Advances in Chemical Engineering and Science, 2012, 2, 435-443
http://dx.doi.org/10.4236/aces.2012.24053 Published Online October 2012 (http://www.SciRP.org/journal/aces)
Effects of Side-Chain on Conformational Characteristics of
Poly(3,5-Dimethyl-Phenyl-Acrylate) in Toluene at 40˚C
Nasrollah Hamidi1*, Stanley Ihekweazu2, Christopher A. Wiredu3, Onize H. Isa4,
Kevin Watley4, Christopher Rowe3, Briante’ Nimmons3, Alexis Prezzy4,5,
Shane Scoville4, Quentin Hills4,5, Judith Salley1
1Department of Biological and Physical Sciences, South Carolina State University, Orangeburg, SC, USA
2Department of Civil and Mechanical Engineering Technology, South Carolina State University, Orangeburg, SC, USA
3North High School, North, SC, USA
4Orangeburg Wilkinson High School, Orangeburg, SC, USA
5Claflin University, Orangeburg, SC, USA
Email: *Nhamidi@scsu.edu
Received August 11, 2012; revised September 13, 2012; accepted September 22, 2012
ABSTRACT
The intrinsic viscosity [η] of poly(3,5-dimethyl-phenyl-acrylate) (35PDMPA) solutions were evaluated throughout the
measurements of the flow times of toluene and polymer solutions by classical Huggins, and Kraemer’s methods using a
Cannon-Ubbelohde semi-micro-dilution capillary viscometer in a Cannon thermostated water bath at 40˚C ± 0.02˚C.
The values of Huggins’ constant estimated ranged from 0.2 to 0.4 which were within expectations. The intrinsic viscosities
and molecular weight relationship was established with the two-parameter classical models of Staudinger-Mark-Houwink-
Sakurada and Stockmayer-Fixman. Conformational parameter C and σ indicated 35PDMPA be semi flexible. Also, the
rigidity of 35PDMPA was confirmed by Yamakawa-Fuji wormlike theory modified by Bohdanecký. The molecular
parameters were estimated and compared. The results showed that 35PDMPA behaves like a semi-rigid polymer in
toluene at 40˚C rather than a random coil flexible macromolecule.
Keywords: Intrinsic Viscosity; Poly(3,5-Dimethyl-Phenyl-Acrylate); Conformational Parameters; Rigidity Factor;
Kuhn Statistical Length
1. Introduction
The influence of temperature and side chain groups on
the physical properties of polyethylene chains is well
documented [1]. In the case of polyacrylates, interests
have focused on the changes induced by altering the
length of alkyl ester group [2] or identity of the ester
linkage such as phenyl with alkyl substituent in various
positions [3]. One way to evaluate and analyze the prop-
erties of such polymers is at least to correlate the depend-
ence of their equilibrium configuration to their structure.
Among the methods of evaluating configurational prop-
erties are the application of matrix methods in the form
of rotational isomeric state (RIS) model to calculate
conformational properties such as Flory’s characteristic
ratio (C) [4] and or application of the wormlike model
based on Yamakawa-Fujiitheory [5] and its simplified
form byBohdanecký [6]. Neither the RIS nor the worm-
like model has been applied to evaluate the influence of
side chain on unperturbed dimensions of 35PDMPA. This
paper presents experimental findings pertaining to dilute
solution properties of 35PDMPA in toluene at 40˚C.
The intrinsic viscosity of a macromolecule in a dilute
solution is a measure of its hydrodynamic average size,
form, and shape in the solution. Many studies were found
that explored the empirical relationships between coil
dimensions of synthetic polymers with their intrinsic
viscosity [1-7]. The most frequently used relationship
between intrinsic viscosity, [η], and the weight-average
molecularmass, Mw, is the Mark-Houwink-Kuhn-Saku-
rada (MH) Equation:
w
K
M; (1)
where, the parameter α is a measure of the thermody-
namic power of solvent and Kα is a measure of coil vol-
ume for an unperturbed condition or ideal solvent called
θ-condition for random coil polymers. Numerous re-
searchers [1-8] have demonstrated the validity of the MH
equation applied to random coiled polymers for molecu-
lar weights ranging in several orders of magnitude. By
increasing thermodynamic strengths of solvents, the
magnitude of coefficient α would increase while the
magnitude of Kα would decrease. Generally, for the ran-
*Corresponding author.
C
opyright © 2012 SciRes. ACES
N. HAMIDI ET AL.
436
dom coil flexible polymer molecules, the value of α
would be between 0.50 and 0.80. For non-flexible and
rigid (worm-like or rod-like) macromolecules higher
values of α larger than or equal to unity have been ob-
served. Thus, the numerical value of α provides informa-
tion concerning polymer conformation as well.
In this work, the viscosity of 35PDMPA samples are
treated according to the Huggins’ [9] and Kraemer’s [10]
relationship to evaluate the intrinsic viscosity of the
polymer samples; the constant of each method has been
determined and related to the nature of the polymer sol-
vent system. The intrinsic viscosity, in conjunction with
the molecular mass data of 35PDMPA solutions, is
treated according to the theories of intrinsic viscosity of
random flexible and worm-like polymers developed by
Yamakawa-Fuji and simplified by Bohdanecký.
2. Experimental
2.1. Monomer
3,5-dimethyl-phenyl-acrylate (35DMPA) was obtained
by the reaction of corresponding phenol and acryloyl
chlorideat low temperature (in an ice bath)using triethyl-
amineas a base to trap HCl produced and hexanes as sol-
vent (Scheme 1). Acryloly chloride and 3,5-dimethyl-
phenol are slightly soluble in hexanes but 35DMPA is
miscible in hexanes. It was purified by re-distillation
under reduced pressure (~7 torr). The monomer was
characterized by NMR and IR.
CH3
CH3
OH O
Cl CH3
CH3
OO
+
Scheme 1. Reaction of preparing the monomer.
2.2. Polymer
Poly(3,5-dimethy-phenyl-acrylate), (35PDMPA) was syn-
thesized by bulk polymerization of 35DMPA under ni-
trogen atmosphere in a sealed flask using 2,2'-azo-bis-
iso-butyro-nitrile (~0.02 % of monomer) as the radical
initiator at 333 K (Scheme 2). The obtained polymer
dissolved in dichloromethane, re-precipitated in hexanes
three times, and deride under vacuum (~2 torr) at 298 K.
The sample was fractionated using dilute (~1%) toluene
solution with hexanes as precipitants [11].
CH3
CH3
O
O
CH3
CH3
O
O
[ ]n

Scheme 2. Reaction of preparing the monomer.
2.3. Molecular Mass Characterizations
To estimate molar mass of 35PDMPA two methods were
used: absolute method, light-scattering and relative me-
thod, size exclusions. Absolute methods are classified by
the type of average they yield such as colligative tech-
niques, for example, membrane osmometry measures
number average, light scattering yields weight average,
and ultracentrifuge determines z-average molar mass.
The absolute methods require extrapolation to infinite
dilution for rigorous fulfillment of the requirements of
theory. Relative methods require calibration with the
samples of known molar masses and include viscosity,
vapor pressure osmometry and size exclusion chroma-
tography (SEC) [12-14].
AViscotek GPCMAX 303 with a two angle light scat-
tering detector, a refractive index detector, and two Vis-
cotek universal bed size exclusion columns, all housed in
a thermo stated oven at 30˚C was used to evaluate weight
average (Mw), number average (Mn), and polydispersity
of the samples [15].
2.4. Viscosity Measurements
The intrinsic viscosity of a polymeric solution is defined
as
11
10
0
1
10
ln( /)
lim lim
lim
sp
C
C
CC
C
 




 





(2)
Applying the virial series the two equivalent forms
known as the Huggins and Kraemer relationships
rounded at second term applied to diluted polymer solu-
tions:
 
2
1
1
H
kC
C
 



 (3)
 
2
1
ln
K
kC
C
 



 (4)
where η1, is the viscosity of the pure solvent, and η is the
viscosity of the solution at zero shear conditions. Table 1
shows the values of [η], kH and kK + kH solutions of
35DMPA in toluene at 40˚C [16].
The dilute solution viscosities were measured with a
semi-micro Cannon-Ubbelohde capillary dilution vis-
cometer, thermostated in a water bath at 40˚C (313.2 ±
0.02 K) where solvent flow times (t1) were at least 110 s.
Linear least-squares fit of specific viscosity and inherent
viscosities versus concentration were used to obtain the
intrinsic viscosity as a common intercept. Figure 1
shows the plot of viscosity number versus concretization
for eleven samples of polymer.
Copyright © 2012 SciRes. ACES
N. HAMIDI ET AL. 437
Table 1. Values of intrinsic viscosity [η], kH, and kH + kK of
35PDMPA in toluene at 40˚C.
Sample kH <[η]> kH + kK
F1 0.407 282.9 0.525
F2 0.312 272.6 0.457
F3 0.388 192.0 0.516
F4 0.267 183.8 0.438
F5 0.308 174.9 0.465
F6 0.272 139.2 0.451
F7 0.389 107.1 0.519
F8 0.237 87.63 0.454
F9 0.377 63.41 0.511
F10 0.27 43.45 0.482
F11 0.364 26.60 0.502
50
100
150
200
250
300
350
400
450
500
00
ViscosityNumberorInherentViscosity(mLg
–1
)
C
.005
(gmL
–1
)
F1
F2
F3
F4
F5
F6
F7
F8
F9
25
26
27
28
29
0.006
20
30
40
50
00.002 0.004
C(gmL–1)
F10 F11
Figure 1. Estimation of limiting viscosity number by plot of
variation of viscosity number (t t1)/ct1 versus concentra-
tion of samples of 35PDMPA in toluene at 313.15 K.
3. Results and Discussion
Figure 1 shows the variation of (t t1)/t1C and (Ln
t/t1)/C versus C (g/mL); the data fit well into a straight
line with a common intercept which is the value of in-
trinsic viscosity and from the slopes Huggins’ (kH) and
Kraemer’s (kK) constants were estimated.
3.1. Huggins (kH) and Kraemer (kK) Constants
The values of Huggins’ constant kH can be used as an
index to describe polymer solvent and polymer-polymer
interactions [17,18]. For flexible, linear, nonpolar or not
very polar vinyl polymers in good solvents the values of
kH usually lie between 0.3 to 0.4. The values of kH for
35PDMPA and toluene solution range 0.27 - 0.41 which
are within the expected scope. Figure 2 shows the varia-
tion of kH and kK versus molar mass of polymer. The val-
ues are scattered from 0.27 to 0.41. The list square fitted
to the data shows a positive slope: as molar mass in-
creasing the kH also increases.
The equality of Equations (2) and (3) demands that the
kH + kK = 1/2, which has been confirmed in this work.
3.2. The Intrinsic Viscosity and Molar Mass
Figure 3 shows the double logarithmic graph of intrinsic
viscosity and molar mass at 40˚C. The molecular weight
dependence of [η] are expressed in the values of Kα and α
of MH. Several factors contribute to enhance the expo-
nent α. [19]. Among them are: 1) chain stiffness, 2) ex-
cluded volume, and 3) partial drainage. It is universally
accepted that the value of α that corresponds to a nond-
raining coil unperturbed by the excluded volume effect is
0.5; this does not include the low-molecular mass region
[17], and temperatures under theta condition where the
values of α are found to be less than 0.5. Besides the
above mentioned parameters, the chain thickness is the
only contributing factor that reduces the value of α in the
limit of molecules having thickness equal to length
(sphere), α = 0.
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
050100 150 200 250
K
Mw x10000
kH kK
Figure 2. Variation of Huggins’ and Kreamer’s constatants
versus viscosity number.
Copyright © 2012 SciRes. ACES
N. HAMIDI ET AL.
438
3.0
4.0
5.0
11 12 13
LN[]
LN(Mw) 14 15
Figure 3. Double logaritmic graph of intrinsic viscosity and
molar mass of 35PDMPA in toluene at 40˚C.
Figure 3 shows the treatment of viscosity data in the
light of MH double logarithmic plot. The Kα and α of the
plot are summarized in Table 2. According to the values
of Table 2, the solvation capacity of toluene increases as
temperature increases from 25˚C to 40˚C.
3.3. Unperturbed Dimensions
The unperturbed dimensions of a linear flexible polymer
are obtained either by light scattering over an angular
range or dilute solution viscometric of macromolecules
in ideal solvent so called Θ-conditions. The square of
end-to-end dimensions 2
R00 for a random distribution
of n particle with bond length of l is expressed as nl2.The
expansion of a covalently bonded polymer chain is re-
stricted by valence angles θ between each chain atom,
2
R00 modified to allow for short-range interactions
called 2
0
f
R:


22
0
1cos
1cos
f
Rnl
(5)
For C-C backbone polymers such as 35PDMPAlthe
bond length is 1.54 Å, and n is the total number of back-
bone bonds. For the simplest case of an all carbon back-
bone chain such as polyethylene, cos(109.5) ~ –1/3 so
that the Equation (5) becomes


22
0
1 cos
1 cos1
f
Rnl
2
109.5 2
09.5 nl
(6)
This indicates that the polyethylene chain is twice as
extended as the freely jointed chain model when the
short-range interactions are considered. In fact, in butane
and carbon chains with more atoms, steric repulsions
impose restrictions to bond rotations [20]. This feature in
Equation (6) causes further modifications:




22
1c
os
1cos
o
Rnl 1cos
1c
os
(7)
where cos
is the average cosine of the angle of ro-
tation of the bonds in the backbone chain. The parameter
Table 2. The slopes and intercepts, Kα and α, of the double
logarithmic plot of [η] and Mw in toluene at 25˚C and 40˚C.
t˚C Kα α
40 0.0320 0.612
25 0.0472 0.5894
2
R
of o is the average mean square of the unperturbed
dimension, which is the main characteristic parameter of
a polymeric chain.
For a 35PDMPA chain, the unperturbed dimension
may be obtained directly from the intercept of the MH
plot, Kθ, in an ideal solution. The Kθ is related to the un-
perturbed dimension of the polymer as:
32
2
0
0
R
KM


 

(8)
where Φ0 is the Flory universal constant; it depends on
molecular mass of the polymer and the type of polymer
with the best experimental value of 2.51 × 1023 to 2.87 ×
1023 when the intrinsic viscosity is expressed in mL/g [21].
3.4. Unperturbed Dimension by Stockmayer-
Fixman Method
The unperturbed dimensions of a polymer in a thermo-
dynamically good solvent usually are estimated by ex-
trapolation methods using a number of plots based on
theoretical or semi-theoretical equations developed for
this purpose, for example, applications of the excluded
volume equations between the molecular weight and in-
trinsic viscosities in good solvents. Stockmayer-Fixman
(SF) proposed one such relationship for treating data
covering the usual range of molecular weights encoun-
tered in experiments.
12 12
0
0.51
M
KBM
 
(9)
The constant Kθ is the intercept; it is equal to the KMH
at the theta conditions [22]. The plot of
12
M
against
12
w according to the Equation (9) for 35PDMPA in
toluene illustrated in Figure 4. The value of Kθ in toluene
at 40˚C was estimated by fitting a straight line into a data
point using the least square method. These findings are
summarized in Table 3 for 35PDMPA at 25˚C, and 40˚C.
As can be seen, the values of Kθ decreased as the tem-
perature increased and the quality of solvent improved.
This was not within expectations.
M
12
M
w
Based on Equation (9) the plot of versus
M1/2 should be linear only for long enough chains (n >
103) where the function of excluded volume z approaches
its limit. As Figure 4 shows the two low-molecular-
weight samples did not meet these conditions since their
n < 1000. Thus, precaution is necessary to evaluate di-
mensional parameters based on SF under these condi-
tions. For ideal solvent, the slope of the SF equation must
Copyright © 2012 SciRes. ACES
N. HAMIDI ET AL. 439
0.08
0.11
0.14
0500 1000
[]Mw
–1
Mw
1/2
1
222
00f
RR
1500
Figure 4. Stockmayer-Fixman plot, Equation (9), for
35PDMPA in toluene at 40˚C.
Table 3. Values of Kθ,

12
2
0
RM , σ and C from SF plot
and Bohdaneck ý.
Method Kθ

12
2
0
RM
s C
SF 25˚ 0.122 0.783 3.37 22.78
SF 40˚ 0.109 0.753 3.25 21.08
H-Mw 40˚ 0.124 0.786 3.39 22.98
At M 0.170 0.875 3.77 28.44
Bohdaneck ý 0.171 0.877 3.78 28.56
be zero. In a good solvent such as toluene, the slope is
positive. Two different factors may contribute in deter-
mining a high value of Kθ for a polymeric chain such as
35PDMPA: the nature of the main chain and the effects
of side chains and solvent. In the case of 35PDMPA, the
nature of the main chain, which is composed of a simple
hydrocarbon chain, may not contribute to the Kθ as the
hindered voluminous side phenyl ester groups. The
3,5-dimethyl-phenyl lateral chains occupy a large volume
and hinder the backbone internal rotations by establish-
ing orientational correlations between themselves.
3.5. Evaluation of Conformational
Characteristics
Reliable values of the characteristic parameters of the
conformation and flexibility of polymer chains such as
Flory characteristic ratio C, steric factor σ, and Kuhn
statistical segment length lK are needed for the interpreta-
tion of various properties, including the rheological be-
havior of melts. The conformation of 35PDMPA chains
currently can be characterized by the Flory characteristic
ratio C or the steric factor σ. The latter two quantities
are defined by the Equations (10) and (12). For more
complex chains, such as 35PDMPA containing ring and
heteroatom, an estimated σ is obtained from
(10)
The mean square unperturbed end-to-end distance,
2
R0 can be obtained experimentally from the value of
Kθ, Equation (8), which is related to the rigidity factor σ,
or to the characteristic ratio C, by the expression
12 13
212
00
20
02
f
RKM
l
R











(11)
23
2
00
2
20
00 2
R
K
M
Cl
R



 (12)
where M0 is the molecular mass of the monomer. The
values of σ and C based on Equations (11) and (12) are
also tabulated in the Table 3.
3.6. Wormlike Cylinder
Another method of evaluation of the characteristic pa-
rameters of 35PDMPA is by the theory for the worm-like
touched-bead model [23,24]. Based on this theory, the
intrinsic viscosity at theta condition depends not only on
the unperturbed mean-square end-to-end distance 2
R0,
but also on the cross-sectional dimensions of polymer-
called the diameter of the bead, db, the small units that
compose the macromolecule. The results of the theory
have been expressed in a simple form convenient for use
even with very short chains by Bohdaneck ý [25]
12
0
0
A
KM

 (13)
32
2
00,0
KRM

with: (14)
12
00brk
A
KAd M
 (15)
brb K
ddl (16)
2
0
K
L
lRMM
(17)
1
M
K
KL
lM (18)
2
0
RM 2
0
R is the ratio of and M is the random
coil limit, and Φ0, is the Flory viscosity constant for
random coils in the non-draining regime, A0(dbr) is a
function of the reduced bead diameter dbr, db is the bead
diameter, lK and MK are, respectively, the length and mo-
lecular weight of the Kuhn statistical segment, and ML is
the shift factor which is usually set equal to the molecu-
lar weight per unit contour length of the chain at full ex-
tension. One of the simplest forms of description of mo-
lecular-weight dependence of the intrinsic viscosity in
good solvents by theoretical and semi-empirical equa-
1LK 2q λ–1.
Copyright © 2012 SciRes. ACES
N. HAMIDI ET AL.
440
tions is [26]

1K
Cn z
31.5
3
3
0

 (19)
This is valid for only [27]. It is used here
because most of the
values are in this range. The
symbol αη stands for the viscosity-radius expansion fac-
tor, nK is the number of Kuhn segments in the chain, z is
the excluded-volume variable and B reflects the poly-
mer–solvent interaction.
32
2
12
zB
M




32 0
3
2π
R
M


 (20)
The impact of chain stiffness on the onset of the ex-
cluded-volume effect becomes manifested in the chain-
length dependence of the coefficient Cη(nK) [28-32]. This
function is not known. In practice, it is usually replaced
by the function (3/4). CηK(nK) where K(nK) was derived
by Yamakawa and Stockmayer [12] from the expansion
factor 222
0
RR
R
. This function is approximated
by the equations:


1
0.875 K
12
4 312.033
KK
K
nn n

for nK > 6 (21A)

12 1
exp 6.6110.9198
KKK 0.03516 K
K
nn n


n




Cź
 
for nK < 6 (21B)
Then, Equation (19) can be modified to
31
(22)
where ź is the scaled excluded-volume variable [24,25]

34 K
ź
K
nz

1.14C

(23A)
(23B)
Combining Equations (13), (19), (20), (22) and (23),
yields:




3
2
12
33
42π
C
 
 
 
12
0
32
2
0
1
K
AKM
RKn BM
M

 





(24A)


(24B)2



3
0K
K
322
20
3
322
20
12
0
33
42π
33
42π
R
A
AC M
R
KnBK
M
KC M


 

  

 









KnBM






12 6
15.640.16205.691 10
M
M
  (24C)
Therefore, the interpretation of the intrinsic viscosity
of 35PDMPA requires estimation of three characteristic
parameters: cross sectional chain diameter, Aη, flexibility
of the chain, K0, and polymer–solvent interaction, B.
Polynomial regression of [η] and 12
M
in Figure 5
results in Equation (24C). By comparing Equations (24B)
and (24C) we get:
15.6A
(25A)
 
3
322
20
0
33 0.162
42πK
R
AC KnBK
M


 


 

 

(25B)
 
3
322
20
0
33 5.69E 6
42πK
R
KC KnB
M

 


 

 

00.1625K
(25C)
(25D)
 
3
322
20
33 6.45E3
42πK
R
CKnB
M

 


 

 

(25E)
3.6.1. Application of Equation (24) by Plotting
[η] vs 12
M
Equation (24) shows that the plot of [η] vs 12
M
should
be linear over the whole range of molecular weights in
theta solvents where B = 0. In good solvents where B > 0,
linearity is restricted to a region where the term

32
2
0
K
BR MKn
is very low, such as in the case
of 35PDMPA in toluene at 40˚C. This implies alsothat
the ratio
2
0
RM
is very high which is the case of
stiff chains. Moreover, Equation (24) will be linear
where K(nK) ~ 0 represents short chains for both flexible
and stiff polymers. At higher molecular weights the plot
becomes curved upward as the function K(nK) and the
value of z increases with increasing M.
Toluene at 40˚C is not a theta solvent, therefore B 0.
In good solvents where B > 0, linearity is restricted to the
condition that the term

32
2
0K
BRM Kn

is very
2


3
322
2012 12
0
3
322
20
12
0
3
34 2π
3
34.
2π
K
K
R
A
AC KnBMKM
M
R
KMCK nBM
M
 


 













Copyright © 2012 SciRes. ACES
N. HAMIDI ET AL. 441
y=0.173x‐ 19.77
=0.999
y=5.691E06x
2
+1.620E01x
1.564E+01
=9.992E01
20
30
80
130
180
230
280
330
05001000 1500 2000
[](cm
3
g
–1
)
Mw
1/2
Figure 5. Plot of [η] versus Mw1/2 for 35PDMPA in toluene
at 40˚C.
low such as in the case of 35PDMPA in toluene at 40˚C,
Equation (24E). In this case, the ratio
2
0
RM
is
very high which represent stiff chains. Since 35PDMPA
is composed of the unit -CH2-CHR- the backbone of the
polymer does not introduce rigidity. Then the rigidity
must be caused by the side chains effects. Hence, the
excluded-volume effect also is not negligible with the
lowest molecular weights.
As Figure 5 shows, also, the plot of [η] vs 12
Mw for
35PDMPA homologues series fits to a straight line with
r2 = 0.9986.
112
0.1729 w
2
019.663AKM
M
  (26A)
32 0.173M
2
00
, 0
KF R
(26B)
The value of Kθ calculated in this manner is only 6.4%
higher than the former polynomial adjustment. Table 4
summarizes the molecular parameters of 35PDMPA in
toluene at 40˚C. The molecular weight of the Kuhn sta-
tistical segment MK is about 15 times higher than that of
the chain repeating unit. This is an indication of chain
stiffness of the 35DMPA in toluene at 40˚C.
Most of the vinyl polymers and derivatives of poly
(acrylic acid) and poly (methacrylic acid) with various
side groups showed the proportionality of [η] and 12
M
over a broad span of molecular weights as reported in
reference [25]. However, they do not show semi-rigid
characteristics as in the case of 35PDMPA. In the case of
35PDMPA, large size side chains increases the cross-
sectional chain diameter and the orientation of side chains
produce a high impediment around the polymer chain.
To verify the value of Kθ, a plot of
12
w
M
vs
12
M
w such as shown in Figure 6 will be useful. The
intercept of the plot Kθ, = 0.170 obtained at infinite Mw.
Table 4. Characteristics parameters of 35PDMPA. Data of
other polymer also is gathering to compare PHE [25] and
PDiPF [24].
Polymer 35PDMPA PHE PDiPF
Characteristics LinealPolynom Ref 25 Ref 24
ML (cm) × 10–8 57 57 20 134
K0 (cm) 0.173 0.163 0.150 -
2
0
R
M × 1016 0.782 0.751 0.711 -
lK (cm) × 10–8 45 43 14 220
MK 2560 2456 278 29,480
Mk/M0 15 14 1 294
-A 19.77 15.64 0.000 -
-A0 2.259 1.942 0.000 -
dbr 0.120 0.179 0.540 -
db (cm) × 108 5.36 7.68 7.60 14.00
0.1
0.13
0.16
00.001 0.002 0.003 0.004
[]Mw
–1 /2
(Mw)
–1 /2
Figure 6. Plot of [η]/Mw–1/2 versus M–1/2. Extrapolation to
infant Mw gave account for Kθ,.
Kθ, is very close to the value of the slope of [η] and
12
M
02.95.36 br
w
According to the Yoshizaki-Nitta-Yamakawa theory
[23], the hydrodynamic interaction depends on the re-
duced bead diameter dbr which, in the range 0.3 dbr
0.8, is related to the A0 parameter by [33]
which is the value of K0, of Equation (26B).
A
d (27)

Table 4 shows the characteristic parameters of
35PDMPA. Also, for the sake of comparison, character-
istics parameter of a very flexible chain such as bisphe-
nol-A based poly(hydroxyethers) (PHE) from reference
[25] and an stiff polymer, Poly(disopropylfumarate),
(PDiPF) from reference [24] are sited. The high values of
lK and MK of 35PDMPA suggests a semi flexible mac-
romolecule.
3.6.2. Comments on 12
M
vs 12
M
(SF) plot [34,35]
12
w
M
Based on Equation (24), the plot of versus
Copyright © 2012 SciRes. ACES
N. HAMIDI ET AL.
442
12
M
should be linear only for long enough chains (n <
103) where the absolute value of Aη is much lower than
12
K
0w
M and the function K(nK) approaches its limit. As
Figure 4 illustrates the two low-molecular-weight sam-
ples are not met in this condition. Thus precaution is nec-
essary to evaluate dimensional parameters based on BSF.
In the case of Aη = 0, the BSF plot can be modified to
12
M
vs

12
Kn M
K which should be linear and
can be extrapolated to M = 0. This, however, is not the
case of 35PDMPA in toluene that has a negative Aη value.
If Aη is not equal to zero, both the original and modified
SF plots are non-linear as shown in Figure 4. They can
have a minimum if Aη > 0 or bend downward with de-
creasing molecular weight if Aη < 0 (such asin the case of
35PDMPA, Figure 4). In either case, the extrapolation to
M = 0 based on BSF is not justified [36].
3.7. Conclusions and Remarks
As previously mentioned, the nature of the main chain of
a 35PDMPA polymer may not contribute to the high
value of C and σ as much as the 3,5-dimethyl-phenyl
ester side chains. The 3,5-dimethyl-phenyl lateral chains
occupy a larger volume (thus posing steric hindrances)
and more importantly, they may hinder the backbone
internal rotations by establishing orientational correla-
tions between themselves. The stiffening of the polymer
chain due to the presence of large aromatic groups and
long n-alkyl pendant groups has already been reported
for some other polymers by several researchers. Also, it
is known that the interaction of elements of polymer
chains with solvent molecules could affect the probabil-
ity distribution of the angles of internal rotation in the
chain [37]. This observation was confirmed both theo-
retically and experimentally by a number of researchers
[38,39] and here is confirmed by application of wormlike
cylinder model.
The values of C of 35PDMPA (21 - 23) are much
higher than values observed for other polyacrylates. For
example, the value of C for polyphenylmethacrylate,
PPMA, both theta solvents and good solvents (12.2 and
13.3) are larger than ones for many atactic vinyl polymers,
which are in the range of 5 < C <10 usually found in the
literature. It should also be remarked that the value of C
in good solvents probably has been underestimated as
they were obtained by extrapolating to M = 0 the mo-
lecular weight region of the Stockmayer-Fixman plot in
which the effect of stiffness is coupled with excluded
volume. And, also, it is overestimated by extrapolation to
M = . However, chain rigidity may be contributing to
the slope so that the results obtained for Kθ and C could
be inaccurate. An indication that the positive slope in this
plot may include the effect of chain stiffness comes from
the convergent trend observed in the curves at high mo-
lecular weights. This leveling of the slope cannot be ac-
counted for by the theory of flexible coils perturbed by
excluded volume but has been predicted by wormlike
models of stiff chains.
The value of C of 35PDMPA (29) obtained by ex-
trapolating to M = using SFthe molecular weight region
in which the effect of excluded volume levels is much
higher than values observed for the same polymer by SF
extrapolation to M = 0. The same effect was observed for
other polymers. An example is polyphenylmethacrylate,
PPMA, both theta solvents and good solvents.
4. Acknowledgements
We appreciate the financial support of 1890 Research at
South Carolina State University, and the U.S. Air Force
Laboratory/Clarkson Aerospace/Minority Leadership Pro-
gram to financially support teachers and high school stu-
dents involved in this project. Also, many thanks to the
Department of Biological and Physical Sciences for pro-
viding lab space, materials, supplies and instrumentation
in conjunction with 1890-Reserch Grant Project SCX-
420-24-04 and the USDA Evans-Allen Research pro-
gram. Many thanks to MS. P. Laursen for the helps in
technical writings.
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