Supporting Information Hollow Casein-based Polymeric Nanospheres ...
Supporting Information Hollow Casein-based Polymeric Nanospheres for Opaque Coatings Fan Zhang†, Jianzhong Ma†, ‡,*, Qunna Xu†, ‡, Jianhua Zhou†, ‡, Demetra Simion┴, Gaidău Carmen┴, John Wang§, Yunqi Li ║ †
College of Resource and Environment, Shaanxi University of Science and Technology, Xi’an 710021, Shaanxi Province, PR China
‡
Shaanxi Research Institute of Agricultural Products Processing Technology, Xi’an 710021, Shaanxi Province, PR China
┴
R&D National institute for Textile and Leather-Division Leather and Footwear Research Institute, Bucharest 031215, Romania §
Department of Materials Science and Engineering, National University of Singapore, Singapore 117574, Singapore
║
Key Laboratory of Synthetic Rubber, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, 130022, PR China
*Corresponding Author: Jianzhong Ma, College of Resource and Environment, Shaanxi University of Science and Technology, Xi’an 710021, Shaanxi Province, China. E-mail: [email protected]. Tel.: +86-029-86168010. Fax: +86-029-86168012
S-1
Figure S1. Picture of the samples for SAXS
Figure S2. TEM image of caprolactam-modified casein micelles
S-2
Small angle X-ray scattering (SAXS)： ： The total scattering intensity I(q) of one particle system (identical and randomly oriented) can be generally formulated as I(q) = nP(q)S(q),where n is the number density of the particles in solution, S(q) is the static structure factor, which comes from the inter-particle interactions, and P(q) is the oriented averaged form factor, which comes from the intra-particle interactions and contains all the information about the particle(shape, size and internal electron density fluctuation). Pair distance distribution function p(r) is computed using GNOM while inverse Fourier transformation of P (q) is calculated by the GIFT technique.
= 4
In p(r) − r plots, the maximum of diameter at the low-r part of p(r) comes from the convolution of negative and positive electron density fluctuations of the solid/hollow core and shell in spheres, respectively. Dmax is the r value at which p(r) goes to zero. The diameter of core is calculated from the distance corresponding to the inflection point located at the high-r side of the local minimum. In our calculation, a core-shell structure factor model was used for casein-based core-shell spheres. The casein-based hollow spheres experimental data were fitted with spherical shell sphere and hard sphere form factors. For casein-based core-shell spheres, we assume that all the core-shell spheres are common. So the fitting of the SAXS data is performed using scattering intensity I(q) defined as: I(q)≈P(q), P(q)is the form factor of a sphere and is
=
+
!"# %
$ + &'g
Where()* = sin * − * cos *⁄* % , = + 3and45 = 4 ⁄3 5 .The returned value is S-3
scaled to units of [cm-1].
Figure S3-a core shell model for casein-based core-shell spheres
For casein-based hollow spheres, we use spherical shell model for obtaining the shell thickness of casein-based hollow spheres and hard sphere model for entire spheres radius. 7
Ishell(q)=[K(q,R1,∆η)-K(q,R2,∆η(1-µ))]2and K(q,R1, ∆η)= π9 :;3
?@< , A
where R1, R2, and η are radius of spherical shell, radius of core and scatting length density difference between shell and matrix, respectively.
∆η R1
R µ∆η
Figure S3-b spherical shell model for casein-based hollow spheres
Icore(q)=K(q, R, ∆η) 2
with
7
K(q, R, ∆η)= π9 :;3
?@< , A
radius of sphere.
2R
Figure S3-c hard sphere model for casein-based hollow spheres
S-4
where R is
College of Resource and Environment, Shaanxi University of Science and Technology, Xi’an 710021, Shaanxi Province, PR China
‡
Shaanxi Research Institute of Agricultural Products Processing Technology, Xi’an 710021, Shaanxi Province, PR China
┴
R&D National institute for Textile and Leather-Division Leather and Footwear Research Institute, Bucharest 031215, Romania §
Department of Materials Science and Engineering, National University of Singapore, Singapore 117574, Singapore
║
Key Laboratory of Synthetic Rubber, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, 130022, PR China
*Corresponding Author: Jianzhong Ma, College of Resource and Environment, Shaanxi University of Science and Technology, Xi’an 710021, Shaanxi Province, China. E-mail: [email protected]. Tel.: +86-029-86168010. Fax: +86-029-86168012
S-1
Figure S1. Picture of the samples for SAXS
Figure S2. TEM image of caprolactam-modified casein micelles
S-2
Small angle X-ray scattering (SAXS)： ： The total scattering intensity I(q) of one particle system (identical and randomly oriented) can be generally formulated as I(q) = nP(q)S(q),where n is the number density of the particles in solution, S(q) is the static structure factor, which comes from the inter-particle interactions, and P(q) is the oriented averaged form factor, which comes from the intra-particle interactions and contains all the information about the particle(shape, size and internal electron density fluctuation). Pair distance distribution function p(r) is computed using GNOM while inverse Fourier transformation of P (q) is calculated by the GIFT technique.
= 4
In p(r) − r plots, the maximum of diameter at the low-r part of p(r) comes from the convolution of negative and positive electron density fluctuations of the solid/hollow core and shell in spheres, respectively. Dmax is the r value at which p(r) goes to zero. The diameter of core is calculated from the distance corresponding to the inflection point located at the high-r side of the local minimum. In our calculation, a core-shell structure factor model was used for casein-based core-shell spheres. The casein-based hollow spheres experimental data were fitted with spherical shell sphere and hard sphere form factors. For casein-based core-shell spheres, we assume that all the core-shell spheres are common. So the fitting of the SAXS data is performed using scattering intensity I(q) defined as: I(q)≈P(q), P(q)is the form factor of a sphere and is
=
+
!"# %
$ + &'g
Where()* = sin * − * cos *⁄* % , = + 3and45 = 4 ⁄3 5 .The returned value is S-3
scaled to units of [cm-1].
Figure S3-a core shell model for casein-based core-shell spheres
For casein-based hollow spheres, we use spherical shell model for obtaining the shell thickness of casein-based hollow spheres and hard sphere model for entire spheres radius. 7
Ishell(q)=[K(q,R1,∆η)-K(q,R2,∆η(1-µ))]2and K(q,R1, ∆η)= π9 :;3
?@< , A
where R1, R2, and η are radius of spherical shell, radius of core and scatting length density difference between shell and matrix, respectively.
∆η R1
R µ∆η
Figure S3-b spherical shell model for casein-based hollow spheres
Icore(q)=K(q, R, ∆η) 2
with
7
K(q, R, ∆η)= π9 :;3
?@< , A
radius of sphere.
2R
Figure S3-c hard sphere model for casein-based hollow spheres
S-4
where R is
