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Nanoscale free volume hole distribution and its correlation with physico-chemical properties of polymers
Pushkar N. Patil
Radiochemistry Division,Bhabha Atomic Research Centre,
Trombay, Mumbai 400 085
Polymeric system: Study of synthetic polymers has received enormous attention due to their wideapplications in the various fields
Utility of the polymer for desirable purpose depends on their physical and chemicalproperties
Designing the polymeric system for specific application is always a challenging task
Free volume is one of the important factors that explains the degree of segmental andterminal relaxation of the polymeric chains which ultimately affects thermo-mechanicalproperties.
Synthesis of few industrial polymeric systems in various methods is carried out tomodify free volume holes and its related physico-chemical properties
Positron: Positron Annihilation Spectroscopy is an established technique to measure the freevolumes
Positrons have propensity to get localized at low electron density region like defects inmetallic systems and free volume nanoholes in polymers.
Introduction
P. A. M. Dirac (1928) predicted the existence of a positron in
C. D. Anderson (1933) observed the positrons in cloud chamber
• Positron is an antiparticle of electron• Same mass as that of electron (rest mass = 511keV)• Opposite in their charges and their attendant properties
P. A. M. Dirac
C. D. Anderson
Positron in Polymeric medium
Step-1: Thermalization
Step-2:Free positron annihilation OR Positronium (Ps) formation
Para-Positronium Ortho-PositroniumNotation p-Ps o-PsIntrinsic lifetime 0.125 ns 142 nsMode of annihilation 2 (of 511keV) 3 (0-511 keV)Spin state (Anti-parallel) (parallel)Fraction of formation 1/4 3/4
Positron loses its kinetic energy in the sample due to the inelastic collision,(10-12 ps)
e+e-
511 keV
Ps 511 keV
Lifetime reduces from 142 ns to 1- 10 ns
Step-3: Ps “Pick-off” annihilation
Experimental TechniquesPositron annihilation Spectroscopy
Positron Source : 22Na
(i) Positron annihilation lifetime spectroscopy (PALS)(free volume size, concentration and their distribution)
(ii) Doppler broadening spectroscopy (DBS)(defect/free volume and electron momentum)
(iii) Age momentum correlation (AMOC) spectroscopy(electron momentum at different positron age)
Slow positron beam
(i) Depth dependent defect studies (DBS)
Supplementary techniques: XRD, DMA, mDSC
Positron annihilation lifetime spectrometerWe measure the time difference between the birth (1275 keVprompt gamma) and death of a positron/Positronium (511 keVgamma) using a fast-fast coincidence circuitry.
1( ) ( ) * i
tki
i i
IF t R e B
200 400 600 800 1000 120010
100
1000
10000
Cou
nts
Channels
Doppler broadening spectrometerMeasurement of 511 keV gamma line (which undergoes line width broadening) using high resolution Gamma-ray spectroscopy
2Zp CE
Doppler broadening of annihilationgamma line proportional to electron kinetic energy
Age momentum correlation (AMOC) spectrometerAMOC involves the correlated measurement between positronlifetime and electron momentum distribution from the sameannihilation event. It can differentiate the positron states indifferent media.
BaF2STOP
BaF2START
High Voltage
High Voltage
High Voltage
HPGe det.
Spec. Amplifier
TFA TSCA
CFDD
GDG
GDG
CFDD Delay Delay Amp.TAC
Universal C
oincidence Unit
Linear Gate and Stretcher / G
DG
Multiparam
eter data acquisition system
Nanoscale free volumes in Polymer
Free-volume influences,
1) mechanical properties (viscoelastisic nature)2) transport properties (diffusion of liquid/gas molecules)3) phase transition (Tg and sub Tg)
Excluded volumeFree-volume
Positronium (Ps) is sensitive to free volumes Ps life time gives the information about free volume size, concentration and their distribution
• due to the segmental and terminal motion of molecular chains
1 1 2( ) 2 1 sin2
R RnsR R R R
The Tao-Eldrup equation
Molecular packing and swelling properties of polymer hydrogels
Structure-property relationships in modified epoxy resins
Free volume nanoholes and interfacial interaction in Epoxy/modified clay composites
Bulk and surface studies in Ag nanoparticles incorporated Nafion membrane
Objectives
Influence of free volume properties of poly (N-isopropyl acrylamide) on their swelling in water
Hydrogel, potential uses in biomedical applications, drug delivery systems, separation sciences etc.
N-isopropyl acrylamide (NIPA), a thermo-responsive hydrogel with lower critical solution temperature (LCST) of about 32˚C
But, still a swelling study of the hydrogels is debatable
Many attempts have been made to improve the swelling kinetics of these gels by altering the preparation procedures and introducing other copolymers into the gel network
Therefore, in this study, the effect of the chemical nature of crosslinkers and synthesis solvent in the swelling properties of these gels has been studied in the context of their free volume properties
two different synthesis solvents,
1) Dimethyl formamide (DMF), aprotic solvent 2) Methanol (MeOH), protic solvent
All Hydrogel samples were prepared by U.V. polymerization using α,α-dimethoxy-α-phenylacetophenone as a photo initiator
Chemical structures of the crosslinkers
CC
C
C
C
C
C
C
C
C
C
C
C
C
C
O
OO
O
O
O
O
H2
H2
H2H2
H2
H2
H2
H
H
H
O
CC
H2
H
Ethylene Glycol Dimethacrylate (EGDM), tetrafunctional, straight chain
Penta erythritol Tetraacrylate (PETA), octafunctional, branched
1,4 – Butanediol diacrylate (1,4 B), Short chain
1,6 – Hexanediol diacrylate (1,6 H), Long chain
CHCH2
C O
NHCH(CH3)2
N-isopropyl acrylamide
CH2OC
C
O
O
H2CC
CO
H
H
CH2OC
C
O
O
H2CC
CO
H
H
CH2OC
C
O
O
H2CC
CO
CH3
CH3
2 3 4 5 6 7 8 9 10 110
100
200
300
400
500
Perc
enta
ge E
quili
brum
Sw
ellin
g
mole % of cross linker
EGDM-MeOH EGDM-DMF
2 3 4 5 6 7 8 9 10 110
50
100
150
200
250
300
350
400
mole % of cross linker
Perc
enta
ge E
quili
brum
Sw
ellin
g PETA-MeOH PETA-DMF
Effect of synthesis solvent on Swelling
The percentage equilibrium swelling (PES) at room temperature in deionizedwater
PES = 100w d
d
W WW
where, Ww is the weight of the swollen gel
Wd is the weight of dry gel
2 3 4 5 6 7 8 9 10 111.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
mole % of cross linker
Frac
tiona
l fre
e vo
lum
e (r
elat
ive)
EGDM-MeOH EGDM-DMF
2 3 4 5 6 7 8 9 101.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Frac
tiona
l fre
e vo
lum
e (r
elat
ive)
mole % of cross linker
PETA-MeOH PETA-DMF
fractional free volume can’t explain the effect of solvent
Fractional free volume
fv=c(4/3ΠR3)I3
2 3 4 5 6 7 8 9 10 1118
19
20
21
22
23
24
25
26 EGDM-MeOH EGDM-DMF
wid
th o
f rad
ius d
istri
butio
n (R
elat
ive)
mole % of cross linker 2 3 4 5 6 7 8 9 10 11
18
20
22
24
26
28
30
32
mole % of cross linker
wid
th o
f rad
ius d
istri
butio
n (R
elat
ive)
PETA-MeOH PETA-DMF
Relative width of free volume radius distribution
nicely explains the experimental results
MeOH is less polar and Protic solventDMF is more polar and Aprotic solvent
Swelling is facilitated by not the free volume fraction but, the free volume hole size distribution
Polym. Bull., 65 (2010), 577-581
Neil Graham in 1998, indicated the microgelation and macrogelation formation duringthe polymerization.
the solubility parameter is the fundamental thermodynamic property for polymers and isused extensively for the discussion of the miscibility of the polymers in the solvents.
The solubility parameter for the NIPA gel is 11.2 (cal/cm3)1/2 whereas, the solubilityparameters for the DMF and methanol are 12.1 and 14.5 (cal/cm3)1/2, respectively
DMF leads to homogenous crosslinking with well defined microstructure
Methanol leads to inhomogeneous crosslinking results into the cluster formation
Mater. Sci. Forum, 733 (2013), 155-158
Influence of free volumes on the thermo-mechanical properties in epoxy resin
Epoxy resins are considered as model systems to study the relaxation phenomena. Therelaxation behavior is profoundly influenced by the chemical structure of the polymers.
A series of epoxy-poly ether diamine networks has been prepared with systematicvariation in the degree of crosslinking.
Chemical structures of epoxy resins and diamines:
characteristic length of glass transitions is evaluated using modulated DSC (MDSC).
viscoelastic parameters and crosslink density are evaluated from DMA
Molecular topology of the networks is determined by PALS
Glassy Rubbery
Characteristic length of glass transition from MDSC
Glass transition, Tg and length scale of cooperativity, ξ(Tg) are evaluated using the derivative of reversing heat capacity (Cp) signals.
ξ(Tg) has calculated from Donth thermal fluctuation theory -
3/1
2
2
)()/1(
TCkT V
EPD-230
EPED-900
Reversible Cp and its derivative for EPD-230 (glassy) and EPED-900 (rubbery) networks are shown in figures,
Sample ID (g/cm3) Tg (K) (1/Cp) δT (K) (nm)
Pure epoxy 1.140 257 0.2812 2.33 3.42
EPD-230 1.174 361 0.0338 2.55 2.00
EPD-400 1.154 320 0.050 2.62 2.07
EPED-600 1.169 291 0.0325 2.87 1.58
EPED-900 1.163 265 0.0456 3.69 1.41
Thermal fluctuation parameters at Tg :
Rubbery networks require smaller cooperative volume for Tg
Dependence of the ξ(Tg) on chemical nature of diamines
α relaxation characteristics α relaxation phenomenon is attributed to the glass transition (Tg)
storage modulus, E′ vs. T and tanδ vs. T have been measured for all epoxy networks.
In each case E' drops sharply in the high temperature range where the dissipation factor (tan δ) displays a maximum.
α relaxation peak is single and well defined (absence of any phase separation)
low temperature tan δ peak characterizes the subglassy relaxation process (β relaxation)
Two relaxation zones for all the epoxy networks are present in both the plots.
crankshaft motion of the hydroxyl ether groups in epoxy-amine networks
various parameters of the α relaxation
α relaxation temperature (Tg) increases with increasing crosslink density.
These effects are consistent with the decreased intensity of the rotational andtranslational modes of molecular motion with increasing crosslink density and hence thedecreased length of the interjection distances
Consequently, the value of E' (at Tg+ 30 K) decreases with decreased crosslink density(enhanced molecular mobility)
Sample ID α relaxation
temperature
(Tg) (K)
tan δ
(peak intensity)
Width
(K)
Storage modulus,
E′(MPa) at
Tg + 30K
Crosslink
density,
(ν x103 )
(moles/m3)
EPD-230 369.0 1.08 9.50 17.2 1.90
EPD-400 336.0 1.35 9.63 10.6 1.26
EPED-600 296.8 1.58 12.50 8.9 1.20
EPED-900 275.1 1.28 14.81 6.1 0.89
The crosslink density (υ) of the epoxy-amine networks was evaluated from E' vs. T plots at Tg + 30 K, using
υ = E'/3RT, where R is the gas constant and T is the absolute temperature
β relaxation characteristics occurrence of a clearly well defined β transition is seen for all the networks, inagreement with the reported results
Glassy (EPD-230 and EPD-400 ) networks, similar relaxation characteristics
Rubbery (EPED-600 and EPED-900), markedly different relaxation pattern
β transition Glassy Epoxy Rubbery Epoxy
width Broad Narrow
amplitude Lower Higher
Temperature at Higher Lower
characteristics of the β transitions used for quantitative treatment of sub-glassy process:
Sample ID β maxima
(K)
Relaxation
Intensity
Width
(K)
Ea,max
(kJmol-1)
EPD-230 217.61 130.43 69.76 72.5
EPD-400 208.68 74.61 50.31 66.3
EPED-600 198.80 64.85 37.26 54.8
EPED-900 193.78 129.6 26.42 -
lower crosslink densitynetworks (EPED 600and 900),regarded as internallyplasticized systems dueto the presence offlexible POE blocks.
to gain further understanding of the β relaxation process, the activation energy wascalculated from frequency dependence of the relaxation process
E" vs. temperature plot of the model epoxy networks as a function of frequency
)/exp( RTEAf a The activation energy depends on both the intramolecular contributions (internalrotation barriers) and intermolecular components (environment of the relaxing units).
the peak maxima shifts towards high temperature and the intensity of the peakincreases with increasing frequency.
with decreasing crosslink density, the Ea,max of the epoxy-amine networks decreases.
thermally activated relaxation frequencies represent an Arrhenius type expression
Arrhenius plot for EPD-230 sample
Slope = Ea,max.= 72.5kJ/mole
Sample ID o-Ps lifetime
τ3 (ns)
o-Ps Intensity
I3 (%)
Free volume
radius R (nm)
Fractional free
volume fv
EPD-230 1.61 ± 0.01 19.45 ± 0.20 0.246 2.18
EPD-400 1.69 ± 0.01 20.25 ± 0.19 0.255 2.53
EPED-600 1.81 ± 0.01 18.79 ± 0.17 0.267 2.69
EPED-900 1.95 ± 0.01 21.00 ± 0.14 0.281 3.51
The free volume parameters of the networks obtained from PALS
two classes of the networks (similar to MDSC and DMA results)
For the same kind of networks, both τ3 and I3 increase with decreasing crosslink density of the networks, as expected. Free volume hole size distribution and its parameters for all epoxy networks
The glassy networks show relatively lower values of free volume radius (R), volume υh, dispersionσ (υh) compared to the rubbery networks.
Free volume analysis
Sample ID Centroid
(υh) (nm3)
Dispersion
σ (υh) (nm3)
EPD-230 0.062 0.045
EPD-400 0.073 0.050
EPED-600 0.083 0.057
EPED-900 0.095 0.069
Further, we calculated the mean distance between crosslinks (l), where the intrinsic holevolume elements can be localized to interpret the free volume data as 2R (diameter offree volume)
Theoretical ‘l’ values:3/1 dXl where, Xd is the theoretically calculated crosslink density and can be calculated by,
avd NMbMaX 2211 /)2(/)2(
The experimental l values were calculated from the DMA results by using the followingequation
s
As M
N
32
νs is the effective crosslink density of network sites, ρ is the density of the networks, NA is the Avogadro number and Ms = ρ/υ, where υ is the crosslink density values obtained from DMA
Experimental ‘l’ values:
Dependence of the mean distance between crosslinks (l), (l-2R) of the networks.
Sample ID l, theoretical (nm) l, experimental (nm) l-2R (nm)
Theor. Expt.
EPD-230 0.75 1.09 0.26 0.59
EPD-400 0.82 1.25 0.31 0.74
EPED-600 0.88 1.28 0.35 0.53
EPED-900 0.97 1.35 0.41 0.78
can assume only the sub-glassy β relaxation time scales.
The β relaxation time τβ is known to have Arrhenius temperature dependence
)/exp( RTE
where τβ∞ is of the order of 10-13-10-16 s [Johari et al., 1970; 1971]. τβ∞ value of 10-14 s is used for thecalculation of τβ.Eβ is an activation energy of β relaxation obtained from DMA.
Thus, it can be emphasized that the time scale of relaxation associated with the sub-glassy β relaxation process has a bearing on the mean size of the free volume holes of glassy epoxy networks.
Whereas, the rubbery networks, does not follow this relation due to the danglingchains in the networks, leading to higher l values.
Is time scale of relaxation of the networks commensurate with the o-Ps lifetime of1.61 - 1.95 ns ?
From the results it is evident that the τβ (298 K) values are slower than the mean o-Pslifetimes of the networks, i.e. 4.7Χ10-2 s for EPD-230 and 3.9 Χ 10-3 s for EPD-400
Soft Matter, 9 (2013), 3589-3599
Investigation of the microstructure in the epoxy\clay composite system
In recent years, polymer nanocomposite have attracted a great attention owing to theirunexpected hybrid properties that are synergistically derived from multicomponent.
Epoxy/clay nanocomposites were synthesized using modified clay to investigate thefree volume properties and interfacial interactions.
Clay was modified with the organic modifier,
Nanocomposites have been prepared with different weight % of clay i.e. 1, 3, 5, 7.5.
Clay dispersion has been studied using XRD and SEM
Free volume properties and Positron/Positronium states were examined by PAS
C H 2 C H 3N +
C H 3
H TH T - H ydrogenated T allow
(65% C 18; 30% C 16; 5% C 14)
C loisite 10A
Chem Phys Chem, 13 (2012), 3916-3922
strong intercalation of epoxy matrix in between two consecutive silicate layers
no characteristic diffraction peak in EPJ1 (clay exfoliated morphology)
smooth fractured surface of the EPJ1 in SEM scan
diffraction peaks appear in EPJ3, 5 and 7.5 samples (clay intercalated morphology)
deformed regions resulting from the coarseness of the fractured surface in SEM scans
Characterization of nanocomposites
EPJ1
EPJ7.5EPJ5
EPJ3
2θ = 4.69°
d = 1.92nm
2θ = 2.68°
d = 3.29nm
Free volume and interfacial properties
nanocomposites have lower fv as compared to pristine epoxy
fv decreases with clay loading upto 3 wt. % and saturates at higher concentration
Simple law of mixing - reduction in fv (exp) is more than fv (calc) – interfacial interaction
the deviation between experimental and calculated I2 values is maximum for EPJ1sample and further reduces with increase in clay concentration
exfoliated morphology in EPJ1 sample enhances the interfacial interaction while theclay agglomeration at higher clay concentration reduces the interfacial interaction aswell as the fractional free volumes
● experimental
○ calculated
● experimental
○ calculated
AMOC measurements
S(t) parameter profilefor pristine epoxy iswell consistent with thereported literature
Low average S-parameter valuein pure clay →crystalline nature
same chemical environment trapping of positron atinterfacial layer
positrons trapped andannihilate from clayagglomerate and notfrom the epoxy/clayinterface
Clay concentration
Clay morphology fv Free positron trapping and
annihilation from
Interfacial interaction
(I2)Low Exfoliated High Interfacial layer Strong
High Intercalated Low Clay agglomerates Weak
1.60
40( ) ( )Z E E
Implantation depth of positron depends upon positron energy and polymer density,
Surface analysis: depth dependent measurementsSlow Positron Beam Setup at Radiochemistry Division, BARC.
• In present case, the surface morphology (about 2 μm) is studied using the positronenergy range of 0.2 to 15 keV
0 2 4 6 8 10 12 14
0.455
0.460
0.465
0.470
0.475
0.480
0.485
0.490
2.3721.8541.3840.9690.6110.3190.1050.000
Mean Implantation Depth (m)
Positron energy (keV)
S-pa
ram
eter
EPJ0 EPJ1 EPJ3
VEPFIT analysis
d t t bd c dD v c I z k n c cdz dz
2
2 ( ) 0 ,
Time averaged positron density c(z) is given by the following equation
Where, c(z) = the time averaged positron density,vd(z) = E(z) = the drift velocity with positron mobility and electric field E,I(z) = positron trapping rate at depth z,nt(z)= the defect density,kt = rate constant for positron trapping at defects,b = bulk annihilation rate andD+ = positron diffusion coefficient
The general solution for vd=0 in the ith interval
ii i i i i
i
pc z A z B z( ) exp( ) exp( ) ,
i i ii t t bi
DLL k n
2 1/ 2,
, ,
1 , [ ]( )
L+ is the positron diffusion length in ith layer
0 2 4 6 8 10 12 14
0.455
0.460
0.465
0.470
0.475
0.480
0.485
0.4902.3720.9690.3190.105 1.8541.3840.6110.000
EPJ0 EPJ5 EPJ7.5
Positron energy (keV)
S-pa
ram
eter
Mean Implantation Depth (m)
Sample lD (nm) S0 ± 0.001 Sb ± 0.001
EPJ0 196.2 ± 7.71 0.4577 0.4859EPJ1 117.6 ± 6.04 0.4616 0.4831EPJ3 72.21 ± 5.04 0.4689 0.4830EPJ5 154.1 ± 9.81 0.4662 0.4836EPJ7.5 117.3 ± 6.48 0.4618 0.4818
• Decrease in diffusion length with clay loading (0-3%): Increase in the number of trapping sites (interfaces between clay and polymer).Exfoliation of clay at lower concentrations.
• Increase in Diffusion length at 5 % clay loading: formation of clay microparticles effectively reducing the no. of interfaces.
• Positron diffusion length follows bulk S-parameter profile.
Various parameters from VEPFIT analysis:
Chem Phys Chem, 13 (2012), 3916-3922
Microstructural studies on the silver nanoparticles incorporated poly (perfluorosulfonic acid) membrane
Inclusion of the silver nanoparticles (AgNps) in host poly (perfluorosulfonicacid) membrane (Nafion-117) has been carried out
Two different reducing agents were used:Sodium borohydride (NaBH4), anionicFormamide, non-ionic
Nanoparticles (Nps) size were determined by XRD measurements
PALS was employed to measure free volume properties in the AgNps dopedand undoped Nafion membranes
Depth dependent S-parameter and Positronium fraction (3γ/2γ ratio)measurements have been carried out using variable slow positron beam
Journal of Physics: CS, 262 (2011), 012045, 1-4
Nafion-117 One of the ion exchange membrane Selective permeability to cations (separation science) Low resistance to current flow (batteries and fuel cells) Excellent chemical, thermal and mechanical stability (industrial engineering)
Thickness : 178 m IEC: 0.91 mmol/g Density: 1.95 g/cc
Washed with deionized water
Nafion-117 with
organic impurities
Conc.HNO3
3-4 hrswashed with excess boiled water
Pure Nafion-117
1 hr
1 hr 1M HCl 1M NaOH
three times each
H+ form0.5M NaCl
30 hrs
0.25M AgNO3
48 hrsNa+ formAg+ form
30 mins
Na+/Ag
H+/Ag
C F 2
C F
C F 3
O HS
x y
z
C F 2
C F 2
C F 2
C F 2
C F 2
C F
O O O
OSample preparation:
3 4 3 4[ ] [ ] [ ] [ ] [ ]mem aq mem aq memR SO Ag NaBH R SO Na BH Ag
The membrane samples were loaded with Ag+ ions by ion-exchange mechanism,
74 2 3 3 22[ ] [ ] 3 [ ] [ ] ( )o
aq mem aq memBH Ag H O H BO Ag H g
with Formamide, (distributed across the thickness of the membrane)0
3 2 2 3 22[ ] [ ] [ ] 2[ ] [ ] 2[ ]mem aq mem mem aq memR SO Ag HCONH H O R SO H NH COOH Ag
3 3[ ] [ ] [ ] [ ] [ ]mem aq mem aq aqR SO H NaCl R SO Na H Cl
3 3[ ] [ ] [ ] [ ]mem aq mem aqR SO Na Ag R SO Ag Na
with NaBH4, (near the surface region of the membrane)
Reducing agents AgNps size (nm) AgNps size (nm)Kumar et al., 2010
NaBH4 15 ± 5 15 ± 4
Formamide 10 ± 3 9 ± 2
XRD measurements:
Among the ionic forms the most hydrated form has maximum o-Ps intensity andlifetime.
Ag+ is a good scavenger of electrons – inhibits the Positronium formation
Less o-Ps intensity in the nanoparticles doped membrane nanoparticles blocks the freevolume holes in the Nafion membrane
In Formamide case (H+/Ag), distinguishable change in the free volume nature
In NaBH4 case (Na+/Ag), marginal change in the free volume nature
Bulk characterization
1.60
40( ) ( )Z E E
Implantation depth of positron depends upon positron energy and polymer density,
Surface analysis: depth dependent measurementsSlow Positron Beam Setup at Radiochemistry Division, BARC.
• In present case, the surface morphology (about 1 μm) is studied using the positronenergy range of 0.2 to 10keV
• AgNps doped membranes shows high S-parameter values and high 3γ /2γratio
• increase in free volumes or high surface open porosity due to chemical reduction process
• Higher S-parameter value in Ag+ membrane with lower 3g/2g ratio is due to the formation of metallic silver layer at surface region
Summary
Positron annihilation spectroscopy (PAS) complemented by conventionalcharacterization techniques has been used to investigate the correlations between thenanostructure and physico-chemical properties of polymers.
In chemically identical samples, the free volume size distribution plays a key role inthe swelling properties of the hydrogels.
The backbone chain length of polyether diamines plays a significant role indetermining the structural relaxations as well as macroscopic properties, which in turnexhibits the free volume properties in the epoxy systems.
Free positron trapping/annihilation events provide the information about the filler-matrix interfacial layers.
