Abstract
This survey deals with the fundamental morphological parameters of foamed polymers including size, shape and number of cells, closeness of cells, cellular structure anisotropy, cell size distribution, surface area etc. The methods of measurement and calculation of these parameters are discussed. Attempts are made to evaluate the effect and the contribution of each of these parameters to the main physical properties of foamed polymers namely apparent density, strength and thermoconductivity. The cellular structure of foamed polymers is considered as a particular case of porous statistical systems. Future trends and tasks in the study of the morphology and cellular structure-properties relations are discussed.
Nichts ist drinnen, nichts ist draussen: Denn was innen, das ist außen. J. W. v. Goethe
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Abbreviations
- FL-1:
-
Soviet grade resol phenol-formaldehyde foam
- FRP-1:
-
Soviet grade resol-formaldehyde foam
- GSE:
-
Gas-Structural Element
- PPU-3:
-
Soviet grade rigid polyurethane foam
- PSB, PSB-S, PS-4:
-
Soviet grades polystyrene foam
- PVKH-1:
-
Soviet grade rigid poly(vinyl chloride) foam
- A:
-
normalization constant
- b:
-
side of cube
- B:
-
number of angles
- C:
-
constant
- d:
-
cell diameter
- dcr :
-
critical (minimum) cell diameter
- dmax :
-
maximum cell diameter
- D:
-
cell diameter, width of cell
- Da :
-
arithmetical cell diameter
- Dg :
-
geometrical cell diameter
- Di :
-
current cell diameter
- Dn :
-
nominal cell diameter
- Ds :
-
surface cell diameter
- Dp :
-
probable cell diameter
- Dv :
-
volume cell diameter
- D‖, D⊥ :
-
cell diameters parallel and perpendicular to heat flux
- Ef :
-
flexibility modulus
- Ep :
-
modulus of polymer phase
- EO :
-
modulus of rod
- g:
-
weight of polymer phase
- gc :
-
weight of polymer per cell
- G:
-
gas filling
- Gf :
-
gas-filling factor
- Gm :
-
active gas filling
- h:
-
height of cell
- k:
-
length ratio; parameter
- KO :
-
Hankel function
- l:
-
intermediate layer depth
- m:
-
mass of dry foam
- mg :
-
mass of gas in foam
- mw :
-
mass of wet foam
- Mp :
-
mass of polymer phase of foam
- N:
-
total number of cells (spheres)
- Nb :
-
number of cells in a cubic
- Ni :
-
current number of cells
- NV :
-
number of cells having a volume V
- p:
-
parameter
- P:
-
probability; load
- q, q1, q2, q3 :
-
anisotropy coefficients
- q*:
-
effective anisotropy coefficient
- Q:
-
weight of foam
- r:
-
cell (spherical) radius
- rc :
-
curvature radius
- rh :
-
hydraulic radius
- rmax :
-
maximum radius
- rp :
-
planar projection radius
- RB :
-
roughness factor
- Rc :
-
inscribed circle radius
- S:
-
surface area
- ΔS:
-
surface area increment
- Sa :
-
cross-sectional area
- Sc :
-
surface area of cell
- Sd :
-
surface area of conducting cells
- Sext :
-
external surface area
- Sint :
-
internal surface area
- Ss :
-
surfase area of spherical cell
- Ssp :
-
specific surface area
- S Ksp :
-
kinetic specific surface area
- S Msp :
-
mass specific surface area
- S Vsp :
-
volumetric specific surface area
- Svis :
-
visible surface area
- SΣ :
-
total surface area
- SO :
-
original cross-sectional area
- ΔT:
-
temperature gradient
- U:
-
filling ratio
- v, v1, v2, v3 :
-
wave propagation velocities
- vg :
-
wave propagation velocity in gas phase
- vp :
-
wave propagation velocity in polymer phase
- V:
-
packed volume
- Vc :
-
cell volume
- Vd :
-
volume of dry foam
- Veff :
-
effective cell volume
- Vg :
-
volume of gas phase
- Vm :
-
volume of cells not participating in filtration process
- Vmax :
-
volume containing a maximum number of cells
- Vs :
-
volume of solid (polymer) phase
- Vsp :
-
specific cell volume
- VO :
-
net volume of foam
- W:
-
sphere size distribution function
- x:
-
depth of cell; distance between spheres
- X:
-
section plan
- Z:
-
transparency
- α:
-
angle; parameter
- αS :
-
surface aspect ratio
- αV :
-
volume aspect ratio
- β:
-
width-to-length ratio
- γ:
-
apparent density (volumetric weight) of foam
- γp :
-
density of polymer phase; density of unexpanded polymer
- γm :
-
minimum of γ
- γy :
-
value of γ at distance “y”
- γ1 :
-
increment of γ
- γ*:
-
true apparent density of foam
- Δγ:
-
gradient of γ
- Γ:
-
gamma function
- δ:
-
wall thickness of cell
- δcr :
-
critical (minimum) wall thickness of cell
- ε:
-
deformation; strain
- εc :
-
compressive deformation
- εmax :
-
maximum deformation
- εt :
-
tensile deformation
- η:
-
distribution median
- ϑg :
-
volume fraction of gas phase
- ϑp :
-
volume fraction of polymer phase
- ϑ cp :
-
value ϑp for closest packed foam
- ϑw :
-
volume fraction of water phase
- ϑ cw :
-
value ϑw for closest packed foam
- ϑα :
-
volume fraction of open cells
- ϑ cα :
-
value ϑα for closest packed foam
- κ:
-
coefficient of variation
- λ:
-
thermoconductivity
- λc :
-
convective thermoconductivity
- λg :
-
thermoconductivity of gas phase
- λr :
-
radiative thermoconductivity
- λs :
-
thermoconductivity of solid phase
- μi :
-
Di/D
- ν:
-
number of contacts
- ν:
-
Ni/N
- ξ:
-
G/U
- σ:
-
standard deviation; root-mean-square deviation
- σc :
-
compressive strength
- σt :
-
tensile strength
- ϕ:
-
roundness of cell shape
- ψ:
-
sphericity of cell shape
- ω:
-
configuration factor
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Shutov, F.A. (1983). Foamed polymers. cellular structure and properties. In: Industrial Developments. Advances in Polymer Science, vol 51. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017587
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