Supplemental Information for Manuscript NANO5443
1 Contact
Please feel free to contact us and discuss this paper and our research with us anytime.
Martin Rudolph
Institute of Mechanical Process Engineering and Mineral Processing
TU Bergakademie Freiberg
Agricolastraße 1
09599 Freiberg / Sachsen
Germany
phone: +49 3731 39 3450
fax: +49 3731 39 2947
E-mail: martin.rudolph@mvtat.tu-freiberg.de
Martin Rudolph
Helmholtz-Institute Freiberg for Resource Technology
Helmholtz-Zentrum Dresden-Rossendorf
Halsbrücker Str. 34
09599 Freiberg / Sachsen
Germany
phone: +49 351 260 4410
E-Mail: m.rudolph@hzdr.de
Prof. Dr.-Ing. Urs A. Peuker
Institut of Mechanical Process Engineering and Mineral Processing
TU Bergakademie Freiberg
Agricolastraße 1
09599 Freiberg / Sachsen
Germany
phone: +49 3731 39 2916
fax: +49 3731 39 2947
E-mail: urs.peuker@mvtat.tu-freiberg.de
2 Dynamic Light Scattering in Dispersions Containing Primary
Particles and Agglomerates
Certainly dynamic light scattering is a straight forward method when it comes to determining the
size of nanoparticles. Yet we would like to emphasize, based on numerous experiences with
different nanoparticulate systems, that this method is not reliable for dispersions with small
primary particles and large agglomerates which tend to settle rapidly. Generally, for a broad
particle size distribution the volume or number weighted particle size distribution cannot be
assessed quantitatively, i.e. the fractions of the sizes are difficult to be determined. A certain
fraction of agglomerated nanoparticles can even make it impossible to identify the primary
particles.
In the following graphs in Figure 1 we present correlation coefficient of a single dynamic light
scattering experiment at different time steps of ricinoleic acid transferred particles containing
agglomerates. Furthermore we depict the intensity weighted frequency distributions.
Figure 1: (left) correlation coefficient and (right) frequency distribution intensity weighted of one single DLS
experiment for ricinoleic acid transferred particles containing agglomerates at time steps t1 through t4 which are 2
minutes apart each; additionally the result for the sample after centrifugation containing only primary particles
There are three fractions found where the smallest clearly represents the primary particles. Two
larger fractions appear at about 100 nm and between 400 nm and 1 µm. The quantity of the
fractions changes with measurement time. This is even more obvious for the correlation
coefficient which can be regarded as the data of DLS which has the least impact of mathematical
artifacts. The correlation coefficient for longer correlation times (plotted on the abscissa) which
correspond to the larger particles (agglomerates) decreases with increasing measuring time. This
concludes that the sample is “losing” larger particles due to sedimentation. For the purpose of a
statistically reliable sample the measurement time should even be longer when larger particles
occur, due to longer correlation times.
Finally there are at least two reasons why DLS should not be used for such samples. First of all
the size range is too broad and secondly and most importantly the sample is not stable due to
sedimentation of the agglomerates.
3 Calculation of Hansen Solubility Parameters of the Fatty Acids
(FA) in Dichloromethane (DCM)
Details on the theory and usage of Hansen Solubility Parameters (HSP) can be found in (Hansen
2007). For the fatty acids capped onto the magnetite nanoparticle surface we apply Hoy’s method
as described in (Brandrup et al. 1999) with the input parameters Ft,i, Fp,i, Vi, ΔT,i(P), B = 277 of the
groups i which are defined as follows (Brandrup et al. 1999). The parameter ni stands for the
number of each group i within the substance (capped fatty acid)
Ft   ni  Ft,i
(1)
i
Fp   ni  Fp,i
(2)
i
V   ni  Vi
(3)
i
(TP )   ni  (TP,)i
(4)
i
The Hildebrandt parameter δt, which is a more general solubility parameter, is defined with the
three HSPs δd, δp and δh and the Hoy parameters.
F  B n~
 t   d2   p2   h2  t
(5)
V
The polar contribution is δp:
1
Fp  2
 1

 p   t   ( P ) 
Ft  B n~ 

The contribution due to hydrogen bonding δh is.
(6)
1
  ( P)  1  2
 h   t   ( P ) 
 
 ,
(7)
with
 ( P) 
777  (Tp )
V
.
(8)
Consequently the disperse term of the HSPs is:
 d   t2   p2   h2
(9)
.
The solubility distance between the fatty acid capped particles (FA) and dichloromethane (DCM)
DFA-DCM is defined as follows (Hansen 2007).
DFADCM  4   d,FA   d,DCM    p,FA   p,DCM    h,FA   h,DCM 
2
2
2
(10)
The smaller this value the more soluble the fatty acid in the solvent DCM.
In the following table we list the Hoy parameters of the chemical groups found in the fatty acids
discussed.
Table 1: Hoy parameters as defined in eqs. (1) - (4) of the chemical groups relevant for the fatty acids used, taken
from (Brandrup et al. 1999)
group
-CH3
-CH2=CH-CHOH-COOH
Ft,i in
(J∙cm3)1/2/mol
303.5
269.0
249.0
591.0
565.0
Fp,i in
(J∙cm3)1/2/mol
0
0
59.5
591
415
ΔT,i(P)
Vi
cm3/mol
21.55
15.55
13.18
12.45
17.30
0.0220
0.0200
0.0185
0.0490
0.0400
The next table lists the number of the aforementioned groups in the individual fatty acids, which
are capped to the particle surface, therefore the number of carboxylic groups –COOH is 0 in each
case, when assuming chemisorption of the fatty acids.
Table 2: number of chemical groups within each fatty acid, when chemisorbed on the magnetite surface
Fatty Acid
Rinoleic Acid (RA)
Linoleic Acid (LA)
Oleic Acid (OA)
Myristic Acid (MA)
Caprylic Acid (CA)
-CH3
1
1
1
1
1
-CH213
12
14
12
6
=CH2
4
2
0
0
-CHOH1
0
0
0
0
-COOH
0
0
0
0
0
Using eqs. (1) - (10) as well as the information given in Table 1 and Table 2 one can calculate the
HSP and the solubility distances.
Table 3: Hildebrandt and Hansen solubility parameters of the adsorbed FAs (calculated) as well as for DCM (taken
from literature) with the solubility distance of the FA-Fe3O4 in DCM
Fatty Acid
capped Fe3O4
RA-Fe3O4
LA-Fe3O4
δt in
MPa1/2
19.40
18.07
δd in
MPa1/2
17.27
17.61
δp in
MPa1/2
6.89
4.02
δh in
MPa1/2
5.55
0.50
DFA-DCM
in MPa1/2
2.03
6.16
OA-Fe3O4
MA-Fe3O4
CA-Fe3O4
DCM1
1
17.90
17.66
17.38
20.20
17.68
17.66
17.38
18.20
2.81
0
0
6.30
0
0
0
6.10
7.11
8.83
8.92
n/a
(Brandrup et al. 1999)
It is to notice that the best solubility of the C18 fatty acids is given for ricinoleic acid mainly due
to the polar and hydrogen bonding parameters.
4 Determination of the intrinsic viscosity for PMMA in DCM
Figure 2: Determination of the intrinsic viscosity by plotting the specific viscosity on the ordinate versus the
concentration on the abscissa and linear fitting to obtain the y-intercept
For determination of the viscosity we plot the specific viscosity as a function of the polymer
concentration and the ordinate-intercept of a linear fit leads to the intrinsic viscosity.
[ ]  lim
c 
 0
0  c
We obtain the value:
[η] = (0.03643±0.00576) l/g
And thus the critical concentration of overlap is:
c* = (27.45±4.34) g/l
5 Particle Size Distributions of the Spray Dried Composite
Microparticles
Figure 3: Particle size distributions of the spray dried composite microparticles for the PMMA composites (left) and
the PVB composites (right) with the different fatty acids. Determined with Laser Diffraction.
6 References
Brandrup J, Immergut EH, Grulke EA, Abe A, Bloch DR (1999) Polymer Handbook (4th
Edition). John Wiley & Sons,
Hansen CM (2007) Hansen Solubility Parameters. A User’s Handbook. 2nd edn. CRC Press,
Boca Raton