48, 503 (2007).
Li, Z., Jaroniec, M.: Colloidal Imprinting: A Novel Approach to the Synthesis of Mesoporous
Carbons. J. Am. Chem. Soc. 123, 9208–9209 (2001).
Marczewski, A.W.: Analysis of kinetic Langmuir model. Part I: Integrated kinetic Langmuir equation (IKL): a new complete analytical solution of the Langmuir rate equation. Langmuir. 26,
15229–15238 (2010)(a).

Supporting information
Marczewski, A.W.: Application of mixed order rate equations to adsorption of methylene blue on mesoporous carbons. Appl. Surf. Sci. 256, 5145–5152 (2010)(b).
Marczewski, A.W., Deryło-Marczewska, A., Słota, A.: Adsorption and desorption kinetics of benzene derivatives on mesoporous carbons. Adsorption. 19, 391–406 (2013).
McKay, G., El Geundi, M., Nassar, M.M.: Pore Diffusion During the Adsorption of Dyes Onto
Bagasse Pith. Process Saf. Environ. Prot. 74, 277–288 (1996).
Reichenberg, D.: Properties of ion-exchange resins in relation to their structure. III. Kinetics of exchange. J. Am. Chem. Soc. 75, 589–597 (1953).
Weber, W.J., Morris, J.C.: Kinetics of Adsorption on Carbon from Solution. J. Sanit. Eng. Div. 89,
31–60 (1963).