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Sem
idilu
te S
olut
ions
Dilu
te b
lobs
C*
Net
wor
k of
mes
h SC
C SW
CHA
PTER
111
8 P
olym
ers i
n Co
smet
ics10
1
Sem
idilu
te S
olut
ions
Net
wor
k of
mes
h co
nsist
s of b
lobs
of r
adiu
s r=
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
102
Poly
mer
s in
good
solv
ent i
n se
mi-d
ilute
so
lutio
n
Blo
b ra
dius
For r
> th
at is
out
side
the
blob
For r
> th
at is
out
side
the
blob
The
repu
lsiv
e in
tera
ctio
ns
betw
een
mon
omer
s are
sc
reen
ed o
ut
The
blob
s con
nect
in a
rand
om fl
ight
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
103
Sum
mar
y
g(r)
rC
*cros
sove
r
Sing
le sw
olle
n ch
ains
g(r )
=r-4
/3a-5
/3
insi
de th
e bl
ob
R IS
TH
E C
OIL
SI
ZE
g(r )
= c
/r
outs
ide
the
blob
g(r )
0
for r
> R
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
104
DIL
UTE
SO
LUTI
ON
VI
SCO
SITY
DIL
UTE
SO
LUTI
ON
VI
SCO
SITY
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
105
Poly
mer
Sol
utio
n Vi
scos
ity
The
visc
osity
of a
solu
tion
depe
nds u
pon
the
prop
ensi
ty o
f the
solv
ent t
o flo
w
In a
pol
ymer
solu
tion,
the
poly
mer
mol
ecul
e ‘s
low
s’ th
e flo
w o
f the
solv
ent
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
106
Poly
mer
Sol
utio
n Vi
scos
ity IF T
HE
SOLV
ENT
DO
ES
NO
T FL
OW
TH
RO
UG
H
THE
CO
IL –
IT IS
C
ALL
ED A
NO
N-F
REE
D
RA
ININ
G C
OIL
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
107
Poly
mer
Sol
utio
n Vi
scos
ity IF T
HE
SOLV
ENT
FLO
WS
THR
OU
GH
TH
E C
OIL
–IT
IS C
ALL
ED A
FR
EE D
RA
ININ
G C
OIL
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
108
Visc
osity
Visc
osity
tube
tube
flow
ing
liqui
dflo
win
g liq
uid
O
OO
O
O
O
O O O
flow
fast
est i
n ce
nter
of t
ube
flow
fast
est i
n ce
nter
of t
ube Flow
is s
tatio
nary
at w
all
Flow
is s
tatio
nary
at w
all
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
109
Poly
mer
Sol
utio
n Vi
scos
ity
The
Mar
k-H
ouw
ink
Equa
tion
Intri
nsic
Vis
cosi
ty, [
]=K
Ma
[] i
s the
hy
drod
ynam
ic
size
of t
he
poly
mer
mol
ecul
e in
solu
tion
(dl/g
)
A fa
ctor
that
de
pend
s upo
n th
e ‘s
wol
len’
size
of
the
poly
mer
m
olec
ule
a =
0.5
for n
on-f
ree
drai
ning
a =
1.0
for F
ree
drai
ning
For G
auss
ian
Cha
ins
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
110
Mea
sure
men
t of V
iscos
ityM
easu
rem
ent o
f Visc
osity
Mea
sure
tim
e of
sol
vent
flo
w th
roug
h vi
scom
eter
t o
Mea
sure
tim
e of
sol
utio
n flo
w th
roug
h vi
scom
eter
t
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
111
Visc
osity
Visc
osity
•We
mea
sure
solu
tion
(an
d so
lven
t (vi
scos
ity se
para
tely
•Rel
ativ
e Vi
scos
ity =
(r
•th
at re
veal
s how
muc
h m
ore
visc
ous t
he so
lutio
n is
com
pare
d to
the
solv
ent
•Spe
cific
Visc
osity
= [(
r -1
•sp
•re
mov
es th
e so
lven
t visc
osity
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
112
Dete
rmin
ing
the
Intr
insic
Visc
osity
•Tim
e th
e flo
w o
f sol
vent
and
pol
ymer
solu
tions
th
roug
h a
capi
llary
•The
spec
ific
redu
ced
visc
osity
,
sp/c
=(
-o)
/ oc
•Mea
sure
the
(sp
/c) f
or a
serie
s of d
ilute
po
lym
er so
lutio
ns
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
113
Wha
t is
the
Intr
insi
c Vi
scos
ity?
Wha
t is
the
Intr
insi
c Vi
scos
ity?
•The
uni
ts a
re d
ecili
tre/
gram
•vo
lum
e pe
r uni
t wei
ght
•Th
e in
trin
sic v
iscos
ity g
ives
the
volu
me
occu
pied
by
one
gram
of p
olym
er in
so
lutio
n
•[].M
= th
e vo
lum
e oc
cupi
ed b
y on
e m
ole
of p
olym
er in
solu
tion
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
114
Redu
ced
Spec
ific
Visc
osity
Redu
ced
Spec
ific
Visc
osity
hydr
odyn
amic
inte
ract
ion
thro
ugh
the
solv
ent
hydr
odyn
amic
inte
ract
ion
thro
ugh
the
solv
ent
sp/c
= [
] +
k[]2
csp
/c =
[]
+ k[
]2 c
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
115
Visc
osity
Visc
osity
•Red
uced
Spe
cific
Visc
osity
=
sp/c
•a
mea
sure
of t
he sp
ecifi
c cap
acity
of t
he p
olym
er to
incr
ease
the
rela
tive
visc
osity
•Bu
t it c
onta
ins t
he h
ydro
dyna
mic
inte
ract
ion
cont
ribut
ion
•Rem
ove
this
cont
ribut
ion
by e
xtra
pola
ting
to in
finite
dilu
tion
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
116
Dete
rmin
ing
the
Intr
insic
Visc
osity
sp/c
Cpo
lym
er
[]
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
117
Visc
osity
–H
uggi
ns P
lot
sp/c
Cpo
lym
er
[]
Dilu
te S
olut
ion-
Poly
mer
Mol
ecul
es d
o no
t tou
ch
Sem
i-Dilu
te S
olut
ion-
Poly
mer
Mol
ecul
es d
o in
terp
enet
rate
C*
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
118
Rept
atio
n•A
bove
the
chai
n en
tang
lem
ent t
hres
hold
•The
pol
ymer
mol
ecul
es w
riggl
e pa
st e
ach
othe
r •L
ike a
snak
e m
ovin
g al
ong
a tu
be m
ade
up o
f sna
kes
•Visc
osity
= (c
oncn
)2.2
-3.4
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
119
The
Gla
ss T
rans
ition
Tem
pera
ture
, Tg
•Bel
ow th
e Tg
,•
Chai
ns h
ave
insu
fficie
nt e
nerg
y to
rept
ate
past
eac
h ot
her
•Abo
ve th
e Tg
•Po
lym
er ch
ains
‘wrig
gle’
and
hav
e en
ough
exc
lude
d vo
lum
e to
wrig
gle
past
ea
ch o
ther
•Pla
stici
zers
are
smal
l mol
ecul
es th
at lo
wer
the
Tg o
f a p
olym
er o
r po
lym
er sy
stem
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
120
Plas
ticiza
tion
•Sm
all m
olec
ules
inte
rspe
rsed
bet
wee
n th
e po
lym
er m
olec
ules
can
assis
t rep
atat
ion
•Th
is is
plas
ticiza
tion
•The
re is
a ti
me
elem
ent
•If
the
appl
ied
forc
e m
ust l
ast l
ong
enou
gh fo
r the
po
lym
ers t
o m
ove
•If
the
forc
e is
of sh
ort d
urat
ion,
ela
stic
defo
rmat
ion
and
reco
very
will
occ
ur•
Debr
a Nu
mbe
r
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
121
The
Mar
k H
ouw
ink-
Saku
rada
Equ
atio
n.
[] =
KMa
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
122
Rheo
logy
of P
olym
er
solu
tions
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
123
Ther
mal
Beh
avio
r of G
els
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
124
http
://w
ww
.bre
nnta
g-sp
ecia
lties
eu
rope
.com
/en/
dow
nloa
ds/F
ood_
pres
s_re
view
/TB
_Hyd
roco
lloid
s_FN
FN20
1009
Ther
mal
Beh
avio
r of G
els
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
125
http
://w
ww
.bre
nnta
g-sp
ecia
lties
eu
rope
.com
/en/
dow
nloa
ds/F
ood_
pres
s_re
view
/TB
_Hyd
roco
lloid
s_FN
FN20
1009
Ther
mal
Beh
avio
r of G
els
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
126
http
://w
ww
.bre
nnta
g-sp
ecia
lties
eu
rope
.com
/en/
dow
nloa
ds/F
ood_
pres
s_re
view
/TB
_Hyd
roco
lloid
s_FN
FN20
1009
Ther
mal
Beh
avio
r of G
els
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
127
http
://w
ww
.bre
nnta
g-sp
ecia
lties
eu
rope
.com
/en/
dow
nloa
ds/F
ood_
pres
s_re
view
/TB
_Hyd
roco
lloid
s_FN
FN20
1009
RHEO
LOGY
SCC
SW
CH
APT
ER 1
118
Pol
ymer
s in
Cos
met
ics
128
STR
ESS
RAT
E O
F ST
RA
IN
New
toni
an
Pseu
dopl
astic
Dila
tant
RHEO
LOGY
SCC
SW
CH
APT
ER 1
118
Pol
ymer
s in
Cos
met
ics
129
STR
ESS
RAT
E O
F ST
RA
INBIN
GH
AM
B
OD
Y
ELLI
S
Thixo
trop
y
SCC
SW
CH
APT
ER 1
118
Pol
ymer
s in
Cos
met
ics
130
Vis
cosi
ty
Tim
e
Cea
se sh
ear
Rheo
pexy
SCC
SW
CH
APT
ER 1
118
Pol
ymer
s in
Cos
met
ics
131
Vis
cosi
ty
Tim
e
Cea
se sh
ear
Elas
tic a
nd V
iscou
s
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
132
http
://w
ww
.jero
n.je
/ang
lia/le
arn/
sec
/sci
ence
/forc
emot
/pag
e08.
htm
A S
prin
g is
an
elas
tic so
lidH
ooke
's la
wFo
r a N
ewto
nian
Liq
uid:
http
://fin
earta
mer
ica.
com
/feat
ured
/po
urin
g-liq
uid-
tom
isla
v-
Visc
oela
stic
ity
•Pol
ymer
s are
visc
oela
stic
mat
eria
ls•P
urel
y el
astic
mat
eria
ls de
form
whe
n st
ress
is a
pplie
d an
d co
mpl
etel
y re
cove
r the
ir or
igin
al sh
ape
whe
n th
e st
ress
is re
mov
ed.
•Pur
ely
visc
ous l
iqui
ds d
efor
m w
hen
a st
ress
is a
pplie
d bu
t rem
ain
defo
rmed
whe
n th
e st
ress
is re
mov
ed•
The
high
er th
e st
ress
, the
gre
ater
the
rate
of s
trai
n•
The
visc
osity
is th
e pr
opor
tiona
lity
fact
or th
at re
late
s the
mag
nitu
de o
f the
ap
plie
d st
ress
to th
e ra
te o
f str
ain.
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
133
Visc
oela
stic
ity•i
f the
stre
ss is
hel
d co
nsta
nt, t
he st
rain
incr
ease
s with
tim
e (c
reep
);•i
f the
stra
in is
hel
d co
nsta
nt, t
he st
ress
dec
reas
es w
ith
time
(rela
xatio
n);
•the
effe
ctiv
e st
iffne
ss d
epen
ds o
n th
e ra
te o
f ap
plica
tion
of th
e lo
ad;
http
://w
ww.
yout
ube.
com
/wat
ch?v
=f2X
Q97
XHjV
w•i
f cyc
lic lo
adin
g is
appl
ied,
hys
tere
sis (a
pha
se la
g)
occu
rs, l
eadi
ng to
a d
issip
atio
n of
mec
hani
cal e
nerg
y;
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
134
Visc
oela
stic
ity
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
135
Line
ar v
isco
elas
ticity
Appl
ied
stre
ssIm
med
iate
st
rain
Cree
pss
Appl
ied
stra
inIm
med
iate
st
ress
Rela
xatio
n
•tis
time,
is
stre
ss,
is
stra
in
•is
inst
anta
neou
sel
astic
mod
ulif
or c
reep
, I
s
inst
anta
neou
sel
astic
mod
ulif
or re
laxa
tion
•K(t)
is th
ecr
eep
func
tion,
F(
t)is
the
rela
xatio
n fu
nctio
n
Stor
age
and
Loss
Mod
uli
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
136
Stor
age
Mod
ulus
(th
e el
astic
co
mpo
nent
)
Loss
Mod
ulus
(th
e vi
scou
s co
mpo
nent
)
The
elas
tic
com
pone
nt ca
n be
m
odel
ed a
s a sp
ring
of sp
ring
cons
tant
E
The
visc
ous c
ompo
nent
ca
n be
mod
eled
as a
da
shpo
t hav
ing
a liq
uid
of v
iscos
ity η
Sprin
gs a
nd D
ashp
ots
•The
Max
wel
l Mod
el SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
137
http
://up
load
.wik
imed
ia.o
rg/w
ikip
edia
/com
mon
s/d/
db/M
axw
Pred
icts
strai
n in
crea
sing
with
tim
e fo
r con
stan
t stre
ss..
But
real
pol
ymer
s usu
ally
sh
ow st
rain
rate
dec
reas
ing
with
tim
e
•Th
e Ke
lvin
-Voi
gt M
odel
Goo
d fo
r mod
elin
g cr
eep
Not
so g
ood
for m
odel
ing
rela
xatio
n
Sprin
gs a
nd D
ashp
ots
•The
Sta
ndar
d Lin
ear S
olid
Mod
el
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
138
http
://up
load
.wik
imed
ia.o
rg/w
ikip
edia
/com
mon
s/d/
db/M
axw
Mor
e ac
cura
te th
an M
axw
ell a
nd K
elvi
n-Vo
igt f
or m
ater
ial
reso
nses
……
but
inac
cura
te fo
r spe
cific
load
s
In R
ealit
y th
ere
is a
Dist
ribut
ion
of R
elax
atio
n Ti
mes
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
139
http
://up
load
.wik
imed
ia.o
rg/w
ikip
edia
/com
mon
s/d/
db/M
axw
ell_
dia
Part
icul
ate
Gel
s
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
140
Part
icul
ate
Gel
s
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
141
Rheo
logy
of '
gel’
stru
ctur
es a
t equ
ilibr
ium
ωSC
C SW
CHA
PTER
111
8 P
olym
ers i
n Co
smet
ics14
2
Yiel
d St
ress
Flu
ids
and
failu
re o
f the
Cox
-Mer
zRul
e•
At lo
w st
rain
s , th
e st
ruct
ured
‘gel
s’ sh
ow e
last
ic re
cove
ry•
That
is, t
hey
beha
ve li
ke e
last
ic so
lids
•Ho
wev
er, u
nder
stea
dy sh
ear,
thes
e ge
ls flo
w li
ke li
quid
s•
Whe
reas
solid
s wou
ld fr
actu
re•
Ther
efor
e, st
ruct
ured
gel
s beh
ave
like
solid
s at l
ow st
rain
s•
Abov
e a
cert
ain
stre
ss (y
ield
stre
ss) t
hey
flow
like
liqu
ids.
•Th
e em
piric
al C
ox-M
erzr
ule
stat
es th
at th
e vi
scos
ity/r
ate
of st
rain
beh
avio
r is
com
para
ble
to th
e co
mpl
ex v
iscos
ity/f
requ
ency
beh
avio
r•
The
Cox –
Mer
zrul
e is
obey
ed fo
r man
y so
lutio
ns•
How
ever
, str
uctu
red
gels
usua
lly d
isobe
y th
e Co
x-M
erzr
ule
•Be
caus
e th
ey ce
ase
to b
e flo
wab
leflu
ids b
elow
the
yiel
d st
ress
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
143
CON
SIDE
R A
POLY
MER
AS
A ST
ICKY
PAR
TICL
E
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
144
Stic
ky P
olym
er P
artic
les
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
145
Rela
xatio
n Pr
oces
s A
–Di
ffusi
on b
etw
een
enta
ngle
men
t poi
nts
The
Mod
ulus
at
tim
e t
Initi
al
Mod
ulus
Rela
xatio
n fu
nctio
n at
tim
e t
From
the
Rous
e M
odel
, The
initi
al
mod
ulus
= k
Tpe
r cha
ini.e
. (nu
mbe
r den
sity
of ch
ains
).kT
(ρN
o/M
).kT
For e
ntan
gled
syst
ems
M b
ecom
es M
e
Stra
in te
nsor
in th
e di
rect
ion
of th
e ve
ctor
bet
wee
n en
tang
lem
ents
,Th
e m
olec
ule
is ou
tsid
e its
equ
ilibr
ium
con
form
atio
n.
The
rela
xatio
n m
odul
us
for t
he A
pro
cess
The
initi
al R
ouse
Mod
ulus
dep
ends
on
the
dens
ity o
f cha
ins i
n th
e en
tang
lem
ent r
egio
n (B
lob)
Long
rela
xatio
n tim
es co
ntrib
ute
to a
hi
gher
mod
ulus
at t
ime
t.SC
C SW
CHA
PTER
111
8 P
olym
ers i
n Co
smet
ics14
6
Rela
xatio
n Pr
oces
s B
–Re
trac
tion
of th
e ch
ain
to it
s orig
inal
den
sity
For r
e-eq
uilib
ratio
n ac
ross
slip
-link
sRe
trac
tion
in th
e co
nfin
ed
geom
etry
is d
omin
ated
by
the
low
est o
rder
R-Z
mod
e
Retr
actio
n re
laxa
tion
time
dep
ends
on
the
sam
e pa
ram
eter
s as p
roce
ss A
AND
THE
NUM
BER
OF
ENTA
NGLE
MEN
TS P
ER C
HAIN
Retr
actio
n M
odul
us d
epen
ds o
n th
e sa
me
para
met
ers a
s R-
Z b
ut th
e slo
wer
R-Z
mod
es d
omin
ate.
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
147
Rela
xatio
n Pr
oces
s C –
Reco
very
of t
he o
rigin
al c
onfo
rmat
ion
by re
ptat
ion
The
char
acte
ristic
tim
e fo
r a re
puta
tion
mot
ion
is:
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
148
Cellu
losic
thic
kene
rs
Hyd
roxy
ethy
lcel
lulo
se H
EC
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
149
•Deg
ree
of S
ubst
itutio
n (0
-3) a
nd M
olar
su
bstit
utio
n
•Non
ioni
c th
icke
ner
•She
ar-th
inni
ng R
heol
ogy
http
://or
igin
-ars
.els
-cdn
.com
/con
tent
/imag
e/1-
s2.0
-S00
0888
4612
0006
95-g
r2.jp
g
Rel
axat
ion:
Proc
ess A
:
Proc
ess B
Proc
ess C
:
The
Rheo
logy
of A
queo
us S
olut
ions
of
Hyd
roxy
ethy
lcel
lulo
se
Tanδ
is G”
/G’.
Ther
efor
e al
l HEC
solu
tions
>3%
ar
e m
ore
elas
tic th
an
visc
ous
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
150
The
Rheo
logy
of A
queo
us S
olut
ions
of
Hyd
roxy
ethy
lcel
lulo
se
151
Rel
axat
ion:
Proc
ess A
:
Proc
ess B
Proc
ess C
:
Fast
el
astic
re
spon
se
Slow
vi
scou
s re
spon
se
The
slow
visc
ous r
espo
nse
arise
s fro
m:
The
long
est
Rous
e-Zi
mm
Mod
es
The
coil
wou
ld b
e ex
pect
ed to
st
retc
h un
der s
hear
(De
Genn
es).
Th
e ‘d
ashp
ot’ r
elax
atio
n in
this
case
wou
ld b
e th
e st
retc
hing
and
re
-form
atio
n of
the
coil.
Rept
atio
nis
prob
ably
not
sig
nific
ant i
n di
lute
solu
tion.
It
may
be
impo
rtan
t in
conc
entr
ated
solu
tions
.
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
Rheo
logy
and
Sen
soria
l Att
ribut
es
•For
Hyd
roge
ls, g
el-li
ke su
spen
sions
/em
ulsio
ns•
Rheo
logi
cal p
aram
eter
s tha
t can
be
corr
elat
ed w
ith se
nsor
y pe
rcep
tion
inclu
de•
Yiel
d st
ress
•
Thixo
trop
y•
Wal
l slip
•Sh
ear b
andi
ng
•The
se a
ll sh
ould
be
mea
sure
d fo
r cor
rela
tion
of rh
eolo
gy w
ith
sens
oria
l pro
pert
ies
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
152
S. O
zkan
, T. W
. Gill
ece,
L. S
enak
and
D. J
. Moo
re, C
hara
cter
izat
ion
of y
ield
stre
ss a
nd sl
ip b
ehav
iour
of s
kin/
hair
care
ge
ls us
ing
stea
dy fl
ow a
nd L
AO
S m
easu
rem
ents
and
thei
rco
rrel
atio
n w
ith se
nsor
ial a
ttrib
utes
, In
tern
atio
nal J
ourn
al o
f Cos
met
ic S
cien
ce, 2
012,
34,
193
–201
Exte
nsio
n of
coi
ls an
d ro
ds
A co
oper
ativ
e co
il-ro
d tr
ansit
ion
occu
rs a
t a
criti
cal e
long
atio
nal
shea
r rat
e
Orde
red
stru
ctur
es sh
ow u
p as
bi
refr
inge
ntsh
ear b
ands
Ther
e is
no cr
itica
l she
ar ra
te
for r
ods -
--th
ey sh
ow
incr
easin
g al
ignm
ent w
ith th
e sh
ear f
ield
as t
he sh
ear r
ate
incr
ease
s
The
alig
nmen
t sho
ws u
p as
a
gene
raliz
ed b
irefri
ngen
ce in
th
e hi
gh sh
ear r
egio
ns o
f the
4-
roll
mill
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
153
Cellu
losic
thic
kene
rs: H
ydro
xypr
opyl
cellu
lose
HPC
SCC
SW
CH
APT
ER 1
118
Pol
ymer
s in
Cos
met
ics
154
•Deg
ree
of S
ubst
itutio
n (0
-3) a
nd M
olar
subs
titut
ion
•Non
ioni
c th
icke
ner
•She
ar-th
inni
ng R
heol
ogy
•Low
LC
ST (4
0C)
2-ph
ase
1-ph
ase
met
asta
ble
bino
dal
spin
odal
T max
and
Tmin
arise
from
chan
ge in
chai
n fle
xibi
lity
with
tem
pera
ture
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
155
The
Mas
ter C
urve
for R
elax
atio
n un
der
exte
nsio
nal f
low
for H
ydro
xypr
opyl
cellu
lose
Norm
alize
w.r.
t, De
bra
Num
ber
Stre
ss re
laxa
tion
time
=Ti
me
of o
bser
vatio
n
Belo
w Tp
Sam
e re
laxa
tion
proc
ess a
t diff
eren
t te
mps
.
Abov
e Tp
Diffe
rent
rela
xatio
n pr
oces
ses:
th
e cu
rves
do
not f
it on
a
singl
e m
aste
r cur
ve
Mas
ter c
urve
wrt
shea
r rat
e in
dica
tes s
ame
rela
xatio
n pr
oces
s at
diff
eren
t tem
pera
ture
s SC
C SW
CHA
PTER
111
8 P
olym
ers i
n Co
smet
ics15
6
Hyd
roxy
prop
ylce
llulo
se
The
hydr
odyn
amic
vo
lum
e de
crea
ses w
ith
T in
crea
se
(bel
ow T
p)i.e
. the
Kuh
n le
ngth
get
s sh
orte
r
Criti
cal s
train
rate
indi
cate
s co
il-ro
d tra
nsiti
on b
elow
Tp
Tran
sitio
n to
rod
alig
nmen
t i.e
. rod
s pre
sent
prio
r to
shea
r in
met
asta
ble
regi
on
In tw
o ph
ase
regi
on a
bove
Tp,
th
e ro
d al
ignm
ent i
s mor
e pr
omin
ent
The
criti
cal s
train
rate
in
crea
ses w
ith T
unt
il the
ph
ase
tran
sitio
n (K
uhn
Leng
th D
ecre
asin
g)
The
criti
cal s
train
rate
di
sapp
ears
at t
he b
inod
alte
mp
( the
pol
ymer
be
com
es ro
d-lik
e)
Bire
fring
ence
du
e to
coil-
rod
tran
sitio
n
durin
g ex
tens
ion
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
157
Coop
erat
ive
Tran
sitio
ns w
ith T
empe
ratu
re
kT/ε
0Va
n De
r W
aals
H-Bo
nd
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
158
Zipp
er m
odel
for t
he fo
rmat
ion
of ju
nctio
n zo
nes
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
159
Zipp
er m
odel
for t
he fo
rmat
ion
of ju
nctio
n zo
nes
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
160
Zipp
er m
odel
for t
he fo
rmat
ion
of ju
nctio
n zo
nes
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
161
K-CA
RRAG
EEN
AN
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
162
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
163
Carr
agee
nan
AFM
2-su
lfate
pr
even
ts
crys
talli
zatio
n of
the
doub
le
helic
es
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
164
Carr
agee
nan
–th
e ro
le o
f ion
s in
hier
arch
ical
stru
ctur
e fo
rmat
ion
•Ab
ility
to fo
rm g
els f
ollo
ws t
he se
quen
ce:
Thes
e se
em
to b
e sp
ecifi
c st
ruct
urin
g io
ns
Helix
form
atio
n ca
n be
follo
wed
by
mea
surin
g sp
ecifi
c op
tical
ro
tato
ry p
ower
Hyst
eres
is be
twee
n ge
lling
and
m
eltin
g –
aggr
egat
ion
of h
elice
s.
No h
yste
resis
/no
gel w
ith N
aCl–
but h
elice
s for
m!
Spec
ific
ion
effe
cts.
–se
e ne
xt
slide
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
165
Carr
agee
nan
–th
e ro
le o
f ion
s in
hier
arch
ical
stru
ctur
e fo
rmat
ion
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
166
Carr
agee
nan
–th
e ro
le o
f ion
s in
hier
arch
ical
stru
ctur
e fo
rmat
ion
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
167
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
POLY
ELEC
TRO
LYTE
S &
INTE
RACT
ION
BE
TWEE
N IO
NIC
ION
ASS
OCI
ATIO
N
PRO
PERT
IES
POLY
ELEC
TRO
LYTE
S &
INTE
RACT
ION
BE
TWEE
N IO
NIC
ION
ASS
OCI
ATIO
N
PRO
PERT
IES
168
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
PPoly
elec
trol
yte
Mod
elPo
lyel
ectr
olyt
e M
odel
Fuos
s, R.
M.;
Katc
halsk
y, A.
; Lifs
on, S
.; Pr
oc. N
at. A
cad
Sci.
1951
, 37,
579
Man
ning
, G.S
.; Q
uart
erly
Rev
iew
s of B
ioph
ysics
, 197
8, 2
, 179
Gao,
J.Y.;
Dub
in, P
.L.;
Sato
, T.;
Mor
ishim
a, Y.
; J. C
hrom
atog
raph
y, A;
199
7, 7
66,2
36
+--
____
____
__
____
__
_
__
__
___
__
___
+ +
+ +
+ +
+ + +
++
++
++
+
+ +
+ +
+ +
+ +
+
++
+
+ +
+ +
++
+ +
+ ++
++
+
+ +
+ +
+ +
+ +
+ +
+ +
+
+
+ + +
++
++
+
169
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
Coun
terio
nDi
strib
utio
nCo
unte
rion
Dist
ribut
ion +
++fre
e in
solu
tion
free
in so
lutio
n++
Donn
an
Equi
libriu
mDo
nnan
Eq
uilib
rium
Boun
d &
Hydr
ated
+
Boun
d &
Dehy
drat
ed
Oosa
wa,
F.; P
olye
lect
roly
tes,
Mar
cel D
ekke
r Co.
; NY.;
197
117
0
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
Poly
elec
trol
yte-
Coun
terio
n
Int
erac
tion
Poly
elec
trol
yte-
Coun
terio
n
Int
erac
tion
•Tw
o th
eorie
s:
•Ce
ll T
heor
y (P
oiss
on-B
oltz
man
n)
•M
anni
ng th
eory
(Co
unte
rion
Cond
ensa
tion)
171
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
Poiss
on-B
oltz
man
n M
odel
Poiss
on-B
oltz
man
n M
odel
+--
____
____
__
____
__
_
__
__
___
__
___
+ +
+ +
+ +
+ + +
++
++
++
+
+ +
+ +
+ +
+ +
+
++
+
+ +
+ +
++
+ +
+ ++
++
+
+ +
+ +
+ +
+ +
+ +
+ +
+
+
+ + +
++
++
+
l
ra
R
leng
th
infin
ite
172
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
Poiss
on-B
oltz
man
n M
odel
Poiss
on-B
oltz
man
n M
odel
•Inf
inite
ly lo
ng ro
d, ra
dius
‘a’
•med
ium
of c
onst
ant d
iele
ctric
•fixe
d po
lyio
nch
arge
spre
ad e
venl
y al
ong
the
rod
•cou
nter
ions
cont
aine
d w
ithin
a co
ncen
tric
cylin
der,
radi
us ‘R
’
•Inf
inite
ly lo
ng ro
d, ra
dius
‘a’
•med
ium
of c
onst
ant d
iele
ctric
•fixe
d po
lyio
nch
arge
spre
ad e
venl
y al
ong
the
rod
•cou
nter
ions
cont
aine
d w
ithin
a co
ncen
tric
cylin
der,
radi
us ‘R
’
173
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
Man
ning
The
ory
Man
ning
The
ory
belo
w
crit
belo
w
crit
174
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
Man
ning
The
ory
Man
ning
The
ory
abov
e cr
itab
ove
crit
free
free
boun
dbo
und
175
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
Man
ning
The
ory
Man
ning
The
ory
•Tw
o-st
ate
theo
ry
•co
unte
rions
free
or b
ound
•Dim
ensio
nles
s cha
rge
dens
ity is
redu
ced
to u
nity
by
coun
terio
nco
nden
satio
n
•
•Tw
o-st
ate
theo
ry
•co
unte
rions
free
or b
ound
•Dim
ensio
nles
s cha
rge
dens
ity is
redu
ced
to u
nity
by
coun
terio
nco
nden
satio
n
•kT
lzkT
lz
176
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
Man
ning
The
ory
Man
ning
The
ory
llcr
it=
crit
= z iz i
177
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
Man
ning
The
ory
Man
ning
The
ory
•For
vin
yl m
onom
er h
omop
olye
lect
roly
tes:
•l =
0.2
5nm
•P b
= 1-
(
)
•65%
of m
onov
alen
t ion
s con
dens
e•8
2% o
f div
alen
t ion
s con
dens
e
•For
vin
yl m
onom
er h
omop
olye
lect
roly
tes:
•l =
0.2
5nm
•P b
= 1-
(
)
•65%
of m
onov
alen
t ion
s con
dens
e•8
2% o
f div
alen
t ion
s con
dens
e
zz
178
Gel
/net
wor
k fo
rmat
ion
from
hel
ical
junc
tion
zone
sIn
ord
er to
from
a g
el, h
elica
l ‘ju
nctio
n zo
nes’
mus
t be
conn
ecte
d in
to a
effe
ctiv
e ne
twor
k; T
wo
poss
ible
ne
twor
k st
ruct
ures
are
show
n be
low.
Intr
amol
ecul
ar h
elice
s•
the
junc
tion
zone
is
form
ed b
y a
doub
le
helix
bet
wee
n tw
o ch
ains
;•
The
bran
chin
g is
form
ed a
t ‘ki
nks’
in
the
chai
n th
at ca
nnot
be
wou
nd in
to th
e he
lical
stru
ctur
e
Aggr
egat
ion
of fu
lly
deve
lope
d he
lices
•br
anch
ing
is fo
rmed
by
ben
ding
of t
he
helic
es to
form
ju
nctio
ns b
etw
een
the
aggr
egat
ed
‘junc
tion
zone
s’
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
179
Evid
ence
for G
ellin
g by
Hel
ix A
ggre
gatio
n
Non-
gel h
elica
l k-
carr
agee
nan
In 0
.3M
LiCl
0.3M
KCl
dial
yze
gelle
dk-
carr
agee
nan
Now
add
0.
3M Li
Cl
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
180
‘Sta
te D
iagr
am’ f
or
K-Ca
rrag
eena
nDe
grad
ed k
-ca
rrag
eena
n
Inta
ct k
-ca
rrag
eena
n
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
181
Note
the
shar
p di
vidi
ng li
ne a
t xC
s:Na
= 0.
4Do
es th
is im
ply
spec
ific b
indi
ng?
Spec
ific
site
bin
ding
of
ions
on
K-Ca
rrag
eena
n?
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
182
Spec
ific
site
bin
ding
of
ions
on
K-Ca
rrag
eena
n?
Cf12
.7kJ
/mol
for n
on-s
pecif
ic sa
lts
Use
Poiss
on-B
oltz
man
n Ce
ll th
eory
and
law
of
Mas
s Act
ion
to ca
lcula
te
the
chem
ical p
oten
tial o
f po
lyio
nsfre
e an
d bo
und
to co
il an
d he
lix–
calcu
late
the
enth
alpy
an
d en
trop
ies o
f bin
ding
SC
C SW
CHA
PTER
111
8 P
olym
ers i
n Co
smet
ics18
3
Spec
ific
site
bin
ding
of
ions
on
K-Ca
rrag
eena
n?
Cf12
.7kJ
/mol
for n
on-s
pecif
ic sa
lts
The
OH
grou
ps o
n k-
Carr
agee
nan
are
not w
ell
conf
igur
ed to
com
plex
with
the
coun
terio
ns–
How
ever
, in
a do
uble
-hel
ical c
onfo
rmat
ion,
the
OH
grou
ps w
ould
be
conf
igur
ed c
orre
ctly
and
the
doub
le h
elica
l con
form
atio
n w
ould
be
stiff
.
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
184
Conc
lude
that
ag
greg
atio
n (a
nd g
ellin
g)
is ca
used
by
spec
ific
bind
ing
of io
ns to
the
asse
mbl
ed h
elix
( ra
ther
th
an to
the
coil)
Zipp
er M
odel
Algi
nate
s and
Pec
tin
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
185
Algi
nate
s
•Ex
opol
ysac
char
ides
ext
ract
ed fr
om b
row
n se
awee
ds a
nd so
me
bact
eria
•Lin
ear b
lock
copo
lym
ers o
f man
nuro
nate
and
gulu
rona
telin
ked
with
alte
rnat
ing
resid
ues
•Bi
osyn
thes
is Pa
thw
ay•
Man
nuro
nan
is po
lym
erize
d an
d th
en p
ost-m
odifi
ed b
y ep
imer
ase
enzy
mes
whi
ch co
nver
t m
annu
rona
teto
gul
uron
ate
•Ep
imer
ase
enzy
mes
are
now
bei
ng u
sed
indu
stria
lly to
crea
te a
lgin
ates
with
opt
imum
pro
pert
ies
for s
pecif
ic a
pplic
atio
ns.
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
186
Algi
nate
s•T
he g
ulur
onat
ere
sidue
s sel
ectiv
ely
bind
alk
alin
e ea
rth
met
als
•The
egg
-box
mod
el*:
•Th
e G-
bloc
ks fo
rm a
2/1
hel
ical c
onfo
rmat
ion
and
diva
lent
catio
nsar
e co
ordi
nate
d w
ithin
the
cavi
ties f
orm
ed th
ereb
y•
The
‘egg
-box
’ dim
er se
quen
ces a
ssoc
iate
late
rally
•To
form
junc
tion
zone
s
*SC
C SW
CHA
PTER
111
8 P
olym
ers i
n Co
smet
ics18
7
Algi
nate
s
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
188
Algi
nate
s
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
189
Algi
nate
s
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
190
Algi
nate
s
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
191
Pect
ins
•Pec
tin is
com
pose
d of
long
se
quen
ces o
f par
tially
met
hyl
este
rifie
d (1
-4)-l
inke
d α-
D-gl
actu
rona
tere
sidue
s•G
alac
turo
nate
is st
ruct
ural
ly th
e m
irror
imag
e of
gul
uron
ate
•The
refo
re, s
imila
r egg
-box
st
ruct
ures
to a
lgin
ate
may
be
expe
cted
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
192
Pect
insc
.f.Al
gina
tes
Sim
ilar i
nitia
l bi
ndin
gSe
cond
ary
bind
ing
(egg
-box
) is m
uch
mor
e en
erge
tical
ly
favo
rabl
e fo
r al
gina
te
(gul
uron
ate)
than
fo
r pec
tin
(gal
actu
rona
te)
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
193
Pect
insc
.f.Al
gina
tes
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
194
Chai
n St
iffne
ss o
f Pol
ysac
char
ides
1: g
lucu
rona
n, 2
: man
nuro
nan,
3: g
ulur
onan
, 4: g
alac
turo
nan.
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
195
Mod
elin
g G
elat
ion
of A
lgin
ates
The
antip
aral
lel c
hain
pai
ring
gave
rise
to a
n ef
ficie
nt h
ydro
gen
bond
net
wor
k w
ith tw
o co
mpl
emen
tary
hyd
roge
n bo
nds:
O2â
ââO
6, 2
.73
Å (2
.88
Å), a
nd O
3âââ
O5,
2.8
7 Å
(2.9
1 Å)
. It a
lso p
rovi
ded
a un
ique
per
iodi
c ch
elat
ion
site
for c
alciu
m io
ns.
It is
not p
ossib
le to
disc
rimin
ate
betw
een
the
two
form
s of t
hese
chai
n pa
iring
s bas
ed o
n to
tal
ener
gy; h
owev
er, t
he a
ntip
aral
lel a
rran
gem
ent i
s pr
obab
ly fa
vore
d in
the
gel s
ince
it h
as b
een
repo
rted
that
ure
a su
bsta
ntia
lly w
eake
ns th
e ge
l.Th
e sh
ape
of th
is st
ruct
ure
is c
lose
to th
at o
f the
pop
ular
“eg
g bo
x m
odel
”.
Cal
cium
coo
rdin
atio
n: o
nly
four
liga
nds f
rom
the
chai
ns, O
2 an
d O
6 of
bot
h ch
ains
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
196
Mod
elin
g G
elat
ion
of P
ectin
sirr
espe
ctiv
e of
the
helic
al fo
rm, t
he a
ntip
aral
lel
arra
ngem
ent w
as th
e m
ost f
avor
able
one
.
this
bes
t ant
ipar
alle
l ass
ocia
tion
is si
mila
r to
the
“egg
box
stru
ctur
e”.
But
……
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
197
Mod
elin
g G
elat
ion
of A
lgin
ates
and
Pec
tins
For P
ecta
te, t
he c
aviti
es fo
rmed
by
the
join
ed c
hain
s do
not
have
the
prop
er si
ze fo
r cal
cium
ions
; the
y ar
e fa
r too
larg
e (F
igur
e 6b
).
The
pres
ent c
alcu
latio
ns c
lear
ly d
emon
strat
e th
at th
e “e
gg b
ox
mod
el”
cann
ot c
orre
spon
d to
the
pairw
ise
asso
ciat
ions
of
pect
ate
chai
ns th
at fo
rm th
e ju
nctio
n zo
nes i
n ca
lciu
m p
ecta
tege
ls.
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
198
SCC
SW C
HAPT
ER 1
118
Pol
ymer
s in
Cosm
etics
199
CaBE
REx
tens
iona
l Rhe
omet
er
http
://w
ww.
cam
poly.
com
/file
s/81
13/5
216/
6124
/CaB
ER.p
dfSC
C SW
CHA
PTER
111
8 P
olym
ers i
n Co
smet
ics20
0
