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Euro food’s water, March 2004
NMR Study of the Water Diffusion in NMR Study of the Water Diffusion in Casein Systems.Casein Systems.
Effect of the Effect of the MicellarMicellar Casein Casein ConcentrationConcentration
F. Mariette A. MétaisCEMAGREF, Food process engineering research unit,
Rennes
Euro food’s water, March 2004
ObjectivesObjectives
Ø To study the effect of casein micelle concentration on the water diffusion coefficient
Ø To find a model to explain the water diffusion in casein systems
Ø To study the effect of coagulation by rennet on the water diffusion coefficient
Euro food’s water, March 2004
How to measure the water diffusion by How to measure the water diffusion by NMR ?NMR ?
v To obtain a NMR signal, the sample is introduced into a magnetic field
if the magnetic field is homogenous, the NMR signal is insensitive to molecular diffusion.
But, if the magnetic field is inhomogeneous, then the NMR signal become sensitive to molecular diffusion.
So, a linear field gradient is applied in order to measure the Diffusion coefficient.
- +- +
mag
net
mag
net
sample
Euro food’s water, March 2004
NMR signal with gradient
How to measure the water diffusion by How to measure the water diffusion by NMR ?NMR ?
NMR signal without gradient (g=0)
90°x90°x 180°y180°yR
F P
uls
e
RF
Pu
lse
90°x90°x 180°y180°y
RF
Pu
lse
RF
Pu
lse
g
Euro food’s water, March 2004
How to measure the water diffusion by How to measure the water diffusion by NMR ?NMR ?
∆ NMR signal with gradient
90°x90°x
RF
Pu
lse
RF
Pu
lse
180°y180°y
g
∆= Dd 6
∆
90°x90°x 180°y180°yR
F P
uls
e
RF
Pu
lse
NMR signal with gradient
g
d
d
Euro food’s water, March 2004
[ ]kDtgI
tgI−=
=exp
),0(),(
0
K = F(g ,∆)
g, the gradient strength and ∆, the diffusion time
How to measure the water diffusion by How to measure the water diffusion by NMR ?NMR ?
g
Ln(I/I0) D
Euro food’s water, March 2004
How to measure the water diffusion by How to measure the water diffusion by NMR ?NMR ?
v by changing g with ∆ = cte
g
Ln(I/I0)
No restriction, D is the self-diffusion coefficient
Restriction D is an apparent diffusion coefficient
g
Ln(I/I0)
g
Ln(I/I0)
g
Ln(I/I0)
Heterogeneous diffusion processApparent diffusion coefficientHomogeneous diffusion process
Self diffusion coefficient
v by changing g for different ∆ values
Euro food’s water, March 2004
Why using NMR to measure the water Why using NMR to measure the water diffusion coefficient ?diffusion coefficient ?
v Non invasive technique, Ø So the measurements could be done without any perturbation of the
diffusion process.v no tracer, Ø the measurements could be done without any specific chemical
preparation.v the diffusion could be measured in any directionØ If Dx=,Dy=Dz then the diffusion is isotropicØ If Dx≠,Dy ≠ Dz then the diffusion is anisotropicØ so diffusion anisotropy could be detected.
v the diffusion could be measured for different travelling distances,
Deff=D0 Deff< D0
d
2*r>> d
d
2*r≤ d
Euro food’s water, March 2004
Why using NMR to measure the water Why using NMR to measure the water diffusion coefficient ?diffusion coefficient ?
v Non invasive technique, Ø So the measurements could be done without any perturbation of the
diffusion process.v no tracer, Ø the measurements could be done without any specific chemical
preparation.v the diffusion could be measured in any direction, Ø so diffusion anisotropy could be detected.
v the diffusion could be measured for different travelling distances, Ø so “restricted diffusion” from impermeable barrier could be observed
v as NMR is molecular specific Ø so the diffusion coefficient from several molecules could be
measured simultaneously.
Euro food’s water, March 2004
Milk composition and structureMilk composition and structure
Water : 87%
Milk is an o/w emulsion : Fat 3-4%
protein : 3.2-3.4%
Lactose : 4.6%Ash : 0.7%
Casein micelle 80% Milk is a colloidal
suspension of caseinSoluble protein 20%
Casein micelle plays a major role in the functional properties of the milk
Euro food’s water, March 2004
Casein micelles Casein micelles
Caseins are organised as "micelles"
roughly spherical
highly hydrated with about 4 – 6 g water/g
protein .
Largemean diameter: 300 nm
The integrity involves many interactions such as
hydrophobic bonding, hydrogen bonding,
electrostatic interaction, disulphide bonding and
calcium bonding.Schmidt’s model
Euro food’s water, March 2004
Materials and methodsMaterials and methods
v The micellar casein solutions were prepared :Ø with a native micellar casein powder (INRA, Rennes)Ø Rehydrated in a water – NaCl solution (80 mM), Ø from 1 to 22 g/100g of water
vThe gel was obtained :Ø After renneting at 30°C during 120 minutes
vThe NMR measurements were performed at 20°CØ A low field NMR (0.47 Tesla) “The Minispec” (Bruker)Ø With a pulsed field gradient unit with a maximum strength of 4 T/m
Euro food’s water, March 2004
Attenuation of the NMR signal according Attenuation of the NMR signal according to the pulsed field gradient strengthto the pulsed field gradient strength
A linear variation was observed for all the samples for both protein solutions and gels
So the diffusion coefficient is the self diffusion coefficient
-1,1
-0,9
-0,7
-0,5
-0,3
-0,1
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8
k (109 rad2 s m-2)
Ech
o a
tten
uat
ion
ln (
I g/I 0
)
(rel
ativ
e u
nit
s)
NPC solution DM=19%NPC solution DM=17%Linéaire (NPC solution DM=19%)
-1,2
-1,0
-0,8
-0,6
-0,4
-0,2
0,0
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8
k (109 rad2 s m-2)
Ech
o a
tten
uat
ion
ln (
I g/I 0
)
(rel
ativ
e u
nit
s)
NPC gel DM=19%NPC gel DM=17%
In solution In gel
Euro food’s water, March 2004
Effect of the observation time D on the Effect of the observation time D on the water diffusion coefficientwater diffusion coefficient
Whatever the diffusion time ,
a straight variation of the echo attenuation was observed
The self-diffusion is constant, the diffusion mechanism is the same.
-1,40
-1,20
-1,00
-0,80
-0,60
-0,40
-0,20
0,00
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9
k (109)
Ln(I/
I 0)
∆ = 60 ms
∆ = 210 ms∆ = 160 ms
∆ = 110 ms
Euro food’s water, March 2004
v From the diffusion time, the distance over which the water molecules diffused could be deduced from :
(6D∆)1/2
v So the distance probed by the water molecules was between Ø 8 µm (∆ = 7.5 ms)Ø 43 µm (∆ = 210 ms)
v so the self-diffusion is measured on a micrometer length-scale “micro-diffusion”
Effect of the observation time D on the Effect of the observation time D on the water diffusion coefficientwater diffusion coefficient
Euro food’s water, March 2004
Effect Effect of of the casein the casein concentration on concentration on the the water water selfself--diffusion coefficientdiffusion coefficient
0,60
0,65
0,70
0,75
0,80
0,85
0,90
0,95
1,00
0 5 10 15 20 25casein / water (g / 100 g)
D /
D0(
10-9
m2 s-1
)In solution
More the casein concentration increase more the water diffusion decrease.
Euro food’s water, March 2004
0,60
0,65
0,70
0,75
0,80
0,85
0,90
0,95
1,00
0 5 10 15 20 25
casein / water (g / 100 g)
D /
D0(
10-9
m2 s-1
)
Effect Effect of of the casein the casein concentration on concentration on the the water water selfself--diffusion coefficientdiffusion coefficient
In gel
� In solution
p In renneted gel
The water diffusion is not modified after the aggregation of the casein induced by the rennet.
Euro food’s water, March 2004
How to explain the water mobility reduction in How to explain the water mobility reduction in casein dispersion ?casein dispersion ?
First case : we suppose an obstruction effect induced by the impenetrable slow moving casein micelles.
Euro food’s water, March 2004
How to explain the water mobility reduction in How to explain the water mobility reduction in casein dispersion ?casein dispersion ?
First case : we suppose an obstruction effect induced by the impenetrable slow moving casein micelles.
+=
21
10 φ
DDeff
The self-diffusion can be described by :
Effective self-diffusion coefficient
Pure water self-diffusion coefficient
Volume fraction occupied by the micelles
Euro food’s water, March 2004
V = 0,62 cm3/g
0,60
0,70
0,80
0,90
1,00
0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16
φ (%)
D/D
0
Obstruction effect induced by Obstruction effect induced by impermeable micelle ?impermeable micelle ?
The model do not explained the experimental results
So another effect should be considered
Euro food’s water, March 2004
How to explain the water mobility reduction in How to explain the water mobility reduction in casein dispersion ?casein dispersion ?
Second case : we suppose two fluxes, one around the micelle and one through the micelle
Euro food’s water, March 2004
Obstruction model included two water fluxesObstruction model included two water fluxes
C2,D2
C1,D1
D1 is the water self-diffusion inside the micelleC1 is the water content inside the micelle
D2 is the water self-diffusion outside the micelleC2 is the water content outside the micelle
According to the model proposed by Jönsson et al*, the self-diffusion can be decomposed in :
*B. Jönsson, H. Wennerstrom, P. G. Nilsson, P. Linse , Self-diffusion of small molecules in colloidal systems, Colloid & Polymer Sci 264 (1986) 77-88.
Euro food’s water, March 2004
⋅⋅+⋅+
⋅−⋅+
⋅
⋅+⋅=
water
cas
water
cascas
water
cas
water
cascas
water
cascaswaterwater
eff
mm
Kmm
mmK
mm
mm
DD5.01
110
υ
υυ
Obstruction effect induced by permeable Obstruction effect induced by permeable micelle ?micelle ?
The water diffusion according to the cell-model is given by :
Euro food’s water, March 2004
+×= cas
water
cas
VKυυ
β
1122
1122
5.0 CDCDCDCD
+−
=β
where
C1, D1
C2, D2
C1, D1
C2, D2
Obstruction effect induced by permeable Obstruction effect induced by permeable micelle ?micelle ?
with
• The water diffusion inside the casein micelle D1 ?• The micelle hydration C1 ?• The water diffusion outside the micelle D2• The water concentration outside the micelle C2
Euro food’s water, March 2004
0,60
0,70
0,80
0,90
1,00
0 0,05 0,1 0,15 0,2 0,25
casein/water (g/100g)
D/D
0
Obstruction effect induced by permeable Obstruction effect induced by permeable micelle ?micelle ?
The best fit is obtained with K = 1,60 ± 0,01
Euro food’s water, March 2004
From k and if a casein voluminosity of V = 5 g water/g casein was assumed *, the water self-diffusion inside the micelle D1 could be estimated
++
−+×=
kV
kV
CCD
Dcas
eau
cas
caseau
cas
5.01
221
υυ
υυ
Obstruction effect induced by permeable Obstruction effect induced by permeable micelle ?micelle ?
with C2 = 1 g.cm-3, D2 = DO
= 0.75 cm3.g-1,
= 1 cm3.g-1
caseinυwaterυ
Euro food’s water, March 2004
The water diffusion coefficient inside the miceIle was 1.45 10-9 m2 S-1
Obstruction effect induced by permeable Obstruction effect induced by permeable micelle ?micelle ?
If we compare to the self-diffusion of pure water (1.99 10-9 m2 S-1) • the water diffusion is slightly reduced • the reduction could be explained by the obstruction induced by the protein molecules
If we compare to the self-diffusion of protein (3 10-12 m2 S-1) • the water diffusion is very high, • the water diffusion reduction could not be explained by strong water-protein interaction
Euro food’s water, March 2004
ConclusionConclusion
Ø The self-diffusion coefficient could be measured and the water molecules are free to diffuse for large distances (micrometer scale)
Øin solutions ØIn gels
Ø No restriction from impermeable barriers was involved in the hindrance of the water diffusion
Ø The water self-diffusion coefficients were not modified by the coagulation with rennet D sol = D gel.
Ø The water diffusion in casein micelle could be explained by two water fluxes
ØOne around the casein micellesØOne through the casein micelles
Euro food’s water, March 2004
PerspectivePerspective
v Could we generalized this approach to other protein systems (globular protein) ?v Could we include in the model other effects ?Ø Amount of soluble compounds Ø Amount of fat
v Could we describe the water diffusion in real product (cheese…) ?v Could we relate the water diffusion in micro-length scale to macroscopic length scale ?
Work in progress….