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Foamed polymers. cellular structure and properties

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Industrial Developments

Part of the book series: Advances in Polymer Science ((POLYMER,volume 51))

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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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