draft influence of physics of tablet compression presenter: alberto cuitino november 4 th, 2010
TRANSCRIPT
DRAFTINFLUENCE OF PHYSICS OF TABLET COMPRESSION
Presenter: Alberto Cuitino
November 4th, 2010
DRAFTDesign Pharmaceutical Solids
-12-10 -8 -6 -4 -2 0 2 4
-1000-800-600-400-200
0200
Die Filling Compression Breakup DissolutionMixing
EXPERIMENTS
MODELING & SIMULATIONS
Integrated
Integrated
DRAFTDie Filling – Feed frame
EXPERIMENTS
initial
exit 1 exit 2
exit 3
152.3mmA
B
DRAFTDie Filling – Feed frame
Void/porous MicrostructureIMPACTS
STRENGTH and DISSOLUTION
MODELING & SIMULATIONSSmaller ParticlesMore Surface Area
Larger ParticlesLess Surface Area
DRAFT
Pressure (MPa)
Den
sity
(g/m
l)
0 5 10 15 20 250
0.5
1
1.5
Sample Info
Mass = 0.4 g
Size = 996.1 mm3
Composition = 55% (D),
15%(S2), 15%(S3)
15%(S4)
Expected solid density =
1.68 g/ml
Long-range prediction
Pressure (MPa)
Den
sity
(g/m
l)
0 0.5 1 1.5 2 2.50
0.5
1
1.5
predictexpt1expt2
0
2
4
6
8
10
0
2
4
6
8
Z
0
2
4
6
X Y
Z
dens
1.251.21.151.11.0510.950.90.85
Density distribution
0
2
4
6
8
10
0
2
4
6
8
Z
0
2
4
6
X Y
Z
Szz
-0.53-0.55-0.57-0.59-0.61-0.63-0.65-0.67
Pressure distribution
0
2
4
6
8
10
0
2
4
6
8
Z
0
2
4
6
X Y
Z
dens
1.251.21.151.11.0510.950.90.85
Density distribution
0
2
4
6
8
10
0
2
4
6
8
Z
0
2
4
6
X Y
Z
Szz
-0.53-0.55-0.57-0.59-0.61-0.63-0.65-0.67
Pressure distribution
Micro-structure from X-ray CT
ConsolidationMODELING & SIMULATIONS
EXPERIMENTSMultiscale Modeling – Concurrent particle-continuum description
Tablet Compaction Model:
– Multiscale
– Preserves local heterogeneous structure of the powder bed
– Predicts macroscopic trends
DRAFT
Displacement fields in a uniaxially loaded tablet during the formation of a crack.
Bonding-DebondingEXPERIMENTS
Crack
Non-uniform fields
Fracture dominated by weakest regions
DRAFTBonding-Debonding
MODELING & SIMULATIONS
0
20
40
60
80
100
120
0 5 10 15 20 25 30 35
Time
Bo
nd
ing
Str
eng
th
σ A – contact area
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
0 2 4 6 8 10 12 14 16 18 20
Separation
Fo
rce
an
d P
ote
nti
al
-12 -10 -8 -6 -4 -2 0 2 4
-1000
-800
-600
-400
-200
0
200
Inter-particle Kernel
development ofhistory dependent inter-particle bonding
Microscopic
Macroscopic
Compact Strength
Evolving Force Field
force
Displacement
COMPRESSION
TENSION
TABLET
Non-uniform fields
DRAFTStructure “carried” downstream
DissolutionMODELING & SIMULATIONS
EXPERIMENTS
VALIDATION
0
20
40
60
80
100
0 20 40 60 80Time (min)
%
Dru
g R
ele
as
e
Blend 6 640rpmBlend 3 160rpmModel Tablet Blend 6 640rpmModel Tablet Blend 3 640rpm
DRAFT• A ballistic deposition technique is used to simulate die-filling.
• Powder composition• Particle size distribution• Powder cohesion
Die Filling
DRAFT• Individual particles are dropped from the top of the container,
falling until they reach a stable position.
• Multiple powders can be considered with different size distributions and physical properties.
Multicomponents
DRAFT• Particle cohesivity determines the stability of structures in
the powder bed.• Cohesion is considered through the critical angle, at which a
particle will start rolling.
Cohesion
DRAFTNo cohesion Cohesion
Cohesion
DRAFTParticle Rearrangment
DRAFT• Once the particles are closely packed, further increases in pressure
lead to particle deformation as the only mechanism available for volume reduction.
• The compaction stage is modeled using a mixed discrete-continuum approach.
• The particle motion is constrained by a grid with dimensions of the same order as the size of the system.
• Standard Finite Element techniques are utilized to generate a grid, with the motion of each simulated particle described in terms of the behavior of the vertexes of the grid’s nodes. Inter-particle interactions are modeled using local constitutive relations.
Compaction
DRAFT2
3
2 3
4
R
E
R
F
• The particle interactions during the compaction process have a strong influence on the mechanical properties of solid product. The types of interactions include contact forces (elastic, elastic-plastic, fully plastic) as well as tensile forces. •In the current implementation of the numerical method, the elastic contact is modeled using a Hertzian law.
2
22
1
21
21
111,
111
EEERRR
where
Ei and νi are the Young’s moduli and Poisson ratios of the particles in contact and Ri are their radii. The plastic regime following the elastic response is modeled using a power law, characterized by a hardening exponent.
Compaction Forces
DRAFTparticle-particle distance
inte
rac
tio
n p
ote
nti
al
R
α
θ
Hd
Where γ is the liquid surface tension
• Caused by the formation of liquid bridges – as liquid vapors from the ambient gas phase condensate on the particle surfaces, a liquid meniscus forms, bonding particles to each other.
dH
RF
/1
cos2
Compaction Forces
DRAFT 2
212
221
2
221
221
221
221 ln
22
6 rrR
rrR
rrR
rr
rrR
rrA
21 rrR
• Van der Waals forces – short range forces, usually dominant for either small particles or during the particle fragmentation stages of compaction.
particle-particle distance
inte
rac
tio
n p
ote
nti
al
Δ – the distance between the particles.
Compaction Forces
DRAFTTertiary MixtureD and S2, S3, S4
0
2
4
6
8
10
0
2
4
6
8
Z
0
2
4
6
X Y
Z
dens
1.251.21.151.11.0510.950.90.85
Density distribution
0
2
4
6
8
10
0
2
4
6
8
Z
0
2
4
6
X Y
Z
Szz
-0.53-0.55-0.57-0.59-0.61-0.63-0.65-0.67
Pressure distribution
Initial configuration
Configuration after rearrangement
Pressure (MPa)
De
nsi
ty(g
/ml)
0 5 10 15 20 250
0.5
1
1.5
Sample Info
Mass = 0.4 g
Size = 996.1 mm3
Composition = 55% (D),
15%(S2), 15%(S3)
15%(S4)
Expected solid density =
1.68 g/ml
Long-range prediction
Pressure (MPa)
De
nsi
ty(g
/ml)
0 0.5 1 1.5 2 2.50
0.5
1
1.5
predictexpt1expt2
Mass (g)Dimensions
(mm)Number ofParticles
ExpectedSolid Density
(g/ml)0.4 9×9×6.1 33,764 1.68 0.75
V
Filling/Rearrangement/Compaction
DRAFT• PressterTM tablet press simulator
• Set to mimic Stokes B2 press• Tooling
• Oval, deep cut• i.e., tablets are oval with domelike top and
bottom surfaces• Presster data:
• Upper compression force• Tablet x-section area • Tablet thickness • Tablet weight • radial die wall force, ejection forces, stage speed
…
Presster™ Studies
DRAFTPresster data collected at different compaction forces (10kN, 15kN, and 20kN )
Presster™ Studies
DRAFT• The model can be used to simulate the evolution of the configuration of the powder bed with time as well as monitor the values of various quantities indicative of its mechanical properties. • Several different powders have been considered, both individually and in a blend to demonstrate the versatility of the method.
• Each blend can be mapped to granulation parameters by:
• Simulations vs. PressterTM Data• Error minimization
Identification of critical blend properties from 500 simulations
DRAFT0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 5 10 15 20 25 30
Separation
Fo
rce
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
0 2 4 6 8 10 12 14 16 18 20
Separation
Fo
rce
and
Po
ten
tial
Modified Logistic Equation
21
311
1.01
13
01.01ln
1
1
dce
F
cdecdU
cd
cd
0
20
40
60
80
100
120
0 5 10 15 20 25 30 35
Time
Bo
nd
ing
Str
eng
th
σ A – contact area
Bonding Force
History-dependent strength
History-Dependent Bonding
DRAFTColor represents
the strongest bond a particle has with
its neighbors.
Young’s ModulusE=25GPa
Poisson Ratioν=0.3
Size RangeAvicel 101: 60±10μm - 50%Avicel 102 :110±10μm - 50%
History-Dependent Bonding
DRAFT-12 -10 -8 -6 -4 -2 0 2 4
-1000
-800
-600
-400
-200
0
200
Displacement
Pressure
Compressive Loading
Relaxation
Tensile Loading
Failure
Tablet Compaction and Tensile Loading
DRAFTTablet Compaction and Tensile Loading
DRAFT
Here goes the connection with the Abbott Data (Steve)
DRAFTConclusion