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ENITIAA, UMR CNRS 6144 GEPEA, Nantes, France ! ! ! ! ! ! poncelet@enitiaa"nantes.fr
SIZE DISTRIBUTION ?Denis poncelet
ENITIAA, UMR CNRS 6144 GEPEA, Nantes, France ! ! ! ! ! ! poncelet@enitiaa"nantes.fr
Size ?! Diameter = first property of the capsules
! Define largelly
• the membrane or coating surface, then quantity
• the mechanical resistance
• the fluidisation and flowing properties
• the active loading and quantity
! Needed for most modelling of
• the membrane formation
• the release profile
• the biocatalyst kinetics #mass transfer$
ENITIAA, UMR CNRS 6144 GEPEA, Nantes, France ! ! ! ! ! ! poncelet@enitiaa"nantes.fr
Size ?
From a few micrometers ... to a few millimeters
ENITIAA, UMR CNRS 6144 GEPEA, Nantes, France ! ! ! ! ! ! poncelet@enitiaa"nantes.fr
Size distribution ?
! Mono"dispersion ?
• do not believe pictures
! Narrow size distribution allows
• better microcapsule formation control
• easier modelling
• more homogeneous properties
! Narrow size distribution
! ! ! = higher cost & lower production
ENITIAA, UMR CNRS 6144 GEPEA, Nantes, France ! ! ! ! ! ! poncelet@enitiaa"nantes.fr
Size distribution ?
Controlled release
!
dc
dt= "D
(c " c')
e
!
ln(c " co
c# " co) = "k t
Burst e%ect ? ... no size distribution
Burst
!
ln(c " co
c# " co)
!
t!
c = 6% co
ENITIAA, UMR CNRS 6144 GEPEA, Nantes, France ! ! ! ! ! ! poncelet@enitiaa"nantes.fr
Size distribution ?
Mechanical resistance
!
vbreakage ÷ d4
d = 500 to 1000 !m
vbreakage varies from 1 to 16
ENITIAA, UMR CNRS 6144 GEPEA, Nantes, France ! ! ! ! ! ! poncelet@enitiaa"nantes.fr
How to measure the size ?
! Sieving analysis
! Microscopy
! Counting
! Laser di%raction
! Acoustic spectroscopy
http://en.wikipedia.org/wiki/Particle_size_distribution
ENITIAA, UMR CNRS 6144 GEPEA, Nantes, France ! ! ! ! ! ! poncelet@enitiaa"nantes.fr
Size distribution
ENITIAA, UMR CNRS 6144 GEPEA, Nantes, France ! ! ! ! ! ! poncelet@enitiaa"nantes.fr
0
0,50
1,00
1,50
2,00
0 1,00 2,00 3,00 4,00
Histograms
!
f =dF
dx=
1
" 2#exp
$(x$x)
2
2 " 2
x = log#d$
100 &
75 &
50 &
25 &
0 &
f F
xd 1 10 100 1000 10 000 !m
0
1
2
3
4
0 100,00 200,00 300,00 400,00
& of particles per 20 µm
!
Fx = f dx
0
x
" or f #x0
x
$
ENITIAA, UMR CNRS 6144 GEPEA, Nantes, France ! ! ! ! ! ! poncelet@enitiaa"nantes.fr
0
1
2
3
4
0 100,00 200,00 300,00 400,00
Histograms
0
0,50
1,00
1,50
2,00
0 50 100 150 200 250 300 350 400
& of particles per class
& of particles per 20 µm
ENITIAA, UMR CNRS 6144 GEPEA, Nantes, France ! ! ! ! ! ! poncelet@enitiaa"nantes.fr
Frequency !Frequency
! Numeric, fn #microscope$
! Volumic, fv #Malvern$
! Massic, fm #sieving$
! ...
!
fs = k x3
fn
ENITIAA, UMR CNRS 6144 GEPEA, Nantes, France ! ! ! ! ! ! poncelet@enitiaa"nantes.fr
Fv versus Fn
• Sampling is the key point• Use raw data, avoid conversion• Make tendencies not absolute values
ENITIAA, UMR CNRS 6144 GEPEA, Nantes, France ! ! ! ! ! ! poncelet@enitiaa"nantes.fr
Artefacts
< 5 &
0,5 µm
Most probably defaults assimilated to particles
ENITIAA, UMR CNRS 6144 GEPEA, Nantes, France ! ! ! ! ! ! poncelet@enitiaa"nantes.fr
Mean size ?
! Median = diameter of 50 & cumulative frequency = d50&
! Mode = diameter of maximum frequency
! Mean size ?
• numeric #microscope$
• volume #Malvern$
• surface
!
dn = d10 =ni di"ni"
= fn di
!
d43 =ni di
4"
ni di3"
=vi di"vi"
= fv di
!
ds = d32 =ni di
3"
ni di2"
=si di"si"
= fs di =1
as!
dv = d30 =ni di 3"ni"
3
ENITIAA, UMR CNRS 6144 GEPEA, Nantes, France ! ! ! ! ! ! poncelet@enitiaa"nantes.fr
Mean size ?
Mean size could be computed for all distributions
Multi"peaks ? multi"means ?
ENITIAA, UMR CNRS 6144 GEPEA, Nantes, France ! ! ! ! ! ! poncelet@enitiaa"nantes.fr
Which mean ?
! Function of the applications / model
EmulsificationMass transfer
!
d32
Fluidisation
!
d10
LoadingYield
!
d30
Sometime, mix of mean diameters
ENITIAA, UMR CNRS 6144 GEPEA, Nantes, France ! ! ! ! ! ! poncelet@enitiaa"nantes.fr
Size dispersion ?
! standard deviation, !
• graphically #!$
• ! = #d64&"d16&$/2 #!$
•
! Distribution
• numeric or volumic
• normal or log"normal
0
0,50
1,00
1,50
2,00
1,00 1,50 2,00 2,50 3,00
!
!
" 2 =fi (xi # x)
2$fi$
!
0
0,50
1,00
1,50
2,00
0 100,00 200,00 300,00 400,00
? ?
100 &
75 &
50 &
25 &
0 &
ENITIAA, UMR CNRS 6144 GEPEA, Nantes, France ! ! ! ! ! ! poncelet@enitiaa"nantes.fr
Standard deviation ?
0
0,50
1,00
1,50
2,00
1,00 1,50 2,00 2,50 3,00
! multi"peaks ?
• !’ = ! / d50&
ENITIAA, UMR CNRS 6144 GEPEA, Nantes, France ! ! ! ! ! ! poncelet@enitiaa"nantes.fr
Span ?
! Span = = #d90&"d10&$/d50&
! relative dispersion
! could be applied to all distributions
! take into consideration most particles
! deviations often under d10& and over d90&
0
0,50
1,00
1,50
2,00
1,00 1,50 2,00 2,50 3,00
100 &
75 &
50 &
25 &
0 &
ENITIAA, UMR CNRS 6144 GEPEA, Nantes, France ! ! ! ! ! ! poncelet@enitiaa"nantes.fr
Conclusions
! Even #apparently$ simple measurement needs standard
! Use simplest tool to measure the size
! Beware of the sampling
! Define your mean value
• mode or median are easier
• avoid conversion between distribution
! Use span to define dispersion
! Size distribution are not absolute value
