Effects of Side-Chain on Conformational Characteristics of Poly(3,5-Dimethyl-Phenyl Acrylate) in Toluene at 40℃

doi:10.4236/aces.2012.24053

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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: *[email protected]

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:







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.

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

OH O

Cl CH3

CH3

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

[ ]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

ln( /)

lim lim

lim



 













 











(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:

 

 









 (3)





 

 







 (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.

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

100

150

200

250

300

350

400

450

500

ViscosityNumberorInherentViscosity(mL∙g

–1

)

C

.005

(g∙mL

–1

)

0.006

00.002 0.004

C(g∙mL–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

Mw x10000

kH kK

Figure 2. Variation of Huggins’ and Kreamer’s constatants

versus viscosity number.

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,

R00 modified to allow for short-range interactions

called 2



1cos

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



1 cos

1 cos1

Rnl





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:



1cos

Rnl 1cos













 (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

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:







 



(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

0.51

KBM





 



(9)

The constant Kθ is the intercept; it is equal to the KMH

at the theta conditions [22]. The plot of





 against

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.







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

N. HAMIDI ET AL. 439

0.08

0.11

0.14

0500 1000

[]Mw

–1

Mw

1/2

222

00f







1500

Figure 4. Stockmayer-Fixman plot, Equation (9), for

35PDMPA in toluene at 40˚C.

Table 3. Values of Kθ,



RM , σ and C∞ from SF plot

and Bohdaneck ý.

Method Kθ



 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,

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

RKM

















(11)

00 2













 (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]







 (13)





00,0

KRM





with: (14)





00brk

KAd M



 (15)

brb K

ddl (16)







lRMM



 (17)

lM (18)









RM 2

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.

N. HAMIDI ET AL.

440

tions is [26]











Cn z





31.5











 (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 0

2π





 (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

RR



. This function is approximated

by the equations:





0.875 K

4 312.033

nn n





for nK > 6 (21A)



12 1

exp 6.6110.9198

KKK 0.03516 K

nn n





n









Cź





 

for nK < 6 (21B)

Then, Equation (19) can be modified to





(22)

where ź is the scaled excluded-volume variable [24,25]



34 K

nz



1.14C





(23A)

(23B)

Combining Equations (13), (19), (20), (22) and (23),

yields:





42π





 

 

 









AKM

RKn BM













 















(24A)





(24B)2



322

42π

AC M

KnBK

KC M

 













 



  



 



















KnBM

















12 6

15.640.16205.691 10





  (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

in Figure 5

results in Equation (24C). By comparing Equations (24B)

and (24C) we get:

15.6A



(25A)





 

322

33 0.162

42πK

AC KnBK









 





 



 



(25B)

 

322

33 5.69E 6

42πK

KC KnB









 







 



 



00.1625K

(25C)

(25D)



 

322

33 6.45E3

42πK

CKnB









 







 



 



(25E)

3.6.1. Application of Equation (24) by Plotting

[η] vs 12

Equation (24) shows that the plot of [η] vs 12

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







BR MKn

 is very low, such as in the case

of 35PDMPA in toluene at 40˚C. This implies alsothat

the ratio





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



BRM Kn







is very



322

2012 12

322

34 2π

34.

2π

AC KnBMKM

KMCK nBM

 













 













N. HAMIDI ET AL. 441

y=0.173x‐ 19.77

R²=0.999

y=5.691E‐06x

+1.620E‐01x

‐1.564E+01

R²=9.992E‐01

‐20

130

180

230

280

330

05001000 1500 2000

[](cm

–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







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

019.663AKM



  (26A)





32 0.173M



, 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

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







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 -





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

02.95.36 br

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).

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



vs 12



(SF) plot [34,35]





Based on Equation (24), the plot of versus

N. HAMIDI ET AL.

442

should be linear only for long enough chains (n <

103) where the absolute value of Aη is much lower than

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









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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